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Astronomy/Y1004213416-m13_globular_cluster.org
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:PROPERTIES:
:ID: e5dc49a0-af4f-4546-b1d0-624fd54435ad
:END:
#+title: M13 Globular Cluster
#+filetags: :celestial_objects:
#+STARTUP: latexpreview
Messier 13 is one of the best-known globular clusters in the night sky.
Messier number: 13
New General Catalogue (NGC) number: 6205
Constellation: Hercules
Distance from Earth: 25,100 ly
Discovered by: Edmond Halley in 1714
* Physical Characteristics
- M13 contains several hundred thousand stars.
- The stars are metal-poor and densely packed in the center.
- Stars have low-,etallicity, which means they wre likely formed in environments which fewer heavy metals.
* Notable Features
- M13 has a diameter of about 145 ly.
- M13 contains many blue-stragglers, which are stars that appear hotter and younger than all the other stars.
- Contains many variable stars, especially RR Lyrae variables, useful for determining distance and properties of globular clusters.
- There is onginog research into whether or not M13 contains a central medium-sized black hole.
* Observation and Viewing
- Viewed best in Summer and early Fall.
- Seen in the nothern hemisphere
- Spans 22 arcminutes of the sky. For comparison, the Moon only spans 30 arcseconds of sky.
- Diameter of 145 ly calculated using distance, angular size, and simplifying using the small-angle approximation.

36
Bible/20240219155951-bible_110_survey_of_the_new_testament_the_intertestamental_period.org
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:PROPERTIES:
:ID: a94c6689-860f-46cf-96e1-8f1ad145f4dc
:END:
#+title: BIBLE 110: Survey of the New Testament: The Intertestamental Period
#+filetags: :bible:lecture_notes:
* Early Judaism
- Early Christianity was a primarily Jewish movement
- There is a "parting of ways" when the temple is destroyed however. After this point, most Christians are Gentiles.
- Jews have to start practicing their faith without a temple
- When the jews returned from exile and rebuilt the temple, many of them felt as if a true "spritual" return had not yet happened.
- The same glory as post-exilic Israel had not truly returned.
* Israel Between the Testaments
- After the Persian came to close and Cyrus the great allowed the Jews to return, the Greeks and Alexander the Great spread their influence.
- He conquers much of the known world in just ten years. As a result, Greecan culture is spread across the world as new citiees form and mimic the large, free cities of the Greecan homeland.
- After Alexander's death, his four generals split the world between them.
- It is during this time that King Antiochus sacrifices to Zeus in the Temple of God. This leads to the Jewish family of the Hasmoneans to revolt, also called the Macobean revolt.
- As a result, Israel experiences about 100 years as an independent state...that is, until internal conflicts make them ripe for conquest for an new empire in town.
- General Pompeii of the Roman Empire completely conquers the whole region of Judea, placing it under the jurisdiction of the Roman Empire.
* Institutions of Early Judaism
- Pharisees, Sadducees, Essenes, and Zealots.
* Pharisees were the most influential, and they believed in a rigorous application of the Torah
* Sadducees had the most control in the temple itself. However, they didn't believe in angels nor other spiritual things
* The Essenes started their own communities in the wilderness, separated form others
* The Zealots were militaristic and thought they could bring the kingdom back through force

54
Bible/20240219161611-bible_110_survey_of_the_new_testament_the_gospels.org
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:PROPERTIES:
:ID: b7750bff-94e5-4d4f-87a9-c89a1d52a620
:END:
#+title: BIBLE 110: Survey of the New Testament: The Gospels
#+filetags: :bible:lecture_notes:
* The Gospel According to Matthew
- Audience was primarily to Jewish Christians
- Emphasized that Jesus was the "New Moses"
* Flees to Egypt, but then returns to homeland
* Goes into the wilderness for 40 days
* Gives 10 beattitudes/commandments
- Shown to be the embodiment of YHWH
- Lots of language regarding the coming of the Kingdom of Heaven" or "Kingdom of God"
* The Gospel According to Mark
- Traditionally authored by Peter's scribe
- Gospel of action
- Divine Messiah
* Divinity of Jesus Proclaimed
* Jesus will immerse you in the Holy Spirit
* "The Kingdom of God has come near"
- Transfiguration
* Jesus reveals his true nature and is clothed in Glory
- The Suffering Servant
* Mark highlights many instances of Jesus foretelling his future death
* Mark also highlights the failures of the disciples
* The Gospel According to Luke
- Written for "Theophilus" which means "God lover"
- Gives more details on the birth of John and Jesus
- Highlights the concept of good news to the poor and socially outcast
* Contains many parables that relate to this
- Elavates women more so than any other gospel
- Highlights the theme of Salvation for all, including the Gentiles
* The Gospel According to John
- A more theological gosepl instead of just narration
- Begins with a prologue that mirrors Genesis 1
- Includes 8 of Jesus' "I am" statements
- Highlights 7 specific signs that Jesus performed during his ministry
- Highlights Jesus' teachings on loving one another, keeping His commandments, and praying for unity.

32
Bible/20240219162920-bible_110_survey_of_the_new_testament_acts.org
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:PROPERTIES:
:ID: a52ed84d-c4da-4958-a883-f832e637f8a7
:END:
#+title: BIBLE 110: Survey of the New Testament: Acts
#+filetags: :bible:lecture_notes:
- Written by Luke but has an abrupt ending, which may mean it was written before Paul's death.
* In Jerusalem
- The Pentecost is the most important event.
- Undoes the Tower of Babel
- Peter and Stephen preach key sermons
* In Judea and Samaria
- The "conversion" of Paul
- Peter has the vision of the animals on the sheet, symbolyzing that Gentiles are no longer unclean
- Spirit is sent out among the Gentiles]
* To the Ends of the Earth
- Narrative shift from Peter to Paul
- Jerusalem council provided ways for Gentiles to behave around Jewish Christians so as not to offend them
- Key sermon: Paul in Athens
- Spirit among the ends of the Earth
- The book ends with Paul awaiting trial in Rome

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Biology_and_Chemistry/20240127165818-bio_224_lecture_notes_section_1.org
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:PROPERTIES:
:ID: 31c67d6e-01be-48f1-ad1c-6a91f6d3f1b8
:END:
#+title: BIO 224 Lecture Notes: Functional Groups and Carbohydrates
#+filetags: :biology:lecture_notes:
* Lecture 1: Why Study Biology
- We study Biology to discern how organisms function, where they live, and what they do. It helps develop and refine ideas about life and God the Creator
- What is life? Life consists of:
1) Cells
2) Contains DNA
3) Uses genetic info to reproduce
4) Can extract energy to do work
5) Can convert molecules from environment into new biological ones
6) Can regulate the interanl and respond to the external
7) Is genetically related
- Growth is adding new cells to the body while development is adding awareness to environment and increasing in maturity
- Organisms can be separated into a hierarchy:
Cells -> Tissues -> Organs -> Multicellular Organism -> Population -> Community -> Ecosystem -> Biosphere
- How do we Investigate Life?:
The scientfifc method combines observations with logic.
Ask questions, form hypotheses, test to see if hypothesis is correct, and analyze the results to draw conclusions.
- Controlled Experiments:
One or more variables are manipulated
The "Control Group" is unmanipulated.
Response that is measured is the dependent variable.
- Comparitive Experiments:
Starts with prediction that there will be a difference between multiple samples or groups.
Variables are not controlled
Look at the natural environment
- Good Elements of an Experiments:
Experimental groups
control groups
replication
Testable hypothesis that is able to be falsified
Repeatability
* Lecture 6: Functional Groups
- Functional Groups are a particular group of atoms that can convey a specific function to an organic molecule
Most are covalently bonded to carbon backbone
They are responsible for most of the chemical reactions
1) The Amino Group:
- Nitrogen atom bonded to two hydrogen atoms, with nitrogen bonded to carbon chain
- Often ionizes to accept and H+ ion. Therefore they are polar with a *full positive charge*
- Commonly found in amino acids, which have and amino group at one end and a carboxyl group at the other.
2) Carbonyl Group:
- Double-bonded oxygen attatched to carbon chain
- *Partially Polar* due to electronegativity differences
- *Aldehyde* if oxygen bound to the end carbon
- *Ketone* if oxygen bound to a middle carbon
3) Hydroxyl Group:
- A single hydrogen bonded to an oxygen
- *Partially Polar*
- Organic molecules containing these are known as *alcohols*
4) Carboxyl Group:
- Both a carbonyl and a hydroxyl group combined into one
- COOH
- Moleulces contianing these are known as *organic acids*
- Electron is stripped from the H atom and it is released as a H+ ion (proton)
- *Full negative charge*
5) Methyl Group:
- Carbon with 3 hydrogens
- *Nonpolar*
- Very common group
6) Phosphate Group:
- P bonded to 3 hydroxyl and one oxygen
- OHs go away when ionized, leaving O- behind.
- *Two full negative charges*
7) Sulfate Group:
- Central Sulfur bonded to four oxygen atoms
- *One full negative charge*
- Not found on nucleotides
8) Sulfhydryl Group:
- Sulfur bonded to hydrogen
- Molecules with these are known as *Thiols*
- Nonpolar but almost polar
- Can form *Disulfide Bridges*, especially in proteins, which are stronger than hydrogen bonds
* Lectures 7-8: Types of Organic Molecules
- *Isomers*
* Same chemical formula, different structural formula
* When a carbon has 4 groups attached to it, it is called an *alpha* carbon
* Structural isomers behave differently from one another
* Common types of isomers are D (dextrorotary) and L (levorotary)
* Living things only have L-amino acids and only have D-monosaccharides!
- *Polymers*
* All biologically important molecules are made of subunits called monomers
* Constructed using dehydration reactions
* Water is removed from monomers, usually from two hydroxyl groups, and held together by and oxygen atom
* In a *hydrolytic reaction* the reverse happens. Water is inserted and breaks the *Glycosidic linkage*
- *Carbohydrates*
* Each middle carbon contains a hydrogen on one side and an OH on the other side
* Contains one carbonyl group
* Rings nearly always predominate over chains
* In *Alpha form*, the OH is pointed *down* on Carbon #1
* If it is pointing up, it is in *Beta form*
* In an alpha glycosidic linkage, the plane of the bond projects below the plane of the ring. Beta glycosidic linkages project above the plane of the ring.
* *amino sugars* are specially derived carbohydrates that have an amino group attached to them.

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:PROPERTIES:
:ID: 92a41c17-d3d8-460d-be82-ab36de2e88a3
:END:
#+title: Chemistry the Central Science: Liquids and Intermolecular Forces
#+filetags: :textbook_notes:Chemistry_the_Central_Science
#+STARTUP: latexpreview
There are three main types of Intermolecular Forces:
- Dispersion forces
- Dipole-dipole interactions
- hydrogen bonding
* Dispersion Forces
- This force depends on the *polarizability* of the molecule, or, the ease with which the molecule's electrons can be "squished" to one side.
At times, electron distribution is unequal, making a molecule temporarily polar.
This can then *induce* nearby molecules to also become polar, creating a slight attraction.
- Force is significant only when molecules are near to each other.
- Additionally, polarizability increases with increasing molecular weight or atomic size.
Linear molecules with higher surface area are more prone to creating tempary dipoles than spherical molecules.
* Dipole-dipole Attractions
- Results from permanent dipole moments in polar molecules. Effective only when molecules are close to each other.
- For molecules of approximately the same size and mass, the strength of intermolecular attractions increases with increasing polarity.
* Hydrogen Bonding
- These creat "abnormal" levels of IFs, explaining why some compounds have higher than expected boiling points.
- Hydrogen bonding only occurs when hydrogen is covalently bonded to an F, O, or N molecule.
- The very small, electron-depleted hydrogen atom can come quite close to larger, more elctronegative atoms.
* Ion-dipole Forces
- This kind of IF exists between an ion and a dipole
- Often found in solutions and/or mixtures
* Comparing the Forces
- When molecules of two substances have compatible molecular weights and shapes,
dispersion forces are approximately equal in the twosubstances
- When molecules of two substances differ widely in molecular weight and there is no Hydrogen bonding,
dispersion forces determine which substance has the stronger intermolecular forces.
* Properties of Liquids
- *Viscosity*
* units = Kg/meters*seconds
* Relates how well a fluid's molecules flow past one another. Depends on strength of IFs and shape.
* Decreases with increasing temperature.
- *Surface Tension*
* Water makes "beads" because of surface tension. The tension pulls the molecules into a sphere because a sphere has the lowest surface area per volume.
* The surface tension can be described as the energy needed to increase the surface area of a liquid by a unit amount.
* units = Joules/meter^2
- *Critical Temperature and Pressure*
* Critical temperature is the point at which a gas becomes so hot that it cannot be compressed into a liquid
* The critcal pressure is thus the amount of pressure needed to compress a gas that is at critical temperature
* A liquid that is formed under these conditions is known as a *supercritical liquid.*
- *Vapor Pressure*
* Any volatile liquid creates vapor pressure
* After a time, the pressure attains a constant value, which is the vapor pressure and it is at *Dynamic Equilibrium.*
* Clausius-Clapeyron Equation
- The Clausius-Clapeyron equation relates vapor pressure and temperature. It can be defined as follows:
\begin{equation}
\ln\left(\frac{P_1}{P_2}\right) = -\frac{\Delta H_{vap}}{R T} + C
\end{equation}
Where: R = 8.314 Joules/mol-K
The graph of $\ln{P}$ vs. $\frac{1}{T}$ shows a straight line with slope equal to:
\begin{equation*}
\frac{\Delta H_{vap}}{R}
\end{equation*}
* Liquid Crystals
- The state between solid and liquid
- *Nematic liquid crystals*
* long axes of molecules are aligned, but ends are not aligned.
- *Smectic A*
* Molecules aligned in layers, long axes perpendicular to the layer planes.
- *Smecitc C*
* Molecules aligned in layers, long axes of molecules inclined with respect to the layer planes.
- *Cholesteric*
* Molecules packed into layers, each subsequent layer has the long axes of the molecules rotated with respect to the preceeding layer.

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:PROPERTIES:
:ID: 55e307af-7e19-47dc-ae32-6442afbe0b00
:END:
#+title: Chemistry the Central Science: Solids and Modern Materials
#+filetags: :Chemistry_the_Central_Science:textbook_notes
#+STARTUP: latexpreview
Solids are classified into four main groups:
- Metallic solids, which are held together by metallic bonds and a delocalized "sea" of electrons.
- Ionic solids, which are held by the electrostatic force and do not conduct electricity very well.
- Covalent-network solids, which are giant, interconnected molecules.
- Molecular solids, held by dispersion forces and other IFs.
For more information on Intermolecular Forces:[[id:92a41c17-d3d8-460d-be82-ab36de2e88a3][Chemistry the Central Science: Liquids and Intermolecular Forces]]
Solids are either *crystalline* or *Amorphous*. Crystalline solids have repeatable 3D shapes of molecule arrangements, while Amorphous solids have no definite arrangement shapes
* Lattices
A lattice is defined by a *unit cell*, which is the smallest unit of arranged molecules. A unit cell is made up of *lattice points* defined by lattice vectors.
These vectors have their vertices on given lattice points.
In terms of cubic lattices:
* Primitive lattice: Only the corners of the unit cell are included as lattice points.
* Body-centered lattice: One extra lattice point is included in the center of the unit cell.
* Face-centered lattice: lattice points placed at every face of the cubic unit cell.
Some structures have an atom at each lattice point, but many are made up of *motifs*, a group of molecules/atoms arranged in a certain manner in a unit cell.
* Metallic Solids
Metals are held together by metallic bonds, like positive cations placed in a sea of delocalized elctrons.
Each lattice point consists of *one atom*.
Metallic solids either have have *Hexagonal Close Packing* or *Cubic Close Packing*:
* In Hcp, the atoms stack in layers of ABABA....
Every other layer linee up.
* In Ccp, the atoms stack in layers of ABCABC....
Every three layers line up.
Usually consistent with face-centered lattice.
Alloys are solutions of solids, primarily metals. There are four types of alloys:
* Substitutional
* Interstitial
* Heterogeneous
* Intermetallic Compounds
In substitutional alloys, atoms of solute occupy positions originally occupied by the solvent's atoms.
In interstitial alloys, the atoms of solute occupy positions *in between* the atoms of solvent.
In heterogeneous alloys, the components are not dispersed uniformly.
In intermetallic alloys, there are compounds of different units of metals. Often used in high temperature applications
* Models of Metallic Bonds
- The Electron Sea Model:
Metals appear to consist of metal ions floating in a sea of electrons.
This is becouase metlas do not have enough valence electrons to satisfactorily share between all the atoms.
- Molecular Orbital Model:
Much more accurate.
As the number of valence electrons increases in the metal, more potential molecular orbitals become available.
Electrons then fill these orbitals. When they reach the top of these Molecular Orbital (MO) "bands," it requires energy *very little* energy to "promote" them to higher energy orbitals.
As electrons fill these higher-energy, *non-bonding* orbitals, the bonds in metals become weaker.
This can be used to analyze conductivity, bonding, heats of fusion, hardness, etc.
* Ionic Solids
These solids are composed of anions and cations.
When shear stress is applied, layers separate due to elctrostatic repulsive forces when ions of like charge line up with one another.
As Cation size *decreases* the coordination number *decreases*.
This is becuase as the cation gets smaller, lass number of anions are able to pack together without touching each other.
* Covalent-Network Solids
These solids a large network of covalent bonds, which are very strong.
Includes diamond and graphene
- *Semiconductors*:
* Conductivity determined by *valence band* and *conduction band*.
* The energy difference between these two bands is the *Band Gap*
* Adding *dopants*, or impurities, can make a substance conductive, either when impurities contain more electrons than the substance, or fewer,
in which case a positively charged "hole" moves about through the lattice.
* The dopants are either *n-typed* (for dopants with more elctrons) or *p-typed* (for dopants with fewer electrons).
* Nanomaterials
The point at which individual MOs can be thought of as "bands," is when the molecule reaches about 1nm - 10nm in length. (about 10 - 100 atoms across).
Semiconductors that are in this size range are called *Quantum Dots*.
One interesting feature of Quantum dots is that the Band Gap changes drastically as crystal size changes in the 1 - 10nm range.
As the particles get *smaller*, the Band Gap gets *larger*.
So larger crystals are black, since all light is absorbed and excites the electrons into the conduction band.
Smaller crystals have varying colors all the way to the smallest size, which is white, in which all visible light is not absorbed but reflected due to the large Band Gap.

79
Biology_and_Chemistry/20240203103229-chemistry_the_central_science_solutions.org
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:PROPERTIES:
:ID: b39cff9d-6279-42a3-8660-5edb5cd960e6
:END:
#+title: Chemistry the Central Science: Solutions
#+filetags: Chemistry_the_Central_Science:textbook_notes
#+STARTUP: latexpreview
Solutions, specifically aqeous solutions, are an integral aspect of chemistry.
To create a solution, the solute particles must be separated $\Delta H_{solute}$ . This is *always endothermic*.
Then, the solvent particles must also be separated $\Delta H_{solvent}$ . This is *always endothermic*.
The particles must then mix $\Delta H_{mix}$ . This is *always exothermic*. Thus,
\begin{equation*}
\Delta H_{solution} = \Delta H_{solute} + \Delta H_{solvent} + \Delta H_{mix}
\end{equation*}
Depending on the values of these energies, a solution can be either exothermic or endothermic.
* Solubility
A solution is saturated when it is in dynamic equilibrium between solution formation and crystallization.
/The solubility of a certain solute is the maximum amount that can be dissolved in a given amount of solvent so as to attain a saturated solution/
More solute than this leads to a *supersaturated* solution which, when cooled, can lead to crystallization.
* Factors Affecting Solubility
General Rule: Like IFs dissolve like IFs. For more info on IFs:[[id:92a41c17-d3d8-460d-be82-ab36de2e88a3][Chemistry the Central Science: Liquids and Intermolecular Forces]]
Pressure affects solutions of gases in liquids. As pressure increases, gas solubility increases.
*Henry's Law*:
\begin{equation*}
S_g = K P_g
\end{equation*}
Where S = solubility of the gas and P = partial pressure of the gas.
Temperature affects solid and liquid solutions. As the temperature increases, solubility increases, at least most of the time.
* Colligative Properties
When nonvolatile *solute* is placed in a volatile *solvent*, the vapor pressure of the solvent above the solution *deacreses*.
*Raoult's Law*:
\begin{equation*}
P_{solution} = X_{solvent} P^{\circ}_{solvent}
\end{equation*}
Where X = the *mole fraction* of the solvent.
This law assumes ideality. Many solutions don'ts follow the law perfectly.
Because vapor pressure decreases, a higher temperature is required for the solvent to reach its boiling point, which is when the vapor pressure equals the atmospheric pressure.
This is *Boiling Point Elevation*:
\begin{equation*}
\Delta T_b = T_b(solution) - T_b(solvent) = K_b mi
\end{equation*}
Where: $T_b$ = boiling point
$K_b$ = molal boiling point elevation constant
$m$ = molality
$i$ = Van't Hoff Factor (number of fragments a solute breaks up into)
Additionally, another effect of colligative properties includes *Osmotic Pressure*, $\Pi$:
The equation for osmotic pressure is not too dissimilar from that of the ideal gas law:
\begin{equation*}
\Pi = i M R T
\end{equation*}
Where M = the molarity of the solution.

33
Biology_and_Chemistry/20240207230306-bio_225_lecture_notes_fertilization_blocks_to_polyspermy.org
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:PROPERTIES:
:ID: c9eb990e-a4ea-4730-b199-02d5236d0787
:END:
#+title: Bio 225 Lecture Notes: Fertilization/Blocks to Polyspermy
#+filetags: :bio225:lecture_notes:
This note begins a series of notes on the topic of *Developmental Biology*.
The process goes like this, in a nutshell: Gametes --> fertilization --> Blastulation --> gastrulation --> growth
* Fertilization
We examine the process as it relates to a Sea Urchin, primarily because sea urchin eggs are easy to access and observe.
We also begin with an important question: How does an egg allow only *one* sperm cell to fertilization? i.e., how does the egg prevent *polyspermy?*
- A *vitelline layer* surrounds the egg. On its surface are *sperm binding receptors*, which attach to *egg recognition proteins*.
- Fusion results and the vitelline layer comes up to meet the docked sperm, creating a fertilization cone.
- The moment this happens, *Fast Block* to polyspermy is initiated:
* To begin, the egg is negative on the inside and it is positive outside the egg.
* When the sperm docks, Na+ ion channel opens, and Na+ ions diffuse *into* the egg, *depolarizing* the membrane.
* As soon as this happens, the sperm binding receptors all over the surface of the egg change shape so that *no other* sperm cells can dock on this egg.
- After this, Ca2+ ion channels "feel" the depolarization and they open up, releasing a plethora of Ca2+ ions.
- These ions immediately trigger *cortical granules* in the egg to discharge a hypertonic solution into the space in between vitelline layer and plasma membrane.
- Because of the hypertonicity of the solution, water rushes into this space. This is the *Slow Block* to polyspermy:
* Vitelline layer expands due to incoming water and eventually hardens into the *Fertilization Membrane*.
* The sperm recognition receptors completely degrade and decay.
* this happens 60 seconds into fertilization.
After the process of fertilization, the resulting zygote then enters the next stage of development: Blastulation and theeen Gastrulation [[id:3929d482-7be2-4d7e-a576-1bc6f8081fe0][Bio 225 Lecture Notes: Blastulation and Gastrulation]]

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:PROPERTIES:
:ID: 3929d482-7be2-4d7e-a576-1bc6f8081fe0
:END:
#+title: Bio 225 Lecture Notes: Blastulation and Gastrulation
#+filetags: :biology:lecture_notes:
Continuing on after fertilization [[id:c9eb990e-a4ea-4730-b199-02d5236d0787][Bio 225 Lecture Notes: Fertilization/Blocks to Polyspermy]] the next stages of development are blastulation and grastrulation.
* Beta Catenin in Gray Crescent
- Beta catenin is a cell-to-cell signaling molecule.
- *GSK-3* is an enzyme that breaks down Beta catenin.
- Upon fertilization, vesicles with inhibitor is transported from the vegetal pole of a frog egg to the animal pole, vie microtubules.
- Thus, GSK-3 is breaks down all Beta catenin in areas *except* the area with the inhibitor.
- The inhibitor is taken to the Gray Crescent area of a frog egg, so that area has high concentrations of Beta Catenin.
* Cleavage Patterns
- Radial Cleavage:
* New cells directly on top of each other
* *Regulative Development*: If separated, each blastomere becomes a whole oraganism.
- Spiral Cleavage:
* New cells nested in the cleavage furrows (they pack tightly).
* *Mosaic Development*: Separate blastomeres do not form a whole organsim.
* Blastulation and Gastrulation
- After fertilizaiton, the zygote cleaves and divides its cytoplasm into undifferentiated cells, called *blastomeres.*
- The structure that results is called the *Blastula*, or in mammals, the *Blastocyst*.
- About 10 hours after fertilization, grastrulation starts to occur.
- during this stage, the three *germ layers* start to form: The ectoderm, mesoderm, and endoderm.
- The blastomeres begin to invaginate inwards to create a cavity in the zygot. This is called the *archenteron*.
- From this, coelomic vesicles form, leading to the formation of the mesoderm.
- The ectoderm later forms the epidermis and the nervous system
- The mesoderm later forms things like the muscular, skeletal, cardiovascular, and urogenital systems.
- The endoderm usually forms the lining of the digestive and respiratory systems.
* Coelom Formation
- Schizocoelous:
* means "split"
* Mesoderm cells split off from the ectoderm. They eventually form pouches and create the body/gut cavity.
- Enterocoelous:
* The pouches form in the archenteron
* Pouch grows and fuses, creating gut cavity
- The coelom is usually defined as being lined by *mesodermal peritoneum*.
* Body Plans (Bilaterally symmetric organisms)
- Eucoelomate:
* (Described above), true coelem, fully line with mesodermal peritoneum.
- Acoelomate:
* No coelom; full of mesodermal tissue
- Pseudocoelomate:
* Cavity /partially/ lined with mesodermal peritoneum.

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:PROPERTIES:
:ID: 0856b9fd-822f-4cc7-9ec4-cdcc38c01b5e
:END:
#+title: Chemistry the Central Science: Chemical Kinetics
#+filetags: :chemistry_the_central_science:textbook_notes:
#+STARTUP: latexpreview
The part of Chemistry that deals with reaction rates is known as *chemical kinetics*. Several topics will be explored,
such as factors that affect reaction rates as well as concentrations versus time, and catalysts.
Factors affecting Reaction Rates:
- Physical state of the reactants
- Reactant concentrations
- Reaction temperature
- The presence of a catalyst
Reaction rates depend on the frequency of collisions. /The greater the frequency of collisions, the higher the reaction rate./
* Reaction Rates
Rate of Appearance of [B] =
\begin{equation*}
\frac{\Delta [B]}{\Delta t}
\end{equation*}
and thus the rate of disappearance of [A] =
\begin{equation*}
\frac{\Delta [A]}{\Delta t}
\end{equation*}
To find the *instantaneous* rate of a reaction, one must look at a graph and find the slope to the tangent line at the desired data point (rise over run).
Reaction rates involving stoichiometry can simply be found by dividing the rates of appearance or disappearance by whatever coeficcients they have in the balanced equation.
* Rate Laws
Changing the initial concentrations of any reactant (A and B) changes the reactant rate. This is described as a *Rate Law*:
\begin{equation*}
Rate = k [A]^m [B]^n
\end{equation*}
Where k = the *rate constant*. If we know m and n, we can know the order of the reaction rate.
The *overall reaction order* is the sum of the orders with respect to each reactant represented in the rate law.
Reaction orders are usually either 0, 1, or 2.
/For any reaction, the rate law must be determined experimentally./
- A *first order reaction* is one whose rate depends on the concentration of a single reactant, raised to the first power.
Differential Rate Law:
\begin{equation*}
Rate = k [A]
\end{equation*}
Integrated Rate Law:
\begin{equation*}
\ln[A]_t = -k t + \ln[A]_0
\end{equation*}
- A *second order reaction* is one for which the rate depends either on a reactant concentration raised to the second power or on two reactant concentrations both raised to the first power.
Differential Rate Law:
\begin{equation*}
Rate = k [A]^2
\end{equation*}
Integrated Rate Law:
\begin{equation*}
\frac{1}{[A]_t} = k t + \frac{1}{[A]_0}
\end{equation*}
- A *zero order reaction* is one in which the rate of disappearance of A is independent of [A].
Differential Rate Law:
\begin{equation*}
Rate = k
\end{equation*}
Integrated Rate Law:
\begin{equation*}
[A]_t = -k t + [A]_0
\end{equation*}
Another important concept is that of *half life*. It is the time required for the concentration of a reactant to reach half of its original value.
We see:
\begin{equation*}
t_{1/2} = \frac{0.693}{k}
\end{equation*}
/In a first order reaction, the concentration of the reactant decreases one half in each of a series of regularly spaced time intervals, equal to $t_{1/2}$/.
In a second order reaction, the half life depends on the concentration in an inverse relationship:
\begin{equation*}
t_{1/2} = \frac{1}{k [A]_0}
\end{equation*}
For more information regarding half lives of chemical reactions see[[id:a1acf31f-1722-450b-994c-cf05cf11fe6d][Chem 132 Lecture Notes: Half Lives of Reactions and the Arrhenius Equation]]
* Temperature and Rates
Most rates increase with increasing temperature because the rate constant increases with increasing temperature.
In the *collision* model, what primarily drives a reaction is the collision of molecules in a certain manner. Number of collisions increase with increasing temperature.
Why a in a "certain manner?"
- The Orientation factor: Molecules must be oriented a certain way.
- Activation Energy: The molecules must contain enough energy to reach the *transition state* and thus react. The rate constant depends on activation in an inverse relationship.
At higher temperatures, a greater fraction of molecules have kinetic energy greater than the activation energy.
Given by:
\begin{equation*}
f = e^{\frac{-E_a}{R T}}
\end{equation*}
The *Arrhenius Equation* relates the rate constant to activation energy:
\begin{equation*}
k = A e^\frac{-E_a}{R T}
\end{equation*}
or
\begin{equation*}
\ln \left(\frac{k_1}{k_2}\right) = \frac{E_a}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)
\end{equation*}
This says that as the activation energy increases, the rate constant decreases and vice versa. We can use this to solve for rate constants.
* Reaction Mechanisms
- *Elementary Reactions* occur within a single step.
If it involves one molecule it is *unimolecular*
If it involves two molecules it is *bimolecular*.
If it involves three molecules it is *termolecular*.
- *Multistep Reactions* are composed of two or more elementary reactions, that act as "Steps."
- Molecules that form and then consequently are used up in the midst of steps, they are *intermediates*.
- Rate laws for elementary reactions are based /directly/ on their molecularity (unimolecular, bimolecular, etc.).
- The slowest step in a multistep reaction /determines the overall rate/.
- In general, whenever a fast step precedes a slow one, we can solve for the concentration of an intermediate by assuming that an equilibrium is established in the fast step.
* Catalysis
Catalysts are either homogeneous or heterogeneous.
- Homogeneous catalysts are in the *same phase* as ther reactants.
- Heterogeneous catalysts are in a *different phase* than the reactants. Usually involves a metallic surface that the reactants can *adsorb* to and react with each other once on the surface.

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:PROPERTIES:
:ID: b7905fbc-2bdb-4926-b263-ba9e49b49eeb
:END:
#+title: Chem 132 Lecture Notes: Rate Laws
#+filetags: :chemistry:lecture_notes:
#+STARTUP: latexpreview
In general, $rate = k [A]^x [B]^y$. To find the order of a reaction, take two data points and divide their rates. Order doesn't matter as long as you keep with that order for the
entire equation-solving process. For example:
\begin{equation*}
\frac{rate}{rate_{initial}}
\end{equation*}
Set this value equal to the right side of the equation, substituting in the correct concentrations of A and B at that particular data point For example:
\begin{equation*}
\frac{k (0.3)^x (0.1)^y}{k (0.1)^x (0.1)^y}
\end{equation*}
Everything will cancel except for the values that are of interest. Taking the logarithm of both sides, then, gives us x. The same can be done for y, using a different data point that includes
a concentration change in B instead of A. Thus, the order of the reaction can be found.
To learn more about this as well as the integrated rate laws, see this note -->[[id:0856b9fd-822f-4cc7-9ec4-cdcc38c01b5e][Chemistry the Central Science: Chemical Kinetics]]

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:PROPERTIES:
:ID: 87ec4e62-1fe5-441d-8ca4-53c484933194
:END:
#+title: Bio 224 Lecture Notes: Organic Molecules
#+filetags: :biology:lecture_notes:
#+STARTUP: latexpreview
* Lipids
- Sometimes called hydrocarbons
- Most importantly, these molecules are very *nonpolar*.
- The subunits are called *fatty acids*. They include a long chain of carbon and hydrogen with a carboxy group at the end.
- *Saturated fatty acids* can't hold anymore hydrogen. *Unsaturated fatty acids* have "missing" hydrogens, resulting in double bonds between carbons. The chain then becomes bent.
- *Glycerol* is another monomer of lipids. It contains *3* carbons and 3 hydroxyls attached to those carbons.
- The hydroxyls will be used in condensation reactions in which an *ester bond* is formed between glycerol and a fatty acid.
- Often form *Triglycerides*, which are used for long-term energy storage.
- *Phospholipids* are modified Diglycerides.
- They contain a phosphate group and a charged, nitrogen-containing group.
- One fatty acid that is attached is usually saturated while the other one is unsaturated.
- These molecules are *amphipathic* and are thus major constituents of all biological membranes.
* Proteins
- Monomeres of this class of organic molecule are *amino acids*.
- These consist of an assymetric carbon with the following groups:
* Amino Group
* Carboxyl Group
* Hydrogen Group
* Some "R" side chain.
- Amino acids are polar. The amino group is positive while the carboxyl group is negative.
- There are 20 different possible side chains, and these determine the structure and function of the amino acid. They can be:
* Nonpolar
* Partially polar
* Polalr positive
* Polar nagative
- Amino acids are connected via condensation reactions. This results in a direct carbon-nitrogen bond called a *peptide bond*.
- Proteins are very diverse functionally.
* Four Layers of Protein Structure
- Primary:
* The main sequence of amino acids
- Seconday:
* $\alpha$ - helix
* $\beta$ - Pleated sheets
- Tertiary:
* The overall 3D shape of the larger polypeptide. It is held by several bonds including hydrogen bonds, van der waals (learn more about here[[id:92a41c17-d3d8-460d-be82-ab36de2e88a3][Chemistry the Central Science: Liquids and Intermolecular Forces]] ), and *disulfide bridges*.
- Quaternary:
* Found only in proteins with multiple polypeptides. The overall 3D shape of the mature protein.
* Can be a very complex structure.
* Nucleic Acids
- Mainly DNA and RNA
- Composed of nucleotides, which have a *phosphate group* [[id:31c67d6e-01be-48f1-ad1c-6a91f6d3f1b8][BIO 224 Lecture Notes: Functional Groups and Carbohydrates]], a *pentose sugar*, and a *nitrogen-containing compound.
- On carbon three of the pentose sugar, there is a hydroxyl group. On carbon 6, there is a phosphate group.
- the helix is formed by condensation reactions that lead to a *Phosphodiester linkage*.
- These molecules are also made up of bases. A *pyrimidine base* always links to a *purine base*.
- The bases project into the middle of the molecule and link the two strands together.

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:PROPERTIES:
:ID: 1a144e9b-c4ec-46ea-ae39-219543801238
:END:
#+title: BIO 225 Zoology Lab: Body Tissues
#+filetags: :biology:zoologoy:
* Epithelial Tissue Layers
- *Simple Squamous Epithelium*:
* Single layer of flattened cells
* Designed for diffusion
* Found in capillaries and alveoli of lungs
- *Simple Cuboidal Epithelium*:
* Single layer of cube-shaped cells.
* These cells need more space since they are primarily designed for secretion.
* Often found lining ducts, mucus glands, and kidney nephrons.
- *Simple Columnar Epithelium*:
* Single layer of rectangular cells
* Designed for absorption and secretion
* Primarily found lining the intestine.
* Associated with Goblet Cells
- *Stratified Squamous Epithelium*:
* Multiple layers of cells that are in areas of abrasion like the mouth or the skin.
* If cells are exposed to abrasive and dry conditions, such as the outer layers of the skin, the cells are *keratinized*.
* If cells are not exposed to these conditions, such as in the mouth or in the esophagus, they are not keratinized.
* Anchored in the *basement membrane* and *basal layer* of cells.
* Connective Tissue Layers
- *Areolar Connective Tissue*:
* Common form of loose connective tissue.
* Anchors the skin, blood vessels, muscles, and nerves.
* Contains *Fibroblasts* which make the extracellular matrix.
* Has broad fibers called collagen fibers and thin wiry fibers called elastic fibers.
- *Adipose Tissue*:
* Designed to store lipids and cushion the body.
* Insulates the body.
* The nucleus is pushed to one side.
- *Hyaline Cartilage*:
* Cells called *chondrocytes* sit in lacunae and secrete the extracellular matrix.
* Matrix made of many collagen fibers and firm gel-like substance.
- *Bone Tissue*:
* Contains *Osteons* which are like trunks of trees that run the length of the bone.
* These contain "growth rings" called *lamellae*.
* Only compact bone has Osteons. Spongy bone tissue lacks them.
* In the center of each Osteon, there is a *Central Canal*, through which veins and nerves traverse.
* Contains *Osteocytes*.
- *Blood*:
* *Neutrophils* phagocytize pathogens and have a three-lobed nuclues.
* *Monocytes* are large and have a two-lobed nucleus.
* *Lymphocytes* are involved in the immune response and are colored darkly.
* *Basophils* release histamine which is a substance that allows neutrophils and and monocytes to squeeze out of blood vessels in order to destroy pathogens.
They have dark-purple stained granules in the cell.
* *Eosinophils* release cytotoxic enzymes onto parasites. Have bilobed nuclues with red-stained granules.
* Muscle Tissue
- *Smooth Muscle*:
* composed on long cells with centrally located nucleus.
* found in blood vessels, digestive tracts, and the uterus.
* Usually associated with the autonomic nervous system.
- *Skeletal Muscles*:
* Striated
* Multinucleate
* Under voluntary control.
- *Cardiac Muscle*:
* Also striated, but contain *intercalated discs*.
* These muscle fibers are often branched.

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:PROPERTIES:
:ID: a22d4006-7a2c-4872-bead-5eb7a7c68918
:END:
#+title: BIO 225 Zoology Lab: The Protozoa
#+filetags: :biology:zoology:
* Phylum Amoebozoa
* Protozoans with pseudopods
* Can often be found in freshwater ponds
* Usually propel themselves with *lobopodia*.
* Have gell-like outer ectoplasm and fluid-like inner endoplasm.
* Phylum Foraminifera
* Marine amebas with tests made of calcium carbonate.
* Live primarily on the ocean floor
* Phylum Radiolaria
* Marine amebas with tests made of silica.
* Primarily move by *axopodia*.
* Phylum Stramenopiles
* Amebas that lack tests altogether
* Move only by axopodia.
* Phylum Euglenozoa
* Flagellated protozoans.
* They are autotrophs and are usually green due to chloroplasts
* Can also be heterotrophs
* /Euglena/ contain a red eyespot called the Stigma
* /Trypanosoma/ is a Euglenid that can infect the blood of its host and cause *African Sleeping Sickness*.
* Transmitted by the Tsetse fly.
* Phylum Viridiplantae
* /Volvox/ is found in freshwater environments.
* Forms spherical colonies with somatic and reproductive cells. Green with chloroplasts.
* Cells connected by *protoplasmic strands*
* /volvox/ zygotes are reddish and have spiny cases
* Phylum Diplomonada and Apicomplexa
* Representitive is /Giardia Lamblia/
* Causes diarhea and can be obtained from drinking contaminated water.
* Apicomplexa contains /Plasmodium/, the protist that causes Malaria.
* Mature into the signet ring stage called the *Trophozoite*.
* Phylum Ciliophora
* contain ciliated, multinucleate protists.
* Have an oral groove which leads to the cytostome.
* Can reproduce using binary fission, budding, or conjugation, in which the micronucleus undergoes meiosis.
* Contain trichocysts and toxocysts which are used for defense
* /Stentor/ is shaped like a vase and has a large mouth called the peristome that it uses to sweep food into
* /Paramecium Bursaria/ is usually involved in endosymbiosis with a species of algae
* Phylum Dinoflagellata
* /Peridinium/ is a freshwater dinoflagellate
* contains an equatorial flagellum and a longitudinal flagellum
* Important producers that make up a significant portion of the phytoplankton

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:PROPERTIES:
:ID: a1acf31f-1722-450b-994c-cf05cf11fe6d
:END:
#+title: Chem 132 Lecture Notes: Half Lives of Reactions and the Arrhenius Equation
#+filetags: :chemistry:lecture_notes:
#+STARTUP: latexpreview
The Half life of a chemical reaction is defined as the time required for one half of a reactant to react.
For example:
\begin{equation*}
[A_t] = \frac{1}{2}[A_0]
\end{equation*}
We can use the above relationship to derive half-life equations for first-order, second-order, and zero-order reactions.
*Zero-order half-life equation*:
\begin{equation*}
t_{1/2} = \frac{[A_0]}{2k}
\end{equation*}
*First-order half-life equation*:
\begin{equation*}
t_{1/2} = \frac{\ln(2)}{k}
\end{equation*}
*Second-order half-life equation*:
\begin{equation*}
t_{1/2} = \frac{1}{k [A_0]}
\end{equation*}
If one wants to analyze the effect of temperature vs. rate, one can use the *Arrhenius equation*.
the rate constant increases exponentially with temperature.
Results in more collisions at a higher temperature, though molecules must be oriented correctly.
The *Activation Energy*, $E_a$, is the energy required to initiate a reaction.
At a higher temperature, a larger fraction of the molecules have an energy equal or greater to the Activation energy.
the Arrhenius equation is as follows:
\begin{equation*}
\ln(k) = -\frac{E_a}{R T} + \ln(A)
\end{equation*}
Where A is the frequancy factor.
For more information see[[id:0856b9fd-822f-4cc7-9ec4-cdcc38c01b5e][Chemistry the Central Science: Chemical Kinetics]] and[[id:b7905fbc-2bdb-4926-b263-ba9e49b49eeb][Chem 132 Lecture Notes: Rate Laws]]

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:PROPERTIES:
:ID: 9abe66ad-45f5-4d9b-be27-f91f6b5264de
:END:
#+title: Chem 132 Lecture Notes: Chemical Equilibrium Basics
#+filetags: :chemistry:lecture_notes:
#+STARTUP: latexpreview
-Chemical Equilibrium differs from chemical kinetics in the kinetics asks the question how fast? While equilibrium asks the question at what position?
Equilibrium assumes that both the forward and reverse activation energies are small enough for the reactions to occur.
Rate of /association/ = Rate of /dissociation/.
For reactions at equilibrium, the rate law for the forward and reverse reactions /can/ be written from the stoichiometry.
For example, consider the reaction below that states the the forward reaction is in equilibrium with the reverse reaction:
\begin{equation*}
V_f = k_f[N_2O_4] = k_r[NO_2]^2
\end{equation*}
\begin{equation*}
\frac{k_f}{k_r} = \frac{[NO_2]}{N_2O_4} = K_c
\end{equation*}
Where $K_c$ is the *equilibrium constant*
Thus it can be said that in general:
\begin{equation*}
K_c = \frac{[Products]}{[Reactants]}
\end{equation*}
Any pure solids or liquids are omitted when calculating $K_c$
For more details on this topic refer to [[id:410d2780-127b-4972-ae22-34d9cdbb750b][Chemistry the Central Science: Chemical Equilibirum]]

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:PROPERTIES:
:ID: 410d2780-127b-4972-ae22-34d9cdbb750b
:END:
#+title: Chemistry the Central Science: Chemical Equilibirum
#+filetags: Chemistry_the_Central_Science:textbook_notes:
#+STARTUP: latexpreview
Essentially, chemical equilibrium results because some reaction are reversible. That is the forward reaction can occur and the reverse reaction can occur.
There are several important concepts that relate to equilibrium:
1. At equilibrium, the concentrations of reactants and products no longer change with time.
2. For equilibrium to occur, neither reactants nor products can escape from the system.
3. At equilibrium, a particular ratio of concentration terms equals a constant.
* The Equilibirum Constant
Experiements in the 1800s resulted in an expression known as the *Law of mass action,* which goes as follows:
Suppose a reaction:
\begin{equation*}
a A + b B = d D + e E
\end{equation*}
According to this law, the equilibrium constant can be described by the expression:
\begin{equation*}
K_c = \frac{[D]^d [E]^e}{[A]^a [B]^b}
\end{equation*}
Where $K_c$ is the *Equilibrium constant*.
This constant can simply be thought of as concentration of products over the concentration of reactants.
/The equilibrium constant expression depends only on the stoichiometry of the reaction, not on its mechanism./
We can also express an equilibrium constant in terms of partial pressure, if all reactants and all products are gaseous.
\begin{equation*}
K_p = \frac{(P_D)^d (P_E)^e}{(P_A)^a (P_B)^b}
\end{equation*}
Where $P-A$ is the partial pressure of A given in atmospheres.
We can solve between $K_c$ and $K_p$ using the ideal gas law, making the observation that moles/liter is the same thing as Molar concentration.
When the ideal gas law is used, one can separate out the resulting molarities. This is $K_c$. Then the (RT)s can be grouped together and be given an exponent that is equal to the change in moles
between products and reactants:
\begin{equation*}
K_p = K_c (R T)^{\Delta n}
\end{equation*}
Heterogeneous equilibria arise when the substances in equilibrium are in different phases.
As a general rule, all pure solids and pure liquids are omitted in the calculation of $K_c$.
This is mainly due to the fact that the concentrations of pure solids and liquids is almost always a constant value.
* Calculating Equilibrium Constants
If one does not know all of the equilibrium concentrations there is a process one can follow to obtain these concentrations and thus solve for the Equilibrium Constant.
1. Tabulate all known initial and equilibrium concentrations.
2. For those species which have known concentrations, calculate the change in concentration that occurs as the system reaches equilibrium.
3. Use the stoichiometry of the chemical equation to calculate the changes in concentration for all other species in the expression.
4. Use initial concentrations from step 1. and changes in concentration from step 3 to calculate any equilibrium concentrations not tabulated in step 1.
5. Determine the value of the equilibrium constant.
* Applications of Equilibrium Constants
Often, we need to analyze the concentrations of the species of a reaction during a reaction to compare it with that of equilibrium. In order to do that we use something called Q, or,
the *Reaction Quotient*.
The reaction quotient has the same exact formula as the equilibrium constant, but we plug in the concentration values of the reactants and produts at any point in the reaction.
/The reaction qutient is a number obtained by substituting reactant and product concetrations or partial pressures at any point in a reaction into an equilibrium-constant expression./
1. If Q < K, product concentrations are too small, and the reaction acheives equilibrium by moving in the forward direction.
2. If Q = K, the system is at equilibrium.
3. If Q > k, product concentrations are too large, and the reaction acheives equilibrium by moving in the backward direction.
* Le Chatelier's Principle
Henri-Louis Le Chatelier made a very impactful discovery in the field of chemistry:
/If a system at equilibrium is disturbed by a change in temperature, pressure, or a component concentration, the system will shift its equilibrium position so as to counteract the effect of the disturbance./
To dive deeper into this, if a chemical system is already at equilibrium and the concentration of any substance in the mixture is increased (either reactant or product), the system reacts
to consume some of that substance. Conversely, if the concentration of a substance is deacreased, the system reacts to produce some of that substance.
Likewise in regard to changing the pressure (or changing the volume at constant temperature) of a system at equilibrium, reducing the volume of a gaseous equilibrium mixture causes the system to shift in the direction that reduces the number of moles of gas.
And in regard to temperature, when the temperature of a system at equilibrium is increased, the system reacts as if we added a reactant to an endothermic reaction or a product to an exothermic reaction. The equilibrium shifts in the direction that consumes the excess reactant (or product), namely heat.
For more information regarding this topic see[[id:9abe66ad-45f5-4d9b-be27-f91f6b5264de][ Chem 132 Lecture Notes: Chemical Equilibrium Basics]]

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:PROPERTIES:
:ID: 77cc0227-53ce-4808-aca9-c54be6890596
:END:
#+title: Bio 225 Lecture Notes: Receptors of the Nervous System
#+filetags: :biology:lecture_notes:
* The Gate Control Theory of Pain
- *Nociceptors* send Action Potentials (A.P.s) to the brain, which transmits to pain.
- If, however, you rub the area experiencing pain, you send A.P.s to *inhibitory* neurons, which counteracts the signal (with Cl- ions perhaps). This decreases the number of A.P.s
transmitted by nociceptors, thereofore decreasing the intensity of the signal, i.e., the intensity of the pain.
- Additoinally, the sympathetic nervous system can prevent the feeling of pain until after a certain amount of time.
- A descending serotonin or norepinephrine fiber can intersect a nociceptor in the spional cord. This restricts the release of calcium ions during synapse, thus reducing the pain generated by nociceptors.
* Types of Receptors
- *Mechanoreceptors*
* Mechanically stimulated.
* The nerve ends in a *Pacinian Corpuscle*.
* If pressure is apoplied, the pacinian corpuscle changes shape and that is what causes pressure-sensitiv ion channels to open, creating A.P.s.
- Auditoy receptors in the ear
* The *Tympanic Membrane* wiggles in response to sound.
* The *Cochlea* lies in the inner ear and is composed of numerous canals.
* Contains the *Tectorial membrane* and the *Basilar membrane*
- The place hypothesis of pitch discrimination:
* The "wiggling" is conducted to the *Oval window* which then starts to wiggle as well.
* The fluid in the canals of the cochlea start to move.
* This causes the basilar membrane to flex and this motion pushes up against the hair cells that line the membrane.
* The hair cells then release neurotransmitters which are sent to the brain and iinterpreted as sound.
* Hair cells closer to the oval window get registered as high-frequency sound, while cells further away are registered as low frequency sounds.
- Equilibrium:
* Provides positional information.
* In humans, this is accomplished by the *statolith*, a ball made of calcium. It is surrounded by hair cells and contained in the *utrical* and *saccule*.
* The *semicircular canals* provide rotational position for three degrees of rotation.
- Photoreception:
* Found in the eye. Inregards to humans:
* The *Cornea* is the extension of the *sclera*, which is the whites of the eyes.
* The iris governs the pupil and the lens lies right behind.
* The *Aqueous humor* lies between the cornea and the lens, while the *vitreous humor* makes up the inner eye.
* The *Fovea Centralis* is a dense regions of cones, and light is usually focused in on this region.
* *Rods* provide vision in low-light environments.
* These cells are made up of discs, each of which contains the protein *rhodopsin*, made up of retinal + opsin.
* When a photon hits rhodopsin, the retinal changes shape and swinges around on a chemical bond from /cis/ formation to /trans/ formation.
* This formation triggers enzymatic activity.
* In order for rhodopsin to accept photons again and switch back to the /cis/ form, it must be broken down entirely and reconstructed.
* During this time, rhodopsin cannot respond to photons. In the dark, it takes tims for rhodopsin to form. This is why any amount of intense can wreck one's natural night vision in the dark.
* Cones on the other hand allow for the distinction between colors. They contain red, green, and blue pigments called the *conopsin pigments.*
* Interestingly, the cone cells lie behind the retinal nerve, contrary to what one might expect.
- Thermoreceptors:
* Many snakes have them and they can detect temperature differences of 0.001 degrees celsius.

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:ID: e2a23658-cdca-4c97-891c-dec7d2c00463
:END:
#+title: Bio 225 Lecture Notes: Phylum Platyhelminthes: The Flatworms
#+filetags: :biology:lecture_notes:
#+STARTUP: inlineimages
These organsims are protostomes and they have an acoelomate or pseudocoelomate body plan. Refer to [[id:3929d482-7be2-4d7e-a576-1bc6f8081fe0][Bio 225 Lecture Notes: Blastulation and Gastrulation]] for more information.
Most are free living and parasitic.
The mesoderm of the organism is called the *Parenchyma.*
The following notes will survey several of the more well knkown classes that belong to phylum Platyhelminthes:
* Class Turbellaria
- The common organism is planaria
* The Pharynx of the organism is in the center and it can be elongated to suck in food.
* The intestines are branched around the pharyns, resulting in Diverticula.
* Substances can easily diffuse out of the body. Thus, osmoregulation is accomplished via *Flame cells*.
* Flame cells contains a "flame" that is made up of densely fused cilia. It waves back and forth, pushing water into a *tubule cell* that leads to an opening in the body wall.
* Back where the "flame" is, a vacuum is formed when the water exits, so that additional water is forced into it continuing the process.
* Planarians also have a ciliated ventral side.
* They can perform asexual fission, but can also perform sexual cross-fertilization.
* Class Trematoda
- Common organsim in thsi class is /Clonorchis/ or the human liver fluke.
* No cilia, but they have plenty of hooks and suckers to attach themselves and suck in the host's bile.
* These worms are known for containing *syncytial cells* which are cells that have fused cytoplasm.
* They are *monecious*, that is, they contain the gonads of both male and female.
* They have a gonopore, an opening through which sperm from another fluke travels into to reach the worm's seminal receptacle where it is stored. Eggs are also released here.
* The *ootype* is an organ in which eggs are fetilized with sperm, filled with yoke, and sent to the uterus.
The life cycle of /Clonorchis/ is as follows:
* The eggs which are released via fecal material contain a *miracidium*, which is like a larval stage.
* The miracidium hatches after being eaten by a snail.
* Inside the snail, it forms into a *sporocyst*. After that, it forms a *redia* and then begins to eat the snail from the inside out and is eventually released.
* Once it has emerged from the snail, the redia realeases *Cercaria* which then bore into fish and encyst in them.
* When humans eat a fish with these cysts, they excyst and travel to the liver where they become adult flukes.
* The cercaria of /schistosoma/ another species in class trematoda, penetrates directly into the bare skin of its host.
* It then goes straight to the blood vessels around the bladder or intestinal tracts where they begin to reproduce. The eggs have spines which cut up these regions, leading to
bloody diarrhea or bloody urine.
* /schistosoma/ can find its host by literally following its shadow.
* Class Cestoda
- Common organism is the tapeworm.
* The head is the *scolex* which contains hooks and suckers.
* The segments of the worm are called the *proglottids* which go from immature, to mature, to gravid
* Can grow up to 25m and can coil itself in the intestines.
* Gravid Proglottids can be expelled and attach to vegetation which is in turn consumed by animals such as cattle.

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:END:
#+title: Bio 225 Lecture Notes: Phylum Rotifera and Nematoda
#+filetags: :biology:lecture_notes:
The organisms in these phyla are psuedocoelomate, which means that their body cavities are only partially lined with mesodermally derived peritoneum. See[[id:3929d482-7be2-4d7e-a576-1bc6f8081fe0][Bio 225 Lecture Notes: Blastulation and Gastrulation]]
* Phylum Rotifera
- Organisms are mostly benthic
- contain a *corona* with rotating sets of cilia and a *mastax*, which is similar to a jaw.
- They also contain flame cells for osmoregulation. For more information see[[id:e2a23658-cdca-4c97-891c-dec7d2c00463][Bio 225 Lecture Notes: Phylum Platyhelminthes: The Flatworms]]
- Reproduction is *Amictic*. The genes are not mixed, so it is essentially cloning:
* To start, there is an all female population becuase they clone themselves continually. This is the amictic stage.
* At the onset of winter, the *Mictic* stage begins.
* Female creates *unfertilized* eggs which always hatch into *haploid males*.
* Males are always haploid while females are always diploid.
* These males produce sperm which intercept other haploid cells and a resulting dormant, diploid fertilized egg is formed.
* Eggs hatch into females and the amictic cycle starts again.
* This process is called *Parthenogenesis*.
* Phylum Nematoda
- Can be either parasitic or not.
- Cuticle made of collagen
- Move with a thrashing motion
* This is due to contraction of *longitudinal muscles*. The collagen on side opposite the bend is stretched a great amount.
* Thus, when the nematode relaxes muscles, it *snaps* back into place.
- Organisms are dioecious, meaning the genders are separate.
- Sperm move by pseudopods.
- *Hookworms* suck blood and can cause anemia. Juveniles in the soil can bore through bare skin.
- *Trichina* worms can be attained through raw pig meat. The young can travel to skeletal muscles. The only way they can become adults is through...canabalism...
- *Pinworms* (12mm in length) live in the intestines and lays eggs in the anus. Most common nematode parasite in the U.S. Lifecycle is thankfully only about 6 weeks.
- *Filarial worms* live in and damage a person's lymphatic system.

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#+title: Bio 225 Lecture Notes: Phylum Mollusca
#+filetags: :biology:lecture_notes:
Phylum Mollusca is a very diverse phylum. The organsims contained within are Eucoelomate (see[[id:3929d482-7be2-4d7e-a576-1bc6f8081fe0][Bio 225 Lecture Notes: Blastulation and Gastrulation]])and they are protostomes.
They contain all of the major organ systems, but have an open circulatory system.
The *mantle* is a thin layer of tissure that secretes the shell and encloses the *mantle cavity* that also contains the gills/lungs.
Most Mollusca have a *radula*:
* The radula is like a tough, hard tongue made out of *chitin*.
* Made up of radula teeth surrounding the *Odontophore*.
* The odontophore is a big piece of cartilage.
* *Odontophore protractor* muscles drop the radula out of the mouth, while *odontophore retractor* muscles reel it back in.
* The *Radula protractors* wind the radula teeth around the odontophore, while the *radula retractors* are used once the radula is out of the mouth to move radula around in order to scrape in food.
The shell is made by the *Mantle*
* Outer layer of shell is called the *periostracum*.
* The *Prismatic layer* becomes visible once the periostracum rubs off and is no longer in contact with the mantle tissue so that it cannot be regenerated.
* The *Nacrous layer* is on the inside and is always in contact with the mantle.
An open circulatory system means that there are no capillaries between arterie and veins.
* oxygen is carried in the blood by *Hemocyanin*, which is blue when oxygenated. This means that the organisms' blood is blue.
Life cycles include *Trocophore larvae*
* Adult --> egg --> trocophore --> adult
* However, octupi and squids produce juveniles instead of trocophore larvae.
* Class Polyplacophora
- Organisms in this class are dorsoventrally flattened and have 8 plates along their dorsal side.
- They cling to intertidal rocks where waves pound them continually. How do their gills survive the intense force of water?
- The gills are actually located in small chambers/channels that run underneath the organism. This way, only small amounts of water can access them at a time.
* Class Gastropoda
- These organims mainly feed by radula.
- *Nudibranchs* (Naked gilled):
* Eat cnidarians like sea anemonies.
* These organisms use "stolen," undigested nematocysts and place them in their own pouches called *cerata* to use for its own defense.
- *Cone shells*:
* Have a single radula tooth with deadly neurotoxins called conotoxins.
* They inhibit ion channels that are normally opened by acetylcholine.
* Before attacking, the organism releases large amounts of insulin into the water. This causes the prey's blood suger to plummet so far that is cannot even move. This makes it easier to hunt.
* Some conotoxins are actually used as very effective yet non-addictive pain-killers.
- *Snails*
* Some are Pulmonates and have many pulmonary vessels in the mantle cavity.
* Air enters through a *Pneumostome*.
* Class Bivalvia
- Organisms have, unsurprisingly, 2 shells.
- Use *adductor muscles* to close.
- Draw water in through *incurrent aperture* or *incurrent siphon*.
- The intestines and gonads are found in the *foot*, its primary method of mobilization.
- The gills surround the foot and contain *water tubes* that carry water through the gills and to the *suprabranchial chamber*.
- Water flows out of this chamber and food or wates are left attached to the gills' surface
- *Giant Clams*:
* Can grwo up to 500 lbs
* Contains intracellular symbionts that photosynthesize
- *Zebra muscles* accidentally introduced in the 1980s.
* wreak havoc on industry and use *byssal threads* to attach themselves to various surfaces
- *Reproduction*:
* Most have external fertilization, but some have internal fertilizaiton with a larva called a *glochidia*.
* The Glochidia are released and then parasitize the gills of fish for several weeks before dropping off.
* How does a parent get a fish close so that in can release glochidia onto it?
* The adult's mantle actually has a section that looks exactly like a small fish. It waves this around and and baits in certain fish (most likely predators). When the fish gets close enough,
the clam releases its glochidia into the water.
* Class Cephalopoda
- These organisms are the only ones in phylum Mollusca that have closed circulatory systems.
- *Nautilus*:
* Has a chambered shell and lives in the most recent chamber
* A pipe called the *Siphuncle* runs the length of the shell and removes fluid, replacing it with gas to adjust bouyancy.
- Organsims in this class contain a *systemic heart* which pumps blood thorugh the body. Blood returns to gills and flows through the *branchial heart* which then increases the blood pressure through this
region
- Organisms like squids move by drawing water into their mantle cavity.
- The *siphon* or *funnel* is closed while muscles around the mantle cavity contract.
- Water pressure increases and the siphon suddenly opens and lets the water shoot out. the organism then swims forward by using jet propulsion.
- In the *escape response*, the *radial muscles* contract, decreasing the *thickness* of the mantle cavity but increasing the *diameter.*
- This allows for even more water to be jetted out, resulting in faster movements
- A squid or octopus can squeeze "ink" out of the *sepia*.
- Spermatozoa is encased in spermatophores, which are transferred to the female via a specialized arm during fertilization.

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:END:
#+title: Bio 225 Lecture Notes: The Endocrine System
#+filetags: :biology:lecture_notes:
The Endocrine system contains organs and glands that release certain substances into the bloodstream that target certain cells in order for them to perform specific actions in response to stimuli.
Thus, the molecules involved are chemical messengers that are often (though not always) lipds.
The target cells need certain receptors that can recognize these chemical messengers.
* Examples of Endocrine Glands and their Hormones
- The *Pineal Gland* releases *melotonin*, a chemical that prepares the body for sleep.
* However, blue light disrupts its production
* Made from the amino acid *Tryptophan*
- The *Hypothalmus*
* Releases ADH *Anti Diuretic Hormone) and *Oxytocin* as well as other *releasing hormones* that control anterior pituatary hormones
- *Pituatary Gland*
* Anterior lobe produces primarily growth hormones.
* Posterior lobe has *hypothalmic neurosecretory cells*.
- *Thyroid Gland*
* Releases *thyroxine* (which controls metabolism) and *calcitonin* (which controls bone formation)
- *Parathyroid*
* Releases *parathyroid hormone* (which controls bone resorption)
- *Adrenal Glands*
* Releases *epinephrine* and *cortisol*
- *Pancreas*
* releases *insulin* and *glucagon* which control blood glucose levels
* Interaction Between Hypothalmus and Pituatary
- These two glands are closely connected, with the hypothalmus influencing the pituatary gland
- Cytoskeletal motor molecules transport ADH and Oxytocin to synaptic region in the posterior pituatary via vesicles.
- These then await a signal to be released.
- When the neuron begins to carry an Action Potential, calcium ion gates open, acetylcholine is released in the synaptic region and this triggers the hormones there to be released into the
circulatory system.
- For the anterior lobe of the pituatary, releasing hormones from the hypothalmus are released into a *Portal System*.
- A portal system is any blood vessel that connects two cappilary beds to each other.
- This triggers growth hormones in the anterior lobe to be released.
* Mechanisms of Hormone Action:
- Many hormones operate using a type of regulation called *feedback inhibition*.
- For example, in the hypothalmus, the hormone TRH (thyroid releasing hormone) triggers the anterior pituatary to release TSH (thyroid stimulating hormone) which in turn stimulates the thyroid
to produce increased levels of thyroxine.
- However, thyroxine can be sent to the anterior pituatary *and* the hypothalmus acting as a negative feedback that restricts the production of TRH and TSH.
- Polar Hormones:
* Don't cross membrane easily
* Bind to receptors on cell surface
* Second messenger affects process in targe cell
* Epinephrine binds to liver cell and generates cAMP. This then in turn activates enzymes to break glycogen into glucose
* For 1 molecule of epinephrine, 1,000 cAMP is produced
* A billion glucose molecules could then be released into the bloodstream.
- Nonpolar or Lipid Hormones:
* Pass through membrane
* Bind with protein in cell that leads to gene activation
* Estrogen, for example, activiates genes in uterus that encourages cell growth. This is obviously good for someone experiencing pregnancy
* For example, in the Pancreas, insulin and glucagon is made.
* When insulin is released, cells increase glucose uptake. This is accomplished by "moving" glucose transporter intermembrane proteins from the cell interior to plasma membrane.
* This of course decreases blood glucose levels and stimulates the Pancreas to release glucagon.
* Glucagon travels to the liver and encourages the breakdown of glycogen into glucose.
* Hormones of the Adrenals
- Controls fight orf flight
- First, the sympathetic nervous system is engaged and norepinephrine is released at the target organ.
- Then, the adrenals (specifcally, the *Medulla* region)), release epinephrine as well as norepinephrine. The Medulla is the inner region of the adrenals.
- The medulla is actually derived from nervous tissue. You can think of it as a large sympathetic nerve ending.
- After 5 minutes, *cortisol* from the *cortical* region of the adrenals is released.
- It is a type of *corticosteroid and derived from cholesterol.
- Effecets similar to epinephrine.
- Suppresses immune system momentarily.
- In the hypothalmus, neurosecretory cells release *corticotropin releasing hormone* (CRH) which travels to the anterior pituatary.
- Cells here then release *adrenocorticotropic hormone* (ACTH) which triggers the cortex of the adrenal gland to release cortisol.
- This system operates via feedback inhibition
- Cortisol and melotonin have an inverse relationship.

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#+title: Bio 225 Lecture Notes: Muscle Movement Part 1
#+filetags: :biology:lecture_notes:
Muscle movement is a very complex process involving the contraction of muscle fiber cells. Since only contractions are permissible, each movement must be accompanies by two sets of "opposing" muscles.
The skeletal muscles are voluntary while smooth muscles are involuntary. Here we will focus on the skeletal muscles.
* Anatomay of Skeletal Muscles
- muscle fibers are striated.
- Form from cells called *myoblasts* which fuse together into a multinucleic fiber cell.
- Some of these myoblasts remain and form *myosatellite cells* which line the peripheral of the fiber cell.
- These cells can usually repair the fiber cells.
- Fiber cells are actually gathered into large bundles.
- Each fiber is composed of many tubular *myofibrils*, which are composed of actin and myosin filaments.
- On the myofibrils, there are stripes called *Z-lines*. These define segments on the myofirbil called *Sarcomeres*.
- When the muscle contracts, all the fibers shroten, which means all the myofibrils shorten, which in turn means *each Sarcomere shortens*
- The fiber cell membrane has holes in it that lead to *t tubule systems* that wrap around each and every myofibril.
* Basic Structure of the Myosin Filament
- Composed of myosin molecules, which have a bulbous head and a body.
- On the head there are two activation sites: The *Actin-binding* site and the *Myosin-ATPase* site.
* Basic Structure of the Actin Filament
- *Troponin* - 3 globular proteins: (1 for binding to Ca2+ ions, 1 for actin binding, and 1 for tropomyosin binding)
- *Tropomyosin* - 2 strands, normally cover the active sites.
- *Actin* - 2 strands to which myosin can bind.
* Process Leading to Contraction
- Motor neurons can innervate 3 to 2,000 muscel fibers
- To start the process, a motor neuron releases acetylcholine at the synaptic cleft region.
- Muscle fibers have chemically gated Na+ ion channels that then open when binded by acetylcholine.
- The muscle fibers then depolarize. This happens at the *myoneural junction* with many *junctional folds*.
- The depolarization is spread via the t tubule system, and this causes the release of Ca2+ ion from the *sarcoplasmic reticulum*.
- This is because t tubules come into direct contact with the sarcoplasmic reticulum.
- But how exactly are the Ca2+ released?
- There are two junctions between the t tubule system and the sarcoplasmic reticulum.
- Membrane of t tubules contain a voltage-sensitive protein, which changes shape as a result of depolarization.
- When it changes shape, it butts up against the *foot protein* in the sarcoplasmic reticulum. This creates a gap in the membrane.
- Finally, the Ca2+ ions flow out through this gap.

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#+title: Chemistry the Central Science: Acid-Base Equilibria
#+filetags: :Chemistry_the_Central_Science:textbook_notes:
#+STARTUP: latexpreview
Acids can be defined many ways. We start by analyzing the different types of acids and how they are defined.
* Arrhenius Acids and Bases
Arrhenius defined acids and bases in the following manner:
- An /acid/ is a substance that, when dissolved in water, increases the concentration of $H^+$ ions.
- A /base/ is a substance that, when dissolved in water, increases the concentration of $OH^-$ ions.
However, these definitions are restricted to aqueous solutions
* Bronsted-Lowry Acids and Bases
The concept of this definition is that acid-base reactions involve the transfer of $H^+$ ions from one substance to another.
For example, consider the reaction below:
\begin{equation*}
HCl(g) + H_{2}O(l) \rightarrow Cl^-(aq) + H_{3}O(aq)
\end{equation*}
The reaction above involves a proton that was donated to a substance that accepted it. This is central to the Bronsted-Lowry definition:
An acid is a substance that /donates/ a proton to another substance
A base is a substance that /accepts/ a proton from another substance
- In other words, an substance can function as an acid only if another substance simultaneously behaves as a base and vice versa.
- In addition, a substance can act as either an acid or a base and these substances are termed *amphiprotic*.
- In acid-base equilibrium reactions defined by Bronsted-Lowry acids and bases, there is a *conjugate acid-base pair.* Every acid, after it donates its proton, then becomes a *conjugate base* and every
base upon accepting a proton becomes the *conjugate acid*.
- /The stronger an acid, the weaker its conjugate base, and the stronger a base, the weaker its conjugate acid./
- the ions $H_3O$ and $OH^-$ are the strongest possible acid and strongest possible base respectively that can exist at equilibrium in aqueous solution.
- /In every acid-base reaction, equilibrium favors the transfer of the proton from the stronger acid to the stronger base to form the weaker acid and the weaker base./
* Autoionization of Water and the pH Scale
- In a given sample of water, one molecule can donate a hydrogen to another, creating the hydronium and hydroxide ions. This is called the *autoionization* of water.
- At room temperature, only about 2 out of every $10^{9}$ molecules are ionized. It is minimal, but important.
- The equilibrium constant expression for this process is shown below:
\begin{equation*}
K_c = [H_3O^+] [OH^-]
\end{equation*}
- For more information refer to [[id:410d2780-127b-4972-ae22-34d9cdbb750b][Chemistry the Central Science: Chemical Equilibirum]]
- For this expression, we usually use $K_w$ which is the *ion-product constant*
- At 25 degrees Celsius, $K_w = 1.0 \times 10^{-14}$
- A solution in which proton concentration equals hydroxide concentration is said to be *neutral*.
- Since these numbers are usually quite small, we express proton concentration in terms of *pH* which is the negative logarithm of the proton concentration:
\begin{equation*}
pH = -\log[H^+]
\end{equation*}
- For a neutral aqueous solution, the concentration of one species of ion is $1.0 \times 10^{-7} M$
- The pH of this number then equals 7.00
- Likewise, the pOH is the negative logarithm of the hydroxide concentration.
- At 25 degrees celsius:
\begin{equation*}
pH + pOH = 14.00
\end{equation*}
* Weak Acids and Bases
- Most acidic substances are weak acids and only partially ionize in aqueous solution.
- We can create an equilibrium constant expression for the equilibrium equations of weak acids:
\begin{equation*}
K_a \frac{[H_3O^+] [A^-]}{HA}
\end{equation*}
- Where: $K_a$ is the *acid-dissociation constant* for the acid HA
- The magnitude of this constant indicates the tendancy of the acid to ionize in water.
- /The larger the value of $K_a$, the stronger the acid./
- Another way of measuring acid strength is by *percent ionization*:
\begin{equation*}
Percent Ionization = \frac{[H^+]_{equilibrium}}{[HA]_{initial}} \times 100
\end{equation*}
The stronger the acid, the greater the percent ionization, which makes sense because the ionized concentration would be greater (more protons donated) if the acid is stronger.
* Using K to Calculate pH
- Knowing $K_a$ and the initial concentration of a weak acid, we can calculate the concentration of $H^+$ in a solution of the acid.
1. Write the ionization equilibrium reaction
2. Write the equilibrium-constant expression and the value for the equilibrium constant
3. Express the concentrations involved in the equilibrium reaction
4. Substitute the equilibrium concentrations into the equilibrium-constant expression and solve for x
Let's walk through an example. See the ionization equilibrium reaction below:
\begin{equation*}
CH_3COOH(aq) \rightleftarrows H^+(aq) + CH_3COO^-(aq)
\end{equation*}
For example, suppose $K_a = 1.8 \times 10^{-5}$. We write the equilibrium-constant expression as follows:
\begin{equation*}
1.8 \times 10^{-5} = \frac{[H^+] [CH_3COO^-]}{[CH_3COOH]}
\end{equation*}
Next we must express the concentrations involved in this reaction and this requires a bit of accounting. Say we started with 0.30 Molar of acetic acid.
Naturally, the concentrations for hydrogen and acetic acid's conjugate base are 0 at this time.
Let's say for x moles per liter of hydrogen that forms, x moles of conjugate base must form and thus x moles per liter of acetic acid must be ionized.
Change in concentration:
$CH_3COOH = 0.30 - x$
$H^+ = 0 + x$
$CH_3COO^- = 0 + x$
Finally, substitute the equilibrium concentrations into the expression and solve for x:
\begin{equation*}
K_a = \frac{(x) (x)}{0.30 - x} = 1.8 \times 10^{-5}
\end{equation*}
Solving for x using quadratic equation yields:
\begin{equation*}
[H^+] = x = 2.3 \times 10^{-3} M
pH = -\log(2.3 \times 10^{-3}) = 2.64
\end{equation*}
Now, as a general rule, /if x is more than about 5% of the initial concentration value, it is better to use the quadratic formula./
/If x is less than about 5% of the initial concentration value, it can be neglected./
Another important fact to note is that as the concentration of a weak acid increases, the percent ionization decreases, that is, a smaller percentage of hydrogen dissociates from the acid.
* Polyprotic Acids
Acids with more than one ionizable hydrogen atom are known as *polyprotic acids.*
In polyprotic acids, it is always easier for the first acid to dissociate. This is due to the electrostatic force. As the first hydrogen dissociates, the other hydrogen(s) feel an attraction to the rest of the usually negatively charged molecule. In terms of equilibrium constants:
\begin{equation*}
K_{a1} > K_{a2}
\end{equation*}
If subsequent K values for polyprotic acids differ by $10^{3}$ or more, one can estimate the pH of a polyprotic acid solution by only taking into account $K_{a1}$
* Weak Bases
There are two catagories of weak bases:
- Neutral substances with an atom that contains a nonbonding pair of electrons that can accept a proton.
* These substances usually contain nitrogen
* A common type of molecule in this category are *amines*.
- Anions of weak acids i.e. the conjugate bases of weak acids.
Like with acids, we can write an equilibrium constant expression for weak bases with $K_b$ equaling the *base-dissociation constant*.
* Relationship Between Ka and Kb
If you mulitply the equilibrium reactions of an acid's ionization with the reaction of its conjugate base, you can multiply $K_a$ and $K_b$.
However, when you do this, everything cancels out except for the following:
\begin{equation*}
K_a \times K_b = [H^+] [OH^-] = K_w
\end{equation*}
As we saw earlier =, this value is equal to $1.0 \times 10^{-14}$.
As a result, we can take the negative logarithm of both sides and obtain a useful equation:
\begin{equation*}
pK_a + pK_b = pK_w = 14.00
\end{equation*}
At 25.0 degrees celsius.
* Acid-Base Properties of Salt Solutions
Many salts can affect the pH of a solution. How do they do this?
Well, many ions are the either the conjugate bases or conjugate acids of other substances. Thus, they may be able to react with water to change the pH.
- *How ions reacts to water*
* If an ion is the conjugate base of a strong acid (one of the seven), it will not affect the pH of a solution. These anions will always be spectator ions.
* However, if it is the conjugate base of a weak acid, it is able to take on a hydrogen, creating hydroxide ions and increasing the pH
- *How cations react with Water*
* Polyatomic cations with one or more protons are considered the conjugate acids of weak bases and can thus react with water molecules to give off a proton, decreasing the pH.
* However, some metal salts can also decrease the pH. This is done if the metal cation has a charge greater than 2+.
* This cation atracts the polar negative oxygens of water molecules all around it. This weakens the bond between an oxygen and its hydrogen
* Eventually, another water molecule comes into contact and takes this hydrogen from the weak bond, creating a hydronium ion and decreasing the pH
* Acid-Base Behavior and Chemical Structure
Some important facts regarding what determines the strength of an acid structurally:
- /In general, as the H--A bond polarity increases, to draw more electron density from H, the stronger the acid./
- /In general, as the H--A bond strength decreases, the stronger the acid./
- /In general, the greater the stability of the conjugate base, the stronger the acid./
The strength of the H--A bond is the most important factor for acid strength within a /group./
The bond polarity between H--A is the most important factor for acid strength within a /period./
With these facts, we can conclude that acid strength increases moving left to right down a /period/ and increases moving down a /group./
Additionally, in *oxyacids*, the number of oxygen atoms in the conjugate base is directly proportional to acid strength, since it allows the molecule to have resonance and bring stability by "spreading"
the negative charge.
* Lewis acids and Bases
To conclude, there is one more definition of an acid and a base:
- A Lewis acid is an electron-pair acceptor.
- A Lewis base is an electron-pair acceptor.
This definition allows us to analyze reactions in solvents other than water as acid-base reacitons.
In fact, the interaciton of lone pairs on one molecule or ion with vacant orbitals on another molecule or ion is one of the most important concepts in chemistry.

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:PROPERTIES:
:ID: a8356651-4155-4ed4-8129-d13ca9b448f7
:END:
#+title: Chemistry the Central Science: Additional Aspects of Aqueous Equilibrium
#+filetags: :Chemistry_the_Central_Science:textbook_notes:
#+STARTUP: latexpreview
* The Common-Ion Effect
We consider a weak acid and a soluble salt of that acid. Thus, the two substances will share a common ion.
For example, if we have a solution of acetic acid in water and add to that solution sodium acetate, the added acetate ion from sodium acetate will then shift the equilibrium of the acetic acid to the left, that is towards reactants. This then reduces pH because it favors the production of the acid, not the conjugate base and aqueous proton. See[[id:410d2780-127b-4972-ae22-34d9cdbb750b][Chemistry the Central Science: Chemical Equilibirum]]
In summary: /Whenever a weak electrolyte and a strong electrolyte containing a common ion are together in solution, the weak electrolyte ionizes less than it would if it were alone in solution./
* Buffers
A buffer solution is one that contains an acid and its conjugate base. It is very stable and does not change pH very much at all.
There are two ways to make a buffered solution:
1. Mix a weak acid or a weak base with a salt of that acid or base.
2. Make the conjugatae acid or base from a solution of weak acid or base by adding a strong acid or base.
The results are the same. In the end, you get a solution with large amount of an acid/base conjugate pair.
For more information see: [[id:b55f18de-5836-46d4-b52a-f62c9d2c4bea][Chemistry the Central Science: Acid-Base Equilibria]]
If we construct a simple equilibrium expression for the dissociation of a weak acid:
\begin{equation*}
HA(aq) \Longleftrightarrow H^+(aq) + A^-(aq)
\end{equation*}
\begin{equation*}
K_a = \frac{[H^+] [A^-]}{HA}
\end{equation*}
Thus, if we solve for the proton concentration:
\begin{equation*}
[H^+] = K_a\frac{[HA]}{[A^-]}
\end{equation*}
This tells us that the pH depends on:
- The acid-disocciation constant
- The ratio of the concentrations of the acid/base conjugate pair
If OH or H is added to the solution, as long as the concentrations of the acid/base and its conjugate are sufficiently large, the ratio should not change too much and thus the pH should not change too much either.
To find the pH of a buffer solution, we use the *Henderson-Hasselbalch equation*:
\begin{equation*}
pH = pK_a + \log\frac{[A^-]}{[HA]}
\end{equation*}
The buffer *capacity* is the amount of acid or base the buffer can neutralize before an appreciable change in pH occurs.
The pH range is the range of pH over which a buffer is effective at minimizing the pH Usually, the pH range has a value of $pH = pK_a \pm 1$
Now, what happens when we add strong acids or bases to a buffer? To calculate how the pH of the buffer responds to the addition of a strong acid or base, we must adopt two strategies.
1. Perform a *limiting reactant stoichiometry calculation*
2. Then perform an *equilibrium calculation* using the Henderson-Hasselbalch equation as described above.
Part one is accomplished using a BCA table (Before Change After), noting that *all* of the moles of strong acid or base react the weak base or acid. the resulting moles of acid/base conjugate pair can then be used in the Henderson-Hasselbalch equation.
* Acid-Base Titrations
Three different types of titrations will be examined:
- Strong acid - strong base titrations
- weak acid - strong base titrations
- polyprotic acid titrations
Each of these can examined using a *pH titration curve*. By analyzing this curve, the type of titration can be determined as well as the pKa value for the reaction.
This curve has an equivalence point (where the amount of base equals the amount of acid) where the pH changes rapidly. However, the pH halfway to this point corresponds to the pKa since the ratio of the weak acid and its conjugate base is 1.
In a strong acid - strong base titration, the equivalance point occurs right at 7 and the pH change during this time is very dramatic.
In a weak acid - strong base titration, the equivalance point occurs at a pH *above* 7 because the salt that forms contains the conjugate base which reacts with the water to produce hydroxide, thus raising the pH. The pH also does not change as quickly at the equivalence point.
In a polyprotic acid titration curve, there are multiple (usually two) equivalance points, one for each proton dissociation.
* Solubility Equilibria
We examine the the equilibrium of a strong electrolyte at the point where a saturated solution of this electrolyte is in contact with the solid precipitate of this electrolyte:
\begin{equation*}
BaSO_4 \Longleftrightarrow Ba^{2+} + SO_4^{2-}
\end{equation*}
The equilibrium constant that describes how soluble the solid is in water is called the *Solubility-product constant*.
For this example it equals:
\begin{equation*}
K_{sp} = [Ba^{2+}] [SO_4^{2-}]
\end{equation*}
It is vastly important to note that the solubility of a substance can change quite a lot in response to numerous factors especially the pH and the concentrations of other ions in solution especially common ions.
The common-ion effect states that if there are already ions in a solution or added to a solution that make up a solid precipitate, the formation of that precipitate will be favored and the solubility will be reduced. In general, /the solubility of a slightly soluble salt is decreased by the presence of a second solute that furnishes a common ion./
For metal hydroxides pH often plays a role in changing solubility. An example solubility-product constant expression:
\begin{equation*}
K_{sp} = [Mg^{2+}] [OH^-]^2
\end{equation*}
If the solution is equilibrated in a buffer with a lower pH, the pOH increases and this can be used to solve for [OH]. Then, using the equilibrium constant for the reaction, the new concentration of [Mg] can be found. It will be /much/ more, since lowering the pH increases the proton concentration and decreases the OH concentration. As a result, to keep the equation consistent, the amount of soluble Mg must increase.
/In general, the solubility of a compound containing a basic anion increases as the solution becomes more acidic (as pH is lowered)./
Another important concept is *amphoterism*.
There are amphoteric oxides and amphoteric hydroxides. They can dissolve in acidic solution, because their anions react with acids. However, they can /also/ dissolve in basic solutions by forming *complex ions*.

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:PROPERTIES:
:ID: cb48fe6b-d4ba-4ade-8a92-656d0553026a
:END:
#+title: Bio 225 Lecture Notes: Muscle Movement Part 2 and Sliding Filament Model
#+filetags: :biology:lecture_notes:
The Sliding filament model of muscle contraction attempts to explain how myofibrils and muscle cells contract in response to electrical signals from motor neurons.
It involves the mechanical motion of certain proteins within the myofibril to accomplish the reduction in length of the individual fiber.
The process will be outlines below:
Please refer to[[id:0a30b99e-e601-4502-8283-5895fd49f95b][Bio 225 Lecture Notes: Muscle Movement Part 1]]
* Step 1
Before $Ca^{2+}$ binds, *tropomyosin* covers the binding sites on the actin molecules of the actin filament.
The released calcium ions then first bind to *troponin*, the protein with three globular domains. As a result, troponin's bond to actin weakens, but its bond to tropomyosin *remains intact*.
Thus, the troponin and tropomyosin then slide off of the actin molecules in such a way as to reveal the active sites on the actin.
*Myosin heads* in a high energy state from the hydrolysis of ATP. ADP occupying the *ATPase active site* with *actin binding site* free to bind.
* Step 2
The actin binding site on the myosin head binds to the exposed active sites on the actin molecules that the tropomyosin is no longer bonded to.
The thick and thin filaments are now linked together by a temporary chemical bond called a *cross-bridge*.
* Step 3
The myosin filaments then transisiton to a low energy state.
This happens due to the release of the hydrolyzed ADP.
As a result of transitioning to a lower energy state, the myosin head then rotates toward the central *M-line* while attached to the actin filament. (This is the power stroke).
The actin filament then slides inward.
Additionally, the ATPase binding site on the myosin head is now freed.
* Step 4
ATP binds to the free myosin ATPase site, then myosin's actin binding site breaks its bond with actin as a result.
However, at this point, there are still many, many other myosins still attached and performing power strokes throughout the whole myofibril.
In fact, there are six actin filaments per myosin filament.
* Step 5
ATP is then hydrolyzed to ADP + P.
This "recocks" the myosin head back to a low energy state.
If enough clacium ions are present in the sarcoplasm, the sarcomere continues to shorten as long as it is receiving a signal from motor neurons.
The calcium binding is reversible but there will usually be other calcium ions in the viscinity that can replace ones that detatch.
However, the membrane must continue to be polarized.
This process continues to repeat itself, with millions of other myosin proteins perfomring this same action at the same time each instant you decide to contract. It is truly a remarkable process that
happens in the blink of an eye. the inner complexities of this process points to an inherent complexity of life that highly suggests a careful fine-tuning and design. Even as I write this, the muscles in my fingers are undergoing this very process.

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:PROPERTIES:
:ID: 2197395d-4587-4832-a419-aeb43a77f3af
:END:
#+title: Bio 225 Lecture Notes: Basic Support Structures
#+filetags: :biology:lecture_notes:
* Coloration
There are two ways animals can create colors on the surface of their skin:
1. Pigments in *chromatophores*
2. Crystals in *iridophores*
In regard to chromatophores, different organisms can have different distributions of pigments within the cells.
The pigment can be centered in the cell, or spread out throughout the whole chromatophore.
Some species can also control whether the pigment is spread or not:
- When *radial muscles* contract, the pigment then spreads out through the cell.
- If the radial muscles on only one side of the cell contract, the effect can add a wavy pattern of color to the animal's skin.
Iridophore cells contain nanocrystals.
Close spacing of the crystals reflects shorter wavelengths.
Wide spacing reflects longer wavelengths.
* Melanin
Most mammals are only colored with melanin, not chromatophores.
Specialized cells called *melanocytes* produce melanin inside *melanosomes*.
The melanosomes are then exported to *keratinocytes*, which produce both keratin and Vitamin D.
The melanosomes cluster around the keratinocytes' nuclei, protecting the DNA from dangerous levels of UV light.
Genetics and UV light determine melanin production.
Too much UV light can corrupt melanocytes and cause skin cancer.
* Skeletal System
Let's first look at worms:
- They have *hydrostatic skeletons*.
- To move, the worm contracts circular muscles at its very tip.
- This decreases the diameter of the segments, but as a result, the length of the segments increase.
- It repeats this for the whole length of the body and thus moves forward.
Other species have rigid exo or endoskeletons. Let's observe endoskeletons:
- In *Endochondrial bones*, the bones start formation as a *cartilage model* but later osteoblasts invade the model and begin osifying it.
- *Intramembranous bones* do not start with a cartilage model.
- *Compact bones* have *osteons* that run the entire length of the bone. They are designed to handle longitudinal forces.
- *Spongy bones* lack osteons but they hve *trabeculae*. These are designed to handle forces in all directions.
- Osteoblasts build bones, while osteoclasts resorb bones.

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:PROPERTIES:
:ID: 2129e424-56a4-4bb3-bf14-01cd4097e5e6
:END:
#+title: Bio 225 Lecture Notes: Phylum Arthropoda
#+filetags: :biology:lecture_notes:
Phylum Arthropoda is a massive taxonomic group of animals. It is perhaps the most diverse phylum in all of creation and no doubt includes the largest number of species.
Arthropods are bilaterally symmetric, they are protostomes, they have efficient locomotion, and contain great sensory systems.
Some major subphyla will be explored along with the aspects that make each group unique:
* Subphylum Chelicerata
These organisms have *no* antennae.
They have six pairs of apendages, with four of them being wlaking legs.
The first pair, which often include fangs, are the *chelicerae*.
The second pair are the *pedipalps*, which are often used in reproduction.
Class Arachnida; Spiders:
- Perhaps the most recognizable organism of this subphyla.
- Spiders envenomate their prey to paralyze or kill them, eating with a vacuum-producing, pumping stomach.
- The body is aligned with a cephalothorax and abdomen.
- Spinnerets can extrude silk and can create a drag-line.
- Males transfer sperm via "clubbed" pedipalps.
- The Black Widow spider releases a neurotoxin that causes massive release of acetylcholine at myoneural junctions in muscle cells. (See [[id:0a30b99e-e601-4502-8283-5895fd49f95b][Bio 225 Lecture Notes: Muscle Movement Part 1]] )
* Subphylum Myriapoda
The name of this subphylum means "many legs."
Class Chilopoda:
- Includes the centipedes
- One pair of legs per body segment
- Fast and venomous
Class Diplopoda:
- Includes the millipedes
- Multiple pairs of legs per body segment
- Slower moving
* Subphylum Crustacea
These organisms have two pairs of antennae and have antennal glands, which act as kidneys.
*Ecdysis:*
- Parts of old cuticle are recycled
- Rupture point forms and absorbs water to expand the rupture
- The animal crawls out, but new exoskeleton is soft so it absorbs more water to expand the exoskeleton for it to grow into later.
* Subphylum Hexapoda
By far, the largest subphylum with the most species. Otherwise known as the insects. In fact, 3/4s of all living species are insect species.
They have three pairs of walking legs.
Composed of head, thorax, and abdomen, with the thorax usually containing the locomotion structures such as wings.
The *ovipositor* is an organ many insects have and is used to deposit eggs.
The Process of Flight:
- There are two muscular systems that insects use to fly.
- The first one uses *sternotergal flight muscles* which are connected to the ventral and dorsal side. These contract, pulling the dorsal side down and thus the wings up.
Then, *Direct flight muscles* attatch directly to the the wings and contract to pull them down.
- In another method, the sternotergal flight muscles behave the same exact way. However, this time there are *indirect flight muscles* which are bulbous in shape. When they buldge, the wings are pulled down.
In *synchronous* flight, nerve impulses stimulate the muscle contraction each time.
In *Asynchronous* flight, only periodic nerve impulses are required to move the wings. Associated with indirect flight musculature.
Insects are known to have three primary section of their intestinal tract:
- The *foregut* goes from the mouth to the crop/gizzard.
- The *midgut* goes from the stomach to the *cecae*. This is where most of the digestion takes place. The ceca is a place where food is stored to be digested.
- The *hindgut* goes from the intestine to the rectum. Most water absorption and feces production happens here.
Insects also have an unusual way to go about gas exchange:
- Oxygen gas diffuses through the *tracheal system*, a series of tubes throughout the organism that is responsible for gas exchange, performing the same operations, blood and lungs would do.
- Holes at the surface of the organism are called *spiracles* and a *hypodermis valve* opens or closes them.
- Inside, the tracheae are kept open by long, coiled structures called *taenidia*.
Some insects have Compound eyes, which let them see in nearly all directions at once:
- Each eye is composed of many smaller "eyes" called *ommatidia*.
- Each one of these contains a lens along with pigment cells.
- Some insects, like bees, can even see in UV wavelengths.
Metamosphosis:
- The larva hatches from the egg and after some time enters the *pupa* stage and creates a *chrysalis*.
- A brand new form of the adult then emerges in what is called *holometabolous* metamorphosis.]
- In *hemimetabolous* metamorphosis there is a nymphal stage that transforms into the adult without the pupal stage.
In a Beehive:
- There are female worker bees, a queen, and male drones.
- The drones fertilize the queen, who stores the sperm.
- Drones are haploid and develop parthenogenetically.
- The queen begins to produce the Queen Pheromone.
- The Q.P. causes other worker bees to stay sexually inactive.
- However, if Q.P. concentration is low, some of the workers produce royal jelly and feed it to young female larvae that may eventually develop into queen bees.

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:PROPERTIES:
:ID: 4780b3ee-aeb1-4df3-a901-de3e5d242e51
:END:
#+title: Bio 225 Lecture Notes: Homeostasis and Osmoregularity
#+filetags: :biology:lecture_notes:
#+STARTUP: latexpreview
Before we start talking about the topic of homeostasis and eventually the kidney nephron, we must clarify terms:
*Osmolarity* - The total solute concentratrion in a 1.0 Liter aqueous solution.
For example, 1M NaCl has 2 osmoles or 2 osm and are osmotically active.
Isotonic is in an osmotically neutral environment, hypotonic refers to a solution that has lower solute concentration thatn its surroundings, and hypertonic refers to a solution that has more solute
concentration than its surroundings.
Tonicity can be described in terms of water movement as it relates to solutes that are *non-penetrating*.
* Osmotic Regulation in Fish
Fish's gills are permeable to water and ions.
Fish in freshwater are *hyperosmotic regulators*, meaning that they keep their internal fluids at *higher* solute concentration than their surroundings.
the challenge is, however, that the fish is going to be gaining water passively by osmosis.
As a result, it must lose excess water, but keep the solute:
1. The fish then urinates very dilute urine
2. Chloride pumps are used to pump $Cl^-$ into cells against their concentration gradient. This also attracts $Na^+$ and replaces the salt lost by urination.
Marine fish, however, are *hypo-osmotic regulators* in that the keep their internal fluid concentration *less* than that of their surroundings.
As a result, the fish will lose water to the sea b osmosis. It can mitigate this effect by:
1. Urinating a very small volume
2. Get water by simply drinking seawater
3. Chloride pumps pump chloride ions *out* of the cells against their concentration gradient.
Some fish are stenohaline, like the ones described above, but others are euryhaline, that is, able to live in environments with varying solute concentration.
* In Sharks
Sharks actually retain *urea* in their blood, which is osmotically active.
Thus, the osmotic potential is slightly higher inside than in the seawater. As a result, water passes *into* the shark through the gills via osmosis.
However, salt also diffuses passively into the shark. How can this be?
It is because the concentration is composed of both urea and salt, with the salt only accounting for a small percentage. Thus, it diffuses from the Ocean, into the animal.
The shark then uses a *salt gland* to concentrate the salt.
* Terrestrial Organisms
All live in a dessicating environment.
Must excrete wasts, but keep sugars and amino acids.
Most proteins and amino acids are brken down into "NH" groups.
From here it is either broken down into ammonia (NH3) which is very toxic and must be kept quite dilute.
Or it may be broken down into urea, like in mammals. It is less toxic than ammonia.
It may also be broken down into uric acid as in birds and reptiles. This is the least toxic and doesn't need to be very dilute.
Flat worms and rotifers have Protonephridia, which are very simplistic filtration systems (See [[id:e2a23658-cdca-4c97-891c-dec7d2c00463][Bio 225 Lecture Notes: Phylum Platyhelminthes: The Flatworms]] )
Earthworms are often found with Metanephridia, one in each segment, to remove wastes.
* The Mammalian Kidney/Bladder
The tube from the kidney is the *ureter* and these collect in the *bladder*, which can hold up to 1 Liter.
The *urethra* is the tube that leaves the bladder.
There are two primary muscles in the bladder, called *Sphincters*.
They are normally closed, but the smooth muscle opens involuntarily if the bladder is too full. (internal sphincter)
The skeletal muscle sphincter is voluntary and must be relaxed at the right time. (external sphincter)
This all sets the stage for an overview of the most complex type of filter and waste removal: The kidney Nephron.

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:PROPERTIES:
:ID: efc6bedf-c518-4614-ae4d-338936e0f695
:END:
#+title: Bio 225 Lecture Notes: The Kidney Nephron
#+filetags: biology:lecture_notes:
#+STARTUP: latexpreview
There are 1 million nephrons in the average human kidney. They serve as the basic filter unit that cleans and filters the blood of the organism.
The *Afferent arteriole* brings the blood into a tuft of capillaries and the *glomerulus* called the *Bowman's Capsule*.
The *Proximal Convoluted Tubule* then leads to the *Loop of Henle*.
This then leads to the *Distal Convoluted Tubule* that eventually deposits into the *collecting duct*,
Standard urine output is about 1 liter per day.
However, reabsorption by the nephrons accounts for 170 liters per day.
Basic Overview:
*Step 1:*
Renal Corpuscle: Rapid filtration of blood (water, urea, ions, nutrients.)
*Step 2:*
Proximal convoluted tubule: variable reabsorption of water, ion, and /all/ nutrients.
*Step 3:*
Loop of Henle: water reabsorption (descending limb) and NaCl reabsorption (ascending limb).
*Step 4:*
Distal convoluted tubule: variable reabsorption of NaCl under hormone control.
*Step 5:*
Collecting duct: variable reabsorption of water and urea under hormone control.
* 1: Renal Corpuscle
- Mechanical filtration process
- Blood cells, proteins, etc. do not pass through
- Only electrolytes, water, and small solutes can pass through
- The Glomerulus is packaged inside the Bowman's capsule and this makes up the renal corpuscle
- *Podocytes* wrap themselves around the capillaries in the glomerulus, which are *fenestrated capillaries*, with tiny holes through which the filtrate passes through
- The *Basal Lamina* links the capillary to the podocyte
- Filtrate must be forced through the capillary, basal lamina, and then the podocytes
- Now, the blood in the capillary is hypertonic to the fluid in the Bowman's capsule. (See [[id:4780b3ee-aeb1-4df3-a901-de3e5d242e51][Bio 225 Lecture Notes: Homeostasis and Osmoregularity]] )
However, blood pressure forces the fluids through the holes in the capilarry, against what it would do passively, since water wants to diffuse into the blood vessel by osmosis
- Thus, B.P. must exceed the osmotic pressure
B.P. Regulation at the Glomerular level:
- If efferent arteriole, which takes blood /away/ from the nephron, vasoconstricts, the B.P. rises.
- Afferent arteriole can also vasodialate.
- If B.P. drops by 20%, pressure = colloidal osmotic potential and thus there is no movement.
* 2: Proximal Convoluted Tubule (PCT)
- Active transport of salt, amino acids, and glucose into the *peritubular capillary network*, which extends from the efferent arteriole.
- PCT membrane is composed of the apical membrane and the *Basolateral membrane*.
- *Key to Reabsorption:* The ion exchange pump. 3 sodium ion pumped out of PCT for every 2 potasium ions pumped in (via basolateral membrane).
- $[Na^+]$ concentration then goes down in the PCT membrane naturally. Therefore it diffuses into the PCT via the apical membrane but is actively transported into the peritubular capillary against its concentration gradient.
- Chloride ions, glucose, and amino acids are cotransported along with the sodium ions into the PCT membrane. They then /passively/ diffuse into the capillary since the capillary is low in concentration of those things.
- As a result, as solute concentration rises outside of the membrane, water diffuses outside as well.
- One should recover 100% of amino acids and glucose in this process.
- 60% of the filtrate is reabsorbed.
* 3: The Loop of Henle
- Countercurrent multiplier system
- The *descending limb* (made of simple squamous tissue) is water permeable but impermeable to salt.
- The thin part of the *ascending limb* is permeable to salt, but impermeable to water.
- The thick part of the ascending limb (made of simple cuboidal tissue) is also water impermeable.
- The water diffuses out of the descending limb because the outside *medulla region* is hypertonic. The water is reabsorbed by the *vasa cava* vein. Thus, filtrate osmolarity is increasing as you go down the descending limb.
- It eventually gets to the point where concentration is higher than that of the outside medulla region (happens on the loop), and thus, salt begins to passively diffuse out of the ascending limb.
- However, during the thick region, salt must be pumped out, because as the filtrate ascends, osmolarity decreases from the previous passive diffusion of salt.
But why does the medulla region's osmolarity increase the deeper you descend?
- This is because when the salt passively diffused out of the *lower*, thin portion of the ascending limb, its osmolarity was much *greater* than higher up in the ascending limb. So for a given volume that diffused, its concentration was greater. Thus, the deeper you go into the medulla region, the more concentrated it is.
- This is directly responsible for the water diffusion in the descending limb.
- There is a positive feedback system between the two limbs.
- Then, because water diffuses out, it increases the concentration of the filtrate, which only continues the process.
- By the time the filtrate reaches the Distal Convoluted Tubule, /80% of the filtrate has been reabsorbed./
* 4: Distal Convoluted Tubule (DCT)
- Hormonally controlled.
- If dehydrated, *aldosterone* is released by the adrenal glands, which increase the reabsorption of sodium ions.
- As a result, it follows that more water will diffuse out of the filtrate if it becomes less concentrated with solute i.e. sodium ions.
* Collecting Duct
Maintainence of B.P. critical. Where is this done?
- In the *juxtaglomerular apperatus*: If the B.P. in the renal corpuscle is too low, it releases more *rensin.*
- This cascades to activate *angiotensin II*.
- This then simulates aldosterone release, a feeling of thirst in the individual, the constriction of peripheral blood vessels, and an increase of ADH production. (See [[id:e04dda10-33de-4750-931b-fbd324fd646c][Bio 225 Lecture Notes: The Endocrine System]] )
- This brings us back to the collecting duct. The collecting duct is under hormone control via ADH.
- If dehydrated, ADH in the blood increases. The effect of this is to increase the water permeability of the collecting duct membrane.
- the ADH binds to receptors on collecting duct cells, causing them to /insert more aquqporins/ into their membranes.
- As a result, more water is reabsorbed and retained by the individual and the urine becomes very concentrated.
Now, some urea is also reabsorbed in the collecting duct region. Why is this?
- Urea actually increases the osmolarity in the medulla region, assisting in even more reabsorption of water.
What if you could not produce ADH?
- It would affect the number of aquaporins in the collecting duct.
- Water would not be reabsorbed but would be excreted along with the urine.
- Resulting in very large urine output. This disease is called diabetes insipidus.
What if glucose levels are too high in the blood?
- The glucose exceeds its *transport maximum*.
- As a result, glucose appears in the urine.
- Occurs from both Type 1 and Type 2 diabetes.
- If there's glucose beyond the PCT, osmolarity of filtrate increases. Thus, less water is able to diffuse through the membrane because of the smaller concentration difference.

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:PROPERTIES:
:ID: 798e1b8d-bf5c-42b2-ad30-222d70057c88
:END:
#+title: Bio 225 Lecture Notes: Internal Fluids and Respiration
#+filetags: biology:lecture_notes:
#+STARTUP: latexpreview
Red blood cells are the basic units that carry oxygen throughout an organism.
In a typical organism, there can be anywhere from 5 million to 5 billion RBCs per mL.
The RBCs are produced in bone marrow tissue by multipotential stem cells.
When mature, the nucleus of the RBC is ejected and contains about 280 million molecules of *hemoglobin*, each with 4 oxygen binding sites.
RBCs only hve a lifespan of about 4 months, and 10 million made and destroyed per second. Iron is recycled, but *bilirubin* and other compounds are broken down in the liver.
*Hemostasis* is the process of decreasing blood loss.
When there is a wound in a blood vessel, it could constrict upstream.
A more effective process includes *clotting agents* (13 of which have been identified).
In a wound, *platelets* wll stick to collagen fibers, forming a *platelet plug*.
Other clotting factors that include plasma proteins are synthesized in the liver.
for example, *Prothrombin*, which circulates in the blood, is transformed into *Thrombin*, which is combined with *Fibrinogen* to produce a *Fibrin meshwork* at the wound site.
* Circulatory Systems
There are single circuit systems and double circuit systems. Fish have single circuits, while most other animals have double circuit systems
In double circuits, the right side of the heart pumps to the lungs, while the left side ultimately pumps towards capillaries.
The two circuits are the pulmonary circuit and the systemic circuit.
However, in reptiles, the ventricle of the heart is undivided, but in such a way as to prevent mixing.
*In the Mammalian Heart*:
- Blood comes from the right atrium then towards the right ventricle, which squeezes blood into the pulmonary artery.
- The *Tricuspid valve* prevents back flow.
- Pulmonar veins bring blood back to the left atrium.
- Blood then passes through the *Bicuspid valve* and into the left ventricle, which facilitates the pumping of blood to the rest of the body.
- The *semilunar valves* prevent backflow to heart from the aorta and pulmonary artery.
- *Systole* refers to muscular contraction of the hear while *diastole* refers to the muscle relaxation of the heart.
- The *SA node* contains a leaky voltage-gated sodium ion channel and allows for sodium ions to leak into the heart's membrane, depolarizing it. Thus, the heart does not need external innervation; it is *myogenic*.
- The *Atrioventricular node* in the ventricles has an *atrioventricular bundle* which carries signals to the bottom of the ventricles via *purkinje fibers* to initiate the contraction from the bottom up, which necessary for pumping blood.
*In an EKG:*
- P = Atrial depolization
- QRS = ventricular depolarization
- T = ventricular repolarization
* Arteries, Veins, and Capilarries
Arteries are vessels leading /away/ from the heart.
They have thicker smooth muscel layers around them than veins do.
Oxygen content is high, but rather low in the pulmonary circuit.
They expand during systole but relax during diastole.
Veins, on the other hand, are vessels that lead /back/ to the heart.
The return-flow of blood in veins is assisted by *one-way valves*. Skeletal muscle contractions force the blood through these valves.
Now, in between the arteries and the veins are capillary beds, containing a plethora of capillaries.
Most of the time, blood passes between an artery and a vein via only one capillary bed.
The *Precapillary Sphincters* lead into the bed from the *arteriole,* a small extension from the artery.
The hydrostatic pressure /drops/ over the course of the gas exchange that happens along the bed.
The boundaries between endothelial cells allows for a gap for ions, glucose, and amino acids to pass through and into the interstitial tissue. This happens only on the *arteriole side*.
On the *venule side*, gases pass /into/ the capillary.
Why does this happen?
On the arteriole side, the hydrostatic pressure hasn't dropped by much and it sill exceeds the osmotic potential and as a result, it "pushes" the material out of the arteriole side.
Once the pressure declines, however, osmotic potential then begins to force things into the capillary.
The hydrostatic pressure drops going from arteriole to venule side because of the steady loss of water from it being pushed out, and osmotic potential increases because of the resulting high blood concentration.
* Lymphatic Systems
- Lymphatic vessels can recover excess water pushed out of the arteriole.
- There are usually lymphatic vessels within the capillary.
* Respiration
- Some organisms have cutaneous respiratory systems.
- In mammals, lungs are vascularized, invaginated, and internal.
- The Trachea branches into a bronchus, which then branches into many bronchioles, filled with many alveoli.
- During inhalation, diaphragm contracts, thoracic cavity increases, and the lung volume increases. This decreases the pressure in the lungs, which forces air into them because of the pressure difference with the atmosphere.
- Carbon dioxide actually controls the desire to breathe by decreasing the pH of the cerebrospinal fluid. (for more on pH see [[id:b55f18de-5836-46d4-b52a-f62c9d2c4bea][Chemistry the Central Science: Acid-Base Equilibria]])
- The lungs themselves are held together by the *pleural space*, which is a vacuum that runs the perimeter of the lung. The negative pressure allows the lungs to expand when filled with air.
- Atmospheric gas has more oxygen and is drawn into alveolar air space.
- Thus, by diffusion, oxygen travels into the blood, and carbon dioxide diffuses into the alveolar air space.
- At the cell, oxygen diffuses from blood into the cell (because cell is low in oxygen) and carbon dioxide diffuses into the blood from the cell.
* Transport of Oxygen
- Oxygen binds to hemoglobin, but spcifically the *heme* protein.
- There are 4 hemes per hemoglobin.
- Hemoglobin itself is composed of $\alpha$ and $\beta$ subunits and the hemes are interspersed between.
Oxygen saturation curves:
- Saturation % versus partial pressure of oxygen.
- However, the *Bohr effect* takes into account the effect pH has on hemoglobin.
- As pH decreases, the Heme has /reduced affinity/ to oxygen.
- With the Bohr effect, pH is lower near the cells as opposed to the lung environment. Thus, since Heme has lower affinity, /more oxygen is unloaded./
- The transport of carbon dioxide in the blood is accomplished by the *carbaminohemoglobin* protein, or in a dissolved state.
- However, most is carried as $H_2CO_3$ which is released from the RBC as $HCO_3^-$

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:PROPERTIES:
:ID: 2d65e714-dae9-4427-9bc2-5534b37bcdd0
:END:
#+title: Bio 225 Lecture Notes: Phylum Chordata
#+filetags: :biology:lecture_notes:
There are five key characteristics organisms in Phylum Chordata contain:
1. Notochord
2. Dorsal nerve cord
3. Post-anal tail
4. Pharyngeal pouches
5. Endostyle or Thyroid gland (for information on the thyroid gland see [[id:e04dda10-33de-4750-931b-fbd324fd646c][Bio 225 Lecture Notes: The Endocrine System]] )
The subphylum *Urochordata* contains the *tunicates*. While they do have a notochord and a dorsal nerve cord, only the larval stage possesses chordate characteristics.
The subphylum *Cephalochordata* contains the *lancelets*. They also have a notochord, dorsal nerve cord, and an endostyle, as well as pharyngeal slits.
The organisms in these too subphyla are referred to as *Protochordates*, which means they are invertabrates that are closely associated and have similar characteristics to vertabrates.
* Subphylum Vertabrata
*Superclass Agnatha*:
- Contains hagfish and lampreys.
- Hagfish create a slime that rapidly expands in water and engineers are looking to model a substance after it to produce a new kind of protective material.
- Lampreys have a life cycle that includes living 1-3 years in large lakes, then travelling upstream to reproduce, before coming back again to their lake habitat.
- However, they used to live in the Ocean. How ddi they get inland to the lakes?
- Lampreys travelled up the Hudson River, but when the Eerie canal was built, they were able to reach Lake Ontario.
- Then, when the Welland canal was built, the fish were able to then reach Lake Eerie, allowing them to bypass Niagra falls.
*Superclass Gnathostomata*:
*Class Chondrichthyes*:
- Most organisms in this class are marine.
- Their teeth can be continuously produced.
- Vibrations are picked up by the *Lateral Line*.
- It has small openings that are exposed to the water, and when the water near the animal (in this case a shark) is agitated, the shark will feel the water enter the spaces and interact with
*Neuromast cells* at the base of the structure.
- Some sharks also have *Ampullary organs of Lorenzini*, which can detect bioelectric signals.
- This organ is composed of pores that have jelly-filled canals through which an electrical current can be conducted.
- Nerves at the base of the canal release neurotransmitters due to voltage-gated calcium ion channels.
- Sharks can reproduce in one of three ways, depending on the species:
* Oviparous - Egg case is released.
* Ovoviviparous - Egg case formed but not released; embryo nourished by yolk.
* Viviparous - Egg not released; mother nourishes via placenta.
*Class Actinopterygii*
*Gills*:
- Water flows over gills in a countercurrent/crosscurrent manner to blood.
- This always favors the movement of oxygen from the the water to the blood.
- Oxygen diffusion happens all along the gill *lamellae*.
- Some fish actually have lungs and gills, while others can get oxygen from simply drawing water in through the mouth, and yet others can oxygen directly from their swim bladder.
*Swim Bladder*:
- Allows neutral bouyancy
- Impermeable to gas except at *Ovale* and *gas gland*.
- When a fish dives, the pressure compresses the gases in the swim bladder. Thus, the fish must add gas to prevent it from sinking out of control.
- The gas gland produces lactic acid, which reduces the pH inside the swim bladder. (for more information on pH see [[id:b55f18de-5836-46d4-b52a-f62c9d2c4bea][Chemistry the Central Science: Acid-Base Equilibria]] )
- The blood then brings oxygen to the swim bladder at the gas gland area but because of the low pH, more oxygen is released from Heme due to the Bohr effect. (See [[id:798e1b8d-bf5c-42b2-ad30-222d70057c88][Bio 225 Lecture Notes: Internal Fluids and Respiration]] )
- Thus, more oxygen gets inputed into the swim bladder.
- In the reverse scenario, *constrictor muscles* near the ovale guide gas through the ovale opening, where blood vessels pick up oxygen through diffusion in order to remove it.
*Migration*:
- Catadromous: Move *downstream* to breed (eels).
- Anadromous: Move *upstream* to breed (salmon).

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:ID: e9bcefad-2915-4e17-a315-034308927664
:END:
#+title: Chemistry the Central Science: Chemical Thermodynamics
#+filetags: :Chemistry_the_Central_Science:textbook_notes:
#+STARTUP: latexpreview
The discussion of chemical thermodynamics will start with a description of the concept of *spontaneity*.
A spontaneous process is one that occurs on its own without any outside influence.
Thus, a process that /does/ require outside influence is *nonspontaneous.*
Another important conclusion to make is that a process that is spontaneous in one direction is nonspontaneous in the other direction.
In addition, a *reversible* process is one to which we can restore the system back to its original state without changing the surroundings.
An *irreversible* process is one to which this cannot be done.
In fact, /all real processes are irreversible./
Thus, /all spontaneous processes are irreversible./
* Entropy and the Second Law of Thermodynamics
*Entropy* is simply a measure of the tendency of energy to spread out or to become less useful over time. It can reflect the general "disorder" of a system.
In *isothermal* situations (for example, during a phase change), the entropy is given by a simple equation:
\begin{equation*}
\Delta S = \frac{\Delta H}{T}
\end{equation*}
Where H = the heat released by the phase change process.
The *Second Law of Thermodynamics* states that:
/The entropy of the universe increases for any spontaneous process./
* Molecular Interpretation of Entropy and the Third Law of Thermodynamics
Entropy can be described in the following manner:
Imagine that you take a snapshot of system. for example, if the system contains one mole of gase, each molecule having a specific speed and position, then we define a *microstate* as the set of those
6.02 x 10^23 positions and speed at that given instant.
A microstate is a single possible arrangement of the positions and kinetic energies of molecules when the molecules are in a specific thermodynamic state.
Thus, the number of microstates in a given system can be massive.
The relationship between the number of microstates W and the entropy S is described in Boltzmann's famous equation:
\begin{equation*}
S = k \ln(W)
\end{equation*}
Where k = Boltzmann's constant which is 1.38 x 10^-23
Thus, /entropy is a measure of how many microstates are in a given particular macrostate./
And /entropy increases with increasing number of microstates./
The *Third Law of Thermodynamics* states that:
/The entropy of a pure, perfect crystalline substance at absolute zero is zero./
* Entropy Changes in Chemical Reactions
Molar entropies for substances in the standard state are called *standard molar entropies*.
- Standard molar entropies of elements at 298 K are not zero
- standard molar entropies of gases are greater than those of liquids and solids.
- standard molar entropies increase with increasing molar mass.
- standard molar entropies generally increase with an increasing number of atoms in the formula of a substance.
Calculating the standard molar entropy change that occurs over the course of a reaction is simple and given as follows:
\begin{equation*}
\Delta S = \Sigma n S(products) - \Sigma m S(reactants)
\end{equation*}
Recall that the entropy is always increasing for any spontaneous reaction. The change in entropy of the univers can be given by:
\begin{equation*}
\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings}
\end{equation*}
For spontaneous reaction, $\Delta S > 0$
* Gibbs Free Energy
Gibbs Free Energy is a concept that takes in to account both the enthalpy of a system and the entropy of a system.
For an isothermal process, the Gibbs free energy is given by:
\begin{equation*}
\Delta G = \Delta H - T\Delta S
\end{equation*}
A reaction is spontaneous if $\Delta G < 0$
If $\Delta G = 0$ the reaction is at equilibrium. (for more information on chemical equilibrium, see [[id:410d2780-127b-4972-ae22-34d9cdbb750b][Chemistry the Central Science: Chemical Equilibirum]] )
Gibbs free energy is a more effective tool to determine if a reaction is spontaneous or not.
* Free Energy and the Equilibrium Constant
The relationship between the change in free energy in standard conditions and the change in free energy in any other condition is given as:
\begin{equation*}
\Delta G = \Delta G^{\circ} + R T \ln(Q)
\end{equation*}
And thus, at equilibrium, we have:
\begin{equation*}
\Delta G^{\circ} = -R T \ln(K)
\end{equation*}

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:PROPERTIES:
:ID: 0112a2f0-e713-4fe6-bbab-6c768665c923
:END:
#+title: Chem 132 Table of Equations
#+filetags: :lecture_notes:equation_table:
#+STARTUP: latexpreview
*The Clausius-Clapeyron Equation*
- Relates Vapor Pressure to Boiling Point
\begin{equation*}
\ln\frac{P_1}{P_2} = \frac{\Delta H}{R}(\frac{1}{T_2}-\frac{1}{T_1})
\end{equation*}
*Henry's Law*
- Relates Gas Solubility to Partial Pressure of the gas.
\begin{equation*}
\frac{S_1}{P_1} = \frac{S_2}{P_2}
\end{equation*}
*Roult's Law*
- Relates how the partial vapor pressure lowers when solute is added to a solution
\begin{equation*}
P_{solution} = X_{solvent} P^{\circ}_{solvent}
\end{equation*}
*Boiling Point Elevation*
\begin{equation*}
\Delta T_b = k_b m i
\end{equation*}
*Osmotic Pressure Elevation*
\begin{equation*}
\Pi = M R T i
\end{equation*}
*Zero-order Rate Law*
\begin{equation*}
[A_t] = -k t + [A_0]
\end{equation*}
- Half-life:
\begin{equation*}
t_{1/2} = \frac{[A_0]}{2 k}
\end{equation*}
*First-order Rate Law*
\begin{equation*}
\ln[A_t] = -k t + \ln[A_0]
\end{equation*}
- Half-life:
\begin{equation*}
t_{1/2} = \frac{0.693}{k}
\end{equation*}
*Second-order Rate Law*
\begin{equation*}
\frac{1}{[A_t]} = k t + \frac{1}{[A_0]}
\end{equation*}
- Half-life:
\begin{equation*}
t_{1/2} = \frac{1}{k [A_0]}
\end{equation*}
*Arrhenius Equation*
- Relates the Rate Constant to the Temperature
\begin{equation*}
\ln\frac{k_1}{k_2} = \frac{E_a}{R}(\frac{1}{T_2}-\frac{1}{T_1})
\end{equation*}
*Relating Kc to Kp*
\begin{equation*}
K_p = K_c(R T)^{\Delta n}
\end{equation*}
*Relating acid-base equilibria constants to Auto-ionization of Water*
\begin{equation*}
K_a \times K_b = K_w
\end{equation*}
*The Henderson-Hasselbach Equation*
- Relates pH to pKa
\begin{equation*}
pH = pK_a + \log\frac{[A^-]}{[HA]}
\end{equation*}
*Relating Gibbs Free Energy to Enthaply and Entropy*
\begin{equation*}
\Delta G = \Delta H - T \Delta S
\end{equation*}
*Relating Equilibrium Constant to Temperature*
\begin{equation*}
\ln\frac{K_1}{K_2} = \frac{\Delta H}{R}(\frac{1}{T_2}-\frac{1}{T_1})
\end{equation*}
*Relating free energy change in standard conditions to free energy change in all other conditions*
\begin{equation*}
\Delta G = \Delta G^{\circ} + R T \ln(Q)
\end{equation*}
*Finding the Electrical Potential of a Voltaic Cell*
\begin{equation*}
E_{cell} = E_{red} - E_{ox}
\end{equation*}
*Relating free energy change to electrical potential*
\begin{equation*}
\Delta G = -n E F
\end{equation*}
*The Nernst Equation*
- Relates standard potential to potential under any other conditions
\begin{equation*}
E = E^{\circ} - \frac{R T \ln(Q)}{n F}
\end{equation*}
*Radioactive half life*
\begin{equation*}
N_t = N_0 e^{-k t}
\end{equation*}

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:PROPERTIES:
:ID: 9f7355c6-3fd3-4229-a9ac-37310192dbdb
:END:
#+title: Bio 225 Lecture Notes: Immunity
#+filetags: :biology:lecture_notes:
The basic need of the immune system is to identify self from non-self.
There are different types of defenses:
1. Innate (non-specific)
2. Adaptive (specific)
The innate response include:
- Skin
- Lysozymes in tears and saliva to destroy cell walls of pathogens
- Mucus trapping microbes
- inflammatory response
The adaptive response includes:
- the *Humoral* immune response
- the *cellular* immune response
The Lymph is composed of water/plasma with white blood cells but no red blood cells.
*T cells* mature in the *Thymus*
*B cells* mature in *bone marrow* (see [[id:2197395d-4587-4832-a419-aeb43a77f3af][Bio 225 Lecture Notes: Basic Support Structures]] )
* Innate Inflammatory Response
Upon the detection of something perceived as a threat or pathogen (something nonself) in an innate response, several things happen:
*Mast cells* and *basophils* release *histamine*, i.e. they degranulate.
Histamine causes capillaries to become leaky.
Additionally, the capillary also vasodialates.
As a result, white blood cells can escape from the blood vessels. Specifically, when *monocytes* escape from the blood, they become known as *macrophages*.
The *Compliment* is a set of proteins that tag pathogens for destruction by these macrophages.
What if you cannot contain the pathogens at the site where they were introduced?
If that is the case, the humoral immune response is triggered, which is what will be discussed next.
* Humoral Response
- *Step 1*
* *Antigen Presenting Cells* (APCs) like macrophages or dendritic cells in lymph nodes identify non-self organism/virus/molecule. (these cells can also be in barrier regions like the skin.)
* It can do this based on the coating that the pathogen received from the compliment or from glycoprotein molecules on the cell surface of the pathogen.
* The APC then phagocytizes and presents the antigen.
* The *antigen* could be the whole pathogen or simply the fragment that causes the immune response.
* Once antigen is devoured, its fragments are sent over to newly-synthesized *Class II MHC* (Major Histacompatibility Complex) proteins on the cell surface of the APC.
* Thus, the cell "presents" a portion of the antigen on its cell surface.
* Then, the APC migrates to a lymph node.
- *Steps 2 and 3 (T cell Activation and Proliferation)*
* T cells (in this case *helper T cells*) have surface receptors with *constant regions* and *variable regions*.
* The T cell has another surface protein, called the *cd4* protein, that must recognize the class II MHC protein on the APC.
* Then, when there is a match, and the variable region of the receptor fits the antigen as well as the cd4 protein is satisfied, the APC releases *cytokines* and activates the T cell.
* And activated T cell now has the capacity to activate a *B cell* and to undergo clonal expansion.
- *Step 4 (B cell Activation)*
* B cells are covered with B cell receptors (BCRs) which are like membrane-bound antibodies.
* The BCR has variable regions and constant regions. The variable region fits well with the *epitope* of the antigen (the part of the antigen which fits into a receptor).
* This "fitting" is not very specific and it could work with multiple epitopes.
* There are up to 100,000 BCRs per B cell and they are all identical in the same cell, but vary between cells.
* As humuans, we can respond up to 10 million different pathogens, which means that we have 10 million different types of B cells.
* If the epitope fits in the receptor, receptor-mediated endocytosis occurs and the antigen is displayed on a Class II MHC protein, much like in step one with APCs.
* In fact, this step can happen sequantially, /or/ concurrently with step 1. The point is that a B cell comes into contact with the same pathogen and is now displaying the antigen on its surface proteins.
- *Step 5*
* Helper T cells that have been activated then find the B cell with the antigen and bind to it.
* the T cells then release cytokines of their own. This in turn activates the B cell.
* The B cell then clones itself.
- *Steps 6 and 7 (Cell Differentiation)*
* Memory cells or plasma cells are made from the activated B cell.
* *Plasma cells* are antibody factories.
* *Memory cells* have variable regions that fit the specific antigen.
* Next time you encounter the antigen, the memory cell becomes a plasma cell and begins to create large amounts of antibodies.
* Because of this, the response is /faster/ and /greater./
- *Step 8*
* The plasma protein creates *IgM* antibodies followed by *IgG* antibodies.
* A pathogen that is coated in these antibodies helps facilitate the phagocytosis of that pathogen by a macrophage.
* The constant region of the antibody attaches to the macrophage receptor and the variable region attaches to the epitope of the pathogen.
* The Cellular Immune Response
No antibodies are produced in this response.
*Class I MHC* proteins are on all nucleated cells.
Viral DNA or cancerous products can be displayed on these.
*Tc cells* (cytotoxic T cells) have *cd8* proteins which recognize the Class I MHC proteins.
If the Tc cell binds to the products on these Class I MHCs, the cell then clones itself and the cell which had these products is then *lysed* or initiated to perform apoptosis.
The humoral and cellular immune responses are connected in that if a dendritic cell comes across the debris of a destroyed cell with the antigen, it can pick up the antigen fragments and present them, thus starting the humoral response process.
* Hypersensitivity
In this scenario, the antibodies that are produced are IgE (This is determined by the cytokine from the helper T cell.)
These can stick into mast cells and basophils.
During second exposure, the antigen binds to the IgEs, which cause the basophil to degranulate.
The released histamine causes a strong inflammatory response.
*Anti-histamines* bind to the histamine receptors of cells, blocking them.
*Autoimmune disorders* is when the immune system goes after itself.
Certain deletions of T cells and B cells fail.
You want to check B and T cells to see if any of them have receptors that can bind to the certain epitopes that are expressed on any one of /your own cells/.
Otherwise, these T and B cells will initiate an attack response against your own cells.
Thus, they must be destroyed before they are released in the body.
* Blood Typing and the Rh Factor
A-type blood has "A" carbohydrates with anti-b antibodies
B-type blood has "B" carbohydrates with anti-a antibodies
O-type blood has both anti-a and anti-b antibodies but has no carbohydrates on its membrane.
AB-type blood makes no antibodies but has both "A" and "B" carbohydrates on its mambrane.
Thus, O blood is recognized as the universal *donor* and AB blood as the universal *acceptor*.
Blood can be transfered between similar types because RBCs are not nucleated and thus do not have Class I MHC proteins that the body would be able to detect and thus reject.
When, for example, A blood is mixed with B blood, the anti-a antibodies from the B blood will cause the A blood to coagulate together into clumps.
Additionally, blood is "positive" when it has the Rh protein attached to it.
It is "negative" if it lacks the Rh protein.
You can only make antibodies against Rh positive blood, not Rh negative blood.
This is why sometimes when mothers are exposed to their baby's blood (and it happens to be Rh positive), the mother will make anibodies against it.
Then, if her second baby is also Rh positive, then if the mother's antibodies cross the placenta, the antibodies and destroy the baby's blood and ultimately kill it.
This condition is called *erythroblastosis fetalis*.

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:ID: 3f1c94fd-d396-4825-81ae-46e8ad2bc09d
:END:
#+title: Bio 225 Lecture Notes: Digestive Systems
#+filetags: :biology:lecture_notes:
* Avian Digestion
- Birds have a *crop* for temporary food storage.
- The *proventriculus* connects the crop to the gizzard.
- At the end of the intestine, birds have a *cloaca* an opening through which wastes and gametes can exit.
* Mammalian Digestion (Humans)
- While swallowing, the trachea moves up, closes the glottis, and allows the *bolus* (chunk of food) to go down the esophagus correctly.
- *Peristalsis* is the contraction of muscles in the esophagus that giudes the food down to the stomach. (Esophagus is stratified squamous)
- The *cardiac* valve connects the esophagus to the stomach.
- *parietal cells* create HCl which helps to dissolve the extracellular matrix, breaking food down into small fragments.
- *Chief cells* create *pepsinogen* which is activated to *pepsin* which breaks down proteins in the food into individual polypeptides.
- Then, the *pyloric* valve leads from the stomach to the *duodenum*, the first part of the small intestine.
- The small intestine has about 200 square meters of surface area. There is general looping ;those loops have smaller loops called *plicae*; and plicae are covered with *villi*; villi are in turn covered with *microvilli.*
- The pancreas releases bicarbonate, which helps to neutralize the pH.
- Lipase, amylase, lactase, and nuclease are also produced here.
- *Trypsin* and *chymotrypsin* help break down proteins.
- *Bile* is stored in the *gall bladder*. It is an emulsifier that breaks large clumps of fat down into smaller fragments. This allows increased surface area for lipase to break down the fat.
- *ileocecal* valve regulates flow between small and large intestine.
- The Large intestine also has more micro-organisms in it than cells in your entire body.
- In fact, a large portion of serotonin and GABA are produced by the organisms here.
* Hormones of Digestion
- *Gastrin* stimulates secretion of HCl which thus activates the chief cells to secrete pepsin.
- As pH decreases, gastrin levels decline.
- This negative feedback system fluctuates the pH level a little, preventing it from getting too low.
- When chyme enters the small intestine, *cholecystokinin* is produced, which stimulates the release of bile from the gall bladder and enzymes from the pancreas.
- Additionally, *secretin* stimulates the release of bicarbonate from the pancreas.
- Vitamins A, D, E, and K are fat soluble but are toxic in high doses. Since they are fat soluble, you cannot get rid of them via urination.
- The other vitamins are not fat soluble and can thus be urinated out.

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:PROPERTIES:
:ID: 3d6b9f4c-d514-421a-b7fb-98003b5137f4
:END:
#+title: Bio 225 Lecture Notes: Nervous Coordination
#+filetags: :biology:lecture_notes:
* Resting Membrane Potential (RMP)
The RMP is the measure of electric potential across an axon's membrane when the neuron is in a state of rest and not firing.
It usually has a value of -70mV.
How does the RMP change and thus induce a change in potential and a current traveling down the length of the neuron?
- Inside the axon, there are large anions and some potassium ions.
- Outside the axon, there are large amounts of sodium and chloride ions.
- Buried in the membrane is a sodium/potassium pump which pumps in 2K+ and pumps out 3Na+.
- Changes in ion concentration, and thus charge, across the membrane is what primarily facilitates neuron firing.
How is RMP maintained?
- Potassium ions actually flow out of the axon via *leak channels*. They flow toward concentration gradient and thus *out* of the cell.
- The extracellular environment increases in positivity until no more potassium ions are able to flow out.
- Equilibrium is established and this happens at anywhere between -40 to -90 mV.
How to alter RMP?
- What if only sodium ion channels were opened? Na would thus flow into the cell and *depolarize* it.
- If we opened only chloride ion channels, then chloride would flow inside the cell and *hyperpolarize* it due to its negative charge.
- However, if potassium ion channels were opened, potassium would flow out of the cell and this would also *hyperpolarize* because positive charge is leaving the cell.
* The Process Leading to an Action Potential
Before we discuss this process, two terms must be clarified:
*Activation Gates* refer to gates on channels that respond to voltage changes.
*Inactivation Gates* refer to gates on channels that do not respond to voltage changes but do respond to threshold, which we will talk about in a moment.
*VGNaIC* - Voltage-Gated sodium ion channels.
*VGKIC* - Voltage-Gated potassium ion channels.
The steps of an action potential (AP):
- The neuron starts at RMP and the sodium/potassium ion pump works diligently in the background.
- Now, at a certain point in time, several VGNaIC open, allowing Na to diffuse into the cell. This depolarizes cell to *-50mV*.
- Threshold happens at this point. Three main things happen during threshold:
1. All VGNaIC open via *activation gates*.
2. Then, the *inactivation gates* on those same channels begin to slowly shut to "plug in" their openings.
3. The *activation gates* on VGKIC begin to open.
- During threshold. lots of Na diffuses into the cell and depolarizes it to *+50mV*.
- Then, at this point, the inactivation gates on the VGNaIC slap shut.
- Activation gates on VGKIC open and the cell *repolarizes* by letting potassium ions diffuse out of the cell (axon). This is the *Absolute Refractory Period* and the neuron cannot fire at this time.
- However, the cell actually hyperpolarizes, i.e. it repolarizes /past/ RMP. A few VGNaIC open once more to balance it out.
- This is the *Relative Refractory Period* and the neuron can once again fire at this time.
Some things to remember:
- The sodium/potassium pump is working faithfully this whole time but its effect is "masked."
- 1 ion is moved across the membrane for every 10 million.
- Concentrations are restored.
- The neuron /can/ fire again /before/ RMP conditions are fully restored.
* More on Action Potentials
APs move along an axon in a chain reaction fashion:
- As the sodium ions travel into the axon, they diffuse into the adjacent membranes/cells.
- The activation gates of VGNaIC "downstream" feel the depolarization and that membrane goes through threshold, continuing the chain reaction.
- The reaction only goes in one way, however. Why is this?
- The VGNaIC "upstream" have their *inactivation gates* closed. They cannot respond to polarity changes for the time being. The VGNaIC "downstream" have *activation gates* closed, and these open in response to the voltage change.
- The frequency of APs = the intensity of the signal.
* Synapses
Synapses usually are facilitated by chemical means, i.e. a *neurotransmitter*.
Some terms to know before the synapse process is discussed:
*Synaptic knob* - The ending of a neuron.
*Post and Pre-synaptic membranes* - refer to the membranes that receive and release the neurotransmitter, respectively.
*Synaptic Cleft* - The region between the post and pre-synaptic regions.
*Acetylcholine* - widespread and common neurotransmitter.
- The Knob region has VGCaIC in it.
- These feel the APs moving down the axon and towards the knob.
- Ca channels open and calcium ions flow into the synaptic knob region.
- This starts a cascade that results in the exocytosis of acetylcholine in vesicles. It is then dumped into the cleft region.
- The acetylcholine binds as a ligand to ligand-gated sodium ion channels in post-synaptic membrane. Then, sodium flows inside the post-synaptic cell.
- Sodium flows into the *Axon Hillock* region which contains a plethora of VGNaIC.
- The activation gates sense this and start to reach threshold. Thus, signals can be transmitted between neurons and across the body.
How can you turn this process off?
- *Achase* sits in the cleft region and breaks down acetylcholine.
- If there is less acetylcholine than achase, that means the AP ceases in the pre-synaptic cell. Then acetylcholine will be broken down.
- RMP is restored.
- If post-synaptic excitatory potential does not reach -50mV, no AP will be generated.
Proximity to axon hillock region determines the creation of an AP. Gates closer to the hillock region have a greater effect.
*Cancellation* happens when two ion gates of opposite charge open, leading to a cancellation of the charges.
*Spatial Summation* is when two or more synapses give inputs to induce an AP. The /sum effect/ leads to a firing response.
*Temporal Summation* is when enough APs lead to a sum effect that leads to a post-synaptic AP and threshold. Only one pre-synaptic source.

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:END:
#+title: Genetics: DNA and the Molecular Structure of Chromosomes
#+filetags: :genetics:textbook_notes:
#+STARTUP: latexpreview
* Proof that DNA Mediates Transformation
- Frederick Griffith worked with the bacteria /Streptococcus Pneumoniae/ and tested it with mice. This bacteria has virulent strains (S type) and avirulent strains (P type).
- When injected with S type, the mice died and the bacteria cells were recovered from their corpses.
- When injected with R type, the mice survived, because the cells were avirulent.
- However, when Griffith heat-killed the S type, and then mixed those dead bacteria with the living ones, the mice still died. What happened?
- From the corpses, Griffith actually found living S type bacteria! Something from the dead S type must have transformed the living R type into living S type.
- The hunt for the "Transforming Principle" began.
- Several years later, a team led by Oswald Avery determined that DNA was the molecule that facilitated this transforming principle.
- They used *DNase, RNase,* and *protease* to reach this conclusion. When DNase was used, no living S type colonies were formed, because the DNase destroyed the DNA, the transforming principle.
- In 1952, Hershey and Chase determined that DNA was the source of genetic information to produce bacteriophages in the cells of /E. coli/.-
- They used radioactive sulfur and phosphorus to label the proteins and DNA respectively.
- Upon exposing the cells the phage coats toshearing forces in a blender and then centrifuging the results, it was clear that the substance inside the cell (and thus the substance that coded for new bacteriophages), was DNA.
* Nature of the Chemical Subunits in DNA and RNA
Nucleic acids are compososed of:
1. A *Phosphate Group*
O-
|
O- = P = O
|
O-
2. A five-carbon sugar (called a *pentose*).
In RNA it is *Ribose* and in DNA it is *Deoxyribose*.
In deoxyribose, the second carbon is missing a hydroxyl group and only has a hydrogen bound to it.
3. A cyclic, nitrogen-containing base.
There are *purines*, which have two rings, and *pyrimidines* which have only one ring.
The purine bases are Adenine and Guanine.
The pyrimidine bases are Cytosine, Thymine, and Uracil (usually only found in RNA).
Adenine and thymine form two hydrogen bonds with each other, while cytosine and guanine form three hydrogen bonds.
*Chargaff* found that concentrations of *thymine* was always equal to the concentrations of *adenine*. The same was true for cytosine and guanine.
The base pairs in DNA are stacked about 0.34 nm apart, with ten base pairs per 360 degree turn of the helix.
The two helical strands of DNA are complimentary and *antiparallel*, as well as *right-handed.*
The hydrophobic core of the stacked base pairs inside the DNA molcule offers it much stability.
The DNA described is called *B-DNA* and is the form it takes in aqueous solutions with low concentrations of salt. Most DNA in your cells take on this conformation.
In higher salt concentrations, DNA takes on an *A-DNA* form. A-DNA contains 11 nucleotides per turn instead of 10 and is shorter and thicker.
In addition, *Z-DNA* has been found. Z-DNA has left-handed helical structure and is very G:C rich. It also has 12 base pairs per turn. The purpose of Z-DNA in cells is unclear.
Most DNA in cells are *negatively supercoiled*, meaning that the DNA is cleaved at some attachment point by a specifric enzyme, then rotated 360 degrees /against/ the right-handed direction of its helix.
* Chromosome Structure in Viruses and Prokaryotes
- Most DNA in viruses and bacteria are *folded genomes*.
- they are also negatively supercoiled.
- Bacterial chromosomes contain circular DNA molecules organized into 40-50 loops or domains.
- Each domain can then be negatively supercoiled.
- DNase and RNase can be introduced to relax the folded genome, but in different ways.
* Chromosome Structure in Eukaryotes
- DNA is entangled with many proteins, a complex structure called *Chromatin*.
- *Histones* are proteins that assist in packaging DNA. There is Histone 1 (H1), H2a, H2b, H3, and H4.
- There is scientific evidence that suggests that each chromosome in a eukaryote is just one, masive DNA molecule.
- How do these massive molecules (sometimes measuring several centimeters long) manage to fit in a space half a micrometer in diameter?
*Nucleosomes* are small "beads" that have DNA coiled around them.
- 146 base pairs are wrapped around the nucleosome, which is made up of the histone proteins. This is known because this many base pairs survives the introduction of DNase.
- The DNA winds 1.65 times around this core.
- The core is actually an octamer of histones, two each of each type of histone (excluding H1).
- The width of these ellipsoidal "beads" is *11 nm*.
- Usually all that is required for interphase DNA.
*30 nm Fiber* arises from these necleosome cores being wrapped and stacked around each other.
- chromatin, and the fibers, and expand or contract based on chemical modifications of the histones.
- H1 is the linker histone and can link the nucleosomes together into a tight arrangement.
*Protein Scaffold* can package the fibers into the tightly wound chromosome.
- Forms negatively supercoiled loops and domains.
- happens during *metaphase.*
* Centromeres and Telomeres
- Much of a chromosome contains highly repetitive gene sequences.
- Some of these repititions can move throughout the chromosome, and these are called *transposons.*
- *Centromers* are the central portion of the chromosome which microtubules bind to during mitosis and meiosis.
- The region around the centromere, is the *heterochromatin* and is packaged more tightly than the surrounding *euchromatin.*
- Telomeres are the termini of chromosomes and they consist of highly repetitive sequences upwards of 500 - 3000 times.
- In mammals and vertabrates, the telomere sequence is TTAGGG.
- Telomeres are also known to form *t-loops* where the single-stranded, G-rich 3' end is inserted into the upstream telomeric repeats and displaces the DNA strand previously occupying that space.
- The DNA in t-loops are protected from degradation.

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#+title: Genetics: DNA Replication
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
Two important facts about DNA replication is:
1. It is *semiconservative*
2. It is *bidirectional*
Semiconservative means that when each strand is separated for replication, each strand is used as a template for a new strand.
This fact was determined by Messelson and Stahl. They grew /E. coli/ cells in an environment with heavy $^{15}N$ instead of the more naturally occurring, lighter $^{14}N$ isotope. This effectively makes the nitrogen on the DNA of the cells heavier than normal.
They put the DNA from the cells in a Cesium chloride density-gradient centrifugation process. The heavy DNA sits lower in the solution than lighter DNA.
After several generations in the heavy nitrogen, they transferred them to an environment with lighter nitrogen and they sat there for one generation of replication.
Once put in the density-gradient again, there appeared to still be some heavy DNA, as well as "hybrid" DNA, whicih sat in between the heavy position and the light position.
This essentially confirmed semiconservative replication.
Replication is also bidirectional. A "bubble" forms in the DNA and each replication fork grows away from each other.
* Origins of Replication
In /E. coli/ cells, the replication origin is called the /ori C/.
The /ori C/ has two elements:
- First is a 13 base-pair-long sequence that exists in 3 tandem repeats. They are very AT-rich, and because of having only 2 H-bonds, they serve to separate first, before the rest of the other DNA.
- Second is a 9 base-pair-long sequence that exists in 4 repeats with some other sequences interspersed within. These sequences facilitate the binding of proteins such as *DnaA proteins*.
In Yeast, and other eukaryotes, origin sites are referred to as *Autonomously Replicating Sequences, or ARS.*
In SV40 virus, the origin site is 64 bp-long sequence.
- It is very AT-rich.
- serves as a protein binding site
- T-antigen binds to palindrome 27bp long.
* Bidirectional Replication
- Shnos and Inman made features, almost like physical markers, on a bacteria plasmid, by heating the DNA to a point to where only the AT-righ regions denatured.
- They used these 'landmarks' to visually see which direction the replication fork was travelling.
- from these landmarks, they determined it was bidirectional.
* The Players
- *DNA Polymerase I*
* Also known as Kornberg's enzyme, after the person who first purified it.
* Needs a template and a primer
* Directions is *always* 5' --> 3'
* Utilizes 5' triphosphates of each deoxynucleoside. (dNTPs)
* 2 phosphates get cut off when attached to the backbone, releasing a lot of energy. (See [[id:d4ec4698-96e7-4cce-93a3-27e7b9eb5965][Genetics: DNA and the Molecular Structure of Chromosomes]] For more information)
* *Pyrase* recycles the phosphates.
This enzyme incredibly has 3 different functions:
1. 5' --> 3' polymerase
2. 5' --> 3' exonuclease, meaning it can remove objects in front of it that may be blocking it. Important for removing primers, which will be disussed below.
3. 3' --> 5' exonuclease, meaning it can clip out something incorrect that it placed. The base can drift away bit must receive 3 phosphates before it can bind again.
- *DNA Polymerase III*
* Also needs a template and a primer.
* Contains 20 different proteins.
* $\alpha$ subunits are responsible for polymerase activity.
* $\epsilon$ subunits are responsible for proof-reading.
* $\theta$ subunits bind with $\alpha$ and $\epsilon$ to create the *minimal core*. This in itself does not have function, but it is necessary for structure.
* t subunits link both of the domains together; they are responsible for dimerization.
* $\beta$ subunits physically grab the DNA template. This makes DNAP III much more stable on the strand than DNAP I.
- *Lagging Strand/Leading Strand and more Players*
* composed of *Okazaki fragments*.
* results in covalent breaks between the fragments (since DNAP III cannot remove things in its path like DNAP I, as long as it's in an environment with more than one strand).
* These breaks are remedied by *DNA Ligase.*
* Each fragment must also be primed.
* Leading strand does not have these fragments and thus must only be primed once (however, leading strand on side may be lagging strand on the opposite side. Remember that replication is bidirectional).
* *DNA primase* lays down this primer, *which is made of RNA*. These provide the 3' OH needed by DNAPs.
* DNAP I can go back and remove these primers afterword, using its exonuclease function.
* Unwinding the DNA Strands
- Before replication can take place, DNA must first be unwound, at an estimated rate of 3,000 revolutions per minute. This is accomplished by *DNA Helicase*.
- Opened DNA is kept open by *single-strand DNA-binding proteins, or SSB proteins*.
- *Topoisomerases* remove positive supercoils (also by introducing negative supercoils) created by the rapid unwinding of the DNA strand.
* These come in two classes: Class I and Class II
* Class I removes supercoils by nicking just one strand (no ATP).
* Class II breaks the double-strand and pulls each side out of the coil and reattaches them, thus solving two coils at once. It breaks the strand and literally pulls it through the coil.
* Eukaryotic Differences
- DNA replication restricted to S-phase.
- Multiple replicons per chromosome.
- Two or more polymerases at each fork; RNA primers have to be removed by *RNase H1/RNase FEN-1*. the polymerases lack a 5' --> 3' exonuclease activity.
* Problems with Telomeres
- Occurs on lagging strand.
- At the end of a DNA strand, when RNA primer is cleaned up, there is nothing there to build it up again.
- This creates a *3' overhang*.
- *Telomerase* makes the 3' end longer, using its very own RNA template.
- The RNA template is the same in every telomerase, making it a very repetitive and predictable sequence.
- The lengthening of the 3' end allows for a primer to be put in. Not as much real estate is lost.
- However, there will still be some sort of overhang left over in the end.

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#+title: Genetics: DNA Transcription
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
RNA is the vessel upon which transcription takes place.
An intermediary molecule must be needed since DNA never leaves the nucleus but protein synthesis occurs in the cytoplasm. RNA is the molecule that brings the message from DNA to the ribosomes, which contruct the protens. Thus, RNA is a /messenger./
Two scientists, Volkin and Astrachan, used radioactive Phosphorus to:
* Show a burst of RNA synthesis following bacteriophage infection.
* Labeled RNA degraded quickly.
Spiegelman saw that RNA could be made from a viral genome.
This brings us to the *Central Dogma of Biology:*
DNA
|\
v/ transcription
RNA
|\
v/ translation
Protein
There are also many types of RNA, each with specific functions that will be touched on in other notes.
* mRNA: Codes for proteins
* rRNA: structural component for ribosomes and other complexes
* tRNA: Responsible for facilitating the contruction of polypeptide chains
* snRNA: Responsible for assisting in pre-mRNA splicing
* miRNA: used to block the expression of mRNA
* Transcription Overview
- RNA is made first as *pre-mRNA*
- Then, it is spliced/cut/etc.
- Precursors for RNA synthesis are called *ribonucleoside triphosphates* or (RNTPs)
- Only *one* strand of DNA serves as the template for the new RNA
* RNA is complimentary to template only
* This means RNA is *identical* to non-template strand (but with uracil instead of thymine)
- RNA chains can be synthesized /de novo/ *they don't need a primer.*
- Synthesis is in the 5' --> 3' direction. (For more info see[[id:3a5368b9-d120-40d0-907f-9b59cc53d653][Genetics: DNA Replication]])
- The current base in question on a strand is labeled as +1. bases ahead of it (downstream) are +2, +3, etc. Bases behind (upstream) are -1, -2, -3, etc.
Transcription comes in these steps:
1. Initiation
2. Elongation
3. Termination
4. Splicing
5. RNA Editing
* Initiation (From Perspective of Bacteria)
- Binding of *RNA Polymerase*
* Holoenzyme contains 5 subunits
* $\alpha$ subunits are involved in assembly
* $\beta$ subunits contain rNTP binding site
* $\beta$' subunits contain template binding region
* $\sigma$ subunits recognize *promoter sites* (specific sequences that function as the anchor site for RNAP)
- Actual chain synthesis is not recognized to happen at least for another 5-9 base pairs after the promoter sequence. After 10 base pairs, much more stability is acheived. the length of the RNAP enzyme may also contribute to this.
- $\sigma$ subunits prevents random transcriptional initiation.
* -10 and -35 promoter sequence
* -35: TTGACA (non-template)
* -10: TATAAT (non-template)
* After these promoter sequences, there is a /range/ over which RNAP begins to polymerize (Transcription Start Site).
* /The actual RNA is usually begun with a purine, that is, an A or a G./
* So when there a lost of Cs and Ts...you can be confident that the polymerizing began at a conspicuous A or G. In reality it may be harder to visualize the start of an RNA molecule.
- There are four types of sigma factors, which are activated based on the nature of the external environment:
* $\sigma^{70}$: normal factor
* $\sigma^{32}$: heat shock response
* $\sigma^{54}$: nitrogen metabolism
* $\sigma^{23}$: viral infection
- Sigma is released after initiation.
* Elongation
- Unwinding and rewinding
- 2,400 nucleotides/min in /E.coli/
- RNA:DNA hybrid is very short.
- The single-stranded RNA is mostly "grown" off the DNA template strand, threaded through the RNAP.
* Termination
There is Rho-dependent and Rho-independent termination processes.
*Rho-independent:*
* Termination region in DNA
* G:C - rich region followed by a stretch of of T's
* For example: CGGCCCATTTTTTT (non-template)
* A hairpin can form from the strong, tighly-knit interactions between C's and G's. The T's form a weaker bond with A's.
* So essentially it is a strong hairpin region followed by a weak region.
* RNA folds sharply in on itself due to C:G interactions. And what's left (all those U's) is weakly bound to the DNA. Thus, it can detach and terminate easily.
*Rho-dewpendent*:
* 50-90 bp long stretch of C's
* *Rho* binds to the RNA and moves 5' --> 3'
* when Rho "catches" RNAP, it literally pulls the chain free
* Rho appears to chase the RNAP
* However, in prokaryotes, translation happens concurrently with transcription. Eventually the ribosomes encounter their stop sequences and disengage.
* This allows Rho to bind to it and engage the RNAP.
* Transcription in Eukaryotes
- There are multiple Polymerases
* 10 or more subunits each
* RNA polymerase I, II, and III
* RNAP I: Nucleolus, rRNA, not 5S rRNA
* RNAP II: Nucleus, nuclear pre-mRNA (does much of the process as the prokaryote RNAP discussesd above)
* RNAP III: Nucleus, tRNA, snRNA, 5S rRNA
- However, these RNAP's /cannot initiate by themselves./
* Uses transcription factors, TFIID, TFIIA, TFIIB, (Transcription Factor for polymerase II A, etc.)
* *TFIID* binds first. It contains *TBP* which searches for the eukaryotic promoter region called the "Tata-box" (found at -30)
* *TFIIA and TFIIB* then follow, helping TFIID bind more securely
* *TFIIE and TFIIH* then bind. TFIIH can use ATP.
* *TFIIB* defines the directionality of the transcription. If you think about this, this also mean it determines which strand is the template and which is the non-template. Sometimes, divergent transcription can happen. The purpose is not known, but it may actually serve to help the process. TFIIB also acts as a molecular "ruler" for RNAP II.
- RNAP I promoters are typically bipartite. Both are G:C-rich. These are not "Tata-boxes"
- RNAP III promoters are typically /downstream/ of the TSS. This means it binds to the DNA before its promoter sequence, meaning that sequence is actually included on the fabricated pre-mRNA strand.
* mRNA Processing
- 7-methyl guanosine cap
* Initiation of translation
* Protects growing mRNA strand
- Poly(A) Tail
* Protects mRNA from degradation]
* Aids in transportation
* Added /after/ transcription
* Splicing
- Removal of introns from pre-mRNA
- The recognizable features of introns are given below
5' GT........UACUAAC.........AG 3'
GT and AG can be thought of as "bookends" of the introns.
- These introns don't have caps or tails, so they are digested.
*Type 1 Splicing*
* Shape driven
* Requires endonuclease and ligase
* Enzymes recognize shape and clip intron by location, not by base-pair.
*Type 2 Splicing*
* No protein activity
* Requires guanosine with 3' OH end
* Two phosphodiester bond transfers
*Type 3 Splicing (Spliceosome)*
* Involves spliceosomes, which are RNA/protein structures
* U1, U2, U4, U5, U6.
* *U1* binds to 5' splice site (GT)
* *U5* binds to other end (AG)
* *U2* recognizes the UACUAAC sequence on the intron
* *U4* and *U6* do not make contact with the RNA but provide structure.

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#+title: Organic Chemistry: Structure and Stereochemistry of Alkanes
#+filetags: :organic_chemistry:textbook_notes:
#+STARTUP: latexpreview
* IUPAC or Systematic Names
To name and Alkane we follow 4 general rules:
1. Find the longest continuous chain of carbon atoms, and use this chain as the base name.
2. Number the longest chain, beginning with the end nearest a branch
3. Name the substituents on the longest chain (as alkyl groups). Give the location of each substituent by the number of the main-chain carbon atom to which it is attached.
4. When two or more substituents are present, list them in alphabetical order. When two or more of the /same/ alkyl group is present, use the prefixes /di, tri, tetra, etc./ (ignored in alphabetizing) to avoid having to name the alkyl group twice.
* General Alkane Properties
- Alkanes are nonpolar and generally are not too reactive.
- Most alkanes are refined from petroleum by distill fractions.
- *Catalytic Cracking* can break down larger, less-useful hydrocarbons into smaller, more useful ones. Hydrogen gas is used in the process.
* Newman Projections
- Newman's projections are used to analyze the different *conformations* of a molecule, and in this context, alkanes.
- Newman projections look head-on through a particular carbon-carbon bond. Based on the angles between substituents on the molecule, the energies and thus the stabilities of each conformation can be analyzed
- *totally eclipsed* conformation have the highest energy (and are less stable) because the substituents are all aligned.
- *gauche* confomration is 60 degrees offset from totally eclipsed.
- *eclipsed* is when a substituent and a hydrogen are aligned, instead of two substituents being aligned.
- *anti* is when the substituents are offset from each other as much as possible. This represents the lowest energy and thus the highest stability.
- It is important to note that at room temperature, molecules have enough energy to move through all of the possible conformations, but for the majority of the time, the bonds would be in the anti conformation.
- Another useful concept is the *torsional energy*, which is the energy needed to break free from high-energy conformations. It is usually measured in kJ/mol.
- When molecules are in a totally eclipsed conformation, something called *steric strain* happens. This strain arises from the electron clouds of the hydrogens on the substituents that are so close to each other that they begin to repel one another. Steric strain is responsible for how many molecules align themselves in space. It also has an effect of the reactivity of molecules.
* Cycloalkanes
- Cycloalkanes have many factors that determine their stability.
- These are *angle strain* and *torsional strain* (which arises from differences in torsional energy)
- Both of these aspects contribute to the total *ring strain* of the cycloalkane molecule.
- In cyclopropane and cyclobutane, the angles of the sp3 hybridized orbitals are forced to 60 and 90 degrees respectively. This literally reduces the contact between each carbon's sp3 hybrid orbital in relation to the next. Additionally, the bonds experience a totally eclipsed conformation.
- Larger cycloalkanes like cyclohexane have less angle strain and are arranged in staggered conformations.
- The combustion energy can be determined through bomb calorimetry and then that value can be divided by the number of *methylene groups* (CH2 groups) to determine how unstable each group is and thus the total instability or stability of the molecule.
- The most stable form of cyclohexane is the *chair formation*. Slightly less stable but still often found is the *twisted boat formation*
- The molecule fluctuates between these formations many times in a fraction of a second.
- In these formations, there are *axial bonds* and *equatorial bonds*.
- when these cycloalkanes have substituents, it is preferred that these substituents occupy equatorial bonds so as to limit the steric strain between themselves and the molecule.
- The molecule can cycle through the chair-formation and the twisted-boat formation to accomodate this.

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:ID: cf824a5f-d7a6-45c5-82e5-d5de3241d3fa
:END:
#+title: Organic Chemistry:The Study of Chemical Reactions
#+filetags: :organic_chemistry:textbook_notes:
#+LATEX_HEADER: \usepackage{chemfig}
#+STARTUP: latexpreview
For more general information discussing chemcial reactions see[[id:0856b9fd-822f-4cc7-9ec4-cdcc38c01b5e][Chemistry the Central Science: Chemical Kinetics]]
[[id:410d2780-127b-4972-ae22-34d9cdbb750b][Chemistry the Central Science: Chemical Equilibirum]]
[[id:a8356651-4155-4ed4-8129-d13ca9b448f7][Chemistry the Central Science: Additional Aspects of Aqueous Equilibrium]]
* Reactions Involving Free Radicalis
What is a free radical? /A free radical is a very reactive species with an odd number of electrons./
Often, free radicals can be made from halogens, using heat and light.
Then, these free radicals can literally /abstract/ a hydrogen from a hydrocarbon. Hydrogen abstraction is different than protonation, because in protonation, the proton itself is all that leaves the substance.
However, in hydrogen atom abstraction, both the proton and its respective electron is taken from the species. Thus, there is a single electron left at with the carbon in the hydrocarbon, creating a free radical.
Consider the overall reaction:
$\chemfig{H-C(-[2]H)(-[6]H)-H} + \chemfig{Cl-Cl} \longrightarrow \chemfig{H-C(-[2]H)(-[6]H)-Cl} + \chemfig{H-Cl}$
Reactions involving free radicals follow a specific pattern:
1. Initiation
2. Propagation
3. Termination
Within the context of these steps, let's analyze the reaction given above:
*Initiation:*
\begin{equation*}
\chemfig{Cl-Cl} \longrightarrow \chemfig{\charge{0=\.}{Cl}} + \chemfig{\charge{0=\.}{Cl}}
\end{equation*}
In this step, heat and light are used to break a chlorine molecule into two free radicals.
*Propagation:*
\begin{equation*}
\chemfig{H-C(-[2]H)(-[6]H)-H} + \chemfig{\charge{0=\.}{Cl}} \longrightarrow \chemfig{H-\charge{0=\.}{C}(-[2]H)(-[6]H)} + \chemfig{H-Cl}
\end{equation*}
\begin{equation*}
\chemfig{H-\charge{0=\.}{C}(-[2]H)(-[6]H)} + \chemfig{\textcolor{green}{Cl-Cl}} \longrightarrow \chemfig{H-C(-[2]H)(-[6]H)-\textcolor{green}{Cl}} + \chemfig{\textcolor{green}{\charge{0=\.}{Cl}}}
\end{equation*}
We can see from the two propagation steps that free radicals are always being created in a type of chain reaction.
*Initiation steps* generate a reactive intermediate.
*Propagation steps* see the reactive intermediate react with a stable molecule to form a product and another reactive intermediate, allowing the chain to continue until the supply of reactiants is exhausted.
*Termination steps* are side reactions which destroy reactive intermediates and end the process
*Homolytic cleavage* occurs when a bond breaks and each atom retains one electron from the bond. Thus, homolytic cleavage yields free radicals.
*Heterolytic Cleavage* occurs when a bond breaks and one of the atoms takes all the electrons. Thus, heterolytic cleavage yields ions.
* Transition States
- Transition states represent the highest energy that the components of a reaction go through.
- In transitions states, bonds are being dissolved at the same time bonds are being formed.
*Hammond's Postulate* says that /related species that are closer in energy are also closer in structure. The structure of a transition state resembles the structure of the closest stable species./
Hammond's postulate can be used to explain the behavior of alkane halogenation. For example, Flourine is very reactive, and so is chlorine, but bromine is more selective about where it froms bonds on an alkane and the reaction happens very slowly. Iodonation (with iodine) rarely happens in this manner (via free radical halogenation) if not at all.
If we look at chloronation, the reaction is very exothermic. This means the transition state is actually closer in energy to the reactants. Thus, there is not much energy difference between the two transition states. This then means that chlorine cannot be as selective.
However, with bromonation, the reaction is endothermic, which means the transition state resembles the products. This means that the hydrogen bond is nearly broken in the transition state. This allows bromine the "chance" to be selective about where it forms its bonds (i.e. the most substituted) since highly substitued carbons form more stable free radicals.
* Reactive Intermediates
- These are short-lived species that react quickly when they are formed. Thus, they never exist in high concentrations.
*Carbocations*
\begin{equation*}
\chemfig{H-C^+(-[2]H)(-[6]H)}
\end{equation*}
* Compounds with a carbon that has a positive charge.
* No nonbonding electrons
* /sp2/ hybridized
* Trigonal planar geometry
* Since it has one completely empty p-orbital, it is a very stron electrophile
* Stabilized by alkyl substitutions
- 3 > 2 > 1 > methul
- tertiary > secondary > primary > methyl
* This happens through the *induction effect* and *hyperconjugation*, which arises when adjacent alkyl groups' hybrid orbitals align so they overlap with the carbocation's p-orbital.
* Unsaturated carbocations are stabilized by resonance.
*Free Radicals*
\begin{equation*}
\chemfig{H-\charge{0=\.}{C}(-[2]H)(-[6]H)}
\end{equation*}
* Compounds with only one electron occupying the p-orbital
* /sp2/ hybridized
* Stabilized by alkyl substitutions
- 3 > 2 > 1 > methyl
* Can also be satisfied by resonance in unsaturated compounds
*Carbanions*
\begin{equation*}
\chemfig{H-\charge{0=\:}{C^-}(-[2]H)(-[6]H)}
\end{equation*}
* Trivalent carbon with nonbonding electrons, giving it a negative charge
* Since it is electron-rich, it acts as a nucleophile.
* /sp3/ hybridized
* trigonal pyramidal geometry, resembling tetrahedral but with lone-pair
* Order of stability is opposite from the previous two. Less substitution is more stable.
- methyl > 1 > 2 > 3
* Stabilized by resonance. Carbonyl groups and pi bonds adjacent to carbanion serve to delocalize the nonbonding electrons
*Carbenes*
\begin{equation*}
\chemfig{\charge{0=\:}{C}(-[3]H)(-[5]H)}
\end{equation*}
* Uncharged, divalent carbons, with a pair of nonbonding electrons
* /sp2/ hybridized
* trigonal planar geometry
* unshared pair of electrons occupies one of the /sp2/ orbitals.
* Since it has a lone pair of electrons and an empty p-orbital, it can act as a nucleophile or an electrophile.

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:PROPERTIES:
:ID: 409e700e-e5de-402d-8e46-a063de488216
:END:
#+title: Organic Chemistry: Isomers and Stereochemistry
#+filetags: :organic_chemistry:textbook_notes:
#+LATEX_HEADER: \usepackage{chemfig}
#+STARTUP: latexpreview
Stereochemistry is the study of the three-dimensional structure of molecules and atoms in space.
For more information on stereochemistry for alkanes, see: [[id:0a889e6f-d7d5-4c7a-b8d6-e983d6f37d45][Organic Chemistry: Structure and Stereochemistry of Alkanes]]
There are *constitutional isomers* and *stereoisomers*.
Constitutional isomers differ only in the bodning sequence of the carbons in the chain. Stereoisomers differ in the arrangement of atoms in space.
* Chirality
Chirality is defined by taking the mirror image of an object. If the mirror image of an object is nonsuperimposable on the original object, the object is said to be *chiral.*
Chirality can also be defined as "handedness" (like right hand versus left hand)
In chemistry, nonsuperimposable mirror-image molecules are known as *enantiomers*.
A chiral compound /always/ has an enantiomer.
*Assymetrtic carbon atoms* are carbons that are bonded to four different, unique groups. An assymetric carbon atom is a type of *chiral center*, which is the name of any atom bonded to four groups that form a nonsuperimposable mirror-image. Chiral centers are then part of an even broader category called *stereocenters* which are atoms at which the interchange of any two of its groups results in a stereoisomer.
/Any molecule that has an internal mirror plane of symmetry cannot be chiral,/ even though it may contain assymetric carbon atoms.
* (R) and (S) Nomenclature of Isomers
How do we distinguish between stereoisomers? We use the *Cahn-Ingold-Prelog* system. Here's how it works:
* Assign a relative priority to each group bonded to the carbon atom.
- Atoms with higher atomic numbers have higher priority.
- Heavier isotopes have higher priority.
- In the case of ties, use the next atoms along the chain to determine priority.
- Treat double and triple bonds as if each were a bond to a separate atom.
* Using a drawing, place the fourth priority group in the back. Drawn an arrow from the first priority group, through the second, and to the third.
* If the arrow is clockwise, the assymetric carbon is called (R), /rectus/, latin for "upright."
* If the arrow is counterclockwise, the assymetric carbon is called (S), /sinister/, latin for "left."
* Plane Polarization
Different isomers can shift the plane of polarized light. If one isomer shifts light 5 degrees clockwise, the anantiomer will shift the light the same amount, 5 degrees, but counterclockwise. This is called *optical activity.*
A *polarimeter* meausers the shift of the plane of polarization due to isomers. The light travels through a reaction cell and cast through a filter. Optical activity depends on the length of the reaction cell and the concentration of compounds within the cell, according to the following equation:
\begin{equation*}
[\alpha] = \frac{\alpha (observed)}{c * l}
\end{equation*}
Where c is the concentration and l is the length of the cell in /decimeters./
Compounds that rotate light clockwise are labelled as "d" while those that shift light counterclockwise are labelled as "l."
* Racemic Mixture
- Racemic mixtures are mixtures that contain precisely equal amounts of R and S isomers of the same compound.
- Racemic mixtures are thus not optically active.
- Optically inactive reactants cannot produce optically active products. Any chiral products must be yielded in a racemic mixture.
We consider a molecule to be achiral if its chiral conformations are in rapid equilibrium with their mirror-image conformations. For more information on conformations of cyclic alkanes see[[id:0a889e6f-d7d5-4c7a-b8d6-e983d6f37d45][Organic Chemistry: Structure and Stereochemistry of Alkanes]]
* Fisher Projections
- These projections allow for the easy determination of stereoisomers.
- Imagagine that you are looking at an assymetric carbon atom from below.
- Fisher projections appear like a cross, with the vertical bond going away from the viewer and the horizontal bonds coming towards the viewer.
- 180 degree rotation of projections is allowed.
- 90 degree rotation is not allowed, because of the convention stated above.
- If the Hydrogen is on a horizontal bond (coming towards the viewer), then whatever isomer that assymetric carbon is /in the fisher projection/ (R or S), then the actual orientation is /the opposite/ of that.
* Diastereomers
- *Diastereomers* are stereoisomers that are not mirror images of each other. Therefore, they are not enantiomers.
- A common example of diastereomers, are /cis and trans/ isomers.
- diastereomers with compounds with more than one chiral carbon are easily seen in fisher porjections. They usually arise from one interchange of groups on one chiral carbon atom.
- Unlike enantiomers, diastereomers have differing physical properties, usually in boiling point and dipole moment. Therefore, they can be separated by distillation, recrystallization, and chromatography.
* Meso Compounds
- *Meso compounds* are achiral compounds that have chiral centers in them.
- Most of the time, meso compounds contain an internal plane of symmetry.

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:PROPERTIES:
:ID: 6f237745-5dcb-49d2-a5ba-1125d2003e4d
:END:
#+title: Genetics: The Cell Cycle
#+filetags: :genetics:lecture_notes
The cell cycle consists of several phases called *G1, S, G2 and Mitosis*.
The first three cycles belong to *interphase*.
Human cells have 46 individual chromosomes that come in pairs. Therefore, we have 23 pairs.
However, we are *diploid* in that there are only 23 /types/ of chromosomes but they are /duplicated./
In addition to this, each of the 46 chromosomes have a *sister chromatid*, resulting in 92 "sticks" of DNA.
Chromosomes are numbered by length.
They are distinguished by location of the *centromere* the central point where the two sister chromatids of a chromosome meet.
There are 22 *autosomes* and 1 *sex chromosome* in the human genome.
* Mitosis
Mitosis consists of *prophase, metaphse, anaphase, and telophase*.
DNA is replicated in interphase to prepare for mitosis.
*Prophase*:
* Centrosomes (the structures that build microtubules and spindle fibers) duplicate and begin to move apart.
* Replicated chromosomes begin to condense and are held together by centromere.
* Nucleolus disperses
*Metaphase*:
* Nuclear envelope begins to break down.
* Chromosomes move to *metaphse plate*
* Kinetochore and polar microtubules form from centrosomes
* Polar microtubules brace spindle poles so that they don't flow towards each other when the kinetochore microtubules pull chromosomes apart.
*Anaphase*:
* Kinetochore microtubules shorten while polar microtubules lengthen.
* Results in *chromatid disjunction*.
*Telophase*
* Neclear envelope reforms
* Chromosomes decondense
* Undoing of prophase
Meiosis is similar to mitosis except that in the first step, it's not the sister chromatids that are separated, but whole chromosomes. They arrange im pairs along the metaphase plate.
Additionally, recombinants form prior to this step. This is when DNA is mixed between homologous chromosomes.

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:PROPERTIES:
:ID: 7a74d2b5-50ff-4eb8-bfdb-2d07b0ce1585
:END:
#+title: Genetics: Mendelian Genetics
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
Mendel was a monk who experimented with plants such as the pea plant.
From his experiments, he determined several characteristics of inheritance. In fact, he postulated three key principles:
*Principle 1:* /In heterozygotes, one allele may conceal the presence of another./
*Principle 2:* /Two different alleles segregate from each other during the formation of gametes./
*Principle 3:* /Alleles of different genes assort independantly of each other./
- Mendel crossed pure-breeding tall pea plants with pure-breeding dward pea plants.
- It turned out, that when he did this, /all/ of the progeny were tall. These progeny were then self-fertilized.
- The offsrping of the self-fertilization resulted in both tall and dwarf plants. The ratio of tall to dwarf was 3:1
What Mendel did here was a *monohybrid cross*.
The phenotypic ratio for a monohybrid cross is *3:1*
Likewise when a *dihybrid cross* was performed, i.e. a cross that tested two genes (each being heterozygous), a ratio of 9:3:3:1 was observed.
The phenotypic ratio for a dihybrid cross is *9:3:3:1*
The 9 dominant phenotypes often have differing genotypes.
The absolute frequencies of the phenotypes are found by dividing by the total (in this case 16.)
It is important to note Mendel's assumptions while performing these experiments:
1. Genes segregated into alleles
2. These segregations are not linked to each other
Mendel was wrong in the second assumption. Some genes are in fact linked. (see[[id:8c1675c6-1b10-4fb4-9d77-25cd03a373cd][Genetics: Gene Linkage]])
* Test Crosses
Test crosses are performed to test whether a dominant phenotype contained a heterozygous or homozygous genotype.
Test crosses always use an individual that is /double recessive./
If the results include a 1:1 ratio of heterozygote dominant:recessive, the individual being tested must have been a heterozygote.
For example, if an individual has the genotype G g W w and is crossed with g g w w, the resulting phenotypic ratio will be *1:1:1:1*
* Chi-Square Test
A simple test that is done to measure if the error in an experiment is expected or above expected and in that case, not accepted.
It is given by the following formula:
\begin{equation*}
X^2 = \sum \frac{(observed-expected)^2}{expected}
\end{equation*}
As long as the value of the Chi-sqaure method is less than the 5% critical value of the experiment, the error is considered acceptable.
The 5% critical value depends on the *Degrees of Freedom* of the experiment. This can be found as shown below:
\begin{equation*}
Degrees of Freedom = Number of Phenotypes - 1
\end{equation*}
If there are 4 possible phenotypes for a given procedure, then there are 3 degrees of freedom.
Degrees of Freedom|5% Critical Value
1 | 3.841
2 | 5.991
3 | 7.815
* Binomial Probability
Only for *2* phenotypic classes
Takes into account birthing order/all possible patterns
Let's say that there is a family of 4 children. What is the probability that 2 kids will be dominant and 2 will be recessive?
Do a fraction for /every kid./
The odds of being dominant are 3/4 (because of the 3:1 ratio)
The odds of being recessive are 1/4.
The method of getting number of patterns is shown below:
\begin{equation*}
\frac{4(kids)!}{2(dominant)! 2(recessive)!}
\end{equation*}
This expression simplifies to 6.
Thus,
\begin{equation*}
\left(\frac{3}{4}\right)^2 \times \left(\frac{1}{2}\right)^2 \times 6 = \frac{54}{256}
\end{equation*}
If a problem deals with an "at least" type of language, do each case separately. Then, add up all the results to get the answer.

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:PROPERTIES:
:ID: 71224ae5-3568-453a-a33f-14c2e8fa4f34
:END:
#+title: Genetics: Expansion of Mendelian Genetics
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
Mendel set the stage for the foundations of the study of genetics. However, not everything is so simple, and many exceptions have been found to Mendel's principles.
These will be discussed here.
For more information on Mendelian genetics see[[id:7a74d2b5-50ff-4eb8-bfdb-2d07b0ce1585][Genetics: Mendelian Genetics]]
* Incomplete Dominance
This is where the heterozygote actually has a different phenotype than the homozygote, or, true-breeding.
This shows up when crossing red and white flowers: The het will actually have pink flowers.
Explained by the concept of *gene product.* If just one allele is enough to make the necessary proteins neede to have the phenotype, then the phenotype will look normal. This is *Haplo-sufficient*.
However, if one allele does not make enough proteins to produce desired phenotype, a /mix/ forms. This is *Haplo-defficient*.
* Codominance
Heterozygous alleles each display a dominant phenotype.
Common example is blood type.
For example, both $I^AI^A$ and $I^Ai$ produce blood type A. The same can be said but for type B.
$I^AI^B$ produces blood type AB.
$ii$ produces blood type O.
* Epistasis
Genes can interact in a linear or parallel pathway.
A gene is said to be epistatic if it conceals the presence of another mutant allele.
for example:
\begin{equation*}
\overrightarrow{Gene A}\;\;\;\overrightarrow{Gene B}\;\;\;\overrightarrow{Gene C}
\end{equation*}
Even if Gene C is dominant, if Gene B is 'broken' or double recessive, Gene C will /never be reached./
Take a look at the below pathway:
\begin{equation*}
White\;\;\;\overrightarrow{Gene A}\;\;\;Pink\;\;\;\overrightarrow{Gene B}\;\;\;Orange\;\;\;\overrightarrow{Gene C}\;\;\;Red
\end{equation*}
Let's say that a flower with the genotype A a B b C c is self fertilized.
We can determine the odds for each flower color phenotype.
White: Gene A must be broken, so all we need is $aa$
The odds are then 1/4 (once again because of the basic 3:1 ratio)
Pink: We can have either $Aabb$ or $AAbb$.
The odds are 3/4 times 1/4 which equals 3/16
Orange: We can't have Gene C working, so we need $A-B-cc$
The odds are 3/4 times 3/4 times 1/4 which equals 9/64
Red: We need all genes working, so $A-B-C-$
The odds are 3/4 times 3/4 times 3/4 which equals 27/64
* Penetrance and Expressivity
Incomplete penetrence is when a trait doesn't fully show up in an individual with the appropriate genotype.
Expressivity refers to when traits are not manifested uniformly (or to the same extent) in affected individuals.

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:PROPERTIES:
:ID: 82f37229-e178-4881-88a1-b9ee229b339d
:END:
#+title: Genetics: Sex-Linked Chromosomes and Traits
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
Thomas Morgan worked with the eye-color gene in fruit flies, which is on the X-chromosome.
He crossed red-eyed females with red-eyed males.
To his surprise, /all/ the females had red eyes but only 50% of the males had red eyes.
He concluded that eye-color was a *sex-linked trait* because it only occurs on the X chromosome. The cross can be depicted as $w^+w \times w^+$
Since male fruit flies only have one X chromosome 50% owuld get the $w^+$ and the other 50% would get $w$
His assistant, Calvin Bridges, then crossed white-eyed females with red-eyed males and found red-eyed male offspring and white-eyed female offspring.
These outcomes were not expected, and he called them *exceptional flies*.
The white-eyed female offspring could be explained with the fact that the females kept both recessive alleles. This resulted from *anueploidy.* (see[[id:7c91735d-5d8a-41d6-afac-058361daf3ad][Genetics: Types of Ploidy]])
* Sex-linked genes in Humans
A common example is red/green color blindness.
Affected individuals are male. Results from a $X^cY$ genotype.
Since the Y chromosome does not have many genes, it does not contain a gene that could potentially be dominant.
Therefore, the male is *hemizygous.*
* What Determines Sex?
Usually, XX means female and XY means male.
Specifically, the *SRY (Sex-Determining region of Y)*
- If missing, improper development occurs.
- Contains *TDF (Testes Determining Factor)* a gene that contributes to the growth of testes.
- *Tfm (Testicular feminization)* is a condition that only affects people with testes. It causes them to not be fully developed, sometimes even causing a female phenotype.
In insects, *denominator proteins* can inhibit *numerator proteins*. This relationship affects the sex of the organism. This is why it is a /ratio/ of chromosomes that determines sex in this case.
* Gene Dosage
*X-inactivation*
- X chromosomes inactivate and form *Barr Bodies* until there is only one active X chromosome.
- All cells that come from a given parent cell will have the same X chromosome inactivated as that parent cell.
- Inactivation is random to start with, however.

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:ID: 7c91735d-5d8a-41d6-afac-058361daf3ad
:END:
#+title: Genetics: Types of Ploidy
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
Here we discuss the nature of different types of ploidy, such as polyploidy and anueploidy.
* Cytogenetics
Chromosomes are identified by size, shape, and banding pattern.
There are short and long arms on chromosomes. The short arm is labeled /p/ for /petite/ and the long arm i referred to as /q/.
Location of the centromere is also considered: *Metacentric* (in the middle), *submetacentric*, *acrocentric*, and *telocentric* (at the very end).
* Ploidy
- Euploid = Complete set of genome; "normal"
- Polyploid = Having multiple sets of genome; more than 2
* Too many copies of DNA result in inability to split cell to make gametes (infertility)
* Fertile polyploids are rare, but can occur in certain plants.
- Aneuploidy
* Refers to numerical change in the number of chromosomes in a certain part of genome.
* *Hypoploid* means that a chromosome is underrepresented in a cell.
* *Hyperploid* means that a chromosome is overrepresented in a cell.
* *Trisomies* (when there are three copies of a chromosome in a human genome) can occur for chromosomes 13, 18, 21, and sex chromosomes.
* All other trisomies are embryonic lethals!
* Anueploidy results from *nondisjunction*.
* Anueploid Conditions of the Sex Chromosomes
Klinefelter Syndrome (XXY)
- Usually sterile, because there is "traffic jam" along metaphse plate (see[[id:6f237745-5dcb-49d2-a5ba-1125d2003e4d][Genetics: The Cell Cycle]] )
- Caused by nondisjunction in either mother or father.
- X inactivation occurs (see[[id:82f37229-e178-4881-88a1-b9ee229b339d][Genetics: Sex-Linked Chromosomes and Traits]] )
Triplo-X (XXX)
- Limited fertility
- Hyperploid condition
Turner Syndrome (X)
- Almost always sterile
- Reduced viability in the womb
- This actually means that the normally inactivated X chromosome is actually needed or helpful in some way.
- Problem with development leads to infertility.
Somatic *mosaic* Turner females can have cells that are normal and cells that are Turner.
- There are no Barr bodies.
* Chromosomal Rearrangements
Inversions
- *Pericentric inversion* includes centromere. Changes length of chromosome arms.
- *Paracentric inversion* does not include the centromere. Chromosomes loop themselves to line up with homologous pair in this case.
Translocations
- Genes moved between chromosomes.
- DNA exchanged between nonhomologous chromosomes; can cause a problem.
- Still technically euploid, no ploidy issues
Triplo-X (XXX)
- Limited fertility
- Hyperploid condition
Turner Syndrome (X)
- Almost always sterile
- Reduced viability in the womb
- This actually means that the normally inactivated X chromosome is actually needed or helpful in some way.
- Problem with development leads to infertility.
Somatic *mosaic* Turner females can have cells that are normal and cells that are Turner.
- There are no Barr bodies.
* Chromosomal Rearrangements
Inversions
- *Pericentric inversion* includes centromere. Changes length of chromosome arms.
- *Paracentric inversion* does not include the centromere. Chromosomes loop themselves to line up with homologous pair in this case.
Translocations
- Genes moved between chromosomes.
- DNA exchanged between nonhomologous chromosomes; can cause a problem.
- Still technically euploid, no ploidy issues.
- Because of how chromosomes line up, anueploidy can occur in daughter cell after mitosis/meiosis (see[[id:6f237745-5dcb-49d2-a5ba-1125d2003e4d][Genetics: The Cell Cycle]] )

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:ID: 8c1675c6-1b10-4fb4-9d77-25cd03a373cd
:END:
#+title: Genetics: Gene Linkage
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
We know come back to the topic of Mendel's assumption regarding genes: That they are not linked together in any way. It turns out that many genes in fact are linked together.
Independent assortment may not always be the case.
* Linkage
Linked genes can be separated by "crossing over"
* Cytologically - To form *chiasmata*
* Genetically - To form *recombinants*
Much of our analysis will be to determine how linked together certain genes are and thus how likely it is for them to crossed/swapped/separated.
What if the observed is so different from the expected, that the Chi-Squared analysis does not work? (see[[id:7a74d2b5-50ff-4eb8-bfdb-2d07b0ce1585][Genetics: Mendelian Genetics]])
This is probably the result of gene linkage.
We can determine the degree of how much certain genes want to stay linked together.
For these analyses, it can be assumed that linked genes are on the same stick of DNA.
When crosses happen with linked genes, less than 50% of the offspring are *recombinants*.
Most of the genotypes observed contains the same unaltered chromosomes from one of the parents. These are referred to as *parental*.
A *low frequency* of recombinant offspring suggests gene linkage.
For 2 linked genes the frequency is:
\begin{equation*}
Frequency = \frac{Recombinants}{Total}
\end{equation*}
This yields the frequency in units of *Morgans*. If the frequency was 0.18 Morgans, that means the genes will be separated 18% of the time.
Use notation such as $AB/ab$ to denote genes linked on DNA.
When offspring receive these chromosomes it is refered to as *coupling*.
When offspring receive separated/recombinant chromosomes, $Ab/aB$, it is referred to as *repulsive*.
* Three Linked Genes
There are now 8 chromosomal possibilities with 3 linked genes.
If sex-linked, and father has recessive, that is the only chromosome he can give. Most of the offspring will receive chromosomes from the mother /as is./
Two biggest observed numbers are the parental classes.
The rarest event is a *double* crossover in the gene. Sometimes, it is important to note, that /none/ of the offspring have this genotype.
1. Determine the order of the genes on the DNA since gene order is often not certain.
* Can be found by comparing the double crosses with the parental chromosomes. The only different gene when comparing them is the gene that come in the /middle/. The order is then found.
2. Calculate distances between genes in Morgans
* Only look at two genes at a time. /Ignore/ the other one.
* Add up numbers of observed genotypes where the two observed genes are the same as they are on the parental chromosome. Divide by the total to find the Morgans.
* To find total distance, add up all values from preceeding step.
3. Find *theoretical rate* of double crosses by multiplying the two rates together for each single cross (from step 2)
4. Find the *actual rate* of double crosses. Do this by:
\begin{equation*}
Actual\;Rate = \frac{double\;crosses}{total}
\end{equation*}
You will find that the actual rate is /always/ less than the theoretical rate.
This is because of *interference.*
5. Find interference by the following formula:
\begin{equation*}
Interference = 1 - \frac{actual\;rate}{theoretical\;rate}
\end{equation*}
Thus concludes the topic of gene linkage. I hope you can see how Mendel was revolutionary and successful in his hypotheses, yet did not account for certain cases in which certain genes are very close to each other on a given segment of DNA.

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:PROPERTIES:
:ID: e43a2223-ffee-4372-81c6-9520ca97450d
:END:
#+title: Genetics: Techniques of Molecular Genetics
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
* Cloning
1. Inserting gene into self-replicating chromosome
2. Amplifying the DNA (cloning)
- This is facilitated by using *RENS (Restriction Endonucleases)*
* These enzymes bind at a *restriction site* along the DNA
* Usually, it is a 4 or 6-mer *palindrome*
* RENS bind as dimers. Each side cuts one strand. This is why a palindrome is needed.
* When looking for palindromes, search for adjacent bases that are able to bind with each other if they were on complimentary strands:
\begin{equation*}
CAATTG
\end{equation*}
* *sticky cuts* create overhangs. *Blunt cuts* cut down the middle of the palindrome. It is more difficult to paste blunt ends together.
* Bacteria use RENs to protect themselves from outside (viral) genes.
* To protect its own genes, the bacteria methylates its own genes. The methyl groups protect the bacteria's genome from its own RENs.
- * Vectors are what the gene is inserted into.
* Contains Origin of replication
* Contains selectable markers
* Contains unique restriction endonuclease sites
All of the restriction sites on plasmid can be cut with the respective REN. If the target gene is also cut with the same REN, it will bind onto the respective site on the plasmid.
Multiple sites are preferred because that forces the desired gene to insert a certain way.
Plasmids support up to 10kb inserts
Bateriophages support 10-15kb inserts
Cosmids support 35-45kb inserts
A *shuttle* contains plasmids and ARS. Thus, it can be used in prokaryotes and eukaryotes
Plasmids must be mutated to remove undesired sites.
* PCR
- Replication, but in a test tube.
- Need dNTPs, ions, and polymerase. (For more info see[[id:3a5368b9-d120-40d0-907f-9b59cc53d653][Genetics: DNA Replication]])
- Primers must be designed based upon the sequence to be amplified.
- Can use polymerase without 3'- 5' to encourage errors. This is done to figure out what a sequence does when working properly.
- PCR is done in three steps:
1. Denature
2. Anneal
3. Extension
- Denaturing allows primers to bind and polymerase to operate
- Extension can be as long as needed. Length of this phase depends on the length of the segment of DNA being amplified. Extension is stopped by another round of denaturing.
- The temperature of the steps is dependent upon the G-C content of the DNA.
* DNA Libraries
- Genomic DNA Library: Series of DNA clones collectively containing the entire genome.
- cDNA library: Contains only the coding regions of the expressed genes.
* Very /functional/
* Collects RNA
- Foreign DNA can be precisely excised from the vector DNA using the same RENs.
- In cDNA libraries, Poly(T) oligomers are bound to polyA tail. Using *Reverse transcriptase* to create DNA transcripts, a *transcriptome* is made.
* Analysis of DNA
*Southern Blotting*
- Can use nylon blotting paper. Cause DNA to run through gel and buffer, all the way to the surface of the paper on top.
- Paper is heated to get DNA single-stranded, then dried or immobilized with UV irradiation.
- Then, a single-stranded radioactive probe can be used to bind to a standard, known, and non-mutated sequence. The result is subjected to X-rays to visualize the hybridized probes. All else is washed away.
- If the probe does not bind and stick, there is a mutation in the sequence. Thus, this method is often used to test for diseases.
*Northern Blotting*
- Same method can also be done on RNA.
- RNA must be kept denatured as it moves throughout the gel, since RNA has complex secondary structure.
- Denaturing accomplished by adding formaldehyde to the gel buffer.
- This method is very helpful in studies regarding gene expression.
- However, it provides no information about why the accumulation of the given RNA transcripts has occurred.
*Western Blotting*
- Proteins run through a polyacrylamide gel.
- Adhered to nitrocellulose paper.
- Antibodies are used to target specific proteins, instead of a single-stranded DNA probe as in Southern Blotting.
* Restriction Maps and Sequencing
- These are done to learn where restriction sitea are in a given region of DNA.
- Different RENs cut the DNA in different lengths; thus a gel will show this result.
- Location of restriction sites can be deduced by observing the length of the digested DNA fragments.
- In *sequencing*, "poisoned" dNTPs are used. These dNTPs are missing a 3/ OH /as well as/ the 5' OH. Therefore they are *dideoxyribonucleic acids*.
- These compounds act like *chain terminators*.
- In a polymerization reaction, the process can be terminated by adding, for example, ddGTP. When it is terminated, we know that it ends on a "poisoned" G.
- Upon adding all 4 ddNTPs, the sequence can be determined when loaded onto a polyacrylamide gel by comparing the lengths of each fragment that is terminated by one of each of the 4 "poisoned" bases.

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:PROPERTIES:
:ID: 3c1042b7-41e6-4830-a7b9-68a8d1d3b46f
:END:
#+title: Genetics: Genomics
#+filetags: :genetics:lecture_notes:
#+STARTUP: latexpreview
* Structural Genomics
- Deals with the *location* of genes:
* Genetic maps -- Shows distance between genes in Morgans. Only good up to 50 Morgans, because beyond this, independent assortment can be assumed and thus no actual distance can be attributted.
* Cytological maps -- Uses flourescence to locate genes on a chromosome.
* Physical map - Displays the actual bases.
* Restriction Fragment Length Polymorphisms (RFLPs)
- Mutations that change the length of DNA fragments produced from REN digests. The mutation happens within the sequence that a particular REN recognizes.
- They are small nucleotide polymorphisms (SNPs).
- They segregate as codominant alleles.
- They are a useful tool in creating genetic maps.
* Variable Number Tandem Repeats (VNTRs)
- Large areas of tandem repeats.
- The number of times it repeats is different in each person.
- Happen at different *loci*.
- They are not genes.
- They can produce a genetic fingerprint when all loci are analyzed.
* Contiguous Regions
- Using different clones, they can be overlapped to form the gene to form a contiguous map.
* Large DNA regions are fragmented so that they are easier to work with. BACs or YACs are often used.
* Fragments are analyzed for overlapping regions, acheived by looking at restriction sites.
* Once all overlapping positions are determined, they can be put together to create a complete map, giving the positions of genes on the chromosome.
* Sequencing the Human Genome
- Collin's team mapped clone by clone.
- Venter used whole-genome sequence using computer software.
- 30-35K genes were found ot be in the genome.
- Exons are only 1.1% of the genome while introns are 24%.
- About 75% of the genome is intergenic space.
* Functional Genomics
- Study of gene products: mRNA and proteins
- Microarray technologies examine expression of entire genomes (transcriptome) (see[[id:e43a2223-ffee-4372-81c6-9520ca97450d][Genetics: Techniques of Molecular Genetics]])
* A gene chip is used. gene-specific oligonucleotide probes are added to the chip.
* RNA is extracted from experimental and control tissues.
* RT-PCR is used to create cDNAs. The cDNAs are dyed with flourescence.
* The binding of a cDNA to a probe in the microarray chip means that a the specific template RNA was present, which in turn means that particular gene was being expressed.
- Can answer questions such as: What is normal? What is abnormal? What has changed based on the conditions?
* Comparitive Genomics
- The word *homologous* can refer to common ancestry *or* to analog proteins in prokaryotes vs. eukaryotes, or different species.
- Bioinformatics provides information from DNA sequences:
1. Can provide protein data/identify similar proteins with known functions.
2. Hints to crucial amino acids
3. Can provide exon data. Sheds insights on those that show high *conservation*, which usually is found in exons.
* conservation means that mamy different species have the same DNA sequence. This means that the sequence must be important and have a specific function.

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:PROPERTIES:
:ID: 1bd72f13-d051-4084-972a-5440f091a517
:END:
#+title: Introduction to my Knowledge Base
Hello and welcome to my Personal Knowledge Base, started on January 27th, 2024.
The Knowledge base will contain most of the relevant information I have learned throughout the years in my academics and beyond.
It is organized into several different categories for ease of classification and searching.
My topics range from Biology and Physics, to Music and Biblical studies.
I plan to keep this updated and I hope it will continue to grow regularly and serve me in my quests for knowledge and recollection.
Goodbye for now!

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GNU GENERAL PUBLIC LICENSE
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:PROPERTIES:
:ID: ee3d7e4a-fe69-48ab-a240-950586039b76
:END:
#+title: Single Variable Calculus: Integration by Parts
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
Integration by parts is essentially a way to integrate products of functions and it derives from the product rule for derivatives.
It takes the basic form:
\begin{equation*}
\int u dv = u v - \int v du
\end{equation*}
Usually in these calculations, you want to chose a /u/ such that /du/ is simple to calculate.
For example, let us take a look at this integral and use by parts to solve it:
\begin{equation*}
\int (xcos5x)dx
\end{equation*}
\begin{equation*}
u = x;
dv = cos(5x)dx;
du = dx;
v = \frac{1}{5}sin(5x)
\end{equation*}
\begin{equation*}
u v - \int v du \Rightarrow x \frac{1}{5}sin(5x) - \frac{1}{5} \int sin(5x) dx
\end{equation*}
\begin{equation*}
\Rightarrow x \frac{1}{5}sin(5x) + \frac{1}{25}cos(5x) + C
\end{equation*}

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:PROPERTIES:
:ID: 913f05b5-8387-41c0-af2b-fd340dc45e82
:END:
#+title: Single Variable Calculus: Integration by Trigonometric Substitution
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
Oftentimes, one will come across integrals with many trig expressions in them.
If there is a trig expression that has a power to an odd number, it is best to split it into multiple expressions with exponents that total the original power.
If there is a trig expression that has a power to an even number, it is best to use the half angle identities, given below:
\begin{equation*}
cos^2x = \frac{1}{2}(1 + cos(2x))
\end{equation*}
\begin{equation*}
sin^2x = \frac{1}{2}(1 - cos(2x))
\end{equation*}
Let's use and example to practice this method:
\begin{equation*}
\int (sin^2xcos^3x)dx
\end{equation*}
\begin{equation*}
\Rightarrow \int (sin^2xcos^2xcosx)dx = \int sin^2x(1 - sin^2x)cosx dx
\end{equation*}
\begin{equation*}
u = sinx;
du = cosxdx
\end{equation*}
\begin{equation*}
\Rightarrow \int u^2(1 - u^2)du = \frac{u^3}{3} - \frac{u^5}{5} + C
\end{equation*}
\begin{equation*}
= \frac{sin^3x}{3} - \frac{sin^5x}{5} + C
\end{equation*}

61
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@ -1,61 +0,0 @@
:PROPERTIES:
:ID: 5ebb753e-70ce-4a34-afd3-d6c8e3019890
:END:
#+title: Single Variable Calculus: Integration by Trigonometric Substitution Part 2 @Math_and_Physics #calculus #integrals
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
For integrals involving radical expressions, it is often useful to use trig substitution.
For integrals involving:
\begin{equation*}
\sqrt{a^2 - x^2}
\end{equation*}
Use substitution:
\begin{equation*}
x = a sin\theta
\end{equation*}
And use identity:
\begin{equation*}
1 - sin^2\theta = cos^2\theta
\end{equation*}
For integrals involving:
\begin{equation*}
\sqrt{a^2 + x^2}
\end{equation*}
Use substitution:
\begin{equation*}
x = a tan\theta
\end{equation*}
And use identity:
\begin{equation*}
1 + tan^2\theta = sec^2\theta
\end{equation*}
For integrals involving:
\begin{equation*}
\sqrt{x^2 - a^2}
\end{equation*}
Use substitution:
\begin{equation*}
x = a sec\theta
\end{equation*}
And use identity:
\begin{equation*}
sec^2\theta - 1 = tan^2\theta
\end{equation*}

40
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:PROPERTIES:
:ID: 0498a903-5277-455b-ad60-b82f06bbcc1a
:END:
#+title: Single Variable Calculus: Integration by Partial Fractions
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
Often, if one comes across an integral with a complex fraction involving polynomials, partial fractions must be used.
We examine several cases that may be utilized:
* Case 1
The denominator is a product of distinct, linear factors.
\begin{equation*}
\frac{A}{(x_1+a_1)} + \frac{B}{(x_2+a_2)} + \frac{C}{(x_3+a_3)}
\end{equation*}
* Case 2
The denominator is a product of linear factors, some of which are repeated.
\begin{equation*}
\frac{A}{(x_1 + a_1)} + \frac{B}{(x_2 + a_2)} + \frac{C}{(x_2 + a_2)^2} + \frac{D}{(x_2 + a_2)^r}
\end{equation*}
* Case 3
The denominator contains irreducible quadratic factors, none of which are repeated.
\begin{equation*}
\frac{A}{x - 2} + \frac{Bx + C}{x^2 + 4} + \frac{Dx + E}{x^2 - 1}
\end{equation*}
Using these rules complex fractions of polynomials can be broken up and reduced. Often, the integrals can then be broken up into multiple integrals (by their linear characteristic) and each one can often be solved given the anti-differentiation rules for $\ln(x)$ and $tanx$.

37
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:PROPERTIES:
:ID: 0b8c9409-c440-4baf-ada8-8a563adc5dc0
:END:
#+title: Single Variable Calculus: Indefinite Integrals @Math_and_Physics #calculus #integrals
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
Indefinite integrals are integrals in which one or both of the bounds is infinity. For example:
\begin{equation*}
\int_1^\infty \frac{1}{x^2} dx
\end{equation*}
How do we calculate such an integral?
We actually create a limit out of it. Say we substitute infinity for a variable, let's call it "b."
Then the integral becomes:
\begin{equation*}
\lim_{b\to\infty} \int_1^b \frac{1}{x^2} dx
\end{equation*}
Then, the integral can be solved by evaluating it first and then substituting infinity in for "b" and solving:
\begin{equation*}
\lim_{b\to\infty} -\frac{1}{x} \Big|_1^b
\end{equation*}
\begin{equation*}
\lim_{b\to\infty} -\frac{1}{b} + 1
\end{equation*}
\begin{equation*}
-\frac{1}{\infty} + 1 = 1
\end{equation*}

39
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:PROPERTIES:
:ID: dfd71f95-658a-465d-a6c7-86fc897f27f8
:END:
#+title: Single Variable Calculus: Arc Length @Math_and_Physics #calculus #integrals
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
To find a given length of a curve in two-dimensional space, we must have a graph with no cusps, points, etc.
We also want the graph to be smooth, i.e. *continuously differentiable*.
*Definition:* Let f be a smooth function on [a, b]. Then, the arc length of the graph of f from P(a, f(a)) to Q(b, f(b)) is:
\begin{equation*}
L = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
\end{equation*}
Let's look at an example:
\begin{equation*}
y = \sqrt{2 - x^2}; \frac{dy}{dx} = \left(-\frac{x}{\sqrt{2 - x^2}}\right)
\end{equation*}
\begin{equation*}
L = \int_0^1 \sqrt{1 + \frac{x^2}{2 - x^2}} dx \Rightarrow \int_0^1 \sqrt{\frac{2 - x^2 + x^2}{2 - x^2}} dx
\end{equation*}
\begin{equation*}
\int_0^1 \frac{\sqrt{2}}{\sqrt{2 - x^2}} dx \Rightarrow \sqrt{2}\left(sin^{-1}\left(\frac{x}{\sqrt{2}}\right)\right)\Big|_0^1
\end{equation*}
\begin{equation*}
\sqrt{2}(\frac{\pi}{4} - 0) = \frac{\sqrt{2}\pi}{4}
\end{equation*}

40
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:PROPERTIES:
:ID: 3109e144-f74c-416e-80b2-070710ad705b
:END:
#+title: Single Variable Calculus: Surfaces of Revolution
#+filetags: :calculus:integrals:
#+STARTUP: latexpreview
Given a curve in two-dimensional space, one can revolve that profile around an axis to create a three-dimensional solid. We can calculate the surface area of this solid using an integral.
*Definition:* Let f be a non-negative, smooth function on [a, b]. The surface area created when we rotate f about the x-axis is:
\begin{equation*}
S = 2\pi \int_a^b f(x) \sqrt{1 + \left(\frac{dy}{dx}\right)}
\end{equation*}
You can think of it as "ribbons" from a to b. Each one can be treated as part of a cone. As each one goes infinitessimal, the result gets more accurate.
The cone's surface area is:
\begin{equation*}
S = 2 \pi r l
\end{equation*}
Where:
\begin{equation*}
r = \frac{r_1 + r_2}{2}
\end{equation*}
This then translates to the equation in the definition because:
\begin{equation*}
f(x) = r
\end{equation*}
Which is the radius of the cone as a result of the revolution.
l = Arc Length, whose definition is given in [[id:dfd71f95-658a-465d-a6c7-86fc897f27f8][Single Variable Calculus: Arc Length
]]So we see that this method is merely treating each infinitessimal piece of the revolved solid as individual cones and summing up their surface areas.

52
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:PROPERTIES:
:ID: 6b3d2dbb-7c50-4ebf-b66c-4b0d1f20cdd1
:END:
#+title: Physics 231 Calculus and Vectors
#+filetags: :physics:textbook_notes:
#+STARTUP: latexpreview
A vector is *a mathematical entity with both a direction and a magnitude.*
* Vectors and Complex Numbers
it turns out that vectors are methematically awkward in 3D space. Dimensions such as 1, 2, and 4 allow for multiplication, addition, and division to make sense, as well as magnitudes such as distance to have meaning. Thus, 3D vectors can lead to awkward methematics.
complex numbers can be added to the x-axis to create a vector that gives the location of a point (let's say r). There is the real number part and the imaginary number part. The distance (or magnitude) of this vector can thus be found using the *pythagorean theorem*. Then, the angle could be found by taking the inverse tangent of the two components of the vector.
In this way, we could use complex numbers to describe physics in 2D, since 2D vectors have similar characteristics to that of complex numbers.
The 3D vectors we use today are imaginary components of William Hamilton's *quaternions*. These quaternions had 4 components to them and were a "sum" of a scalar and 3 imaginary components.
The vector portion of this concept was later extracted and used to describe the laws of physics such as E&M and gravity in an effective way. However, few people bothered to explore any further with quternions to see if they were more efficient. That being said, the paradigm of today is to use vectors, and they still are quite powerful.
* The Vector
In the modern vector, all of the parts are real numbers, but they still cannot be added together because they are each multiplied by a specific *unit vector* which points in a specific direction.
With vectors *components can be negative, but vectors themselves can never be negative.*
Any vector can be thought of as its own magnitude multiplied by its own direction, such as
\begin{equation*}
\vec{a} = |\vec{a}| \hat{a}
\end{equation*}
By rearranging this equation, one can find the direction of the vector by dividing each component of the vector by its magnitude. this gives the unit vector.
*unit vectors have no units in a dimensional sense.*
* Direction Cosines
Any unit vector can be described by:
\begin{equation*}
sin(x) = cos(\frac{\pi}{2} - x)
\end{equation*}
Thus, if the x-component of a unit vector is 3/5, then the cosine of the angle with respect to the x-axis equal 3\5.
Thus, direction cosines can be written as:
\begin{equation*}
\hat{a} = cos(\theta_x) \hat{i} + cos(\theta_y) \hat{j} + cos(\theta_z) \hat{k}
\end{equation*}
Direction cosines can be used to find how much of a vector point along one of the coordinate directions.

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:PROPERTIES:
:ID: 2a02b387-4fd0-4f83-9eac-131887b7abc8
:END:
#+title: Physics 231: Kinematics
#+filetags: :physics:textbook_notes:
#+STARTUP: latexpreview
Before diving into the topics of kinematics, we must ponder the questions that are raised when we think of an object all alone in the universe.
Imagine a rock in space that is far enough away from any star or planet, that it can interact with nothing. Answering the following questions will allow us to understand what will happen when the object is /not/ alone:
1. Could the rock speed up or slow down on its own?
2. Could it turn?
3. If the rock is observed to have motion, what would the properties of this motion be?
The laws of nature say that the rock's motion will be constant. Where it is going now, it will continue to go forever, unless acted upon.
This is referred to as the /inertia/ of an object.
This is Newton's first law of motion: *To the extent that objects are unaffected by external influences, objects at rest remain at rest, and objects in motion remain in constant-speed, straight-line motion.*
A deep implication that this hints towards is that there is fundamentally no difference between an object at rest and one that is in motion. This provides some of the underpinnings of Einstein's Theory of General Relativity.
*Motion can only be defined relative to another object.*
* Position
A definition of position: *The position of an object is a vector that describes the object's location with respect to some agreed-upon coordinate system. Both the location of the origin and the orientation of the axes must be known to make any sense of a position vector.*
The position vector is usually denoted as $\vec{r}$
The change in position is referred to as *displacement* and is denoted by $\Delta \vec{r}$
For more information regarding the basics of vectors see[[id:6b3d2dbb-7c50-4ebf-b66c-4b0d1f20cdd1][ Physics 231 Calculus and Vectors]]
Oftentimes, position vectors are functions of time, t.
* Velocity
Velocity is the derivative of the position vector with respect to time.
\begin{equation*}
\vec{v} = \frac{d\vec{r}}{d t}
\end{equation*}
To determine the direction, just divide the vector by its magnitude to find the *unit vector*.
To find the velocity vector from position, simply take the derivative of each component.
It is also very important to realize that the integral of a velocity vector does not result in the position vector but the *change in position* or the displacement.
We can find the latter position by adding the change to the first position, quite simply:
\begin{equation*}
\vec{r_2} = \vec{r_1} + \Delta \vec{r}
\end{equation*}
But notice that the first position is a piece of information that cannot be attained from the velocity vector!
To find the average velocity over a specific range, simply employ this calculus technique of dividing the result of an integral by its range:
\begin{equation*}
\vec{v}_{avg} = \frac{\int_{t_1}^{t_2} \vec{v} dt}{t_2 - t_1}
\end{equation*}
It is also important to note that the magnitude of the average velocity can be /different/ than the average speed. This is because the average velocity vector takes into account the direction of the straight-line path from point A to point B, while the average speed is dependent on the actual path that is different.
For example, if you run one lap around a running track, you should end up right where you started. Thus, the magnitude of your average velocity is 0, but of course, your average speed was definitely not 0 (hopefully).
* Acceleration
Acceleration can then be difined as the derivative of the velocity vector.
\begin{equation*}
\vec{a} = \frac{d \vec{v}}{d t}
\end{equation*}
And, like with integrating velocity, we can get:
\begin{equation*}
\vec{v}_2 = \vec{v}_1 + \Delta \vec{v}
\end{equation*}
We can continue to find information about the displacement as well:
\begin{equation*}
\Delta \vec{r} = \int \vec{v} dt = \int (\vec{v}_1 + \Delta \vec{v}) dt
\end{equation*}
Now, describing acceleration in terms of both change in speed /and/ direction is very useful and is given by (derived by the first equation in this sections and using the product law of derivatives):
\begin{equation*}
\vec{a} = \frac{d v}{d t} \hat{v} + \frac{d \hat{v}}{d t} v
\end{equation*}
We can see that the first term describes a change in speed only, which we know from natural observation, takes place in the direction of the velocity, such as a car speeding up or slowing down without changing direction.
The second term describes acceleration as a change in the direciton of the unit vector with time (radians per unit time) at constant speed.
The direction of the acceleration is perpendicular to the velocity vectors, just like the velocity vectors are perpendicular to the position vectors. This gives acceleration a direction in the $-\hat{r}$
* Eliminating the Time Variable
We now seek an expression that relates velocity to position, but contains no time variable.
If we want to eliminate the time variable, we must use the chain rule:
\begin{equation*}
\frac{dv_x}{d x} = \frac{d v_x}{d t} \frac{d t}{d x} = a_x \frac{1}{v_x}
\end{equation*}
Simplifyling, we have:
\begin{equation*}
\frac{d v_x}{d x} = \frac{a_x}{v_x}
\end{equation*}
From this simple equation we can create a host of kinematic equations that model physical systems with:
1. Constant acceleration
2. Position-dependent acceleration
3. Velocity-dependent acceleration
For *constant acceleration* applications, we can simply separate the terms and then integrate, ultimately leaving us with this equation (after some simplification):
\begin{equation*}
v_x^2 = v_{x0}^2 + 2 a_x(x - x_0)
\end{equation*}
However, it is very important to realize that these equations do not have a built-in sense of the correct passing of time (after all, we have eliminated the time variable). So, according to these equations, there are two values for time. However, only one is correct given the context. For example, the two time values express the time it takes for a ball to fall from a point and hit the ground, and the time that it would take for the ball to climb upwards from the ground to the point at which it was thrown, respectively.
For *Postion-dependent* accelerations, we can have an expression that depends on the slope:
\begin{equation*}
a_x = -g(slope)
\end{equation*}
Where g is the gravitational acceleration.
If we simply plug this expression in for the acceleration and separate and integrate like we have been doing before, we get an equation like this (after simplification):
\begin{equation*}
v_x^2 = v_{x0}^2 - (slope(x))g(x - x_0)
\end{equation*}
Where slope is a function of x, the position.
For *velocity-dependent* accelerations, let us give an example. Let's say that a car is rolling to a stop and its acceleration is a function of its velocity (since friction and air drag depend on velocity). Let's say this is:
\begin{equation*}
a_x = -0.2 v_x
\end{equation*}
\begin{equation*}
\frac{d v_x}{d x} = \frac{-0.2 v_x}{v_x}
\end{equation*}
From this, we see how easy this calculation can be, especially after cancelling out the velocity term.
Then, after separating and integrating, we arrive at this simple equation for velocity-dependent accelerations (ignoring air drag).
\begin{equation*}
v_x - v_{x0} = -0.2(x - x_0)
\end{equation*}
* Drag-free Projectile Motion
Using what we know about position, velocity, and acceleration, and what it means to take their derivatives and integrals, we can combine all of these things to create a glorious, complete equation.
\begin{equation*}
\vec{r} = (r_{x0}+v_{x0}t)\hat{i} + (r_{y0} + v_{y0}t-\frac{a_g t^2}{2})\hat{j}
\end{equation*}
/This equation does not account for landing or impact with the ground./
After solving for the time of flight using the y-component of the position equation given above, one can use it to find the range, or the distance in the x-direction the object goes before it hits the ground. The velocities in the x and y directions are just simply the components of the overall velocity vector. After doing this (substiuting the time of flight into the equation) we find that the range is:
\begin{equation*}
r_x = \frac{v_0^2 sin(2\theta)}{a_g}
\end{equation*}

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# Personal_Knowledge_Base
The Repository that houses my second brain :D

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Templates/astronomy.org
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Templates/compsci.org
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Templates/intro.org
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Templates/manuscript.org
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Templates/music.org
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Templates/physics.org
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Templates/science.org
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Templates/scripture.org
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Templates/writing.org
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