Biophysics

Cell Overview Plasma Membrane Outer shell of the cell responsible for seperating the cell from the enviornment Regulates transport of nutrients and waste of the cell Consists of a phospholipic bilayer (seperates hydrophobic materials on the interior of the membrane from the aqeous enviornment The heads are hydrophilic, while the tails are hydrophobic Lots of things are embedded in and pierce the bilayer (peripheral proteins, protein channels, Alpha-Helix proteins etc.) The proteins which pierce the membrane can be asymetric (re: inside has one structure, outside has a different structure) Cytoplasm refers to the intracellular content 80% of interior is water consists of cytosol (intracellular fluid) and organelles (internal structures) cytosol is a non-newtonian fluid and is colorless Cytoskeleton Protein filaments in the cytoplasm Holds cellular structure, aids in migration, signalling, and chromosome segregation during cytokinesis There are more specialized cytoskeleton structures: flagella, cilia, filopodia, lammelipodia etc. There are 3 board classes of cytoskeleton: actin, microtubules, and intermediate filaments. Actin are physically the smallest, microtubules are physically the largest Cell shape dictated by microtubules main branches, with smaller actin branches doing fine shape Organelles Nucleus Nucleus is present in eukaryotic cells It’s enclosed by double membrane (re: two bilayers) supported by lamina (re: cytoskeleton support) The outermost membrane folds onto itself into the endoplasmic reticulum (ER) nuclear pores pieces into the interior of the nucleus the interior is filled with chromatin (linear DNA molecules in complex with other proteins) has other suborganelles (nucleolus/speckles) Purpose: stores genetic material site of DNA replication and translation ribosome synthesis Endoplasmatic Reticulum Purpose: lipid synthesis membrane protein synthesis Ca++ ion storage detoxification Network of interconnected closed membrane tubules and vesicles composed of smooth ER and rough ER (called “rough” because it has ribosomes) The rough ER helps transpose hydrophobic materials within their bilayers as well as ribosomes The smooth ER generates new lipids and membranes Golgi Apparatus Looks like the rough ER Packages ER produces into small vesicles (exocytotic, secretory, lysosomal) which get transported to their final destination Lysosomes single membrance vesicle which decomposes things pH of 5 Peroxisomes Like lysosomes, but specifically fatty acids and toxic compounds single membrance They have a crystalline core Mitochondrium drives ATP production for aerobic metabolism has an double membrane, cristae, and a matrix Chloroplast Photosynthesis site for plants Plants also have mitocondria for some reason Tissue Cultures The term “tissue culture” is used to denote a population of cells to be examined “Culturing” a tissue means to grow them in a lab Can be “In Vitro” (in a test tube /glass) or “In vivo” (in a living organism) Depends on the subject of study Why use cultures? Controlled enviornment Ease of access Problems with tissue culture: They are outside the body, so they aren’t a perfect replica of the system Cells grow in 2D in vitro, while they grow in 3D in humans Human cells divide roughly once a day in vitro, but rarely do in vivo First proof of concept of tissue culture in 1885 by Wilhelm Roux was able to maintain chicken embryos in vitro for a couple of days HeLa cells was the first cell culture line (1951) From Henrietta Lack’s cervical cancer cells Tissue Cultures are grown in dishes with a medium that has the correct nutrients, pH buffer ,indicator etc. These dishes are stored in incubators To work with these cells, you need to shove them into a sterile fume hood Microscopy in Cell Biology Light Microscopy resolution of 200 nm Oldest form of microscopy. Passes light through a thin section of cell tissue More modern versions involve more lenses, but the same idea holds For liquid sames, we need to invert the microscope (light coming from above, objective lenses below) for many lense systems, you can insert “tube lenses” to circumvent the finite focal lengths of lenses We can modulate the incoming light of a microscope to generate constrast Humans are good at seeing changes in wavelength and amplitude, but bad at seeing phase and polarization changes Most biological specimens respond to phase, so the trick is to convert the phase shifts to something that we can see The idea is that: you let light pass through your cells. Most will pass through just fine, but some will get phase shifted as they pass through things Using a phase ring, you shift the diffracted light by a factor of $\frac{\pi}{4}$, leaving the phase of the unpeturbed light unchanged Damp the amplitude of the unpeturbed light to the amplitude of the phase-modulated version Look at the interference patterns between the two Another method (Differential Interference Constrast Microscopy (DIC)) Send linearly polarized light through your sample You have two equal polarization components Use a Wollaston prism to seperate the two components away from each other Pass the components through your specimen, which shifts the two polarizations a different amount Recombine the components with a prism, then pass through an analyzer lens Fluorescense Microscopy Idea: Shine one wavelength in, the dye you put into the cells reacts and produces a difference wavelength which you can see The shift between the maximum of the emission and the absorption spectra is called the Stokes shift You are limited to 4 colors: Constrained to visible spectrum for obvious reasons UV regime can be cyto-toxic to your cells These is also some spread associated with each source How do you make biological molecules fluorescent? You get lucky and there is some compound which can naturally bind to the molecule you want to study Phalloidin: a mushroom toxin that binds to actin Mitotracker: synthetic binder which binds mitochondria Design florescent anti-bodies which bind to the target structure You permeate the cell (poke a bunch of holes into it), flush a bunch of these antibodies in and let them bind, and then flush a clean buffer solution to clear up the free floaters obviously, this only works on dead cells Direct chemical labelling for your Molecule of Interest GFP (Green Florescent Protein) Jellyfish proteins which can attached to living cell structures Accomplished by modifying the genes which produce a protein of interest by attaching the genome of GFP in an appropriate place Can attach to nearly any protein No need for the microinjection with anti-bodies Electron Microscopy Resolution of 1 nm Uses DeBroglie wavelength of electron to increase the resolution compared to optics Uses tunnelling to produce a modulating current which gets reconstructed to an image Disadvantages: Very high vacuum required Specimens need to be fixed, embedded, sectioned an stained with an electron-dense material Central Dogma of Molecular Biology DNA (deoxyribonucleic acid) to RNA (ribonucleic acid) via transcription RNA to Protein via translation DNA A polymer of highly charged polyelectrolytes the monomers of DNA (nucleotides) are made of a phosphate group, a sugar, and an organic base The sugar for DNA is deoxyribose, while for RNA it’s ribose The organic bases are thymine (T), cytosine(C), adenine(A), guanine(G), and uracil(U) T for DNA and U for RNA T and A are purines (double ring structures) while C, G and U are pyrimadine (single ring) A and T pair up for DNA (A and U for RNA), while C and G pair up in both You match a purine and pyrimadine together to maintain the width of DNA The pairing occurs via hydrogen bonding (A and T have 2 hydrogen bonds, while C and G have 3 hydrogen bonds) When describing the double band structure, there is a 3’ and a 5’ end The 3’ side is attached to an oxygen of a phosphate The 5’ side is connected to the $CH_{2}$ side The 3’ and 5’ sides have opposite polarity on each strand There are 3 variants of DNA (A,B and Z) DNA is not in isolation in the nucleus. They are complexed with histones Since DNA is negatively charged from the phosphates, the histones are positively charged The charge on the histones is modulated by the acetylation of its’ tails RNA RNA is shares a lot of similarities to DNA One big difference is that RNA has a flexible backbone The three main types of RNA are messenger RNA, transfer RNA and ribosomal RNA RNA Polymerase There are 3 polymerases which synthesis the RNA (RNA polymerase I synthesises rRNA. II for mRNA and II for tRNA) These polymerases need a couple of things to do transcription: A start sequence The TATA box is a common one, but it’s not unique Transcription factors are used to unwind and prepare the DNA A stop sequence like, 200 A base pairs a 5’ cap The polymerase starts translating from the 3’ to the 5’ end (the strand that it works on is called the leading strand) For mRNA, there are exon (protein encoding regions) and introns (non-protein encoding regions) Proteins Consists of polymers A string of 20 monomers Each monomer has 3 components: The amino group ($NH_{3}$) The acid group ($CO_{2}H$) A central carbon atom, which bridges the acid and amino groups (via single bond to N and C) The R group: Gives all of the variance between the monomers The monomers get chained together via peptide bonds The process forms a single covalent bond between the carbon and nitrogen of the acid and amino group, producing water as a biproduct The menagerie of Amino Acids side groups: Nonpolar, aliphatic Aromatic Positively charged Polar, uncharged Negatively charged There is a hierarchy to Proteins Primary: the sequence of monomers Secondary structure: $\alpha$ helices an $\beta$ pleated sheets Tertiary structure: the 3D shape of your protein Quaternary structure: multiple proteins complexing together There is a well known mapping from RNA base pairs to monomers (re: codons) Lipids Lipids are partitioned into polar heads and nonpolar tails This partitioning allows lipid to self assemble (align the heads towards water and tails away from water) There is also a whole zoo of lipids: phospholipids gangliosides free fatty acids Cholesterol Steroids Carbohydrates Vary in size: monosaccarides, oligosacharides, and polysacchardies the number of rings determines which category they fall into Consists of hydrogens and carbons (and some oxygens) They can be energy sources, or serve a structural function (cellulose and chitin) Mesoscopic Forces Van der Waals These are dipole-dipole interactions There are 3 types: between 2 permanent dipoles (Keesom orientation energy) between 2 induced dipoles (London’s dispersion force) between 1 permanent and 1 induced (Debye energy) The interaction potential of a Van der Waals force between two point particles scales like $r^{-6}$ This does not hold for other geometries. You can derive other geometries via taking infinitesimal masses which do scale like $R^{-6}$ The proportionality constants come from quantum mechanic (Hamaker constant) They are long range (> 10 nm) They are weak (~ 1 $kJmol^{-1}$) Hydrogen Bonds Occurs between a donor (strong polar group) and a proton acceptor (slightly electronegative) They are weaker than ionic and covalent bonds (~ 10-40 $kJmol^{-1}$) Used in molecular self-assembly Hydration forces The polar nature of water leads to an electrostatic interaction The large dipole moment of water + water’s capacity for hydrogen bonding gives rise to a short range-order of water molecules Described by an exponential decay ($f = f_{0} exp(-\frac{t}{\lambda})$) These are very short range (~1 nm) Electrostatics point to point (Coulomb): scales like $r^{-2}$ point to dipole: scales like $r^{-3}$ dipole to dipole: scales like $r^{-3}$ the dominant long-range interaction Debye-Hueckel Theory There is some screening of counter ions around the macro ion The distribution of the counter ions as a function of the potential is $\rho_{i}(\phi) = \rho_{0} exp(-\frac{\phi}{kT})$ You can plug this charge distribution into the Poisson equation to yield: $\Delta \phi(\vec{r}) = \frac{1}{\epsilon_{0}\epsilon} \Sigma_{i=1}^{N} z_{i} e \rho_{i}(\infty) exp(-\frac{ - z_{i}e \phi(\vec{r})}{kT})$ DLVO Theory A Theory which describes forces between charged colloidal particles in a solution $\frac{V(r)}{B} = -\frac{A}{12\pi r^{2}} + \frac{64 k T \epsilon_{0} \Gamma_{0}^{2}}{\kappa} exp(\kappa T)$ There is once again, competition between Van der Walls attraction and electrostatic repulsion Depletion Forces Mediated by polymers or small particles Imagine that you have an isotropic distribution of smaller particles (polymer chains for instance) If you have two particles, then they feel an isotropic pressure from these particles If these two particles are close enough (re: smaller than the average size of the polymer chains), then this will break the isotropy and push the particles together generally attractive driven by entropy gain of polymers leads to colloidal aggregation The joining pressure is $\Pi = \frac{N}{V} kT$ Undulation Forces Imagine that you have a very think membrane which you stretch out to sizes that are several orders of magnitude larger than the thickness An energy of size kT is sufficient to substantially deform the system Steric Forces mediated by polymers The polymers act as a spring which repells particles away from a surface The repulsive energy per unit area is $W(r) \approx 36 k T e^{-\frac{r}{R_{g}}}$ Bridging Flocculation The polymers get attached to colloids, and between two colloids, the polymers intertwine Aggregating Self-Assembly Systems try to self-assemble so as to minimize $F_{min}$ errors in assembly can lead to disease: sicle cell anemia amyloidosis (prions) Alzheimer’s disease (self-assembled beta sheets amyloidplaques) Self-Assemblies: aggregating (micellization of lipids) non-aggregating (folding of globular proteins) morphologies produced by phase separation Self-Organization: actively bringing/moving parts together (re mitosis) Entropy loss of the assembling molecule is counteracted by entropy gain in solvent molecules Self assemblies aim to minimize the surface energy, which runs contrary to Entropy maximization Ostwald Ripening You have two particles which exchange particles via the solvent This is a purely thermodynamic process Surfactants they are ambiphiles (they have both hydrophilic and hydrophobic effects) Phospholipids are an example of this type of molecules These lipids tend to get attached to surfaces first prior to forming self assemblies These phospholipids can get joined at their tails to self-assemble Liquid Crystals Mesostate (between solid and liquid) Anisotropic (preferred direction in behavior) Ability to flow (liquid-like) Lots of biological molecules for these crystals biologically important (membranes, spider slik, cellulose etc.) Roughly 4 types: Rod-like, disk-like, banana-like, and conical-like Nematic: molecules tend to align in the same direction Semetic: molecules tend to arrange themselves in layers The order parameter $S = <P_{2}(\cos\theta)>$ determines which category the LC falls into $\theta$ refers to the angle between the z-axis and the primary axis of the LC $P_{2}$ is the 2nd order Legendre polynomial Diffusion Brownian Motion Discovered by Brown in 1826 via pollen wiggling around Einstein in 1905 gave kinematic formulation for Brownian motion Random Walk You have a process described by: $x_{i}(n) = x_{i}(n-1)_\epsilon$ On average, the displacement is 0 The mean squared displacement is non-zero ($n\epsilon^{2}$) This can be related to the diffusion constant: $D = \frac{\epsilon^{2}}{2\tau}$ $tau$ is the time step of your simulation On a macroscopic level, Fick’s Law states: $J_{x} = -D \frac{\partial c}{\partial x}$ J is the particle flux and c is the concentration These concentrations are very dependent on the boundary conditions of your system