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PHYS 380 (1)


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University of Waterloo
PHYS 380
Firas Mansour

MODULE 1 – Introduction to molecular physics Fundamental properties of life:  Self-replication – without it, you would remain stagnant o Rate of self-replication – the population within each generation is governed by an exponential relative to time.  Death – allows generations to be replaced  Mutation – aspect of evolution from one form of life to another. Must have undergone specific mutations, and death must have occurred. Cellular structure and composition:  Cells can be prokaryotic or eukaryotic  Prokaryotes o Present in lower organisms e.g., bacteria o DNA molecule more randomly folded within the cell; has no enclosing structures  Eukaryotes – present in complex organisms e.g., humans o Genetic material is assembled in chromosomes (1-50) within nucleus o Structural proteins are involved in the arrangement of the chromosomes. MODULE 2 – Introduction to basic protein structure Covalent bonding:  Hydrogen is the simplest atom with 1s orbital that contains max 2e  Other atoms bond to H2 by donating an e to the 1s orbital, filling the shell  An e in an orbital close to the nucleus has an energy which is lower relative to an e in an orbital further away from the nucleus. E orbitals and quantum mechanics  Pauli exclusion principle – no 2 e can have identical values for all 4 quantum #s o N = principle quantum # (Shell) = 1, 2, 3… o L = angular momentum (subshell) = 0, 1, 2, (n-1)… (s, p, d, f) o M = magnetic quantum # (orientation) = 0, +/- 1, +/-2… o Ms = spin quantum # = +/- 1/2  Hund’s rule – total energy of an atom with more than 1 e occupying a set of degenerate orbital is lowest of electrons occupy different atomic orbitals and have parallel spin. Bond lengths and energies:  C-H bond – relatively strong; C-C bond – weaker bond; C=C bond – very strong Amino acids:  20 principle amino acids, and are able to ionize in water.  There are 2 different conformations of the structure (stereoisomers = mirror images) o L form (found in eukaryotes) – R group is to the left of the path o D form – R group is to the right of the path  Polypeptide = amino acids joined by peptide bonds, water is always given off.  Peptide bond becomes non-rotating with resonance.  Exam Q: Why does the charge redistribute with bond resonance? o C=C bond takes on ~40% of single bond character, and the single bond takes on ~40% double bond character, thus preventing it from rotating as easily as well.  Non polar/hydrophobic R groups o Alanine – Ala o Valine – Val o Leucine – Leu o Isoleucine – Ilu o Proline – Pro (only AA where R group prevents rotation of peptide bond) o Phenylalanine – Phe o Trytophan – Trp o Methionine – Met  Polar, uncharged R groups  Exam Q: Interact with water more easily. Water is an electric dipole which allows it to align its polarity with that of the R group. o Glycine – Gly o Serine – Ser o Threonine – Thr o Cysteine – Cys o Tyrosine – Tyr o Glutamine – Glu o Asparagine – Asn o Histidine – His  Polar, acidic R groups – negatively charged at pH 7 o Aspartic acid – Asp o Glutamic acid – Glu  Polar, basic R groups – positively charged at pH 7 o Lysine – Lys o Arginine – Arg Electrophoresis:  Used to measure charge properties of AA and proteins due to interaction between the medium and protein causing resistance to motion. Frictional effects must also be considered. Proteases:  Proteins that can break down peptide bonds and are found in GI tract.  Very specific on which bond they break.  E.g., Trypsin breaks peptide bond at carboxyl end of lys and arg (both + charged AA) Polarity:  Generated by a particular charge distribution which is not spherically symmetric  Polar molecules have an affinity for water MODULE 3 – Molecular interactions and energetics Free energy:  Interactions between AA and those between AA and water are often weak = at the cellular level, bonds must be broken and reformed on a continuous basis in order for large scale motion and muscular contraction and relaxation to occur. Gibbs free energy: - used for large quantities  ΔG = ΔH - T ΔS o ΔG = G2 – G1 o ΔG < 0, bonds form o ΔG > 0, bonds don’t form o ΔG = 0, nothing happens.  2 law of thermodynamics – during a real process, the entropy of an isolated system always increases. Heat is released and order tends to increase when bonds are formed.  Bond formation – System favors minimum energy = ΔG is at a maximum where there is a minimum energy and the bind is formed.  Bond breakage – Total E= U + KE o The ratio of ΔG/RT, bond energy to KE, will determine the fraction of bonded molecules. o If ΔG = 0, Keq = 1 and formation and breakage of bonds are equally favored o If ΔG < 0, Keq > 1, bond formation favored o If ΔG >0, Keq <1, bond breakage favored Weak bonds:  Ionic (electrostatic) o If force is -, => attractive; if force is +, = repulsive o Dielectric constant – charges within the protein will not be evenly distributed (variable) o Entropically driven reactions: ion-pair formation.  For aqueous solvents, the entropy of the water increases substantially so that there is a net overall increase in entropy within the system”  ΔH for ion-pair formation is +  ΔS for ion-pair formation is –  Dipole (permanent dipoles) o Antiparallel – attraction; parallel – repulsion. o Examples: OH, C=O, NH, peptide bond  Van der Waals (London dispersion forces) o Occurs between 2 fluctuating, non-permanent dipoles o In proximity, the electron cloud distribution can shift momentarily due to unpredictable quantum fluctuations, producing a transient dipole-like interaction. o Fluctuations continue in such a way that a net attraction exists. o As atoms come close together, electron orbitals start to overlap and a repulsive force will result in keeping with the Pauli exclusion principle = called the hard sphere potential o You can also add 2 vanderwaal forces (+) + (-) = called the Lennard-Jones potential  Hydrogen bonds o Strongest weak bond with energy of up to 5 kcals/mole o 4 bonds are possible for each water molecule o H bond has direction and flexibility. o Structure of water:  MP and BP are higher than H2S even though it shouldn’t be.  For Ne, as temp decreases, density increases  For water, density reaches a max at 4 C, and then decreases as temp decreases  For hexagonally close-packed spheres, filling factor = 0.74  Ne approximates this filling factor ~ 70% of max  Ice has a more open structure ~ 57% of max  MW of water appears larger than its true MW because of the larger structure associated with ice.  At 10C majority of molecules form ~2.3 H bonds in water.  There are many possible polyhedral structures present in liquid water but for short times – most stable is pentagon.  Therefore, MW of water appears larger due to this structure, thus increasing the values of MP and BP.  H bonds are rapidly made and broken, and are also called the transient network of H bonds. o Polarity of water:  If ΔGt < 0, AA is polar  If ΔGt > 0, AA is nonpolar  ΔGt is the change in Gibbs free energy as a result of the transfer of the AA from the nonpolar to the polar medium.  Ethanol is a useful polar medium – its similar dielectric constant allows for the gentle migration of the AA  Hydrophobic bonds o Water tends to form clathrate structures around the non-polar molecules. o Clathrate structure is induced by the nonpolar surface of hydrocarbons. o For bulk water, there are 2.3 H bonds formed per water molecule. For clathrate structures, there is on average an increase in the number of hydrogen bonds formed. o Clathrate structures cause lower entropy within the system when non-polar molecules are added to water. o This situation is not favorable since ΔG = ΔH – TΔS  The reason nonpolar molecules don’t like to go into water has to do with entropy. o More H bonds result in a higher degree of order; fewer H bonds result in lower order. o In state 2, there is an overall decrease in surface area, volume of clatharated molecules decreases, entropy increases and this reaction is favorable. o Nonpolar AA will also tend to aggregate if they can in order to get away from water molecules o Aggregation and folding will occur in some way to maximize the # of non-polar AA that come together in the interior of a protein molecule. Stabilization of the folded state:  The unfolded state (U) is known as the denatured state of the protein  Folded state (N) or native state is more favorable – allows for the minimization of ΔGtotal.  Initial compaction is strongly driven by hydrophobic effect.  Conformational entropy is smaller in the compact case and larger in the expanded case.  The formation of the secondary structure must minimize ΔG, which are stabilized by H bonds  You need to consider all the interactions in both states. HP Lattice model  Involved minimization of ΔG.  H bonds produce the secondary structure that results from the folding of the AA chain.  Model assumes that the hydrophobic interaction dominates folding.  Assumes that representative structure can be found by distributing the beads on a square lattice  There are 3 choices of placement  Ideal conformations: idealized H core, helix and sheet MODULE 4 – Secondary protein structure Ramachandran angles  Ψ – twist clockwise about the Cα-C bond  Φ – twist clockwise about the Cα-N bond  By specifying the angles for all AA, you can specify the folding of the peptide chain Helix  If all Ψ and Φ have the same value, the resulting structure is always helical.  P=nd, but only 2 are independent variables. o Pitch (p) is the vertical climb. If 0, there’s no climb. o D is the separation of the subunits on the z axis.  Right hand rule – wrap right hand around axis of rotation so that your fingers are pointed in the direction of rotation and your thumb points in the direction of angular velocity vector. o + N value = right handed helix o - N value = left handed helix o NMR can be used to ascertain direction.  Helical structures can only be specified using p, d and n. For regular structures in protein molecules, n and d are related to Ψ and Φ.  α – helixes form in the range where Ψ ~ -60   - sheets form in the range where Ψ ~ 60 to 180 and Φ is ~ -60 to -180.  Left handed α – helixes are possible but not as desired energetically, so occur less commonly  Polyproline helix also occurs  The helix becomes more extended as it moves from right-handed helix to beta pleated sheet when the d (vertical distance between the AA) value increases. o For the right handed α – helix, n = 3.6 o Energetically, the driving force behind the structure is H bonding. o ΔH is the driving force in this reaction, increasing the number of bonds and leading to a greater PE well for the structure (important to maximize # of H bonds) o Entropy of the water bath increases so that the overall entropy is greater in the system.  AA has a defined length, extending form the carbonyl carbon to the alpha carbon and on to the N atom  The R groups of the AA are bulky and would cause stearic hinderance effects if they weren’t oriented to the outside of the cylinder, which is less desirable energetically.  α – helix structure is an example of intramolecular H bonding (occurs within the unit)  Intermolecular H bonding occurs between molecular units. Polyproline helix  Left handed helix  R groups are oriented to the outside of cylinder to avoid stearic hinderance effects  Slight polarity associated with C-H group so weak H bonds form o Important in intermolecular bonding between helices o H bonds help to form bundles of helices in stable structures o H bonding between helices form the stable sheet structure Beta pleated sheet  Can be parallel or anti parallel (more common) More possible structures  Φ = Ψ = 180 is also known as the extended conformation.  At Φ = -60, the bulky carbonyl group is as far away from the R group as possible, so the stearic effects are minimized and this is the most energetically favourable conformation.  Structures become increasingly favorable energetically as they are extended (all extensions of the 5 member ring)  Hydrogen bonding patterns: intrachain H bonds o There is actually a strain/misalignment of the bond in the 3.10 helix o When the strain is removed, in the case of the α – helix, it becomes the more energetically favoured conformation. o Intramolecular H bonding does not tend to occur because of the strain o Intermolecular H bonding occurs, forming structures such as the beta pleated sheet  Q: Is the 2.2 helix an extended or contracted form of the 2.7 helix? Potential energy calculations  3 main interactions contributing to the energy: o Nonbonded van der Waals interactions – perform the sum to find the total potential contribution for the AA o Dipole interactions (largely between the amide dipole) – amide group dipole contributes the largest extent. Dipole is parallel to the N-H bond and pointing towards the H. o Torsional potential – hindrance to rotation due to intrinsic potential resulting from barrier to rotation about single bonds. Contour plots  Represent energies of equal value.  Energy profile is specific to this group of AA (x-gly-z)  If glycine is between two other AA, the total PE is due largely to the contribution of the glycine.  As the number of the associated contour line decreases, the PE decreases.  Lowest PE value represents the most desirable state (values still spread over a range) o Range of values suggest that glycine is a very flexible AA wrt conformation  Q: Discuss the structure of the AA alanine. o R group for alanine consists of one CH3 group. o Beta sheet conformation occurs in this energetic region. o Right handed α – helix and left handed α – helix structures also occur o Right handed α – helix gives one of the lowest energies for the alanine group. o Left handed α – helix structure has a higher energy and is found less commonly. o Unproven theory that L form of the AA is connected to the right handed α – helix  Special cases: o X-pro-z = the proline AA is able to take part in the α – helix and beta sheet structures  Surrounding AA influence the proline AA o Ala-pro-z = much reduced accessible domain. If gly is substituted for ala, contour map is not very different.  This combination of AA cannot form an α – helix  Proline is a helix breaker, and can also be at the beginning of the α – helix Structural proteins Man-made examples:  Polyethylene plays structural role in the plastic to generate the desired material  Polystyrene – used to make latex beads  Nylon and polyester Alpha keratin  α – keratin is an essential α –helix  AA composition consists of very little proline as it can be a helix breaker in a certain position  Most helices found in nature are right handed, formed by intramolecular H bonding, and R groups are small and not bulky  2 α –helices come together to form a dimmer.  By convention, the head of the dimmer is the carboxyl end, and the tail is the amino end.  Dimmer is a twisted pair of helices similar in nature to a rope.  Right handedness is independent of orientation  Dimmers combine to form protofilaments which are paired and typically offset for strength  Microfibrils combine to form macrofibrils, which combine to form cells and then hair, nails or hooves.  α –helix is intramolecularly connected by H bonds and intermolecularly connected by van der waals type interactions. Disulfide cross-links  Strength is supplied by disulfide cross-links  There is a sliding effect of one α –helix over the next  A covalent bond is formed between the two AA with an energy of 80-100 kcal/mole.  If there are few cysteine AA in the chain, the chain is low sulfur and has fewer cross-linkages o Low sulfur chains are more extensible and the α –helix can be stretched (H bonds break)  Ex: wool and hair  If there are many cysteine AA in the chain, the chain is high sulfur and has more cross-linkages o High sulfur chains are less extensible, less flexible and more rigid  Ex: fingernails and hooves Structure-function relationship  The structure of a particular material at the molecular level is related to its macroscopic function and properties.  Hair is made up of α keratin and ultimately α helices tied together by a certain # of disulfide bridges. As it grows and forms disulfide bridges, o If it is under tension, hair will curl and remain curly o If it is NOT under tension, hair will be straight and remain straight  In getting a perm: apply reducing agent to hair to break disulfide bridges, then apply oxidizing agent once hair is curled to reform the disulfide linkages  To straighten it, hair is straightened after the application of the reducing agent and before the application of the oxidizing agent.  Hair grows ~6 inches/year = 9.5 turns of α helix/sec. Silks and insect fibres  Beta pleated sheet o Reflects the properties and function of material on macroscopic level o Helix with n=2 (intramolecular H bonding maintaining the helix structure is not energetically favorable) o H bonds that form the intermolecular H bonds forming the extended sheet structure o Silk – secondary structure is the beta pleated sheet and quite different from that of wool o This difference gives more strength to the material such that silk cannot be pulled or stretched like wool o Wool fibre structure is composed of bundled α helices  3D structure o Beta pleated sheets are layered to form the 3D structure of the material and give it thickness o Antiparallel arrangement allows for the most efficient H bonding  AA composition o Silk fibre – simple with few different types of AA present in the structure  Gly (-H): ala (-CH3): ser (-CH2OH) = 3:2:1  A six-residue unit repeat: gly-ser-gly-ala-gly-ala-  Interactions o Even though the AA chains are very extended, silk material still has some extensibility o Covalent bonds would have to be broken if the material is pulled along the direction of the AA chains o Many H bonds must be broken if the material is pulled in the direction perpendicular to the AA chains o Contact between sheets is largely governed by van der Waals interactions, which gives the material a great deal of flexibility o These properties give silk its lack of extensibility but exceptional flexibility o Other insect fibres are similar to silk, but their AA composition differs. Collagen  Polyproline helix o Collagen is found in skin, tendons, parts of muscle, cartilage tissue, cow hide. o In the polyproline helix, little intramolecular H bonding, but some weak intermolecular bonding takes place  AA composition o Proline not the only AA involved in making up the collagen material o 1/3 of the AA in collagen are glycine o ¼ of the composition is proline, another ¼ is hydroxyproline o Hydroxyproline – one of the CH2 groups of proline is replaced by H and OH groups  Intermolecular H bonding is now possible.  Typical sequences: gly-x-pro or gly-x-hypro  Structure o α –keratin combines helices to form a dimmer, then dimmers combine to form higher order structures o Similarly, collagen combines 3 helices to form tropocollagen o Each tropocollagen molecule is offset by quarter of its length o The tropcollagen molecules are offset in order to give strength to the collagen material’s structure. o H bonds are present between the chains within the molecules and between the tropocollagen molecules o Hydroproxyproline residues make the intermolecular hydrogen bonding possible. o The tropocollagen molecule forms the tertiary structure o Each of the helices making up the tropocollagen molecule is defined by its secondary structure. o There are strong similarities between the different levels of structure. o Q: how do desired physical properties in an organism connect with the molecular structural details that lead to these properties? Ex: extensibility, flexibility etc.  Examples of collagen in tissues o Skin – very thin, yet tough and flexible. Combines several proteins to give it the unique properties it possesses. o Cartilage – attached to the ends of bones of articulating joints. Must be very smooth so there is no friction caused by movement of the joint. Main components are collagen and protoglycan (large, negatively charged molecule). Acts as a shock absorber in joints.  Collagen prevents over-extension of the tissues because there is a strong tendency for the tissue to take up water, and as a force is applied, water is pushed out of the joint. As force is released, water gushes back into the tissue. MODULE 5 – TERTIARY STRUCTURE Globular proteins  Supersecondary structure o A turn is composed of a set of AA, tied together covalently, which form a regular or irregular turn in the structure (often composed of a random coil arrangement). o A motif is a supersecondary structure composed of a specific arrangement of a few secondary structural elements.  Hairpin loop (beta-t- beta)  Greek key motif – example is Staphylococcus nuclease, an enzyme that breaks up nucleic acids and is used by the bacteria as a protective mechanism against invading nucleic acids.  Domains – polypeptide chain that can fold into a stable tertiary structure. o Organization of structure:  Primary structure, secondary structure, motifs, domain, protein (tertiary) Alpha domain structures The 4-helix bundle  Most frequently occurring α –helical domain  Cytochrome B is an electron transfer protein – arrangement can be varied with combinations of parallel and antiparallel helices.  4-helix bundle often exists specifically on the outside of proteins – polarity is involved.  There must be a regular repeating pattern so that all polar molecules are oriented to the outside and nonpolar to the inside of the helix.  Helical wheel – used to determine the polarity of the α –helix faces o If the AA are mostly polar, this polar region will be exposed to the water. o If the AA are mostly hydrophobic, this region will be buried either within the protein or within the helix bundle. o If there’s an alternating arrangement of polar and nonpolar, this arrangement is known as amphipathic. o Helices composed of nonpolar AA are also common (e.g., transmembrane helices of membrane proteins) Molecular carriers  Globin fold proteins are proteins that have a folded region in their structure e.g., myoglobin and hemoglobin.  Oxygen is taken up by the lungs and attached to the Hb molecule, and is transported through blood vessels to muscle tissue where it is released by the Hb to Mb, which hold the O2 until needed.  Myoglobin (Mb) – 1 polypeptide chain of 153 AA o Contains a heme group which has an iron atom where O2 binds.  Hemoglobin (Hb) – 4 polypeptide chains. o Made up of 4 myoglobin-like chains = tetrahedral arrangement.  Heme group – functional group for Mb and Hb o O2 binding occurs here, and is the same structure for both Hb and Mb o 4 planar rings are covalently bonded to form a porphyrin ring. o 4-way or 4-fold coordination is involved in the binding of the iron atom, but the iron atom is not bound covalently. o Weak bonding is important, as O2 must bind temporarily for later release. o Porphyrin ring is also enclosed by the globular protein preventing strong bonding by the O2.  Function – O2 binding o Mb + O2 MbO2 o K =[MbO2]/[Mb][O2]  K indicates how tightly bound the O2 is to the Mb  K also affected by pH and temp  [MbO2] vs [O2] plot indicates binding constant  [O2] differs in lungs than in muscle tissue  Partial pressue of O2 in lungs is 100, so you have l
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