First Problem Set, Due 30 Sep. (1st midterm is 7 Oct.) If you want it graded by 6 Oct, turn in on or before 30 Sep. at 5 pm.

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1 First Problem Set, Due 30 Sep. (1st midterm is 7 ct.) If you want it graded by 6 ct, turn in on or before 30 Sep. at 5 pm. Show your work calculations / steps!! Problems from Chapter 1 1 EM of a eukaryotic cell: provide a name for each of the 8 numbered structures 2 Textbook problem 3, but instead of doing the problem for E. coli, do this for bacterium with dimensions 1.6 µm length, and 1.2 µm diameter, (the pinhead is still 0.5 mm), intracellular glucose concentration of 1.3 mm, number of ribosomes = 20,000 and they are still 20 nm in diameter, chromosome mass is 4x10 9 daltons, and the typical protein is still 360 amino acids long.

2 3 In order for life to persist at 80 C what interactions would have to change? (30 words or less) How would they have to change? (1/2 a page or less). 4 Debate the statement "living cells represent an equilibrium" 200 words or less for R 200 words or less against (choose to argue that the statement is true R false). 5 List four essential properties of a living system as per our text. Then argue one of these: either that one is not an essential property of life, or that an additional property is an essential characteristic of life. 6 Provide one stucture each for a sugar, a fatty acid, a nucleotide and an amino acid. Problems from Chapter 2 1 Calculate the ph of the following: 2 x 10-3 M HCl 1 mm KH A solution with a total acetic acid + acetate concentration of 0.1 mm A solution with a total acetic acid + acetate concentration of 0.1 M 2 Textbook problem 5 except prepare a ph of Textbook problem 7 except use ph Given the data supplied for textbook problem 10, which species of citric acid/citrate will predominate at ph 7.0?, ph 4.5? 5 Draw the ph titration curve for anserine (pk A s are quoted below figure 2.16). Your axes will be ph vs. equivalents of H - added. You are welcome to use excel or other software to do this.

3 Problems from Chapter 3 1 In 50 words or less, explain why!g =!G ' for reactions that neither consume nor produce any protons or H -. You may use equations freely. 2 Thinking of reaction thermodynamics in terms of entrophic and enthalpic contributions, which pass from favouring reagents to favouring products depending on temperature: analogy to a phase transition between unfolded and folded protein. We can illustrate the opposing roles of enthalpy and entropy in protein folding with very simple models. The following example from Ken Dill is so simple it is known as a 'toy model'. Imagine a protein with 'N' amino acids made up of only two kinds of amino acids: and, and the amino acid occurs 'n' times. To keep the problem extremely simple, we work in 1-dimensional space instead of 3-d, however this simplification means that when we look at a string such as, we do not mean that this is the sequence of the amino acids in the protein, but that the amino acids are placed in space with three instances of next to and two instances of next to and no instances of next to, for the case of N=6 and n = 2. We do not consider that this ordering is made permanent my covalent bonding, but instead allow that the units can re-order themselves in 1-d space as they diffuse around and the protein explores different structures (it is a dynamic protein). Use the definition for entropy that S=k ln(w) where W is the number of ways in which a condition can occur and k is Boltzmann's constant. a Write expressions for W and S, for the condition of a protein of N residues with n=2. b Now write expressions for W and S for the general case of N residues and 'n' s (your expression should be interms of N and numbers, or N and n, respectively. Recall what you know of probabilities and statistics.) Comparison of cases with residues in a pair ('p' states) vs. cases with residues separated ('np', not paired states), for two in a protein of N residues (n=2). In some of the cases above, the two will be side-by-side. c What is W p, the number of ways in which two can be side-by-side in a protein of N residues? What is S p for this case? d Based on the above, what is W np, the the number of ways in which two are NT side-by-side in a protein of N residues? What is S np for this case? Consider that those cases in which two are side-by-side have an enthalpy H p =- ", whereas cases where the are surrounded by have enthalpies of H np =0. e Write expressions for G p and G np. Plot each as a function of T on the same graph, choosing axes so that the resulting plot shows what sort of a plot each expression yields,

4 how they differ and where (if ever) they intersect. Label the temperature range in which paired are favoured, and the temperature range in which dispersed are favoured. f Write an expression for!g unpairing = G np - G p. When G np - G p =0, the two plots intersect. Derive an expression for the temperature T at which the plots interset, and use it to calculate the temperature at which the system will undergo a phase transition (unfolding transition) between a phase in which paired are favoured and one favouring dispersed. Your answer for this transition T will be in terms of ", k, N and numbers. 3 Compound A undergoes hydrolysis to yield B + C. Write the chemical reaction as an equation including all the participants. Pure A is dissolved in water to produce an initial concentration of 2 mm (before any reaction has occurred). After A has had time to reach equilibrium with the products B and C the concentration of A is 1.8 mm. Calculate the standard free energy of the reaction. 4 While class discussions have skirted the matter, Figure 3.16 shows that if extreme phs were to occur, they would have a large effect on the free energy of ATP hydrolysis. Consider the physiological pks of ATP, ADP and inorganic phosphate (P i ). ATP ADP P i NN 2 H 2 C P P P H H H NN 2 H 2 C P P H H H - - H P H - pk 1 = 6.95 H + pk 2 = 6.88 H + pk 3 = 7.20 H + NN 2 H 2 C P P P H H NN 2 H 2 C P P H H - P H - At ph 7.4, what fraction of ATP is in the 4- form (lower structure, deprotonated with respect to the pk A of 6.95)? At ph 7.4, what fraction of ADP is in the 3- form (lower structure, deprotonated with respect to the pk A of 6.88)? What is the stoichiometry of protons released upon hydrolysis of ATP at ph 7.4 due to just those two pks? Repeat the above three calculations for ph = 8, to learn the stoichiometry of proton release from those two equilibria, in the event of a ph swing up to ph 8.

5 At phs below the pair pk A s, there will be an analogous decrease in net proton release, because both ATP and ADP will become more fully protonated. Therefore, we conclude that because the reagent and the product we have considered so far have closely matched pk A s, their contribution to ph dependence will never be very large *, and we turn our attention to the pk A of 7.20 pertaining to P i and use!g = -32 kj/mol for the reaction (1) (Figure3.16). Consider ATP 4- + H 2 # ADP P i (the net proton-free reaction) (1)!G = -32 kj/mol Also consider P i - # P i 2- + H + (2) pk A = 7.2 a Write an expression for the equilibrium constant of reaction 1 in terms of the concentrations of the relevant chemicals. b Write an expression for the equilibrium constant of reaction 2 in terms of the concentrations of the relevant chemicals. 2- c Write an expression for the total concentration of [P i,tot ] = [P i- ] + [P i ], in terms of the K A of P - i and any other relevant concentrations. d Use the results of a and c to write an expression for the equilibrium constant of reaction 1 in terms of [P i,tot ]. e We define an effective free energy for the hydrolysis of ATP,!G eff, related to an effective K eq, K eq,eff defined as follows: K eq,eff = [ADP][P ] i,tot [ATP] Write an expression for K eq,eff in terms of K eq, the K A of P - i and any other relevant concentrations. f Use the result of e, simplify assuming relatively low [H] ([H + ] << K A, because we will be studying trends at high ph). Take the natural ln of both sides, exploit the fact that ln(x) = 2.3 log 10 (x), and derive an expression for!g eff g Does your result agree with what is shown in Figure 3.16? (yes/no AND a sentence explaining the basis for your choice.) * While there are other ionizable protons (with other pk A s, these are not considered here because these very high or low pk A s have the significance that the affected groups will always be protonated or always deprotonated: they will not change protonation state under our conditions. Problems from Chapter 4 1 Write equations for the proton equilibria of just the side chains of Arginine, Tyrosine, Cysteine and Glutamic acid, providing structural formulae for each of the acid

6 and the conjugate base forms. (You must indicate which proton is labile with the pk A binding described.) 2 Draw the 2-d structure (no stereochemistry required) of the tetrapeptide DRAT, including all H atoms present at ph 7. Circle all chiral centres. Put boxes around all the peptide linkages (including only the atoms that are coplanar. 3 Look up the structure of DTNB, which is used to quantify free sulfhydryl groups, and draw it. Draw a simple mechanism for the reaction of a cysteine sulfhydryl with DTNB. 4 In what order will Glu, Leu, Phe, Lys elute from Dowex? Problems from Chapter 5 1 Provide a definition for 'homomultimeric' (30 words or less) Provide a definition of 'heterotetrameric' (30 words or less). 2 ur text states that upon trypsin digestion, a protein will be cleaved into a number of fragments equal to one plus the number of Lys and Arg residues. What are two exceptions to this rule? 3 Both Ser and Tyr are subject to phosphorylation,, which results in the modified amino acid side chain becoming charged. Considering the most common locations of each of Ser and Tyr, which modification will be more likely to disrupt the protein structure, and why (30 words or less). 4 A heptapeptide is fully digested and analyzed, and revealed to be composed of the amino acids FKMNPQV (here listed in alphabetical order, NT their order of occurrence in the peptide.) Consider the following results and deduce the primary structure of the peptide. Trypsin cleavage results in formation of a tetrapeptide and a tripeptide. Subsequent digestion with chymotrypsin has no effect on the tetrapeptide but resolves the tripeptide into a dipeptide and P. This dipeptide has an absorption maximum at 258 nm. Reaction of the tetrapeptide with Edman's reagent, followed by acid hydrolysis releases the compound shown below. N N H C S H H 3 C CH 3

7 Reaction with cyanogen bromide converts the tetrapeptide into two dipeptides, of which one dipeptide has a mass of Which are likely to be most similar? (a) the triose phosphate isomerase from humans and triose phosphate isomerase from a mushroom or (b) triose phosphate isomerase from humans and phosphofructose kinase from humans? Why? (30 words or less). Problems from Chapter 6 1 The structure below shows only backbone atoms of a small protein. What atoms are backbone atoms? (list them for one amino acid that is not at either end of the chain). Circle an $ helix NLY (Clearly, you will not draw a perfect circle, but some irregular bag shape). Draw another bag, this time around two strands of %-sheet NLY. Label each bag so that it is clear which is which. Say whether the two strands of %-sheet you identified are parallel or antiparallel.

8 3 Discuss the potential contributions of the side chains of Ile, Lys, Gln and Glu to hydrophobic, van der Waals, ionic and hydrogen bonding interactions. 4 Children retain regions called growth plates at the ends of their bones, where de novo synthesis persists and allows elongation of the bones. For a bone to gain 1 cm of length in a month, how many new molecular lengths of tropocollagen must be added per hour in order for collagen fibers to keep pace. Imagining that a bone is 2 cm across and that half of its cross-sectional area is tropocollagen, how many molecules per minute must be added. Devise a human-scale model for tropocollagen based on everyday objects (analogous to Prof. Miller's model for a bacterial chromosome, described in class). 5 A protein with an as-isolated molecular weight of 240,000 Da is found to behave as only an 80 kda species upon treatment with 6 M Guanidinium HCl. However in the presence of 10 mm %-mercaptoethanol as well two species are found, of molecular weights 15 kda and x kda. What is x? Explain the above observations, including how the two treatments each act to produce different molecular weights from that of the native protein. If you wished to convert the protein to an 80 kda unit, what sort of interactions will you probably have to disrupt? Suggest three different amino acid substitutions that should accomplish this. 6 Draw a stretch of antiparallel %-strand composed of three residues in each strand separated by a two-residue tight turn. If the amino acids in the first strand are Asn, Trp, Val, in that order, suggest energetically-favourable amino acid identities for the 6 th, 7 th and 8 th amino acids. Practice drawing 1.5 turns of $-helix, a three-residue length of parallel % strand and a three-residue length of antiparallel % strand. (As noted in class, you must be able to draw all 20 amino acids.)