HW2 - Department of Chemical Engineering ChE 170 University...

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Unformatted text preview: Department of Chemical Engineering ChE 170 University of California, Santa Barbara Fall 2010 Problem Set No. 2 Due: 10/21/10 at the start of class Objective : To develop a understanding of the thermodynamics and kinetics of protein folding, binding, and enzyme catalysis. Review problems You should pay special attention to these questions after reading. Note that the answers are given in the back of the book. Formulate your answers fully first and then check them. This can be a significant aid in your understanding of the material, and similar questions may be asked on the final. You do not need to provide written answers in the solutions you hand in. • ECB 4-10 • ECB 4-14 • ECB 4-15 • ECB 4-17 • ECB 4-21 Problem 1 Name the amino acid: a) contains sulfur but cannot form disulfide bonds; always the first amino acid synthesized in newly-translated proteins b) not often found in helices or beta sheets; main constituent of collagen c) biochemical precursor to serotonin; thought to be effective as a sleep aid d) side chain is an analogue of methanol; it’s -OH group is often the site of the attachment of sugars (glycosylation) or phosphate groups (phosphorylation) e) small shifts in pH near neutral conditions can cause large shifts in net charge due to protonation/deprotonation; as a result, often present in catalytic sites f) negatively-charged amino acid often used as a flavor-enhancer in food (in a salt form) Problem 2 Consider a two-state folding protein described by the reaction: g G ¡ ¢ £ ¤ ¥¢¦ ¥g¦ where “U” stands for unfolded and “F” folded. Imagine now that a denaturant “D” is added to the system, such as the small molecule urea, that destabilizes the folded state. One possible (approximate) mechanism by which this might occur is through binding to the unfolded state: g § ¨ G © ¡ g¨ £ ª ¤ ¥g¨¦ ¥g¦¥¨¦ a) Find an expression for the fraction of protein that is folded, « , in terms of £,£ ª , and ¥¨¦ . Hint: consider that the total concentration of protein, regardless of state, must be some constant, say ¬ ­ . b) Find an expression for the ratio of the folded to the unfolded protein concentration, ® ¤ ¥¢¦/¯¥g¦ § ¥g¨¦° , in terms of £,£ ª , and ¥¨¦ . c) In the limit that no denaturant is added, £ ¤ ® . On the other hand, for finite denaturant concentration, one might define an “effective” equilibrium constant £ eff ¤ ® . On this basis, find an expression for the effective folding free energy Δ± eff in terms of the actual (zero-denaturant) folding free energy Δ± , £ ª , ¥¨¦ , and ² . d) A series of spectroscopic experiments measures ® for various denaturant concentrations ¥¨¦ , giving the data below. Using these and an appropriate linear regression , determine both £ and £ ª . If the temperature is 300 £ , also estimate the folding free energy Δ± in kcal/mol....
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HW2 - Department of Chemical Engineering ChE 170 University...

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