Problem Set 4 Solution - Answers to Problem Set#4 1 A The...

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Answers to Problem Set #4 : 1. A. The plot is figure 1 from an excellent review on the stability of thermophilic proteins ( Protein Science , 15 , 1569-1578 ’06). Plugging T = T m into the given equation yields ! G(T) = 0. But ! G(T) = -RT ln(K), so when ! G = 0, K = 1. To show the T S and T H relations, just start from ! G(T) = - RT ln (K) = ! H T ! S . The maximum protein stability will be at the T where ! G is at a maximum. To find this temperature, note the derivative of ! G with respect to T is just ! S. So ! G will be maximized when ! S is 0, which is the definition of T S . Similarly, after some simple algebra and calculus, we find the derivative of K with respect to T is ( ! H/RT) exp(- ! H/RT + ! S/R), which will be equal to 0 when ! H is 0. Thus, K is maximal when ! H is 0, or at T H . B. Just from the shape of the plot, we can see that the curve bends downward, so linear extrapolation of DG based on the slope of the curve in the near-linear region around T M will overestimate the protein stability at room temperature. The linear extrapolation would be exactly correct if ! C P were equal to 0.
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  • Fall '11
  • PONDER
  • Proteins, AiB, folding rate, maximum protein stability

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