# The multiplicity w of a protein with 60 binding sites

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the multiplicity (W) of a protein with 60 binding sites and 5 molecules binding to it. B) What is the probability of a four of a kind (meaning having a hand that has all four suits of a particular card)? C) What is the probability of a full house (three of a kind and two of a kind)?

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Problem #3 A protein can fold into four different conformations A) If the states are iso-energetic, and the system has 1 mole of protein equally mixed between the four states, what is the entropy change of forcing it all into a single confirmation on a per mole basis? (This might occur for example during the process of crystallization.) B) Instead imagine that states B, C, D have a +1 k b T, +2 k b T, and +3 k b T energy increase compared to state A, respectively. What is the probability of finding the protein in each of the states? C) For the system in part (B), now what’s the entropy change (on a per mole basis) of forcing the equilibrium mixture all to state A?
Problem #4 Consider the equation A + B 2C + D A) Write an equation that describes the relationship that must be obeyed between the chemical potentials ( μ A , μ B , μ C , μ D ) of A, B, C, and D at equilibrium B) Based on the log-dependence of chemical potential of each species on its concentration and its standard chemical potential, and the equilibrium requirement in part a) above, derive how the ratio of concentration of A, B, C, and D (i.e., the equilibrium constant) must be related to the differences in their standard chemical potentials (i.e., the G ̊ ). \ C) Suppose that the reaction is occurring in non-equilibrium conditions and that K eq is 10 -6 with concentration of [A] = [B] = 10 -5 M, and [C] = [D] = 10 -4 M. Will the reaction proceed spontaneously, and how much work can be done by the reaction on a per mole basis (if it’s not spontaneous, then how much work can be done by the reverse reaction?)?
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