Consider the coil-helix transition for a polypeptide containing 50 amides. At a certain temperature, the equilibrium constant for adding an amide to a helical region is s = 1; the helix initiation parameter is σ = 10-4. Statistical weights are relative to the species that is 100% coil.
a. Write an expression in terms of σ and s for the statistical weight of the species that has all the possible amides in the α -helix conformation.
b. Write an expression in terms of σ and s for the statistical weight of the species that has 20 amides in the α-helix conformation in three separate helical regions.
c. Which of all the possible species is in the highest concentration? That is, which of all the possible species has the highest statistical weight?
d. If s were 10, which of all possible species would have the highest concentration?
e. Roughly sketch a plot of f = fraction of amides in the σ-helix conformation vs. temperature. The ΔH° for the reaction helix to coil is negative. Label which temperature region corresponds to the helix and which to the coil.
f. Write an equation for fin terms of σ s, and Q.
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