The Helix-Coil Transition in a Solvent

In section 4.7.2, we developed the theory of helix-coil transition in the vacuum. We have seen that the theory is based on the reduction of the entire two-dimensional configurational space of a single amino acid residue, (piy/i into three coarse states helix (H), coiled (C), and impossible (/). These roughly correspond to the a-helix, the /3-strand, and the inaccessible regions in the Ramachandran maps. Since the / states involve large positive energies, their probability of occurrence is very small and therefore can be ignored. Thus, for a linear system of M amino-acid residues, each microstate of the system is translated into a sequence of macrostates, symbolically 

This classification of states leads to a simplification of the configurational partition into a sum of terms of the form 

The helix-coil transition as a function of temperature is a result of the competition between the difference in energies and the ratio of degeneracies. In terms of the quantities 

Thus u/v is essentially the ratio of the degeneracies of the two states, and w/v depends essentially on the difference in the energies of the two states. A simplified 1-D model of this kind was treated in section 4.4.2. 

The situation becomes markedly different if the same model is inserted in water. Although the reduction from the detailed microstates to the coarser macrostates, as accomplished in (8.6.33), can be retained, one cannot represent the contribution to the PF of a specific sequence of Hs and Cs by a term of the form (8.6.34). 

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