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Thermodynamics of the collapse transition of the all-backbone peptide Gly15

Simulations show Gly$_{15}$, a polypeptide lacking any side-chains, can collapse in water. We assess the hydration thermodynamics in this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here the end-to-end distance ($r$) in the chain. To examine the role of the various conformations for a given $r$, we study the conditional distribution, $P(R_g | r)$, of the radius of gyration for a given value of $r$. $P(R_g|r)$ is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this insight within a multistate generalization of the potential distribution theorem, we calculate a reasonable upper bound for the hydration free energy of the peptide for a given $r$. On this basis we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intra-peptide and hydration effects, with intra-peptide contributions favoring collapse by a small margin. The favorable intra-peptide interactions are primarily electrostatic in origin, and found to arise primarily from interaction between C=O dipoles, hydrogen bonding interaction between C=O and N-H groups, and favorable interaction between N-H dipoles.