Entropy in molecular association and folding: Theory and computation

This thesis addresses two central questions regarding entropy changes in protein folding and molecular recognition: (1) Can the entropy of a system be decomposed into individual components arising from particular atomic groups or physical interactions? and (2) Can molecular association thermodynamics be reliably calculated using current computational methods? To address the first question, the statistical-mechanical justification for entropy decomposition is theoretically investigated via cumulant and beta-derivative expansions of the entropy. The cumulant expansion demonstrates that entropy components may indeed be meaningfully ascribed to particular groups or interactions, although these components are coupled both explicitly via cross-terms and implicitly through the Boltzmann factor. The beta-derivative expansion ($\beta$DE) is shown to yield a complete decomposition of entropy, in that, the total entropy is completely partitioned amongst the contributing groups or interactions, with no individually unattributable cross-terms remaining. The question of calculating molecular association thermodynamics is examined via computational analysis of binding and solvation in a model peptide system. In particular, the gas $\Leftrightarrow$ crystal $\Leftrightarrow$ solution phase equilibrium thermodynamics of cyclic di-glycine (cGG) and cyclic di-alanine (cAA) is computed using a variety of techniques, and the results are compared to experimental data. The calculated cGG gas-to-solution free energy and gas-to-crystal enthalpy agree very well with experimental values; however, the gas-to-crystal entropy is overestimated by 15 eu. Of particular note, a reliable value of 14 eu is obtained for the association entropy barrier to gas $\Rightarrow$ crystal transfer, the unfavorable net result of exchanging translational and rotational freedom in the gas phase for vibrational motion in the crystal. A mean-field Einstein Model underestimates the vibrational entropy of the crystal by 15 eu and, thus, appears too crude for this study. Consequently, the gas-to-crystal transfer thermodynamics is reanalyzed using a Lattice Dynamical Model of the crystal. The calculated cGG gas-to-crystal enthalpy lies within 0.5 kcal/mol of the experimental value, while the calculated gas-to-crystal entropy change still significantly overestimates the experimental value, suggesting an incompatibility between the molecular parameterization and calculations of the thermodynamics of low-frequency modes of vibration