(700b) The Hydrophobic Effect: Developing a Simple Yet Quantitatively Accurate Coarse-Grained Model

Hydrophobic solvation free energies undergo a cross-over at nanometer length-scales. For small solutes, the free energies grow roughly as the volume of the solute and for larger solutes, they grow as the surface area of the solute. Several problems of biological assembly, notably protein folding, involve a collapse process that takes the system from one regime to the other. Hence, a model that aspires to capture the hydrophobic effect has to accurately describe the crossover between these two regimes. The theory of the hydrophobic effect proposed by Lum, Chandler and Weeks (LCW) successfully describes this cross-over by coarse-graining the solvent density and analytically integrating out solvent fluctuations on length-scales smaller than the coarse-graining length. Since the implementation of LCW theory can be computationally demanding for biological systems, ten Wolde and Chandler proposed a simple lattice gas model. In this work, we extend the lattice gas model and make it quantitatively accurate, while retaining much of its simplicity. We propose using a modified lattice gas to better capture the surface area dependence at large length-scales as well as improve upon the model by relaxing certain assumptions about the unbalancing of attractive interactions on length scales smaller than the coarse-graining length. We demonstrate quantitative agreement between results obtained using our model and those from atomistic simulations, and proceed to apply the model to several systems relevant to biological assembly.