Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent-induced interactions between exposed hydrophobic sidechains or solute-solvent dispersion interactions. These "nonpolar" effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many-body character. We have explored an alternate, Lazaridis-Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini-protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.

We describe methods for physics-based protein design and some recent applications from our work. We present the physical interpretation of a MC simulation in sequence space and show that sequences and conformations form a well-defined statistical ensemble, explored with Monte Carlo and Boltzmann sampling. The folded state energy combines molecular mechanics for solutes with continuum electrostatics for solvent. We usually assume one or a few fixed protein backbone structures and discrete side chain rotamers. Methods based on molecular dynamics, which introduce additional backbone and side chain flexibility, are under development. The redesign of a PDZ domain and an aminoacyl-tRNA synthetase enzyme were successful. We describe a versatile, adaptive, Wang–Landau MC method that can be used to design for substrate affinity, catalytic rate, catalytic efficiency, or the specificity of these properties. The methods are transferable to all biomolecules, can be systematically improved, and give physical insights.

Computational protein design relies on simulations of a protein structure, where selected amino acids can mutate randomly, and mutations are selected to enhance a target property, such as stability. Often, the protein backbone is held fixed and its degrees of freedom are modeled implicitly to reduce the complexity of the conformational space. We present a hybrid method where short molecular dynamics (MD) segments are used to explore conformations and alternate with Monte Carlo (MC) moves that apply mutations to side chains. The backbone is fully flexible during MD. As a test, we computed side chain acid/base constants or pKa’s in five proteins. This problem can be considered a special case of protein design, with protonation/deprotonation playing the role of mutations. The solvent was modeled as a dielectric continuum. Due to cost, in each protein we allowed just one side chain position to change its protonation state and the other position to change its type or mutate. The pKa’s were computed with a standard method that scans a range of pH values and with a new method that uses adaptive landscape flattening (ALF) to sample all protonation states in a single simulation. The hybrid method gave notably better accuracy than standard, fixed-backbone MC. ALF decreased the computational cost a factor of 13.

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