ProteinLigand Binding  Implicit Solvation
We use statistical thermodynamics concepts to develop models and computational algorithms to study biophysical processes. Given the complexity of biological systems, it is important to strike a balance between theoretical rigor and physiochemical intuition to capture essential features of the systems and deliver accurate yet computationally tractable models. Because computer hardware and algorithms continue to advance, the rigor/computational complexity "sweet spot" is a continuously moving target. Many models that were computationally intractable only a few years ago are not routine. Therefore in this area, it is important to be on top of both theoretical concepts as well as the latest technological advances.
Thermodynamics of ProteinLigand BindingStatistical Thermodynamics Theory and Computer Models. Thermodynamically, the strength of the association between a ligand molecule and its target receptor is measured by the standard free energy of binding. Rigorous statistical mechanics theories of molecular association equilibria exist. I have authored a book chapter (Gallicchio & Levy 2011a) reviewing the latest theoretical developments on the theory of noncovalent association and their implications for computer models aimed at binding free energy estimation. The theoretical account covers the role of conformational heterogeneity, and entropic and conformational reorganization concepts that, although crucial for the understanding of binding equilibria, are generally underappreciated and rarely properly accounted for in computer models. We have recently developed an analytical model of alchemical molecular binding (Kilburg & Gallicchio 2018) based on the idea that the interaction energy between the receptor and the ligand is the convolution of two random processes, one that follows the central limit statistics and the other that follows max statistics. Even more recently we used this analytical model to identify novel perturbation potentials and softcore functions to accelerate the convergence of alchemical binding free energy calculations (Pal & Gallicchio 2019). Computational binding free energy models are commonly based on molecular mechanics force fields and ways to efficiently sample molecular configurations (Gallicchio & Levy 2011b). Some of the most promising approaches we have identified employ extended ensembles combined with Hamiltonianhopping techniques. The SingleDecoupling Binding Free Energy Method (SDM) While at Rutgers, I led the development of a novel approach to absolute binding free energy estimation and analysis we called the Binding Energy Distribution Analysis Method (BEDAM)(Gallicchio et al. 2010). More recently, we implemented the method in the OpenMM molecular simulation software and we renamed it the SingleDecoupling Binding Free Energy method to underscore the fact that it requires only one free energy leg rather than two with the more commonly used DoubleDecoupling Method. The model is based on sound statistical mechanics theory of molecular association and efficient computational strategies built upon parallel Hamiltonian replica exchange sampling and multistate thermodynamic reweighting. The ability to carry out extensive conformational sampling is one of the main advantages of SDM over existing FEP and absolute binding free energies protocols with explicit solvation which suffer from a limited exploration of conformational space (Pal & Gallicchio 2019).Why implicit solvation? Solvent models used in
molecular simulations can be roughly divided into two camps. Models in the first category explicitly include individual solvent molecules with their interactions described at the same level of theory as solute interactions. These are called explicit solvent models. Models in the second camp describe the solution as a continuous medium often described by macroscopic parameters such as density,
dielectric permittivity, and surface tension. These implicit solvent models take a variety of forms and are often described as approximate versions of explicit models. Although this is often true in practice,
statistical thermodynamics theory tells us that the level of accuracy achievable by implicit models is no more nor less high than explicit models. This is because both models are to be judged on how accurately they describe the solvent potential of mean force of the solute, a welldefined statistical thermodynamic quantity which measures the distribution of conformations of the solute in solution.
AGBNP also includes nonelectrostatic terms incorporating lessons learned over a decade of research. We found that models based on the decomposition of nonpolar hydration into a cavitation free energy (described by the solute surface area) and van der Waals dispersion forces (modeled using a function based on the atomic Born radii) give a better description of fundamental processes such as protein folding and association. The research community is recognizing the benefits of this decomposition and is progressively abandoning the traditional surface area (SA) models of nonpolar hydration in favor of these new models. One of the design principles of AGBNP is to reduce as much as possible the use of empirically adjusted parameters. For example, many commonly used GB/SA implicit solvent models employ empirically adjusted functional forms not only for energetic terms but also for essentially geometrical quantities, such as surface areas and Born radii. I believe that this practice leads to inaccuracies and poor transferability. We were able to show that advanced computational geometry algorithms make the parametrization of geometrical quantities unnecessary and, by doing so, leads to models that are accurate not only on average but also in the details. Being able to accurately model both large and small conformational changes are important in many applications and in particular in proteinligand binding. We are continuously updating the AGBNP model to expand its range of applicability. Recent efforts have been focused on the GPU implementation of AGBNP as part of OpenMM molecular simulation software (Zhang et al 2017).

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