Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., single-step or unified) alchemical transformations com- monly used in the prediction of hydration and relative binding free energies (RBFE). We first classify several known challenges in these calculations into three categories: catastrophes have long been resolved using softcore potentials, the remaining two large values of the softcore parameters, as might be used in trying to solve the particle problems occur much more sporadically and can result in either numerical instabil- ity (i.e. complete failure of a simulation) or inconsistent estimation (i.e. stochastic convergence to an incorrect result). The particle collapse problem stems from an im- balance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to collapse issue. Often no satisfactory compromise exists with the existing softcore po- tential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial func- tions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple, yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides a vast improvement in terms of consistency across all cases. Lastly, we compare the concerted SSC(2) approach against the gold- standard stepwise (a.k.a., decoupled or multi-step) scheme over a large set of RBFE calculations as might be encountered in drug discovery. 

Journal of Chemical Theory and Computation