Faster Binding Free-Energy Landscape Calculation by Virtual-State Coupled Adaptive Umbrella Sampling

Abstract

Accurate calculations of binding free-energy landscapes provide useful thermodynamic quantities to understand a given biological process. Adaptive umbrella sampling (AUS) aims to calculate such binding free-energy landscape along a given reaction coordinate. Typically, AUS requires a biasing force, which is defined from a canonical probability distribution of the reaction coordinate; and the distribution is updated iteratively until the system randomly walks along the reaction coordinate. However, convergence of the above iterative process may require enormous sampling, and hence computationally expensive. We established a novel method “virtual-state coupled adaptive umbrella sampling” (V-AUS) by enhancing the sampling along a virtual degree of freedom. The V-AUS quickly estimates free-energy landscape compared to AUS. We applied this method successfully to obtain the free-energy landscape for flexible binding between two Aβ-peptides in explicit water at room temperature (J. Comput. Chem. vol. 36, p1489, 2015). To further improve the V-AUS ensuring even faster convergence to uniform sampling we designed a set of methods on top of V-AUS. We define grids around a receptor in which its ligand is placed to obtain a better initial set of conformations. Secondly, sampling errors from the estimated canonical probability distribution due to inadequate sampling are removed by Markov state modeling. Thirdly, we introduce a set of novel fitting schemes to parameterize the biasing force in terms of reaction coordinate. These set of methods to improve V-AUS are tested for Ala-pentapeptide dimerization. We conclude that by using such advanced set of methods faster free-energy calculation of flexible molecular docking is possible. Currently a study for larger biological system is ongoing.