Improving the Computational Efficiency of the Adaptive Biasing Force Sampling by Leveraging the Telescopic-Solvation Scheme

Abstract

The number of solvent molecules present in the system during molecular dynamics is the balancing act between the need to remove the boundary effects present in the system and the computational cost. Application of the telescopic-solvation box scheme during the estimation of the potential of mean force (PMF) can be advantageous in situations where the contribution of solvent far from the site of interest toward the whole PMF is negligible, as previously demonstrated in the case of adaptive steered molecular dynamics and umbrella sampling. This work explores the application of the telescopic-solvation box scheme during enhanced sampling by the stratified adaptive biasing force (ABF) family of methods, including ABF, extended ABF, welltempered-metadynamics extended ABF, and multiwalker extended ABF. During this scheme, the number of water molecules differed in each stratified window, whose number depended on the value of the collective variable being sampled in that window. Two systems were used to verify the viability of the telescopic scheme: unfolding (Ala) 10 peptide in water and insertion of α-tocopherol in a bilayer membrane. In the first system, the 1D and 2D PMFs obtained by the telescopic-solvation scheme matched well with the benchmark PMFs estimated with a standard solvation box. The minimal energy path connecting the α-helical and extended conformational states revealed that the unfolding process of (Ala) 10 in water involved multiple closely spaced metastable states. As for the second system, the PMF, equilibrium location of α-tocopherol, and the free energy associated with the desorption and flipping of α-tocopherol obtained within the scope of the telescopic-solvation box scheme agreed with their standard solvation box values. Enhanced sampling with ABF and its variants in conjunction with the telescopic-solvation scheme results in a similar quality of the estimated PMF compared to sampling with a standard solvation box, albeit with reduced computational cost.