Telescoping-Solvation-Box Protocol-Based Umbrella Sampling Method for Potential Mean Force Estimation.

Previously, it was shown that the telescoping box scheme, in combination with adaptive steered molecule dynamics (ASMD), can be used to estimate the potential of mean force (PMF) with a decrease in computational cost associated with large solvation boxes. Since ASMD reduces to umbrella sampling (US) in the limit of infinitely slow pulling velocity, a hypothesis was made that the telescoping box scheme can be extended to include the US method. The hypothesis was tested using the unfolding pathway of a polyalanine peptide in a water box and translocation of α-tocopherol through the human membrane. Two different approaches were tried: telescoping US (TELUS), in which the number of solvent molecules was linearly coupled to the reaction coordinate, and Block-TELUS, which was a compromise between the fixed solvation box of the US and the window-wise variable solvation box of TELUS. In the case of polyalanine peptide in a water box, both approaches gave overlapping potential of mean force (PMF) concerning the benchmark US-PMF. Window-wise comparison of properties like root-mean-square inner product, Ramachandran plot, α-helix content, and hydrogen bond formation was used to verify that both approaches captured the same dynamics as the US method. Applying the Block-TELUS protocol in the system with diffusing α-tocopherol through the bilayer resulted in overlapping PMF to its US benchmark. A comparison between the window-wise orientation of the chromanol headgroup also produced almost identical results. This study concluded that with the careful application of telescoping solvation boxes, a less computationally expensive US could be performed for systems where the effect of distant solvent molecules on the configurational space sampled in the window depends on the value of the reaction coordinate.