Implementation of telescoping boxes in adaptive steered molecular dynamics (ASMD)

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics. The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jaryzinski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the use of the very large solvent boxes required to simulate the entirety of the steered coordinate. We introduce a scheme, called a telescoping box, within ASMD in which we adjust the solvent box between stages, and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long alpha-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.