Infinite switch simulated tempering in force (FISST)

Many proteins in cells are capable of sensing and responding to piconewton-scale forces, a regime in which conformational changes are small but significant for biological processes. In order to efficiently and effectively sample the response of these proteins to small forces, enhanced sampling techniques will be required. In this work, we derive, implement, and evaluate an efficient method to simultaneously sample the result of applying any constant pulling force within a specified range to a molecular system of interest. We start from simulated tempering in force, whereby force is added as a linear bias on a collective variable to the system's Hamiltonian, and the coefficient is taken as a continuous auxiliary degree of freedom. We derive a formula for an average collective-variable-dependent force, which depends on a set of weights learned on-the-fly throughout a simulation, that reflect the limit where force varies infinitely quickly. Simulation data can then be used to retroactively compute averages of any observable at any force within the specified range. This technique is based on recent work deriving similar equations for infinite switch simulated tempering in temperature, which showed that the infinite switch limit is the most efficient for sampling. Here, we demonstrate that our method accurately samples molecular systems at all forces within a user defined force range simultaneously and show how it can serve as an enhanced sampling tool for cases where the pulling direction destabilizes states that have low free-energy at zero-force. This method is implemented in and freely distributed with the PLUMED open-source sampling library, and hence can be readily applied to problems using a wide range of molecular dynamics software packages.