title: Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories.
abstract: Use of harmonic guiding potentials is the most commonly adopted method for implementing steered molecular dynamics (SMD) simulations, performed to obtain potentials of mean force (PMFs) using Jarzynski's equality and other nonequilibrium work (NEW) theorems. The stiff spring approximation (SSA) of Schulten and co-workers enables calculation of the PMF by using the work performed along many SMD trajectories in NEW theorems. We discuss and demonstrate how a high spring constant, k, required for the validity of the SSA can violate another requirement of SSA, the validity of Brownian dynamics in the system under study. These result in skewed work distributions with their width increasing with k. The skew and broadening of work distributions result in biased estimation (through invoking NEW theorems) of the PMF. Remarkably, the skewness and the broadening of work distributions are independent of the average drift velocity and physical asymmetries and can only be attributed to using too-stiff springs. We discuss the proper upper limit for k such that the inertial effects are minimized. In the presence of inertial effects, using the peak value (rather than the statistical mean) of the work distributions vastly reduces the bias in the calculated PMFs and improves the accuracy.
authors.affiliation: Department of Physics, University of Guelph , Guelph, Ontario N1G 2W1, Canada.
authors.forename: Mostafa
authors.identifier: 0000-0002-6843-5321
authors.initials: M
authors.lastname: Nategholeslam
authors.affiliation: Guelph-Waterloo Physics Institute and Department of Physics, University of Guelph , Guelph, Ontario N1G 2W1, Canada.|Department of Physics and Biophysics Interdepartmental Group, University of Guelph , Guelph, Ontario N1G 2W1, Canada.
authors.forename: C G
authors.initials: CG
authors.lastname: Gray
authors.affiliation: Department of Physics and Biophysics Interdepartmental Group, University of Guelph , Guelph, Ontario N1G 2W1, Canada.|Department of Physics, Capilano University , North Vancouver, British Columbia V7J 3H5, Canada.
authors.forename: Bruno
authors.initials: B
authors.lastname: Tomberli