Springs and speeds in free energy reconstruction from irreversible single-molecule pulling experiments

The nonequilibrium work relation allows for the calculation of equilibrium free energy differences between states based on the exponential average of accumulated work from irreversible transitions. Here, we compare two distinct approaches of calculating free energy surfaces from unidirectional single-molecule pulling experiments: the stiff spring approximation and the Hummer-Szabo method. First, we perform steered molecular dynamics simulations to mechanically stretch the model peptide deca-alanine using harmonic potentials with different spring stiffnesses and at various constant pulling velocities. We then calculate free energy surfaces based on the two methods and their variants, including the first and second cumulant expansion of the exponentially weighted work and the Gaussian position approximation for the delta function in Hummer and Szabo's expression. We find that with large harmonic force constants, the second cumulant expansion performs well in conjunction with either the stiff spring approximation or the Hummer-Szabo method. When interpreting dynamic force spectroscopy (pullings at different speeds), the second cumulant expansion of the stiff spring approximation performs the best when pulling velocities are similar, but variants of the Hummer-Szabo perform the best when they are spread over a large spectrum. While these conclusion are not definitive for all systems, the insights should prove useful for scientists interpreting nonequilibrium pulling experiments.