An Exactly Solvable Stochastic Kinetic Theory of Single-Molecule Force Experiments

The unfolding of a protein in single-molecule pulling experiments subjected to a constant force (force-clamp) and constant velocity (force-ramp) is analyzed by introducing an exactly solvable two-state kinetic model framed based on the general stochastic approach of discrete state and continuous time formulation. The effect of perturbation is interpreted in the presence of dynamic disorder, resulting from intrinsic conformational fluctuations, by deriving an exact analytical expression for the unfolding time distribution, which in turn allowed us to calculate the expressions for the quantities of experimental interest explicitly. In particular, the novelty of our method lies in the fact that it reduced the need for a lengthy calculation, contrary to the previous dynamic disorder studies, and provides a fairly concise but sufficient mathematical analysis, which becomes much easier to implement quantitatively. We tested our results against the measured data from a number of force unfolding experiments on various proteins, ubiquitin, titin, and filamin, and the force unzipping of DNA and observed excellent agreement in each case. This asserts the reliability of the present technique, which suggests a plausible extension of the stochastic kinetic theory in single-molecule force experiments beyond its present-day widespread implications.