While seemingly straightforward in principle, the reliable estimation of rate constants is seldom easy in practice. Numerous issues, such as the complication of poor reaction coordinates, cause obvious approaches to yield unreliable estimates. When a
reliable order parameter is available, the reactive flux theory of Chandler allows the rate constant to be extracted from the plateau region of an appropriate reactive flux function. However, when applied to real data from single-molecule experiments or molecular dynamics simulations, the rate can sometimes be difficult to extract due to the numerical differentiation of a noisy empirical correlation function or difficulty in locating the plateau region at low sampling frequencies. We present a modified version of this theory which does not require numerical derivatives, allowing rate constants to be robustly estimated from the time-correlation function directly. We compare these approaches using single-molecule force spectroscopy measurements of an RNA hairpin.
Single-molecule force spectroscopy has proven to be a powerful tool for studying the kinetic behavior of biomolecules. Through application of an external force, conformational states with small or transient populations can be stabilized, allowing the
m to be characterized and the statistics of individual trajectories studied to provide insight into biomolecular folding and function. Because the observed quantity (force or extension) is not necessarily an ideal reaction coordinate, individual observations cannot be uniquely associated with kinetically distinct conformations. While maximum-likelihood schemes such as hidden Markov models have solved this problem for other classes of single-molecule experiments by using temporal information to aid in the inference of a sequence of distinct conformational states, these methods do not give a clear picture of how precisely the model parameters are determined by the data due to instrument noise and finite-sample statistics, both significant problems in force spectroscopy. We solve this problem through a Bayesian extension that allows the experimental uncertainties to be directly quantified, and build in detailed balance to further reduce uncertainty through physical constraints. We illustrate the utility of this approach in characterizing the three-state kinetic behavior of an RNA hairpin in a stationary optical trap.
