Precisely and Accurately Inferring Single-Molecule Rate Constants

The kinetics of biomolecular systems can be quantified by calculating the stochastic rate constants that govern the biomolecular state vs time trajectories (i.e., state trajectories) of individual biomolecules. To do so, the experimental signal vs time trajectories (i.e., signal trajectories) obtained from observing individual biomolecules are often idealized to generate state trajectories by methods such as thresholding or hidden Markov modeling. Here, we discuss approaches for idealizing signal trajectories and calculating stochastic rate constants from the resulting state trajectories. Importantly, we provide an analysis of how the finite length of signal trajectories restricts the precision of these approaches and demonstrate how Bayesian inference-based versions of these approaches allow rigorous determination of this precision. Similarly, we provide an analysis of how the finite lengths and limited time resolutions of signal trajectories restrict the accuracy of these approaches, and describe methods that, by accounting for the effects of the finite length and limited time resolution of signal trajectories, substantially improve this accuracy. Collectively, therefore, the methods we consider here enable a rigorous assessment of the precision, and a significant enhancement of the accuracy, with which stochastic rate constants can be calculated from single-molecule signal trajectories.