Extending the absorbing boundary method to fit dwell-time distributions of molecular motors with complex kinetic pathways

Abstract

Dwell-time distributions, waiting-time distributions, and distributions of pause durations are widely reported for molecular motors based on single-molecule biophysical experiments. These distributions provide important information concerning the functional mechanisms of enzymes and their underlying kinetic and mechanical processes. We have extended the absorbing boundary method to simulate dwell-time distributions of complex kinetic schemes, which include cyclic, branching, and reverse transitions typically observed in molecular motors. This extended absorbing boundary method allows global fitting of dwell-time distributions for enzymes subject to different experimental conditions. We applied the extended absorbing boundary method to experimental dwell-time distributions of single-headed myosin V, and were able to use a single kinetic scheme to fit dwell-time distributions observed under different ligand concentrations and different directions of optical trap forces. The ability to use a single kinetic scheme to fit dwell-time distributions arising from a variety of experimental conditions is important for identifying a mechanochemical model of a molecular motor. This efficient method can be used to study dwell-time distributions for a broad class of molecular motors, including kinesin, RNA polymerase, helicase, F1 ATPase, and to examine conformational dynamics of other enzymes such as ion channels.myosin ͉ single molecule ͉ waiting-time distributions ͉ pause durations T he movements of molecular motors are frequently recorded in biophysical experiments using tools such as optical trap assays and single molecule fluorescence assays. Due to transitions of conformational and chemical states, the motions of molecular motors usually show alternations between an enzyme's moving and pausing behaviors. For example, doubleheaded myosin VI moving on an actin filament demonstrates a mechanical stepping behavior ( Fig. 1a) (1), whereas the events of actin binding and unbinding of a single-headed myosin V construct show alternate phases of oscillating and pausing (Fig. 1b) (2). Collecting a large number of these events and performing statistical analysis provides insight into the kinetics and mechanochemical characteristics of an individual molecule.Dwell events arise from pauses in mechanical stepping (Fig. 1a) or stochastic delays before a binding-unbinding transition (Fig. 1b). Each dwell represents an experimentally observable event, which can be a single conformational or chemical state, or a collective number of states. The dwell time, or the duration of a dwell, is determined by the probability of exiting a dwell after the time entering it. Histograms of dwell times, also called dwell-time distributions, waiting-time distributions, or distributions of pause durations, are widely used to decipher single molecule kinetics.The dynamics of an enzyme's activity can be modeled as a number of kinetic states using kinetic equations (3) or mechanical coordinates using diffusion-based (Fokker-Planck) equations (4). For quest...

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