Dwell time symmetry in random walks and molecular motors

Abstract

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this paper, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits. Key words: motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor; Markov process; non-equilibrium fluctuations.

revtex, 15 pages, 8 figures, 2 tables. v2: Minor revision, corrected typos, added references, and moved mathematical parts to new appendices

References in corpus (6)

• A Simple Kinetic Model Describes the Processivity of Myosin-V
• Elastic lever arm model for myosin V
• Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes
• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Back-stepping, hidden substeps, and conditional dwell times in molecular motors
• Renewal processes and fluctuation analysis of molecular motor stepping

Cited by in corpus (10)

• Stochastic mechano-chemical kinetics of molecular motors: a multidisciplinary enterprise from a physicist's perspective
• Stochastic kinetics of ribosomes: single motor properties and collective behavior
• Distribution of dwell times of a ribosome: effects of infidelity, kinetic proofreading and ribosome crowding
• Discrete step sizes of molecular motors lead to bimodal non-Gaussian velocity distributions under force
• The efficiency of the molecular motors
• Dynamics of non-Markovian exclusion processes
• Stochastic kinetics of a single headed motor protein: dwell time distribution of KIF1A
• Cycle completion times probe interactions with environment
• First-passage problems in DNA replication: effects of template tension on stepping and exonuclease activities of a DNA polymerase motor
• Decay times in turnover statistics of single enzymes