NDLI: Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lawley, Sean D. Miles, Christopher E. Keener, James P.
Copyright Year	2018
Abstract	We propose and analyze a mathematical model of cargo transport by nonprocessive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position follows a stochastic differential equation (SDE) that depends on the discrete states of the motors. The resulting system for the cargo position is consequently an SDE that randomly switches according to a Markov jump process governing motor dynamics. To study this system we (1) cast the cargo position in a renewal theory framework and generalize the renewal reward theorem and (2) decompose the continuous and discrete sources of stochasticity and exploit a resulting pair of disparate timescales. With these mathematical tools, we obtain explicit formulas for experimentally measurable quantities, such as cargo velocity and run length. Analyzing these formulas then yields some predictions regarding so-called nonprocessive clustering, the phenomenon that a single motor cannot transport cargo, but two or more motors can. We find that having motor stepping, binding, and unbinding rates depend on the number of bound motors, due to geometric effects, is necessary and sufficient to explain recent experimental data on non-processive motors.
Sponsorship	National Science Foundation
Starting Page	2511
Ending Page	2532
Page Count	22
File Format	PDF
ISSN	00361399
DOI	10.1137/17M1156824
e-ISSN	1095712X
Issue Number	5
Volume Number	78
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-20
Access Restriction	Subscribed
Subject Keyword	Equations and systems with randomness switching SDEs intracellular transport Applications of Markov renewal processes stochastic hybrid systems Stochastic ordinary differential equations Applications of continuous-time Markov processes on discrete state spaces renewal reward theory Biophysics molecular motors
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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