Quasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Search

Handle URI:
http://hdl.handle.net/10754/599433
Title:
Quasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Search
Authors:
Newby, Jay M.; Bressloff, Paul C.
Abstract:
We present a quasi-steady state reduction of a linear reaction-hyperbolic master equation describing the directed intermittent search for a hidden target by a motor-driven particle moving on a one-dimensional filament track. The particle is injected at one end of the track and randomly switches between stationary search phases and mobile nonsearch phases that are biased in the anterograde direction. There is a finite possibility that the particle fails to find the target due to an absorbing boundary at the other end of the track. Such a scenario is exemplified by the motor-driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker-Planck (FP) equation, which has an additional inhomogeneous decay term that takes into account absorption by the target. The FP equation is used to compute the probability of finding the hidden target (hitting probability) and the corresponding conditional mean first passage time (MFPT) in terms of the effective drift velocity V, diffusivity D, and target absorption rate λ of the random search. The quasi-steady state reduction determines V, D, and λ in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3-state model and show that our quasi-steady state reduction yields results that are in excellent agreement with Monte Carlo simulations of the full system under physiologically reasonable conditions. We then consider a more complex multiple motor model of bidirectional transport, in which opposing motors compete in a "tug-of-war", and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets. © 2010 Society for Mathematical Biology.
Citation:
Newby JM, Bressloff PC (2010) Quasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Search. Bull Math Biol 72: 1840–1866. Available: http://dx.doi.org/10.1007/s11538-010-9513-8.
Publisher:
Springer Nature
Journal:
Bulletin of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
19-Feb-2010
DOI:
10.1007/s11538-010-9513-8
PubMed ID:
20169417
Type:
Article
ISSN:
0092-8240; 1522-9602
Sponsors:
This publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Award No. KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST). PCB was also partially supported by the Royal Society Wolfson Foundation.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorNewby, Jay M.en
dc.contributor.authorBressloff, Paul C.en
dc.date.accessioned2016-02-28T05:51:02Zen
dc.date.available2016-02-28T05:51:02Zen
dc.date.issued2010-02-19en
dc.identifier.citationNewby JM, Bressloff PC (2010) Quasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Search. Bull Math Biol 72: 1840–1866. Available: http://dx.doi.org/10.1007/s11538-010-9513-8.en
dc.identifier.issn0092-8240en
dc.identifier.issn1522-9602en
dc.identifier.pmid20169417en
dc.identifier.doi10.1007/s11538-010-9513-8en
dc.identifier.urihttp://hdl.handle.net/10754/599433en
dc.description.abstractWe present a quasi-steady state reduction of a linear reaction-hyperbolic master equation describing the directed intermittent search for a hidden target by a motor-driven particle moving on a one-dimensional filament track. The particle is injected at one end of the track and randomly switches between stationary search phases and mobile nonsearch phases that are biased in the anterograde direction. There is a finite possibility that the particle fails to find the target due to an absorbing boundary at the other end of the track. Such a scenario is exemplified by the motor-driven transport of vesicular cargo to synaptic targets located on the axon or dendrites of a neuron. The reduced model is described by a scalar Fokker-Planck (FP) equation, which has an additional inhomogeneous decay term that takes into account absorption by the target. The FP equation is used to compute the probability of finding the hidden target (hitting probability) and the corresponding conditional mean first passage time (MFPT) in terms of the effective drift velocity V, diffusivity D, and target absorption rate λ of the random search. The quasi-steady state reduction determines V, D, and λ in terms of the various biophysical parameters of the underlying motor transport model. We first apply our analysis to a simple 3-state model and show that our quasi-steady state reduction yields results that are in excellent agreement with Monte Carlo simulations of the full system under physiologically reasonable conditions. We then consider a more complex multiple motor model of bidirectional transport, in which opposing motors compete in a "tug-of-war", and use this to explore how ATP concentration might regulate the delivery of cargo to synaptic targets. © 2010 Society for Mathematical Biology.en
dc.description.sponsorshipThis publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Award No. KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST). PCB was also partially supported by the Royal Society Wolfson Foundation.en
dc.publisherSpringer Natureen
dc.subjectAxonsen
dc.subjectDendritesen
dc.subjectIntracellular transporten
dc.subjectMolecular motorsen
dc.subjectQuasi-steady stateen
dc.subjectRandom searchen
dc.titleQuasi-steady State Reduction of Molecular Motor-Based Models of Directed Intermittent Searchen
dc.typeArticleen
dc.identifier.journalBulletin of Mathematical Biologyen
dc.contributor.institutionUniversity of Utah, Salt Lake City, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-4en

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