Asymptotic analysis of microtubule-based transport by multiple identical molecular motors

McKinley, Scott A.; Athreya, Avanti; Fricks, John; Kramer, Peter R.

doi:10.1016/j.jtbi.2012.03.035

Cited by 25 publications

(43 citation statements)

References 79 publications

(207 reference statements)

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“…We thus ask the question: what features are necessary to produce this behavior? Now, if the step rate is independent of the number of bound motors, m, then it follows immediately from (34) and (36) that V is independent of M . In particular, if the dimensional step rate is k step (m) ≡ k 0 for all m ∈ {1, .…”

Section: Biological Applicationmentioning

confidence: 99%

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Miles¹,

Lawley²,

Keener³

2018

SIAM J. Appl. Math.

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We propose and analyze a mathematical model of cargo transport by non-processive 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 non-processive clustering, the phenomenon that a single motor cannot transport cargo, but that 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.

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Section: Biological Applicationmentioning

confidence: 99%

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Miles¹,

Lawley²,

Keener³

2018

SIAM J. Appl. Math.

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“…The behavior follows almost identically with the mean-field model (2.1), but now binding and unbinding can be neglected due to the analysis only being of a single run. In [25], the authors also study the behavior of motors without binding dynamics and find that multiple motors can actually produce a lower cargo velocity than a single motor. However, we are only interested in the mean behavior of the motors and therefore the explicitness of their description is not necessary for this work.…”

Section: Ornstein-uhlenbeck Motivationmentioning

confidence: 99%

Bidirectionality from cargo thermal fluctuations in motor-mediated transport

Miles

Keener

2017

Journal of Theoretical Biology

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Molecular motor proteins serve as an essential component of intracellular transport by generating forces to haul cargoes along cytoskeletal filaments. Two species of motors that are directed oppositely (e.g. kinesin, dynein) can be attached to the same cargo, which is known to produce bidirectional net motion. Although previous work focuses on the motor number as the driving noise source for switching, we propose an alternative mechanism: cargo diffusion. A mean-field mathematical model of mechanical interactions of two populations of molecular motors with cargo thermal fluctuations (diffusion) is presented to study this phenomenon. The delayed response of a motor to fluctuations in the cargo velocity is quantified, allowing for the reduction of the full model a single "characteristic distance", a proxy for the net force on the cargo. The system is then found to be metastable, with switching exclusively due to cargo diffusion between distinct directional transport states. The time to switch between these states is then investigated using a mean first passage time analysis. The switching time is found to be non-monotonic in the drag of the cargo, providing an experimental test of the theory.

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“…Understanding such effects will not be possible by looking only at experimental results, but will necessitate modeling a variety of possible modes of interaction to test which most closely recapitulates experimental data. So far, some such models have begun to both predict and compare with experimental results the expected effects of factors such as the number of motors, their mechanical linkages, viscosity of the medium, motor velocity, and the relative populations of forward- and backward-directed motors that may pull against each other in a tug-of-war (Klumpp and Lipowsky, 2005; Beeg et al, 2008; Kunwar et al, 2008, 2011; Müller et al, 2008, 2010; Zhang, 2009; Driver et al, 2010, 2011; Berger et al, 2012; Xu et al, 2012; McKinley et al, 2012). As experimental tools for creating and controlling multiple-motor systems advance, analyses such as these will become even more essential for interpreting the experimental results.…”

Section: Feedback Between Modeling and Experiments Will Be Essential Tmentioning

confidence: 99%

Future Challenges in Single-Molecule Fluorescence and Laser Trap Approaches to Studies of Molecular Motors

Elting

Spudich

2012

Developmental Cell

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Single-molecule analysis is a powerful modern form of biochemistry, in which individual kinetic steps of a catalytic cycle of an enzyme can be explored in exquisite detail. Both single-molecule fluorescence and single-molecule force techniques have been widely used to characterize a number of protein systems. We focus here on molecular motors as a paradigm. We describe two areas where we expect to see exciting developments in the near future: first, characterizing the coupling of force production to chemical and mechanical changes in motors, and second, understanding how multiple motors work together in the environment of the cell.

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Asymptotic analysis of microtubule-based transport by multiple identical molecular motors

Cited by 25 publications

References 79 publications

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Bidirectionality from cargo thermal fluctuations in motor-mediated transport

Future Challenges in Single-Molecule Fluorescence and Laser Trap Approaches to Studies of Molecular Motors

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