Bidirectional sliding of two parallel microtubules generated by multiple identical motors

Allard, Jacques; Doumic, Marie; Mogilner, Alex; Oelz, Dietmar

doi:10.1007/s00285-019-01369-w

Cited by 8 publications

(24 citation statements)

References 35 publications

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“…The vertical axis is plotted on a log scale to allow for visualization of differences between effective diffusivity estimated from simulations and analytical approximations. b Percent error of the first passage approximation in red circles and of the renewal reward calculation in yellow triangles with respect to the simulation results in Allard et al (2019)…”

Section: Reattachment In Models Of Cargo Transportmentioning

confidence: 99%

“…A main point of this study is that parallel microtubules may slide bidirectionally with respect to each other, with a zero mean velocity due to symmetry; thus, the long-term microtubule transport is characterized by diffusive behavior. The effective diffusivity of the microtubule pair driven by a total of 35 motors is measured in Allard et al (2019) through fitting the slope of the mean squared displacement in stochastic simulations at long time (stars in Fig. 6a) and comparing to a theoretical approximation in terms of a first passage time problem (open circles in Fig.…”

Section: Microtubule Sliding Modelmentioning

confidence: 99%

“…Explicit solutions for these models are rarely available, so asymptotic or numerical methods are often deployed to investigate and characterize the model's predictions. The study of deterministic models often relies on numerical simulation using PDE integration methods (Wang et al 2003;Cox and Matthews 2002;Trong et al 2015), while stochastic models are simulated with Monte Carlo/Gillespie algorithms (Müller et al 2008;Kunwar and Mogilner 2010;Müller et al 2010;Allard et al 2019) to generate individual trajectories that are then analyzed statistically. However, these computations can be quite costly, especially when one wants to understand how bulk transport properties (like effective velocity or diffusivity) depend on individual model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Our primary motivating examples are related to intracellular transport. Some prominent recent investigations include the study of mRNA localization in oocyte development (Zimyanin et al 2008;Trong et al 2015;Ciocanel et al 2017), cell polarization in the budding yeast (Bressloff and Xu 2015), neurofilament transport along axons (Jung and Brown 2009;Li et al 2014), interactions of teams of molecular motor proteins (Klumpp and Lipowsky 2005;Müller et al 2008;Kunwar and Mogilner 2010;Müller et al 2010;Tjioe et al 2019), and sliding of parallel microtubules by teams of cooperative identical motors (Allard et al 2019). Microtubule-based transport of cargo is typically mediated by kinesin motors moving material to the cell periphery and by dynein motors carrying it to the nucleus.…”

Section: Introductionmentioning

confidence: 99%

“… 2010 ; Allard et al. 2019 ) to generate individual trajectories that are then analyzed statistically. However, these computations can be quite costly, especially when one wants to understand how bulk transport properties (like effective velocity or diffusivity) depend on individual model parameters.…”

Section: Introductionmentioning

confidence: 99%

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Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport

et al. 2020

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In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion dynamics is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection–reaction–diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed renewal reward framework are illustrated for several case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of molecular motor proteins.

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Section: Reattachment In Models Of Cargo Transportmentioning

confidence: 99%

Section: Microtubule Sliding Modelmentioning

confidence: 99%