Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Miles, Christopher E.; Lawley, Sean D.; Keener, James P.

doi:10.1137/17m1156824

Cited by 17 publications

(29 citation statements)

References 51 publications

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“…The calculation framework also results in an expression for the expected run length of cargo undergoing switching diffusion. Our approach builds on previous applications of renewal reward processes modeling motor-stepping and chemical cycles of bead-motor assays (Krishnan and Epureanu 2011;Hughes et al 2011Hughes et al , 2012Miles et al 2018;Shtylla and Keener 2015) and extends the technique to accommodate more complex models with dynamics depending on the amount of time spent in the current state, as described in Sect. 2.…”

Section: Summary Of Methods Based On Regeneration Cyclesmentioning

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: Summary Of Methods Based On Regeneration Cyclesmentioning

confidence: 99%

“… 2011 , 2012 ; Miles et al. 2018 ; Shtylla and Keener 2015 ) and extends the technique to accommodate more complex models with dynamics depending on the amount of time spent in the current state, as described in Sect. 2 .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…The calculation framework also results in an expression for the expected run length of cargo undergoing switching diffusion. Our approach builds on previous applications of renewal-reward processes modeling motor-stepping and chemical cycles of bead-motor assays (Krishnan and Epureanu, 2011;Hughes et al, 2011Hughes et al, , 2012Miles et al, 2018;Shtylla and Keener, 2015) and extends the technique to accommodate more complex models with dynamics depending on the amount of time spent in the current state, as described in §2. Given the renewal-reward framework, the analysis of the model reduces to computing the correlated spatial displacement and time duration of each cycle, which we study in §3.…”

Section: Summary Of Methods Based On Regeneration Cyclesmentioning

confidence: 99%

Renewal reward perspective on linear switching diffusion systems

Ciocanel,

Fricks,

Kramer

et al. 2019

Preprint

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In many biological systems, the movement of individual agents of interest is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport, micro-organisms like bacteria, or animals moving within and responding to their environment. For example, in cells the movement of vesicles, organelles and other intracellular cargo are 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 the 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

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“…Under this setting, several motor properties can be measured, particularly their speed, diffusivity, and detachment rate as a function of the applied optical trap force [83,60,61,2,48,9,89]. The above experimental work can be used as a basis for parameterizing biophysically mechanistic models for individual motors in theoretical models exploring their interactions [45,44,51,38,36,10,35,57,84,21,59]. For the purpose of experimentally measuring the interaction of molecular motors, and in particular for motivation for and comparison against theoretical models, an important experimental development has been to use DNA origami for cargo, which specifies closely arranged handle sites onto which specified motor types attach [25,35,26].…”

Section: Introductionmentioning

confidence: 99%

Effective behavior of cooperative and nonidentical molecular motors

Klobusicky¹,

Fricks²,

Kramer³

2020

Preprint

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Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load. Dedicated to Andy Majda for his 70th birthday, with gratitude for his lasting inspiration starting from my undergraduate and graduate days on the creative deployment of mathematical modeling and the beautiful application of analysis techniques as a lens for exploring and understanding the dynamics of physical systems -PRK

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Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

Cited by 17 publications

References 51 publications

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

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

Renewal reward perspective on linear switching diffusion systems

Effective behavior of cooperative and nonidentical molecular motors

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