Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport
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Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport Maria-Veronica Ciocanel1 Scott A. McKinley4
· John Fricks2 · Peter R. Kramer3 ·
Received: 18 November 2019 / Accepted: 24 August 2020 © The Author(s) 2020
Abstract 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.
MVC was supported by The Ohio State University President’s Postdoctoral Scholars Program and by the Mathematical Biosciences Institute at The Ohio State University through NSF DMS-1440386. JF, PRK, and SAM are supported by NIH R01GM122082-01.
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Maria-Veronica Ciocanel [email protected]
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Keywords Renewal reward theory · Intracellular transport · Processive motor transport Mathematics Subject Classification 60J20 · 60J27 · 92B05 · 92C37
1 Introduction Microscale biological agents frequently change biophysical state, which results in significant changes in their movement behavior. Intracellular cargo, for example, switches among active transport, diffusive transport, and paused states, each resulting from different mechanochemical configurations of the cargo, cytoskeletal filaments, and the molecular motors that bind them (Han
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