Math @ Duke

Publications [#353551] of MariaVeronica Ciocanel
Papers Published
 Ciocanel, MV; Fricks, J; Kramer, PR; McKinley, SA, Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport.,
Bulletin of Mathematical Biology, vol. 82 no. 10
(September, 2020),
pp. 126 [doi]
(last updated on 2021/11/27)
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 longtime 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 largetime analysis to direct homogenization for linear advectionreactiondiffusion partial differential equation models. Moreover, it applies to a general class of semiMarkov 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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

