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.

中文翻译：

---

细胞内运输模型中线性切换扩散系统的更新奖励视角


在许多生物系统中，个体主体的运动具有由各种生物物理状态产生的多种性质不同的行为。例如，在细胞中，囊泡、细胞器和其他细胞内货物的运动受到它们通过分子运动蛋白与细胞骨架丝（例如微管）的结合和解除结合的影响。此类系统模型的理论或数值分析的典型目标是研究有效的传输特性及其对模型参数的依赖性。虽然经历切换扩散动力学的粒子的有效速度通常很容易用粒子在每种状态下花费的长时间分数来表征，但有效扩散率的计算更为复杂，因为它不能简单地用某一时刻粒子输运状态的统计平均值。然而，这些系统通常是可再生的，因为它们可以分解为以返回基态为标志的独立循环。使用这种分解，我们通过计算每个周期内的动力学矩，然后应用更新奖励理论来计算有效传输属性。该方法为线性平流-反应-扩散偏微分方程模型的直接均质化提供了一种有用的替代长时间分析。此外，它适用于一般类别的半马尔可夫过程和细胞内运输模型中出现的某些随机微分方程。 所提出的更新奖励框架的应用通过几个案例研究进行了说明，例如发育中卵母细胞中的 mRNA 运输和分子运动蛋白团队的持续货物运动。