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

Area of Science:

• Biophysics
• Cell Biology
• Theoretical Biology

Background:

• Intracellular cargo transport involves complex behaviors driven by motor proteins binding to cytoskeletal filaments.
• Effective transport properties like velocity and diffusivity are crucial for understanding cellular processes.
• Calculating effective diffusivity in switching diffusion dynamics is challenging due to its dependence on time-varying states.

Purpose of the Study:

• To develop a novel theoretical framework for calculating effective transport properties in biological systems with switching diffusion dynamics.
• To provide an alternative analytical method to direct homogenization for modeling intracellular transport.
• To apply renewal reward theory to semi-Markov processes and stochastic differential equations relevant to cell biology.

Main Methods:

• Decomposition of regenerative systems into independent cycles based on returns to a base state.
• Calculation of transport properties by computing moments of dynamics within each cycle.
• Application of renewal reward theory to analyze effective transport properties.

Main Results:

• The renewal reward theory framework effectively calculates effective transport properties for systems with multiple distinct behaviors.
• This method offers a robust alternative to direct homogenization for advection-reaction-diffusion models.
• The approach is applicable to a broad range of semi-Markov processes and stochastic differential equations.

Conclusions:

• Renewal reward theory provides a powerful tool for analyzing complex intracellular transport dynamics.
• The framework accurately captures effective transport properties, including diffusivity, which are difficult to determine with traditional methods.
• This research offers valuable insights into mRNA transport and molecular motor protein function in cellular systems.