Rapid calculation of maximum particle lifetime for diffusion in complex geometries

TL;DR

This paper introduces a rapid method to accurately compute the maximum particle lifetime in complex geometries, improving upon mean lifetime estimates, especially in obstacle-rich environments, aiding biological diffusion modeling.

Contribution

The paper presents a simple, efficient approach for calculating the maximum particle lifetime, addressing limitations of mean lifetime estimates in complex, crowded geometries.

Findings

Maximum particle lifetime estimates are more accurate than mean estimates.

The method performs well in geometries with obstacles.

Differences between mean and maximum lifetimes increase with crowding.

Abstract

Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an absorbing boundary. Calculating the particle lifetime provides valuable information, for example, by allowing us to compare the timescale of diffusion and the timescale of reaction, thereby helping us to develop appropriate mathematical models. Previous methods to quantify particle lifetimes focus on the mean particle lifetime. Here, we take a different approach and present a simple method for calculating the maximum particle lifetime. This is the time after which only a small specified proportion of particles in an ensemble remain in the system. Our approach produces accurate estimates of the maximum particle lifetime, whereas the mean particle lifetime always underestimates this value compared with data from stochastic simulations. Furthermore, we find that differences between the mean and maximum particle lifetimes become increasingly important when considering diffusion hindered by obstacles.