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

Transport of lysosomes decreases in the perinuclear region: Insights from changepoint analysis

Lysosomes are membrane-bound organelles that serve as the endpoint for endocytosis, phagocytosis, and autophagy, degrading the molecules, pathogens, and organelles localized within them. These cellular functions require intracellular transport. We use fluorescence microscopy to characterize the motion of lysosomes as a function of intracellular region, perinuclear or periphery, and lysosome diameter. Single particle tracking data is complemented by changepoint identification and analysis of a mathematical model for state-switching. We first classify lysosomal motion as motile or stationary. We then study how lysosome location and diameter affects the proportion of time spent in each state and quantify the speed during motile periods. We find that the proportion of time spent stationary is strongly region-dependent, with significantly decreased motility in the perinuclear region. Increased lysosome diameter only slightly decreases speed. Overall, these results demonstrate the importance of decomposing particle trajectories into qualitatively different behaviors before conducting population-wide statistical analysis. Our results suggest that intracellular region is an important factor to consider in studies of intracellular transport.

A Random Walk Approach to Transport in Tissues and Complex Media: From Microscale Descriptions to Macroscale Models

The biological processes necessary for the development and continued survival of any organism are often strongly influenced by the transport properties of various biologically active species. The transport phenomena involved vary over multiple temporal and spatial scales, from organism-level behaviors such as the search for food, to systemic processes such as the transport of oxygen from the lungs to distant organs, down to microscopic phenomena such as the stochastic movement of proteins in a cell. Each of these processes is influenced by many interrelated factors. Identifying which factors are the most important, and how they interact to determine the overall result is a problem of great importance and interest. Experimental observations are often fit to relatively simple models, but in reality the observations are the output of complicated functions of the physicochemical, topological, and geometrical properties of a given system. Herein we use multistate continuous-time random walks and generalized master equations to model transport processes involving spatial jumps, immobilization at defined sites, and stochastic internal state changes. The underlying spatial models, which are framed as graphs, may have different classes of nodes, and walkers may have internal states that are governed by a Markov process. A general form of the solutions, using Fourier-Laplace transforms and asymptotic analysis, is developed for several spatially infinite regular lattices in one and two spatial dimensions, and the theory is developed for the analysis of transport and internal state changes on general graphs. The goal in each case is to shed light on how experimentally observable macroscale transport coefficients can be explained in terms of microscale properties of the underlying processes. This work is motivated by problems arising in transport in biological tissues, but the results are applicable to a broad class of problems that arise in other applications.