Mass-Conservation Increases Robustness in Stochastic Reaction-Diffusion Models of Cell Crawling

Abstract

The process of polarization determines the head and tail of single cells. A mechanism of this kind frequently precedes the subsequent cell locomotion and it determines the direction of motion. The process of polarization has frequently been described as a reaction-diffusion mechanism combined with a source of stochastic perturbations. We selected a particular model of amoeboid cell crawling for the motion of Dictyostelium discoideum and studied the interplay between pattern formation and locomotion. Next, we integrated the model in a two-dimensional domain considering the shape deformations of the cells in order to characterize the dynamics. We observed that the condition of pattern formation is finely tuned and we propose a modification based on the use of a mass-conservation constraint to substantially increase the robustness of the mathematical model.

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

“…At its essence, SPDEs elegantly merge the unpredictability of stochastic processes with the foundational principles of partial differential equations (PDEs), providing a robust framework for the mathematical modeling of physical phenomena with randomness, alongside the spatial and temporal dynamics inherent in them. The versatility and depth of SPDEs have led to their application in a diverse range of fields, from the intricate patterns of physics to the innovative designs of engineering [1][2][3][4][5], the fluctuating dynamics of financial markets [6][7][8][9][10], and the complex processes within biological sciences [11][12][13][14][15][16]. This cross-disciplinary enthusiasm highlights the crucial importance of SPDEs in deepening our understanding of the world, connecting theoretical exploration with pragmatic resolutions to complex problems.…”