A Stochastic Model For Protrusion Activity

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics [4], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.

PHENOMENOLOGY OF REACTION–DIFFUSION BINARY-STATE CELLULAR AUTOMATA

We study a binary-cell-state eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semi-totalistic transitions rules: every cell switches from state 0 to state 1 depending on if the sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if the sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still-life compact patterns). We explore reaction–diffusion like patterns produced as a result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.