A stochastic hybrid model with a fast concentration bias for chemotactic cellular attraction

We reproduce the phenomenon of chemotaxis through a hybrid random walk model in two dimensions on a lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, which reproduces its diffusion through the environment from its local sources. The cell is treated discretely and it is considered immersed in a medium with concentration gradients, so that its path is affected by these chemical anisotropies. Therefore, the direction taken in each iteration of the walk is given by a stochastic process that must be biased by the chemical concentrations, giving preference towards the highest values. For this purpose, we model the intensity of the bias by a single parameter, which is related to how much a cell is attracted to a source and, consequently, how efficient this source is with respect to the cellular capture. Since the model is intended for later hybridization with cellular automata models, a thorough quantitative analysis of the parameter space has been carried out. Finally, we also illustrate the efficiency of the cellular capture due to the concentration sources by using stochastic basins of attraction. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

We reproduce the phenomenon of chemotaxis using a hybrid random walk model on a two-dimensional lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, while the cell is treated discretely and influenced by concentration gradients. The bias towards higher chemical concentrations is determined by a stochastic process, which is controlled by a single parameter related to the attractiveness of the source and its efficiency in cellular capture. The model has been thoroughly analyzed in terms of parameter space and the efficiency of cellular capture is illustrated using stochastic basins of attraction.