Chemotaxis and Reactions in Anomalous Diffusion Dynamics

TL;DR

This paper investigates how chemotactic attraction influences reactions and reproduction in biological systems modeled by anomalous diffusion, using fractional Laplacian PDEs to better capture superdiffusive behaviors.

Contribution

It extends previous models by incorporating fractional Laplacian-based anomalous diffusion into chemotaxis-reaction equations, offering a more accurate mathematical framework for cellular processes.

Findings

Fractional Laplacian models superdiffusion more accurately.

Chemotactic attraction significantly impacts reaction dynamics.

The model aligns with experimental evidence of anomalous diffusion.

Abstract

Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction. In this work, we extend the investigation initiated by kiselev et al. [17] by examining the impact of chemotactic attraction on reproduction and other processes in the context of anomalous diffusion of gamete densities. For that, we consider a partial differential equation, with a single density function, that includes advection, chemotaxis, absorbing reaction, and diffusion, incorporating the fractional Laplacian $\Lambda^\alpha$. The inclusion of the fractional Laplacian is motivated by experimental evidence supporting the efficacy of anomalous diffusion models, particularly in scenarios with sparse targets. The fractional Laplacian accommodates the nonlocal nature of superdiffusion processes, providing a more accurate representation than traditional diffusion models. Our proposed model represents a step forward in refining mathematical descriptions of cellular behaviors influenced by chemotactic cues.