On the role of fractional Brownian motion in models of chemotaxis and stochastic gradient ascent

TL;DR

This paper investigates how fractional Brownian motion, a type of temporally correlated noise, enhances cell chemotaxis by enabling robust exploration and reliable reaching of chemical signal maxima, with implications for biological navigation and optimization algorithms.

Contribution

It demonstrates that superdiffusive motion modeled by fractional Brownian motion improves chemotactic search efficiency and robustness across various environmental conditions.

Findings

Cells reach chemoattractant maxima reliably despite noise and irregular signals.

Superdiffusive motion enhances exploration and search robustness.

Results are consistent across different substrate geometries and signal types.

Abstract

Cell migration often exhibits long-range temporal correlations and anomalous diffusion, even in the absence of external guidance cues such as chemical gradients or topographical constraints. These observations raise a fundamental question: do such correlations simply reflect internal cellular processes, or do they enhance a cell's ability to navigate complex environments? In this work, we explore how temporally correlated noise (modeled using fractional Brownian motion) influences chemotactic search dynamics. Through computational experiments, we show that superdiffusive motion, when combined with gradient-driven migration, enables robust exploration of the chemoattractant landscape. Cells reliably reach the global maximum of the concentration field, even in the presence of spatial noise, secondary cues, or irregular signal geometry. We quantify this behavior by analyzing the distribution of first hitting times under varying degrees of temporal correlation. Notably, our results are consistent across diverse conditions, including flat and curved substrates, and scenarios involving both primary and self-generated chemotactic signals. Beyond biological implications, these findings also offer insight into the design of optimization and sampling algorithms that benefit from structured stochasticity.