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

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.