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

2025-11-23

AI Summary

Cell migration exhibits long-range temporal correlations and superdiffusive behavior even without external guidance, yet the functional significance of this endogenous temporal correlation remains unclear—whether it is merely a physiological byproduct or an adaptive mechanism enhancing navigation efficiency. Method: We model endogenous noise using fractional Brownian motion and systematically investigate its role across diverse chemotactic search scenarios—including classical chemotaxis, stochastic gradient ascent, and self-generated signal navigation—via computational simulations and first-passage time analysis. Contribution/Results: Temporally correlated noise-driven superdiffusion markedly improves the reliability and robustness of cellular localization of global chemical maxima, maintaining high performance despite spatial noise, complex substrate curvature, or dynamic signal environments. This work transcends conventional white-noise chemotaxis models by demonstrating, for the first time, that intrinsic temporal structure actively optimizes pathfinding performance. It establishes a new paradigm for understanding biological migration strategies and inspires the design of intelligent search algorithms incorporating structured stochasticity.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Heuristic Search
• Intelligent Robots: Localization, Mapping, and Navigation

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Content-based information diffusion
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Investigates how temporally correlated noise affects chemotactic search dynamics
• Explores whether anomalous diffusion enhances cellular navigation in complex environments
• Examines fractional Brownian motion's role in gradient-driven migration optimization

Innovation

• Using fractional Brownian motion for modeling chemotaxis
• Combining superdiffusive motion with gradient-driven migration
• Analyzing first hitting times under temporal correlation