Stochastic Modeling and Simulation of Collective Gradient Detection by Bio-nanomachine Clusters

Gradient detection is a fundamental task for bio-nanomachines operating in molecular communication environments such as inside the human body. Due to their microscopic size, individual bio-nanomachines cannot reliably detect concentration gradients from pointwise measurements. To address this limitation, previous studies proposed a biologically inspired method in which a linear cluster of bio-nanomachines compares local and global molecular concentrations to infer gradient direction. This paper extends the previous deterministic model by incorporating stochastic fluctuations into the concentration dynamics of both local and global molecules. We develop a set of stochastic differential equations and numerically solve them using the Euler–Maruyama method. Simulation results demonstrate how local and global concentrations evolve under molecular noise, how the coupling coefficient controlling molecule exchange affects detection accuracy, and how the cluster can move along a signal gradient in noisy environments. Our findings show that stronger coupling improves robustness and directional reliability through spatial averaging, enabling effective gradient detection even in the presence of noise.