Biased Random Walk by Stochastic Fluctuations of Chemoattractant-Receptor Interactions at the Lower Limit of Detection

Binding of ligand to its receptor is a stochastic process that exhibits fluctuations in time and space. In chemotaxis, this leads to a noisy input signal. Therefore, in a gradient of chemoattractant, the cell may occasionally experience a “wrong” gradient of occupied receptors. We obtained a simple equation for Ppos, the probability that half of the cell closest to the source of chemoattractant has higher receptor occupancy than the opposite half of the cell. Ppos depends on four factors, the gradient property ∇C/C, the receptor characteristic Rt/KDRt/KD, a time-averaging constant I, and nonreceptor noise σB. We measured chemotaxis of Dictyostelium cells to known shallow gradients of cAMP and obtained direct estimates for these constants. Furthermore, we observed that in shallow gradients, the measured chemotaxis index is correlated with Ppos, which suggests that chemotaxis in shallow gradients is a pure biased random walk. From the observed chemotaxis and derived time-averaging constant, we deduce that the gradient transducing second messenger has a lifetime of 2–8 s and a diffusion rate constant of ∼1 μm2/s. Potential candidates for such second messengers are discussed.