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

Abstract

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 P(pos), the probability that half of the cell closest to the source of chemoattractant has higher receptor occupancy than the opposite half of the cell. P(pos) depends on four factors, the gradient property delC/sq. root of C, the receptor characteristic R(t)/K(D), a time-averaging constant I, and nonreceptor noise sigma(B). 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 P(pos), 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 approximately 1 microm(2)/s. Potential candidates for such second messengers are discussed.

External and internal constraints on eukaryotic chemotaxis

“…Cells that were exposed to an average local concentration in a 1-to 10-nM range are shown as circles whereas cells with an average local concentration within 10-30 nM are plotted as squares. For the 1-to 10-nM concentration range, the cells failed to recognize the shallowest gradient (1.25%) but responded with increasingly accurate directionality to the steeper gradients (2.5-10%) with a maximum CI that is consistent with previous reports (20).…”

“…Recently, the role of fluctuations in chemotaxis has received significant attention (15,16,18,20,26,27). Most studies, however, were either purely theoretical or performed under conditions that were difficult to quantify.…”

Receptor Noise and Directional Sensing in Eukaryotic Chemotaxis

“…The chemotactic efficiency CE is then defined as the total displacement in the direction of the gradient divided by the total number of decision intervals and can take on values between −1 and +1. We note that defining an alternative measure of the chemotactic efficiency using the SNR of A f − A b ( [4,5]) leads to qualitatively similar results.…”

“…In fact, at threshold the difference in the number of bound receptors at the front and the back can be estimated to be on the order of 20 while the total number of bound receptors is only a few hundred. This immediately raises the question of the effect of noise on chemotaxis, a topic that has been studied previously using a variety of approximative techniques [3][4][5][6]. What has been lacking, however, is a formalism that simulates quantitatively the receptor noise and its correlations and uses this as input for an intracellular chemotactic model.…”

“…This simplified model ignores all the complex and largely unknown steps between directional sensing and motility including the cytoskeleton machinery. Specifically, we calculate (5) after each "decision" interval T dec and where we have introduced the integration time T int . Motivated by typical pseudopod lifetimes in Dictyostelium we choose T dec = 30 s and T int = 10 s although similar qualitative results were obtained using different values.…”