Receptor noise and directional sensing in eukaryotic chemotaxis

Abstract

Chemotacting eukaryotic cells are able to detect very small chemical gradients (approximately 1%) for a large range of background concentrations. For these chemical environments, fluctuations in the number of bound ligands will become important. Here, we investigate the effect of receptor noise in a simplified one-dimensional geometry. The auto- and cross-correlations of the noise sources at the front and the back of the cell are explicitly computed using an effective Monte Carlo simulation tool. The resulting stochastic equations for the investigated directional sensing model can be solved analytically in Fourier space. We determine the chemotactic efficiency, a measure of motility for the cell, as a function of several experimental parameters, leading to explicit experimental predictions.

FIG. 1

(color online). Schematic representation of our one-dimensional cell.

FIG. 2

(color online). The auto (a) and cross correlation (b) for a semisphere computed using MCell. The red curves are the fits using the formulas from the main text with as results: A_c = 37, τ_c = 1:56 s and τ_a = 1:15 s. Parameters are based on data from Dictyostelium: N = 70 000 receptors, D_l= 200 µm²/s, R = 5 µm, k₋ = 1/s and K_d = 30 nM with c = 1 nM.

FIG. 3

(color online). Example of the input signal (a) and the output signal of balanced inactivation model (b). Parameter values are A_c = 0, τ_a = 1:3 s, k_a = 0.01 s⁻¹, k_i = 1000 µm(s molecule)⁻¹, k_b = 3 µms⁻¹, k_−a = 0.2 s⁻¹, k_−b = 0.2 s⁻¹ and D = 10 µm² s⁻¹. The distance between the front and the back is L = 10 µm, p = 0.01, K_d = 30 nM and c = 1 nM. (c) The chemotactic efficiency as a function of the amplitude of the noise cross-correlation. The solid point corresponds to the amplitude found using the MCell simulation and represents a typical experimental value. Parameter values are as above and in Fig. 1 with T_dec = 30 s, T_int = 10 s and θ = 0.95.

FIG. 4

The chemotactic efficiency as a function of the steepness of the gradient (a), the autocorrelation time scale (b) and the background concentration (c). Fixed parameter values are as in Fig. 3 and 4 with θ = 0.95 (a), p = 0.01 and θ = 0.65 (b) and τ_diff = 0.3 s, p = 0.01 and θ = 0.85 (c). In (d) we have plotted the onset of chemotaxis, defined as a CE value larger that 0.5, as a function of the background concentration (τ_diff = 0.3 s and θ = 0.95).