External and internal constraints on eukaryotic chemotaxis

Abstract

Chemotaxis, the chemically guided movement of cells, plays an important role in several biological processes including cancer, wound healing, and embryogenesis. Chemotacting cells are able to sense shallow chemical gradients where the concentration of chemoattractant differs by only a few percent from one side of the cell to the other, over a wide range of local concentrations. Exactly what limits the chemotactic ability of these cells is presently unclear. Here we determine the chemotactic response of Dictyostelium cells to exponential gradients of varying steepness and local concentration of the chemoattractant cAMP. We find that the cells are sensitive to the steepness of the gradient as well as to the local concentration. Using information theory techniques, we derive a formula for the mutual information between the input gradient and the spatial distribution of bound receptors and also compute the mutual information between the input gradient and the motility direction in the experiments. A comparison between these quantities reveals that for shallow gradients, in which the concentration difference between the back and the front of a 10-mum-diameter cell is <5%, and for small local concentrations (<10 nM) the intracellular information loss is insignificant. Thus, external fluctuations due to the finite number of receptors dominate and limit the chemotactic response. For steeper gradients and higher local concentrations, the intracellular information processing is suboptimal and results in a smaller mutual information between the input gradient and the motility direction than would have been predicted from the ligand-receptor binding process.

Fig. 1.

The chemotactic response of cells in exponential gradients depends on the gradient steepness. (A) The concentration as a function of the position along the gradient direction in the microfluidic device. The exponential gradient spans a 550-μm-wide region and the concentration can be described by , where L = 10 μm and p is a measure of the steepness of the gradient. The steepness is expressed as the fractional difference in the concentration across 10 μm and measures 5% for the data shown. (B and C) Typical cell tracks, with their origins brought to a common point, are shown for a steep (10%) gradient (B) where the concentration within the microfluidic device varies between 1 and 256 nM and for a shallow (1.25%) gradient (C) where the concentration spans values between 1 and 2 nM. The arrow indicates the direction of the gradient. (Scale bars: 20 μm.)

Fig. 2.

Dependence of the chemotactic index, CI, on the gradient steepness and the local concentration. (A) Mean value of the CI as a function of the gradient steepness for cell migration trajectories with an average local concentration between 1nM and 10nM (○) and between 10nM and 30nM (■). (B) The CI as a function of the local concentration for two different values of the gradient steepness. Each data point is an average value for cells exposed to local concentrations in a twofold (for p = 1.25%) or fourfold (for p = 2.5%) range, with the plotted value of corresponding to the geometric mean of the range. In both figures, the error bars represent the standard error of the mean.

Fig. 3.

Dependence of the mutual information (MI) on the gradient parameters. (A) Histogram of the instantaneous response angle θ_r for the cell tracks in a 10% gradient, showing a pronounced peak at θ_r = π, the gradient direction. (B and C) The external and internal MI between the input gradient angle, θ_s, and θ_r calculated using the experimental data (dashed lines), and the external MI between θ_s and the spatial distribution of bound receptors Y, calculated numerically (solid lines), as a function of the gradient steepness for cells with an average local concentration between 1 and 10nM (B) and as a function of the mean local concentration for a 2.5% gradient (C). Parameters used for the computation of the external MI are N = 70,000 and K_d = 30 nM.