High fidelity information processing in folic acid chemotaxis of Dictyostelium amoebae

Abstract

Living cells depend upon the detection of chemical signals for their existence. Eukaryotic cells can sense a concentration difference as low as a few per cent across their bodies. This process was previously suggested to be limited by the receptor-ligand binding fluctuations. Here, we first determine the chemotaxis response of Dictyostelium cells to static folic acid gradients and show that they can significantly exceed this sensitivity, responding to gradients as shallow as 0.2% across the cell body. Second, using a previously developed information theory framework, we compare the total information gained about the gradient (based on the cell response) to its upper limit: the information gained at the receptor-ligand binding step. We find that the model originally applied to cAMP sensing fails as demonstrated by the violation of the data processing inequality, i.e. the total information exceeds the information at the receptor-ligand binding step. We propose an extended model with multiple known receptor types and with cells allowed to perform several independent measurements of receptor occupancy. This does not violate the data processing inequality and implies the receptor-ligand binding noise dominates both for low- and high-chemoattractant concentrations. We also speculate that the interplay between exploration and exploitation is used as a strategy for accurate sensing of otherwise unmeasurable levels of a chemoattractant.

Keywords: Dictyostelium; chemotaxis; information theory.

Figure 1.

Measured chemotaxis response for a range of gradients and mean concentrations. (a) Distribution of cell displacement angles for the peak response for the gradient dc/dx = 1.6 nM µm⁻¹ and mean concentration c₀ = 2500 nM. Each radial step represents 15 data points. (b) CI for experiments with variable FA concentration in the top channel, which changed both the mean concentration and the gradient. The controls denote CI for experiments performed with no gradient with mean FA concentrations of 0, 2500 and 10 000 nM. The error bars and grey area denote standard error of the mean (s.e.m.).

Figure 2.

Comparison of the total mutual information I_tot and external mutual information I_ext. (a) I_tot (dashed line) and I_ext (solid line) for the same experiments as in figure 1a, both averaged over all local concentrations (see the electronic supplementary material). Error bars for I_tot represent s.e.m. The shaded range for I_ext denotes its spread owing to the range of local concentrations the cells were exposed to in the microfluidic device (see text). Dotted line denotes the I_tot for control experiments without a gradient. Annotation 1 shows the range where the data processing inequality is strongly violated, I_tot > I_ext. (b) (i) Calculated values for I_ext (equation (2.1)); shaded area denotes the combinations of c₀ and dc/dx inaccessible in our experiment owing to the geometry of the microfluidic device and low solubility of FA in development buffer (approx. 0.1 mM). (ii) the range of concentrations and gradients where cAMP chemotaxis has been measured, coloured by the value of measured CI. The measurement with annotation 1 (c₀ = 500 nM = 17 K_d, dc/dx = 0.5 nM µm⁻¹ = 0.08 K_d R⁻¹, CI = 0.25) is done in the approximate range where we detected the greatest violation of the data processing inequality (c₀ = 5000 nM = 33 K_d, dc/dx = 3.2 nM µm⁻¹ = 0.11 K_d/R, CI = 0.13, I_tot = 0.16 bits) if we compare them by rescaling the concentrations with their respective K_ds (K_d(cAMP) = 30 nM, K_d(FA) = 150 nM [16,18]). I_tot and I_ext for experiments with fixed gradient, where mean concentration changed is shown in (c) and experiments with fixed mean concentration where the gradient is changed are shown in (d). In the range investigated here, increasing the concentration and reducing the gradient reduced the chemotaxis response, I_tot but the violation of the data processing inequality persists. (Online version in colour.)

Figure 3.

I_tot and I_ext for models with additional assumptions. (a) Fit of our data to the model with multiple receptor types; see text for details. (b) Fit of our data to the model with multiple receptor types and the hypothesis that they can be phosphorylated to states with three-fold higher K_d = 1350 nM. (c) Calculation for biased I_tot and I_ext, where the uniform prior distribution was replaced with a circular normal distribution. Both I_tot and I_ext are plotted as a function of bias parameter K (large K values correspond to very sharp prior distributions), showing that the violation of data processing inequality persists even for biased cells. (d) Comparison of I_tot and I_ext for a model with multiple independent measurements of receptor occupancy which still results in the violation of the data processing inequality. (e) Model with combined effects of (a) and (d) does not result in the violation of the data processing inequality and successfully explains the data.