Diffusion-limited phase separation in eukaryotic chemotaxis

Abstract

The ability of cells to sense spatial gradients of chemoattractant factors governs the development of complex eukaryotic organisms. Cells exposed to shallow chemoattractant gradients respond with strong accumulation of the enzyme phosphatidylinositol 3-kinase (PI3K) and its D3-phosphoinositide product (PIP(3)) on the plasma membrane side exposed to the highest chemoattractant concentration, whereas PIP(3)-degrading enzyme PTEN and its product PIP(2) localize in a complementary pattern. Such an early symmetry-breaking event is a mandatory step for directed cell movement elicited by chemoattractants, but its physical origin is still mysterious. Here, we propose that directional sensing is the consequence of a phase-ordering process mediated by phosphoinositide diffusion and driven by the distribution of chemotactic signal. By studying a realistic reaction-diffusion lattice model that describes PI3K and PTEN enzymatic activity, recruitment to the plasma membrane, and diffusion of their phosphoinositide products, we show that the effective enzyme-enzyme interaction induced by catalysis and diffusion introduces an instability of the system toward phase separation for realistic values of physical parameters. In this framework, large reversible amplification of shallow chemotactic gradients, selective localization of chemical factors, macroscopic response timescales, and spontaneous polarization arise naturally. The model is robust with respect to order-of-magnitude variations of the parameters.

Fig. 1.

Phase separation in the presence of isotropic or 5% anisotropic receptor activation switched on as described in the text (D = 0.4 μm²/s, [Rec] = 30 nM). The 5% activation gradient pointed in the upward vertical direction. (a–d) For isotropic receptor activation, a–d show the difference between local PIP₃ and PIP₂ concentrations at times t = 0(a), 10 (b), 30 (c), and 90 (d) min. Red zones correspond to PIP₃-rich phases; blue zones correspond to PIP₂-rich phases. (e) The time evolution of Binder's cumulant g, measuring the degree of phase separation of the phosphoinositide mixture, and of the relative weight of the first harmonic component C₁ (see text), measuring the formation of phosphoinositide patches of the size of the system. (f–j) For anisotropic receptor activation, the corresponding data for phosphoinositide concentrations are given in f–i, and the evolution of g and C₁ is given in j. In the presence of activation gradient phase separation is faster and takes place along the gradient direction.

Fig. 2.

Dynamic phase diagram. Average phase-separation times and average cluster sizes are shown using color scales as functions of receptor activation [Rec] and diffusivity D for isotropic and 5% anisotropic activation. Simulations were performed on a uniform grid of points spaced by 5 nM in the [Rec] direction and 0.2 μm²/s in the D direction. (a–c) In the isotropic case, shown are the following. (a) Average phase-separation time. (b) Average cluster size as a function of [Rec] and D.(c) Average cluster size as a function of D for fixed [Rec] values. (d–f) In the anisotropic case, d–f show the following. (d) Average phase separation time. (e) Average cluster size. (f) Correlation r_ρφ between deviations from the mean of receptor activation δρ and phosphoinositide differences δφ. For anisotropic activation phase separation is faster, takes place in a larger region of parameter space, and is correlated with the anisotropy direction.

Fig. 3.

PIP₃ phase separation in response to low concentrations and multiple sources of chemoattractant. (a) For low receptor activation ([Rec] = 5 nM) stationary phase separation does not take place; however, small intermittent PIP₃ clusters arise. (b) Under the simulated influence of two opposite chemoattractant sources multiple PIP₃ patches are observed.

Fig. 4.

Amplification of simulated chemoattractant signal. The system was exposed for 1 min to a 25% gradient in receptor activation in the upward vertical direction. PIP₃ concentration and receptor activation, normalized with their mean (a) or maximum (b), were sampled around a great circle passing through the North and South poles and divided in 40 bins. (a) Cell response plotted against receptor activation. (b) Cell response and receptor activation as functions of the deviation from the North Pole.

Fig. 5.

For small diffusivities the cluster size grows as and saturates when it reaches the system size; for higher diffusivities, diffusion mixes up the two phosphoinositide species, and the cluster size drops abruptly ([Rec] = 50 nM).