Diffusion-limited phase separation in eukaryotic chemotaxis
Andrea Gamba *, 
,
Antonio de Candia 
,
Stefano Di Talia 
,
Antonio Coniglio ,
Federico Bussolino ¶, and
Guido Serini , ¶
*Department of Mathematics, Polytechnic of Torino, 10129 Turin, Italy; Department of Physical Sciences, University of Naples "Federico II," Istituto Nazionale di Fisica Della Materia, and Istituto Nazionale di Fisica Nucleare, Unit of Naples, 80126 Naples, Italy; Laboratory of Mathematical Physics, The Rockefeller University, New York, NY 10021; and ¶Department of Oncological Sciences and Division of Molecular Angiogenesis, Institute for Cancer Research and Treatment, University of Torino School of Medicine, 10060 Candiolo, Italy
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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.
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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.
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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.
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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).
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between deviations from the mean of receptor activation 
