Fig. 3: Turing foam in the in vitro Min system.
From: Protein pattern morphology and dynamics emerging from effective interfacial tension
a, In vitro, the E. coli Min system can form mesh patterns made up of thin MinE branches (cyan) separating MinD domains (magenta). Total concentrations: [MinD] = 1.5 μM and [MinE-His] = 3 μM (compare Extended Data Fig. 1; experimental data obtained and described in ref. 20). Branches of triple vertices are marked in white and four-fold vertices are labelled with black circles (‘Pattern analysis’ in Methods). b,c, The instability of four-fold and higher-order vertices (b) and branch rearrangement at triple vertices towards 120° junction angles (c) can be explained based on the curvature dependence of net attachment (blue) and detachment (red). d–f, Histograms of the angles at the triple vertices (d), the number of edges of each MinD domain (e) and the MinD domain areas (f) are determined from the experimental data in a (Extended Data Fig. 1a and see ‘Pattern analysis’ in Methods). For comparison, the vertex-angle histogram of vertices with random angles is shown (black line; Supplementary Section 5). The largest MinD domains have an internal MinE domain disconnected from the mesh (green). g, Reaction network of a minimal model of MinD (magenta) and MinE (cyan) membrane attachment and detachment supplemented by a conformational MinE switch and persistent membrane binding of MinE. h, This model reproduces stationary mesh patterns of MinD (magenta) and MinE (cyan) in two-dimensional simulations (model equations and parameters given in ‘Min system’ in Methods). i,j, Histograms of the vertex angles (i) and the edge number of the MinD domains (j) are determined from six independent simulations (‘Pattern analysis’ in Methods).
