Fig. 4: Analytical solution of the ODE model.
From: Multi-condensate state as a functional strategy to optimize the cell signaling output
For A–C, a perfect hemisphere is considered. A Bifurcation analysis. Each panel shows the functional value of \(\frac{{dF}}{{dt}}\) (Eq. 1) at a given value of Arp density (α). The red circles refer to the “roots” of Eq. (1), that is, the values of F where \(\frac{{dF}}{{dt}}=0.\) The arrow represents the direction of “flow”; it is rightward for a region where \(\frac{{dF}}{{dt}} \, > \, 0\) and leftward otherwise. Flow towards a root signifies stability. B Solution of F-actin (F) as a function of Arp density. The dotted line indicates the bifurcation point where F production starts to happen. The density of Arp at this point is termed \({\alpha }_{{critical}}\). C Value of \({\alpha }_{{critical}}\) (color-coded) as a function of k1 and C (Eq. 2). D Trend of Arp-dependent F production as a function of the cluster’s HemiSphericity. Creating a spheroid-like geometry from a sphere increases the surface-to-volume ratio. For a fixed number of Arp, the surface density of Arp goes down with smaller HemiSphericity (Supplementary Text 3). E Amount of F produced per cluster in a n-cluster system. F Amount of cumulative F, which integrates contributions from all the clusters. Different colors represent distinct HemiSphericity.
