Figure 1

Formation of contractile ring by aggregation of broad band of nodes. (A) Images of dividing wild-type cells expressing myosin marker Rlc1p-3GFP [9]. A broad band of nodes bound in the inner part of the cell membrane condenses into a ring in $\sim 10\mathrm{minutes}$. The ring subsequently constricts. (B) Images of mitotic cdc12p-112 cells (formin mutants) expressing Rlc1p-GFP at the restrictive temperature: clumps form instead of rings [18]. (C) 2D stochastic aggregation model. Left: nodes attract one another through transient connections by actin filaments polymerized by formins at the nodes. Right: model parameters. $l$, average distance between neighboring nodes; $d$, size of pairwise node movement per connection event; and $\lambda$, typical length of actin filaments.Reuse & Permissions

Figure 2

Monte Carlo simulations of node aggregation showing kinetics of clump formation in Regime 1 ($d\ll l\ll \lambda$). Nodes were placed according to a 2D uniform probability distribution. $q(r)$ was set to zero for $r>3\lambda$. Periodic boundary conditions were used. (A) RMS displacement vs time. Slope $1/2$ regime: active diffusion up to $t^{*}$; slope 1 regime: clump formation that ends at $t_{\mathrm{clump}}$; slope 0 regime: nodes trapped in isolated clumps. (B) Snapshots of node configurations at different times. (C) Test of $t_{\mathrm{clump}}{Q}^{\prime }\approx l/d$, Eq. (4). $t_{\mathrm{clump}}$ is the time at which the slope of the linear regime in A decreases by 20% $\pm 10\%$. Solid (black) line: $t_{\mathrm{clump}}{Q}^{\prime }=0.044(6)l/d$ is a linear fit to the subset of the data most asymptotic in R1. Dashed lines are guide-to-the-eye curves indicating approach to common asymptotic regime; deviations occur for $l$ approaching $\lambda$. Inset shows $t_{\mathrm{clump}}=0.73(3)t_{\lambda }$, in agreement with Eq. (4).Reuse & Permissions

Figure 3

Simulations as in Fig. 1, but for Regime 2 ($l\ll d\ll \lambda$). (A) RMS displacement vs time. Slope $1/2$ regime: active diffusion; slope 0 regime: nodes trapped in clumps. (B) Snapshots of node configurations. (C) Test of Eq. (6). Thick (red) lines show predicted slopes in R1, R2; thin (black) lines show fits. $t_{\mathrm{clump}}$ is time required to reach RMSD plateau (panel A) and $r_{\mathrm{clump}}$ is corresponding distance.Reuse & Permissions

Figure 4

Simulations of condensation of a band of nodes (periodic boundary conditions vertically). Nodes were placed according to Gaussian distribution with variance $w/2$. (A) Initial distribution (first panel) and snapshots of successful condensation or clump formation for different $\lambda$ ($l/w=0.0315$, $d/w=0.0125$, $a/w=0.25$). (B) Condensation time (time required for the standard deviation to decrease by $1/2$) vs $\lambda /w$ using $a/w=0.25$. For $\lambda /w<0.28$ the band does not shrink. (C) Test of $t_{\mathrm{shrink}}\approx l^2/(Qad)$. Solid (black) line is linear fit to R1 data: $t_{\mathrm{shrink}}=0.078(5)l^2/(Qad)$.Reuse & Permissions