A theory for coexistence and selection of branched actin networks in a shared and finite pool of monomers

TL;DR

The paper addresses how branched actin networks can coexist when competing for a finite pool of actin monomers. It develops a minimal, diffusion-aware growth model that couples network elongation and branching to a shared monomer pool, yielding a central density dynamics equation: $\dot{x_i} = \left( \frac{\mathcal{A}_i}{1 + \sum_{j=1}^N \frac{x_j^{3/2}}{1 + \mathcal{B} x_j}} \frac{1}{1 + \mathcal{B} x_i} - 1 \right) x_i$. The main findings show that local depletion in the branching zone creates a negative feedback that supports coexistence of multiple networks, while stronger competition drives selection of the fittest networks; these predictions are validated by spatial FEM simulations. The work highlights local depletion as a universal size-control mechanism for branched actin architectures and offers a phase diagram linking coexistence and selection to experimentally tunable parameters. This framework provides a quantitative link between microscopic branching physics and macroscopic network organization in cells and biomimetic systems. $\dot{x_i}$ represents the growth dynamics of each network’s density, while parameters $\mathcal{A}$ and $\mathcal{B}$ encode branching-capping balance and diffusion/turnover, respectively.

Abstract

Cellular actin structures are continuously turned over while keeping similar sizes. Since they all compete for a shared pool of actin monomers, the question arises how they can coexist in these dynamic steady states. Recently, the coexistence of branched actin networks with different densities growing in a shared and finite pool of purified proteins has been demonstrated in a biomimetic bead assay. However, theoretical work in the context of organelle size regulation has mainly been focused on linear architectures, such as single filaments and bundles, and thus is not able to explain this observation. Here we show theoretically that the local depletion of actin monomers caused by the growth of a branched network naturally gives rise to a negative feedback loop between network density and growth rate, and that this competition is captured by one central equation. A comprehensive bifurcation analysis shows that the theory leads to well-defined steady states even in the case of multiple networks sharing the same pool of monomers, without any need for specific molecular processes. Under increasing competition strength, coexistence is replaced by selection. We also show that our theory is in excellent agreement with spatiotemporal simulations implemented in a finite element framework. In summary, our work suggests that local monomer depletion is the decisive and universal factor controlling growth of branched actin networks.

Figures (8)

• Figure 1: Experimental situation of interest. (a) Actin networks grown from beads with high (blue) and low (orange) coating densities of nucleation promoting factor coexist in a shared pool of actin monomers. The “strong” beads create denser networks (black tails) than the “weak” beads (grey tails). They consume more monomers per time and thus deplete the local actin monomer concentration to a higher degree, indicated by the color gradient from red (high actin monomer concentration) to white (low concentration). Even though all beads share one pool of monomers, the local concentration of actin monomers is higher at the weak bead. (b) Sketch of an actin network growing from the bead surface. (c) Schematic sketch of the mechanisms underlying network growth: Arp2/3 is activated at the surface and leads to a thin branching zone. There, the balance of branching and capping determines the filament density of the network. The network grows in length by filament elongation at the front and is disassembled by ADF/cofilin-mediated severing at the back, leading to an exponential density profile along its length with a constant network width. The position at which the density drops below the percolation threshold defines the network size. Branching and filament elongation speed are limited by the local concentration of actin monomers, which are locally depleted in the branching zone and are replenished by diffusive fluxes.
• Figure 2: Effect of local monomer depletion. (a) Monomer concentration as a function of radial distance $r$ for different filament densities $n$, including local and global depletion. The dashed line corresponds to the constant concentration of $A_{\text{tot}} = 6 \ \mu$M in the absence of any monomer consumption. (b) Monomer concentration in the branching zone ($r=R$) as function of filament density $n$ considering only global depletion (blue curve), only local depletion (orange curve with $G(n) \equiv 6 \ \mu$M fixed), and the combination of both (green curve).
• Figure 3: Bifurcation diagram for a single network obtained by numerical continuation. (a) Filament density $n$ of the network in the branching zone as a function of effective branching rate $\mathcal{A}$ for different values of the depletion parameter $\mathcal{B}$. The dimensionless parameters $\mathcal{A}$ and $\mathcal{B}$ correspond to the rates $k_{\text{branch}}$ and $k_{\text{sev}}$, respectively. (b) Projected area of the network given by $2R$ times the network length $L$. (c) Local concentration $g(n)$ of actin monomers in solution inside the branching zone, independent of $\mathcal{B}$. (d) Global actin monomer concentration as average over the whole microwell.
• Figure 4: Competition between equivalent networks. (a) Projected network area per network and (b) total amount of polymerized actin within all networks as functions of the number of networks $N$. Rapid turnover corresponds to the value of the severing given in Table \ref{['tab: Parameter values']}. For slow turnover, the rate is four times smaller.
• Figure 5: Coexistence of one weak and one strong network. (a) The amount of polymerized actin in the strong network without (dashed lines) and with competition (solid lines). The markers indicate FEM results of the spatial diffusion model. Insets show the respective bifurcation points associated with the onset of network formation. Dotted lines indicate the experimental value of $A_{\text{tot}}$ used in guerinBalancingLimitedResources2025. (b) Same for the weak network. (c) The relative change in network size between with and without competition for the strong network. (d) Same for the weak network. Note the different y-scale.