Branch regulation by phosphate, mechanics, and regulatory proteins. (A) Reaction scheme of the regulation of actin filament branches as a function of force and Pi in solution. After branch initiation by the coordinated action of membrane-bound NPFs, actin and inactive ATP-Arp2/3 complex, ATP-Arp2/3 quickly becomes ADP-Pi-Arp2/3. Depending on Pi concentration, branches are in rapid equilibrium between ADP- and ADP-Pi states. The gray box represents the force-sensitive stage. In the low pulling force regime (below 6.5 pN), for Arp2/3 complexes in either the ADP or ADP-Pi state, the interface with daughter filaments is more likely to rupture before the Arp2/3 complex–mother filament interface. Surviving ADP-Pi-Arp2/3 complexes detach very slowly from mother filaments. Pi release from the surviving ADP-Pi-Arp2/3 complex is slow enough to allow actin to bind to the Arp2/3 complexes and regrow a branch, without the need to exchange ADP for ATP in Arp2/3. The surviving ADP-Arp2/3 complex is more unstable, and rapidly reloads ATP to allow actin to bind to renucleate a branch where ATP in Arp2/3 complex will be hydrolyzed. Rate of the dissociation of surviving ADP-Arp2/3 complex from mother filaments is from previously published work (Ghasemi et al., 2024). (B) Actin filament branches are initiated by membrane-bound NPFs that activate Arp2/3, and recruit two actin monomers to the pseudo-barbed end formed by Arp2 and Arp3. Upon ATP hydrolysis within the Arp2/3 complex, the cytoplasmic Pi concentration sets the equilibrium between the ADP and ADP-Pi states of the Arp2/3 complex at branch junctions. Pulling force accelerates debranching. Capping proteins limit the growth of branches. Branch renucleation is favored by elevated concentrations of actin, ATP, or Pi in the cytoplasm. GMF and cortactin do affect ADP-Pi-Arp2/3 complex branch stability. GMF accelerates debranching and dissociation of surviving ADP-Arp2/3. Cortactin stabilizes branch junctions and favors renucleation from ADP-Arp2/3 complexes.