Coupling of actin hydrolysis and polymerization: Reduced description with two nucleotide states

The polymerization of actin filaments is coupled to the hydrolysis of adenosine triphosphate (ATP), which involves both the cleavage of ATP and the release of inorganic phosphate. We describe hydrolysis by a reduced two-state model with a cooperative cleavage mechanism, where the cleavage rate depends on the state of the neighboring actin protomer in a filament. We obtain theoretical predictions of experimentally accessible steady state quantities such as the size of the ATP-actin cap, the size distribution of ATP-actin islands, and the cleavage flux for cooperative cleavage mechanisms. Introduction. – Actin filaments are an important structural element of the cytoskeleton, and their ATPdriven polymerization dynamics plays an important role in cell motility [1]. The ATP hydrolysis in actin filaments is the basis for treadmilling, i.e., the simultaneous polymerization and depolymerization at the two ends of a filament, and is necessary for actin-mediated force generation and motility [2]. Actin monomers (G-actin) assemble into polar actin filaments (F-actin) with a fast polymerization dynamics at the barbed end and a slow polymerization dynamics at the pointed end. Actin monomers can bind ATP, which is then hydrolyzed in a two-step process into adenosine diphosphate (ADP) and inorganic phosphate (Pi). First, ATP is cleaved into the complex ADP-Pi, from which Pi is released in a second step. After incorporation into a filament the actin protomers can therefore be in three different states: a T-state (ATP-actin), a Θ-state (ADP-Piactin), and a D-state (ADP-actin). Past studies have focused on two sorts of cleavage processes in actin filaments. In random cleavage, T-protomers are cleaved independent of the state of their neighbors [3–5]. In vectorial cleavage, there is a sharp interface between the ATP-cap containing only T-protomers and the remaining filament consisting of Θand D-protomers, and cleavage can only occur at the TΘ-interface [6–9]. In this Letter, we investigate cooperative hydrolysis mechanisms, where the cleavage rate of each monomer depends on the state of its neighbors and which contain random and vectorial mechanisms as special cases. Cooperative hydrolysis was previously discussed in Ref. [10] for actin and Ref. [11] for microtubules. One important piece of evidence for a cooperative hydrolysis is the small hydrolysis rate of G-actin as compared to F-actin, which acts as a very effective ATPase with a fast hydrolysis rate. This pronounced change of the ATP hydrolysis rate after inclusion of G-actin monomers into filaments suggests that the cleavage rate is affected by binding to other protomers in the filament. Furthermore, structural differences between Tand D-state protomers indicate that cleavage might be affected by the same structural elements that are also involved in the binding of protomers [12, 13]. A complete model of ATP hydrolysis involves all three nucleotide states of actin protomers. We have studied such three-state models for cooperative ATP hydrolysis in Ref. [14]. In this Letter, we will consider a reduced two-state model by combining the Θ-state and the D-state of protomers into a single D-state. This means that we focus on the cleavage of T-protomers and ignore the subsequent process of Pi-release. The reduction to two protomer states can be justified for fast growth at high Tmonomer concentrations. The reduced model has the advantage that we are able to obtain analytic predictions for important steady state observables, such as the size of the