A thermodynamic framework for nonequilibrium self-assembly and force morphology tradeoffs in branched actin networks

Reviewer #1 (Public review):

Summary:

This paper investigated the dynamic self-assembly of branched actin networks and the relation between the nonequilibrium features of the dynamics with the thermodynamic cost. The authors constructed a chain model to describe the self-assembly process of a branched actin network, including events like nucleation, polymerization, and capping. The forward and backward transition rates associated with the events allowed them to investigate the entropy production rate of the dynamics. They then used the fact that the entropy production rate has to be greater than zero to derive inequalities that set bounds for the maximum force produced by the branched actin network. The idea is similar to estimating the polymerization force of actin filament via the equation F_{max} = dG/delta, which sets a bound on the maximum force by the thermodynamic potential dG which is the chemical energy associated with ATP hydrolysis and delta is the length increment upon monomer insertion. Furthermore, they speculated the dissipative cost beyond what is necessary to move the load may be necessary to maintain an adaptive steady state.

Strengths:

The authors developed a simple model that is capable of qualitatively reproducing some mechanical phenomena for a branched actin network. The model has captured the essential dynamic elements in the branched actin network and built connections between the maximum load and the adaptation behavior with the energetic cost. It is an interesting study that provides a new perspective to look at the mechanical response of the branched actin network.

Weaknesses:

The text needs to be improved, particularly in the model introduction part. It is unclear to me what happens to the state when the reverse reaction in Figure 2 occurs.

Furthermore, what the authors have done is similar to estimate the polymerization force of actin filaments but in a more complicated scenario. Their conclusion that "dissipative cost in the system beyond what is necessary to move the load may be necessary to maintain an adaptive steady state" is skeptical. The branched actin network is a nonequilibrium system driven by active processes like ATP hydrolysis that converts chemical energy into mechanical work. There has to be a gap between the actual E-C_f curve and that when dissipation rate dot{S} = 0. If the authors want to make the claim, they have to decompose the dissipation into different parts and show that a particular part is associated with adaption. Otherwise, the conclusion about the gap is baseless.

Reviewer #2 (Public review):

Summary:

Rennert et al. developed a thermodynamic framework for the assembly of branched networks to calculate the entropy dissipation associated with this process. They base their model on the simplest possible experimental system consisting of four proteins: actin, Arp2/3, capping protein, and NPF. They decompose the network assembly into a linear model where the order of events (polymerization, capping, and nucleation) is recorded sequentially. Polymerization and capping are sensitive to load and affected by Brownian ratchet effects, while nucleation is not. This simplified model provides an analytical solution that describes the load sensitivity of actin networks and agrees well with experimental data for a given set of transition rates.

Strengths:

(1) These thermodynamic approaches are original and fundamental to our understanding of these non-equilibrium systems.

(2) The fact that the model fits experimental data is encouraging.

Weaknesses:

(1) The possibility of describing branched actin assembly as a Markov process is not well justified.

(2) The choice of parameters controlling the system is open to question. Some parameters are probably completely negligible, while other ignored effects are potentially significant.

(3) The main conclusion of the manuscript, linked to the existence of a dissipation gap, is quite expected. The manuscript would have been more valuable if the authors had been able to decompose dissipation into different components in order to prove that a particular fraction is associated with adaptation.