A thermodynamic framework for nonequilibrium self-assembly and force morphology tradeoffs in branched actin networks
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eLife Assessment
Rennert et al. developed a valuable thermodynamic framework to study the force response of branched actin networks from the crucial and unexplored perspective of energetic cost. They used the fact that the entropy production rate must be positive to derive inequalities that set limits on the maximum force produced by branched actin networks, and speculate that the dissipative cost beyond that required to move the load may be necessary to maintain an adaptive steady state. This work is highly innovative, but remains incomplete until the hypotheses of the model are better justified and the conclusions about the dissipative cost of the system are better established.
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Abstract
Branched actin networks are involved in a variety of cellular processes, most notably the formation of lamellipodia in the leading edge of the cell. These systems adapt to varying loads through force dependent assembly rates that allow the network density and material properties to be modulated. Recent experimental work has described growth and force feedback mechanisms in these systems. Here, we consider the role played by energy dissipation in determining the kind of growth-force-morphology curves obtained in experiments. We construct a minimal model of the branched actin network self assembly process incorporating some of the established mechanisms. Our minimal analytically tractable model is able to reproduce experimental trends in density and growth rate. Further, we show how these trends depend crucially on entropy dissipation and change quantitatively if the entropy dissipation is parametrically set to values corresponding to a quasistatic state. Finally, we also identify the potential energy costs of adaptive behavior by branched actin networks, using insights from our minimal models. We suggest that the dissipative cost in the system beyond what is necessary to move the load may be necessary to maintain an adaptive steady state. Our results hence show how constraints from stochastic thermodynamics and non-equilibrium thermodynamics may bound or constrain the structures that result in such force generating processes.
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eLife Assessment
Rennert et al. developed a valuable thermodynamic framework to study the force response of branched actin networks from the crucial and unexplored perspective of energetic cost. They used the fact that the entropy production rate must be positive to derive inequalities that set limits on the maximum force produced by branched actin networks, and speculate that the dissipative cost beyond that required to move the load may be necessary to maintain an adaptive steady state. This work is highly innovative, but remains incomplete until the hypotheses of the model are better justified and the conclusions about the dissipative cost of the system are better established.
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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 …
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.
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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 …
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.
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