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  1. Author Response:

    Reviewer #1:

    Reviewer 1 expresses some concerns regarding concentrations of soluble proteins during our experiments. This is a good point and, in response, we are rewriting the manuscript to more clearly describe the metastable nature of the soluble protein pool. The key feature of our reaction mixture is that it contains both profilin and capping protein, which work together to suppress filament assembly. Spontaneously nucleated filaments are rapidly capped at their barbed ends. Profilin then effectively prevents elongation from the pointed ends of these filaments and they disassemble. We will cite relevant work that establishes and discusses these synergistic activities. Young et al. (1990) found that factors that cap >90% of filament barbed ends increase the critical concentration from that of the barbed end to that of the pointed end, and several groups demonstrated that profilin and barbed-end capping proteins work together to suppress filament assembly and promote disassembly of filaments with free pointed ends (e.g. DeNubile, 1985; Blanchoin, 2000; Pernier, 2016). This combination produces a large pool of monomeric actin that is capable of transiently elongating any newly formed barbed ends. We previously described this pool as ‘metastable’ (Pollard, 2000) while others have described it as ‘dynamically stable’ (Pernier, 2016). Only the branched actin networks formed by the micro-patterned nucleation promoting factors have an appreciable lifetime and consume a significant fraction of the soluble proteins, because filaments can only be formed by continual rounds of nucleation and only remain stable when their pointed ends are capped by the Arp2/3 complex (Blanchoin, 2000). In addition, the total amount of protein incorporated into the micro-patterned branched networks is only a small fraction of the total protein present in the reaction mix. This is demonstrated by the fact that the network growth rate is constant over the course of each experiment. We will mention this in the revised manuscript and provide the following simple calculation to emphasize this point: The concentration of actin in our reaction mixes is 5 µM, with a total volume of 150 µl. The maximum concentration of actin in our networks is 1.25 mM, but the maximum total volume of these networks is only <0.002 µl (based on a total of 400 WAVE1 patches with an average area of 50 µm^2, generating networks with a maximum height of <100 µm). The fraction of actin used up during an experiment, therefore, is less than 0.3%.


    Blanchoin L, Pollard TD, Mullins RD. (2000) Interactions of ADF/cofilin, Arp2/3 complex, capping protein and profilin in remodeling of branched actin filament networks. Curr Biol. 10(20):1273-82.

    DeNubile MJ, Southwick FS. (1985)Effects of Macrophage Profilin on Actin in the Presence and Absence of Acumentin and Gelsolin J. Biol. Chem. 260(12):7402-7409.

    Pernier J, Shekhar S, Jegou A, Guichard B, Carlier MF. (2016) Profilin Interaction with Actin Filament Barbed End Controls Dynamic Instability, Capping, Branching, and Motility. Dev Cell. 36(2):201-14.

    Young CL, Southwick FS, Weber A. (1990) Kinetics of the Interaction of a 41-Kilodalton Macrophage Capping Protein with Actin: Promotion of Nucleation during Prolongation of the Lag Period. Biochemistry, 29:2232-2240.

    Reviewer #2:

    Reviewer #2’s comments about the molecular mechanism underlying the force-induced increase in free barbed ends make it clear that our explanation was not as clear as it should have been. We will provide more detailed derivations for our mathematical methods, but in the meantime, we hope that the following explanation will clear up any misunderstanding.

    Reviewer 2 rightly notes that “…for both capping and branching, the authors find that they decrease the same way with increasing loads - as they should: this is imposed by their being at steady state, where the birth rate of growing barbed ends (branching) must match their death rate (capping).” This steady state condition is actually the starting point for our analysis. At steady state the overall rates of nucleation and capping must be equal (Rcapping = Rnucleation). Importantly, the overall rate of nucleation is a complicated function that depends on the occupancy of the WH2 domains, the surface-associated Arp2/3 complex, and the local density of polymeric actin. On the other hand filament capping in our system appears to be a simple bimolecular interaction between soluble capping protein and free barbed ends. We demonstrated this by showing that the average filament length (i.e. the ratio of polymeric actin to capping protein in the growing network) varies as a simple inverse function of the capping protein concentration. This means that the overall rate of nucleation (Rnucleation) must equal the product of the capping protein concentration ([CP]), the surface density of free barbed ends (E), and an appropriate capping rate constant (kc). This yields,

    kc[CP]E = Rnucleation

    Which can be rearranged to give the density of free barbed ends,

    E = Rnucleation/(kc*[CP])

    As the reviewer notes, this equation describes a density, not a unitless number. Note that a sudden decrease in per-filament capping rate (e.g. a decrease in the rate constant, kc) with no change in overall nucleation rate will cause the number of free barbed ends to increase until the overall rate of capping (kc[CP]E) once again matches the overall rate of nucleation. This equation is an “iron law” imposed by the steady-state (or quasi-steady state) character of the system, and it means that any increase in the density of free barbed ends must reflect EITHER an increase in the overall rate of nucleation OR a decrease in the per-filament capping rate (or possibly both). Our direct measurements of the overall nucleation rate (the quantity in the numerator) rule out the first possibility, meaning that the per-filament capping rate MUST go down with applied force. Furthermore, our measurements demonstrate that this capping rate displays the same force sensitivity as actin filament elongation. The best explanation for this phenomenon is that the insertion of a capping protein onto a filament barbed end is subject to the same constraints as the insertion of an actin monomer. This could have been predicted from Brownian Ratchet theory, but as the reviewer points out, it was not. Our “bulky capping protein” experiments are a direct test of whether Brownian Ratchet theory can account for the force sensitivity of filament capping, and they demonstrate that it can.

    In summary, we stand by our original explanation, namely that applied forces cause a decrease in the rate at which individual filaments are capped (via a change in the rate constant for filament capping, kc). This decrease, which can be explained by Brownian Ratchet Theory, leads directly to an increase in the steady-state barbed end density.

  2. Evaluation Summary:

    This in vitro study proposes to explain why branched actin filament networks, similar to the ones encountered in migrating cells, become denser when they grow against a mechanical load. This question is of broad interest, and has long been waiting for a molecular-scale explanation. Building on their previously published tools and results, the authors perform a series of elegant and clever experiments, and convincingly identify key molecular mechanisms. Importantly, the results also confirm the Brownian ratchet model for actin assembly. This study captures several important features of branched filament networks, and should become a reference on the topic.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. The reviewers remained anonymous to the authors.)

  3. Reviewer #1 (Public Review):

    Here, Tai-De Li et al. exploit an AFM system established by the same team in 2016 to measure precisely rates of actin filament elongation, nucleation and CP binding when branched actin networks grow under force. They observe that all rates decrease when growth stress increases, albeit to different extent. Rate of capping decreases faster, leading to a densification of actin networks as stress increases. A nice observation is that capping and elongation follow the same trend, suggesting a similar mechanism. A logical explanation is that insertion of both G-actin and CP are limited by the same Brownian ratchet mechanism, an idea which seems to be coherent with the fact that a larger CP has even more difficulty to insert between actin filament barbed ends and the surface.

    This is also a beautiful and very informative experimental setup. Data are convincing although their presentation should be improved for clarity. Few controls are missing (mainly whether bulky CP diffuses at the same rate than CP within branched networks and checking if the protein pool is the same at the time the AFM measurements are performed in experiments at different CP concentrations ), but the authors should be able to control these points by running some additional experiments.

  4. Reviewer #2 (Public Review):

    This study proposes to explain why branched actin filament networks become denser when they grow against a mechanical load. This important property provides these networks with mechanical adaptability (nicely demonstrated by the authors in Bieling et al. Cell 2016), and has yet to be understood from a molecular perspective.

    Here, the authors use a suite of very powerful in vitro experiments, which they have developed over the past years, to study the impact of force on the main molecular reactions involved in the growth of branched network. They convincingly show that: (1) the incorporation of actin monomers and capping protein into the network is limited, when a mechanical load is applied, by a Brownian ratchet mechanism; while (2) the incorporation of Arp2/3, responsible for branching, is limited by the unavailability of its surface-anchored activator, as it interacts with the free barbed ends of filaments from the network. This 'barbed end interference' mechanism was recently identified by the authors (Bieling et al. EMBO J 2018, Funk et al. Nat Comm 2021) and they show here that it provides a negative feedback on branch nucleation, to control network density when a mechanical load is applied.

    These are new and important results. A clear demonstration of the Brownian ratchet mechanism for actin polymerization has been missing for decades, observing it on single filaments seems out of reach, and the present study provides the best evidence to date. The authors also show the relevance of the Brownian ratchet for capping, which had been mostly overlooked until now.

    However, I disagree with the the way the authors compare the impact of load on the capping and branching rates, and with their claim that it explains why networks become denser when a load is applied.

    The authors write that, upon the application of force, the drop in the rate of filament capping is larger than the drop in the rate of nucleation (Arp2/3-mediated branching) but this is because they are comparing the capping rate per filament to the nucleation rate per surface area. This presentation is misleading: the difference between the two rates simply reflects the change in filament density, by definition, and does not explain it. If the same definition of the rate is used (i.e. per filament, or per area) for both capping and branching, the authors find that they decrease the same way with increasing loads - as they should: this is imposed by their being at steady state, where the birth rate of growing barbed ends (branching) must match their death rate (capping).

    The new and interesting result is that the two identical drops in branching and capping rates have different molecular origins, but the authors do not explain how this leads to an increase in density. However, I think that this explanation is within reach, thanks to the experimental results provided by this study: the Brownian ratchet and the barbed end interference mechanisms depend on filament density in very different ways.

  5. Reviewer #3 (Public Review):

    In this paper, the authors' goal was to identify the molecular mechanisms behind the results the obtained in a previous paper (Bieling, Li et al, 2016). The authors reused similar experimental setup and some previously acquired data and performed a deeper analysis of the data to determine the effect of load on different parameters related to actin subunits, filaments barbed ends, capping protein and the Arp2/3 complex.

    The experimental novelties in this paper are the clever use of an arrest and quenching strategy to determine the relative amount of actin monomers and barbed ends bound to the WH2 domain of the Arp2/3 complex activator.

    The quantitative analyses of this paper are quite interesting and nicely demonstrate the authors' points. The clever use of a larger capping protein also clearly demonstrates the effect of size on the on-rate constants under load.

    The only major point that remained unclear to us is whether the conclusions are universal for all Arp2/3 complex activators. What would happen to the results if another activator was used, if activators were prevented from binding to the barbed ends or monomers, or able to bind several actin monomers or barbed ends at the same time? The authors could also discuss more the effect of other proteins usually present in branched actin networks (e.g. crosslinkers, severing proteins), ideally with new experiments, or at least as speculations in the discussion.

    Overall the authors do a good job at convincing the reader.