We apply the Kim and Hummer (2008) Model A (KH-A), where each residue is represented by its C _α atom, as described in Horan et al. (2020); Smith et al. (2021). In the KH-A model, pairs of non-bonded residues interact through a Lennard-Jones (LJ)-type potential, either attractive or repulsive, based on the Miyazawa and Jernigan (1996) pairwise interaction matrix. There is no explicit solvent in the simulation systems. Debye-Hückel elactrostatics is used with uniform dielectric constant 80 and screening length 10 Å corresponding to ∼ 100 mM monovalent salt concentration. All LJ-like pairwise interactions were cutoff at a distance of three σ, where σ is the corresponding LJ parameter, while electrostatic interactions were cutoff at 35 Å.

During the simulations, protein domains with confirmed experimental structures are set as rigid and thus the interactions within these domains are neglected. The simulations didn’t include the nucleotides and associated divalent ion that are bound to Arp2, Arp3 or actin. Other flexible residues are connected to the neighboring residues by harmonic springs with equilibrium length 3.81 Å and spring constant 189 kcal/(mol Ų).

Simulations were performed using LAMMPS (Plimpton, 1995; in ’t Veld et al., 2008) and the KH-A model implementation of Smith et al. (2021) available at https://github.com/aah217/KH_LAMMPS. Depending on the system studied, serial simulations or replica exchange MD (REMD) simulations are performed. We used a time steps 10 fs. Our neighbor lists were updated every 1,000 steps. Langevin dynamics is applied with a damping parameter of 1,000 fs

For REMD simulations, 28 temperatures between 180 K and 540 K were used, to explore binding ensembles where protein complexes become bound (unbound) at low (high) temperatures. Temperature swapping was attempted every 100 steps. In REMD simulations the KH-A pairwise interactions strengths were independent of temperature. REMD simulations were run for sufficiently long to sample all candidate bound states, which we checked by repeat of REMD simulations or by checking that replicas span multiple temperatures (Qi et al., 2018). An example of typical dwell time distributions from Figure 1A is shown in Supplementary Figure S1.

All simulations were visualized in Visual Molecular Dynamics (VMD) (Humphrey et al., 1996).

We used two reference conformations for the inactive and active Arp2/3 complex. For the inactive Arp2/3 complex we used the cryo-EM structure of Zimmet et al. (2020) (PDB 6UHC), which is a structure of the human Arp2/3 complex with two bound N-WASP CA domains. We didn’t add any of the missing residues in PDB 6UHC for the inactive complex. We note that a few missing Arp2 residues (M1-G5, L389-R394), especially the N-termini ones, might be involved in actin monomer and C domain binding. The missing residues in Arp3 N- and C-terminal regions can play an inhibitory role for actin monomer binding (Rodnick-Smith et al., 2016). However, since in this complex Arp3 is sterically blocked by Arp2 and not available for actin binding, we didn’t add the missing residues. ArpC1 binds the A domain, however the missing residues are far from that site. Other missing residues include residues in subdomain two of the Arp2/Arp3, as well as residues in ArpC2, ArpC3, ArpC4, and ArpC5; these residues aren’t involved in the binding of daughter filament actin or CA domain, so they were also left missing.

For the active Arp2/3 complex we use the structure of branch junctions obtained by cryo-ET of NIH-3T3 fibroblast cells by Fäßler et al. (2020) (PDB 7AQK). The missing N-terminal residues of Arp2 (K388-R394) were added using MODELLER (Martí-Renom et al., 2000; Webb and Sali, 2016) in a configuration that doesn’t prevent actin monomer binding to its hydrophobic groove. The Arp3 doesn’t have any missing residues in the PDB file. For subunits ArpC1-C5, ArpC5 isn’t expected to be involved in binding to either the mother filament or the daughter filament (Fäßler et al., 2020). Therefore, the N-terminal residues of ArpC5 were left missing. The missing residues in ArpC2 C-terminal region were built for the study of binding to the mother filament, as discussed in the corresponding section of Results. Because this PDB file contains not only the active Arp2/3 complex, but also the mother and daughter actin filaments, the Arp2 and Arp3 are supposed to be in conformations that are ready for actin binding. During the writing of this work, a higher resolution cryo-EM structure of activated Arp2/3 complex from Bos taurus was obtained in vitro (Ding et al., 2022). The latter structure is overall very similar to that of Fäßler et al. (2020) so we expect the results presented here to hold for both activated structures.

The VCA domain sequence was taken from human WASP (UniprotKB P42768). The V and C helical regions were set as rigid bodies. The V domain configuration (R431-I442) was taken from PDB 2A3Z (Chereau et al., 2005) and the C domain (G465-I481) generated by aligning the WASP sequence to the N-WASP C-helix on the Arp2 or Arp3 binding site of PDB 6UHC (Zimmet et al., 2020). Other residues were assumed flexible.

For actin monomers binding to Arp2 and Arp3 we used the cryo-EM structure of ADP-Pi F-actin [PDB 7K21 from Chou and Pollard (2019)]. The missing N-terminal residues (D1-D3) were added using MODELLER (Martí-Renom et al., 2000; Webb and Sali, 2016). Each actin monomer was set as a rigid body except for D-loop region (H40-S52) that was assumed flexible, similar to Horan et al. (2020).

For mother actin filament, we used the structure from Fäßler et al. (2020) (PDB 7AQK). All eight actin subunits were kept in a rigid configuration relative to each other, but with the D-loops (residues 40–51), many of which are in close proximity to subunits of the Arp2/3 complex, assumed flexible. All the mother filament actin subunits had residues D1-E4 missing. They were left missing during the simulations as they aren’t considered essential for Arp2/3 complex binding. We note that we also explored using the higher resolution F-actin structure from Chou and Pollard (2019) (PDB 7K21) for the mother filament. The F-actin structures in 7K21 and 7AQK are very similar to each other, indicating that Arp2/3 complex does not significantly perturb the mother filament conformation (Fäßler et al., 2020; Ding et al., 2022). However, the Fäßler et al. (2020) structure lead to more stable Arp2/3 complex binding, presumably because even small differences complicate aligning the Arp2/3 complex along the large interface with the mother actin filament.

Distance root mean-square (dRMS) is calculated to quantify the similarity between a simulated conformation with respect to a reference conformation (Kim and Hummer, 2008). Only residue pairs near the binding interface (within 10 Å) of the reference conformation were included for the dRMS calculation. The conformations are considered to be similar to a reference conformation when dRMS is as small as a few Å. The reference conformations are either directly taken from published experimental conformation, or obtained by aligning different components to the experimental conformation using MultiSeq (Roberts et al., 2006) plugin in VMD.

Horan et al. (2020), who used KH-A to study association among actin subunits, found that the dissociation constant (K _d ) of actin complexes was sensitive to the LJ cutoff when comparing results at three σ versus four σ cutoff. Larger cutoff values increased complex binding affinity (decreased K _d ) but favored the most compact configurations, due to the directional nature of long range interactions in these implicit solvent simulations. However, the basic set of binding ensemble configurations was approximately maintained, independently of the three σ versus four σ cutoff, as well as independently of the temperature, provided it was low enough to keep the association. In this study we don’t aim to derive precise predictions on the absolute or relative magnitude of K _d values, a task largely beyond the limits of the KH model. Thus, similar to Horan et al. (2020), we characterize bound complexes at the lowest REMD temperature of 180 K, where the bound configurations occur with higher probability. Serial simulations were also performed at 180 K. We note that even at 180 K, disordered regions in our simulations don’t collapse into a globule, unlike KH model D which has stronger interactions among solvent accessible residues when compared to KH-A, and has thus been used to model chain collapse (Dignon et al., 2019).

We performed simulations to explore the binding of the CA domain of WASP to the Arp2/3 complex (Figure 1). The binding of CA domain to Arp2/3 complex at two distinct binding sites, the Arp2-ArpC1 site and the Arp3 site, is an important step in its activation (Zimmet et al., 2020).

We also performed simulations to study the delivery of actin to Arp2 and Arp3 of the active Arp2/3 complex, where both Arp2 and Arp3 sites (i.e., D1 and D2 subunit locations) are available (Figure 4). We examined the delivery of actin by REMD simulations. We fixed the C domain to either binding site on a rigid Arp2/3 complex, as in Figure 2B. The V domain was rigidly attached to the actin subunit in the F-actin configuration with flexible D-loop as in Figure 2B. The reference configurations for the dRMS calculation were the same as in Figure 2B for each of the simulations.

We found that the actin subunits bind to Arp2/3 complex in a few different conformations, which include low energy states with actin placed very close to the anticipated D1 or D2 locations (low dRMS hotspots in Figure 4). When C is attached to Arp2, the actin subunit can form various bound states with Arp2/3 complex, including close to the reference configuration at the D2 site (Figure 4A). The probability of finding the actin subunit at the D2 location was smaller, and the energy between actin and Arp2/3 complex higher, than in the corresponding simulations with the inactive complex of Figure 3B. However, the different resolution and different missing residues between the active and inactive complexes, as well slow simulation equilibration time prevents us from reaching definite conclusions regarding differential affinities for actin or VCA with the active or inactive Arp2/3 complex. When C is attached to Arp3, the actin subunit mainly formed two types of complexes with the Arp2/3 complex, with the one close to the D1 reference having the higher probability and lower energy between actin and Arp2/3 complex (Figure 4B).

In simulations with single free actin monomers interacting with Arp2/3 complex, the actin monomers were also found to associate close to the Arp2 and Arp3 sites (Supplementary Figure S8).

Given the success of reproducing actin and CA delivery to Arp2/3 complex, we wondered if the KH-A model can also be used to study the binding of active Arp2/3 complex to mother actin filaments. We thus performed serial simulations to study these interactions (Figure 5A). In these simulations, we used a rigid active Arp2/3 complex from Fäßler et al. (2020) (PDB 7AQK), as in Figures 1, 2, 4, but we allowed the regions of subdomain two of Arp2 and Arp3 that correspond to the D-loop of actin (40–53 for Arp2 and 45–58 of Arp3), which can potentially interact with the mother actin filament, to be flexible. For the mother filament, all eight actin subunits were kept in a rigid configuration relative to each other, but with the D-loops (residues 40–51), many of which are in close proximity to subunits of the Arp2/3 complex, assumed flexible (see Methods).

Both structures with Arp2/3 complex bound to actin filaments (Fäßler et al., 2020; Ding et al., 2022) lack the C-terminal tail region of ArpC2, likely a flexible region. In simulations where Arp2/3 complex was started with the ArpC2 tail missing, the complex progressively tilted away from the mother filament, opening a gap around the location of ArpC2 tail (Supplementary Figure S9). We thus added the ArpC2 C-terminal tail as a flexible region between the ArpC1 protrusion helix and ArpC4 and set it as a flexible region (Figure 5B).

With the added ArpC2 tail, the binding was stable and the system remained at low energies for the first 800 ns, after which the complex tilted as it diffused towards higher binding energies (Figure 5C, D, Supplementary Movie S7). The binding energy reflects the contribution of each subunit. In agreement with studies showing the importance of the ArpC1 protrusion helix in Arp2/3 complex activation (Ding et al., 2022), ArpC1 is the subunit that contributes the most. This is followed by ArpC2 and ArpC4, subunits known for their role in mother actin filament binding. The flexible tail of ArpC2 interacted with the region between subdomain one and two of F-actin subunit M6, in a typical configuration shown in the inset of Figure 5B. ArpC3 bound to the filament more stably over time, with weaker energies compared to ArpC1, ArpC2, and ArpC4. Arp2 and ArpC5 weren’t involved in the binding to the mother filament according to our criteria.

We note that the missing ArpC2 C-terminal tail can lie on either side of the ArpC1 protrusion helix. In Figure 5B we started with the ArpC2 tail between ArpC1 and ArpC5. We also run simulations with ArpC2 C-terminal region built between ArpC1 and ArpC3 (Supplementary Figure S10, Supplementary Movie S8). However, in this case the interaction energy between ArpC2 and the mother actin filament started much weaker and binding of Arp2/3 complex became unstable within 300 ns The ArpC2 tail unbound from the filament quickly and went through a gap between Arp2 and Arp3. Our simulations thus suggest that the ArpC2 tail localizes between the ArpC1 protrusion loop and ArpC5.

We also performed REMD simulations to see if active Arp2/3 complex will bind to the sides of an actin filament when starting from a separate state (Supplementary Figure S11). In order to sample the possible binding conformations efficiently, we reduced the LAMMPS mass variable of the Arp2/3 complex by a factor of 100, which allows faster diffusion of fully rigid objects (Horan et al., 2020). Therefore, the whole Arp2/3 complex was set as a rigid body and the ArpC2 tail was left missing. Preliminary simulations showed high affinity between the Arp2/3 complex and the ends of the actin filament, as well as between the Arp2/Arp3 interface and the actin filament, so we capped these ends with extra large beads (Supplementary Figure S11, magenta spheres). Even though many possible binding conformations have been avoided by these repulsive capping beads, the Arp2/3 complex formed a series of low energy complexes that differed compared to the expected side binding configuration (hotspots with dRMS tens of Å away from the 7AQK reference in Supplementary Figure S11). These configurations had stronger (lower) binding energies compared to ∼−8 kCal/mol when ArpC2 tail was absent (Supplementary Figure S9) and thus occurred with higher probability. It’s possible that these configurations correspond to the strongly bound “dead-end” complexes that don’t lead to daughter branches in prior single molecule imaging of Arp2/3 complex binding to actin filament (Smith et al., 2013).

Despite the simplifications involved in the CG approach, and without any modification of the interaction potentials, the KH-A model successfully reproduced the binding of the C region to the inactive Arp2/3 complex (Figure 1A). The stronger affinity of CA to the Arp2-ArpC1 site is also in agreement with experimental measurements of K _d values for the two binding sites (Zimmet et al., 2020). The model showed that upon C helix binding, the A domain fluctuated around the inactive complex, consistent with the lack of electron density for most of the A region in the cryo-EM structure of Zimmet et al. (2020), though the last four A domain residues weren’t strongly tethered to ArpC1, possibly reflecting limitations of the CG model.

The model also reproduced stable binding of two F-actin subunits to Arp2 and Arp3 of the activated complex (Figure 2A). Single actin subunits also bound stably to Arp2 and Arp3 (Supplementary Figure S5), though they exhibited larger fluctuations compared to the simulation with two actin subunits, which stabilized each other through short-pitch helix interactions. The D-loop of subdomain two held the fluctuating actin attached to Arp2 and Arp3, while subdomain four was less stably attached. We note however that the strength of the long-pitch interaction involving subdomain four might be underestimated in the KH-A model of an actin filament (Horan et al., 2020).

Serial simulations also kept the active Arp2/3 complex bound to the mother actin filament (Figure 5). This observation provided estimates of the predicted contribution to the binding free energy of each subunit of Arp2/3 complex. Interestingly, Arp3 interacted with the filament both attractively and repulsively with the mother filament, as its flexible loop (the loop between β4 and β5 corresponding to actin’s D-loop) exhibited fluctuating interactions with subunit M5 and the fluctuating D-loop of subunit M6. This observation may help explain why this loop play a dampening role in branch formation (Liu et al., 2013). The added ArpC2 C-terminal tail, though missing from experimental conformations (Fäßler et al., 2020; Ding et al., 2022), was important to stabilize this binding. Presumably, this region was not detected experimentally due to sampling of various conformations and extended linear shape, as in our CG simulations. Prior studies showed that antibodies for the ArpC2 C-terminal region inhibited side-branching (Bailly et al., 2001).

We focus on the mechanism supported by Zimmet et al. (2020), being one of the most recent models based on structural data, noting that it combines data and mechanism from extensive prior works, and that some aspects may be different for the yeast Arp2/3 complex. According to this model, the first step is the delivery of actin to Arp2 along with binding of CA to the Arp2/ArpC1 site. This is a pathway that we essentially reproduced in our simulations. When we attached C to inactive Arp2/3 complex, V-bound actin could be delivered to Arp2 (Figure 3B) and vice versa, when V-actin was attached to Arp2, CA could bind close to the Arp2/ArpC1 site (Figure 3C). However, in simulations where both V-actin and CA started detached from the inactive Arp2/3 complex, we only observed either C or actin close to their respective binding sites, but not both together. Precise placement of the C helix and the flexible actin D-loop near the same spot on Arp2 in a way that they don’t block each other might depend on atomistic-level features, beyond the abilities of the coarse-grained model; this may be the reason why such a structure wasn’t observed in these simulations.

The subsequent activation step is the binding of VCA-actin in a long pitch to Arp3 (Zimmet et al., 2020). This step is enabled by the binding of VCA-actin to Arp2/ArpC1, which is expected to induce (or make more frequent) a conformational change bringing Arp2 and Arp3 into a short-pitch helix. Our simulations showed that such delivery of actin to Arp3 is possible: V-actin was delivered when C was attached to the Arp3 site of the active complex (Figure 4B). Our simulations also suggest that the proposed final complex of activated Arp2/3 complex with two bound actin subunits and two VCA domains is a viable possibility (Figure 2B).

In cells, the above VCA-mediated activation processes should occur close to membrane regions with bound dimers or high concentrations of VCA-containing proteins. Presumably, free actin and profilin-actin can bind to Arp2 of the inactive Arp2/3 complex in the cytoplasm (Figure 3A), but should be unable to activate it in the absence of VCA.

After binding of the complex with two VCA-actin subunits to the side of a mother actin filament, the final step is detachment of VCA from the Arp2/3 complex and growth of the daughter filament by polymerization. We note some observations in our simulations that may relate to VCA detachment. When comparing the inactive and active cases, the binding site of the C helix to the active complex was slightly displaced compared to the Arp2 site of the active complex (lying in between Arp2 and ArpC1 Figure 1). The delivery of V-actin to the Arp2 site of the active complex (Figure 4A) also occurred with lower probability when compared to the inactive complex (Figure 3B). These observations could reflect internal strains that develop upon completion of Arp2/3 complex activation, promoting VCA release.

While we reproduced C helix binding to the Arp3 site of the inactive complex, we didn’t observe the same for the active complex (Figure 1). Given the weakness of the inactive complex interaction however, it’s unclear if this might also indicate a tendency for C detachment. We note that in the yeast Arp2/3 complex, the affinity of CA for that site increases 40-fold upon binding to the mother filament (Ti et al., 2011).

Our simulations also showed structures that may reflect non-specific complexes, such as a crossed binding mode of CA domain to the active Arp2/3 complex. This binding may potentially pull Arp3 and ArpC1 close to each other, pushing the complex towards an active configuration in a non-canonical way. To our knowledge, there have been no experimental results supporting this hypothesis so far.

The KH-A coarse-grained model as employed here required the folded domains of proteins to be set as rigid. The transition between the inactive and active conformations cann’t be directly studied with this method. CG-MD simulations with added flexibility or higher resolution that can capture protein backbone motions, followed by all-atom MD simulations informed by CG models, should help to study this essential transition.