*2.2. Identification and MD Simulations of Productive Actin–Domain V Encounter Complexes*

The binding mechanism of N-WASP domain V to actin was further investigated using MD simulations of productive encounter complexes selected on the basis of the position and orientation of regions 9–18 or 37–46 in the cognate actin binding groove. More specifically, among the 7030 most probable complexes generated by docking, we identified those with residues 9–18 or 37–46 contacting at least six actin residues over the nine observed in contact with the N-WASP region 37–46 in the X-ray structure (Y143, G146, T148, G168, Y169, L349, T351, M355, and F375). We found a total of 194 complexes which have one of the two recognized segments in contact with at least six of the nine actin hot-spot residues. However, in a large number of these complexes, the segment 9–18 or 37–46 is oriented in the opposite direction of the crystallographic helix, so that the consensus sequence "LKKV" would not be able to reach its cognate binding site. Thus, we further filtered the 194 complexes based on the angle between the principal axis of segment 9–18 or 37–46 and that one of the helical region 37–46 in crystal. We obtained 16 and 18 complexes in which this angle is lower than 30◦ for N-WASP regions 9–18 and 37–46, respectively (Tables S2 and S3).

In these 34 productive actin–domain V encounter complexes, the recognized regions 9–18 and 37–46 are surprisingly not completely folded in *α*-helix, but can have various local conformations with 0–6 over 10 residues in helical structures. Nevertheless, it should be noted that the lack of helical residues is often balanced by several residues with a turn motif. This is notably the case for four over the five complexes which have region 9–18 or 37–46 RMSD lower than 5 Å relative to the crystallographic structure (Tables S2 and S3). In the 34 actin–domain V complexes, the consensus segments "LKKV" are variously far off from their cognate binding site on actin, as indicated by their RMSD values ranging from 8.7 to 37.7 Å. To study the complete association process of N-WASP WH2 motifs, we performed MD simulations of actin–bound domain V conformational changes starting from the two structures which have region 9–18 or 37–46 with the lowest RMSD relative the structure 2VCP (Figure 3). These selected productive encounter complexes are hereafter denoted CplxA and CplxB.

**Figure 3.** Side view of the two best 1:1 actin–domain V encounter complexes with N-WASP segment 9–18 (**left**) or 37–46 (**right**) located and oriented as in structure 2VCP. Black balls are N-terminal C*α*-atoms of domain V. Red and magenta ribbons represent its regions 9–18 or 37–46 and consensus sequences "LKKV", respectively. As a reference, yellow and green ribbons indicate the helical and 50LKSV53 regions of domain VC in 2VCP.

For each selected encounter complex, two MD simulations of about 350 ns were performed from the same coordinates but with different initial velocities. These four simulations will be referred to as CplxA\_MD1, CplxA\_MD2, CplxB\_MD1, and CplxB\_MD2. In all complex trajectories, the actin tertiary structure remains stable, with RSMD relative to structure 2VCP fluctuating below 5.2 Å (Figure 4). Regarding the N-WASP regions 9–18 and 37–46 (which are bound to actin in CplxA and CplxB, respectively), their position and orientation are maintained in the actin binding site in three over four simulations (CplxA\_MD1, CplxA\_MD2, and CplxB\_MD1), as indicated by their average RMSD values relative to the complex 2VCP (4.4, 4.4, and 2.7 Å, respectively). A visual inspection of the CplxB\_MD2 trajectory showed that segment 37–46 slid toward the bottom of actin, explaining its higher RMSD (8.2 Å on average). For the three other simulations, the N-WASP regions 9–18 and 37–46 remain attached to their binding site after the formation of productive encounter complexes.

**Figure 4.** Time evolutions of RMSD relative to structure 2VCP, after fitting MD trajectories on crystallographic actin, for actin (black) and segments 9–18 (orange) and 37–46 (cyan) of N-WASP domain V.

Next, we monitored the dynamics of residues 22LKKV25 and 50LKSV53 relative to their cognate binding site on actin. As shown in Figure 5, segments 22LKKV25 and 50LKSV53 had large amplitude motions in all four simulations, without reaching stable bound positions on actin. Strikingly, the minimal distance to actin of these residues and their RMSD relative to structure 2VCP seem to be highly correlated, which can be explained as follows: Once N-WASP domain V helical region 9–18 or 37–46 is correctly positioned and oriented in its cognate binding site, if segment 22LKKV25 or 50LKSV53 is detached from actin's surface, it is largely free to move in solvent, accounting for large RMSD values. However, when it is bound to actin, its accessible space is narrowed down to a region close to the cognate site on actin, decreasing the RMSD relative to X-ray structure. However, in none of simulations, these segments were observed to persistently bind to their cognate binding site: In simulations CplxB\_MD1 and CplxB\_MD2, RMSD of residues 50LKSV53 relative to the crystallographic structure never decreased below 13.8 Å. The observed large RMSD values are mainly due to the fact that segment 50LKSV53 is, most of the time, detached from actin's surface in simulations of CplxB. In simulations of CplxA, segment 22LKKV25 was able to reach its cognate site, with minimal RMSD of 2.4 and 4.3 Å in CplxA\_MD1 and CplxA\_MD2, respectively, but these associations were only transient (Figure 5). Overall, in three over four simulations, residues 22LKKV25 or 50LKSV53 were observed to bind the actin's surface during quite long periods, but not necessarily at their cognate locations, confirming that these N-WASP segments are not primary recognition sites for actin. Finally, we should point out that the auto-correlation functions of minimal distances to actin of residues 22LKKV25 or 50LKSV53 are characterized by relaxation times of 102, 126, 164, and 133 ns for simulations CplxA\_MD1, CplxA\_MD2, CplxB\_MD1, and CplxB\_MD2, respectively. This notably indicates that the two short simulations of CplxA still provide reliable information about the dynamics of segment 22LKKV25.

**Figure 5.** Time evolutions of minimal distance to actin of segments 22LKKV25 (black) and 50LKSV53 (brown) of N-WASP domain V. RMSD relative to structure 2VCP, after fitting trajectories on actin, are also displayed as a function of time for segments 22LKKV25 (orange) and 50LKSV53 (cyan).

The actin residues that have high probabilities to be contacted by these segments are shown in Figure 6. In both simulations of CplxA, segment 22LKKV25 was found in contact with several actin residues close to the cognate binding site. In contrast, due to the sliding of region 37–46 toward the bottom of actin in simulation CplxB\_MD2, the segment 50LKSV53 is too far to reach and bind its cognate site on actin. All together, despite their limited number and length, our simulations suggest that CplxA (which has the N-WASP helical region 9–18 recognized by actin) is likely a productive encounter complex that can lead to a subsequent binding of segment 22LKKV25 to its specific site on actin. In contrast, simulations of CplxB suggest that the complete binding of N-WASP second WH2 motif is less favorable than for the first WH2 motif. Beyond the limited statistics, this could result from the fact that segment 50LKSV53 is less positively charged than 22LKKV25, whereas their cognate binding site on actin has two negatively charged residues (D24 and D25). Another possible explanation is that N-WASP region 37–46 has a higher propensity to form *α*-helices than segment 9–18. This would increase the stiffness of the second WH2 motif that might restrict the motion of residues 50LKSV53 and their ability to reach their cognate binding site on actin.

Finally, we studied the dynamics of domain V regions 28NSRPVS33 and 56GQESTP61 following the conserved sequences 22LKKV25 and 50LKSV53, respectively. Indeed, as mentioned in the introduction, most crystallographic structures of actin–WH2 motif lack atomic coordinates for regions after the consensus sequence "LKKV", indicating that they are highly flexible in their bound state. We thus characterized the preferential location of these two regions on actin's surface in our MD simulations. Figure 7 plots the minimal distance of regions 28NSRPVS33 and 56GQESTP61 to actin as a function of time in CplxA and CplxB simulations, respectively. It can be observed that these two regions mostly contact the actin's surface when the preceding conserved sequences 22LKKV25 or 50LKSV53 are already attached to actin, except in CplxB\_MD1. In the latter, residues 56GQESTP61 make frequent contacts with actin when segment 50LKSV53 is not bound to actin.

**Figure 6.** (**A**) Probability of actin residues to be distant by less than 4 Å from N-WASP segments 22LKKV25 or 50LKSV53 in CplxA\_MD1 (red), CplxA\_MD2 (orange), CplxB\_MD1 (cyan), and CplxB\_MD2 (blue). Brown dashed lines indicate the actin residues (G23, D24, D25, R28, and S344) in contact with N-WASP segment 50LKSV53 in structure 2VCP [27]). (**B**–**D**) Front views of the actin's surface colored proportionally to the previous probabilities. Red, orange, and blue colors indicate actin residues with high probabilities to be contacted by N-WASP segments 22LKKV25 or 50LKSV53 in simulations CplxA\_MD1 (**B**), CplxA\_MD2 (**C**), and CplxB\_MD2 (**D**), respectively. As a reference, yellow and green ribbons represent the helical region and the conserved sequence LKSV of the second WH2 motif observed in structure 2VCP [27].

**Figure 7.** Time evolutions of minimal distances between actin and segment 28NSRPVS33 in simulations of CplxA (red and orange lines) and segment 56GQESTP61 in simulations of CplxB (cyan and blue lines). For comparison, time evolutions of minimal distances between actin and segments 22LKKV25 and 50LKSV53 are displayed with black and brown lines, respectively.

The actin residues that have high probabilities to be contacted by regions 28NSRPVS33 and 56GQESTP61 are displayed in Figure 8. In both simulations of CplxB, segment 56GQESTP61 was mostly found in contact with residues of the actin subdomain 3. In CplxB\_MD1, this might be the reason the conserved segment 50LKSV53 cannot reach its cognate binding site on actin. In CplxB\_MD2, this is probably because the helix 37–46 slid toward the bottom of actin and that segment 50LKSV53 is improperly located between actin subdomains 1 and 3 (Figure 6). Strikingly, in simulations of CplxA in which the helical segment 9–18 and conserved sequence 22LKKV25 are both satisfactorily positioned on actin's surface, the region 28NSRPVS33 is observed to contact several separated patches on actin's surface, mainly located on subdomains 2 and 4. This might explain why these disordered regions cannot crystallize in one homogeneous conformation and, therefore, are not visible in most crystallographic actin–WH2 complexes.

**Figure 8.** Actin residues distant by less than 4 Å from N-WASP segments 28NSRPVS33 or 56GQESTP61 in CplxA\_MD1 (red), CplxA\_MD2 (orange), CplxB\_MD1 (cyan), and CplxB\_MD2 (blue). As a reference, yellow and green ribbons represent the helical region and the conserved sequence LKSV of the second WH2 motif observed in structure 2VCP [27].
