**3. Discussion**

The debate between conformational selection and induced fit mechanisms of binding is being reconciled into a mixture of the two [7], with different balance of each depending of the system. In the MDM2/p53 system, the protein undergoes a small conformational change from its apo (unbound) to holo (bound) structure, whereas the IDP peptide folds upon binding to the active site. MD simulations of the free *p53* sequence shows its intrinsically disordered nature, with little propensity for helical conformations. Querying the *p53* binding motif in the PDB returns twelve structures, covering four different protein targets: MDM2 [30], MDMX [20], p300 [31], and the CREB-binding protein [32]. In all cases, the *p53* N-terminal domain adopts a helical conformation, but with different sidechain rotameric states [32]. Our binding simulations reproduce these trend, with the size of the conformational ensemble considerably shrinking upon binding (see Figures A2 and A7). Our MELD×MD simulations lose the kinetic information of binding, but, following a particular replica as it goes up and down the replica ladder, we can observe the series of events that lead to binding. In general, we observe a higher helical content for *p53* near the protein surface, consistent with excluded volume effects [33]. The spacing of the anchoring residues (*i*, *i* + 4 and *i* + 7), combined with the size of the hydrophobic pocket favors binding in helical conformations. The funneling towards the binding site driven by hydrophobic interactions in MELD responds to our knowledge that the hydrophobic anchoring residues were vital for binding. Hydrophobic residues on the surface of the protein are more likely in the active site, hence accelerating binding towards it. A different choice of information (e.g., using polar residues) would have resulted in less directed sampling, as polar and charged residues are frequent in the protein surface. Visual inspection shows binding through different modes, with one of the hydrophobic residues anchoring in the cavity and driving the rest; although the peptide does not bind as a helix, it quickly adopts a partial helical structure (see Figure A8) consistent with experiments. The tryptophan seems to be critical for adopting the correct experimental binding conformations: we observe many instances of the peptide bound in the cavity as a helix with the bulky tryptophan interacting with MDM2 hydrophobic sidechains not in the binding pocket, leading to kinks in the backbone structure (see cluster 1 in Figure A2). These incorrect bindings have a long life time in our simulations and require at least partial unbinding before correctly binding according to the experimental motif, which, in our simulations, is sampled but is not the predominant state.

The *pdiq* inhibitor binds experimentally with longer helical motifs covering all amino acids. Analyzing PDB codes 1ycr and 3jzs reveals differences in the secondary structure (using STRIDE [34] as incorporated in VMD (Visual Molecular Dynamics) [35]). The difference in helicity affects the last anchoring residue (leucine), which is in a coil rotameric state for *p53* and in a helical state for *pdiq*. Our simulations show that *pdiq* forms a significant amount of helix in its free form, which favors binding significantly in our binding simulations (see Figures A1 and A8). For *pdiq*, we observe pre-binding in helical confor-

mations, shifted with respect to the experimental binding site, and fast rearrangement of the peptide, sometimes involving rapid helix unfolding and refolding in the binding site leading to the experimental structure. The helical behavior is further accentuated for the *ATSP*-7041 inhibitor, where all binding takes place through helical conformations thanks to the chemical staple. Rearrangements in the active site involve displacements of the alpha helix to allow better interaction of the alpha helices; this is done through partial unbinding of the helix without loosing the helical character. Both control sequences access the binding site unfolded and explore many possible conformations. *Ala1* can sample the helical conformations which favor strong binding as seen from the top clusters (see Figure A3), but they have significantly lower population than the other three binding peptides (see Figure 4). On the contrary, *Ala2* has no anchoring residues and is rarely observed adopting helical conformations in the binding site (see Figure A4). These observations are supported by looking at the narrow conformational binding ensembles sampled at the lowest temperature replica for the peptides that bind (see Figures 2, A1, and A2), in contrast with the broader ensembles of the control peptides (see Figures A3 and A4). Taken together, the results show that the anchoring residues are necessary to adopt the helical conformations associated with good binding to MDM2 but not enough on their own to promote this helical state.

The ensembles at different replica index depict the nature of the binding/unbinding dynamics. The control peptides rapidly lose any memory of the bound conformation as the replica index increases (see Figures A7 and A10). For the other three peptides, we observe a bimodal distribution of states: for *p53* centered at 2/4 Å and at 1/2 Å for *pdiq* and *ATSP*-7041. As we increase the temperature in the replica ladder, the higher RMSD state becomes more prevalent. By replica 20, all peptides are sampling broad distributions with very low populations of the 1 RMSD state for the peptide, except for *ATSP*-7041, which, due to the chemical staple, even at high temperatures can sample conformations close to the bound conformation. However, at the highest replica, all peptides have lost memory of the bound conformation. Overall, we can distinguish three regions: an unbound conformation in which the peptide explores conformations far from its bound conformation, a pre-bound conformation, and a bound conformation. Both pre-bound and bound conformation lock the protein close to its holo conformation. For the poly-ala peptide, the bound state is rarely seen, while, for the poly-ala with binding side-chains, it is easier but not the predominant state. The pre-bound state for *pdiq* and *ATSP*-7041 is very close to the bound conformations, while, for *p53*, it is further away.

The binding free energy can be separated into a contribution coming from the conformational preferences of the peptide and protein systems, as well as an interaction contribution (∆*Gbind* = ∆*Gcon f ormation* + ∆*Ginteraction*), where ∆*Gcon f ormation* can further be separated into the protein and peptide contributions (∆*Gcon f ormation* = ∆*G peptide con f ormation* + ∆*G protein con f ormation*). <sup>∆</sup>*Ginteraction* is dictated by the specific interactions between the protein and peptide, which, in this case, arises from the three anchoring residues highlighted in Table 1, as shown by alanine scan mutagenesis studies [25]. Given a force field, MELD×MD samples multiple binding/unbinding events, effectively capturing both free energy contributions, even if it cannot decompose the contribution of each. Using the same protocol for all peptides allows us to identify differences in their binding preferences and peptide conformations. The main advantage is that, in this process, the peptide is completely flexible, free to adopt conformations in response to the environment. We observe the active site changing in response to the presence—and conformation—of the peptide.

Our studies hint that the binding mechanisms for *pdiq* and *ATSP*-7041 both favor initial binding as helices, with different mechanisms for rearrangement. Since kinetics are lost in our replica exchange ladder, testing this hypothesis will require future work in which the states discovered from our ensembles can be used for seeding unbiased simulations to construct markov models that show the binding pathways [36–38]. The chemical staple successfully increases the helical content, but it also plays a role in reducing side chain rotamer freedom through the steric volume it occupies (see Figure A11). Thus, *ATSP*-7041 is predisposed to make helical conformations, and to establish the right interactions. Figure 2 shows only two clusters: a major cluster binding as a helix with the three anchoring residues in the active site and a minor one with the staple in the active site. For *pdiq*, we see a higher number of minor clusters (see Figure A1) exhibiting helical conformations, in which at least one anchoring residue is not in the active site.

Thus, for accurate modeling of the *p53*-MDM2 interaction, we need to capture: (1) the intrinsic peptide propensity to helical conformations and (2) type and alignment of the anchoring residues inside the binding cavity. Peptides that, in their free form, favor helices seem to favor binding (given the same interface residues) by reducing the ∆*G peptide con f ormation*. However, even when shifting the helical propensities, binding simulations are needed as the binding mode can change (as we see for *ATSP*-7041 and *pdiq*).
