*2.3. Peptides Become More Structured in Proximity to MDM2*

MELD×MD binding simulations show a higher fraction of helical conformations for all peptides with respect to their free simulations (see middle column in Table 2). However, the increase in helical content for the peptide is not always associated with binding at the correct binding site (right column in Table 2). A 2D-RMSD clustering calculation on all replicas (see Figures 4 and A6) reveals the funneled nature of binding for three peptides. We can identify three broadly defined regions in the funneling plots based on the RMSD distribution: between 0–5 Å (high accuracy binding), 5–15 Å (pre-bound), ∼15–30 Å (misbound), and a fourth region for unbound conformations sampled by higher replicas (see Figure A5). All five peptides identify the binding pocket as the binding site, but the two control sequences bind through multiple backbone conformations with little structural preference. *ATSP*-7041 exhibits the most funneled behavior, rapidly converging onto a large high accuracy native-like cluster. Both *pdiq* and *p53* exhibit a similar behavior, in which all three regions are explored even at the lower replicas, with funneling to one major state. For *p53*, the native configuration is sampled, but is not identified as the most populated cluster. The observed binding mode introduces a kink in the backbone between the helical and non-helical region that is not observed in the experimental structure. The control *Ala1* sequence contains the three anchoring residues present in *p53*, but exhibits a binding profile more similar to control *Ala2*, which lacks the anchoring residues. Thus, the control sequences show that the MELD×MD setup is not over-constraining the peptide to bind

in the binding pocket or in the binding conformation, and large cluster populations are reflective of significant binding.

**Figure 3.** MELD×MD simulations explore unbound states, and different possible binding regions of *p53* on the surface of the protein. The left panel shows a superposition of all peptide conformations (heavy atoms of each conformation are drawn as orange dots) sampled at different replicas. The right panel shows the internal backbone RMSD of the peptide with respect the experimental conformation versus the RMSD of the peptide when aligning to the protein.

We compare all peptide binding ensembles on equal footing by projecting them on the same eigenvector space as the free peptides. Figure 2 compares the free peptide ensemble with those produced from MELD×MD at the lowest/highest replica index (bound/unbound) for *ATSP*-7041. The figure also shows the clusters arising from the free peptide ensemble, as well as the highest population clusters, from the binding simulations. The preferred conformation for *ATSP*-7041 in its free peptide is the same conformation needed for binding, resulting in significant binding observed throughout the simulations. A similar behavior is observed for *pdiq*, where the ensemble of the free peptide is larger due to the absence of the chemical staple (see Figure A1). For the three IDP peptides (see Figures A2–A4), the ensembles are even broader than for *pdiq* resulting in a larger number of clusters. The free peptide clusters for these IDP peptides are low in population and lack agreement with the preferred binding mode. However, in binding simulations at low temperature, *p53* explores a narrow conformational ensemble similar to *pdiq* and very different from the broader ensembles sampled by the control sequences. For the two control sequences, the minima of the free ensemble distribution is displaced with respect to the three other peptides, disfavoring bound-like conformations, which result in broader ensembles for the two control peptides during MELD×MD binding simulations.

**Figure 4.** Funneling binding plot for the five peptides. Each dot corresponds to a cluster center from a 2D-RMSD based on all replicas. The larger the circle the larger the population of the cluster. Each circle is plotted at the average RMSD inside that cluster with respect to the native conformation and the mode of the index replica in that cluster. The color code is green (*RMSD* < 5) or blue (*RMSD* > 5) when the mode of the replica index is lower than 15, and red otherwise.

Complementary knowledge for the binding process emerges from looking at the internal structure of the peptide (radius of gyration) with respect to the position of the peptide to MDM2 (RMSD, see right column in Figures 3 and A7). At high replica index, all peptides sample conformations far from the protein, with large fluctuations in the radius of gyration (between 5 and 12 Å except for the *ATSP*-7041 peptide, where the chemical staple prevents conformations with a radius of gyration above 9 Å). When binding in the MDM2 hydrophobic pocket, the peptide adopts compact conformations with a radius of gyration around 7 Å. This happens early in the binding process (higher replica index) for the *pdiq* and *ATSP*-7041 peptides and is not observed for the *Ala2* control due to the lack of anchoring residues.
