**Appendix A**

**Figure A1.** Comparison of the conformational space for free peptide versus binding simulations for the *pdiq* peptide. (**a**) The peptide ensembles are projected onto two tICA eigenvectors common to all five peptides. (**b**) The metastable states sampled for the free peptide. (**c**) Top clusters by population from MELD×MD binding simulations.

**Figure A2.** Comparison of the conformational space for free peptide versus binding simulations for the *p53* epitope. (**a**) The peptide ensembles are projected onto two tICA eigenvectors common to all five peptides. (**b**) The metastable states sampled for the free peptide. (**c**) Top clusters by population from MELD×MD binding simulations.

**Figure A3.** Comparison of the conformational space for free peptide versus binding simulations for *Ala1*. (**a**) The peptide ensembles are projected onto two tICA eigenvectors common to all five peptides. (**b**) The metastable states sampled for the free peptide. (**c**) Top clusters by population from MELD×MD binding simulations.

**Figure A4.** Comparison of the conformational space for free peptide versus binding simulations for *Ala2*. (**a**) The peptide ensembles are projected onto two tICA eigenvectors common to all five peptides. (**b**) The metastable states sampled for the free peptide. (**c**) Top clusters by population from MELD×MD binding simulations.

**Figure A5.** Clustering MELD×MD ensembles correctly identifies the MDM2 pocket as the binding site. Clustering is done by aligning on the MDM2 protein and using that alignment and the RMSD of the peptide between conformations as a distance metric. We define high accuracy binding (left) as the peptide binding in the right pocket with the right conformation (RMSD < 5 Å). For many clusters, the peptide is at least partially occupying the experimental binding site, with incorrect peptide conformations. Our approach samples these conformations at higher replica index, with a few progressing to the experimentally bound conformation. Finally, we find some conformations interacting with MDM2 at different sites in the protein (right panel).

**Figure A6.** 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 average of the index replica in that cluster. The color code is green (*RMSD* < 5) or blue (*RMSD* > 5) when the average of the replica index is lower than 15, and red otherwise.

**Figure A7.** Radius of gyration versus RMSD of the peptide (protein align) for different replicas in MELD×MD for all peptides studied. The red lines for peptides *pdiq* and *ATSP*-7041 depict the region of the radius of gyration explored at the lowest temperature replica.

**Figure A8.** Secondary structure profiles for each peptide in MELD×MD runs. Each line represents a different replica (different H and T). Replicas with higher percentage of secondary structure are sampling at low temperature and ambiguous restraints guiding the peptide to the protein at full strength. Red bars represent the location of the three anchoring residues for each peptide.

**Figure A9.** MDM2 protein ensembles with respect to holo and apo experimental structures at the lowest and highest index replicas. Simulations used a flat-bottom harmonic restraint on C*<sup>α</sup>* positions with a 3.5 flat-bottom region.

**Figure A10.** MDM2 versus peptide RMSD ensembles for the five peptides.

**Figure A11.** RMSF (Root Mean Square Fluctuation)comparison of the two best peptide binders. The red bars indicate the locations of the anchoring residues. Both peptides have been aligned to match the anchoring residues and end residues removed from *ATSP*-7041 for this analysis.
