*4.5. Projections Onto a Common Feature Space*

We used pyEMMA [54] to featurize our system according to phi and psi dihedrals by choosing a common set of residues on all peptide systems resulting in 22 dihedrals, and we used dihedral shifting to reduce discontinuities in the distibution rather than using sine and cosines on the dihedrals [55]. The ensembles from free *p53*, *pdiq*, and *Ala1* were chosen as a common ensemble before dimensionality reduction of the system by using time-independent coordinate analysis [56] with a lag time of 10 ns, from which we extracted the top 14 eigenvectors that account for 95% of the variance. We then projected each peptide ensemble (from free and bound simulations) into the top eigenvectors. Finally, we performed clustering of the free peptide ensembles in the space defined by the top 14 eigenvectors to produce Figures 2 and A1–A4. Since the vectors were calculated for intrinsically disordered ensembles of the free form of the peptides, they are not representative of the slowest transitions during the binding process, which we cannot extract from the MELD-biased ensembles. Nonetheless, they provide a common set of vectors to represent all free and bound peptide systems studied. For these plots, we decided to project onto the third and fifth eigenvectors since these offered the best separation between clusters for the relevant states during binding.
