*4.3. MELD*×*MD Binding Simulations*

We ran 1 µs-long H,T-REMD simulations using OpenMM [50] with the MELD plugin [26]. MELD allows us to incorporate noisy information to increase the sampling in regions of interest [51,52]. In this case, our interest was in observing the peptide-protein association. We required that there were at least five heavy-atom contacts between the three anchoring residues in the peptide (F, W, and L in *p53*) and any other hydrophobic residue in MDM2, andthe pool of possible contacts was selected from the combinatorics of both sets. The restraints were imposed using flat-bottom harmonic restraints. The flat region was defined as a pair of residues closer than 5 from each other, the restraints increased quadratically up to 7 and linearly beyond, with a force constant of 250 J/K/mol. At every timestep, all possible restraints are evaluated, sorted by energy, and only the lowest 5 in restraint energy are used until the next timestep. In this way, no information is lost as the simulation progresses.

The H,T-REMD protocol includes 30 replicas, where the change in Hamiltonian affects the force constant of the restraints. The 30 replicas are mapped to a value of alpha (*α*) between 0 (lowest replica) and 1 (highest replica). The Hamiltonian and temperature have defined values of the restraint force constant and temperature as a function of alpha. The temperature increases geometrically from 300K (*α* = 0) to 500K (*α* = 0.5) and is kept at this temperature for higher values of alpha. The force constants for the restraints is set to 0 J/K/nm<sup>2</sup> at *α* = 1 and is gradually increased to the value of 250 J/K/nm<sup>2</sup> for *α* ≤ 0.6. Exchanges between active restraints are more likely at higher index replicas.
