**1. Introduction**

Peptide molecule inhibitors have the potential to bind to proteins classified as "undruggable" by small molecules thanks to their flexibility and complementary nature to proteins [1,2]. Rational drug design of small molecules via computational tools (e.g., docking of virtual libraries) is a common practice in the drug discovery process. However, these tools are not well suited to handle the flexible nature of peptide molecules, many of which are intrinsically disordered and only adopt stable structures in the presence of their binding partners [3].

Modeling the binding of flexible molecules continues to be a grand challenge in computational structure prediction. In recent years, with the increase of peptide therapeutics in the market there has been a continuous development and adaptation of docking tools to capture protein-peptide interactions [3,4]. Docking programs address the flexibility of peptides by two main routes: (1) using homology models, PDB (Protein Data Bank)structural motifs, or other sources of structures for docking [5–8]; and (2) provide peptide flexibility for folding upon binding [9–14]. Initial peptide conformations for docking could come from computationally expensive molecular dynamics (MD) simulations of the free peptide. However, many such peptides are intrinsically disordered (IDP), limiting their use [7]. Full exploration of folding upon binding through standard molecular dynamics becomes too computationally demanding [15], requiring advanced sampling strategies to efficiently sample the energy landscape.

In this work, we take a look at binding and free-peptide ensembles (simulating the peptide in isolation) for different peptides to better understand the nature of the *p53*- MDM2 interaction. *p53* is called the guardian of the genome, triggering programmed death (apoptosis) when cells misbehave. MDM2 down-regulates *p53* limiting its tumor suppressor activity. Thus, inhibitors of the *p53*-MDM2 and the closely related MDMX interaction have long been a cancer drug target [16–18]. Multiple studies of the native

interaction [19–22] and the ability to design inhibitors that simultaneously block MDM2 and MDMX [23–25] provide a wealth of data to assess new computational tools. Since binding simulations are more computationally demanding than free peptide simulations, our goal is to identify peptide properties that might make the peptide a better binder–leading to faster computational screening of peptide therapeutics.

The *p53*-MDM2 interaction is characterized by three hydrophobic residues (Phe19, Trp23 and Leu26) from the peptide which anchor into a deep cavity in MDM2. In order for the three hydrophobic residues to align with the pocket, the *p53* epitope adopts a helical conformation. This is in contrast with the IDP nature of the peptide in isolation. We use noisy information to guide binding using our previously developed Bayesian inference approach (MELD×MD [26]) to identify the subset of data that is most compatible with the force field and the resulting bound conformations (see Figure 1). To further test the methodology, we simulated five different peptides, including the peptide epitope from *p53*, two inhibitors, and two alanine-based peptides that we do not expect to be good binders, as control. The work highlights the ability of molecular dynamics tools to capture the two driving forces behind binding: preferences of the peptides to adopt bound-like conformations and the use of binding simulations to differentiate binding preferences.

**Figure 1.** Outline of the MELD×MD setup. We start with the peptide far from MDM2 (system). We use noisy information to favor sampling of binding/unbinding events (middle panel). A statistical mechanics of the posterior distribution coming from the MELD ensemble identifies conformations that are most consistent with the force field and a subset of the data, and we compare these to the experimental structure.
