Harnessing the Peripheral Surface Information Entropy from Globular Protein-Peptide Complexes

TL;DR

This work addresses how non-interacting peripheral surface (NIS) features influence protein–peptide binding by introducing peripheral surface information entropy $S_{\Psi}$, a thermoinformatic descriptor of NIS-state variability across conformational ensembles. Using energy-directed docking with HADDOCK3 and explicit-solvent MD, the study reveals emergent, dominant NIS macrostates that persist across peptides and receptors (including WW, PDZ, and MDM2) and across experimental meta-ensembles, suggesting evolutionary pressure toward particular NIS fingerprints. Proper cognate bindings consistently show lower $S_{\Psi}$ than improper bindings, corroborated by cross-fertilization tests and an experimental WW-domain meta-ensemble, which converge on a small, dominant region in $\mathcal{N}$-space. Collectively, $S_{\Psi}$ provides a quantitative, distribution-level thermoinformatic metric that links global conformational organization of the non-interacting surface to favorable binding, with potential utility in predictive modeling and targeted peptide design.

Abstract

Predicting favorable protein-peptide binding events remains a central challenge in biophysics, with continued uncertainty surrounding how nonlocal effects shape the global energy landscape. Here, we introduce peripheral surface information (PSI) entropy, a quantitative measure of the statistical variability in apolar and charged non-interacting surface (NIS) proportions across conformational ensembles. Using energy-directed molecular docking via HADDOCK3 and explicit-solvent molecular dynamics simulations, it is demonstrated that favorable binding partners exhibit emergent, low-entropy N-states (discrete macrostates in NIS state space) indicative of preferential apolar/charged surface configurations. Across dozens of peptides and multiple receptor systems (WW, PDZ, and MDM2 domains), dominant N-states persisted under varied docking parameters and initial conditions. An experimental meta-ensemble of WW domains from 36 high-resolution structures confirmed the presence of dominant NIS modes independent of in silico methodology, suggesting an evolutionary selection pressure toward specific NIS fingerprints. These findings establish PSI entropy as a thermoinformatic descriptor that encodes favorable binding constraints into unique statistical signatures of the NIS.

Figures (13)

• Figure 1: The $\mathcal{N}$-space hexbin plot generated under the $\mathcal{N}$-state (NIS macrostate) definition. Each hexagon represents a unit cell in the projected $(\mathcal{N}_{a},\mathcal{N}_{c})$ plane, while macrostates were defined by the exact integer tuple $(n_A,n_C,n_P)$ after RSA-thresholding and explicit interface exclusion. The exemplar ensemble contained $\Omega=227$ microstates that partitioned into $N=67$ distinct macrostates, with color indicating the multiplicity, $g(\mathcal{N}_{a},\mathcal{N}_{c})$. The $(\mathcal{N}_{a},\mathcal{N}_{c})$ coordinates were used for visualization, while the full $(n_A,n_C,n_P)$ tuple distinguishes macrostates. The existence of a non-uniform occupancy in $\mathcal{N}$-space indicates that, during an energy-directed search for bound conformations, a preferential subset of peripheral NIS patterns was populated.
• Figure 2: An overview of $\mathcal{N}$-state properties while varying: the Smad7 peptide conformations, number of rigid-body models, and number of models refined by semi-flexible MDS. (top row) Conformations are shown with N-termini on bottom and C-termini on top where backbone geometries are depicted in silver. (SMDA) Was taken from the NMR ensemble 2LTW without modification. (SMDB) This conformation was predicted with AF2. (SMDC) The prior AF2 conformation was equilibrated with MDS where a partial helix emerges. (SMDD) The final conformation was generated using AF3. (a) The number of macrostates, N, vs the number of microstates ($\Omega$) where the number of rigid-body (RB) models was 25000. As the number of microstates increases, the number of emergent macrostates follow a logarithmic trend, reaching a maximum of $N=157$ for SMDB. (b) Kernel density estimations of $\mathcal{N}_{a}$ proportions for the four Smad7 peptides. A dominant $\mathcal{N}_{a}$ mode emerges for all 4 peptide candidates, attaining a higher amplitude for the SMDA and SMDD partners.
• Figure 3: An overview for the cross-fertilization procedure. (a) Under matched protocols, proper ensembles exhibit lower $S_{\Psi}$ than improper ensembles for both receptors. Note, the separation $S_{\Psi}^{\mathrm{phase}}(\mathrm{proper}) < S_{\Psi}^{\mathrm{phase}}(\mathrm{improper})$ persisted even when considering uncertainity (shown by error bars). (b) The enthalpy-weighted contact masses with an upweighting of spatially-dense favorable contacts for the proper ELKS1b peptide engagement. This exemplifies Regime 1 with low $S_{\Psi}$ and low $Q/M$.
• Figure 4: The WW domain side (a) and front (b) views. (a) The binding groove of the WW domain exists within the blue region bound by two highly conserved tryptophans (Trp17 and Trp39). Taking on the activated conformational state, the Tyr28 and Trp39 amino acids exhibit upward orientations relative to the beta sheet, likely due to $\pi$ effects which are known contributors of favorable binding enthalpy. (b) An alignment and superposition of all 36 PDB entries (34 NMR, 2 X-ray diffraction). The varying WW receptors (gray) are complexed with their corresponding peptide, ligand, or small molecule (multicolored ribbons).
• Figure 5: Bivariate distributions derived from a meta-ensemble of varying experimental WW domains complexed with small molecules, ligands, and peptides. (a) The continuous $\mathcal{N}$-space containing all 657 curated experimental protein-partner complexes. It is readily apparent that a dominant mode of the bivariate distribution exists, shown by red/dark-red regions. (b) The discrete $\mathcal{N}$-space (hexbin plot) explicitly shows 3 general regions of high multiplicity across all microstates. Trifurcating the meta-ensemble based on known classification, the corresponding bivariate distributions are shown in (c-e). The dominant class contributions to the meta-ensemble are indicated by (I, II, and III) in (a).