[Paper Review] Harnessing the Peripheral Surface Information Entropy from Globular Protein-Peptide Complexes

Tyler Grear, Donald J. Jacobs|arXiv (Cornell University)|Jan 31, 2026

Protein Structure and Dynamics0 citations

TL;DR

The study introduces peripheral surface information (PSI) entropy SΨ as a thermoinformatic descriptor of non-interacting surface (NIS) organization, showing emergent dominant NIS states across protein-peptide ensembles and validating the phenomenon with both docking simulations and an experimental WW-domain meta-ensemble.

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.

Motivation & Objective

• Motivate a global, information-theoretic description of non-interacting surface (NIS) organization in protein-peptide binding.
• Define and compute PSI entropy SΨ to capture emergent peripheral surface configurations across conformational ensembles.
• Demonstrate that favorable binding corresponds to low-entropy NIS states that persist across diverse receptors and peptides, including experimental meta-ensembles.
• Explore robustness and evolutionary implications by validating NIS-dominant modes in both in silico docking and experimentally characterized WW-domain complexes.

Proposed method

• Convert per-residue solvent-accessible surface area to relative solvent accessibility and assign residues to apolar, charged, or polar classes.
• Define NIS macrostates via (nA, nC, nP) counts and map docking ensembles to NIS-space (Na, Nc).
• Compute macrostate entropy SΨ′ from macrostate multiplicities g(Ni) with p_i = g(Ni)/Ω.
• Introduce normalization K = Q/M using ensemble contact masses M and distinct contacts Q to obtain SΨ = -(Q/M) Σ_i (g(Ni)/Ω) log2(g(Ni)/Ω).
• Weight contact masses by contact-class factors γ(ci, cj) to emphasize favorable interactions, yielding M and Q used in K.
• Anchor analysis with HADDOCK3 docking (three-step protocol) and explicit-solvent MD, plus cross-validation with experimental WW-domain meta-ensemble.
• Use phase-pooled computations to compare proper vs improper peptide ensembles and assess ΔSΨ across steps.

Experimental results

Research questions

• RQ1 Can PSI entropy SΨ quantify emergent, favorable NIS configurations in protein-peptide binding across multiple receptors?
• RQ2 Does favorable binding correspond to low SΨ and a small Q/M (regime I) or otherwise, indicating different peripheral organization patterns?
• RQ3 Is the dominant NIS-mode a robust, evolutionarily conserved feature observable in experimental WW-domain meta-ensembles?
• RQ4 Do cognate (proper) peptide interactions show lower SΨ than non-cognate (improper) interactions under matched docking protocols?
• RQ5 How does SΨ behave across different docking stages (rigid-body docking, semi-flexible refinement, explicit-solvent MD) and peptide conformations?
• RQ6 Is the dominant NIS-state pattern preserved across diverse receptors (WW, MDM2, PDZ) and peptide sets?

Key findings

• Dominant NIS states emerge consistently across diverse peptide-receptor systems under energy-directed docking and MD refinement.
• Normalized PSI entropy SΨ separates proline-rich (PY) peptides from random (RD) sequences, with stepwise increases in sampling yet persistent low-entropy modes.
• Cross-fertilization on proper vs improper peptides yields lower SΨ for proper ensembles across two receptors, indicating specificity of peripheral surface organization.
• Experimental WW-domain meta-ensemble (Ω = 657 microstates) displays a dominant NIS mode, suggesting evolutionary pressure toward conserved NIS fingerprints.
• Phase-pooled analyses show proper ensembles have lower SΨ than improper ones, with quantifiable percent differences (e.g., Δ% values provided for specific receptors).
• The NIS occupancy pattern is heavy-tailed, with most macrostates sparsely sampled and a subset concentrating probability mass across ensembles, robust to experimental determination over 15 years.