Continuous-time quantum-walk centrality for protein residue interaction networks

TL;DR

This paper introduces a quantum-dynamical approach using continuous-time quantum walks to identify key residues in proteins, demonstrating strong agreement with classical methods and biological relevance, with potential for quantum hardware implementation.

Contribution

It develops a novel quantum walk-based framework for protein residue analysis, extending classical centrality measures with quantum interference effects and demonstrating practical quantum hardware applicability.

Findings

CTQW centrality aligns with classical eigenvector centrality in proteins.

Quantum interference signatures extend residue importance beyond classical methods.

Proof-of-concept implementation on IBM quantum hardware shows practical feasibility.

Abstract

We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved structures. By mapping the weighted adjacency matrix to a Hamiltonian, residue importance emerges from the long-time averaged occupation probability, confirmed analytically through its spectral decomposition. Across a dataset of approximately 150 proteins spanning diverse structural and functional classes, CTQW centrality exhibits consistently strong agreement with classical eigenvector centrality in identifying central residues, while extending beyond it through incorporating signatures of quantum interference. Analyzing the time-averaged quantum transition matrix reveals consistently larger spectral gaps than the classical random-walk operator. Furthermore, biological relevance is confirmed through recovery of experimentally established functional residues in proteins kinase A and oxytocin. CTQW-derived centrality rankings are accessible on near-term intermediate-scale quantum hardware, as we demonstrate through a proof-of-principle implementation on IBM superconducting quantum hardware. These results establish continuous-time quantum walks as a computationally tractable framework for protein network analysis, that connects network theoretical treatments of protein structural biology to continuous-time quantum walk dynamics.