A hybrid combinatorial-continuous strategy for solving molecular distance geometry problems

TL;DR

This paper introduces a hybrid combinatorial-continuous method for solving the interval Molecular Distance Geometry Problem, effectively reconstructing protein structures from uncertain interatomic distances.

Contribution

It presents a novel hybrid framework combining combinatorial enumeration with continuous optimization, accommodating uncertainty bounds in distance data.

Findings

Efficiently reconstructs valid protein conformations with wide distance bounds

Integrates torsion-angle and chirality constraints into the model

Outperforms existing methods in handling uncertain distance data

Abstract

The Molecular Distance Geometry Problem (MDGP) is essential in structural biology, as it seeks to determine three-dimensional protein structures from partial interatomic distances. Its discretizable subclass (DMDGP) admits an exact combinatorial formulation that enables efficient exploration of the search space. However, in practical settings such as Nuclear Magnetic Resonance (NMR) spectroscopy, distances are available only within uncertainty bounds, leading to the interval variant (\emph{i}DMDGP). We propose a hybrid combinatorial--continuous framework for solving the \emph{i}DMDGP. The method combines an enumeration process derived from the DMDGP with a continuous refinement stage that minimizes a nonconvex stress function that penalizes deviations from admissible distance intervals. This integration supports a systematic exploration guided by discrete structure and local optimization. The formulation incorporates torsion-angle intervals and chirality constraints through a refined atom ordering that preserves protein-backbone geometry. Numerical experiments show that the approach efficiently reconstructs geometrically valid conformations even under wide distance bounds, whereas most existing studies assume narrow ones.