Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

TL;DR

This paper introduces a polynomial-time graph theory-based algorithm for optimizing discrete protein states, significantly improving efficiency in computational biophysics applications like titration and ligand states.

Contribution

A novel polynomial-time algorithm adapted from image processing that uses maximum flow-minimum cut analysis to optimize discrete states in macromolecular systems.

Findings

Algorithm efficiently finds minimum free energy states.

Applicable to large proteins due to polynomial-time complexity.

Transforms energy optimization into a graph cut problem.

Abstract

There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.