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There are several applications in computational biophysics which require theoptimization of discrete interacting states; e.g., amino acid titration states,ligand oxidation states, or discrete rotamer angles. Such optimization can bevery time-consuming as it scales exponentially in the number of sites to beoptimized. In this paper, we describe a new polynomial-time algorithm foroptimization of discrete states in macromolecular systems. This algorithm wasadapted from image processing and uses techniques from discrete mathematics andgraph theory to restate the optimization problem in terms of "maximumflow-minimum cut" graph analysis. The interaction energy graph, a graph inwhich vertices (amino acids) and edges (interactions) are weighted with theirrespective energies, is transformed into a flow network in which the value ofthe 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, thisalgorithm has the potential to allow for the ionization state of largerproteins to be discovered.

Energy Minimization of Discrete Protein Titration State Models Using Graph Theory