Improving the sampling process in the interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem

Abstract

Protein structure determination using Nuclear Magnetic Resonance (NMR) experiments is one of the most important applications of Distance Geometry, called the Molecular Distance Geometry Problem (MDGP). Using special atomic orders on the protein molecule, the MDGP can be solved iteratively using a combinatorial method, called Branch-and-Prune (BP). In order to deal with uncertainties of NMR data, there is an extension of the BP algorithm, called interval BP, where the idea is to sample values from the interval distances associated to such uncertainties. We propose a method to improve this sampling process, by reducing the interval of uncertain distances before taking the samples. All the mathematical details necessary to understand the proposal and its implementation are provided, along with some computational experiments that indicate the proposed strategy improves the interval BP algorithm.