A Geometric Build-Up Algorithm for Solving the Molecular Distance Geometry Problem with Sparse Distance Data

Abstract

Nuclear magnetic resonance (NMR) structure modeling usually produces a sparse set of inter-atomic distances in protein. In order to calculate the three-dimensional structure of protein, current approaches need to estimate all other “missing” distances to build a full set of distances. However, the estimation step is costly and prone to introducing errors. In this report, we describe a geometric build-up algorithm for solving protein structure by using only a sparse set of inter-atomic distances. Such a sparse set of distances can be obtained by combining NMR data with our knowledge on certain bond lengths and bond angles. It can also include confident estimations on some “missing” distances. Our algorithm utilizes a simple geometric relationship between coordinates and distances. The coordinates for each atom are calculated by using the coordinates of previously determined atoms and their distances. We have implemented the algorithm and tested it on several proteins. Our results showed that our algorithm successfully determined the protein structures with sparse sets of distances. Therefore, our algorithm reduces the need of estimating the “missing” distances and promises a more efficient approach to NMR structure modeling.