Clifford algebra and discretizable distance geometry. (11th May 2017) - Alves, R.; Lavor, C.; Souza, C.; Souza, M.
Abstract : Protein structure calculations using nuclear magnetic resonance (NMR) experiments are one of the most important applications of distance geometry. The chemistry of proteins and the NMR data allow us to define an atomic order, such that the distances related to the pairs of atoms { i −3, i }, { i −2, i }, { i −1, i } are available, and solve the problem iteratively using a combinatorial method, called branch‐and‐prune. The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i −3, i −2, i, with radius given by the atomic distances d i −3, i, d i −2, i, d i −1, i, respectively, to obtain the position for atom i . Because of uncertainty in NMR data, some of the distances d i −3, i may not be precise or even not be available. Using conformal Clifford algebra, in addition to take care of NMR uncertainties, which implies that we have to calculate sphere intersections considering that their centers and radius may not be fixed anymore, we consider a more flexible atomic order, where distances d i −3, i are replaced by d j, i, where j ⩽ i −3. Copyright © 2017 John Wiley & Sons, Ltd.