AbstractNuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i − 3, i − 2, i − 1, with radii given by the atomic distances di−3,i, di−2,i, di−1,i, respectively, to obtain the position for atom i. Because of uncertainty in NMR data, some of the distances di−3,i should be represented as interval distances [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], where {\underline{d}_{i - 3,i}} \le {d_{i - 3,i}} \le {\bar d_{i - 3,i}}. In the literature, an extension of the BP algorithm was proposed to deal with interval distances, where the idea is to sample values from [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}]. We present a new method, based on conformal geometric algebra, to reduce the size of [{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], before the sampling process. We also compare it with another approach proposed in the literature.
NMR Protein Structure Calculation and Sphere Intersections
