A Conformal Geometric Algebra approach to the Discretizable Molecular Distance Geometry Problem (2 hour seminar)

The Discretizable Molecular Distance Geometry Problem (DMDGP) is related to the determination of 3D protein structures using distance information detected by nuclear magnetic resonance (NMR) experiments, which is important in the rational drug design process in the pharmaceutical industry. From the chemistry of proteins and the NMR distance information, we can define an atomic order such that the distances related to each four consecutive atoms are available, implying that the search space of the problem can be represented by a tree. A DMDGP solution can be represented by a path from the root to a leaf node of this tree, found by a method called Branch & Prune (BP). Because of uncertainty in NMR data, some of the available distances may not be precise, being represented by intervals of real numbers. In order to apply BP algorithm in this context, sample values from those intervals should be taken. The main problem of this approach is that if we sample many values, the search space increases drastically, and for small samples, no solution can be found. Conformal Geometric Algebra (CGA) can be used to model uncertainties in the DMDGP and integrate the combinatorial and continuous characteristics of the DMDGP in a unified approach, avoiding sample values and eliminating the heuristic characteristics of BP when dealing with interval distances.