Calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis

The calculation of the 3D structure of a protein molecule is important because it is associated to its biological function. Nuclear Magnetic Resonance (NMR) experiments can provide distance information between atoms that are close enough in a given protein and the problem is how to use these distances to determine the protein structure. Using the chemistry of proteins and supposing all the distances are precise values, it is possible to define an atomic order v1, ⋅⋅⋅, vn, such that the distances related to the pairs {vi−3,vi},{vi−2,vi},{vi−1,vi} are available, and solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). However, due to uncertainty in NMR data, the distances associated with pairs {vi−3,vi} may not be precise, which implies that there are many difficulties in applying the BP algorithm to this scenario. The use of standard interval arithmetic can be directly applied to the algorithm, but it is known that it generates overestimations. This paper proposes a new methodology to compute possible conformations on the presence of uncertainties arising from NMR distance measurements using a constraint interval analysis approach. Some numerical examples are presented.