A Central Partition of Molecular Conformational Space. III. Combinatorial Determination of the Volume Spanned by a Molecular System

摘要

In the first work of this series (Gabarro-Arpa, Comp. Biol. Chem. 27 (2003) 153–159) it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the space into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry, which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work (Gabarro-Arpa, Proc. 26th Ann. Int. Conf. of the IEEE EMBS (San Franciso, 2004) 3007–3010) by sorting the elementary 3-dimensional components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3-D reference frame. This also made possible to find a solution to the problem that is being addressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built.