A central partition of molecular conformational space. IV. Extracting information from the graph of cells

In previous works (Gabarro-Arpa, J. Math. Chem. 42 (2006) 691–706) a procedure was described for dividing the 3 × N-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data sampled in molecular dynamics trajectories: the graph of cells or G, that encodes the set of cells in conformational space that are visited by the system in its thermal wandering. Here we outline a set of procedures for extracting useful information from this structure: (1st) interesting regions in the volume occupied by the system in conformational space can be bounded by a polyhedral cone, whose faces are determined empirically from a set of relations between the coordinates of the molecule, (2nd) it is also shown that this cone can be decomposed into a set of smaller cones, (3rd) the set of cells in a cone can be encoded by a simple combinatorial sequence.