A Central Partition of Molecular Conformational Space. V. The Hypergraph of 3D Partition Sequences

In a previous work a procedure was decribed for dividing the $3 times N$-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, encoding the set of cells in conformational space that are visited by the system in its thermal wandering. The information in G however, is encoded in a great number of fragments that must be aggregated. We describe here the algorithmic procedures 1) for aggregating the information from G into an hypergraph allowing to enumerate the relevant cells from conformational space, and 2) for puttting the data in a very compact format.

Embedding protein 3D-structures in a cubic lattice. I. The basic algorithms

Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.

A Combinatorial Enumeration of Distances for Calculating Energy in Molecular Conformational Space

In previous works it was shown that protein 3D-conformations could be encoded into discrete sequences called dominance partition sequences (DPS), that generated a linear partition of molecular conformational space into regions of molecular conformations that have the same DPS. In this work we describe procedures for building in a cubic lattice the set of 3D-conformations that are compatible with a given DPS. Furthermore, this set can be structured as a graph upon which a combinatorial algorithm can be applied for computing the mean energy of the conformations in a cell.

Heuristic decomposition of cones in molecular conformational space

In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial formula. On the other hand it was constructed a transversal graph structure encoding the region of conformational space accessible to the system. From the information in this graph, it is possible to decompose the main cone into a hierarchy of smaller ones that are more manageable, and are progressively more tightly bound to the region in which the system evolves.