21 research outputs found
A Central Partition of Molecular Conformational Space.III. Combinatorial Determination of the Volume Spanned by a Molecular System
In the first work of this series [physics/0204035] 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 espace 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
[physics/0404052] by sorting the elementary 3D components of the molecular
system into a set of morphological classes that can be properly oriented in a
standard 3D reference frame. This also made possible to find a solution to the
problem that is being adressed 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
A Central Partition of Molecular Conformational Space. IV. Extracting information from the graph of cells
In previous works [physics/0204035, physics/0404052, physics/0509126] a
procedure was described for dividing the -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, 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 hierarchical set of smaller cones, 3rd) the set of cells in a
cone can be encoded by a simple combinatorial sequence.Comment: added an intrduction and reference
Chirality Measures and Graph RepresentationsaaThis work was supported by an operating research grant from the Natural Sciences and Engineering Research Council of Canada.
AbstractChirality (“handedness”) is a geometrical-topological property of many physical systems, a fundamentally important aspect of chemistry (in particular, of molecular shape), and a fascinating feature of mathematical objects such as knots and graphs. In this contribution, some aspects of the quantification problem of chirality are discussed, with special emphasis on chirality measures and their graph representations