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 $3 \times N$-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, 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

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

Physical characteristics in eucaryotic promoters.

For a series of wild type and mutated eucaryotic gene prelude sequences (mainly "promoters" of SV40 early gene (Benoist and Chambon, Nature 290, 304 (1981); Moreau et al., Nuc. Acids Res. 9, 6047 (1982)) and of Herpes Simplex Virus TK gene (McKnight and Kingsbury, Science 217, 316 (1982)), in vivo promoter activity and local stability (denaturability) have been correlated. In agreement with the conclusions drawn in these papers, the correlation points to three major eucaryotic promoter elements and loci: (i) enzyme enabling by an enhancer sequence; SV40 and Moloney Sarcoma Virus enhancers have a striking stability homology; (ii) enzyme activation, occurring 50-70 b.p. upstream the cap site in a high stability domain; the enzyme apparently deactivates exponentially upon moving away to trap site; (iii) enzyme positioning at trap site, 30 +/- 5 b.p. upstream the cap site. The trap site contains the TATA box, or, when absent, other low stability domains downstream the activator. The number and occupancy of cap sites may depend on the stability and size of the trap site-cap site couple and its distance from the activator

An algorithm for studying cooperative transitions in DNA.

Cooperative transitions in DNA (B to Z, B to A, helix to coil, etc.) are known to depend strongly on nucleotide sequence. In general the change in free energy involved in the transition can be expressed as: delta G(seq) = 2RT log (sigma) where sigma is a factor arising from the free energy associated with boundaries of different conformations along the molecule. This formula allows to infer a general algorithm with which DNA sequences can be partitioned into well defined domains in which, under suitable conditions, base pairs change state cooperatively. The different partitions of the sequence that can be generated by varying the values of the physical parameters involved in the above formula, are shown to be embedded into a binary tree hierarchy. Application to a reliable prediction of Z-DNA antibody binding sites will be illustrated for the 0X174 genome. Possible biological implications are briefly discussed

MORCAD, an object-oriented molecular modelling package running on IBM RS/6000 and SGI 4Dxxx workstations

A package for molecular modeling (display, analysis, building, minimization) through user defined parametrization is presented

MORCAD, an Object-Oriented Molecular Modelling Package Running on IBM RS/6000 and SGI 4Dxxx Workstations

International audienceA package for molecular modeling (display, analysis, building, minimization) through user defined parametrization is presented