Conformational hyperspace

Dammkoehler R A, S F Karasek, E F B Shands and G R Marshall 1989. Constrained Search c Conformational Hyperspace. Journal of Computer-Aided Molecular Design 3 3-21. 

In addition to the backbone angles discussed above, the conformational hyperspace of peptides also includes the dihedral angles of the residue side... 

While the number of possible conformers of a macromolecule is practically unlimited, it is a common observation that macromolecules in biological systems occupy only an extremely limited portion of the conformational hyperspace open to them. As a result, they exhibit well-defined shapes which confer upon them the emergent property of functionality (see Section 2.3.3). 

R. A. Dammkoehler, S. F. Karasek, E. F. B. Shands, and G. R. Marshall, Constrained Search of Conformational Hyperspace Segmentation and Parallelism, Abstr. 204th ACS National Meeting, American Chemical Society, Washington, DC, 1992. 

Conformational analysis is becoming a widely utilized tool in drug design, molecular modeling, and the determination of structure-activity relationships. Of the many techniques presently available for conformational studies, classical, empirical potential energy functions hold great promise in providing relatively inexpensive explorations of conformational hyperspace in various simulated solvent environments. An excellent example of the application of these classical techniques is embodied in the CAMSEQ Software System (1,2.,3.). 

Determines hydrogen-bonding energies Generates an energy vs. rotation angle plot Lists all atomic coordinates Allows modification of Lennard-Jones, nonbonded potential function parameters Lists all low energy conformers Performs multi-dimensional minimization Performs random type scan of conformational hyperspace... 

Automatic searches of conformational hyperspace may be requested using the multi-level bond rotation algorithm described above. A selection is made for a uniform sequential scan, a random scan, or a multi-dimensional minimization search of the conformational energy surface. (As indicated above, prototype versions of CAMSEQ/M provide only the sequential scan mode.)... 

Dammkoehler RA, Karasek SF, Shands EFB, Marshall GR. Constrained Search of conformational hyperspace. J Comput-Aided Mol Des 1989 3 3-21. 

Dalby A, J G Nourse, W D Hounshell, A K I Gushurst, D L Grier, B A Leland and J Laufer 1992 Descriphon of Several Chermcal Structure File Formats Used by Computer Programs Developed at Molecular Design Lirmted journal of Chemical Information and Computer Science 32 244-255 Dammkoehler R A, S F Karasek, E F B Shands and G R Marshall 1989. Constrained Search of Conformational Hyperspace Journal of Computer-Aided Molecular Design 3 3-21. 

The problem of finding the right starting point of the conformational hyperspace before minimization is certainly not yet solved. However, different procedures can reduce the number of possibilities in some cases. 

The successful appHcation of pattern recognition methods depends on a number of assumptions (14). Obviously, there must be multiple samples from a system with multiple measurements consistendy made on each sample. For many techniques the system should be overdeterrnined the ratio of number of samples to number of measurements should be at least three. These techniques assume that the nearness of points in hyperspace faithfully redects the similarity of the properties of the samples. The data should be arranged in a data matrix with one row per sample, and the entries of each row should be the measurements made on the sample, as shown in Figure 1. The information needed to answer the questions must be implicitly contained in that data matrix, and the data representation must be conformable with the pattern recognition algorithms used. 

The advantage of the use of the segmental Q-coordinate system becomes apparent when we compare the unfolding trajectories represented in the conformational hypers pace of the segmental Q-coordinates and those in the hyperspace of the Cartesian coordinates (Fig. 2.11) [25]. Because unfolded conformations are very widely distributed in the hyperspace of the Cartesian... 

In principle, the conformation of a peptide with standard bond lengths and bond angles is defined by N backbone and side-chain dihedral angles 0. Thus, a peptide conformation can be considered as a point in W-dimensional hyperspace. Consequently, if one wishes to explore the entire hyperspace with... 

The other dihedral angles, were fixed to their average values. Therefore co(z-3) and (O(z-l) were set to 180°, x,(z-2), (0(z-2), X,.3(z-1) were set to 0° and was set to 90°. This makes a total of 144 well-separated conformations. No region of high density of conformations of the hyperspace volume is omitted. The 144 conformations were then energy minimised. Finally, the 144 structures... 

---