Continuous conformational space

This algorithm has been successfully used to reproduce the conformations of peptide ligands in several X-ray crystal structures. The use of a finite number of discrete templates to simulate the continuous conformational space available to peptides does not seem to be a serious limitation. Comparison to experiment is an important aspect of the GROW approach. 

The simplest model for a quahtative description of protein folding is the lattice hydrophobic jolar (HP) model [12]. In this model, the continuous conformational space is reduced to discrete regular lattices and conformations of proteins are modeled as selfavoiding walks restricted to the lattice. Assuming that the hydrophobic interaction is the most essential force toward the native fold, sequences of HP proteins consist of only two types of monomers (or classes of amino acids) Amino acids with high hydrophobicity are treated as hydrophobic monomers (//), while the class of polar (or hydrophihc) residues is... 

The changes in structure of denatured nuclease as a function of urea concentration (Fig. 3) suggest that, as hydrophobic interactions are weakened and the backbone becomes more highly solvated, the chain expands gradually. The data presented by Millet et al. in this volume suggest that this expansion does not continue asymptotically as predicted by simple polymer physical chemistry. This is the behavior expected for a polypeptide chain trapped in a small region of conformation space. Most, perhaps all, of the conformations accessible in the expanded denatured state may have a native-like topology. 

From the definitions given above it follows that the configurational space (continuous) of a peptide is infinite, even if its conformational space... 

These four conformations are but a few examples. The lowest minimum energy structure found was somewhat more compact and had an energy of 56.3 Kcal/mole. Each of the other minimizations from the molecular dynamics gave unique minima showing that for the 15 picoseconds of simulation the molecule was continually exploring new regions of conformational space. A complete description of these structures will be presented elsewhere(62). 

For the cycloscan, conformational libraries are synthesized by cyclization of continuous or noncontinuous bioactive epitopes and not by their insertion into a scaffold. Originally, the concept of cycloscan was introduced for the generation of backbone-cyclized peptide libraries 467 however, cycloscan can also be applied to other modes of cyclization. In this approach all components of each sublibrary bear the identical sequence, and differ from each other in distinct parameters that affect their conformation, but do not alter their connectivity, and hence their potential bioactivity. This is achieved by gradually introducing discrete conformational perturbations, which allow an efficient screening of the conformational space of the parent peptide. The majority of the components of such libraries should be inactive, because they do not overlap the bioactive conformation. However, the peptide that does fit the bioactive conformation should be very potent and have all the pharmacological advantages of cyclic peptides. 

It is not uncommon for a single molecule to have multiple populations. At non-zero temperatures, the population of different conformations will be dictated by Boltzmann statistics. If we make the approximation that we may neglect the continuous character of conformational space and simply work with discrete potential energy minima, we can replace a statistical mechanical probability integral with a discrete sum, and the equilibrium fraction F of any given conformer A at temperature T may be computed as... 

Constrained Search and the related approach of SCAMPI both integrate the conformational analysis closely with the pharmacophore discovery. This has the advantage that the sampling of conformational space can be more focused on key regions. With both Catalyst and DANTE, conformational analysis was explicitly kept separate, in the latter to allow one to take advantage of any innovations in conformational analysis tools. And, indeed, there continues to be a steady flow of new approaches in conformational analysis—pharmacophore discovery is critically dependent on high-quality exhaustive conformational analysis. Based on our experience thus far, we cannot conclude that either approach is superior (integrated vs. external). Furthermore, a consensus has not yet been reached on the optimal manner to perform conformational search as needed by pharmacophore discovery. This will continue to be a fruitful area of research. 

We have developed a new representation of conformational space and a computer program to prepare it U). This representation, the n-h map, allows many combinations of monomeric geometry and glycosidic linkage angle to be considered. A bonus in our method is that representations for the various polymers are quite different, whereas the Phi-Psi maps (without the iso-n and iso-h contours) are all very similar (3 ). Some polymers are characterized by n-b maps that have large, continuous allowed areas, while others have small or multiple, disconnected areas. 

Molecules are not rigid, with the atoms in a molecule moving continuously. The conformational space of a... 

Oono and Freed (1981b) applied the renormalization procedure of conformational space to describe the dynamics of chains. They performed the scaling transformation of the complete diffusion equation with the free energy of a chain system written in terms of the model of a continuous chain. Besides, the sialic quantities in Equation 13, the friction aHifficieiit of a chain fragment with its size less than a... 

Equation (4.5) assumes that network II is dispersed in network I, yet retains sufficient continuity in space to contribute to the modulus. Since the chain conformation of network II undergoes a minimal perturbation, the quantity ri/rf is further assumed to be unity. 

To illustrate the first point, we note that a PEG chain can be in 10 different conformations (random walk model). In the contact zone there are 10 PEG chains, which results in a total of 10 molecular configurations contributing to the eSFA measurement. Under confinement, the number of possible conformations is reduced continuously, and, due to the high number of possible states, no noticeable transitions ate expected. The presence of fine structures must therefore be undeistood as a significant restriction or degeneration of the polymer conformational space. 

---