Covering Conformational Space

This algorithm will generate the ensemble of conformations at thermodynamic equilibrium, if the conformational variations introduced in step 1 (the so-called moves ) are sufficient to cover all possible regions of conformational space and are locally reversible. It is easy to understand that feature of the Metropolis procedure the transition probability into the higher energy state is given by the Boltzmann factor, the transition probability into the lower energy state is one. The relative population of the two states is then the ratio of the transition probabilities, thus the Boltzmann factor this is the outcome expected from thermodynamics. 

Virtual screening applications based on superposition or docking usually contain difficult-to-solve optimization problems with a mixed combinatorial and numerical flavor. The combinatorial aspect results from discrete models of conformational flexibility and molecular interactions. The numerical aspect results from describing the relative orientation of two objects, either two superimposed molecules or a ligand with respect to a protein in docking calculations. Problems of this kind are in most cases hard to solve optimally with reasonable compute resources. Sometimes, the combinatorial and the numerical part of such a problem can be separated and independently solved. For example, several virtual screening tools enumerate the conformational space of a molecule in order to address a major combinatorial part of the problem independently (see for example [199]). Alternatively, heuristic search techniques are used to tackle the problem as a whole. Some of them will be covered in this section. 

In principle, every conformer of a set of flexible ligands could be stored in a database, and then each conformation could be evaluated with rigid-body docking algorithms. The size of the ensemble is critical since the computing time increases linearly with the number of conformations and the quality of the result drops with larger differences between the most similar conformation of the ensemble and the actual complex conformation. Thus a balance must be struck between computing time requirements and the desire to cover all of conformational space. 

In combination, the class of biflavonoids represents a library of over 20,000 different molecules, each of which is capable of multiple H-bondings and hydrophobic interactions. Not all these have been found to exist in nature so far. However, biflavonoid theoretical library covers a wide range of the configurational and conformational space, thus suggesting that the scope of interesting biological activities may be extraordinary. [2]... 

The strength of our proposed Pocketome engine is best revealed in cases when the pocket models are accurate and cover the essential conformational space. For such cases, the Pocketome can... 

The procedure also used random array initial structures for molecular dynamics algorithm using XPLOR-NIH.12 Sixteen thousand initial structures were subjected to an initial simulated annealing (5,000 K, 80 ps). This means that the initial structures did not cover the entire conformational space, but were randomly distributed all over the space. The conformational... 

Secondly, the scope is extended to cover a much wider range of the conformational space using the following Lagrangian [13] ... 

Minkowski space, M, is assumed embedded in a more general universal closed (compact) space M, the so-called conformal space. This is the projective space proposed as a model of the universe by Oswald Veblen (1933), translated in the Appendix. Roughly speaking, M is obtained from M by adding a light cone at infinity. More precisely, it is the double cover of the space so generated. Segal (1976) refers to M as unispace and to the natural time r in this space as unitime. 

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