Ligand superposition techniques

The Monte Carlo version of minimal steric difference (denoted as MCD) improves the computation of non-overlapping volumes in the standard-ligand superposition, translating thus the topological MSD parameter into the (3D) metric context (Mojoc et al. 1975 Ciubotariu et al. 1983). In order to calculate the MCD, the molecules are described by the Cartesian coordinates and vdW radii of their atoms. The atomic coordinates implicitly specify the way one achieves the superposition all molecules of the series are represented in the same Cartesian coordinate system. The mathematical method used in the MCD-technique for computation of nonoverlapping volumes is the Monte Carlo method (Demidovich and Maron 1987). 

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. 

Powder-like ENDOR spectra obtained with arbitrary Bo orientations show a much less pronounced structure and are usually difficult to interpret For systems with nearly axial g and metal hfs tensors, however, there often exist turning points in the EPR spectrum which conespond to all the Bq orientations in the complex plane. Thus, a setting of the magnetic field at such a turning point results in a powder ENDOR spectrum which is a superposition of the ENDOR spectra arising from all these Bq orientations. We call it therefore a two-dimensional ENDOR spectrum. For a ligand nucleus with I = 1/2, the two extreme values of the hfs in the complex plane can immediately be found For a nucleus with 1 1, however, the evaluation of the two extreme coupling constants of both the hf and the quadrupole interaction, which are not necessarily principal values of A and Q, requires more sophisticated ENDOR techniques (Sect. 4.3). 

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