Molecular Interaction Fields Transformation

The MIFs obtained from qrtochrome enzymes are subsequently transformed and simplified as shown in Fig. 12.4. A three-dimensional grid map (3D map) may be viewed as a 3D matrix that contains forces of attraction and repulsion between a chemical probe and a protein. A 3D map is an image of the CYP-probe molecular interactions in which each pixel contains information about the cartesian coordinates and a physicochemical interaction. In cytochrome, where a catalytic reaction has to take place, all the 3D map information can be compressed and refers to the 

The selected 3D interaction points are used to calculate enzyme fingerprints using the GRIND technology [18]. For each CYP-probe interaction map (see Fig. 

this approach transforms the interaction energies at a certain spatial position (the MIF descriptors) into a number of histograms that capture the 3D phar-macophoric interactions of the flexible protein. Such histograms are called corre-lograms. The correlograms represent the distance between the reactive center of the cytochrome (the oxene in the heme moiety) and the different chemical regions inside the enzyme active site. 

The descriptors developed to characterize the substrate chemotypes are obtained from a mixture of molecular orbital calculations and GRID probe-pharmacophore recognition. Molecular orbital calculations to compute the substrate s electron density distribution are the first to be performed. All atom charges are determined using the AMI Hamiltonian. Then the computed charges are used to derive a 3D pharmacophore based on the molecular electrostatic potential (MEP) around the substrate molecules. 

Once the protein interaction pattern is translated from Cartesian coordinates into distances from the reactive center of the enzyme, and the structure of the ligand has been described with similar fingerprints, both sets of descriptors can be compared. The hydrophobic complementarity (see Fig. 12.5), the complementarity of charges, and H-bonds for the protein and the substrates, are all computed using Carbo similarity [20] indices. The prediction of the site of metabolism is based on 

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Fig. 17.1. Multivariate characterization with VolSurf descriptors. Molecular Interaction Fields (MIF shaded areas) are computed from the 3D-molecular structure. MIFs are transformed in a table of descriptors, and statistical multivariate analysis is performed.

Figure 10.3. Transformation ofthe GRID molecular interaction fields into...

An important feature of GRIND is that, with the use of appropriate software, the original descriptors (molecular interaction fields) can be regenerated from the autocorrelation transform and, thus, the results of the analysis are represented graphically, together with the original molecular structures in three-dimensional plots. The use of the methodology was recently illustrated in examples from the... 

It is presumed that supercritical gaseous molecules are concentrated in the micropore space by affection of the strong molecule-pore interaction to induce an enhanced inter-molecular interaction and the supercritical gas is transformed into a quasivapour. The quasivapour states depend strongly on the micropore width, because the micropore field strength is governed by the pore width. Each quasivapour has its inherent micropore volume Wl which is governed mainly by the molecule-pore interaction. Hence, the DR equation can be extended to the quasivapour of the supercritical gas, as follows[42,43] ... 

Here // < is the Hamiltonian for the radiation field in vacuo, flmo the field-free Hamiltonian for molecule , and //m( is a term representing molecular interaction with the radiation. It is worth emphasising that the basic simplicity of Eq. (1) specifically results from adoption of the multipolar form of light-matter interaction. This is based on a well-known canonical transformation from the minimal-coupling interaction [17-21]. The procedure results in precise cancellation from the system Hamiltonian of all Coulombic terms, save those intrinsic to the Hamiltonian operators for the component molecules hence no terms involving intermolecular interactions appear in Eq. (1). 

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the... 

The field of theoretical molecular sciences ranges from fundamental physical questions relevant to the molecular concept, through the statics and dynamics of isolated molecules, aggregates and materials, molecular properties and interactions, and the role of molecules in the biological sciences. Therefore, it involves the physical basis for geometric and electronic structure, states of aggregation, physical and chemical transformations, thermodynamic and kinetic properties, as well as unusual properties such as extreme flexibility or strong relativistic or quantum-field effects, extreme conditions such as intense radiation fields or interaction with the continuum, and the specificity ofbiochemical reactions. 

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