Interacting fields

Now the Lagrangean associated with the nuclear motion is not invariant under a local gauge transformation. Eor this to be the case, the Lagrangean needs to include also an interaction field. This field can be represented either as a vector field (actually a four-vector, familiar from electromagnetism), or as a tensorial, YM type field. Whatever the form of the field, there are always two parts to it. First, the field induced by the nuclear motion itself and second, an externally induced field, actually produced by some other particles E, R, which are not part of the original formalism. (At our convenience, we could include these and then these would be part of the extended coordinates r, R. The procedure would then result in the appearance of a potential interaction, but not having the field. ) At a first glance, the field (whether induced internally... 

Historically, ligand structure-based design has been the most widely used approach to the design of target-directed chemical libraries. Methods that start from hits or leads are among the most diverse, ranging from 2D substructure search and similarity-based techniques to analysis of 3D pharmacophores and molecular interaction fields (Fig. 15.2). 

Figure 15.2 Historical progress of ligand structure-based approaches from substructure search to analysis of 3-dimensional molecular interaction fields.

Cruciani G, editor. Molecular interaction fields (Vol. 27 of Mannhold R, Kubinyi... 

Clark RD et al. (2004) Modelling in vitro hepatotoxicity using molecular interaction fields and SIMCA. J Mol Graph Model 22(6) 487-497... 

Fig. 1.3 A survey of molecular properties molecular interaction fields MEPs, molecular based on their interdependence and the electrostatic potentials PK,...

Recognition Forces and Molecular Interaction Fields (MIFs)... 

Goodford, P. J. The basic principles of GRID. In Molecular Interaction Fields Application in Drug Discovery and ADME Prediction (Methods and Principles in Medicinal Chemistry), Cruciani, G., Mannhold, R. Kubinyi, H., Folkers, G. 

A, B and V are constant for a given solute (Eig. 12.4 shows the value of A, 0.78, for atenolol). This means that the balance between intermolecular forces varies with the system investigated as would be expected from a careful reading of Section 12.1.1.3. This can also be demonstrated by using a completely different approach to factorize log P, i.e. a computational method based on molecular interaction fields [10]. Volsurf descriptors [11] have been used to calculate log P of neutral species both in n-octanol-water and in alkane-water [10]. 

Mannhold R, Berellini G, Carosati E, Benedetti P (2005) In Craciani G (ed) Molecular interaction fields in drag discovery (Methods and Principles in Medicinal Chemistry), vol 27. Wiley, Weinheim, Germany, p 173... 

Goodford P (2006) In Cruciani G, Mannhold R, Kubinyi H, Folkers G (eds) Molecular interaction fields applications in drug discovery and ADME prediction. Wiley, New York, p 3... 

All human relationships are containers of emotional life, but what are the structures underlying them Nathan Schwartz-Sal ant looks at all kinds of relationships through an analyst s eye. By analogy with the ancient system of alchemy he shows how states of mind can undermine our relationships - in marriage, in creative work, in the workplace -and become transformative when brought to consciousness. It is only by learning how to access the interactive field of our relationships that we can enter this transformative process and explore its mysterious potential for self-realization... 

The interaction of drug molecules with biological membranes is a three-dimensional (3D) recognition that is mediated by surface properties such as shape, Van der Waals forces, electrostatics, hydrogen bonding, and hydrophobicity. Therefore, the GRID force field [5-7], which is able to calculate energetically favorable interaction sites around a molecule, was selected to produce 3D molecular interaction fields. 

A molecular field involves mapping the chemical forces between an interacting partner and a target (macro)molecule. As the information contained in 3D molecular fields is related to the interacting molecular partners, the amount of information in molecular interaction fields (MIFs) is in general superior to other mono-dimensionally or bi-dimensionally computed molecular descriptors. 

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.

Cruciani et al. [92] have developed the program Metasite for the prediction of the site of oxidative metabolism by CYP450 enzymes. Metasite uses GRID molecular interaction fields to fingerprint both structures of CYP450s (from homology models or crystal structures) and test substrates and then matches the fields. Zhou et al. [93] showed that Metasite was able to correctly predict the site(s) of metabolism 78% of the time for 227 CYP3A4 substrates. Caron et al. [94] used Metasite to predict the oxidative metabolism of seven statins. 

Figure 12.2 The X-ray structure of human UGT2B7 (left) showing the UDPGA-binding site (left), and their molecular interaction fields (right) obtained using GRID force field [21], showing the large cavity and the hydrophilic regions (in blue).

Figure 12.3 Rigid and flexible molecular interaction field maps with the hydrogen probe in the active-site cavity for CYP2C9 and UCT2B7 enzymes. It is worth noting that, with flexible side chains, the overall cavity volume changes considerably. This demonstrates the important role played by MIF-flexibility calculations in enzyme-substrate recognition.

Cruciani, G., Aristei, Y., Vianello, R. and Baroni, M. (2005) GRID-derived molecular interaction fields for predicting the site of metabolism in human cytochromes, in Molecular Interaction Fields (ed. G. Cruciani) Wiley-VCH Verlag GmbH, Weinheim, pp. 273-290. 

Wolohan P.R.N. Clark R.D. Predicting drug pharmacokinetic properties using molecular interaction fields and SIMCA. Journal of Computer-Aided Molecular Design, 2003, 17 (1), 65-76. 

In Equations 2.17-2.19, the Boltzmann factor contains contributions arising from the different interactions considered by the molecular theory. For example, 7t(z) and /(z) represent the repulsive and electrostatic interaction fields at z. It should be stressed that these fields are unknowns for the theory and that they depend on the distribution of all the different species across the film, that is. Equations 2.17-2.19. This has two consequences. First, a self-consistent solving process must be used, which means that simplicity is sacrificed in the theory in order to study the system in all its molecular complexity. Second, their interactions in the system are highly coupled and nonlocal [157]. 

In this expression, K is the thermodynamic equilibrium constant, which can be multiplied by Na/p (with Na equal to Avogadro s number) to obtain the commonly used equilibrium constants based on the molar bulk concentration reference state. It is important to note that the exponential term in the right-hand side of Equations 2.20 and 2.21 is an activity coefficient term. This term depends on the interaction field n z), which is nonlocal and therefore it couples with all the interactions and chemical equilibria in all regions of the film. 

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