Continuous molecular fields approach

Continuous Molecular Fields Approach Applied to Structure-Activity Modeling... 

Baskin II, Zhokhova NI (2013) The continuous molecular fields approach to building 3D-QSAR models. J Comput-Aided Mol Des 27(5) 427 2. doi 10.1007/sl0822-013-9656-4 CortesC, Vapnik V( 1995) Support-vector networks. Mach Leam 20(3) 273-297. doi 10.1007/ bf00994018... 

In this section, we consider a new approach to building stracture-activity and structure-property models based on the use of continuous functions on space coordinates (called hereinafter continuous molecular fields) to represent molecular... 

The essence of the Continuous Molecular Fields (CMF) approach consists in performing... 

The CMF approach is not confined to the simplest approximation scheme introduced by Eq. (13.5). Ar r mrmber of Gaussian functions, (both isotropic, i.e. spherically symmetrical, and non-isotropic) as well as any other set of basic functions (such as splines, wavelets, etc.) can be used for approximating continuous molecular fields. This provides the ability to work with complex types of molecular fields, including those derived from the electron density function. 

Scholkopf B, Platt JC, Shawe-Taylor J, Smola AJ, Williamson RC (2001) Estimating the support of a high-dimensional distribution. Neural Comput 13(7) 1443-1471 Karpov PV, Baskin II, Zhokhova NI, Zefirov NS (2011) Method of continuous molecular fields in the one-class classification task. Dokl Chem 440(2) 263-265 Karpov PV, Baskin II, ZhokhovaNI,Nawrozkij MB, ZefirovAN, Yablokov AS, Novakov lA, Zefirov NS (2011) One-class approach models for virtual screening of non-nucleoside HIV-1 reverse transcriptase inhibitors based on the concept of continuous molecular fields. Russ Chem Bull 60(ll) 2418-2424. doi 10.1007/slll72-011-0372-8... 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

In the field of inorganic photochemistry, Zink has presented an interesting molecular orbital analysis of the photochemical reactions of ds and d compounds which complements his previous ligand-field approach and provides predictions in accord with experimental findings. Exceptions to Adamson s empirical rules for photochemical ligand release continue to appear (Kirk and Kelly). Endicott et al. have provided a critical examination of models for photoredox reactions of transition-metal ammine complexes. They stress the role of the solvent in relaxation of the Franck-Condon excited state to the primary radical-pair products. 

One can notice that the performance of CMF is closer to that of the CoMSIA approach in comparison with CoMFA. This could be attributed to the fact that the mathematical form of Eq. (13.5) resembles expressions for similarity indices in CoMSIA. So, in spite of absolutely different underlying ideas, CbMSIA can formally be regarded as a discretized approximation of the current version of CMF, or, vice versa, CMF—as a continuous functional extension of CoMSIA. Therefore, the difference between the models produced by these methods might result from the effect of field discretization, different statistical procedure and parameterization of molecular fields. 

All methods of molecular ahgnment useful for building traditional lattice-based 3D-QSAR models can also be applied in the framewoik of the CMF approach. Meanwhile, thanks to the integrability of continuous functions describing molecular fields, the latter approach offers additional possibilities. 

The CMF approach can offer an alternative solution to this problem. Instead of using discrete sets of representative conformations, one can consider for each molecule an infinite number of conformations organized into a continuous manifold, so-called corrformational space . This provides the ability to apply functional data analysis not only to molecular fields but also to molecular geometry in a consistent way. Such corrformational space can be described by means of some probability density function pdf) in 3N-dimensional Euclidean space, where N is the number of atoms in the molecule under study. Having applied several approximations from the arsenal of statistical physics, one can obtain the following expression for calculating atomic kernels instead of Eq. (13.6) ... 

The CMF approach describes molecules by ensemble of continuous functions (molecular fields), instead of finite sets of molecular descriptors (such as interaction energies computed at grid nodes). The potential advantages of this approach results from the ability to approximate electronic molecular stmctures with any desirable accuracy level, the abihty to leverage the valuable information contained in partial derivatives of molecular fields (otherwise lost upon discretization) to analyze models and enhance their predictive performance, the ability to apply integral transforms to molecular fields and models, etc. 

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