Continuous molecular fields

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

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... 

So far, the direct use of continuous molecular fields in their functional form in statistical analysis was not possible because standard data analysis procedures can only work with finite and fixed number of features (molecular descriptors). Only recently, thanks to the development of the statistical learning theory [5] and the methodology of using kernels [6] in machine learning instead of fixed-sized feature vectors, it has become possible to process data of any form and complexity. 

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

It should be mentioned that continuous molecular fields have already been used in QSAR studies. So, indexes of R. Carbo-Doica, which were used in certain QSAR studies [27], can also be considered as a particular case of continuous molecular fields. 

The method of Continuous Molecular Fields (CMF) performs statistical analysis of functional molecular data by means of joint application of kernel machine learning methods and special kernels which compare molecules by computing overiap integrals of their molecular fields [7, 8]. 

The Use of Continuous Molecular Fields in Conjunction with Regression Kernel-based Machine Learning Methods... 

Tables 13.5 and 13.6 summarize the results of building 1-SVM models on the basis of continuous molecular fields for HIV reverse transcriptase (HIVRT) and trypsin inhibitors. As follows from Table 13.5, the best performance for HIVRT is obtained by the model constracted using the steric kernel and resulting in an AUC value of 0.75. For this target, the use of a hnear combination of several kernels does not improve the AUC value. At the same time, for trypsin inhibitors, rather high AUC values (0.86-0.91) were obtained on the basis of individual models constructed with the use of all three kernels, which is likely due to their mutual correlation. However, for this target, the use of a linear combination of all kernels increases the AUC value up to 0.94.

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. 

Due to the ability to apply methods of funetional analysis, continuous molecular fields can be tailored for solving many different tasks in chemoinformatics. Consider, for example, prediction of physico-chemical properties in diverse datasets. In this case, natural aligmnent corresponds to the uniform probability of molecules to adopt any possible mutual orientation. Therefore, kernel KpA., Mp describing the similarity between the molecular fields of the J k type for the /th and yth molecules can be computed by averaging over all possible mutual orientations ... 

Zhokhova NI, Baskin II, Bakhronov DK, Palyulin VA, Zefirov NS (2009) Method of continuous molecular fields in the search for quantitative stmcture-activity relationships. Dokl Chem 429(1 ) 273-276... 

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... 

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... 

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