Continuous molecular fields methods

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... 

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... 

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... 

Cartesian coordinates system for locating points in space based on three coordinates, which are usually given the symbols x, y, z or i, j, k CBS (complete basis set) an ah initio method CC (coupled cluster) a correlated ah initio method CFF (consistent force field) a class of molecular mechanics force fields CFMM (continuous fast multipole method) a method for fast DFT calculations on large molecules... 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

More recently, with the significant increases in computer power even on desktop PCs, methods for directly matching 3-D features of molecules have become more prevalent. Features here generally refer to various types of molecular fields, some such as electron density ( steric ) and electrostatic-potential fields are derived from fundamental physics (30,31) while others such as lipophilic potential fields (32) are constructed in an ad hoc manner. Molecular fields are typically represented as continuous functions. Discrete fields have also been used (33) albeit somewhat less frequently except in the case of the many CoMFA-based studies (34). 

We continue to believe that the force-field method offers a rapid, convenient and reliable method for the determination of molecular structures and energies. While there are limitations to the method, as there are with each of the experimental methods, the usefulness of this technique now seems generally appreciated. We can forsee only a continuing expansion of the development and applications of force-field calculations in many areas of chemistry. 

Hamiltonian in an extended space, the direct product of the usual molecular Hilbert space, and the space of periodic functions of f e [0,T]. This extension of the Hilbert space can be made somewhat more transparent by introducing a new time-like variable, to be distinguished from the actual time variable t. This new time variable can be defined through the arbitrary phase of the continuous (periodic) field, as done in Ref. [28, 29]. A variant of the idea is found in the (f, t ) method developed by Peskin and Moiseyev [30] and applied to the photodissociation of HJ [31, 32]. We will continue with the more traditional and simpler formulation of Floquet theory here, as this is sufficient to bring out ideas of laser-induced resonances in the dressed molecule picture. 

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. 

Fluorescence microscopy is an essential tool for modern biological research, especially in cellular and molecular biology. In its methods it is a continuously expanding field. New fluorophores are introduced [1,2] and more and more spectral variants of fluorescent proteins are made available as markers [3-5]. 

In 1976 Warshel and Levitt introduced the idea of a hybrid QM/MM (molecular mechanical) method that treated a small portion of the system using a quantum mechanical repre.sen-tation while the rest of the system, which did not need such a detailed description, was represented by an empirical force field. They used their potential to study the reaction catalyzed by the enzyme, lysozyme. Since then, Warshel has continued to use such hybrid methods, most notably his empirical valence bond (EVB) approach, to study a wide variety of reactions in solution and in enzymes. It is undoubtedly he who has made the major contribution, both in terms of method development and in applications, to this area. Warshel has. summarized his work on studying reactions in enzymes and interested readers are recommended to look at that for further details. ... 

Figure 2 Structural alignment methods with continuous properties. Methods are based on continuous properties using the algorithms implemented in MSA (I), HASL (II), and CoMFA (III). A conformational analysis (optional) can be used to select candidate conformations ( bioactive conformation, or alternatively a set of biologically relevant conformations that are used for the alignment). The structure representation is based on molecular shape (I), a four-dimensional lattice (II). or molecular fields (III). The different algorithms for the alignment require that a reference be cho.sen so that comparisons between each ligand and the reference can be made. A statistical measure of molecular similarity is performed to identify the alignment that maximizes the molecular similarity between the ligands in term.s of three-dimensional overlap (MSA, HASL) or electrostatic potential distributions...

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