Quantum QSAR

The presented quantum QSAR model building protocol basically consists of MQSM and derived parameters and represents a self-contained theoretical framework, which offers the appropriate universal application, besides an unbiased parameter structure, as well as a causal relationship between structure and activity. 

Robert D, Girones X, Carbo-Dorca R. Molecular quantum similarity measures as descriptors for quantum QSAR. Polycycl Aromat Compd 2000 19 51-71. 

Carbo-Dorca R. Stochastic transformation of quantum similarity matrices and their use in quantum QSAR (QQSAR) models. Inti J Quant Chem 2000 79 163-177. 

In quantum QSAR of pharmacological properties, several examples involve the description of the antitumor activity of compounds. For instance, both the hydro-phobicity and the LUMO energy were found to determine the activity of a series of alkyl-substituted phenols against Chinese hamster V76 tumor cells according to the following quadratic equation [94]... 

Prabhakar YS. Quantum QSAR of the antirhinoviral activity of 9-benzylpurines. Drug Des Deliv 1991 7 227-239. 

A continuing effort has been maintained by the scientific community to provide a firm theoretical and mathematical basis for molecular quantum similarity. According to Carbo-Dorca et al., the basis of molecular quantum similarity and of quantum QSAR (as described later) is fovmded in the concepts of tagged sets and vector semispaces. To make quantum similarity understandable to the novice, the following explanatory paragraphs provide first the required mathematical basis and second an extensive discussion of some useful aspects of vector semispaces. 

It is appropriate to illustrate these concepts with a worked out example of a typical application of molecular quantum similarity ideas. The example addressed here involves the set of globulin bindings steroids used by Cramer et al. ° and subsequently in other studies to develop QSAR models. " This dataset has also been used by chemists in molecular quantum similarity studies and to develop quantum QSAR models. ° ° ... 

We can also use the MQSM matrices in a field known as quantum QSAR, where QSAR is performed with similarity matrices instead of the more classic molecular descriptors. The Gramer set of steroids have been studied extensively in this regard, and it was found that good QSAR models can be obtained with only the similarity matrices as obtained through molecular quantum similarity. Quantum QSAR is, however, outside the scope of this chapter because of its involved nature, which would require a lengthy and... 

A firm theoretical basis has been estabHshed for molecular quantum similarity, and many computational tools have been developed that allow for the evaluation and quantification of molecular quantum similarity measures among sets of molecules or atoms. Molecular quantum similarity is also the basis of quantum QSAR, another active field of research. 

Molecular Quantum Similarity Measures as Descriptors for Quantum QSAR. 

R. Carbo-Dorca, ]. Math. Chem., 27, 357 (2000). Quantum QSAR and the Eigensystems of... 

Quantum Similarity Matrices and Their Use in Quantum QSAR (QQSAR) Models. 

Quantum QSAR (Q SAR) Equation Extensions, Non-Linear Terms and Generalizations Within Extended Hilbert-Sobolev Spaces. 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

PW91 (Perdew, Wang 1991) a gradient corrected DFT method QCI (quadratic conhguration interaction) a correlated ah initio method QMC (quantum Monte Carlo) an explicitly correlated ah initio method QM/MM a technique in which orbital-based calculations and molecular mechanics calculations are combined into one calculation QSAR (quantitative structure-activity relationship) a technique for computing chemical properties, particularly as applied to biological activity QSPR (quantitative structure-property relationship) a technique for computing chemical properties... 

Computational chemists in the pharmaceutical industry also expanded from their academic upbringing by acquiring an interest in force field methods, QSAR, and statistics. Computational chemists with responsibility to work on pharmaceuticals came to appreciate the fact that it was too limiting to confine one s work to just one approach to a problem. To solve research problems in industry, one had to use the best available technique, and this did not mean going to a larger basis set or a higher level of quantum mechanical theory. It meant using molecular mechanics or QSAR or whatever. 

A Brief Review of the QSAR Technique. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radic, Kier, and Hall [see 23]. Although these structural indices represent different aspects of the molecular structures, their physicochemical meaning is unclear. The successful applications of these topological indices combined with MLR analysis have been summarized recently. Similarly, the ADAPT system employs topological indices as well as other structural parameters (e.g., steric and quantum mechanical parameters) coupled with MLR method for QSAR analysis [24]. It has been extensively applied to QSAR/QSPR studies in analytical chemistry, toxicity analysis, and other biological activity prediction. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least-squares (PLS) analysis has been employed [25]. 

All of these parameters (with the possible exception of SAP) are frequently used in QSAR studies or as filters in virtual screening. The SAP descriptor was included to check for correlations between PSA and quantum chemically calculated charges. 

The SPARC (Sparc Performs Automated Reasoning in Chemistry) approach was introduced in the 1990s by Karickhoff, Carreira, Hilal and their colleagues [16-18]. This method uses LSER [19] to estimate perturbed molecular orbitals [20] to describe quantum effects such as charge distribuhon and delocalizahon, and polarizability of molecules followed by quanhtative structure-activity relationship (QSAR) studies to correlate structure with molecular properties. SPARC describes Gibbs energy of a given process (e.g. solvation in water) as a sum of ... 

Partial Least Squares (PLS) regression (Section 35.7) is one of the more recent advances in QSAR which has led to the now widely accepted method of Comparative Molecular Field Analysis (CoMFA). This method makes use of local physicochemical properties such as charge, potential and steric fields that can be determined on a three-dimensional grid that is laid over the chemical stmctures. The determination of steric conformation, by means of X-ray crystallography or NMR spectroscopy, and the quantum mechanical calculation of charge and potential fields are now performed routinely on medium-sized molecules [10]. Modem optimization and prediction techniques such as neural networks (Chapter 44) also have found their way into QSAR. 

The determination of the three-dimensional conformation of molecules is an important aspect of QSAR, which can be obtained from x-ray crystallography [66], NMR spectroscopy or, in the case of small molecular fragments by quantum-mechanical calculations [67,68]. 

Cherif F. Matta is about to complete his Ph D. in theoretical/quantum chemistry with Professor Richard F. W. Bader at McMaster University (Canada). He has taught general, physical and quantum chemistry for over five years. His main research interest is in developing new theoretical methods for calculating the properties of large complex molecules from smaller fragments. He applied the new method to obtain accurate properties of several opioids molecules. He is also interested in QSAR of the genetically-encoded amino acids. 

Karelson, M. and Lobanov, V.S. (1996). Quantum-chemical descriptors in QSAR/ QSPR studies. Chemical Reviews 96 1027-1043. 

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