Quantitative structure-activity relationship statistical methods

A challenging task in material science as well as in pharmaceutical research is to custom tailor a compound s properties. George S. Hammond stated that the most fundamental and lasting objective of synthesis is not production of new compounds, but production of properties (Norris Award Lecture, 1968). The molecular structure of an organic or inorganic compound determines its properties. Nevertheless, methods for the direct prediction of a compound s properties based on its molecular structure are usually not available (Figure 8-1). Therefore, the establishment of Quantitative Structure-Property Relationships (QSPRs) and Quantitative Structure-Activity Relationships (QSARs) uses an indirect approach in order to tackle this problem. In the first step, numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical and artificial neural network models are used to predict the property or activity of interest based on these descriptors or a suitable subset. 

Basak, S. C., Mills, D., Hawkins, D. M., Kraker, J. J. Quantitative structure-activity relationship (QSAR) modeling of human blood air partitioning with proper statistical methods and validation. Chem. Biodivers., accepted. 

Statistical and computational methods have been used to quantify structure-activi relationships leading to quantitative structure-activity relationships (QSAR). The concqpt of QSAR can be dated back to the work of Crum, Brown and Fraser from 1868 to 1869, and Richardson, also in 1869. Many notable papers were published in the period leading up to the twentieth century by men such as Berthelot and Jungfleisch in 1872, Nemst in 1891, Ov ton in 1897 and Meyer in 1899 (7). Professor Corwin Hansch is now regarded by many as the father of QSAR, because of his work in the development of new and innovative techniques for QSAR. He and his co-woikers produced a paper that was to be known as the birtii of QSAR, and was oititled "Correlation of biological activity of phenoxyacetic acids with Hammett substituent constants and partition coefficients" (2). 

Computational chemistry methodology is finding increasing application to the design of new flavoring agents. This chapter surveys several useful techniques linear free energy relationships, quantitative structure-activity relationships, conformational analysis, electronic structure calculations, and statistical methods. Applications to the study of artificial sweeteners are described. 

Over the past 60 years a multitude of means have been used to capture SARs. We can broadly divide them into two groups those based on statistical or data mining methods (e.g., regression models) and those based on physical approaches (e.g., pharmacophore models). For a comprehensive review of quantitative structure-activity relationship (QSAR) methodologies the reader is referred... 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

The next step was made by Klebe et al. [50]. Two 3D-QSAR methods were applied to get three-dimensional quantitative structure-activity relationships using a training set of 72 inhibitors of the benzamidine type with respect to their binding affinities toward Factor Xa to yield statistically reliable models of good predictive power [51-54] the widely used CoMFA method (for steric and electrostatic properties) and the comparative molecular similarity index analysis (CoMSlA) method (for steric, electrostatic, hydrophobic, hydrogen bond donor, and hydrogen bond acceptor properties). These methods allowed the consideration of various physicochemical properties, and the resulting contribution maps could be intuitively interpreted. 

In addition to the biochemistry introduced in this chapter, a great deal of emphasis is placed on the determination of the activity of a compound by an analysis of its structure. Quantitative structure-activity relationships (QSAR), used judiciously, have the ability to help set testing priorities and identify potentially toxic materials in mixtures. Heavily reliant upon the quality of the toxicity data discussed in Chapter 4, these methods use sophisticated statistical techniques or analysis of interaction of a toxicant with the receptor to estimate toxicity. A method that uses structure-activity relationships coupled with availability and an assumed additive model for toxicity is presented to estimate the risk due to polyaromatic hydrocarbons (PAHs). 

In studies of quantitative structure activity relationships (QSAR), the relative potencies of a series of drugs are subjected to analysis with the hope that biological potency will be described by a mathematical equation. QSAR is an actuarial or statistical method in which only objective data are used with no intrusion of models or mechanistic hypotheses. The equation that is obtained not only accounts for the relative potencies of the compounds, but from it are deduced predictions of the potencies of untested compounds if the equation is valid, the predictions are ineluctable. The method thus has the capacity of yielding new (structurally related) drugs with desired potency, perhaps drugs with enhanced selectivity or fewer side effects. 

THREE-DIMENSIONAL QUANTITATIVE STRUCTURE-ACTIVITY relationship (3D-QSAR) method that uses statistical correlation techniques for the analysis of (a) the quantitative relationship between the biological activity of a set of compounds with a specified alignment and (b) their three-dimensional electronic and steric properties. Other properties such as hydrophobicity and hydrogen bonding can also be incorporated into the analysis. 

Quantitative structure-activity relationships study of herbicides using neural networks and different statistical methods. Chemom. Intell. Lab. Syst., 45, 267-276. 

Elhallaoui, M., Elasri, M., Ouazzani, F., Mechaqrane, A. and Lakhlifi, T. (2003) Quantitative structure-activity relationships of noncompetitive antagonists of the NMDA receptor a study of a series of MK801 derivative molecules using statistical methods and neural network. Int.J. Mol. Sci., 4, 249-262. 

Quantitative Structure - Activity Relationships (QSARs) are estimation methods developed and used to predict certain effects or properties of chemical substances, which are primarily based on the structure of the chemicals. The development of QSARs often relies on the application of statistical methods such as multiple linear regression (MLR) or partial least squares regression (PLS). However, since toxicity data often include uncertainties and measurements errors, when the aim is to point out the more toxic and thus hazardous chemicals and to set priorities, order models can be used as alternative to statistical methods such as multiple linear regression. 

A wide variety of chemometric statistical tools may be used to investigate quantitative structure-activity relationships or more general structure-property correlations. Some of these techniques require expert support. However, the bench chemist may successfully use a number of techniques, when some basic guidelines as discussed in this chapter are followed. The most important methods are ... 

The discipline of chemometrics originates in chemistry. Typical applications of chemometric methods are the development of quantitative structure activity relationships and the evaluation of analytical-chemical data. The data flood generated by modern analytical instrumentation is one reason that analytical chemists in particular develop applications of chemometric methods. Chemometric methods in analytics is the discipline that uses mathematical and statistical methods to obtain relevant information on material systems. 

From this point onwards, the paths diverge. One pathway, as used in this book so far, is to pursue the scientific study of the cytological, biochemical, and distributive clues that provided the lead in the first place. The other pathway is the statistical correlation of several physical properties of the lead molecule with its biological actions. It must be emphasized that statistics lies remote from experimental science and can, at best, indicate only a probability. However, these statistical methods are much used, particularly in industry, and it is proposed to give a brief account of correlation analysis (quantitative structure-activity relationships, or QSAR) which embodies them. 

Non-linear models may be fitted to data sets by the inclusion of functions of physicochemical parameters in a linear regression model—for example, an equation in n and as shown in Fig. 6.5—or by the use of non-linear fitting methods. The latter topic is outside the scope of this book but is well covered in many statistical texts (e.g. Draper and Smith 1981). Construction of linear regression models containing non-linear terms is most often prompted when the data is clearly not well fitted by a linear model, e.g. Fig. 6.4e, but where regularity in the data suggests that some other model will fit. A very common example in the field of quantitative structure-activity relationship (QSAR) involves non-linear relationships with hydrophobic descriptors such as log P or n. Non-linear dependency of biological properties on these parameters became apparent early in the... 

In summary, the support vector machine (SVM) and partial least square (PLS) methods were used to develop quantitative structure activity relationship (QSAR) models to predict the inhibitory activity of nonpeptide HIV-1 protease inhibitors. Cenetic algorithm (CA) was employed to select variables that lead to the best-fitted models. A comparison between the obtained results using SVM with those of PLS revealed that the SVM model is much better than that of PLS. The root mean square errors of the training set and the test set for SVM model were calculated to be 0.2027, 0.2751, and the coefficients of determination (R2) are 0.9800, 0.9355 respectively. Furthermore, the obtained statistical parameter of leave-one-out cross-validation test (Q ) on SVM model was 0.9672, which proves the reliability of this model. Omar Deeb is thankful for Al-Quds University for financial support. 

Computational methods for predicting compounds with specific pharmacodynamic, pharmacokinetic, or toxicological properties are useful for facilitating drug discovery and drug safety evaluation. The quantitative structure-activity relationship (QSAR) and quantitative structme-property relationship (QSPR) methods are the most successfully used statistical learning methods for predicting compounds with specific properties. 

---