Quantitative structure-activity relationship

Quantitative structure-activity relationship (QSAR) (sometimes QSPR: quantitative structure-property relationship) is the process by which chemical structure is quantitatively correlated with a well defined process, such as biological activity or chemical reactivity.

For example, biological activity can be expressed quantitatively as in the concentration of a substance required to give a certain biological response. Additionally, when physicochemical properties or structures are expressed by numbers, one can form a mathematical relationship, or quantitative structure-activity relationship, between the two. The mathematical expression can then be used to predict the biological response of other chemical structures.

QSAR's most general mathematical form is:

• <math>\text{Activity} = f(\text{physiochemical properties and/or structural properties})</math>

SAR and the SAR paradox

The basic assumption for all molecule based hypotheses is that similar molecules have similar activities. This principle is also called Structure-Activity Relationship (SAR). The underlying problem is therefore how to define a small difference on a molecular level, since each kind of activity, e.g. reaction ability, biotransformation ability, solubility, target activity, and so on, might depend on another difference. A good example was given in the bioisosterism review of Patanie/LaVoie.

In general, one is more interested in finding strong trends. Created hypotheses usually rely on a finite number of chemical data. Thus, the induction principle should be respected to avoid overfitted hypotheses and deriving overfitted and useless interpretations on structural/molecular data.

The SAR paradox refers to the fact that it is not the case that all similar molecules have similar activities.

Types

Fragment based (group contribution)

It has been shown that the logP of compound can be determined by the sum of its fragments. Fragmentary logP values have been determined statistically. This method gives mixed results and is generally not trusted to have accuracy of more than ±0.1 units.

Group or Fragment based QSAR aka GQSAR. GQSAR allows flexibility to study various molecular fragments of interest in relation to the variation in biological response. The molecular fragments could be substituents at various substitution sites in congeneric set of molecules or could be on the basis of pre-defined chemical rules in case of non-congeneric set. GQSAR also considers cross-terms fragment descriptors, which could be helpful in identification of key fragment interactions in determining variation of activity.

3D-QSAR

3D-QSAR refers to the application of force field calculations requiring three-dimensional structures, e.g. based on protein crystallography or molecule superposition. It uses computed potentials, e.g. the Lennard-Jones potential, rather than experimental constants and is concerned with the overall molecule rather than a single substituent. It examines the steric fields (shape of the molecule) and the electrostatic fields based on the applied energy function.

The created data space is then usually reduced by a following feature extraction (see also dimensionality reduction). The following learning method can be any of the already mentioned machine learning methods, e.g. support vector machines.

In the literature it can be often found that chemists have a preference for partial least squares (PLS) methods, since it applies the feature extraction and induction in one step.

Data mining

For the coding usually a relatively large number of features or molecular descriptors are calculated, which can lack structural interpretation ability. In combination with the later applied learning method or as preprocessing step occurs a feature selection problem.

A typical data mining based prediction uses e.g. support vector machines, decision trees, neural networks for inducing a predictive learning model.

Molecule mining approaches, a special case of structured data mining approaches, apply a similarity matrix based prediction or an automatic fragmentation scheme into molecular substructures. Furthermore there exist also approaches using maximum common subgraph searches or graph kernels.

Judging the quality of QSAR models

QSARs represent predictive models derived from application of statistical tools correlating biological activity (including desirable therapeutic effect and undesirable side effects) of chemicals (drugs/toxicants/environmental pollutants) with descriptors representative of molecular structure and/or properties. QSARs are being applied in many disciplines for example risk assessment, toxicity prediction, and regulatory decisions in addition to drug discovery and lead optimization. Obtaining a good quality QSAR model depends on many factors, such as the quality of biological data, the choice of descriptors and statistical methods. Any QSAR modeling should ultimately lead to statistically robust models capable of making accurate and reliable predictions of biological activities of new compounds.

For validation of QSAR models usually four strategies are adopted:

1. internal validation or cross-validation;
2. validation by dividing the data set into training and test compounds;
3. true external validation by application of model on external data and
4. data randomization or Y-scrambling.

The success of any QSAR model depends on accuracy of the input data, selection of appropriate descriptors and statistical tools, and most importantly validation of the developed model. Validation is the process by which the reliability and relevance of a procedure are established for a specific purpose. Leave one-out cross-validation generally leads to an overestimation of predictive capacity, and even with external validation, no one can be sure whether the selection of training and test sets was manipulated to maximize the predictive capacity of the model being published. Different aspects of validation of QSAR models that need attention includes methods of selection of training set compounds, setting training set size and impact of variable selection for training set models for determining the quality of prediction. Development of novel validation parameters for judging quality of QSAR models is also important.

Application

Chemical

One of the first historical QSAR applications was to predict boiling points.

It is well known for instance that within a particular family of chemical compounds, especially of organic chemistry, that there are strong correlations between structure and observed properties. A simple example is the relationship between the number of carbons in alkanes and their boiling points. There is a clear trend in the increase of boiling point with an increase in the number carbons and this serves as a means for predicting the boiling points of higher alkanes.

A still very interesting application is the Hammett equation, Taft equation and pKa prediction methods.

Biological

The biological activity of molecules is usually measured in assays to establish the level of inhibition of particular signal transduction or metabolic pathways. Chemicals can also be biologically active by being toxic. Drug discovery often involves the use of QSAR to identify chemical structures that could have good inhibitory effects on specific targets and have low toxicity (non-specific activity). Of special interest is the prediction of partition coefficient log P, which is an important measure used in identifying "druglikeness" according to Lipinski's Rule of Five.

While many quantitative structure activity relationship analyses involve the interactions of a family of molecules with an enzyme or receptor binding site, QSAR can also be used to study the interactions between the structural domains of proteins. Protein-protein interactions can be quantitatively analyzed for structural variations resulted from site-directed mutagenesis.

It is part of the machine learning method to reduce the risk for a SAR paradox, especially taking into account that only a finite amount of data is available (see also MVUE). In general all QSAR problems can be divided into a coding and learning.

Applicability domain

As the use of (Q)SAR models for chemical risk management increases steadily and is also used for regulatory purposes (in the EU: Registration, Evaluation, Authorisation and Restriction of Chemicals), it is of crucial importance to be able to assess the reliability of predictions. The chemical descriptor space spanned by a particular training set of chemicals is called Applicability Domain. It offers the opportunity to assess whether a compound can be reliably predicted.

See also

• ADME
• Cheminformatics
• Computer-assisted drug design (CADD)
• Conformation Activity Relationship
• Differential solubility
• Molecular design software
• Partition coefficient
• Pharmacokinetics
• Pharmacophore
• QSAR & Combinatorial Science – Scientific journal
• Software for molecular mechanics modeling

Further reading

• Selassie CD (2003). "History of Quantitative Structure-Activity Relationships" (PDF). In Abraham DJ. Burger's medicinal Chemistry and Drug Discovery. 1 (6th ed.). New York: Wiley. pp. 1–48. ISBN 0-471-27401-1. 

External links

• "The Cheminformatics and QSAR Society". Retrieved 2009-05-11. 
• "Nature Protocols: Development of QSAR models using C-QSAR program". Nature Protocols. doi:10.1038/nprot.2007.125. Retrieved 2009-05-11. A regression program that has dual databases of over 21,000 QSAR models 
• "QSAR World". Retrieved 2009-05-11. A comprehensive web resource for QSAR modelers 

ca:Relació estructura-activitat quantitativa zh:定量构效关系