Historical Development of QSAR

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Chapter: Medicinal Chemistry : Structure-Activity Relationship and Quantitative Structure Activity Relationship

In early 1868, Crum-Brown and Fraser published an equation, which is considered to be the first general equation of QSAR.


In early 1868, Crum-Brown and Fraser published an equation, which is considered to be the first general equation of QSAR. Richet discovered that the toxicity of organic compounds (aldehyde, alcohol, ethers, ketone, etc.) inversely follow their water solubility. Later, Meyer and Overton have worked independently and observed the linear relationships between lipophilicity (oil-water partition coefficients) and narcotic activities. Further, Fuhner has given the first evidence of additivity of groups contributing to biological activity values in a homologous series of compounds for their narcotic activity. Ferguson postulated that the thermodynamic principles could be related to drug activities.

After 1950, QSAR methodology has progressed remarkably. During this year, Bruice, Kharasch, and Winzler reported group contributions to biological activity values in a series of thyroid hormone analogues; this may be considered as a first Free-Wilson-type analysis. Zahradnik has tried to apply the concept of the Hammett equation. However, significant progress has occurred in the field of QSAR in 1960s through the research work of Bocek and Kopecky, Hansch, Free-Wilson and Fujita. Among these, only Bocek-Kopecky method has become unsuccessful due to the involvement of a number of parameters. Among the different methods, Hansch, Free-Wilson, and modified Free-Wilson approaches are the widely practiced ones for modelling the biological response. Also, QSAR is one of the approaches attracting increasing levels of interest in the pharmaceutical industry as a productive and cost-effective technology in the search for novel lead compounds.

Hansch Analysis

QSAR based on Hammett’s relationship utilize electronic properties as the descriptors of structures. Difficulties were encountered when investigators attempted to apply Hammett-type relationships to biological systems, indicating that other structural descriptors were necessary. In 1962, Hansch et al entered the scenario with the numerical information on lipophilicity, electronic, and steric effect on the model development. The general form of Hansch equation is as follows:

Log BA = a log p + b σ + c Es + constant (linear)

Log BA = a log p + b (log p)2 + c σ + d Es + constant (nonlinear)

Hansch model correlates biological activity with physicochemical properties. The coefficients (a, b, c, d, and constant) are determined by multiple regression analysis.

Free-Wilson Analysis

It is also known as the additivity model or de novo approach. This method is based on the assumption that the introduction of a particular substituent at a particular molecular position always contributes in the same way to the biological potency of the whole molecule, as expressed by the equation:

Log BA = contribution of unsubstituted parent compound + contribution of corresponding substituents 

Log BA = μ + Σi ai aj

where ai = number of positions at which substitution occurs

aj = number of substituents at that position

μ = overall average.

The equation is solved by MLR using the presence (1) or absence (0) of the different substituents as independent parameters, while the measured activity serves as dependent variable.

Mixed Approach

Kubinyi has presented the combination of Hansch and Free-Wilson approach as mixed approach.

Log BA = k1 π + k2 σ + k3 Es + k (Hansch analysis)

Log BA = μ + Σ ai aj (Free-Wilson approach) 

So, the mixed approach can be written as

Log BA =Σ ai aj + Σ ki ϕj + k

Where Σ (ai aj ) is the Free-Wilson part for the substituents

ϕj = σ, π and Es contribution of the parent skeleton.

Among the above-mentioned approaches, Hansch approach became the most popular approach in QSAR. The high-dimensional QSAR analyses (3D, 4D, and 5D) are developed to avoid pitfalls of classical method and to create the hypothetical drug receptor model.


  • It gives quantifying the relationship between structure and activity with their physiochemical property basis.

  • Possible to make predictions of designed compounds before the chemical synthesis of novel analogues.

  • It may help to understand the interactions between functional group of designed molecules and their activity of target enzyme or protein.


  • Due to biological data experimental error it may give false correlations.

  • If training set of molecule is less, the data may not reflect the complete property and it cannot be used to predict the most active compounds.

  • In some 3D QSAR study ligands binding receptor or protein may not be available in that case the

common approach result may not represent the reality.

  • Cannot expect that the QSAR works all the time give successful applications.

A model perfectly predicts that the training data may not be good or even useless for prediction. The problem of QSAR is to find coefficients C0, C1 , ... , Cn such that

Biological activity = C0 + (C1 × P1) + ... + (Cn × Pn

and the prediction error is minimized for a list of given compounds.

Partial least squares (PLSs) is a technique used for computation of the coefficients of structural descriptors.

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