QSAR (A mathematical model for Drug Design)

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The Quantitative Structure Activity Relationship (QSAR) quantifies the relationship between physiochemical properties and biological activities. It is said to be the mathematical expression between the biological activity and the measurable physiological parameters. QSAR modelling helps prioritize a large number of chemicals in terms of their desired biological activities as an in-silico methodology and, as a result, significantly reduces the number of candidate chemicals to be tested with in vivo experiments.

The QSAR aims to identify & quantify the physiochemical properties of the drug and to see whether these properties have any effect on the biological activity.

Various physio-chemical properties being studied are:

• Hydrophobicity of the molecule

• Hydrophobicity of substituents

• Electronic properties of substituents

• Steric properties of substituents

A range of compounds is synthesized in order to vary one physicochemical property and to test if it affects the bioactivity. A graph is then drawn to plot the biological activity on the y axis versus the physicochemical feature on the x axis.

If we draw a line through a set of data points will be scattered on either side of the line. The best line will be the one closest to the data points. To measure how close the data points are , vertical lines are drawn from each point.

Few examples of QSAR software are: coMFA, coMSIA, MSI Catalyst, Serius

ADVANTAGES

• Improving the binding of drugs

• Increasing the selectivity

• Reduce side effects

• Easy synthesisable

VARIOUS PARAMETERS OF QSAR

Various parameters used for QSAR studies are:

• Lipophilic parameters.

• Electronic parameters.

• Steric parameters.

LIPOPHILIC PARAMETERS OF DRUG

Hydrophobic character of a drug is crucial to how easily it crosses the cell membrane and may also important in receptor interactions. Hydrophobicity of a drug is measured experimentally by testing the drugs relative distribution in octanol-water mixture. This relative distribution is known as partition coefficient. 

Partition Coefficient, P = [Conc. Of Drug in octanol] / [Conc.of drug in water]

Activity of drugs is often related to P. 

Biological activity log(1/c) = K1 log P + K2 

The biological activity is expressed as log (1/C), where C is the minimum concentration of the drug required to cause a defined biological response.

And the physiochemical property is expressed as log P

Eg: binding of a drug to serum albumin determined by hydrophobicity

LIPOPHILIC PROPERTIES OF SUBSTITUENTS

Partition coefficient can be calculated by knowing the contribution that various substituents, is known as substituent hydrophobicity constant(π). A measure of a substituent’s hydrophobicity relative to hydrogen. Partition coefficient is measured experimentally for a standard compound such as benzene with or without a substituent (X).The hydrophobicity constant (π x) for substituent X. The equation is 

πx= logPx - logPH

A positive π value shows that the substituent is more hydrophobic than hydrogen A negative value indicates that the substituent is less hydrophobic. The π value is characteristic for substituent.

ELECTRONIC PARAMETERS

The electronic effect of various substituents will clearly have an effect on drug ionisation and polarity. And have an effect on how easily a drug can pass through the cell membrane or how strongly it can interact with a binding site. It is generally measured by dissociation constant. 

Hammet substituent constant(σ) this is a measure of electron withdrawing or electron-donating ability of a substituents on an aromatic ring. σ for aromatic substituents is measured by comparing the dissociation constants of substituted benzoic acids with benzoic acid.

K H = Dissociation constant =   [PhCOO-]/[PhCOOH]

STERIC PARAMETERS

The bulk, size and shape of a drug will influence how easily it can approach and interact with binding site. Like a small substituent can facilitate interaction of the molecule with a receptor freely while a bulky substituents may act like a shield and hinder the ideal interaction between a drug and its binding site. However, in case of some molecule, bulky substituent shows better result. The estimation of lipophilic and electronic parameters are easy but not steric properties.

Thus Taft modified Hammer equation to measure steric parameter, like in case of Taft's constant(Es), which measures the rate of hydrolysis of aliphatic ester under acidic conditions, because here steric properties controls the hydrolysis.

Es = log Kx – log Ko

Where Kx is rate of hydrolysis of substituents

And Ko is rate of hydrolysis of parents ester.

Since Es value of F or H substituents are more that Me (CH3) because they are smaller than methyl, thus hydrolysis is faster.

While Es value of Et (ethyl) or n-Pr (propyl) are less than Me (CH3) because they are larger than methyl, thus takes time in hydrolysis.

VARIOUS STEPS INVOLVED IN QSAR

1. Selection of Lead molecule having certain biological activity

2. Calculation of various physio-chemical parameters

3. Correlation of physio-chemical properties with biological activities by QSAR method

4. Getting equation

5. Designing drug based on equation

6. Predicting the activity of the compound

7. Finally synthesizing the compound

ADVANTAGES OF QSAR

• Quantifying the relationship between drug structure and biological activity provides an understanding of the effect of structure on activity.

• QSAR allows calculation in advance, what the biological activity of the novel drug analogue maybe. Thus cutting down the number of analogs that have to be made by the chemists. Thus it helps the medical chemists in prediction of the result.

• The results can be used to help understand interactions between functional groups in the molecules of greatest activity, with those of their target.

DISADVANTAGES OF QSAR

• QSAR studies are only approximative.

• QSAR may be unuseful when many physiochemical properties are involved since it is not possible to vary one property without affecting the other and the result can cross correlate.

• False correlations may experimental error, arise due to biological data which is subject to considerable.

• If the dataset is not large enough, the data collected may not reflect the complete property. Consequently, many QSAR results cannot be used to confidently predict the most likely compounds of best activity.