QSAR

Question 1

Quantitative Structure-Activity Relationship

Answer 1

• What are they
• Molecular Geometry
• 3D structure optimisation
• Molecular descriptors
• The process of QSAR analysis

Question 2

QSAR- the principle

Answer 2

• You have at your disposal a set of existing compounds where the biological activity has already been measured
• How can you use this information to decide which compounds to make and test next
  
  1. draw the structures of the compounds and optimise their 3D geometries
  2. Calculate molecular properties
  3. Use the descriptors together with the biological data to derive equations that predict the biological activity
  4. Calculate the descriptors for new compounds and use the equation to predict their biological activities

Question 3

Important note

Answer 3

• QSAR does not require any knowledge of the receptor, active site or mechanism of action
• Only the structure of a set of compounds of known biological activity are required
• It is necessary, however, that the compounds all act in the same way at the same receptor or active site

Question 4

General procedure

Answer 4

• Select a set of molecules interacting with the same receptor with known activities =>
• Calculate features (e.g. physicochemical properties)
• Divide the set into 2. One for testing and on for training
  
  • Training set: Build a model- find the mathematical relationship between the activities and properties
  • test the model on the test dataset
  • Testing set:

Question 5

Preparation of the structures (structures of known biological activity)

Answer 5

1. Draw the compounds
2. Clean up the structure of performing a molecular mechanics geometry optimisation
   
   • Change the geometry to minimise the energy of the molecule
3. Identify key rotatable bonds and perform a conformation search**
4. Perform a semi-empirical quantum mechanical (calculate energy difference once the confirmation has occurred- if the energy lowers it is more correct) geometry optimisation on the lowest energy conformation identified in step 3

• NB** see molecular mechanisms geometry optimisation

Question 6

Molecular mechanics geometry optimisation

Answer 6

• Considers atoms as balls and bond as springs
• Does not consider the electrons
• Fast
• Low quality but OK for a quick clean up of a drawn structure

Question 7

Semi-Empirical quantam mechanical geometry optimisation

Answer 7

• The valence electrons (outer shell- governs bonding of the molecule) are used to construct molecular orbitals
• The inner electrons are approximated via a parameter set
• Slower than MM (molecular mechanics) but much better quality
• Several hours per molecule

Question 8

Why is conformation important

Answer 8

• At room temperature, the lowest energy conformer prevails
• We want the molecular properties to be calculated from a relevant conformation
  *

Question 9

Which conformation should be used

Answer 9

• All energy minimisation techniques concentrate on searching downhill- they therefore tend to find the nearest local minimum on the energy surface
• If a much deeper (i.e. better) energy minimum is nearby, but separated from the starting point by a high energy barrier, it will not be found
• Energy minimization is therefore not capable of finding the global energy minimum. Therefore we must use conformation searching
• NB- most drugs conformation they have when they are active tend to be the same as those in the global minimum energy conformation

Question 10

Conformation searching

Answer 10

• Each rotatable in turn bond is stepped round in small increments and the energies of the resulting conformations are calculated
• This is used to find the approximate position of the GLOBAL MINIMUM ENERGY POTENTIAL WELL
• After that a high quality energy-minimisation technique can be used to refine the structure down to the global minimum energy conformation (E.g. Semi-empirical quantum mechanical geometry optimisation)

Question 11

Conformation searching- Exhaustive searching of rotatable bonds

Answer 11

• Conformational explosion
• 1 rotatable bond/ 5 steps => 72 conformations
• 2 rotatable bonds/ 5 steps => 5184 conformations (72²)
• 8 rotatable bonds/ 5 steps => 722204136208736 (72⁸)
• Potential energy surface from 2 search labels
• Cannot be done for drugs with many rotatable bond due to the large amount of time it would take to complete

Answer 12

1. Input the 3D structure
2. Align the molecules about their common core (because some properties are vectorised)- define what the core is
3. Add the biological activity
4. Calculate the molecular descriptors
5. Use multiple regression analysis to derive an equation relating the biological activity to the calculated properties

Question 13

Molecular descriptors- examples DONT NEED TO REMEMBER ALL OF THESE

Answer 13

Question 14

Molecular descriptors- examples

Answer 14

1. Consititutional
2. Geometrical
3. Topological
4. Electrostatic
5. Quantum-chemical
6. Miscellaneous
7. Solubility
8. Electronic
9. Lipophilic
10. Steric

Question 15

Molecular descriptor- examples

Answer 15

Question 16

Molecular descriptors-

Answer 16

• Some descriptors can be calculated rapidly e.g. MW, dimensions
• Other descriptors may be time-consuming to calculate such as those derived from Quantum mechanics (Anything that involves electrons)
  
  • HOMO-LUMO energy gap
  • Polarisability
  • Partial atomic charge
• Some descriptors have an obvious experimental counterpart with which the calculation can be compared e.g. partition co-efficient
• Other descriptors refer to properties of the whole molecule; others refer to the properties of individual atoms
• New descriptor - modern software packages allow you to generate hundreds or even thousands descriptor. Not all of them are useful, for examples dragon provides 1664 mol descriptors

Question 17

Molecular descriptors 2D and 3D

Answer 17

• Some descriptors may be calculated from the 2D structure whilst others require the 3D structure
• If a 3D structure is required then which molecular conformation should be adopted => Usually the global minimum energy conformation
• Some descriptors such as lipole, dipole, moments of inertia have components along the orthogonal x,y,z axes (i.e. they are vectors)
• Thus to compare the values from one molecule to another, each molecule in the set must be orientated in the same way

Question 18

Molecular descriptors 2D and 3D- definition

Answer 18

• Mass- the molecular mass is calculated assuming that the various atomic isotopes occur in their common proportions
• Surface area- connolly surface area- probe radius of 1.4Å
• Volume- the volume within the surface area defined by the van der waals radii of the atoms

Question 19

Molecular descriptors 2D and 3D

Moments of inertia and ellipsoid volume

Answer 19

• A measure of the distribution of mass within a molecule
• The moments of inertia and prinicipal axes of inertia for a molecule are calculated using the inertia tensor
• These results are reported in TSAR as moment 1 size, moment 1 length
• The volume defined by these values is calculated and reported as the ellipsoid volume
• You can view the molecule and an ellipsoid of inertia
• The ellipsoid’s prinipal axes are aligned with the aces of the inertia tensor. The length of each axis is inversely proportional to the moment of inertia around that axis
• The resulting ellipsoid is then scaled so that the atom furthest from the centre of gravity of the molecule appears on the ellipsoid surface

Question 20

Molecular Descriptors 2D and 3D

LogP

Answer 20

• Lipophillicity is a measure of the ability of the molecules to move between fat and water
• It is often used to indicate how easily a molecule may be transported across membranes
• Most people use the partition co-efficient for water/octanol (LogP) as an estimate of lipophillicity
• Atomic values or substituent values are available from a databaser of experimentally determined values
• The values for the appropriate atomic or substituent fragments are simply added together to derive the molecular LogP value

Question 21

Molecular Descriptors 2D and 3D

Molar refractivity

Answer 21

• This is compiled by reference to a database of experimentally determined values- substituent contributions and atomic contributions to molecular molar refractivity values
• MR often shows a strong correlation with ligand binding
• Both LogP and MR increase with alkyl chain length, so log P and MR show a strong correlation
• Polar functional groups increase MR, but decrease logP. Perhaps MR is a measure of non-lipophilic interactions, while logP is a measure of lipophilic interactions
• MR has a strong correlation with the molecular polarisability

Question 22

Molecular Descriptors 2D and 3D

Polarizability

Answer 22

• A measure of the ease with which the electron cloud of the molecule can be distorted by an applied electric field
• The attractive part of the van der Waals interaction is a good measure of the polarisability
• Highly polarisable molecules can be expected to have strong attractions with other molecules
• The polarisability of a molecule can also enhance aqueous solubility

Question 23

Molecular Descriptors 2D and 3D

Dipole moment

Answer 23

• Dipole moment calculations use partial charge information
• Total dipole moment for whole molecules and substituents are calculated using the centre of charge as an origin, and are in Debye units

Question 24

Molecular Descriptors 2D and 3D

Lipole

Answer 24

• The lipole of a molecular is a measure of the lipophilic distribution
• It is calculated from the summed atomic logP values, as dipole is calculated from the summed partial charges of a molecule
• The total lipole for whole molecules and substituents is calculated using the centre of logP as an origin

Question 25

Molecular Descriptors 2D and 3D Verloop substituent parameters

Answer 25

* Verloop preposed a set of multi-dimensional steric parameters to help explain the steric influence of substituents in the interaction of organic compounds with macromolecules or drug receptors * Verloop parameters calculation assume that all atoms have Van der Waals radii and use these to define the substituents space requirements * The 5 verloop parameters define a box that can be used to characterize the shape and volume of the substituent

Question 26

Molecular Descriptors 2D and 3D Verloop substituent parameters continued

Answer 26

* L, the length parameter- the maximum length of the substituent along the axis of the bond between the first atom of the substituent and the part molecule * B1, the width parameter- the smallest width of the substituent in any direction perpendicular to L * B2,3,4 are determined by measuring the width of the substituent, as follows * In the direction opposite to the axis defined by B1 * In the 2 direction perpendicular to this axis and the original bond axis * The 5 verloop parameters define a box that can be used to characterize the shape and volume of the substituent

Question 27

Molecular Descriptors 2D and 3D Topological, connectivity, electropographical and shape indices

Answer 27

* Many of the descriptors which can be calculated from the 2D structure rely upon the molecular graph representation bevause of the need for rapid calculations * Several of these descriptors have been developed which characterise some aspect of molecular shape, connectivity or atom distribution as a single number

Question 28

Constructing the QSAR (Relating the biological activity to the calculated properties)

Answer 28

* Use multiple regression (an extension of linear regression) * This calculates an equation describing the relationship between a single dependent y variable and several explanatory x variables * It is very important to choose variables (calculated properties) that are not correlated * Multiple regression is the usual approach but there are others

Question 29

Techniques employed in quantitative structure- property relationship (QSRP) studies

Answer 29

* **Multiple linear regression analysis (MLRA)** * Free-Wilson analysis * Cluster analysis * Pattern recognition * Factor analysis * Discrimination analysis * Principal component analysis (PCA) * Partial least square (PLS) analysis * Comparative molecular Field analysis (CoMFA) * Artificial neural network (ANN) * Evolutionary algorithms, such as genetic function approximation (GFA)

Question 30

Constructing the QSAR Some regressions

Answer 30

* **Simple multiple regression**- all the input x variables (circulated properties) are used in the equation to predict y (the bio-activity) * **Stepwise multiple regression**- a selection algorithm is used to choose a subset of input x variables

Question 31

Constructing the QSAR Multiple regression

Answer 31

* Multiple regression calculates an equation describing the relationship between a single dependent y variable and several explanatory x variables * a₁,a₂ etc and c are constants chosen to give the smallest possible sum of least squares difference between true y values and the y' values predicted using this equation * y= biological activity * x1= calculated molecular properties

Question 32

Constructing the QSAR Is it reliable

Answer 32

* Having derived an equation for predicting y from a series of independent variables, one needs to know how reliable predictions made with this equation are likely to be * The multiple correlation co-efficient r² describes how closely the equation fits the data * If the regression equation dascribes the data perfectly then r² will be 1.0

Question 33

Constructing the QSAR Overfitting

Answer 33

* The major drawback of regression analysis is the danger of overfitting * This is the risk that an apparently good regression equation will be found, based on a chance numerical relationship between the y variable and one or more the x variables, rather than a genuine predictive relationship * The QSAR equation will fit the training data very well but be useless in predicting the activity of a compound not in training set

Question 34

Constructing the QSAR Dangers of overfitting

Answer 34

* When an overfitted model is used predictively, the predicted values for untested compounds will not be an accurate prediction of the true values (when these are eventually determined) * Thus the regression equation has NO predictive power * Use a of cross-validation technique to estimate the true predictive power of energy regression model * The best way to avoid an overfitted regression equation is to use just a few carefully selected (non-correlated) x variables, and use as many data points as possible (at least 5 per term in the equation)

Question 35

Cross validation of results

Answer 35

* Cross validation provides a rigorous internal check on the models derived using regression, discriminant or patial least squares analysis * It is used to give an estimate of the true predictive power of the model i.e. how reliable predicted values for untested compounds are likely to be * **leave out one row-** Each row is left out in turn, so that the value of each row is predicted from all others * **Leave out groups of rows-** Groups of rows are left out, excluding a thrid of the data from each model in a fixed pattern

Question 36

Cross validation of resilts Continued

Answer 36

* By default, TSAR leaves out groups of rows in a fixed pattern, using three cross validation groups of rows * A third of the data is deleted and the values of these rows predicted using the rest of the data * This is repeated for the second and then the third groups * The model is judged based on these predictions

Question 37

Constructing the QSAR r²(CV)

Answer 37

* R²(CV) is derived from cross validation. It is the cross validated equivalent of r² * This is a key measure of the predictive prower of the model * The closer the value is the 1.0 the better the predictive power * For a good model r²(CV) should be only slightly lower than r² * If r²(CV) \<2 then there is probably overfitting