Comparative molecular field analysis (CoMFA)

A computer implemented methodology for deriving a three dimensional quantitative structure activity relationship (3-D QSAR) among molecules each of which is associated with a measure of activity and whose basic structures, including conformers, have been modeled in a three dimensional lattice comprising the following steps:

• a. selecting a first conformer of a first molecule;
• b. successively placing a mathematical representation of a probe of user specified size and charge at each lattice intersection;
• c. calculating the stearic and electrostatic energies of interaction between the probe and the conformer at each lattice intersection;
• d. entering the stearic and electrostatic interaction energies calculated in step c in a row of a data table identified with the conformer;
• e. selecting a next conformer of the first molecule and repeating steps b and c;
• f. aligning said next conformer to the first conformer;
• g. entering the interaction energies for said next conformer produced by the alignment as the next row in the date table identified with the conformer;
• h. repeating steps e through g for all conformers of the first molecule to be considered;
• i. weighting and then averaged interaction energies in the a row of a 3-D QSAR data table along with the measured activity value associated with the molecule;
• j. repeating steps a through i for all molecules to be considered;
• k. aligning all molecules to said first molecule in the group being considered;
• l. extracting a first component by applying the partial least squares statistical methodology to said 3-D QSAR data table;
• m. performing a cross validation cycle on said 3-D QSAR data table using solution coefficients resulting from the first component extraction;
• n. extracting the next component by applying the partial least squares statistical methodology to said 3-D QSAR data table;
• o. performing a cross validation cycle on said 3-D QSAR data table using coefficient resulting from said next component extraction;
• p. repeating steps n through o until all desired components have been extracted;
• q. adding the extracted components;
• r. rotating the partial least squares solution consisting of the sum of the extracted components back into the original metric space;
• s. driving the solution coefficients;
• and
• t. displaying the solution.

The computer implemented method of determining the likely biological or chemical activity of a test molecule whose basic structure has been modeled in a three dimensional lattice by comparing its three dimensional shape to the shape of other molecules of known biological or chemical reactivity whose 3D-QSAR has previously been determined by the COMFA methodology, comprising the following steps:

• a. successively placing a mathematical representation of a probe of user specified size and charge at each lattice intersection;
• b. calculating the steric and electrostatic energies of interaction between the probe and the test molecule at each lattice intersection;
• c. aligning the test molecule to the molecules in the molecular series used to derive the 3-D QSAR solution coefficients;
• and
• d. applying the solution coefficients derived in the 3-D QSAR COMFA analysis of the molecular series to the interaction energies of the test molecule to predict the biological or chemical parameter value which the test molecule should possess.

The computer implemented method of generating and visualizing a three dimensional structure activity relationship among a group of molecules having related chemical or biological properties comprising the following steps:

• a. generating for each molecule in the group a row in a data table consisting of molecular parameters uniquely associated with each individual molecule;
• b. performing a correlation of all the rows of data in the data table using the partial least squares statistical methodology including cross validation;
• c. rotating the solution back into the original metric space;
• and
• d. displaying the correlations among the molecules in the group.

A computer implemented method for deriving the correlation between molecular descriptors and measured chemical or biological properties of a group of molecules where there are many more molecular descriptors for each molecule in the group than there are number of molecules in the group comprising the following steps:

• a. generating a data table each row of which contains in its columns the molecular descriptors associated with a single molecule of the group as well as the value of the measured chemical or biological property of that molecule;
• b. extracting a first component by applying the partial least squares statistical methodology to the rows of the data table;
• c. performing a cross validation cycle on the data table using solution coefficients resulting from the first component extraction;
• d. extracting the next component by applying the partial least squares statistical methodology to the rows of the data table;
• e. performing a cross validation cycle on the data table using coefficients resulting from said next component extraction;
• f. repeating the steps d and 3 until all desired components have been extracted;
• g. adding the extracted components;
• h. rotating the partial least squares solution consisting of the sum of the extracted components back into the original metric space and deriving the solution coefficients;
• and
• i. displaying the solution.

A system for deriving a three dimensional quantitative structure activity relationship (3-QSAR) among molecules each of which is associated with a measure of activity and whose basic structures, including conformers, have been modeled in a three dimensional lattice comprising:

• a. means for selecting a first conformer of a first molecule;
• b. means for successively placing a mathematical representation of a probe of user specified size and charge at each lattice intersection;
• c. means for calculating the steric and electrostatic energies of interaction between the probe and the conformer at each lattice intersection;
• d. means for entering the steric and electrostatic interaction energies calculated by means c in a row of a data table identified with the conformer;
• e. means for selecting a next conformer of the first molecule and invoking said means b and said means c;
• f. means for aligning said next conformer to the first conformer;
• g. means for entering the interaction energies for said next conformer produced by the alignment as the next row in the data table identified with the conformer;
• h. means for invoking means e through g for all conformers of the first molecule to be considered;
• i. means for weighting and then averaging the interaction energies across all conformers of the first molecule and placing the averaged interaction energies in the first row of a 3-D QSAR data table along with the biological or chemical value associated with the first molecule;
• j. means for invoking means a through i for all molecules to be considered;
• k. means for aligning all molecules to said first molecule in the group being considered;
• l. means for extracting a first component by applying the partial least squares statistical methodology to said 3-D QSAR data table;
• m. means for performing a cross validation cycle on said 3-D QSAR data table using solution coefficients resulting from the first component extraction;
• n. means for extracting the next component by applying the partial least squares statistical methodology to said 3-D QSAR data table;
• o. means for performing a cross validation cycle on said 3-D QSAR data table using coefficients resulting from said next component extraction;
• p. means for invoking means n through o until all desired components have been extracted;
• q. means for adding the extracted components;
• r. means for rotating the partial least squares solution consisting of the sum of the extracted components back into the original metric space;
• s. means for deriving the solution coefficients;
• and
• t. means for displaying the solution.

The system for determining the likely biological or chemical activity of a test molecule whose basic structure has been modeled in a three dimensional lattice by comparing its three dimensional shape to the shape of other molecules of known biological or chemical reactivity whose 3D-QSAR has previously been determined by the COMFA methodology, comprising:

• a. means for successively placing a mathematical representation of a probe at each lattice intersection;
• b. means for calculating the steric and electrostatic energies of interaction between the mathematical representation of the probe and the test molecule at each lattice intersection;
• c. means for aligning the test molecule to the molecules in the molecular series used to derive the 3-D QSAR solution coefficients;
• and
• d. means for applying the solution coefficients derived in the 3-D QSAR COMFA analysis of the molecular series to the interaction energies of the test molecule to predict the biological or chemical parameter value which the test molecule should possess.

The system of generating and visualizing a three dimensional structure activity relationship among a group of molecules having related chemical or biological properties comprising:

• a. means for generating for each molecule in the group a row in a data table consisting of molecular parameters uniquely associated with each individual molecule;
• b. means for performing a correlation of all the rows of data in the data table using the partial least squares statistical methodology including cross validation;
• c. means for rotating the solution back into the original metric space;
• and
• d. means for displaying the correlations among the molecules in the group.

A system for deriving the correlation between molecular descriptors and measured chemical or biological properties of a group of molecules where there are many more molecular descriptors for each molecule in the group than there are number of molecules in the group comprising:

• a. means for generating a data table, each row of which contains in its columns the molecular descriptors associated with a single molecule of the group as well as the value of the measured chemical or biological property of the molecule;
• b. means for extracting a first component by applying the partial least squares statistical methodology to the rows of the data table;
• c. means for performing a cross validation cycle on the data table using solution coefficients resulting from the first component extraction;
• d. means for extracting the next component by applying the partial least squares statistical methodology to the rows of the data table;
• e. means for performing a cross validation cycle on the data table using coefficients resulting from said next component extraction;
• f. means for invoking means d and e until all desired components have been extracted;
• g. means for adding the extracted components;
• h. means for rotating the partial least squares solution consisting of the sum of the extracted components back into the original metric space and deriving the solution coefficients;
• and
• i. means for displaying the solution.

A system for generating and visualizing a three dimensional quantitative structure activity relationship of a series of molecules comprising:

• a. means for defining molecular shape descriptors for each molecule in said series of molecules wherein each molecule is associated with a unique parameter value;
• b. means for aligning each molecule in said series with the common shape elements of all the molecules in said series;
• c. means for correlating the molecular shape descriptors and unique parameter value of each molecule with all the other molecules in said series;
• and
• d. means for visually displaying using computer graphics the correlation among the molecules in said series.

A computer based method of designing a molecule which will bind to a larger molecule which is known to bind other molecules with measured affinities comprising the following steps:

• a. modeling in a three dimensional lattice the basic structures, including conformers, of molecules known to bind with measured affinities to the larger molecule;
• b. selecting a first conformer of a first molecule;
• c. successively placing a mathematical representation of a probe of user specified size and charge at each lattice intersection;
• d. calculating the steric and electrostatic energies of interaction between the probe and the conformer at each lattice intersection;
• e. entering the steric and electrostatic interaction energies calculated in step d in a row of a data table identified with the conformer;
• f. selecting a next conformer of the first molecule and repeating steps c and d;
• g. aligning said next conformer to the first conformer;
• h. entering the interaction energies for said next conformer produced by the alignment as the next row in the data table identified with the conformer;
• i. repeating steps f through h for all conformers of the first molecule to be considered;
• j. weighting and then averaging the interaction energies across all conformers of the first molecule and placing the averaged interaction energies in the first row of a second data table along with the measured activity value associated with the first molecule;
• k. repeating steps b through j for all molecules to be considered;
• l. aligning all molecules to said first molecule in the group being considered;
• m. extracting a first component by applying the partial least squares statistical methodology to said second data table;
• n. performing a cross validation cycle on said second data table using solution coefficients resulting from the first component extraction;
• o. extracting the next component by applying the partial least squares statistical methodology to said second data table;
• p. performing a cross validation cycle on said second data table using coefficients resulting from said next component extraction;
• q. repeating steps o through p until all desired components have been extracted;
• r. adding the extracted components;
• s. rotating the partial least squares solution consisting of the sum of the extracted components back into the original metric space;
• t. deriving the solution coefficients;
• u. displaying the solution;
• and
• v. synthesizing a molecule with atoms arranged to occupy or not occupy, as is required, the three dimensional spaces/volumes indicated in the display as being critical to binding of the molecule to the larger molecule.