Method and apparatus for selecting a molecule based on conformational free energy

A method of using a computer processor to analyze electrical signals and data representative of conformations of molecular complexes to select either a first molecule or a second molecule as the molecule with stronger binding affinity to a host molecule, wherein the molecules have predefined connectivities and exist in a predefined environment, comprising:

• (a) generating four sets of data representative of low-energy minimum conformations of:
• (1) the first molecule,
• (2) the first molecular complex comprising the first molecule bound to the host molecule,
• (3) the second molecule, and
• (4) the second molecular complex comprising the second molecule bound to the host molecule,
• wherein each set of data is derived from:
• (i) connectivity of the corresponding molecule or molecular complex,
• (ii) a potential energy function, and
• (iii) a conformational search method;
• (b) determining conformational free energy of each set by calculating a configuration integral in all degrees of freedom based upon a contribution of each conformation of the set of conformations, wherein the configuration integral is calculated by:
• (i) performing importance sampling multidimensional Monte Carlo integration over a multidimensional volume enclosing a current conformation in a conformational space,
• wherein the volume is dependent on harmonic vibrational frequencies of the current conformation and temperature,
• wherein the importance sampling comprises preferentially sampling regions of the volume in conformational space associated with the current conformation which regions have dominant contribution to the conformational free energy of the current conformation, and
• wherein the importance sampling utilizes a physical background consisting essentially of normal modes of vibration and is performed using an atomic coordinate transformation which is based on eigenvectors of a Hessian matrix associated with the current conformation;
• (ii) repeating step (b) (i) for each conformation in each set;
• and
• (iii) summing conformational contributions determined in steps (b) (i-ii) separately for each set so as to determine a total configuration integral to determine a value representative of conformation free energy of the first molecule, the first molecular complex, the second molecule and the second molecular complex;
• (c) calculating the difference between the conformational free energy value for the second molecule and the value for the first molecule and the difference between the value for the second molecular complex and the value of the first molecular complex, and subtracting the difference between the molecules from the difference between the molecular complexes so as to determine a total difference;
• (d) determining the sign of the total difference calculated in step (c) and selecting the first molecule if the difference is negative or selecting the second molecule if the difference is positive so as to select the molecule with stronger binding affinity to the host molecule.

A method of using a computer processor to analyze electrical signals and data representative of conformations of molecular complexes to select either a first molecule or a second molecule as the molecule with stronger binding affinity to a host molecule, wherein the first and second molecules are sterioisomers and exist in a predefined environment, comprising:

• (a) generating two sets of data representative of low-energy minimum conformations of:
• (1) the first molecular complex comprising the first molecule bound to the host molecule, and
• (2) the second molecular complex comprising the second molecule bound to the host molecule,
• wherein each set of data is derived from:
• (i) connectivity of the corresponding molecular complex,
• (ii) a potential energy function, and
• (iii) a conformational search method;
• (b) determining conformational free energy of each set by calculating a configuration integral in all degrees of freedom based upon a contribution of each conformation of the set of conformations, wherein the configuration integral is calculated by:
• (i) performing importance sampling multidimensional Monte Carlo integration over a multidimensional volume enclosing a current conformation in a conformational space,
• wherein the volume is dependent on harmonic vibrational frequencies of the current conformation and temperature,
• wherein the importance sampling comprises preferentially sampling regions of the volume in conformational space associated with the current conformation which regions have dominant contribution to the conformational free energy of the current conformation, and
• wherein the importance sampling utilizes a physical background consisting essentially of normal modes of vibration and the sampling is performed using an atomic coordinate transformation which is based on eigenvectors of a Hessian matrix associated with the current conformation;
• (ii) repeating step (b) (i) for each conformation in each set;
• and
• (iii) summing conformational contributions determined in steps (b) (i-ii) separately for each set so as to determine a total configuration integral to determine a value representative of conformation free energy of the first molecular complex, and the second molecular complex;
• (c) calculating the difference between the value for the second molecular complex and the value of the first molecular complex so as to determine a total difference;
• (d) determining the sign of the total difference calculated in step (c) and selecting the first molecule if the difference is negative or selecting the second molecule if the difference is positive so as to select the molecule with stronger binding affinity to the host molecule.

An apparatus capable of analyzing electrical signals and data representative of a first molecule to determine conformational free energy of the first molecule so as to determine whether a first molecule is more stable than a second molecule, wherein both molecules exist in a predefined environment, comprising:

• (a) means for generating a set of data representative of low-energy minimum conformations of the first molecule derived from connectivity of the first molecule, a potential energy function, and a conformational search method;
• (b) means for determining conformational free energy of the first molecule by calculating a configuration integral in all degrees of freedom based upon a contribution of each conformation of the set of conformations of the first molecule, wherein the configuration integral is calculated by:
• (i) means for performing importance sampling multidimensional Monte Carlo integration over a multidimensional volume enclosing a current conformation of the first molecule in a conformational space,
• wherein the volume is dependent on harmonic vibrational frequencies of the current conformation and temperature,
• wherein the importance sampling comprises preferentially sampling regions of the volume in conformational space associated with the current conformation which regions have dominant contribution to the conformational free energy of the current conformation, and
• wherein the importance sampling utilizes a physical background consisting essentially of normal modes of vibration of the first molecule and the sampling is performed using an atomic coordinate transformation which is based on eigenvectors of a Hessian matrix associated with the current conformation;
• (ii) means for repeating step (i) for each conformation in the set;
• and
• (iii) means for summing conformational contributions determined in steps (i-ii) so as to determine a total configuration integral for the first molecule to determine the conformational free energy of the first molecule;
• (c) means for repeating steps (a)-(b) for the second molecule;
• and
• (d) means for comparing the conformational free energy of the first molecule with the conformational free energy of the second molecule and determining which molecule has lower conformational free energy to determine which molecule is more stable.

An apparatus capable of analyzing electrical signals and data representative of conformations of molecular complexes to select either a first molecule or a second molecule as the molecule with stronger binding affinity to a host molecule, wherein the molecules have predefined connectivities and exist in a predefined environment, comprising:

• (a) means for generating four sets of data representative of low-energy minimum conformations of:
• (1) the first molecule,
• (2) the first molecular complex comprising the first molecule bound to the host molecule,
• (3) the second molecule, and
• (4) the second molecular complex comprising the second molecule bound to the host molecule,
• wherein each set of data is derived from:
• (i) connectivity of the molecule or the molecular complex,
• (ii) a potential energy function, and
• (iii) a conformational search method;
• (b) means for determining conformational free energy of each set by calculating a configuration integral in all degrees of freedom based upon a contribution of each conformation of the set of conformations, wherein the configuration integral is calculated by:
• (i) means for performing importance sampling multidimensional Monte Carlo integration over a multidimensional volume enclosing a current conformation in a conformational space,
• wherein the volume is dependent on harmonic vibrational frequencies of the current conformation and temperature,
• wherein the importance sampling comprises preferentially sampling regions of the volume in conformational space associated with the current conformation which regions have dominant contribution to the conformational free energy of the current conformation, and
• wherein the importance sampling utilizes a physical background consisting essentially of normal modes of vibration and is performed using an atomic coordinate transformation which is based on eigenvectors of a Hessian matrix associated with the current conformation;
• (ii) means for repeating step (b) (i) for each conformation in each set;
• and
• (iii) means for summing conformational contributions determined in steps (b) (i-ii) separately for each set so as to determine a total configuration integral to determine a value representative of conformation free energy of the first molecule, the first molecular complex, the second molecule and the second molecular complex;
• (c) means for calculating the difference between the conformational free energy value for the second molecule and the value for the first molecule and the difference between the value for the second molecular complex and the value of the first molecular complex, and subtracting the difference between the molecules from the difference between the molecular complexes so as to determine a total difference;
• (d) means for determining the sign of the total difference calculated in step (c) and selecting the first molecule if the difference is negative or selecting the second molecule if the difference is positive so as to select the molecule with stronger binding affinity to the host molecule.