Method and apparatus for analysis of molecular combination based on computations of shape complementarity using basis expansions

A computer readable storage medium storing executable instructions for directing one or more processors to determine whether a first molecular subset is a lead candidate for a target biomolecule, wherein the target biomolecule is represented as a second molecular subset, the instructions comprising:

• providing a basis expansion of volume functions of the molecular subsets by:
• defining a molecular surface for each molecular subset based on locations of a plurality of surface atoms of the corresponding molecular subset;
• generating separately first and second internal volume functions as representations of subsets of corresponding volumes enclosed by the first and second molecular surfaces;
• generating separately first and second external volume functions as representations of subsets of corresponding volumes external to the first and second molecular surfaces;
• representing each of the internal and external volume functions by a respective reference set of expansion coefficients of a basis expansion, where the first reference set is for the first internal and external volume functions and the second reference set is for the second internal and external volume functions;
• defining coordinate based representations for each molecular subset using separate corresponding first and second coordinate systems;
• placing the coordinate based representations of the first and second molecular subsets in a joint coordinate system with separate frames for each molecular subset centered at respective molecular centers of each molecular subset, with an intermolecular axis defined there between;
• defining rigid body transformations and sampling schemes by:
• providing a translation operator associated with an axial sampling scheme comprising a plurality of axial sample points distributed along the intermolecular axis, reflecting discretized relative translation of the first molecular subset with respect to the second molecular subset in the joint coordinate system;
• providing a first rotation operator associated with a first spherical sampling scheme comprising a plurality of spherical sample points distributed on the surface of a sphere centered on the first molecular subset;
• providing a second rotation operator associated with a second spherical sampling scheme comprising a plurality of spherical sample points distributed on the surface of a sphere centered on the second molecular subset;
• providing a third rotation operator associated with an angular sampling scheme comprising a plurality of angular sample points distributed on a circumference of a circle orthogonal to the intermolecular axis;
• defining a shape complementarity score for a molecular configuration, the shape complementarity score representing an overlap between the internal volume function of the first molecular subset with the external volume function of the second molecular subset and the internal volume function of the second molecular subset with the external volume function of the first molecular subset at a given relative position and orientation of the first and second molecular subsets in the joint coordinate system;
• for every axial sample point from the axial sampling scheme:
• constructing a set of translated expansion coefficients for the first molecular subset, corresponding to a given axial sample point, by applying a corresponding translation operator to the first reference set of expansion coefficients for both the internal and external volume functions for the first molecular subset;
• after storing all the sets of translated expansion coefficients, storing all the sets of translated expansion coefficients for the first molecular subset on a recordable media;
• for each axial sample point from the axial sampling scheme:
• a) retrieving, from the recordable media, the corresponding set of translated expansion coefficients for the chosen axial sample point;
• b) constructing a set of transformed expansion coefficients for the first molecular subset, corresponding to a set of all configurations prescribed by the Cartesian product of the chosen axial sample point and the spherical sample points from the first spherical sampling scheme, by applying the first rotation operator to the set of translated expansions coefficients;
• c) constructing a set of transformed expansion coefficients for the second molecular subset, corresponding to a set of all configurations prescribed by the Cartesian product of the spherical sample points from the second spherical sampling scheme and the angular sample points from the angular sampling scheme, by applying in succession the second and third rotation operators to the second reference set of expansion coefficients for both the internal and external volume functions for the second molecular subset;
• and
• d) computing the defined shape complementarity score in terms of the set of transformed expansion coefficients for the first molecular subset, and the set of transformed expansion coefficients for the second molecular subset corresponding to each of a set of sampled configurations associated with the chosen axial sample point;
• and
• storing the plurality of shape complementarity scores.

A computational modeling system for determining whether a first molecular subset is a lead candidate for a target biomolecule, wherein the target biomolecule is represented as a second molecular subset,

• wherein the molecular subsets are represented with a basis expansion of volume functions provided by:
• defining a molecular surface for each molecular subset based on locations of a plurality of surface atoms of the corresponding molecular subset;
• generating separately first and second internal volume functions as representations of subsets of corresponding volumes enclosed by the first and second molecular surfaces;
• generating separately first and second external volume functions as representations of subsets of corresponding volumes external to the first and second molecular surfaces;
• representing each of the internal and external volume functions by a respective reference set of expansion coefficients of a basis expansion, where the first reference set is for the first internal and external volume functions and the second reference set is for the second internal and external volume functions,
• wherein a coordinate based representations for each molecular subset uses separate corresponding first and second coordinate systems and a joint coordinate system with separate frames for each molecular subset centered at respective molecular centers of each molecular subset, with an intermolecular axis defined there between;
• wherein rigid body transformations and sampling schemes include:
• a translation operator associated with an axial sampling scheme comprising a plurality of axial sample points distributed along the intermolecular axis, reflecting discretized relative translation of the first molecular subset with respect to the second molecular subset in the joint coordinate system;
• a first rotation operator associated with a first spherical sampling scheme comprising a plurality of spherical sample points distributed on the surface of a sphere centered on the first molecular subset;
• a second rotation operator associated with a second spherical sampling scheme comprising a plurality of spherical sample points distributed on the surface of a sphere centered on the second molecular subset;
• and
• a third rotation operator associated with an angular sampling scheme comprising a plurality of angular sample points distributed on a circumference of a circle orthogonal to the intermolecular axis,
• the system comprising:
• a configuration data transformation circuit configured to construct, for every axial sample point from the axial sampling scheme, a set of translated expansion coefficients for the first molecular subset, corresponding to a given axial sample point, by applying a corresponding translation operator to the first reference set of expansion coefficients for both the internal and external volume functions for the first molecular subset, the configuration data transformation circuit including at least one suitably programmed microprocessor, at least one application specific integrated circuit (ASIC), or at least one field programmable gate array (FPGA), or any combination thereof;
• a recordable media that stores all the sets of translated expansion coefficients for the first molecular subset;
• a shape complementarity circuit that includes at least one suitably programmed microprocessor, at least one ASIC, or at least one FPGA, or any combination thereof and that, after all the sets of translated expansion coefficients are stored in the recordable media, is configured to, for each axial sample point from the axial sampling scheme:
• a) retrieve, from the recordable media, the corresponding set of translated expansion coefficients for the chosen axial sample point;
• b) construct a set of transformed expansion coefficients for the first molecular subset, corresponding to a set of all configurations prescribed by the Cartesian product of the chosen axial sample point and the spherical sample points from the first spherical sampling scheme, by applying the first rotation operator to the set of translated expansions coefficients;
• c) construct a set of transformed expansion coefficients for the second molecular subset, corresponding to a set of all configurations prescribed by the Cartesian product of the spherical sample points from the second spherical sampling scheme and the angular sample points from the angular sampling scheme, by applying in succession the second and third rotation operators to the second reference set of expansion coefficients for both the internal and external volume functions for the second molecular subset;
• and
• d) compute the defined shape complementarity score in terms of the set of transformed expansion coefficients for the first molecular subset, and the set of transformed expansion coefficients for the second molecular subset corresponding to each of a set of sampled configurations associated with the chosen axial sample point,
• wherein the shape complementarity score represents an overlap between the internal volume function of the first molecular subset with the external volume function of the second molecular subset and the internal volume function of the second molecular subset with the external volume function of the first molecular subset at a given relative position and orientation of the first and second molecular subsets in the joint coordinate system;
• and
• a combination post-processor circuit that determines whether the first molecular subset is a lead candidate based on the shape complementarity scores.