Method for ab initio determination of macromolecular crystallographic phases at moderate resolution by a symmetry-enforced orthogonal multicenter spherical harmonic-spherical bessel expansion
First Claim
1. A method for determining the three-dimensional structure of a molecule of interest, which comprises (a) obtaining x-ray diffraction data for crystals of said molecule of interest;
- (b) selecting as a basis set an orthogonal set of at least one spherical harmonic spherical Bessel functions to represent the three dimensional electron density in the crystal, such that the number of degrees of freedom in the modeled electron density is reduced relative to the number of measured data;
(c) determining the maximum minimal resolution of said spherical harmonic spherical Bessel model to be used to determine the three-dimensional structure of said molecule of interest;
(d) determining a radius and position for a spherical asymmetric unit in a model crystal lattice as derived from said diffraction data for crystals;
(e) determining a computationally efficient grouping of x-ray diffraction intensities;
(f) modifying, each said at least one spherical harmonic spherical Bessel basis function within the selected basis set such that it represents an individual basis function centered at a specific position and becomes a Fourier representation of a positionally translated basis function;
(g) calculating said at least one Fourier representation of the full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function for each basis function in the basis set chosen in (b);
(h) determining at least one complex-valued coefficient of said spherical harmonic spherical Bessel series by comparing said full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function determined in (g) with said experimental x-ray diffraction data;
(i) using said at least one complex-valued coefficient of each spherical harmonic spherical Bessel function in the basis set for said spherical harmonic spherical Bessel series to iteratively update a phased Fourier representation of the 3-dimensional electron density of the crystal; and
(j) calculating Fourier summations based on a combination of said phased Fourier representation and the experimental diffraction intensities to obtain an interpretable 3-dimensional representation of the contents of the unit cell.
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Abstract
A computational method for the discovery and design of therapeutic compounds is provided. The methods used rely on an accurate inter-conversion of three-dimensional molecular spatial information between two alternative orthogonal representations. These methods enhance the accuracy for determining ab initio phases of macromolecular crystallographic structures at any desired experimental resolution limit. The computational technique employed utilizes a software program and associated algorithms. This method is an improvement over the current methods of drug discovery which often employs a random search through a large library of synthesized chemical compounds or protein molecules for bio-activity related to a specific therapeutic use. The development of computational methods for the prediction of specific molecular activity suggests a method for describing the contents of non-centro-symmetric sparsely packed crystals and the information provided therefrom will facilitate the design of novel chemotherapeutics or other chemically useful compounds.
21 Citations
69 Claims
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1. A method for determining the three-dimensional structure of a molecule of interest, which comprises
(a) obtaining x-ray diffraction data for crystals of said molecule of interest; -
(b) selecting as a basis set an orthogonal set of at least one spherical harmonic spherical Bessel functions to represent the three dimensional electron density in the crystal, such that the number of degrees of freedom in the modeled electron density is reduced relative to the number of measured data;
(c) determining the maximum minimal resolution of said spherical harmonic spherical Bessel model to be used to determine the three-dimensional structure of said molecule of interest;
(d) determining a radius and position for a spherical asymmetric unit in a model crystal lattice as derived from said diffraction data for crystals;
(e) determining a computationally efficient grouping of x-ray diffraction intensities;
(f) modifying, each said at least one spherical harmonic spherical Bessel basis function within the selected basis set such that it represents an individual basis function centered at a specific position and becomes a Fourier representation of a positionally translated basis function;
(g) calculating said at least one Fourier representation of the full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function for each basis function in the basis set chosen in (b);
(h) determining at least one complex-valued coefficient of said spherical harmonic spherical Bessel series by comparing said full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function determined in (g) with said experimental x-ray diffraction data;
(i) using said at least one complex-valued coefficient of each spherical harmonic spherical Bessel function in the basis set for said spherical harmonic spherical Bessel series to iteratively update a phased Fourier representation of the 3-dimensional electron density of the crystal; and
(j) calculating Fourier summations based on a combination of said phased Fourier representation and the experimental diffraction intensities to obtain an interpretable 3-dimensional representation of the contents of the unit cell. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 56, 63, 64, 65, 66, 67, 68, 69)
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15. The method of claim 15, wherein said computer is coupled to a display device and there exists a means for presenting the chemical or molecular structural characteristics of said at least one molecule of interest on said display device.
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48. A method for determining the three-dimensional structure of a molecule of interest, which comprises
(a) obtaining x-ray diffraction data for crystals of said molecule of interest; -
(b) choosing, as the basis set, an orthogonal set of at least one, but more often several spherical harmonic spherical Bessel functions to represent the 3-dimensional electron density in the crystal, such that the number of degrees of freedom in the modeled electron density is reduced relative to the number of measured data;
(c) determining the maximum minimal resolution of said spherical harmonic spherical Bessel model to be used to determine the three-dimensional structure of said molecule of interest;
(d) determining a radius and position for a spherical asymmetric unit in a model crystal lattice as derived from said diffraction data for crystals;
(e) determining a computationally efficient grouping of x-ray diffraction intensities;
(f) modifying, in turn, each said spherical harmonic spherical Bessel basis function within the selected basis set such that it represents an individual basis function centered at a specific position and becomes a Fourier representation of a positionally translated basis function;
(g) calculating said at least one Fourier representation of the full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function for each basis function in the basis set chosen in (b);
(h) determining the complex-valued coefficients of said spherical harmonic spherical Bessel series by comparing said full-unit cell, symmetry-expanded spherical harmonic spherical Bessel basis function determined in (g) with said experimental x-ray diffraction data;
(i) using said determined coefficients of each spherical harmonic spherical Bessel function in the basis set for said spherical harmonic spherical Bessel series to update iteratively a phased Fourier representation of the 3-dimensional electron density of the crystal; and
(j) calculating Fourier summations based on a combination of said phased Fourier representation and the experimental diffraction intensities to obtain an interpretable 3-dimensional representation of the contents of the unit cell. wherein the chemical characteristics of said molecule of interest are in the form of a three dimensional representation, said three dimensional representation allowing the identification of the molecular features of said quantum object such that said representation could be used to alter to the chemical characteristics of said at least one molecule of interest. - View Dependent Claims (49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62)
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