High-resolution crystallographic modelling of a macromolecule

A method for modeling an electron density distribution of a macromolecule in an asymmetric unit of a crystal by X-ray crystallography comprising:

• (a) irradiating the crystal lattice with X-rays and recording experimental X-ray diffraction data, said data containing a plurality of reflections;
• (b) determining dimensions of the asymmetric unit of said crystal from said diffraction data;
• (c) obtaining an envelope of the macromolecule within said asymmetric unit and distributing a collection of scattering bodies within said initial envelope, said collection of scattering bodies having various arrangements, each of which has a pattern of Fourier amplitudes;
• (d) condensing said collection of scattering bodies to a condensed arrangement having a storing correlation between the experimental X-ray diffraction data and the pattern of Fourier amplitudes for said collection of scattering bodies;
• (e) determining a phase associated with at least one of the reflections of said X-ray diffraction data;
• (f) calculating an electron density distribution of said macromolecule within said asymmetric unit from the phase determined in procedure e;
• (g) defining a new envelope of said macromolecule within said electron density distribution;
• (h) performing the sequence of procedures c through g successively until a final envelope having a predetermined resolution is obtained, each time said sequence is repeated, determining the phase of at least one new reflection from said diffraction pattern;
• and
• (g) graphically displaying said final envelope defined by the electron density distribution of the macromolecule on a display means.

An apparatus for determining a high-resolution structure of a macromolecular crystal with the aid of a digital computer, said apparatus comprising:

• means for converting a diffraction pattern of the macromolecule crystal into computer usable amplitudes, the diffraction pattern obtained with a diffractometer and having a plurality of reflections;
• means for condensing a plurality of scatterers in an envelope defining the region of the unit cell occupied by said macromolecule in the crystal such that the condensed plurality of scatterers has an associated pattern of Fourier amplitudes having a high correlation with the diffraction pattern of said macromolecular crystal;
• means for extracting the phases of one or more of said reflections from said pattern of Fourier amplitudes;
• means for obtaining an electron density distribution of said macromolecule from said phases of said one or more reflections;
• and
• means for graphically displaying an electron density distribution of the macromolecular crystal constructed from said phases.

A method for constructing an image of a macromolecule crystal with the aid of a digital computer and the crystal's diffraction pattern, said diffraction pattern containing a plurality of reflections, each having an associated resolution, said method comprising the following steps:

• (a) converting the diffraction pattern of the macromolecule crystal into computer usable normalized amplitudes, the pattern being produced with a diffractometer;
• (b) determining from the diffraction pattern dimensions of a unit cell of the crystal;
• (c) providing an envelope defining a region of the unit cell occupied by said macromolecule in the crystal;
• (d) distributing a collection of scattering bodies within said envelope, said collection of scattering bodies having various arrangements, each of which has an associated pattern of Fourier amplitudes;
• (e) condensing said collection of scattering bodies to a condensed arrangement that results in a high correlation between the diffraction pattern and the pattern of Fourier amplitudes for said collection of scattering bodies;
• (f) determining a phase associated with at least one of the reflections of said diffraction pattern from the condensed arrangement of scattering bodies;
• (g) calculating an electron density distribution of said macromolecule within said unit cell from the phase determined in procedure f;
• (h) from said electron density distribution, defining a new envelope defining the region of the unit cell occupied by said macromolecule in the crystal;
• (i) repeating steps (d) through (h), each time with one or more previously un-phased reflections from the diffraction pattern;
• and
• (j) displaying a graphical image of said macromolecule constructed from said electron density distribution obtained after a predetermined number of repetitions of steps (d) through (g).