## Document Type

Dissertation

## Publication Date

9-1968

## Subjects

Crystallography, Macromolecules

## Abstract

New Computer Methods for Protein Crystallography, by Martin Zwick. Submitted to the Department of Biology on 30 August 1968 in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The section, "MYOGLOBIN REFINEMENT," describes the fitting of an idealized polypeptide chain to a set of approximate backbone coordinates for the protein, sperm whale myoglobin. This procedure refines the structure by imposing upon it known bond distances and angles, and simultaneously derives a representation of the polypeptide conformation in terms of the values of the rotation angles about its single bonds. The overall rms and mean deviation between refined and guide points was .39 A and .29 A, respectively; the E, G, and H helical regions were most successfully fitted, with rms deviations of order .12 A. The section entitled "PATTERSON SEARCHES" demonstrates that a partial solution for a protein crystal can be achieved with intensity information alone by making use of "a priori" knowledge of the stereochemistry of large protein substructures, such as alpha helices or heme groups. The orientation of the three largest myoglobin helices, E, G, and H (and with lesser reliability, also those of the A and B helices) can be accurately detected as maxima in a reciprocal space rotation function. The assumption of cylindrical symmetry is used to reduce the domain of the rotation search to two dimensions. With a similar assumption for the heme group, its orientation can also be approximately determined. Focusing attention upon the G helix peak of the rotation function, "spin" searches ascertain in which direction the helix points and determine the orientational angle about the helix axis. Translation searches then quite accurately locate the substructure in the unit cell (to within .25 A), thus solving for the positions of the helix backbone atoms, which constitute only about 8 % of the myoglobin molecule. The final section, "DIRECT METHODS," explains how the Cooley-Tukey fast Fourier Transform algorithm can be used to speed up the calculation of the Tangent Formula or the Sayre Relation, and thus make the use of these equations with protein data computationally practical. Keywords:

Macromolecular crystallography, protein structure, Patterson searching, molecular replacement, density modification, direct methods, rotation function, translation functions, signal detection, fast Fourier Transform, Sayre Relation, Tangent Formula

## Rights

© The Author

## Citation Details

Zwick, Martin, "New Computer Methods for Protein Crystallography" (1968). *Systems Science Faculty Publications and Presentations*. 264.