Principles of Protein X-Ray Crystallography

Transcription

1 Principles of Protein X-Ray Crystallography

2 Jan Drenth Principles of Protein X-Ray Crystallography Third Edition With Major Contribution from Jeroen Mesters University of Lübeck, Germany

3 Jan Drenth Laboratory of Biophysical Chemistry University of Groningen Nyenborgh AG Groningen The Netherlands j.drenth@rug.nl Cover illustration: Courtesy of Adrian R. Ferré-D Amaré and Stephen K. Burley, The Rockefeller University. The four- -helix bundle moiety of transcription factor Max. Reproduced with permission from Nature 363:38 45 (1993). Library of Congress Control Number: ISBN-10: e-isbn-10: ISBN-13: e-isbn-13: Printed on acid-free paper. C 2007, 1999, 1994 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights springer.com

4 Preface to the Third Edition In the 7 years since the publication of the previous edition, protein X-ray crystallography has made rapid progress. This was, to a large extent, triggered by the sudden growth of interest in structural genomics. Impressive technological advances facilitated this development. It required updating Chapter 2 on Sources and Detectors. It is no longer an exception to collect a full dataset in a few minutes and to solve the structure in hours. However, one bottleneck remains and that is the growth of quality crystals. Although accelerated by robotic systems, it is still a trial-anderror process. For the benefit of the novice in crystallization, a chapter on Practical Protein Crystallization written by Dr. Jeroen R. Mesters has been added. Another addition is a section on single-wavelength anomalous diffraction. This technique has gained much popularity in recent years, especially in the highthroughput field. Also SHELXD, a dual-space direct method for substructure determination, equally useful as SnB, has now been added to Chapter 11 on Direct Methods. We are indebted to many colleagues who in some way or another assisted us in the preparation of this edition. Among them are Thomas Barends, Zbigniew Dauter, Rolf Hilgenfeld, Ankie Terwisscha van Scheltinga, Bram Schierbeek George Sheldrick, and Simon Tulloch. Jan Drenth is especially grateful to Bauke Dijkstra for the generous hospitality in his laboratory. Jeroen Mesters Jan Drenth v

5 Preface to the Second Edition Since the publication of the previous edition in 1994, X-ray crystallography of proteins has advanced by improvements in existing techniques and by addition of new techniques. Examples are, for instance, MAD, which has developed into an important method for phase determination. Least squares as a technique for refinement is gradually being replaced by the formalism of maximum likelihood. With several new sections, the book has been updated, and I hope it will be as well received as the previous edition. In the preparation of this second edition, I was greatly assisted by experts who commented on relevant subjects. I acknowledge the contributions of Jan Pieter Abrahams, Eleanor Dodson, Elspeth Garman, Eric de La Fortelle, Keith Moffat, Garib Murshudov, Jorge Navaza, Randy Read, Willem Schaafsma, George Sheldrick, Johan Turkenburg, Gert Vriend, Charles Weeks, and my colleagues in the Groningen Laboratory. I am especially grateful to Bauke Dijkstra for the generous hospitality in his laboratory. Jan Drenth vi

6 Preface to the First Edition Macromolecules are the principal nonaqueous components of living cells. Among the macromolecules (proteins, nucleic acids, and carbohydrates), proteins are the largest group. Enzymes are the most diverse class of proteins because nearly every chemical reaction in a cell requires a specific enzyme. To understand cellular processes, knowledge of the three-dimensional structure of enzymes and other macromolecules is vital. Two techniques are widely used for the structural determination of macromolecules at atomic resolution: X-ray diffraction of crystals and nuclear magnetic resonance (NMR). While NMR does not require crystals and provides more detailed information on the dynamics of the molecule in question, it can be used only for biopolymers with a molecular weight of less than 30,000. X-ray crystallography can be applied to compounds with molecular weight up to at least For many proteins, the difference is decisive in favor of X-ray diffraction. The pioneering work by Perutz and Kendrew on the structure of hemoglobin and myoglobin in the 1950s led to a slow but steady increase in the number of proteins whose structure was determined using X-ray diffraction. The introduction of sophisticated computer hardware and software dramatically reduced the time required to determine a structure while increasing the accuracy of the results. In recent years, recombinant DNA technology has further stimulated interest in protein structure determination. A protein that was difficult to isolate in sufficient quantities from its natural source can often be produced in arbitrarily large amounts using expression of its cloned gene in a microorganism. Also, a protein modified by site-directed mutagenesis of its gene can be created for scientific investigation and industrial application. Here, X-ray diffraction plays a crucial role in guiding the molecular biologist to the best amino acid positions for modification. Moreover, it is often important to learn what effect a change in a protein s sequence will have on its three-dimensional structure. Chemical and pharmaceutical companies have vii

7 viii Preface to the First Edition become very active in the field of protein structure determination because of their interest in protein and drug design. This book presents the principles of the X-ray diffraction method. Although I will discuss protein X-ray crystallography exclusively, the same techniques can in principle be applied to other types of macro-molecules and macromolecular complexes. The book is intended to serve both as a textbook for the student learning crystallography, and as a reference for the practicing scientist. It presupposes a familiarity with mathematics at the level of upper level undergraduates in chemistry and biology, and is designed for the researcher in cell and molecular biology, biochemistry, or biophysics who has a need to understand the basis for crystallographic determination of a protein structure. I would like to thank the many colleagues who have read the manuscript and have given valuable comments, especially Aafje Vos, Shekhar and Sharmila Mande, Boris Strokopytov, and Risto Lapatto. Jan Drenth

8 Contents Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vi vii Chapter 1 Crystallizing a Protein Introduction Principles of Protein Crystallization Crystallization Techniques Crystallization of Lysozyme A Preliminary Note on Crystals Preparation for an X-ray Diffraction Experiment Cryocooling Notes 17 Summary 20 Chapter 2 X-ray Sources and Detectors Introduction X-ray Sources Monochromators Introduction to Cameras and Detectors Detectors The Rotation (Oscillation) Instrument 38 Summary 43 x

9 Contents xi Chapter 3 Crystals Introduction Symmetry Possible Symmetry for Protein Crystals Coordinate Triplets: General and Special Positions Asymmetric Unit Point Groups Crystal Systems Radiation Damage Characterization of the Crystals 61 Summary 63 Chapter 4 Theory of X-ray Diffraction by a Crystal Introduction Waves and Their Addition A System of Two Electrons Scattering by an Atom Scattering by a Unit Cell Scattering by a Crystal Diffraction Conditions Reciprocal Lattice and Ewald Construction The Temperature Factor Calculation of the Electron Density (x yz) Comparison of F(hkl) and F( h k l) Symmetry in the Diffraction Pattern Integral Reflection Conditions for Centered Lattices Intensity Diffracted by a Crystal Scattering by a Plane of Atoms Choice of Wavelength, Size of Unit Cell, and Correction of the Diffracted Intensity 105 Summary 107 Chapter 5 Average Reflection Intensity and Distribution of Structure Factor Data Introduction Average Intensity; Wilson Plots The Distribution of Structure Factors F and Structure Factor Amplitudes F Crystal Twinning 116 Summary 118 Chapter 6 Special Forms of the Structure Factor 119

10 xii Contents 6.1 Introduction The Unitary Structure Factor The Normalized Structure Factor 120 Summary 122 Chapter 7 The Solution of the Phase Problem by the Isomorphous Replacement Method Introduction The Patterson Function The Isomorphous Replacement Method Effect of Heavy Atoms on X-ray Intensities Determination of the Heavy Atom Parameters from Centrosymmetric Projections Parameters of Heavy Atoms Derived from Acentric Reflections The Difference Fourier Summation Anomalous Scattering The Anomalous Patterson Summation One Common Origin for All Derivatives Refinement of the Heavy Atom Parameters Using Preliminary Protein Phase Angles Protein Phase Angles The Remaining Error in the Best Fourier Map The Single Isomorphous Replacement Method 170 Summary 171 Chapter 8 Phase Improvement Introduction The OMIT Map With and Without Sim Weighting Solvent Flattening Noncrystallographic Symmetry and Molecular Averaging Histogram Matching warp: Weighted Averaging of Multiple-Refined Dummy Atomic Models Further Considerations Concerning Density Modification 192 Summary 193 Chapter 9 Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration Introduction Protein Phase Angle Determination with Anomalous Scattering Improvement of Protein Phase Angles with Anomalous Scattering The Determination of the Absolute Configuration Multiple- and Single-Wavelength Anomalous Diffraction (MAD and SAD) 199 Summary 209

11 Contents xiii Chapter 10 Molecular Replacement Introduction The Rotation Function The Translation Function 217 Summary 230 Chapter 11 Direct Methods Introduction Shake-and-Bake SHELXD The Principle of Maximum Entropy 238 Summary 240 Chapter 12 Laue Diffraction Introduction The Accessible Region of Reciprocal Space The Multiple Problem Unscrambling of Multiple Intensities The Spatial Overlap Problem Wavelength Normalization 245 Summary 246 Chapter 13 Refinement of the Model Structure Introduction The Mathematics of Refinement The Principle of the Fast Fourier Transform Method Specific Refinement Methods 264 Summary 278 Chapter 14 The Combination of Phase Information Introduction Phase Information from Isomorphous Replacement Phase Information from Anomalous Scattering Phase Information from Partial Structure Data, Solvent Flattening, and Molecular Averaging Phase Information from SAD 284 Summary 284 Chapter 15 Checking for Gross Errors and Estimating the Accuracy of the Structural Model Introduction 285

12 xiv Contents 15.2 R-Factors The Ramachandran Plot Stereochemistry Check The 3D 1D Profile Method Quantitative Estimation of the Coordinate Error in the Final Model 292 Summary 296 Chapter 16 Practical Protein Crystallization Introduction Gene Cloning and Expression Protein Purification Protein Crystallization 302 Summary 303 Appendix 1 A Compilation of Equations for Calculating Electron Density Maps 305 Appendix 2 A Compilation of Reliability Indexes 308 Appendix 3 The Variation in the Intensity of X-ray Radiation 314 References 316 Index 326