Crystallography Made Crystal Clear:
A Guide for Users of Crystallographic Models  Gale Rhodes, Academic Press, 1993
   In a fit of clear thinking, I wrote this 190-page book as an introduction to crystallography for readers who want to understand how crystallographers obtain molecular models from x-ray diffraction patterns. It should help users of crystallographic models to understand the strengths and weaknesses of models, to read reports of new structures with greater understanding, and to make prudent and thorough use of the information that comes from a crystallographic structure determination. The book ends with chapters on how to read reports of new structures in the literature, and how to study structures using computer graphics.
   Table of Contents, Review Excerpts, and How to get this book .
   Want to know more? Read the Preface:
   Most texts that treat biochemistry or proteins contain a brief section or chapter on protein crystallography. Even the best of such sections are usually mystifying, far too abbreviated to give any real understanding. In a few pages, the writer can accomplish little more than telling you to have faith in the method. At the other extreme are many useful treatises for the would-be, novice, or experienced crystallographer. Such accounts contain all the theoretical and experimental details that practitioners must master, and for this reason, they are quite intimidating to the noncrystallographer. This book lies in the vast and heretofore empty region between brief textbook sections on crystallography and complete treatments of the method aimed at the professional crystallographer. I hope there is just enough here to help the noncrystallographer understand where crystallographic models come from, how to judge their quality, and how to glean additional information that is not depicted in the model, but is available from the crystallographic study that produced the model.
    This book should be useful to protein researchers in all areas; to students of biochemistry in general and of macromolecules in particular; to teachers as an auxiliary text for courses in biochemistry, biophysical methods, and macromolecules; and to anyone who wants an intellectually satisfying understanding of how crystallographers obtain models of protein structure. This understanding is essential for intelligent use of crystallographic models, whether that use is studying molecular action and interaction, trying to unlock the secrets of protein folding, exploring the possibilities of engineering new protein functions, or interpreting the results of chemical, kinetic, thermodynamic, or spectroscopic experiments on proteins. Indeed, if you use protein models without knowing how they were obtained, you may be treading upon hazardous ground. For instance, you may fail to use available information that would give you greater insight into the molecule and its action. Or worse, you may devise and publish a detailed molecular explanation based upon a structural feature that is quite uncertain. Fuller understanding of the strengths and limitations of crystallographic models will enable you to use them wisely and effectively.
   If you are part of my intended audience, I do not believe you need to know, or are likely to care about, all the gory details of crystallographic methods and all the esoterica of crystallographic theory. I present just enough about methods to give you a feeling for the experiments that produce crystallographic data. I present somewhat more theory, because it underpins an understanding of the nature of a crystallographic model. I want to help you follow a logical thread that begins with diffraction data and ends with a colorful picture of a protein model on the screen of a graphics computer. The novice crystallographer, or the student pondering a career in crystallography, may find this book a good place to start, a means of seeing if the subject remains interesting under closer scrutiny. But these readers will need to consult more extensive works for fine details of theory and method. I hope that reading this book makes those texts more accessible.
   I wish I could teach you about crystallography without using mathematics, simply because so many readers are apt to throw in the towel upon turning the page and finding themselves confronted with equations. Alas (or hurrah, depending on your mathematical bent), the real beauty of crystallography lies in the mathematical and geometric relationships between diffraction data and molecular images. I attempt to resolve this dilemma by presenting no more math than is essential, and taking the time to explain in words what the equations imply. Where I can, I emphasize geometric explanations over equations.
   If you turn casually to the middle this book, you will see some forbidding mathematical formulae. Let me assure you that I move to those bushy statements step by step from nearby clearings, making minimum assumptions about your facility and experience with math. For example, when I introduce periodic functions, I tell you how the simplest of such functions (sines and cosines) "work", and then I move slowly from that clear trailhead into the thicker forest of complicated wave equations that describe x-rays and the molecules that diffract them. When I first use complex numbers, I define them and illustrate their simplest uses and representations, sort of like breaking out camping gear in the dry safety of a garage. Then I move out into real weather and set up a working camp, showing how the geometry of complex numbers reveals essential information otherwise hidden in the data. My goal is help you see the relationships implied by the mathematics, not to make you a calculating athlete. My ultimate aim is to prove to you that the structure of molecules really does lie lurking in the crystallographic data -- that in fact, the information in the diffraction pattern implies a unique structure. I hope thereby to remove the mystery about how structures are coaxed from data.
   If, in spite of these efforts, you find yourself flagging in the most technical chapters (4 through 7), please do not quit. I believe you can follow the arguments of these chapters, and thus be ready for the take-home lessons of Chapters 8 and 9, even if the equations do not speak clearly to you. Jacob Bronowski once described the verbal argument in mathematical writing as analogous to melody in music, and thus a source of satisfaction in itself. He likened the equations to musical accompaniment that becomes more satisfying with repeated listening. If you follow and retain the melody of arguments and illustrations in Chapters 4 through 7, then the last chapters and their take-home lessons should be useful to you.
   I aim further to enable you to read primary-journal articles that announce and present new protein structures, including the arcane sections on experimental methods. In most scientific papers, experimental sections are directed primarily toward those who might use the same methods. In crystallographic papers, however, methods sections contain information from which the quality of the model can be roughly judged. This judgment should affect your decision about whether to obtain the model and use it, and whether it is good enough to serve as a guide in drawing the kinds of conclusions you hope to draw. In Chapter 8, to review many concepts, as well as to exercise your new skills, I look at and interpret experimental details in literature reports of a recent structure determination.
   Finally, I hope you read this book for pleasure -- the sheer pleasure of turning the formerly incomprehensible into the familiar. In a sense, I am attempting to share with you my own pleasure of the past ten years, after my mid-career decision to set aside other interests and finally see how crystallographers produce the molecular models that have been the greatest delight of my teaching. Among those I should thank for opening their labs and giving their time to an old dog trying to learn new tricks are Professors Leonard J. Banaszak, Jens Birktoft, Jeffrey Bolin, John Johnson, and Michael Rossmann.
Gale Rhodes  Portland, Maine  August, 1992
Quotes from reviewers: ***
Professor Shaun D. Black, University of Texas Health Center in American Journal of Physiology, vol 267, 1994:
   This terse, well-written book lives up to its title in great measure, and, in my opinion is now the best reference for noncrystallographers who want to know more about X-ray diffraction and the data that result from it. The author uses a clear and logical style to describe nearly every aspect of the X-ray diffraction experiment, and enough mathematics is given to afford readers a relatively sophisticated understanding of the subject.
*** Jonathan Cooper, Department of Crystallography, Birkbeck College, London in Trends in Biotechnology, vol 12, April 1994:
   This excellent book is primarily aimed as researchers involved in molecular modelling who wish to improve their understanding of how crystal structures of proteins are obtained and how to assess their accuracy.
   Although this book is intended for non-specialists who need to learn something about crystallography and, as such, fills a gap in the current literature, it has much material of value to specialized research students. Had it appeared ten years ago, learning the tools of this trade would have beeen easier.
*** M. Rossi, Vassar College in Choice, November 1993:
   Rhodes's book will find a much broader audience, however, as it is a well-written and up-to-date introduction.
   Crystallography is not an easy subject to teach or to learn, and Rhodes provides a comprehensive, yet less intimidating, treatment of the theoretical background, which should be understandable to a novice. The author assumes little mathematical knowledge and explains the physical significance of all equations. A most helpful feature is the use of a published structure report as an example of understanding and interpreting a macromolecular crystal structure determination, frequently the most difficult part for noncrystallographers. Highly recommended as a supplement to standard biochemistry works and as an introduction to the field for students learning crystallography.
*** Norma Allewell, Department of Biochemistry, University of Minnesota in Biophysical Journal, vol 65, November 1993:
   Crystallography Made Crystal Clear bridges the gap between brief chapters and textbooks in biochemistry and proteins and complete treatments aimed at the professional crystallographer.
   Much of the book reads like a transcript of discussions between a wise and tolerant old crystallographer walking a novice through his/her first structure determination. All of the problems one encounters, from recognizing twinned crystals and visualizing the geometry of a precession camera, through identifying heavy atom binding sites from Patterson maps, to fitting electron density maps and refining the structure are dealt with patiently and creatively. Although all of the standard derivations are here, the text has a light touch which both novices and noncrystallographers will appreciate.
   The thirteen color plates are excellent.
   Given the brevity of the text, it is remarkably complete.
   This book will be useful in many contexts - in elementary courses in crystallography, in biochemistry courses as an auxiliary text, in crystallographic laboratories as a handbook for novices, and in molecular biology laboratories as an introduction to the Protein Data Base and molecular graphics. It can be perused in an afternoon which will be well spent.
*** Professor D.A.Waller in Biochemical Education, vol 22, January 1994:
   ... I would recommend this book to anyone who is interested in macromolecules and how their structures are solved. The material is well presented and easy to read and would provide a good stearting point for an undergraduate considering going into the field. It also provides sufficient information to be used as a text in a course on biophysical techniques.
*** Professor Albert C. Claus in Applied Optics, vol 13, May 1995
   Anyone interested in how protein structures are determined should find reading it an enjoyable and satisfying experience.
   Crystallography Made Crystal Clear is clearly written, accurate, and easy to read. The author chose one of the most interesting topics in x-ray crystallography to examine, namely, the structure determination of proteins. Consequently the book can be recommended not only to the biochemists and biologists for whom it was written, but to all those who are curious.
HOME