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