Macromolecular Crystallography

Preface & Contents



Table of Contents

1. Introduction to X-ray Crystallography

Atomic detail from diffraction of molecules held in crystals.

2. light vs x-ray "microscopy"

General case of light scattering in the context of atomic dimensions where x-rays are the wavelength needed.

3.1 Light Scattering

General properties of light waves, and scattering from a single small object, e.g., an atom.

3.2 Molecular Scattering

Scattering of light waves from extended objects.

4.1 Bragg Diffraction

Diffraction as scattering from crystals.

4.2 Diffraction Vector to Reciprocal Space

Imagining Crystal Diffraction, Crystal Lattice effects, Ewald construction

4.3 Crystal of Molecules Diffraction

Intensities from the objects that crystallize.

5. Fourier Transforms

The relationship of Real and Reciprocal space.

6. Patterson Function

Basic approach to get a starting model and initial phases.

7. Phasing by Isomorphous Replacement

The original and still powerful method

8. Phasing using Anomalous Dispersion

Historically useful, now a major method

9. Electron Density Maps

The calculated image and constructing a model of the molecule

10. Evaluation of Quality

Validation as a dynamic and essential process


Overview

Lecture notes for the diffraction section of a Physical Biochemistry course; historically BCH/SBB 291, 2012: BCH/SBB 681

Fall 2012 revised and rearranged to put more emphasis on scattering in general and show x-ray diffraction as a special case of light scattering. However, these notes overall are unabashedly about x-ray crystallography of macromolecules.

The course is not intended to teach you to use current machinery and computer programs to solve crystal structures; it will, however, develop the concepts and equations you would need to build your own diffractometers and write your own computer programs to solve crystal structures. The approach is geometrical rather than algebraic, but the equations derived are complete (but not necessarily in the form for an efficient computer program).

For those who will be producers of crystallographically determined structures, the complete do-it-yourself approach is not, in general, advised, but in the rapidly developing world of crystallographic machinery and programs, it is valuable to understand the fundamental strengths and limitations of the experiments.

Everyone these days is a consumer of crystallographically determined structures. Evaluating the reliability of structural details is critical to using them. Knowing what goes into producing structural models gives an appreciation of the strengths and limitations of those models.

   These notes have accreted over the years, in fits and starts as Jane and I worked over how to present the concepts of crystallography.
   They started as just annotated drawings, and were handed out so that I didn’t have to make my chalk-board drawings quite as accurate, nor did students have to spend all the lecture time trying to reproduce the board drawings. So these notes are indeed quite sketchy and lack much of the words of my actual lectures which I rearrange and make up as I talk each time.
   When these notes were started and for many years the macromolecules that were crystallized were proteins. Thus much of the terminology (like that in many crystallography textbooks) is Protein centric, e.g. FP for native structure factor and FPH for native-with-Heavy-atom derivative.
   Bryan Arendall has imported and improved the original hand drawings into electronic form (Adobe Indesign), as well as added commentary and reorganization to the notes. If ever these notes become a textbook, then it would be “Arendall and Richardson”. Until that time, I own all the mistakes. -Dave Richardson


Resources

Web Site: http://kinemage.biochem.duke.edu/teaching/bch681

Other Web sites:
http://molprobity.biochem.duke.edu/ : protein & RNA analysis, evaluation,...
http://www.rcsb.org/ : Protein Data Bank, get coordinates here
http://eds.bmc.uu.se/eds/ : Electron Density Server, get maps here
http://xray.bmc.uu.se/gerard/embo2001/modval/index.html : model validation tutorial
http://www.ysbl.york.ac.uk/~cowtan/ : Insightful crystallography exercises

Suggested Textbooks for reference or different presentation:

Alexander McPherson “Introduction to Macromolecular Crystallography”, 2nd ed., somewhat different organization than these notes, more information about crystallization and the initial stages of structure determination. This is the nearest thing to a textbook I’ve found to accompany my notes and lectures.

Stout and Jensen, 2nd ed. “X-ray Structure Determination” A very good general crystallography text.

Gale Rhodes 3rd ed. “Crystallography Made Crystal Clear” Informal, less detail but more context.

David Blow “Outline of Crystallography for Biologists” More detail than Rhodes, less math than Drenth, still not quite enough detail in deriving equations and developing the constructions needed by a practicing crystallographer. However more complete description of the scope of information available from macromolecular crystallography.

Jan Drenth “Principles of Protein X-ray Crystallography” More “mathematical”, vector and matrix notation...

Bernhard Rupp (2009) “Biomolecular Crystallography: Principles, Practice, and Application to Structural Biology” Modern, comprehensive textbook.

McPherson for review when you start to actually do crystallography,
Rhodes for overall concepts,
Blow for appreciating results,
Stout & Jensen or Drenth to understand crystallography basics,
Rupp for the most comprehensive and up-to-date textbook.


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