Elastic Scattering

Preface & Contents

Table of Contents

1. Light Scattering

General properties of light waves and scattering from a single small object, e.g. an electron, concentration on Elastic interaction.

2. Molecular Scattering

Scattering of light waves from more than one point, extended objects containing many scattering points. Examples: atom with many electrons, molecule of many atoms, particle of many molecules.

3. Bragg Equation

Distance and direction of scattering units, illustrated as in a crystal.

4. Patterson Function

At least Distance information, direction if object fixed in space. Abstract information to get a starting model (and initial phases for crystallography).

The Equations

Table of the equations. Page 1 is the minimal set, following pages have more detail and explanations.


Lecture notes for the elastic scattering section of a Physical Biochemistry course; (historically BCH/SBB 291) 2013: BCH/SBB 681

Fall 2013 revised and rearranged to put emphasis on the phenomenon of elastic scattering in general and show, for instance, x-ray diffraction as a special case of light scattering. However, these notes are directly derived from long-term development of an introduction to x-ray crystallography of macromolecules.

The general philosophy for this general treatment of elastic scattering remains as before: (except we will leave actually solving crystal structures to a later course for those interested). The course is not intended to teach you to use current machinery and computer programs to, for instance, solve crystal structures; it will, however with a bit more understanding of crystallography, 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) (and this year still in the form and terminology of crystallography).

...and comments and examples are still drawn from crystallography...
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

links to external Resources

Web Site: http://kinemage.biochem.duke.edu/teaching/BCH681

Other Web sites: (particularly useful for crystallography and models made by that technique)
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 Crystallography Textbooks for reference or different presentation: (these include a lot of general scattering stuff)

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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