Aims

• To describe and explain the use of homogeneous transformation matrices.
• To describe in outline how to superpose sets of points.
• To describe methods for protein structural alignment.

Objectives

After this lecture you will:

• understand the form and use of homogeneous transformation matrices;
• understand, in outline, how structure superposition is performed;
• understand the purpose and methods of the DALI structural alignment program.

Supplementary Material

Kearsley's method for finding the rotation matrix that minimses the average distance between sets of atoms is described in:

Kearsley, S.K. (1989) "On the orthogonal transformation used for structural comparisons", Acta Cryst., A45, 208-210. (PDF)

For more information about the DALI algorithm for pairwise protein structure alignment, see the articles "Protein structure comparison by alignment of distance matrices" (J. Mol. Biol. vol 233, 123-138, 1993) and "Mapping the Protein Universe" (Science vol. 273, 595-602, 1996) by Liisa Holm and Chris Sander, and the DALI server web site.