Kabsch algorithm

Kabsch algorithm

The Kabsch algorithm is a method for calculating the optimal alignment of two sets of points. It is useful in graphics, and also in bioinformatics for calculating the RMSD (root mean squared deviation) between two protein structures.

The algorithm works by calculating a matrix of multiplied components. The destination matrix, "A", is a 3 × 3 matrix with "x", "y" and "z" components for each side. The source is two sets of paired points, "P" and "Q".

: A_{ij} = sum_k P_{ki} Q_{kj}

(sum over the points and multiply components).

The formula is

: (A^t A)^{1/2}A^{-1}

or take the square root of the product of the transpose of "A" and "A" itself, then multiply by the inverse of "A".

The algorithm calculates only the rotation matrix. Both sets of coordinates must be transformed to their centroid first.

C source is available at http://www.personal.leeds.ac.uk/~bgy1mm/Bioinformatics/rmsd.html

A free PyMol plugin easily implementing Kabsch is [http://www.pymolwiki.org/index.php/Cealign Cealign] .

References

* Kabsch, Wolfgang, (1976) "A solution of the best rotation to relate two sets of vectors", "Acta Crystallographica" 32:922. doi|10.1107/S0567739476001873

* Lin Ying-Hung, Chang Hsun-Chang, Lin Yaw-Ling (2004) "A Study on Tools and Algorithms for 3-D Protein Structures Alignment and Comparison", "International Computer Symposium", Dec 15-17, Taipei, Taiwan.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   Wikipedia

  • Root mean square deviation (bioinformatics) — The root mean square deviation (RMSD) is the measure of the average distance between the backbones of superimposed proteins. In the study of globular protein conformations, one customarily measures the similarity in three dimensional structure by …   Wikipedia

  • List of mathematics articles (K) — NOTOC K K approximation of k hitting set K ary tree K core K edge connected graph K equivalence K factor error K finite K function K homology K means algorithm K medoids K minimum spanning tree K Poincaré algebra K Poincaré group K set (geometry) …   Wikipedia

  • Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …   Wikipedia

  • DSSP (protein) — The DSSP algorithm is the standard method for assigning secondary structure to the amino acids of a protein, given the atomic resolution coordinates of the protein. The abbreviation is only mentioned once in the paper describing this… …   Wikipedia

  • Chou–Fasman method — The Chou–Fasman method are an empirical technique for the prediction of secondary structures in proteins, originally developed in the 1970s.[1][2][3] The method is based on analyses of the relative frequencies of each amino acid in alpha helices …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”