URMS program for 3-D protein structure comparison

In this version, a single three-dimensional (3D) rigid motion is used to orient the proteins. This is in contrast to methods which allow different rigid motions for different portions of the proteins.

The algorithm is based on a unit-vector representation of the proteins. Instead of comparing alpha-carbon positions we compare direction vectors. The compared vectors are those between adjacent alpha-carbons along the protein backbone. We refer to these direction vectors as unit vectors because, for proteins, these vectors are all the same length (about 3.8Å). By chaining the unit vectors head-to-tail, we obtain the standard model of a protein as a sequence of alpha-carbons in space. Alternatively, we can place all of the unit vectors at the origin; the protein backbone is thus mapped into vectors in the unit sphere.

For the URMS (Unit-vector RMS) distance between two proteins A and B we first compute their representations as unit vectors mapped to the unit sphere. We then determine the rotation (rotation only, no translation) that minimizes the sum of the squared distances between corresponding unit vectors. The square root of the resulting minimum sum is defined as the URMS distance between the original proteins A and B Note that, just like the RMS distance, the URMS distance computation provides two things: (1) the distance between the two proteins and (2) the orientation that achieves that distance. See [J. Comp. Biol. (1999) 6 pp. 313-335] for a discussion of the URMS distance. See [Proceedings of the Symposium on Computational Geometry (2002) pp. 64-73] for how to use the unit-vector representatin to build a consensus shape for a family of proteins, a protein-like structure that provides a compact summary of the significant structural information for a protein family.

This work was supported by the NSF (CCR-#9988519).