Knowledge based modelling of homologous proteins, Part I: Three-dimensional frameworks derived from the simultaneous superposition of multiple structures.

An approach is described for modelling the three-dimensional structure of a protein from the tertiary structures of several homologous proteins that have been determined by X-ray analysis. A method is developed for the simultaneous superposition of several protein molecules and for the calculation of an 'average structure' or 'framework'. Investigation of the convergence properties of this method, in the case of both weighted and unweighted least squares, demonstrates that both give a unique answer and the latter is robust for an homologous family of proteins. Multi-dimensional scaling is used to subgroup of the proteins with respect to structural homology. The framework calculated on the basis of the family of homologous proteins, or of an appropriate subgroup, is used to align fragments of the known protein structures of high sequence homology with the unknown. This alignment provides a basis for model building the tertiary structure. Different techniques for using the framework to model the mainchain of various globins and an immunoglobulin domain in the structurally conserved regions are investigated.