Comparative protein modelling by satisfaction of spatial restraints.

We describe a comparative protein modelling method designed to find the most probable structure for a sequence given its alignment with related structures. The three-dimensional (3D) model is obtained by optimally satisfying spatial restraints derived from the alignment and expressed as probability density functions (pdfs) for the features restrained. For example, the probabilities for main-chain conformations of a modelled residue may be restrained by its residue type, main-chain conformation of an equivalent residue in a related protein, and the local similarity between the two sequences. Several such pdfs are obtained from the correlations between structural features in 17 families of homologous proteins which have been aligned on the basis of their 3D structures. The pdfs restrain C alpha-C alpha distances, main-chain N-O distances, main-chain and side-chain dihedral angles. A smoothing procedure is used in the derivation of these relationships to minimize the problem of a sparse database. The 3D model of a protein is obtained by optimization of the molecular pdf such that the model violates the input restraints as little as possible. The molecular pdf is derived as a combination of pdfs restraining individual spatial features of the whole molecule. The optimization procedure is a variable target function method that applies the conjugate gradients algorithm to positions of all non-hydrogen atoms. The method is automated and is illustrated by the modelling of trypsin from two other serine proteinases.