Discrete representations of the protein C α chain

Abstract

When a large number of protein conformations are generated and screened, as in protein structure prediction studies, it is often advantageous to change the conformation in units of four consecutive residues at a time. The internal geometry of a chain of four consecutive C alpha atoms is completely described by means of the three angles theta 1, tau, and theta 2, where tau is the virtual torsion angle defined by the four atoms and theta 1 and theta 2 are the virtual bond angles flanking the torsion angle on either side. In this paper, we examine the quality of the protein structures that can be obtained when they are represented by means of a set of discrete values for these angles (discrete states). Different models were produced by selecting various different discrete states. The performance of these models was tested by rebuilding the C alpha chains of 139 high-resolution nonhomologous protein structures using the build-up procedure of Park and Levitt. We find that the discrete state models introduce distortions at three levels, which can be measured by means of the 'context-free', 'in-context', and the overall root-mean-square deviation of the C alpha coordinates (crms), respectively, and we find that these different levels of distortions are interrelated. As found by Park and Levitt, the overall crms decreases smoothly for most models with the complexity of the model. However, the decrease is significantly faster with our models than observed by Park and Levitt with their models. We also find that it is possible to choose models that perform considerably worse than expected from this smooth dependence on complexity. Of our models, the most suitable for use in initial protein folding studies appears to be model S8, in which the effective number of states available for a given residue quartet is 6.5. This model builds helices, beta-strands, and coil/loop structures with approximately equal quality and gives the overall crms value of 1.9 A on average with relatively little variation among the different proteins tried.