  By providing new insights into the distribution of a protein's torsion
angles, recent statistical models for this data have pointed the way to more
efficient methods for protein structure prediction. Most current approaches
have concentrated on bivariate models at a single sequence position. There is,
however, considerable value in simultaneously modeling angle pairs at multiple
sequence positions in a protein. One area of application for such models is in
structure prediction for the highly variable loop and turn regions. Such
modeling is difficult due to the fact that the number of known protein
structures available to estimate these torsion angle distributions is typically
small. Furthermore, the data is "sparse" in that not all proteins have angle
pairs at each sequence position. We propose a new semiparametric model for the
joint distributions of angle pairs at multiple sequence positions. Our model
accommodates sparse data by leveraging known information about the behavior of
protein secondary structure. We demonstrate our technique by predicting the
torsion angles in a loop from the globin fold family. Our results show that a
template-based approach can now be successfully extended to modeling the
notoriously difficult loop and turn regions.
