Near-Native Protein Loop Sampling Using Nonparametric Density Estimation Accommodating Sparcity

Unlike the core structural elements of a protein like regular secondary structure, template based modeling (TBM) has difficulty with loop regions due to their variability in sequence and structure as well as the sparse sampling from a limited number of homologous templates. We present a novel, knowledge-based method for loop sampling that leverages homologous torsion angle information to estimate a continuous joint backbone dihedral angle density at each loop position. The φ,ψ distributions are estimated via a Dirichlet process mixture of hidden Markov models (DPM-HMM). Models are quickly generated based on samples from these distributions and were enriched using an end-to-end distance filter. The performance of the DPM-HMM method was evaluated against a diverse test set in a leave-one-out approach. Candidates as low as 0.45 Å RMSD and with a worst case of 3.66 Å were produced. For the canonical loops like the immunoglobulin complementarity-determining regions (mean RMSD 7.0 Å), this sampling method produces a population of loop structures to around 3.66 Å for loops up to 17 residues. In a direct test of sampling to the Loopy algorithm, our method demonstrates the ability to sample nearer native structures for both the canonical CDRH1 and non-canonical CDRH3 loops. Lastly, in the realistic test conditions of the CASP9 experiment, successful application of DPM-HMM for 90 loops from 45 TBM targets shows the general applicability of our sampling method in loop modeling problem. These results demonstrate that our DPM-HMM produces an advantage by consistently sampling near native loop structure. The software used in this analysis is available for download at http://www.stat.tamu.edu/~dahl/software/cortorgles/. Author Summary: A protein's structure consists of elements of regular secondary structure connected by less regular stretches of loop segments. The irregularity of the loop structure makes loop modeling quite challenging. More accurate sampling of these loop conformations has a direct impact on protein modeling, design, function classification, as well as protein interactions. A method has been developed that extends a more comprehensive knowledge-based approach to producing models of the loop regions of protein structure. Most physical models cannot adequately sample the large conformational space, while the more discrete knowledge based libraries are conformationally limited. To address both of these problems, we introduce a novel statistical method that produces a continuous yet weighted estimation of loop conformational space from a discrete library of structures by using a Dirichlet process mixture of hidden Markov models (DPM-HMM). Applied to loop structure sampling, the results of a number of tests demonstrate that our approach quickly generates large numbers of candidates with near native loop conformations. Most significantly, in the cases where the template sampling is sparse and/or far from native conformations, the DPM-HMM method samples close to the native space and produces a population of accurate loop structures.