Kristin P. Lennox

Density Estimation for Protein Conformation Angles Using a Bivariate von Mises Distribution and Bayesian Nonparametrics

Please see the online supplemental material for a correction to this article. Interest in predicting protein backbone conformational angles has prompted the development of modeling and inference procedures for bivariate angular distributions. We present a Bayesian approach to density estimation for bivariate angular data that uses a Dirichlet process mixture model and a bivariate von Mises distribution. We derive the necessary full conditional distributions to fit the model, as well as the details for sampling from the posterior predictive distribution. We show how our density estimation method makes it possible to improve current approaches for protein structure prediction by comparing the performance of the so-called “whole” and “half” position distributions. Current methods in the field are based on whole position distributions, as density estimation for the half positions requires techniques, such as ours, that can provide good estimates for small datasets. With our method we are able to demonstrate that half position data provides a better approximation for the distribution of conformational angles at a given sequence position, therefore providing increased efficiency and accuracy in structure prediction.

Computational analysis of pathogen-borne metallo β-lactamases reveals discriminating structural features between B1 types

BackgroundGenes conferring antibiotic resistance to groups of bacterial pathogens are cause for considerable concern, as many once-reliable antibiotics continue to see a reduction in efficacy. The recent discovery of the metallo β-lactamase blaNDM-1 gene, which appears to grant antibiotic resistance to a variety of Enterobacteriaceae via a mobile plasmid, is one example of this distressing trend. The following work describes a computational analysis of pathogen-borne MBLs that focuses on the structural aspects of characterized proteins.ResultsUsing both sequence and structural analyses, we examine residues and structural features specific to various pathogen-borne MBL types. This analysis identifies a linker region within MBL-like folds that may act as a discriminating structural feature between these proteins, and specifically resistance-associated acquirable MBLs. Recently released crystal structures of the newly emerged NDM-1 protein were aligned against related MBL structures using a variety of global and local structural alignment methods, and the overall fold conformation is examined for structural conservation. Conservation appears to be present in most areas of the protein, yet is strikingly absent within a linker region, making NDM-1 unique with respect to a linker-based classification scheme. Variability analysis of the NDM-1 crystal structure highlights unique residues in key regions as well as identifying several characteristics shared with other transferable MBLs.ConclusionsA discriminating linker region identified in MBL proteins is highlighted and examined in the context of NDM-1 and primarily three other MBL types: IMP-1, VIM-2 and ccrA. The presence of an unusual linker region variant and uncommon amino acid composition at specific structurally important sites may help to explain the unusually broad kinetic profile of NDM-1 and may aid in directing research attention to areas of this protein, and possibly other MBLs, that may be targeted for inactivation or attenuation of enzymatic activity.

Characterizing the regularity of tetrahedral packing motifs in protein tertiary structure

MOTIVATION While protein secondary structure is well understood, representing the repetitive nature of tertiary packing in proteins remains difficult. We have developed a construct called the relative packing group (RPG) that applies the clique concept from graph theory as a natural basis for defining the packing motifs in proteins. An RPG is defined as a clique of residues, where every member contacts all others as determined by the Delaunay tessellation. Geometrically similar RPGs define a regular element of tertiary structure or tertiary motif (TerMo). This intuitive construct provides a simple approach to characterize general repetitive elements of tertiary structure. RESULTS A dataset of over 4 million tetrahedral RPGs was clustered using different criteria to characterize the various aspects of regular tertiary structure in TerMos. Grouping this data within the SCOP classification levels of Family, Superfamily, Fold, Class and PDB showed that similar packing is shared across different folds. Classification of RPGs based on residue sequence locality reveals topological preferences according to protein sizes and secondary structure. We find that larger proteins favor RPGs with three local residues packed against a non-local residue. Classifying by secondary structure, helices prefer mostly local residues, sheets favor at least two local residues, while turns and coil populate with more local residues. To depict these TerMos, we have developed 2 complementary and intuitive representations: (i) Dirichlet process mixture density estimation of the torsion angle distributions and (ii) kernel density estimation of the Cartesian coordinate distribution. The TerMo library and representations software are available upon request.

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 <2.0 Å), the DPM-HMM method performs as well or better than the best templates, demonstrating that our automated method recaptures these canonical loops without inclusion of any IgG specific terms or manual intervention. In cases with poor or few good templates (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/.

Constrained classification for infrastructure threat assessment

Validated computer simulation is an important aspect of critical infrastructure vulnerability assessment. The high computational cost of such models limits the number of threat scenarios that may be directly evaluated, which leads to a need for statistical emulation to predict outcomes for additional scenarios. Our particular area of interest is statistical methods for emulating complex computer codes that predict if a particular tunnel/explosive configuration results in the breaching of an underground transportation tunnel. In this case, there is considerable a priori information as to the properties of this breach classification boundary. We propose a constrained classifier, in the form of a parametric support vector machine, that allows us to incorporate expert knowledge into the shape of the decision boundary. We demonstrate the effectiveness of this technique with both a simulation study and by applying the method to a tunnel breach data set. This analysis reveals that constrained classification can offer substantial benefits for small sample sizes. The technique may be used either to provide a final classification result in the face of extremely limited data or as an interim step to guide adaptive sampling.

Efficient experimental design for binary matched pairs data

The analysis of data from matched pairs binary experiments, often performed with McNemars test, presents a unique experimental design challenge in dealing with the effect of the discordance probability, p. Most approaches for determining size and power use point estimates or maximization, but this fails to account for the considerable variability across values of the nuisance parameter that occur for all common tests. We recommend viewing the size and power functions across the full range of possible discordance probability values, which gives a complete picture of the behavior of a test for any given sample size. This method also allows us to compare the behavior of different hypothesis tests. We present exact power and size functions for several tests, including the original McNemars test and its most common variants, and compare their properties. This analysis reveals that, in general, McNemars test comes closest to the nominal size and has the highest power. We also demonstrate our technique using the transmission/disequilibrium test (TDT) to check for linkage between schizophrenia and a locus related to the D(3) dopamine receptor, and on a hypnosis pain management data set.

A Bayesian Measurement Error Model for Misaligned Radiographic Data

An understanding of the inherent variability in micro-computed tomography (micro-CT) data is essential to tasks such as statistical process control and the validation of radiographic simulation tools. These data present unique challenges to variability analysis due to the relatively low resolution of radiographs, and also due to minor variations from run to run which can result in misalignment or magnification changes between repeated measurements of a sample. Such positioning changes artificially inflate the variability of the data in ways that mask true physical phenomena. We present a novel Bayesian nonparametric regression model that incorporates both additive and multiplicative measurement error in addition to heteroscedasticity to address this problem. We use this model to assess the effects of sample thickness and sample position on measurement variability for an aluminum specimen. Supplementary materials for this article are available online.

Understanding the general packing rearrangements required for successful template based modeling of protein structure from a CASP experiment

As an alternative to the common template based protein structure prediction methods based on main-chain position, a novel side-chain centric approach has been developed. Together with a Bayesian loop modeling procedure and a combination scoring function, the Stone Soup algorithm was applied to the CASP9 set of template based modeling targets. Although the method did not generate as large of perturbations to the template structures as necessary, the analysis of the results gives unique insights into the differences in packing between the target structures and their templates. Considerable variation in packing is found between target and template structures even when the structures are close, and this variation is found due to 2 and 3 body packing interactions. Outside the inherent restrictions in packing representation of the PDB, the first steps in correctly defining those regions of variable packing have been mapped primarily to local interactions, as the packing at the secondary and tertiary structure are largely conserved. Of the scoring functions used, a loop scoring function based on water structure exhibited some promise for discrimination. These results present a clear structural path for further development of a side-chain centered approach to template based modeling.