Learning virulent proteins from integrated query networks
© Cadag et al.; licensee BioMed Central Ltd. 2012
Received: 5 April 2012
Accepted: 20 November 2012
Published: 2 December 2012
Methods of weakening and attenuating pathogens’ abilities to infect and propagate in a host, thus allowing the natural immune system to more easily decimate invaders, have gained attention as alternatives to broad-spectrum targeting approaches. The following work describes a technique to identifying proteins involved in virulence by relying on latent information computationally gathered across biological repositories, applicable to both generic and specific virulence categories.
A lightweight method for data integration is used, which links information regarding a protein via a path-based query graph. A method of weighting is then applied to query graphs that can serve as input to various statistical classification methods for discrimination, and the combined usage of both data integration and learning methods are tested against the problem of both generalized and specific virulence function prediction.
This approach improves coverage of functional data over a protein. Moreover, while depending largely on noisy and potentially non-curated data from public sources, we find it outperforms other techniques to identification of general virulence factors and baseline remote homology detection methods for specific virulence categories.
Though recent decades have seen a decrease in mortality related to infectious disease, new dangers have appeared in the form of emerging and re-emerging pathogens as well as the continuing threat of weaponized infectious agents[1, 2], thus creating a strong need to find new methods and targets for treatment. Underscoring the importance of this issue, the National Institute of Allergy and Infectious Disease maintains a categorical ranking of disease-causing microorganisms (NIAID Biodefense Categories) that could cause significant harm and mortality. Broadly, infectious disease remains a global concern and a problem whose impact is most felt in poorer areas of the world. Fortunately, many pathogen genomes have been sequenced and continue to be sequenced, and hold the promise of expediting new therapeutics. As a result, genomic and proteomic sequences are available for many bacterial and viral causes of disease. The National Microbial Pathogen Data Resource (NMPDR), a curated database of pathogen genomes, lists 801 different species and strains bacteria and eukarya infectious to mankind. The availability and dissemination of this data has allowed many new discoveries in virulence research to stem at least partly from computational methods. The challenge is no longer having to work with limited data, but rather how best to exploit the information available and prioritize targets of study.
A critical set of potential genes of interest within a pathogen are those directly involved in pathogenesis. These genes, or virulence factors, can have varying degrees of importance in the initiation and maintenance of infection, and constitute an attractive group of putative targets. Concrete determination of a gene’s involvement in disease is generally left to experimental results, and many studies rely on knockouts or mutations of putative virulence genes[5, 6]. Resulting attenuation or avirulence would then be strong evidence that the gene is involved in disease, although the exact function or role may still remain a mystery. Proper target selection is important, however, given that laboratory science makes the identification and verification of virulence factors a costly endeavor. Faster methods are preferred early on that can highlight the most likely targets before experimental assays are carried out.
Identifying and annotating these virulence factors is an early and integral part of understanding how a disease causes damage to a host; improvements in accuracy and speed for finding proteins involved in virulence have the potential to increase the analytical throughput of therapeutic research, provide clues towards mechanisms of infection and provide tempting biomarkers for diagnostic techniques. However, prior computational research in quickly identifying virulence factors has been limited, and has only in the last few years become an area of strong interest for researchers. Several public databases have recently been released that focus exclusively on pathogenesis. Among these include: the Virulence Factor Database (VFDB), a repository of genomic and proteomic data for bacterial human pathogens[7, 8]; the Argo database, a collection of virulence factors believed to be involved with resistance for β-lactam and vancomycin families of antibiotics; and MvirDB, a aggregated data warehouse of many, smaller virulence-related databases (including VFDB and Argo). Many of these repositories support standard sequence-based searches against their content, facilitating virulence identification via sequence similarity.
Classification algorithms have also been applied to the problem of virulence recognition for cases where homologies between virulence proteins may be remote. Sachdeva et al., for example, used neural networks to identify adhesins related to virulence. Saha used support vector machines to predict general virulence factors via an approach similar to one proposed in - mapping combinations of the amino acid alphabet to a space such that the presence of a peptide sequence would constitute a classifiable feature. However, the resulting top accuracy for virulence proteins, 62.86%, was relatively low in comparison to the other protein roles predicted (e.g., cellular and metabolic involvement). Work by Garg and Gupta improved on this performance by also relying on polypeptide frequencies in conjunction with PSI-BLAST data in a cascaded support vector machine (SVM) classifier. This approach yielded a higher accuracy of 81.8% and an area under the receiver operating characteristic (ROC) curve of 0.86 for generalized virulence prediction. Other methods have directed attention at specific types of virulence proteins; Sato et al. developed a model for predicting type III (T3) secretory proteins within Salmonella enterica and generalized to Pseudomonas syringae, and McDermott et al. compare multiple computational secretory prediction methods to predict T3/4 effectors on completely novel proteins.
The present work expands upon the recent research in computational virulence prediction relying on noisy, weakly-related annotation information rather than direct sequence data, and describes an approach relying on readily available public data for predicting microbial protein relation to virulence. Information from multiple biologic databases are returned wholesale using a retrieval approach that constructs an interlinked graph of connected information, providing broad functional coverage.
Note that the information retrieved may or may not be specifically relevant or correct with regards to the protein of interest; rather than using that information for direct annotation, the aggregate data are used to build a weighted graph used as input to statistical methods trained to recognize virulence proteins. We apply this approach to both overall and specific virulence, and evaluate its performance against competing methods.
Path-based query retrieval
The methodology we adopt relies on retrieving abundant information regarding a protein sequence using a networked query graph. The core of this approach relies on the notion that leveraging multiple sources simultaneously will improve functional coverage of any given query protein.
We describe the basic query and retrieval model here briefly (refer to[17, 18] for further details of the logical query model): let a query graph G derived from some schema S be G(S) = 〈V,E〉, where V are the nodes and E the relations between the nodes. For any concrete instance of a query graph, V refers to the individual records returned from any protein sequence query, and E the connection between those records (e.g., through external link reference) or the protein sequence directly (e.g., from a pair-wise sequence comparison). S constrains v ∈ V to specific resources (records of information), and the nature of e ∈ E to specific relations between those resources. In this definition, we allow the assignment of weights onto the edges; in the case of pair-wise sequence comparisons, these weights may represent the quality of the alignment between the query protein and other proteins within a resource. Intuitively, a query graph can imagined as a realization of a graph database whose joins are represented by the edges E: v i ⋈ d v j , where v i ,v j ∈ V and d is some primary key-like attribute (e.g., RefSeq identifier in a gene record, referencing its product). This concept can be illustrated via a simple BLAST search: a query is seeded with a protein sequence, s0; the results of the query may be n other sequences, s1,…,s n , for which pairwise alignments ((s0,s i )→v i ) are identified.
We extend the notion of a query graph to exploratory query graphs, or a query graphs expanded to the limit of connections defined in S such that for any given protein query, all possible connections between records and all records are realized. Following the previous example, all sequences aligned to s0 may themselves be used as queries against additional databases, generating a larger query graph whose contents may span multiple sources. Exploratory query graphs thus represent a materialization of the entirety of S for any given protein sequence query.
Notably, the query and retrieval approach we describe has been employed widely in life sciences research for data management and navigation purposes[19–22]. However, whereas these prior works has focused on the retrieval, curation, and provenance of biological records, this present study is less interested in the quality of each individual datum and instead focuses on the use of the query graphs as a whole to infer (possibly latent) annotations on the initial seeding query that may not be explicitly represented in the query graphs.
Constructing weighted query graphs from sequence data
We exploit the notion that within a path-based model, the closer a node is to the initial query, the more relevance it likely has to that query, and that those further from the query itself are theoretically of waning relevance. Naturally, the contents of exploratory query graphs will include records that may be quite distant from the initial query. Prior work by others in the field of biologic data representation explored various methods of exploiting the graph structure for inferring the relevance of individual nodes and paths. Bharat and Henzinger, for example, describe several algorithms, such as those that use the in- and out-degree of nodes, for the analogous problem of determining topical relevance of hyperlinked documents; Tsuda et al. use a diffusion-based approach to assign weights within protein networks, a method readily adaptable to query graphs; Weston et al. apply a rank propagation algorithm on sequence similarity graphs generated from PSI-BLAST hit values; and Detwiler et al. test a variety of methods, such as Monte Carlo simulations and relevance propagation, to rank nodes in similar graphs. In contrast, our interest is less in the relevance of any individual node, and instead in the value of using the graph globally as a representation of the query for classification activities.
After seeding an initial query, retrieving records and fully expanding the query graph, we transform the contents of the graph into a representation more amenable to classification by weighting nodes in the query graphs and representing their records as numerical features that can be used as inputs to statistical classification methods. This approach bypasses the difficulties in comparing query graphs directly, and depending on the weighting scheme used can still leverage the benefits of the graph structure. Because the query graph is generated by a series of linkages across databases, groups of nodes that share edges most often or have strong sequence-similarity to the query can be weighed highest. An ideal scheme would heavily weigh nodes that characterize the query sequence more precisely, and lightly weigh nodes that do not, thereby minimizing noise.
the above being an empirically determined from. All nodes were given initial weights of 0, save the query itself, which is given a weight of 1, and the algorithm iterates until convergence. Applying weights in this manner takes into account the notion that some nodes will be more well-connected than others. Consequently, nodes with more incoming edges will have a higher weight than nodes with less, all other things being equal.
Query subgraphs as features
In the above, w(n) may take the value of any arbitrary weighting scheme. If v has known classification, it would then be possible to use it as a member instance of a label in classification training.
Datasets for general and specific virulence
The above method and implementation provides a means to query a protein, weight the nodes in the query graph and transform the results into a feature representation suitable for training and classification. We evaluated virulence and non-virulent protein prediction using information derived from query graphs using two different datasets – one for general virulence, and one for specific virulence subcategories.
General virulence dataset
We identified a curated set of proteins with which to evaluate the performance of our approach in the form of the non-redundant protein set used by Garg and Gupta to test their own virulence detection system, and adopt their train-test procedure to allow direct comparison. Though composed of virulence proteins with a variety of functions, Garg and Gupta treated the entire set as ‘general virulence’ test cases. The positive, virulent number of examples in the set was 1025, with 820 of these acting as training instances for cross-validation and parameter selection, and the remaining 205 for testing. Likewise, the non-virulent proteins numbered 1030, with a division of 206 and 824 for testing and cross-validation, respectively. This constituted an 80%-20% train-test split, with the larger fraction used to optimize the parameters for each algorithm and the smaller used for final testing.
Specific virulence dataset
The dataset developed by Garg and Gupta lacked the annotation granularity needed to determine specific virulence roles a protein may play, since the dataset was purely binary in classification, and a protein was categorized as either ‘virulent’ or ‘non-virulent’. For a more specific prediction of virulence factors, we relied on a data warehouse of virulence proteins mentioned earlier, MvirDB. In order to transform the protein data in MvirDB into a suitable training and testing set, the first step was curation of the data into a non-redundant, representative set of proteins.
The original MvirDB dataset consisted of 14544 records. The few DNA sequences in this set were translated to protein sequences, beginning at the leading methionine if present, using the longest open reading frame; otherwise, the DNA sequence was removed from the set. Databases whose contents were viral sequences were removed from the set. These initial filters yielded 5052 remaining proteins.
For negative training and test instances, 3000 proteins were randomly drawn from GenBank and filtered for proteins highly likely to be involved in virulence based on regular expression searches on the protein names and annotations. For example, proteins whose names contained ‘drug’ or ‘toxin’ were removed. Proteins from known pathogen organisms were otherwise left undisturbed in the negative set under the notion that not all proteins within an infectious organism are involved in virulence. At the same time, hypothetical proteins whose functions were unknown were also removed from the negative set. Finally, CD-HIT was used to generate non-redundant protein clusters for the positive and negative sets combined, at 40% sequence identity. This last non-redundancy step ensured that proteins used for the evaluation would be dissimilar overall, and permit validation of discrimination in cases of remote homology[39, 40]. The final sequence dataset consisted of 3700 proteins, 1703 of which constituted the negative (non-virulent) set and 1997 of which formed the positive (virulent) classes (see Additional files1 and2).
Once the datasets were curated for non-redundancy, and possible virulence factors in the case of negative set, the positive set proteins were labeled with specific virulence functions. Labeling was done based on the information regarding the protein readily available from the originating virulence data sources; many of the databases that MvirDB integrated used a native classification system. Virulence proteins were annotated manually, based on the original classifications and literature references of the native databases.
Procedure for manual curation of virulence factors
Procedure for manual curation of virulence factors
Examine the source or database of each protein annotation for possible classifications, using the annotation set across
all databases as a starting point. Record annotations according to information from the source or database; each protein
may have more than one annotation. If a protein is directly involved in a virulence process or is a regulator of that process,
record it as such. In this way, proteins may have more than one annotation.
Examine any publications which are linked from the source. Record annotations according to information from the
publication regarding the protein.
If an annotation was unclear or unknown, conduct a keyword publication search of the virulence factor to obtain resolution.
Repeat steps (1-3) across all proteins (i.e. re-annotate) until no further changes were made from the previous annotation.
Transport and uptake
General virulence prediction evaluation procedure
For the general virulence dataset, we compared the above classifiers, trained on inputs generated using integrated query graphs, against the bi-layer cascaded SVM approach originally employed by Garg and Gupta (VirulentPred,). VirulentPred relied on amino acid frequencies, sliding window peptide n-grams and a feature set derived from position-specific scoring matrices generated from PSI-BLAST searches against NBCI’s non-redundant database. Likewise, we included for comparison baseline approaches against which VirulentPred was evaluated; namely, single SVMs trained against amino acid frequencies. In this case, 1-, 2- and 3-mer frequencies of proteins were used as the feature to an SVM classifier, resulting in trainable feature spaces of size 20, 202 and 203, respectively.
Specific virulence prediction evaluation procedure
Unlike the prediction of generalized virulence in the previous section, the problem of specific virulence is multiclass. Each protein was permitted to have multiple virulence labels attached to it, and thus for each classification method and source 11 different SVMs were tested in a one-versus-rest fashion. That is, each virulence category was set as the positive set of interest, and all other proteins (non-virulent proteins and virulent proteins of a differing classification) were treated as the negative set. Two primary experiments were conducted on the specific virulence set.
First, similarly to how evaluation was conducted for generalized virulence, the dataset for specific virulence was split into training and testing components; 80% of the dataset was used for training the various parameters for the classifiers and 20% retained for final testing. For the integrated query graphs, data was generated as in the generalized virulence experiment, with the same data sources and identical schema. As the SVM performed the best overall in the generalized virulence experiment (see Results), this kernel was chosen for the specific virulence classification experiment. Optimal parameters for the integrated query graph were determined via a grid search using the same procedure as generalized virulence. The parameters selected for each source and for each virulence class were those that provided the best AUC performance.
where, respectively, x(+) and x(−) are the positive and negative datasets,,, are the averages of the positive, negative and complete sets of the i th feature, and, are the values of the i th feature of the k th instance of the positive and negative sets. Features whose F-scores were in the top 25%, 50% and 75% were tested, per source in the training set. As with the SVM parameters, the features that yielded the best AUC in training were the features then used for the final test results.
The second experiment involved running six five-fold cross-validations for each class and method with the intention of obtaining measures of variance and deviation for each classifier. For each cross-validation run, the five-fold splits were the same across all classifiers to accommodate direct, paired comparison. In the case of SVM-based baseline methods and sources, Gaussian kernels were used, as they seemed to have the most consistent performance in generalized virulence prediction (see Results); parameters for the kernel and SVM were default and non-optimized, per libSVM. Because 30 individual values are reported for each classifier per virulence class, paired two-tailed t-tests were used to measure the significance of any mean differences between the sources, and between the sources and baseline methods; p-values were adjusted for multiple pair-wise comparisons via Bonferroni correction.
where the set denotes the neighborhood of k-nearest proteins to i (as determined by highest results from BLAST), and 1 n (L) is the indicator function, which is equal to 1 if n ∈ L and 0 otherwise; thus, p is the fraction of the k-nearest neighbors of i that have membership in L. This approach was used since each protein in the dataset could take on multiple classes at once and the formulation in (5) permits the measurement of membership strength for any arbitrary class, given some protein; for present purposes, the cluster size was chosen to be k = 3. The motivation behind this very simple approach is to measure annotation based on data from a single source, and in such a way as to emulate how an annotator may scan the best-scoring BLAST hits of a sequence to determine function.
The third and final baseline classifier used was also based on BLAST, but relies on using SVMs trained on pair-wise hits (with a high e-value threshold) against a BLAST database of the training set. To generate features for this third baseline classifier, each test sequence was queried against the trained BLAST database, resulting in a vector representation of a sequence’s negative log transformed e-value score to the other sequences within the database. This method is referred to as BLAST+SVM and has been used in prior experiments by others, where SVMs based on pair-wise BLAST queries outperformed or were comparable to other methods such as SVM-Fisher, SAM, PSI-BLAST, Smith-Waterman and motifs with SVMs in detecting sequences that were remotely homologous[51, 52].
Results and discussion
Comparison of data sources for predicting virulence
Comparison of generalized classification across sources
SVM classification using different data sources
Comparison with competing methods for predicting virulence
Learned query graph performance using the VirulentPred test set
Feature space sizes across sources
Further analysis of the ROC scores reveals other interesting results. Category 8, Motility, was relatively trivial to classify not merely by GenNav but by other sources as well, including KEGG and InterPro. One explanation for these results was that the motility of bacterial pathogens, and indeed bacteria in general, is a very well characterized process, and proteins related to bacterial motion are well-annotated and unambiguous. Despite its coverage in comparison to sources like TIGRFAM and BioCyc, and contrary to the case in other categories, PDB records failed to predict motility well. This may partly be due to the fact that motility-related proteins, given their high probability of containing transmembrane regions, are difficult to structurally elucidate and thus good exemplars of this class are more absent in this database.
Integrated query graph learning versus baseline methods
Statistical significance of pairwise comparisons are also visible in Figure3 via transitive arrows. It stands out that in all but one virulence class, at least one of the queried data sources outperforms all baseline methods; 3-mer performance on the Surface factor label was exemplary compared to most sources and the other baseline methods (see Additional file3 for exact statistical results). However, it was also the label with the fewest instances. In eight of the virulence classes, the ROC curves of GO-term based methods outperform not just baseline methods, but all other sources as well. Interestingly, for proteins related to antibiotic resistance, such as drug efflux pumps, InterPro does significantly better than all other sources and methods.
These findings strongly illustrate that the performance of some classifiers do not significantly change with the number of instances seen. In the case of the Motility and Secretion classes, both KEGG and GenNav perform essentially the same and with little change, though for other sources such as InterPro the AUC increased with the training set size. This led to the conclusion that some data sources may better characterize classes than other sources, and that in the case of GenNav and KEGG for Secretion, there are likely a set of terms or pathways that commonly describe pathogen secretory mechanisms, and that these annotations are widespread across the set of secretion-related proteins. Also of note was the performance of GenNav under small training set size conditions. Other sources and methods generally tend to perform poorly (< 0.7 AUC) with training sets less than 500 instances, whereas GenNav does considerably better in 7 of the 10 cases often by more than 0.1. This suggests that heavily integrated sources, such as GenNav, may have additional utility over other methods when the number of seen and known instances from which to train are very low, leading to the hypothesis that integrated methods may do better under more ambiguous conditions when compared to competing approaches.
Estimating the advantage of multiple features for specific virulence
Thus far, results have strongly suggested that some categories are much easier to classify than others. For example, Motility was easily predicted across all integrated sources, and for some even at very low numbers of training instances. In comparison, other virulence classes such as Invasion and Defense remain harder to identify with strong confidence. Because many of these nuances in performance are both source- and label-specific, it was of interest to generate ROCs without a classifier, and using only the weights determined from the propagation algorithm in the query graphs. For each category and source, the F-score per (5) was computed, and the highest-performing feature was kept. Recall that each feature was assigned a weight from the query graph; this value was used as the thresholding function for the generation of AUC scores. The result of this was essentially a very basic classifier, Top-F1, which relied only on the single-most discriminating feature of each source for each label. The AUC for this classifier represents predictions ignorant of any value in combining multiple features; comparisons of this with other methods would thus illustrate any advantages or disadvantages from using more sophisticated approaches on the query graph data.
At the same time, other sources benefit greatly from the combination of features, namely InterPro and CDD, the two sources that on average have the highest improvement of using SVMs over Top-F1. At the opposite end, TIGRFAM and BioCyc show the least overall improvement, with the GO-term based sources (AmiGO, GenNav) showing moderate improvement. Examining the GO-term based sources shows interesting differences between using only direct annotation information (AmiGO) and enrichment via traversing the GO hierarchy (GenNav). While most of the changes between the two sources are commensurate, AmiGO strongly benefits from the use of SVMs for the Secretion category. One conclusion from this is that there are several top-level terms in GO that suggest secretion, and that under GenNav these terms are retrieved; under AmiGO, however, this information was not available, but was ameliorated by the availability of terms that may share mutual parents.
In the case of general virulence, and in the majority of specific virulence classes, a classification approach that used integrated queries as input performed significantly better than the baselines and competing approaches. Surprisingly, it was found that the data sources several nodes away from our query were the most predictive, which may at first glance seem counterintuitive. GenNav and AmiGO both are sources indirectly connected to the initial queries in the query graph, yet they were the best performing. A large part of this may be due to their superior coverage, as they are referenced by other data sources, but even when empty graphs are omitted it was found that these data sources still out-scored the other sources directly connected to the query. This reinforces the position that, as it pertains to using biological databases for classifying protein data, shallow queries are generally not sufficient. Manually, this information can be difficult to sift through, and using robust methods to cut through the “chaff” is indispensable. This is particularly salient given the results that learning methods more resistant to noise were the best at identifying virulent proteins.
A limitation that is not explored in this work but is self-evident in implementation is that performance will likely be very dependent on the choice of data sources and cross- linkages. Moreover, as data sources evolve, are expanded or curated, source-specific findings may vary. This caveat is particularly applicable to sources which are directly queried (e.g., CDD); indirect features (e.g., GO terms) may be more robust to this effect as multiple sources are integrated. In either case, query proteins ideally will have some limited sequence similarity to other proteins; truly novel proteins may not provide sufficient results for classification. In such instances, relaxing stringency to provide results with very low homology may be effective, though accuracy and interpretability will likely suffer. Another notable limitation involves evaluating the classifications. The circuitous nature of sequence annotation from biological databases makes it difficult to identify annotations that were derived transitively. While we attempted to address this problem by omitting from the query graph any results with 100% similarity to the query sequences and disallowed sequence results from serving as seeds for other sequence queries, it is likely that protein families or domains with GO assignments, which may have been curated based in part on the query sequence, were returned and used for classification. Based on our analysis of the results, however, we believe the most influential reason for the dominating performance of GO terms may be how informative the features are relative to other sources. Recall that the AUC findings between AmiGO (linked GO terms only) and GenNav (linked and hierarchical GO terms) was greater than the difference between AmiGO and the top-performing non-GO sources (Table4); indeed, InterPro performs similarly to linked GO, but does not outperform hierarchical GO. This leads us to believe that there is inherent value in using a standardized and rich vocabulary for classification beyond coverage alone. We find that there is value in cross-linking across data sources, and that while provenance and quality of data are naturally very important even the most naive retrieval approaches can provide useful information on identifying protein virulence, and perhaps protein class in general.
Notably, our method used each data source, weighted via query integration, to serve as separate inputs to individual classifiers. This approach resulted in multiple source-specific classifiers that only utilized a subgraph of the entire query graph. A perhaps preferable alternative would be single classifier that utilized the entire graph. To that end, we explored additional methods of source integration to augment query weighting, and in particular kernel integration, where kernels generated for each source were additively combined before learning. Our initial findings using this approach resulted in marginal improvement using naïve equal kernel weighting, at prohibitively high computational cost. Achieving full query graph integration for the classification phase is a reasonable extension of this work, however, and further work is needed to explore ways of optimizing kernel weight selection to improve performance and justify the cost.
By presenting a method of exploting this data in the context of virulence and presenting the results, a major insight is that even without extensive manual curation integrated data can be very effective for prioritization of both virulence factors and general function prediction. This approach scales well against both the number of sources incorporated and the amount of ground truth information known, making it an appropriate choice for high-throughput biological research. Towards this end, our methods have been incorporated into the target selection pipeline of the Seattle Structural Genomics Center for Infectious Disease (SSGCID) for down-selecting virulence related proteins for structural elucidation. Lastly, results produced by this research are possible targets of health-related interest in public health and infectious disease biology; highlighting these proteins for 5itional study may further improve knowledge of pathogenesis and disease.
The authors would like to thank Ira Kalet, William Noble and Evan Eichler for their valuable feedback and suggestions. This research was funded in parts by the National Human Genome Research Institute (grant R01HG02288), the National Library of Medicine (grant T15LM07442), the National Institute of Allergy and Infectious Diseases (contract HHSN 272200700057 C) and the U.S. Department of Defense (grant N00244-09-1-0081). This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
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