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Theoretical Biology & Biophysics, T-10 MS K710, LANL, Los Alamos, NM 87545, USA
Correspondence
Peter Hraber
phraber{at}lanl.gov
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Present address: Department of Sociology, UC Davis, CA 95616, USA. 
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). Fast, accurate and reliable classification methods are important for many reasons. Knowledge of viral subtypes is useful because it helps to determine routes of disease transmission, can provide therapeutic decision support, facilitates monitoring of new variants, improves understanding of how genetic diversity influences host immune response and simplifies analysis of treatment-resistance mutations (Korber et al., 2001; Fried et al., 2002; Leitner, 2002; Hadziyannis et al., 2004; Hraber et al., 2006, 2007). Therefore, we seek to facilitate classification of HIV-1 and HCV sequences.
Nomenclature for classification differs between HCV and HIV-1. For HCV, viral genotypes are denoted by an integer, currently 1 through 6, and subtypes are denoted with the genotype followed by a lower-case letter, e.g. 1a, 1b, 1c, etc. There are presently 80 known HCV subtypes, of which 20 have been confirmed by whole-genome sequencing of three independent isolates (Simmonds et al., 2005). In contrast, for the HIV-1 M group, the subtype designation is an upper-case letter, currently A, B, C, D, F, H, J and K (Robertson et al., 2000). A letter and number, i.e. A1, A2, F1 and F2, indicate sub-subtypes. Subtypes B and D are as closely related to each other as are the A1 and A2 sub-subtypes or the F1 and F2 sub-subtypes, but are designated as different subtypes, rather than as sub-subtypes. Circulating recombinant forms (CRFs) of HIV-1, confirmed by whole-genome sequencing of three independent isolates are indicated by the prefix ‘CRF’, then an integer and an indication of the ancestral subtypes, e.g. CRF01_AE (Robertson et al., 2000). Nomenclature for confirmed HCV recombinants follows this model, e.g. RF 01_1b2k (Simmonds et al., 2005). HIV-1 recombinants of unknown ancestry are designated by the prefix ‘U’.
Statistical inference is a logical framework for falsifiable reasoning, which enables its users to articulate and evaluate alternative hypotheses with clearly defined outcomes and quantified confidence levels (Motulsky, 1995; Sokal & Rohlf, 1995). In this approach, a desired overall confidence level is chosen, and mutually exclusive hypotheses are evaluated in light of this level of confidence. The null hypothesis is the hypothesis of no effect, and is contrasted with an alternative hypothesis. Should sufficient evidence exist the chance that a false positive will result from a test will be acceptably low and the null hypothesis can be rejected in favour of the alternative, with known confidence. Otherwise, insufficient evidence to reject the null hypothesis results. For subtype classification, the null hypothesis states that some sequence does not represent or originate from any known subtype. Alternatively, it does, and a subtype designation can be assigned to the sequence.
The challenge of identifying recombinants, those sequences that represent a mosaic of two or more different subtypes, is an extension of the problem of viral subtype classification. For non-recombinants, a sequence fragment may be classified as representative of an entire viral genome. While this assumption may generally be valid, a true recombinant will not be identified when a sequence fragment is analysed for subtype classification, because one clearly defined subtype assignment is expected to result. In the absence of recombination, inferences from different genomic regions of the same isolate should yield the same subtype.
The branching index (BI) was introduced in earlier work to characterize HIV-1 recombinants (Wilbe et al., 2003). It is a ratio that varies from 0 to 1. Here, we study properties of the BI and consider its utility as a test statistic for classification of subtypes of both HCV and HIV-1. To establish critical threshold values and error rates for subtype inference, we tested the hypotheses stated above by computing the BI and comparing it with distributions obtained from experimental situations where test results are known.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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) and HCV (Kuiken et al., 2005) databases at Los Alamos National Laboratory (http://www.hiv.lanl.gov/content/index and http://hcv.lanl.gov/content/hcv-index, respectively), which are freely available and curated to represent the known diversity of viral subtype variants. Reference alignments provide a nomenclature framework for subtype classification with the BI. New sequences were compared with training data with labels assigned previously, in the spirit of supervised learning. Phylogenetic signals in the reference alignments enable classification of new sequences. Subtype labels are assigned to new sequences such that they reflect the nomenclature and classification scheme of the reference sequences.
We used PAUP*, version 4.0b10 (Swofford, 2002), and its implementation of the BioNJ algorithm (Gascuel, 1997) to construct phylogenies based on F84 distances (Felsenstein, 1984). This method has computational speed sufficient for the very large number of trees (>50 000) we needed to construct, and has been shown to infer trees with reasonable accuracy and reliability in previous investigations (Hillis et al., 1994; Leitner et al., 1996; Gascuel, 2000; Felsenstein, 2004; Hraber et al., 2006). Neighbour-joining (NJ) quickly gives an approximate tree for phylogenetic inference, but the more computationally intensive method of maximum-likelihood (ML) is sometimes preferred. To evaluate the robustness of BI values to alternative methods of phylogenetic inference, we performed a comparative analysis using NJ and ML phylogenies from 100 non-overlapping fragments spanning the viral genomes. We compared the resulting BI values using a null hypothesis of no significant difference, which is equivalent to stating that the expected difference between the BI values is equal to zero. Alternatively, a significant difference in BI values resulting from different methods would indicate that the measure is influenced by the methodology with which the tree is obtained.
Because the amount of phylogenetic signal is known to vary with nucleotide position in viral genomes (Leitner et al., 1997; Hraber et al., 2006), we determined the smallest window sizes required to recover phylogenies that properly group sequences of the same subtype together into the same clade. We tested each position in both the HIV-1 and HCV reference alignments iteratively for whether the corresponding tree topology grouped related subtypes together properly, starting with a 10 nt window. If related subtypes were not grouped we increased the window size by 1 nt on the 3' end of the window and repeated the test until either a proper phylogeny was obtained or the window extended beyond the length of the alignment. Resulting window sizes were subsequently used to calibrate BI thresholds.
The tree-topology test for proper subtype groupings applies a reduction rule to Newick-formatted trees: (x, x) maps to x, where x is a taxon label, i.e. viral subtype. When this reduction rule is applied recursively until no difference in trees results, an improper tree topology will not reduce fully, such that each taxon label is represented only once, while a proper tree will. To illustrate, consider two examples, first this tree: (((x, x), (y, y)), (z, z)). It reduces fully to a proper tree: ((x, y), z). In contrast, this second tree groups sequences from subtypes x and y improperly: (((x, y), (y, x)), (z, z)) and yields a tree that does not reduce fully: (((x, y), (y, x)), z).
Applying this criterion to trees in subsequent analysis ensured that the tree topologies are concordant with tree topologies from the whole-genome reference alignment. The trees on which the BI is computed are thus proven to contain sufficient phylogenetic signal to maintain subtype-specific clades, rather than clustering any number of different subtypes together improperly into clades.
BIs.
The BI quantifies how well a query sequence clusters with the nearest subtype clade (Wilbe et al., 2003). It is computed as a ratio: 
a/(a+b), where a is the length of the branch that connects the most recent common ancestor of the query sequence and the nearest subtype clade to the basal portion of the tree, and b is the length of the branch that connects the same ancestor to the subtype clade (see Wilbe et al., 2003). (The length of the branch that contains only the query sequence at its tip does not enter the calculation.) The sum (a+b) is the length of the branch for the subtype clade, and a increases (while b decreases) as the query sequence grows more similar to sequences in the subtype clade. If the query sequence is clearly within a clade of sequences all having the same subtype, the BI is 1 (b=0). Conversely, if the query sequence is connected to the tree above (more basal than) multiple subtype clades, the BI is 0 (a=0). A BI near 0 indicates a distant relationship between the query sequence and the nearest subtype clade, while a value near 1 indicates a close relationship.
BI threshold calibration.
BIs quantify relatedness of a focal taxon with another taxonomic group in a phylogenetic tree. Use of BIs to test hypotheses requires understanding of distributions of BI values obtained from situations where taxonomic relations are known a priori. To establish error rates when using BI thresholds for taxonomic inference, we performed a resampling experiment with whole-genome reference sequence alignments. We performed separate analyses for HIV-1 and HCV. Subtypes treated in this analysis were required to have three or more representatives present in the reference alignment, to maintain clearly defined subtype clades, and thereby satisfy the experimental design described below. As more subtypes are confirmed by whole-genome sequencing from independent isolates, they can be studied similarly. In the interim, we treated available confirmed subtype sequences as representative samples.
The resampling experiment considered two alternative situations, one in which sequences of the same subtype as the query sequence were absent (situation 1) and one where they were present (situation 2). Situation 1 represents the case where a newly obtained sequence is not already represented among known subtypes, or negative-subtype test results, while in situation 2, the subtype has been described previously, yielding positive-test results. We sampled random sequence fragments and computed a pair of BI values for each. The focal taxon was randomly selected, provided that no less than two other sequences of the same subtype were in the alignment, to establish well-defined clades, consistent with methods used in earlier investigations of the BI for HIV-1 (Wilbe et al., 2003). We computed BI values from sequence fragments no smaller than the minimum window size required to obtain trees with proper topologies, as described above. Window sizes from one to four times the minimum window size were randomly chosen. The resulting trees were tested for proper subtype topologies, to ensure that sequences of the same subtype were grouped into proper clades that reflect known phylogenetic relations. We computed pairs of BI values for both alternative scenarios using the same focal taxon, genome location and window size. In this manner, we sampled 10 000 random replicate fragments and computed pairs of BI values for each virus. We hypothesized that the BI should be significantly greater for test outcomes with known positives (situation 2) than for test results from known negatives (situation 1).
The resulting BI distributions were compared to established false-positive (specificity) and false-negative (sensitivity) error rates for statistical hypothesis tests (Motulsky, 1995; Sokal & Rohlf, 1995), and to establish threshold BI values with optimal performance in light of these error rates, as described previously (Wilbe et al., 2003). We used R (version 2.6.1) for data visualization and analysis (R Development Core Team, 2007), and Bioperl (version 1.4.0) to parse trees (Stajich et al., 2002). A web-based utility to compute BIs for viral classification is available for public use. It aligns a query sequence with the viral reference alignment, computes BI values by sliding a window over the length of the query sequence, and reports the results as a profile function of window locations. The sequence provided must be at least 200 nt. Two versions of the utility are available online (http://www.hiv.lanl.gov/content/sequence/phyloplace/ and http://hcv.lanl.gov/content/sequence/phyloplace for analysis of HIV and HCV sequence data, respectively). BI values are sufficiently simple to compute manually from a tree having known branch lengths with no requirement for additional software.
Recombinant detection.
To illustrate BI utility for recombinant analysis, we constructed synthetic recombinants of HIV-1 and HCV, with breakpoints every 1000 nt, from complete genome sequences of two distinct subtypes (HIV-1 B and D and HCV 1b and 2a) not represented in reference alignments (GenBank accession nos AY835770
[GenBank]
, DQ054367
[GenBank]
, M58335
[GenBank]
and AF2384811). These sequences were aligned to the reference genomes with CLUSTAL W, version 1.83 (Thompson et al., 1994), synchronized to the reference alignments via the SynchAligns tool (Calef et al., 2005), and spliced together from alternating 1000 nt blocks, yielding synthetic HIV-1 B/D and HCV 1b/2a recombinants. We computed BI profiles from sliding windows of 400 nt, with 40 nt offsets between windows, i.e. two successive windows overlap by 360 nt, with 40 nt between their midpoints.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). The difference in scale between the two phylogenies indicates greater overall distances for the HCV than for the HIV-1 M group phylogeny.
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, window sizes range from 52 to 1231 nt, with median and mean of 321 and 402 nt, respectively) than for HCV (Fig. 2d, window sizes range from 9 to 473 nt, with median and mean of 44 and 58 nt, respectively). Thus, more sequence information is required from HIV-1 than HCV to recover a phylogenetic signal that groups subtype sequences together into proper clades. The minimum window size required for proper phylogenies varies with genome location, and is greatest at the 5' end of both viral genomes. Indeed, using windows with a size equal to the median provides insufficient phylogenetic signal half the time. Instead, either window sizes specific to their genome location, or larger window sizes should be used for subtype sequence analysis. For HIV-1, window sizes of 692, 842 and 946 nt yield proper topologies for 85, 90 and 95 % (respectively) of all positions in the viral genome. For HCV, window sizes of 73, 86 and 124 nt yield clade-specific tree topologies for 85, 90 and 95 % (respectively) of aligned genome locations.
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), as does the heterogeneous distribution of variable sites (Fig. 2c and f). Small windows correspond to gap-free regions that are enriched for high sequence variability, while large windows are needed to extract phylogenies with proper subtype groupings from gap-rich or highly conserved regions.
BI threshold calibration
Evaluation of cumulative BI distributions from experimental situations with known outcomes provides error estimates for subtype classification inferences (Fig. 3). BI values from positive-test cases are greater than BI values from negative-test cases (Fig. 4). For both HIV-1 and HCV, the difference in BI values for paired observations (positive and negative cases from the same window and focal taxon) is significantly greater than zero (P<10–15 by one-sided, one-sample Wilcoxon signed rank test, 95 % CI >0.63 for HIV-1 and >0.69 for HCV). Cumulative distributions of BI values provide calibration of sensitivity and specificity levels for varied threshold BIs (Fig. 3). Balancing the error rates yields BI thresholds of 0.663 for HIV-1 and 0.711 for HCV, with 93.5 and 95.1 % accuracy, respectively (Table 1). Using different cut-off values alters the balance between sensitivity and specificity, should some trade-off be needed, such as for greater sensitivity or in consideration of specific subtypes (Table 1, Fig. 3).
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). Consider, for example, HIV-1 fragments from subtype B and sub-subtype F1. For subtype B, 23.6 % false positives and 3.7 % false negatives occur at the overall BI threshold of 0.663. When a higher threshold BI of 0.747 is used, false positives and false negatives occur with an equal frequency of 9.1 % (Table 1, Fig. 5b and e). Conversely for sub-subtype F1, the false-positive and false-negative rates are 6.2 and 13.5 %, respectively, at the overall BI threshold of 0.663. Lowering the BI threshold to 0.612 yields equal misclassification rates of 9.6 %. Similarly for HCV subtypes 1c and 2b, imbalanced error rates can be ameliorated with a different threshold than the overall optimum (Table 1, Fig. 6c and e). The overall threshold may suffice in most situations, unless greater sensitivity or specificity is required.
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). When stratified by focal taxon, BI distributions vary less uniformly over the viral genomes (Figs 5 and 6). While BI classification accuracy is very reliable across all subtypes, some regions of particular subtypes are more difficult to classify than others. Regions having wrong subtypes inferred by BI analysis appear as vertical red lines in Fig. 5 for HIV-1 and Fig. 6 for HCV. As expected, the most challenging HIV-1 cases for BI classification are subtypes B and D, and sub-subtypes F1 and F2 (Fig. 5b, d, e, f). These have diverged more recently than other clades (B/D and F1/F2, Fig. 1a). Regions that confound classification with the BI for subtypes B and D are clustered around the vpr region into tat. The 5' end of gag and the gp41 region of env also confound subtype B classification. Challenging regions for sub-subtypes F1 and F2 are clustered around 5' env (gp120), and for F1, 5' gag. For HCV, misclassifications are more uniformly dispersed over the genome, and greatest for subtype 2a, followed by 1c and 2b. Despite infrequent inferential errors, strong separation between BI values from cases with known positive- and negative-subtype assignments is clearly evident across subtypes (Figs 5 and 6).
Recombinant detection
Recombination patterns are clearly evident from profiles of BI values obtained from sliding windows over HIV-1 and HCV genomes (Fig. 7). BI values are lower than the threshold for significance, and thus indeterminate, where windows overlap with recombination breakpoints. Chimeric fragments should and do indicate indeterminate subtype assignments. Conversely, BI values are greatest when sequence fragments are obtained from windows that do not overlap breakpoints. These are contiguous blocks of sequences from one subtype, and should be readily classified. Subtype assignments are most often identified with BI values of 1, though the specific sequences from which synthetic recombinants were derived are absent from the reference alignments. While no misclassifications for HIV-1 are seen for windows that do not overlap breakpoints (Fig. 7a), some window regions yield no subtype classification between nt 7360 and 7960 of the HCV alignment (Fig. 7b) or 7315 and 7815 in the H77 reference genome (Kuiken et al., 2006). This region corresponds to the boundary between NS5a and NS5b and is enriched with gaps to align the start (5' end) of NS5b (see. Fig. 2e). Otherwise, BI values are lowest (classification uncertainty is greatest) for fragments that overlap breakpoint regions. Interestingly, this highlights the vicinity where chimeric splicing is found and locates positions of recombination breakpoints.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Interestingly, to obtain proper subtype trees, HCV requires only surprisingly short sequences, typically fewer than 50 nt, while HIV-1 requires much longer sequences, approximately 340 nt. This is explained partly by the fact that the HCV subtype tree is more diverse and relatively less affected by indels than the HIV-1 subtype tree. Because of these observations, we recommend against using fragments shorter than 300 nt for HIV-1 subtype inferences. Investigators should strive to include at least as many nucleotide characters as suggested in Fig. 2 for subtype classification. Phylogenetic trees used to infer subtypes should be evaluated for proper groupings of known subtypes into clades, or the resulting inferences will be of little worth.
Next, we used a resampling technique to establish inferential error rates (false positives and false negatives) associated with using the BI to classify arbitrary sequence fragments into subtypes, from pairs of observations where sequences from the same subtype were either present or absent from the reference sequences. By creating hypothetical situations in which the query sequence clade has no known siblings, we simulated the distribution of BI values for unknown subtypes, which correspond to negative results for subtype classification. We used the resulting error functions to establish threshold BI values and test the hypothesis that any given fragment originates from a known subtype, with known confidence. Confidence is evaluated in light of the false-positive error rate, which can be made more or less stringent as needed, but with a resulting shift in the false-negative error rate. Such trade-offs are standard among diagnostic tests. Falsifiable hypothesis testing allows for indeterminate outcomes among known subtype classifications when the null hypothesis cannot be rejected. This is a useful and important way to infer when a novel subtype has been discovered, and also to identify a mosaic of multiple subtypes, as is the case for recombinants.
For HIV-1, the threshold value for subtype inference that balances sensitivity and specificity is greater than reported previously, 0.55 (Wilbe et al., 2003) versus 0.66 here. The difference may be explained as resulting from a modified experimental design, with paired observations and inclusion of observations where BI=1 or 0. Also, the earlier study refrained from attempting to distinguish between sub-subtypes F1 and F2, or between subtypes B and D (Wilbe et al., 2003).
Finally, we used synthetic recombinants with known breakpoints to illustrate the utility of the BI for recombinant detection. Recombination is a significant challenge for classifying viral subtypes because a mosaic of multiple different subtypes can be present in a single viral sequence. Single-subtype classifications are unreliable in the presence of recombination. To deconvolve the mosaic phylogenetic signal, recombination breakpoints must be detected. Profiles of BI values from fragments that span long stretches of the HIV-1 and HCV genomes have maxima farthest from breakpoints, and minima at breakpoints. Hence, the BI can be used to classify sequences into subtypes in a falsifiable manner, and also to detect recombinant sequences.
A primary advantage of falsifiability here is that it can indicate when a sequence is unclassifiable among known subtypes. This is important in surveillance for new variants, in epidemiological analysis of transmission patterns and in detection of recombination involving different subtypes (whether or not the subtypes are already known), which might otherwise be misclassified as one new subtype. Previous approaches to the problem of viral subtype classification used pair-wise sequence distances (van Regenmortel, 2007), phylogenetic bootscanning (Salminen et al., 1995; de Oliveira et al., 2005) or probabilistic models (Schultz et al., 2006), but invariably classify a sequence among established subtypes. The BI uses a combination of distance and phylogeny methods to infer subtype classifications falsifiably, and can thereby indicate unclassifiable results.
Despite numerous advantages, no technique is without limitations. Indeed, the classification method used by the BI is basically one of supervised learning, in which an algorithm is applied to training data having known properties, and new test cases are evaluated in the light of the training data. Because misclassified training data can influence the outcome of inferential tests on new data, their accuracy is essential for reliable results. Several authors of this study are actively involved with community-supported activities to formalize HIV and HCV subtype nomenclature (Robertson et al., 2000; Leitner et al., 2005; Simmonds et al., 2005). To support this need, and to facilitate subtype classification and other challenges related to sequence analysis, we maintain carefully curated alignments of reference sequences (see Leitner et al., 2005; Simmonds et al., 2005 for examples). All sequences in the reference alignments are freely available, as are the alignments themselves. Utility of the BI for subtype classification will be limited in other viruses, until reference alignments become available.
We have used a resampling approach that is different from bootstrap resampling of characters for phylogenetic inference. Bootstrap resampling repeatedly computes many replicate trees by randomly sampling characters (e.g. nucleotide positions) with replacement, to quantify support for nodes in phylogenetic trees. We encourage this practice, independent of BI analysis, among investigators who wish to quantify bootstrap confidence. We resampled regions of the viral genome, rather than nucleotide characters, to quantify classification accuracy of the BI, from paired observations with known positive and negative outcomes. Our analysis of minimum window sizes required to recover unambiguous, subtype-specific clades provides confidence that the inferred tree has the topology of the whole-genome reference alignment.
The BI combines distance and phylogenetic approaches to enable fast, accurate, objective subtype inference and recombinant detection. Such inferences facilitate molecular epidemiology investigations, are clinically relevant for anti-HCV therapy, and may ultimately become part of the decision-support process for HIV-1 treatment.
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ACKNOWLEDGEMENTS |
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Received 12 December 2007;
accepted 29 April 2008.
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