Table 1 lists the 12 H. influenzae clinical strains and the reference strain Rd, a largely non-pathogenic strain, used in the comparative genomic studies described herein, their NCBI locus tags, the location where the sequencing was performed, and their clinical origins. Nine of the clinical strains were sequenced using 454 LifeSciences novel pyrosequencing technology 25. The number of sequencing runs, the extent of genomic coverage, and the number of contigs resulting from first and in some cases second pass assemblies are tabulated (Table 2).

Gene clustering parameters for the grouping of homologs were empirically determined by minimizing the change in the number of clusters per change in the parameters (Figure 1). We hypothesize that this minimum point coincides with the best estimate threshold for distinguishing true orthologs from functionally distinct homologs. Some homologs will be more similar than 70%, while some orthologs will be more divergent than 70%, but as a uniform criterion, the threshold is optimized. Visual inspection of the clusters reveals that most clusters are reasonable. Mosaic genes were particularly difficult to cluster due to high levels of rearrangement. In the remainder of the paper, genes in the same cluster are considered to be the same gene.

We identified 2,786 gene clusters among the 13 strains (Table 3). Of these, 52% were found in every strain (core genes) and 19% were found in only a single strain (unique genes). The remaining 29% of genes were found in some combination of two or more strains, but not all (distributed genes; Figure 2). The number of clusters found per strain varied from 1,686 in PittEE to 1,878 in PittII (Table 4). All strains possessed some unique genes not seen in any of the other strains. A pair-wise comparison was performed among all possible strain pairs, which determined the mean number of genic differences between any two strains was 395 with a standard deviation of 94 (Figure 3). This analysis also identified minimal and maximal genic differences of 81 and 577, respectively, for the strain pairs 2866:PittII and 2866:PittAA. The number of coding sequences identified per genome by AMIgene did not correlate strongly with genome size. This is likely due to the presence of split open reading frames (ORFs) in the 454 sequenced genomes as an analysis of the 4 completed genomes showed a linear relationship between gene number and genome size with an R² = 0.910. In contrast, the correlation between total gene clusters and genome size is 0.86, implying that the number of distinct genes found on the genome is linearly related to the genome size.

A dendrogram based on non-core genic differences (Figure 4a) demonstrates the diversity in the NTHi population. A typical strain differs from its nearest neighbor by more than 200 genes. The strains collected from otitis media with effusion (OME) patients at Children's Hospital in Pittsburgh (designated as Pitt strains) show that a genetically diverse population can be isolated contemporaneously from a single geographic location from patients with similar indications. In contrast, two pairs of strains, PittEE/R2846 and PittII/R2866 are relatively similar despite geographically distinct points of isolation. Interestingly, the laboratory strain Rd KW20 is not an outlier among the clinical strains. For comparison, a maximum likelihood tree was generated using sequence from seven multi-locus sequence typing (MLST) housekeeping genes for the same set of 13 strains (Figure 4b). The topology of the trees is significantly different, both in terms of pairwise groupings and overall structure.

The identified number of new genes and core genes found per addition of each genome (as determined by incremental clustering of the 13 strains) shows an exponentially decaying trend in both cases (Figures 5 and 6). Qualitative inspection suggests a diminishing return on new genes found in future sequences, though it is expected that approximately 40 new gene clusters will be found in each of the next few genomes that are sequenced. The number of core genes appears to trend towards a horizontal asymptote near 1,450 genes. A quantitative analysis of these results is developed below in the section 'Mathematical development of a finite supragenome model'.

Whole genome alignments were generated between Rd and each of the 12 clinical strains to quantify genomic insertions and deletions independently of gene identification (Table 5). On average, each of the clinical strains had 127 genomic insertions (>90 base-pairs (bp) in length) that did not correspond to any Rd KW20 sequence. Similarly, each clinical strain contained, on average, 147 genomic deletions (>90 bp) when compared to the Rd KW20 strain. The average total length of non-matching sequences between the 12 clinical strains and Rd was 321 kb, approximately 18% of the genome. The quantity of non-matching sequences reasonably accounts for the average of 390 genic differences between strain pairs. Figure 7 shows a genomic region in which two different forms of an insert, homologous to the plasmid ICEhin, have integrated into the same site of two different genomes, but which is wholly absent from the other strains in the alignment. Similarly, a 40 kb contiguous region in Rd shows extensive deletional diversity among seven of the clinical strains, with only two of the clinical strains demonstrating the same local genomic organization (Figure 8). Interestingly, the two strains, PittAA and PittEE, that are similar in this region are highly divergent overall (Figure 3). Genic diversity also exists on a smaller scale. Figure 9 displays a 20 kb region from 7 clinical strains that shows 5 different combinations of possession and loss of the lic2C gene, the NTHI0683 gene, and the UreABCEFGH operon.

Global genomic alignments of PittEE against R2846 and R2866 were performed (Figures 10 and 11). PittEE and R2846 are very similar at the global level and this is reinforced by the gene cluster analysis, which revealed only 96 genic differences. In contrast, R2866 has a large inversion and several large insertions and deletions with respect to PittEE. This diversity at the global level corresponds to the 377 genic differences identified between these two strains by cluster analysis (Figure 3). Global alignments were not visualized for most strains since the ordering of the contigs had not been determined.

The codon usage of each gene cluster was compared to the typical H. influenzae codon usage pattern by the epsilon-score calculated by CodeSquare 26. A low epsilon score indicates that a gene's codon usage is similar to typical patterns of the organism, while a high score indicates atypical codon usage. Since the epsilon score is partially dependent on the length of a coding sequence, all scores were normalized by length. The average normalized score is 0 and low values continue to indicate typical codon usage. Figure 12 is a scatter plot of the normalized epsilon scores versus the number of strains in which the gene was found. The range of normalized epsilon values is similar for core, distributed, and unique genes, though the median values are slightly higher for distributed and unique genes (Tables 6 and 7). The Mann Whitney U-test was employed to determine the significance of this difference. To eliminate any remaining length bias, only genes with lengths of 200-300 amino acids were analyzed. The median normalized-epsilon value of core genes is significantly smaller than the medians of distributed and unique genes, and as a consequence, these non-core genes are more likely to have foreign origins. Interestingly, there is no significant difference between distributed and unique genes and most of these non-core genes display typical H. influenzae codon usage.

Phage insertion is a common origin of genomic diversity. The influence of phage was quantified by a homology search between all gene clusters and the NCBI NT database. A gene cluster was said to be 'phage associated' if one of the top ten significant matches was annotated as a sequence of phage origin. Overall, 9.3% of gene clusters were phage associated. The distribution of these genes is not uniform among core and non-core genes. Only 0.3% of core genes were phage associated, while 14.6% and 25.8% of distributed and unique genes, respectively, were phage associated (Table 8).

The comparative genomic data presented above are supportive of the DGH and reinforces the concept that, at the species level, there is an H. influenzae supragenome that is much larger than the genome of any single individual strain, and hence many strains must be sequenced to generate an accurate picture of the species supragenome. Among the questions we may ask about the supragenome, the most obvious is, how many strains must be sequenced to observe the entire (or nearly all) of the supragenome?. The problem is similar to determining the read coverage necessary to sequence an entire individual genome using a random shotgun library approach. Lander-Waterman statistics provide an answer in the latter case by using the assumption that reads are independently and randomly sampled from the genome with equal probability. Previously, Tettelin et al. 27 developed a supragenome model for S. agalactiae that, like Lander-Waterman statistics, is based on the assumption that contingency genes are independently sampled from the supragenome with equal probability, except in the case of rare genes, which are modeled as unique events that appear only once in the entire global population. The model requires four parameters: the number of core genes, the number of contingency genes, the probability of finding a contingency gene, and the expected number of 'unique' genes found per strain. This model predicted that the supragenome of S. agalactiae is infinite in size (that is, the expected number of unique genes found in each strain is non-zero). While the model is an insightful attack on the problem, we question the assumption that contingency genes are sampled in the population with equal probability. It is important to compare the existing model against a new model that does not rely on this assumption.

The Supragenome is represented here by a generative model that emits genomes according to a set of probabilistic rules. The supragenome contains N genes that are modeled as Bernoulli random variables with 'success' probabilities that correspond to the population frequency of each gene. A genome is generated by observing the Bernoulli variables: a gene is present if the corresponding trial is a success and otherwise absent. Each gene variable is assumed to be independent of all other genes. This assumption is sometimes violated in real H. influenzae genomes. For example, genomic islands are sets of genes that are not independent. However, we proceed with this assumption since it significantly reduces the complexity of the model and is reasonable in many cases.

The true population frequencies are, in general, unknown. Therefore, population frequencies are also treated in a probabilistic fashion. It is assumed that there are K discrete classes of genes. Each class k has an associated population frequency, μ_k. All genes in class k will have population frequency μ_k. Each of the N genes is assigned to a class according to a probability distribution given by the vector π, where π_k is the probability that a gene is assigned to class k. Conceptually, π_k is the percentage of genes in the supragenome that have population frequency μ_k. The assignment of a gene to a class is independent of all other gene assignments.

The complete model is depicted in plate notation in Figure 13. 'Z' is the hidden class variable in which z_n corresponds to the class of gene n. 'X' is the observed gene variable, where x_n,s corresponds to the presence or absence of gene n in strain s. The outer plate represents the supragenome, while the inner plate represents instances of specific genomes. The model requires 2 × K + 2 parameters: N, K, a mixture coefficient π_k for each class, and a Bernoulli probability μ_k for each class. The number of gene classes, K, and their associated Bernoulli probabilities, μ_k, are fixed in advance. Care must be taken to choose classes that represent low and high population frequencies. Seven classes were selected for this study (K = 7) with associated probabilities μ = <0.01, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0>. The class with probability 1.00 represents 'core' genes that appear in all strains.

The remaining parameters, N and π_k, are selected under a maximum likelihood scheme. Suppose that |S| genomes have been sequenced and a particular gene from class k was observed in n of the |S| strains. The probability of this observation is given by a binomial probability since this result is the sum of independent Bernoulli variables. As a function of π_k and N, the probability is given by:

P ( x = n | z = k , μ k ) = | S | ! n ! ( | S | − n ) ! μ k n ( 1 − μ k ) | S | − n MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGqbWaaeWaaeaacaWG4bGaeyypa0JaamOBaiaacYhacaWG6bGaeyypa0Jaam4AaiaacYcacqaH8oqBdaWgaaWcbaGaam4AaaqabaaakiaawIcacaGLPaaacqGH9aqpdaWcaaqaamaaemaabaGaam4uaaGaay5bSlaawIa7aiaacgcaaeaacaWGUbGaaiyiamaabmaabaWaaqWaaeaacaWGtbaacaGLhWUaayjcSdGaeyOeI0IaamOBaaGaayjkaiaawMcaaiaacgcaaaGaeqiVd02aa0baaSqaaiaadUgaaeaacaWGUbaaaOWaaeWaaeaacaaIXaGaeyOeI0IaeqiVd02aaSbaaSqaaiaadUgaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaadaabdaqaaiaadofaaiaawEa7caGLiWoacqGHsislcaWGUbaaaaaa@5F3B@

However, we do not know the true gene class, so we must consider a mixture of binomial probabilities:

P ( x = n | π → , μ → ) = ∑ k = 1 K P ( x = n | z = k , μ k ) ⋅ P ( z = k | π k ) = ∑ k = 1 K π k | S | ! n ! ( | S | − n ) ! μ k n ( 1 − μ k ) | S | − n MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@84D9@

Now consider the complete set of genes. Let c = <c₀, c₁, ..., c_S>, where c_n is the number of genes observed that appear in exactly n of |S| strains. The probability of the total observation is given by a multinomial distribution:

P ( c → | N , π → , μ → ) = N ! c 0 ! c 1 ! ⋯ c s ! ∏ n = 0 | S | p ( x = n | π → , μ → ) C n = N ! c 0 ! c 1 ! ⋯ c s ! ∏ n = 0 | S | ( ∑ k = 1 K π k | S | ! n ! ( | S | − n ) ! μ k n ( 1 − μ k ) | S | − n ) C n MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@9EF7@

The parameters N and π can be determined by maximizing the log-likelihood of the observation c:

log ⁡ P ( c → | N , π → , μ → ) = log ⁡ N ! − ∑ n = 0 | S | log ⁡ ( c n ! ) + ∑ n = 0 | S | c n log ⁡ ( ∑ k = 1 K π k | S | ! n ! ( | S | − n ) ! μ k n ( 1 − μ k )