Original article Evolutionary rates and HBV: issues of rate estimation with Bayesian molecular methods

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1 Antiviral Therapy 2013; 18: (doi: /IMP2656) Original article Evolutionary rates and HBV: issues of rate estimation with Bayesian molecular methods Remco Bouckaert 1 *, Mónica V Alvarado-Mora 2, João R Rebello Pinho 2 1 versity of Auckland, Auckland, New Zealand 2 Laboratory of Tropical Gastroenterology and Hepatology João Alves de Queiroz and Castorina Bittencourt Alves, Institute of Tropical Medicine, Department of Gastroenterology, versity of São Paulo School of Medicine, São Paulo, Brazil *Corresponding author remco@cs.auckland.ac.nz Background: HBV infection is a public health problem affecting approximately 2 billion people and leading to >350 million chronic carriers of the virus worldwide. Phylogenetic analysis can give valuable insight to help in clarifying the history of viral infections around the world and in elucidating routes of transmission of the different viral strains present in the infected host population. These analyses rely on an accurate estimate of the rate of mutations. Methods: In this study, we investigated the robustness of rate estimations based on Bayesian analysis obtained so far and examined, in particular, the choice of prior for the substitution rate. Results: Most previous studies have concentrated on estimating the parameters of simple demographic models for HBV, such as exponential growth and constant population size. Here, we introduce a method that automatically partitions the genome in components that show a different rate of mutation and fit different substitution models. Conclusions: In conclusion, we find that, due to inaccuracy in the sampling dates from the samples where viral sequences were obtained, lack of a sufficiently large geographical and time spread of available and trustworthy sample dates, sensitivity to priors and model misspecification and rate estimation based on molecular methods, are not reliable. We suggest that rate estimates taking into account calibration points based on relevant historical events are more robust due to the lack of trustworthy sampling dates. For example, the known history of colonization of the Americas should be used to accurately study the current diversity of genotype F, which is the most frequent genotype in almost all Spanish speaking countries in South America. Introduction HBV belongs to the Hepadnaviridae family. Its members are divided into two genera; Orthohepadnaviruses, infecting mammals, and Avihepadnaviruses, affecting birds [1]. HBV infection in humans presents a global health problem. Worldwide, 2 billion people, or one-third of the world's population, have been infected with HBV [2]. The HBV genome is a partially double-stranded circular DNA molecule of approximately 3.2 kb in length. It contains four partly overlapping open reading frames: pres1/ pres2/s (S), precore/core (C), polymerase (P) and X [3]. Molecular variation and sequence changes in the HBV genome over time have resulted in the emergence of ten genotypes, A to J, which HBV has been classified into, based on the sequence divergence over the entire genome [4 7]. Genotype A is found mainly in north and west Europe, North America and Africa. Genotypes B and C are prevalent in south-east Asia and the Far East. Genotype D has worldwide distribution and is found predominantly in the Mediterranean region. Genotype E is predominant in the West/Central African crescent spanning from Senegal to Angola [8 10]. Despite the extensive spread of genotype E in this crescent, the virus is marked by a peculiar low overall sequence diversity of 1.75% over the whole genome [8]. Genotype F has been identified as the most prevalent in Central and South America and it is mainly found among native indigenous people from South America [11]. Genotype F can be further divided into four subgenotypes, F1 to F4, with a genetic divergence of % [12]. Genotype G has been reported in the ted States and France [13]. Genotype H has been mainly described in Central America and Mexico [14]. Genotypes I and J have been identified in Vietnam and Borneo [7]. Two opposing forces can be discerned in terms of the diversity of HBV. First is the error-prone polymerase, 2013 International Medical Press (print) (online) 497

2 R Bouckaert et al. producing a high rate of nucleotide substitutions. Second, the extreme compactness of the genome prevents the occurrence of a large degree of genetic variability due to the overlapping open reading frames [15]. The true age of HBV is still the subject of much debate; however, a closer inspection of available genome sequence data indicates that the evidence for long-term codivergence is weaker than might be expected. The most divergent human genotypes are observed in populations either from the New World (genotypes F and H) or from Asia (genotype B). In some instances genotype F, predominant in the Americas, was the first to diverge, suggesting that the virus arose in the New World; by contrast, in other trees, sequences from genotype B, prevalent in East Asia, were the most divergent [16]. Sampling dates give information about the rate of evolution, and the difference between sampled sequences, together with the rate of evolution, give information about time of most recent common ancestors (MRCA) of a set of sequences. These MRCA times can be related to historic events. In this study, we investigate the factors that affect accuracy of substitution rate estimation based on molecular methods, from the sampling dates available to the diverse substitution rates that are presented in a virus with overlapping open reading frames that code for 1.5 proteins, which would be expected from its genome length. For this goal, we consider a number of previous molecular-method-based analyses and compare the sample dates. Due to the overlapping reading frames of HBV, it is expected that different parts of the genome follow a different evolutionary rate. We introduce a method for automatically partitioning the genome and determine a substitution model and mutation rate for each of the partitions. Methods Robustness of rate estimations Since mutation rate estimates obtained from previous authors varied by 1 order of magnitude, we investigate robustness of the previously published rates by Zhou and Holmes [17], Alvarado-Mora et al. [18], Torres et al. [19] and Harrison et al. [20]. All experiments were performed using Markov Chain Monte Carlo (MCMC) methods, as implemented in BEAST 2.0 [21]. The MCMC chains were run long enough to ensure convergence, which was verified by inspecting the effective sample size. In all experiments, effective sample size was 100, but in most cases was much larger than 200. The sequence dataset utilized by the authors is available upon request. Robustness of sampling dates Mutation rate estimation using molecular methods is based on the dates that sequences are sampled. To test robustness of sampling dates, we used 19 full genome sequences from Harrison et al. [20] and applied the same model as in that study: the Hasegawa, Kishino and Yano (HKY) [22] substitution model with four gamma categories, a coalescent tree prior with a constant population size and an uncorrelated log normal distributed (UCLD) relaxed clock branch rate model. For the sample dates, we subtracted a value uniformly drawn from the interval 0 to 5. Choice of priors Another question that arises in any Bayesian analysis is the choice of priors. We examined, in particular, the choice of priors for the substitution rate. Three different priors were used to achieve more accurate estimated rates. By default, Bayesian evolutionary analysis utility, the graphical user interface used to specify BEAST analysis, suggests a uniform prior. Older versions, for example the one used in the analysis by Zhou and Holmes [17], do not even suggest there is another choice. We considered Jeffreys prior (also known as one-over-x prior) and an uninformative gamma prior (gamma 0.001, 0.001) as alternatives to the uniform prior. These were applied to the full genome alignments (among patients) from Harrison et al. [20] for the HBV A, C, D, E and F genotypes. We used the HKY substitution model with invariant sites, UCLD relaxed clock and coalescent tree prior with constant population. Overlapping reading frames and estimation of the substitution model Overlapping reading frames mean simple substitution models may not be appropriate. Different parts of the genome have different substitution rates. The presence of different coding genes along the HBV genome, using overlapping reading frames, suggest different substitution rates for different regions covering different genes. We propose a new model where we partition the genome in k consecutive parts. The boundaries of the partitions is randomly assigned and changed throughout the MCMC run. For each partition, a different substitution model is used. Since we do not know which substitution model is appropriate beforehand, we estimate the substitution model using a reversible-jump based method. The substitution model jumps between the following models: Felsenstein [23] (F81), HKY, Tamura and Nei [24] (TN93), transitional model (TIM), symmetrical model (SYM) and generalised time-reversible (GTR). The number of free parameters increases from 0 for F81 to 5 for GTR, and these parameters have a gamma (0.2, 5) prior each. An experiment was performed on 68 full-genome HBV genotype F sequences using the above model with four gamma categories and invariant sites, since International Medical Press

3 Hepatitis B substitution rate this model gave the best fit. A UCLD relaxed clock and Bayesian skyline plot coalescent prior were applied. Results Sampling dates To check the robustness of sampling dates, we repeated the experiment cited above 15 times. Results are shown in Figure 1. Another test to see whether there is any information regarding sampling dates is to randomly re-assign dates among sequences. This experiment was repeated 100 times and results are shown in Figure 2. Choice of priors Sensitivity of choice of priors was determined for the substitution rates considering uniform, Jeffreys and gamma priors for full-genome alignments for HBV genotypes A, C, D, E and F. The results are shown in Figure 3. Estimation of the substitution model Estimation of substitution model rates was carried out as described above. Results are shown in Figure 4. Notice that three different substitution models (HKY, GTR and SYM) and different mutations rates are Figure 1. Robustness to sample dates Rate estimates, substitutions/site/year Experiment number Median Lower 95% HPD Upper 95% HPD Random delta 5, median Random delta 5, lower 95% HPD Random delta 5, upper 95% HPD Rate estimates where sample dates had a random number from the interval 0 to 5 subtracted from the sample dates. HPD, highest probability density. Figure 2. Information in sample dates Rate estimates, substitutions/site/year Experiment number Randomized median Randomized lower 95% HPD Randomized upper 95% HPD Median Lower 95% HPD Upper 95% HPD Sampling dates were randomly reassigned to taxa. HPD, highest probability density. Antiviral Therapy 18.3 Pt B 499

4 R Bouckaert et al. Figure 3. Sensitivity of rate to prior Rate estimates, substitutions/site/year A C D E F Prior Rate estimates in substitution per site per year shown as 95% highest probability density (HPD) intervals and indication of the median for HBV genotypes A, C, D, E and F. The first data bar of each genotype displays a uniform prior (), the second Jeffreys prior () and the third a gamma prior. Figure 4. Varying rates in different part of the genome 2.0 Estimated mutation rate, substitutions/site/year HKY GTR SYM GTR X Pre-C HKY C HKY HKY ,000 1,500 2,000 2,500 3,000 Genome site, base pair Estimated mutation rates for different parts of the genome relative to the first partition are plotted against the site in the genome. The model picks up changes in overlapping reading frames. Parts that code for the polymerase (P) gene only have highest mutation rates, whereas the range where S and P overlap has the lowest. C, core; GTR, generalised time-reversible model; HKY, Hasegawa, Kishino and Yano model; Pre-C, precore; SYM, symmetrical model International Medical Press

5 Hepatitis B substitution rate Table 1. Calibrated estimates GTR Partitioned Prior Median 95% HPD Median 95% HPD form to to to to to to Rate estimates for HBV genotype F assuming the time of most recent common ancestor is 300 years ago. Note that the sensitivity to the prior vanishes with this calibration. The generalised time-reversible (GTR) model gives slightly higher estimates than the partitioned model. Note that the partitioned model has a better fit to the data. HPD, highest probability density. the most appropriate in different regions of the HBV genome that approximately correspond to the presence or absence of overlapping reading frames. Time of most recent common ancestor Although the real time for the introduction of HBV genotype is not known and previous estimates for the MRCA vary from 96 to 1, years, we have chosen to use a date corresponding to historical facts. We hypothesized that genotype F had a great increase in its spread after European colonization in Latin America, approximately 300 years ago. This date is included in the time interval cited above. This gives a calibration for the MRCA of HBV genotype F in Latin America. We estimated rates using GTR plus 4 gamma plus I, a UCLD relaxed clock and a Bayesian skyline plot tree prior, as well as the partitioned model with the same clock model and tree prior. Results are summarized in Table 1. Discussion The issue of sample dates Consider the sequence with GenBank identification AB036905, which is a sample of HBV F3 from Venezuela. The GenBank submission year is 2009, whereas the journal submission year as recorded in GenBank is This already provides a choice of two sampling dates, although common sense says that the sampling date of the sequence should be 2000 or before. Anecdotal evidence suggests that these GenBank dates are being used in rate estimation studies. In the study by Harrison et al. [20] a sampling date of 1990 is used. The studies by Zhou and Holmes [17], who contacted all researchers for which there was no explicit sampling date in GenBank, and Torres et al. [19], who appear to have copied these dates, use a sampling date of We do want to point out that the discrepancy in dates could be traced, due to the excellent access to data provided by these studies. Therefore, the range of possible sampling dates for this particular sequence is 27 years. Note that the range of available HBV samples is just a few decades long. Fortunately, most HBV sequences have a less extreme range. But it does raise the question of how sensitive the rate estimates are to the accuracy of the sampling dates. Another issue is that sampling dates tend to be truncated to years [17,19]. For example, a sample taken on 31 December 1999 and another taken on 1 January 2000 are 1 year apart according to the sampling dates, whereas in reality they are just a day apart. Likewise, a sample from 31 December 2000 and another from 1 January 1999 are 1 year apart according to the sampling dates, whereas in reality they are almost 2 years apart. Figure 1 suggests that errors in the 0 to 5 range have a significant effect on substitution rate estimates. The effect is worse for errors in the 0 to 10 interval (unpublished observation). We conclude that accurate sampling dates do matter for estimating substitution rate. Furthermore, rate estimates appear very sensitive to the choice of prior. Note that the y-axis of Figure 3 is in a log scale. The median systematically decreases when using a different prior from the uniform prior. Furthermore, the 95 highest probability density intervals become orders of magnitudes larger. Together, this indicates that rate estimates are very sensitive to the choice of prior. An alternative interpretation is that the prior dominates the rate estimate. The reversible-jump-based substitution model has a posterior that is 100 log points larger than using GTR everywhere, which indicates that this model explains the data significantly better. Most of the genome is best explained using the HKY model, but the parts where S and P overlap and where X and P overlap are best explained by the GTR model. Estimating HBV substitution rates The notion that HBV has codiverged with animal populations over many millions of years is also incompatible with molecular clock estimates of the rate and timescale of viral evolution. The accurate estimation of nucleotide substitution rates in HBV is complicated by a number of factors, the most notable of which is the small size and overlapping nature of the HBV genome [25]. This results in strong selective constraints, so that substitution rates Antiviral Therapy 18.3 Pt B 501

6 R Bouckaert et al. measured in the short term may better reflect the intrinsic rate of mutation rather than the long-term rate of nucleotide substitution [25]. The first study estimating the substitution rate for HBV reported a rate between 1.4 and substitutions per site per year [26], obtained by dividing the amount from a single patient by the total length of the sequence, assuming the common ancestor for the viruses at the patient s birth. By using a similar approach, other studies based on pairwise sequence comparison sampled at different time points estimated a median substitution rate of [27] and [28] substitutions per site per year. Similar evolutionary rates have also been estimated for other Hepadnaviruses, such as duck hepatitis B virus: 0.8 and substitutions per site per year, respectively [29]. More recently, Alvarado-Mora et al. [18] used a coalescent-based approach to estimate the substitution rate for HBV genotype E of approximately substitutions per site per year. The common ancestor for the genotypes of human HBV would be >1 million years old if one assumes cospecies evolution. However, observed mutation rates and calculations based on genotype differences and human migration dates suggest that the HBV genome changes by a rate of approximately to 10-6 substitutions per site per year. Based on such rates, the genotypes would have separated 2,000 40,000 years ago, while subgenotypes and the X/C recombinant would have evolved 1,000 20,000 years ago. The origin of HBV is unclear. How and when the genotypes evolved and spread over the continents in humans and other species is not known. Several theories have been proposed, with both recent and distant emergence. The observation that HBV in apes and human genotypes A to E are more similar than are human genotypes F and H and genotypes A to E also points against cospecies evolution [16,30,31]. HBV genotypes may have evolved as a result of migration to separated geographical areas by humans carrying HBV (10,000 40,000 years ago). This idea is supported by the knowledge that an ice or land connection over the Bering Strait has joined present-day Alaska and eastern Siberia during several periods 10,000 to 25,000 years ago [32]. Finally, another theory suggests that the divergence of HBV has occurred by migration of infected persons into already populated areas. This model fits better with observed mutation rates [33]. The most extreme theory was the proposal that HBV originated from the Americas, and spread into the Old World as recently as 400 years ago [17]. The success of studies of viral evolution has been built on a combination of a growing database of gene and genome sequences coupled with advances in phylogenetic and coalescent methodology [25]. For all these results, an accurate estimate of mutation rates is crucial. As pointed out in the Results section, there are a large number of difficulties in estimating rates using current phylogenetic methods. We demonstrated that rate estimates rely on accurate sampling dates. Unfortunately, accurate sampling dates are not readily available. Furthermore, the rate estimate is rather sensitive to the prior. The implication is that the information before the analysis has a larger effect on the rate estimate than the data. A problem specific to HBV rate estimation is that the genome has overlapping reading frames. Therefore, it can be expected that different parts of the genome have different mechanisms of evolution. This makes it unlikely that a full genome analysis with a single substitution model for the whole genome, as is generally used, leads to good results. In fact, we demonstrated that by automatically partitioning the data allowing each partition to have its own substitution model results in a much better fit to the data. There are a number of other issues that make rate estimation cumbersome. For instance, it is known that hepatitis B e antigen (HBeAg)-postitive patients have a slower rate than HBeAg-negative patients. If the HBeAg status is known, this phenomenon can be modelled by allowing extra mutation towards branches to these taxa [20]. Another issue is that different genotypes evolve at different rates, so genotypes cannot be simply grouped together. Currently, there is not enough information in the sequences due to the small sampling range of just a few decades. Another issue that is specific to HBV is that there is a rather small amount of data available. The genome is just 3.3 kb long, which makes it hard to distinguish between 10-5 substitutions per site per year and lower rates. In selecting sequences for alignments, care should be taken not to include sequences with recombination, since this would increase the estimate. Current phylogenetic analysis techniques do not readily deal with recombination. Finally, it is important that samples need to be from treatment-naive patients. Otherwise rate estimate may be too high due to virus trying to mutate due to pressure by treatment. One step towards getting more accurate rate estimates is by obtaining samples from a wider range in time, for example, by sequencing mummies, as for instance from the recently found Korean case [34]. These samples are difficult to obtain due to lack of sample candidates, and issues with preserving such samples intact through time. Another possibility is finding calibration from historic events. Most of the issues mentioned would be a lot less relevant if a phylogenetic reconstruction would be constrained by a calibration higher up in the tree. We demonstrated that rate estimates incorporating calibration points based on historic events are more robust to the choice of prior for HBV genotype F, and it is our hope that more such events can be found for other genotypes International Medical Press

7 Hepatitis B substitution rate Acknowledgements This work has been supported by Fundação de Amparo à Pesquisa do Estado de São Paulo FAPESP 2011/ and 2011/ , CNPq, Alves de Queiroz Family Fund for Research, Fundação Faculdade de Medicina and HCFMUSP. Eddie Holmes and Philippe Lemey were very helpful in providing sequences in easily accessible file formats and answers to our questions. Disclosure statement The authors declare no competing interests. References 1. King AMQ, Lefkowitz E, Adams MJ, Carstens EB. Virus taxonomy: ninth report of the International Committee on Taxonomy of Viruses. Amsterdam: Elsevier Lee WM. Hepatitis B virus infection. N Engl J Med 1997; 337: Ganem D, Schneider RJ. Hepadnaviridae: the viruses and their replication. In Knipe DM, Howley PM (Editors). Fields Virology. 4th ed. Philadelphia: Lippincott Williams & Wilkins 2001; pp Okamoto H, Tsuda F, Sakugawa H, et al. 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