Population genetic estimation of the loss of genetic diversity during horizontal transmission of HIV-1

Background Genetic diversity of the human immunodeficiency virus type 1 (HIV-1) population within an individual is lost during transmission to a new host. The demography of transmission is an important determinant of evolutionary dynamics, particularly the relative impact of natural selection and genetic drift immediately following HIV-1 infection. Despite this, the magnitude of this population bottleneck is unclear. Results We use coalescent methods to quantify the bottleneck in a single case of homosexual transmission and find that over 99% of the env and gag diversity present in the donor is lost. This was consistent with the diversity present at seroconversion in nine other horizontally infected individuals. Furthermore, we estimated viral diversity at birth in 27 infants infected through vertical transmission and found there to be no difference between the two modes of transmission. Conclusion Assuming the bottleneck at transmission is selectively neutral, such a severe reduction in genetic diversity has important implications for adaptation in HIV-1, since beneficial mutations have a reduced chance of transmission.


Background
The size of the inoculum that initiates infection in HIV-1 is unknown, although the loss of diversity is thought to be substantial following both horizontal [1][2][3][4][5][6][7] and vertical [8,9] transmission. If the bottleneck is selectively neutral, genetic drift will occur because only a small number of variants are chosen at random from the population to propagate the new infection. The smaller the amount of genetic diversity transmitted the greater the magnitude of drift, lowering the probability that adaptive changes that emerge within hosts will survive transmission.
In RNA viruses with a high deleterious mutation rate the majority of variants exhibit a replicative capacity lower than the mean [10][11][12]. Because the fittest variants may only be present at a low frequency, they are susceptible to random loss. Hence when genetic drift is strong, deleterious mutations may accumulate, leading to an irreversible decline in population fitness [13]. Although the high rate of recombination in HIV-1 in vivo [14][15][16] has the potential to rescue debilitated haplotypes [13], if a new infection is initiated by only one or a few viral particles, and if these are chosen at random from the parent population, then the transmission of HIV-1 will likely incur a substan-tial reduction in fitness [17][18][19][20][21]. As the inoculum size increases, potential fitness losses are rapidly reduced [22,23].
Herein we estimate, using population genetic techniques, the proportion of genetic diversity that survives transmission in a single homosexual transmitter pair, with samples available before and after the transmission event. The demographic history of the virus population in both donor and recipient was reconstructed using coalescent methodology, allowing quantification of the diversity present close to the time of infection. The coalescent was implemented within a Bayesian framework, which enabled co-estimation of substitution and demographic parameters using serially sampled sequences [24][25][26].
Through a comparison of different regions of the genome (namely env V1-V4 and gag p24) we also investigate whether selection is likely to be acting during HIV-1 transmission. Finally, we generalise our result by estimating the diversity present close to the time of infection in nine homosexual seroconverters for which donor sequences were unavailable, and compare horizontal and vertical modes of transmission using 27 infants infected at birth.

Results
To directly visualise the change in genetic diversity during horizontal HIV-1 transmission between the donor-recipient pair studied, we first inferred the phylogenetic relationships among their HIV-1 sequences using maximum likelihood methods. The phylogenies for env V1-V4 and gag p24 depicted in Figure 1 show that branch lengths are substantially shortened immediately after transmission, illustrating that a significant reduction in diversity has occurred.
To investigate the demographics of viral transmission in this transmitter pair more closely, four coalescent models were fitted to the sequence data. Crucially, samples were available both before and after the transmission event allowing distinct demographic functions for donor and recipient HIV-1 populations (Equations 1 to 5), with the time of transition between them estimated from the data [26]. In addition to a null model that constrained the effective population size in donor (N D ) and recipient (N R ) to be identical (so that there is no bottleneck at transmission), models with constant, exponential and logistic demographic functions for the recipient population were fitted. In all cases the donor population size was assumed to be constant.
The relative Bayesian posterior scores for each demographic model are listed in Table 1. For both env V1-V4 and gag p24, the model with the lowest AIC (the preferred model) fits a constant population size in the donor and logistic growth in the recipient (Equations 4 and 5). The null hypothesis that there has been no change in population size at transmission was therefore rejected. Using the estimated model parameters we reconstructed the demographic profiles of genetic diversity (Nτ, the product of the effective population size and generation length in days [27]) against time for each gene ( Figure 2).
To further test the extent of the transmission bottleneck, the demographic history of the population was reconstructed using the Bayesian skyline plot [see Methods, [28]]. The results for env V1-V4 and gag p24 are shown in Figure 2. In both cases there is a good fit between the demographic profiles estimated using the two different methods. Noticeably, the timing of the transmission bot- Reconstructed demographic profiles for (a) env V1-V4 and (b) gag p24  Time in days Effective population size Nτ τ τ τ tleneck is the same, and evidence for a bottleneck is readily apparent under both models.
The Bayesian skyline plot also justifies our use of the logistic-constant demographic model to estimate the diversity that survives during horizontal transmission of HIV-1.
Using the logistic growth model (Equations 4 and 5) we were able to calculate diversity in the recipient N R τ at the estimated time of transmission t trans . We estimated t trans to be approximately 30 days prior to collection of the first recipient sample (day 0) for env and 40 days for gag ( Table   2). We calculated N R τ(t trans ) to be 1.6 for env V1-V4, and 2.0 for gag p24 (Table 2). These values are near the lower prior boundary of one and their posterior distributions both exhibit a large positive skew ( Figure 3). The level of diversity in the donor at the time of transmission N D τ was compared with that which was transmitted N R τ(t trans ) as a percentage ratio δ. For env, N D τ was estimated to be 1014, giving a value of δ as 0.17%. For gag p24, N D τ was 771, giving δ as 0.29% (Table 2). Importantly, if selection was acting on env to restrict the proportion of variants capable of establishing a new infection, we would expect a greater loss of diversity in this region when compared to gag, assuming recombination between the two regions. Therefore, the similarity in δ between env and gag argues against strong selection at transmission.
We conclude that > 99% of genetic diversity in the donor viral population, in both env and gag, was lost during this case of horizontal transmission. A reduction in viral diversity after horizontal transmission has been reported fre-quently in the literature [1,[3][4][5][6]. However, information regarding the diversity present in the donor is often lacking, and even in cases where this data exists [2,7] it is difficult to measure levels of diversity close to the transmission event. The method implemented here overcomes this problem, estimating genetic diversity at the inferred time of transmission, and therefore allows accurate quantification of the transmission bottleneck.
To generalise this result we next investigated diversity (Nτ) of the founding viral population in nine patients infected through homosexual contact for which donor sequences were unavailable. Sequences had been published previously [29]. Assuming the best-fit demographic model, Nτ at seroconversion was found to vary between around 1720 and 8 (mean: 406; Table 3). In the recipient of the transmitter pair, Nτ at seroconversion (day 0) was 1150 (HPD upper: 1930), which is not significantly different (p = 0.302; one-sample t-test).
Finally, to compare the diversity present close to the time of infection in patients infected via two different modes of transmission, we estimated Nτ at birth (transmission) in 27 vertically infected infants. The average Nτ at birth was 696 (Table 3). Although we were unable to detect a bottleneck at transmission in eight of the infants (p2, p3, p6, p8, pa, pd, pc and pd), the estimates for Nτ close to the time of infection in the horizontally and vertically infected patient groups were not significantly different (p = 0.320; two-sample t-test).

Discussion
From our analysis of a single donor and recipient transmission pair, we conclude that in this case the viral diversity sampled during homosexual transmission of HIV-1 was very small (< 1%). This result was consistent for both env and gag. Interpretation of our finding is dependent on whether transmission is considered a neutral or selective process. In particular, if transmission is neutral it can be concluded from the severe bottleneck reported here that the consequent genetic drift will be strong, with negative consequences for viral fitness. Natural selection on the other hand is likely to mitigate any deleterious effects of genetic drift associated with transmission.
It is possible that the diversity present in the inoculum itself was larger, and that selection acting on env restricted propagation of the new infection to a few members of the initial population [30]. The similar levels of diversity observed in env and gag could then be explained by genetic coupling between the two regions. The frequency with which recombination occurs in HIV-1 [14][15][16] argues against such linkage, suggesting that independent selective forces acting on env and gag must be invoked to explain this observation. Alternatively, if transmission is neutral then our estimate of the diversity transmitted will be closer to the diversity actually present in the inoculum. This will have implications for the replicative fitness of the viral population responsible for founding a new infection.
Indeed, it has been shown experimentally that a random population bottleneck of a single clone can have severe consequences for the replicative fitness of HIV-1 [21]. Furthermore, by lowering their chances of transmission, genetic drift has the potential to prevent the accumulation of advantageous changes at the population level, thereby impeding the long-term adaptation of HIV-1 [31].
Neutral transmission also means that the degree of genetic diversity passed between individuals is dependent on the diversity present in the donor at the time of transmission. Because diversity in their respective donors is likely to vary greatly depending on the stage of infection [29], this could in part explain our finding of wide variation across patients in diversity of the viral population close to transmission (Table 3). Furthermore, we found the degree of variability across patients infected by the same route to be greater than any difference between groups infected via different modes of transmission (i.e. the difference between groups was not significant). Interestingly, the diversity present early in acute infection in sexually and parenterally infected individuals also appears similar [2].
We can conclude from our results that diversity of the founding population is similarly restricted during both horizontal and vertical transmission. However, it is also clear that further study is required to investigate the variability observed. For example, although a reduction in diversity is frequent [1][2][3][4][5][6][7][8][9], the transmission of multiple variants has also been reported during both horizontal [32] and vertical transmission [33][34][35], suggesting that the bottleneck is not universally restrictive.

Conclusion
Our findings quantify the contraction in genetic diversity that occurs during horizontal transmission of HIV-1. It is clear from the severity of the bottleneck that further work is required to investigate the nature of the selective forces surrounding transmission, if we are to interpret the fitness consequences for HIV-1 in the newly infected individual. Furthermore, the analyses presented suggest that the mode of transmission may not be a significant influence on the genetic diversity transmitted.

Patient material
The donor and recipient patients of the transmitter pair analysed here were recruited as part of an on-going study of acute HIV-1 infection and have been described in detail elsewhere [36]. The donor had been infected for at least two years prior to transmission and exhibited a stable viral load. He had not received any antiretroviral treatment. The recipient was also untreated during the time of sampling but progressed rapidly towards disease with high viral loads and low CD4 + cell counts. The clinical data for Effective population size at transmission N R τ(t trans )

Figure 3
Effective population size at transmission N R τ(t trans ).
The marginal posterior probability density of N R τ(t trans ) is shown for both env V1-V4 and gag p24. The shaded area represents the uniform prior distribution that was used, with a minimum bound of one. Posterior probability density both donor and recipient during sampling is given in Additional file 1.
The first recipient sample (day 0) was collected six weeks after he last tested PCR (polymerase chain reaction) nega-tive for HIV-1 DNA and RNA. Three additional samples from the recipient were available at days 11, 59 and 237. Donor samples were collected 70 and 155 days prior to the first sample from the recipient. Gag p24 (834bp) and the V1-V4 region of the env gene (951bp) were sequenced Null model: N t = N R = N D [1] All substitution and demographic parameters, including the time of transmission t trans , growth rate r, and mid-time of the population t 50 , were estimated from the data within a Bayesian coalescent framework by Markov chain Monte Carlo (MCMC), using the BEAST program [45]. Bayesian MCMC estimates each parameter as the mean of its marginal posterior probability distribution, whilst simultaneously incorporating uncertainty in the underlying genealogy and other parameters. Diversity of the viral population is given as the product of the effective population size and generation length in days Nτ [27].
Uncertainty in the estimated parameter values is summarized by the highest posterior density (HPD) interval, which contains 95% of the marginal posterior distribution. The length of the MCMC chain was chosen so that the effective sample size (ESS) for each parameter was > 100, indicating that parameter space had been sufficiently explored [24]. Since it consistently gave the lowest value, the coalescent ESS (the number of effectively independent log likelihoods sampled from the coalescent posterior distribution) for each model is given in Table 1. All priors were assumed to be uniform on a natural scale, including the effective population size in the recipient at transmission N R τ(t trans ). The prior boundaries for the time of transmission t trans were set from when the recipient was last confirmed HIV-1 negative (53 days before the first recipient sample) to the time at which the first recipient sample was collected (day 0). We placed a minimum prior bound of one on N R τ(t trans ). With the exception of t trans and N R τ(t trans ), the MCMC chain did not impinge on any of the prescribed prior boundaries for the models tested.
The relative fit of each model to the data was assessed using the Akaike Information Criteria (AIC) [46]. The AIC of a given model is twice its marginal log likelihood plus the number of parameters specified (AIC = 2lnLk + 2p). The model with the lowest AIC is selected as the best representation of the data.
Selection of the appropriate demographic model allowed us to calculate N R τ(t trans ) and quantify the amount of diversity lost at transmission through a comparison of N R τ(t trans ) with N D τ as the percentage ratio δ.

Bayesian skyline plot
The skyline plot is a piecewise-constant model of population size that estimates Nτ for each coalescent interval of the genealogy [47,48]. It allows the demographic history of a population to be reconstructed without a priori specification of a particular model. The Bayesian skyline extends the generalised skyline plot [48] to take into account serial sequence sampling times and an uncertain genealogy [28]. The distribution of skyline plots is sampled using MCMC according to their posterior probabili-  [ ] ties given the sequence data, to produce an estimate and HPD confidence intervals of the effective population size through time. The Bayesian skyline plot was estimated using BEAST [45], allowing ten steps in Nτ through time.