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1 Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
2 Theoretical Biology and Biophysics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Correspondence
Narendra M. Dixit
narendra{at}chemeng.iisc.ernet.in
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Supplementary material is available with the online version of this paper.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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; Clavel & Hance, 2004; Simon et al., 2006; Thomson et al., 2002). Several competing factors influence HIV diversification in infected individuals: the high mutation rate of HIV, approximately 3x10–5 mutations per nucleotide per replication (Mansky & Temin, 1995), and the enormous production rate, approximately 1010 virions per day in a chronically infected individual (Perelson et al., 1996), enable rapid sampling of broad spectra of genomic variations by HIV. Consequently, viral genomes with drug resistance mutations may exist in individuals prior to the onset of therapy (Lech et al., 1996; Ribeiro & Bonhoeffer, 2000). On the other hand, random genetic drift, significant in the suggested small effective cell populations in vivo (Shriner et al., 2004b), and fitness selection (Kils-Hutten et al., 2001) may impede HIV diversification. Experiments reveal complex patterns of the genomic evolution of HIV in patients and suggest that the patterns are correlated with disease progression (Herbeck et al., 2006; Markham et al., 1998; Shankarappa et al., 1999). Several recent studies present insights into the complex interplay of mutation, drift and fitness selection that underlies HIV diversification in vivo (Frost et al., 2000, 2001; Rouzine et al., 2001; Williamson et al., 2005; Yuste et al., 2002). The role of recombination, however, remains poorly understood (Bocharov et al., 2005; Bretscher et al., 2004; Fraser, 2005; Otto & Lenormand, 2002).
HIV has a high recombination rate, several times larger than its point mutation rate (Jetzt et al., 2000; Levy et al., 2004; Shriner et al., 2004a; Suryavanshi & Dixit, 2007). Further, recent studies suggest that infected cells harbour multiple HIV proviruses (Chen et al., 2005; Dang et al., 2004; Jung et al., 2002; Levy et al., 2004), which enables the formation of heterozygous virions and presents the necessary substrate for recombination to induce genomic diversification (Rhodes et al., 2003). Recombination may thus significantly accelerate viral diversification (Bocharov et al., 2005; Charpentier et al., 2006) and facilitate the emergence of multi-drug resistance in infected individuals (Althaus & Bonhoeffer, 2005; Blackard et al., 2002; Christiansen et al., 1998; Kellam & Larder, 1995; Moutouh et al., 1996).
Conversely, just as recombination may induce the accumulation of favourable mutations, it may also drive beneficial combinations of mutations apart and therefore not necessarily benefit HIV (Bonhoeffer et al., 2004; Fraser, 2005). Mathematical models (Bretscher et al., 2004; Fraser, 2005) suggest that the effect of recombination depends sensitively on epistasis (E), which is a measure of the influence of interactions between mutations on viral fitness (in a two-locus-two-allele model, where haplotype ab has fitness fab, E=fabfAB–faBfAb). In particular, when drug– sensitive loci interact antagonistically in reducing viral fitness, i.e. when E>0, recombination may decelerate the emergence of multi-drug resistance in a large population of cells (Bretscher et al., 2004). Recent experiments suggest that the HIV-1 fitness landscape is characterized by mean E>0, raising doubts on the benefits of recombination to HIV-1 (Bonhoeffer et al., 2004). With moderate values of the effective population size, Ne, recombination may accelerate the emergence of drug resistance significantly even with E>0 (Althaus & Bonhoeffer, 2005). When Ne is smaller than a critical value, however, the viral population in an individual may converge to a clone in the absence of mutation, leaving little opportunity for recombination to induce diversification (Rouzine & Coffin, 2005). Current estimates of Ne in vivo have large discrepancies (Kouyos et al., 2006a) and leave unclear the benefit of recombination to HIV.
Our aim is to develop a fundamental understanding of the effect of recombination on HIV diversification in an infected individual. Mathematical modelling of HIV diversification requires integration of the effects of mutation, multiple infections of cells, random genetic drift, fitness selection, and recombination, which remains difficult especially when fitness interactions between multiple loci are important. Conversely, experimental approaches suffer from the difficulty involved in the deconvolution of the effects of recombination from those of mutation, drift and selection. Here, we develop computer simulations that elucidate the influence of recombination on the genomic diversification of HIV.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). We commenced simulations with a pool of identical homozygous virions that synchronously infect a pool of uninfected cells. Following infection, viral RNAs in cells are reverse-transcribed into proviral DNA. During reverse transcription, mutation and recombination introduce genomic variations. The proviral DNAs are transcribed into viral RNAs, which are assorted randomly into pairs, copackaged and released as new virions. The progeny virions form a new viral pool from which virions are chosen according to their fitness to infect a new pool of uninfected cells, and the replication cycle is repeated. In each generation, we determine the average diversity and fitness of the proviral DNA and their average divergence from the proviral DNAs at the start of infection. Below, we present details of the simulation procedure.
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per nucleotide (see below) and let the resulting sequence be the starting or founder sequence. The founder sequence is copied to the two substrings of length L in each of the Nv virions to form the initial viral pool.
Infection of cells.
We let M virions infect each cell in a pool of Ne cells. Virions are chosen for infection from the viral pool according to their relative fitness (see below) and their genomes are transferred to cells.
Reverse transcription.
Following infection, reverse transcription converts the RNA strands (length 2L) to proviral DNA (length L). Reverse transcription involves recombination, which we simulate first, and mutation (Bocharov et al., 2005).
Recombination
The average recombination rate, 
, is approximately 8x10–4 per site per reverse transcription (Levy et al., 2004; Suryavanshi & Dixit, 2007) so that for the genome lengths we consider (L=40–100), more than one crossover per reverse transcription is unlikely. Thus, during each reverse transcription, we allow a single crossover with probability L. The crossover occurs at position lc, which we choose randomly from a uniform distribution on 1 to L. We begin reverse transcription from the first nucleotide of one of the two substrings of the viral RNA chosen randomly with probability 0.5. We copy the nucleotide sequence of the starting substring from the first to the lcth position to the first lc positions of the resulting proviral DNA. The template is then switched and the sequence from the (lc+1)th position to the last position of the other substring is copied to the corresponding positions in the proviral DNA. This process is repeated for all infecting virions.
Mutation
Mutations in HIV are dominated by substitutions of which approximately 90 % are transitions (A
G and CT) (Mansky & Temin, 1995). For simplicity, we therefore consider transitions alone. Thus, starting from the first position of a proviral DNA, ‘A’ is substituted with ‘G’ and ‘C’ with ‘T’, and vice versa, at all positions, each substitution occurring with probability equal to the mutation rate, µ.
Calculation of diversity, divergence and fitness.
The normalized Hamming distance between two proviral DNAs, i and j, is
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| (1) |
is the nucleotide in the kth position of provirus i, and 
if 
and 
if 
(2). dij is thus the number of differences per position between sequences i and j; dij=0 if the two strings are identical, whereas dij=1 if the two strings are different at every position.
We determine the average diversity of the Q (=MNe) proviruses in any generation as
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| (3) |
Similarly, the average divergence of the proviruses in any generation from those at the onset of infection, is
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| (4) |
The fitness landscape for the protease and reverse transcriptase regions of HIV-1 has recently been determined (Bonhoeffer et al., 2004). On this landscape, the relative fitness, fi, of genome i depends on the Hamming distance, diF, between the amino acid sequence of genome i and that of the fittest genome, F. As an approximation, we assume that unit Hamming distance between two nucleotide sequences is equal to unit Hamming distance between the corresponding amino acid sequences. We find then that the experimental fitness landscape is captured by (Supplementary Fig. S1, available with the online version of this paper),
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| (5) |
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| (6) |
Translation, assortment and viral production.
Following reverse transcription, each infected cell produces P virions. For each progeny virion arising from a cell, two of the M proviral DNAs from the cell are chosen at random and their sequences are copied to the two L-bit substrings to form the RNA genome of the virion. When M=1, the same proviral sequence is copied to all the new virions arising from that cell. The new virions thus formed constitute the viral pool for infecting the next generation of target cells.
Fitness selection.
The relative fitness of a virion is determined by equation 5 with diF the average Hamming distance of its two RNA strands from the fittest sequence. The virion is chosen for infection randomly with a probability equal to its relative fitness. The process is repeated for other virions in the pool until every cell is infected with M virions.
The above infection and replication process is repeated and the evolution of viral diversity, divergence and fitness with the number of replication cycles determined. Several realizations are averaged to determine the expected evolution. The simulations are implemented using a computer program written in C++.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Mutation
We examine first the effect of mutation. We consider a viral pool of Nv=40 virions, each virion with a genome of L=40 nucleotides. We assume individual cells to be infected by single virions (M=1) and let each infected cell produce a single progeny virion (P=1). The cell pool contains Ne=40 cells. We ignore recombination (=0) and assume a flat fitness landscape (fi=1).
In Fig. 2, we present the evolution of diversity, dG, and divergence, dS (Methods), with the number of replication cycles or generations, , for different values of the mutation rate, µ. As expected, dG=dS=0 when =0, as all the virions in the initial viral pool are identical. As increases, both dG and dS increase due to mutation. The rate of increase is higher for larger values of µ. For large , both dG and dS approach equilibrium values, 
and 
, respectively, in an exponential manner; we find that = =0.5 independent of µ.
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) and provide a quantitative understanding of the influence of mutation on HIV diversification as well as a successful test of our simulation procedure.
Recombination (>0) does not alter the genomic evolution in Fig. 2 because, in the absence of multiple infections, all progeny virions are homozygous and no substrate exists for recombination to induce diversification (Supplementary Fig. S2). We therefore introduce multiple infections of cells next.
Multiple infections of cells
With Ne=40 cells, we expand the viral pool to Nv=NeM so that every cell is infected by M virions, and let P=M, so that all progeny virions infect cells. We choose µ=0.001 substitutions per nucleotide per replication, =0 and fi=1.
In Fig. 3(a), we present the evolution of dG for different values of M=P. For M=1, the evolution is identical to that in Fig. 2. For M=2, surprisingly, dG decreases significantly from that for M=1. The decrease in dG despite multiple infections is attributed to enhanced viral production from cells. When P=2, each cell produces two progeny virions, which can be identical. The production of identical virions lowers the diversity of the proviruses in the following generation, and, in consequence, dG. This effect is emphasized in Fig. 3(b), where we present dG for M=1 and P=2, 3 and 4. As P increases, the probability that identical virions infect target cells increases and causes a decrease in dG. We note, however, that when P>M, the decrease in dG is the combined effect of the production of identical virions and random genetic drift, as only a fraction of the progeny virions infects cells. The effect of drift is minimized when P=M.
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). Enhanced multiple infections increase the likelihood of diverse proviruses forming progeny virions and cause the observed increase in dG. This phenomenon is illustrated further in Fig. 3(c), where we present the evolution of dG for M=1, 2 and 3, but for fixed P=3. As M increases, dG increases. Multiple infections (M>1) and drift (P>M) do not influence HIV divergence; in the absence of fitness selection and recombination, the evolution of individual sequences is governed by mutation. dS therefore remains unaltered by variations in M and P (Supplementary Fig. S3).
Even with multiple infections, recombination (>0) does not alter HIV diversification (Supplementary Fig. S4). Whereas recombination can bring mutations together, it can also drive mutations apart. Thus, when no fitness benefit exists for accumulating (or separating) mutations, i.e. when no non-random association of mutations is favoured, HIV diversification remains independent of recombination. We examine next the role of fitness selection.
Fitness selection
To delineate the effect of fitness selection, we ignore multiple infections (M=1) and select virions for infection according to equation 5 from a pool of size Nv=NeP with P>1. Without loss of generality, we let the founder sequence be the fittest (=0) (Methods). The fitness of individual genomes is thus a function of their divergence.
In Fig. 4, we present the evolution of dG, dS, and the average fitness, favg, for P=3 and different values of µ (when =0). We find that fitness selection influences both dG and dS. and decrease compared with their values with a flat fitness landscape (Figs 2, 3 and 4). The relative fitness of genomes decreases as their divergence increases (equation 5). Thus, fitness selection lowers (Fig. 4b). The fewer variations allowed due to fitness penalties also lower correspondingly (Fig. 4a). A higher µ, however, forces the sampling of larger genomic variations and causes and to increase (Fig. 4). Correspondingly, the equilibrium fitness, 
, decreases as µ increases (Fig. 4c), in accordance with the classical mutation–selection balance (Hartl & Clark, 2007).
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). For small and large values of µ, dG increases monotonically to . For intermediate values of µ, the evolution is non-monotonic: dG first rises and then declines to (Fig. 4a inset). To understand this non-monotonic evolution, we recognize that, as dS increases with (Fig. 4b), the average number of mutations per genome increases. Initially (
0), when all genomes are nearly identical, mutations tend to occur at distinct positions on different strands, causing dG to rise. As the number of mutations accrued increases, the likelihood that new mutations occur at novel positions decreases. Eventually, new mutations occur increasingly at positions where other strands carry mutations, causing dG to decline until the mutation–selection balance is attained. When µ is small, the maximum number of mutations accrued is so small that no reduction in dG occurs, whereas when µ is large, forceful diversification outweighs fitness selection and results in the monotonic evolution of dG, similar to that in the absence of fitness selection (Fig. 2).
Recombination does not alter the HIV diversification observed in Fig. 4 as expected from the lack of multiple infections of cells and the consequent absence of heterozygous virions (Supplementary Fig. S5).
Recombination
With multiple infections of cells and fitness selection, recombination influences HIV diversification. In Fig. 5(a–c), we present the evolution of dG, dS and favg with M=2 and fitness selection according to equation 5 for different recombination rates, . Remarkably, we find that recombination does not alter the initial rate of evolution of dG, dS or favg, but alters , and . As increases, and increase and decreases (Fig. 5a–c). These qualitative effects of recombination are robust to variations in the mutation rate and quantitative variations in the fitness landscape (i.e. changes in d50 or fmin in equation 5) (not shown), but are sensitive to the effective population size.
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, increases because a larger number of genomic variants is likely to exist in larger populations. At the same time, increases, and hence decreases, because fitness selection operates more effectively in larger populations (Fig. 5). Remarkably, however, as Ne increases, first increases upon increasing (Fig. 5a and d) and then decreases (Fig. 5g). The difference in , which we denote 
, upon increasing from 0 to 0.02 crossovers per nucleotide per replication cycle, decreases from approximately 0.015 at Ne=40 to approximately –0.028 at Ne=5000 (Fig. 6a). Thus, recombination increases HIV diversity for small Ne but decreases diversity for large Ne. The corresponding difference in the fitness (divergence), (), is positive (negative) for all values of Ne considered (Fig. 6a), indicating that recombination consistently increases (lowers) the mean fitness (divergence) of the viral population. The extent of the increase in fitness, however, decreases upon increasing Ne. We discuss these intriguing results in the light of modern population genetics theories below.
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) and M=3 (Jung et al., 2002). The viral burst size in vivo is estimated to be in the range 102–104 (Haase et al., 1996; Hockett et al., 1999). Most virions produced, however, may be non-infectious (Dimitrov & Martin, 1995; Dimitrov et al., 1993; Piatak et al., 1993) and individual cells may yield as few as 2–3 infectious virions (Dimitrov & Martin, 1995). Here, we therefore choose P=5. We assume fitness selection to follow equation 5. We vary from 0 to 9x10–3 crossovers per position per replication, approximately tenfold higher than the experimental recombination rate (Levy et al., 2004), to emphasize the influence of recombination. The best current estimates of the effective population size are of the order of 103 (Shriner et al., 2004b). We therefore vary Ne from 40 to 104. We also consider a larger genome length, L=100, corresponding to the variable portion of the V1V2 region of env (Bocharov et al., 2005). With L=100, we span the experimental fitness landscape, which extends to a Hamming distance of approximately 60 (Supplementary Fig. S1).
In Fig. 6(b), we present the resulting effect of recombination and Ne on , and . In agreement with our observations above (Fig. 6a), we find that, for small values of Ne, recombination increases both the mean fitness and the diversity of the viral genomes, whereas, for large values of Ne, recombination increases the mean fitness but lowers viral diversity (Fig. 6b).
Links with patient data
We demonstrate finally that the predicted evolution of diversity and divergence are consistent with corresponding observations in HIV patients. In Fig. 7, we compare our simulations with the evolution following seroconversion of the diversity and the divergence of the C2–V5 region of the HIV-1 env gene in one (Patient 2) of nine patients observed experimentally (Shankarappa et al., 1999). The patient data are reported as the mean pairwise distance between viral DNA sequences determined using either a two-parameter Kimura model or a general time-reversible model with site-to-site variation in substitution rates, both methods yielding similar results (Shankarappa et al., 1999). When the distances are small, as is the case in the experimental data, the Kimura two-parameter distance reduces to the Hamming distance (Kimura, 1980), allowing us to compare our simulation results directly with the data.
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=9x10–4 crossovers per position per replication (Levy et al., 2004), and let the viral generation time be 1 day (Dixit et al., 2004; Markowitz et al., 2003; Perelson et al., 1996; Rodrigo et al., 1999). , which determines the fitness of the founder sequence, and Ne for the patient remain unknown. We vary these parameters and find that good comparisons between our simulations and the patient data are obtained for Ne=1500, =0.05–0.08 and Ne=5000, =0.05–0.06 (Fig. 7). In the patient, viral diversity rises following seroconversion, appears to attain a maximum and then declines slightly to an equilibrium value. With =0.05 and Ne=1500 or 5000, our simulations capture accurately the initial rise and the equilibrium diversity (Fig. 7a and b). The evolution of diversity, however, is monotonic. Given the large uncertainties associated with the experimental data, whether the maximum observed is significant remains to be ascertained.
Our simulations with the same parameter values also capture the evolution of viral divergence in the patient (Fig. 7c and d). We find here that the experimental data are encompassed by our predictions with =0.05 and 0.08 for Ne=1500 and =0.05 and 0.06 for Ne=5000. We assume a unique founder sequence in our simulations. In the patient, however, even if infected with a unique founder, a mixture of genomes, perhaps with fitness values in the range determined by the above ranges of , may exist at seroconversion. Note that variation of has little impact on the evolution of diversity (Fig. 7a and b).
The reasonable agreement between the data and our simulations (Fig. 7) suggests that our simulations are representative of the scenario in vivo. The agreement also suggests that Ne in the patient considered is in the approximate range of 1500–5000 cells. [Simulations with Ne=500 underpredict and Ne=10000 overpredict the patient data (Fig. 7). Note that does not influence the equilibrium diversity or fitness but alters equilibrium divergence (Supplementary Information). Also note that the error bars in Fig. 7 are extreme values and not standard errors of the mean.] With Ne1500–5000, our simulations predict that recombination enhances mean viral fitness but lowers viral diversity in the patient (Fig. 6b). Whether recombination exerts a similar influence in other patients remains to be ascertained.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). With E>0, the reduction due to recombination of the mean time for the establishment of double mutants is predicted to increase, reach a maximum, and then decrease as the effective population size, Ne, increases (Althaus & Bonhoeffer, 2005). In our simulations, the equilibrium diversity, , provides a qualitative measure of the waiting time for the establishment of drug resistance. The larger the value of , the greater is the likelihood of the existence of diverse genomes in the viral pool, and hence the shorter is the waiting time for the establishment of desired mutants. Our simulations employ the fitness landscape identified experimentally (Bonhoeffer et al., 2004). Indeed, we find that recombination increases when Ne is small and decreases when Ne is large (Fig. 6).
Recent computer simulations suggest that recombination and multiple infections act synergistically in the evolution of HIV diversity (Bocharov et al., 2005). With multiple infections, the mean diversity and fitness of HIV increase in the presence of recombination. Our simulations are in agreement with these predictions and provide further insights. We note first that recombination enhances both viral fitness and diversity when Ne is small. Second, an increase in the frequency of multiple infections (M) increases diversity when viral production per cell (P) is relatively unaffected. If P increases with M, which may happen when viral production is limited by a viral rather than a host-cellular factor, then HIV diversity may first decrease and then increase as the frequency of multiple infections increases (Fig. 3).
In vivo, recombination allows the conservation of genomic regions affected by evolutionary bottlenecks and increases diversity in other regions (Charpentier et al., 2006). Thus, where selection dominates, as with large Ne, recombination facilitates selection of fitter genomes, and where selection is weak, recombination increases diversity, as observed in our simulations (Figs 5 and 6).
The patterns of change of viral diversity, dG, and divergence, dS, predicted by our simulations have been observed in experiments (Herbeck et al., 2006; Markham et al., 1998; Shankarappa et al., 1999). For instance, dG in patients gradually increased following infection, reached a maximum and then either stabilized or declined, whereas dS increased monotonically to a plateau (Shankarappa et al., 1999). In our simulations, these patterns arise due to the interplay of mutation and fitness selection (Fig. 4). The observed patterns may also arise due to HIV-mediated collapse of the immune system, i.e. immune relaxation (Williamson et al., 2005), which we ignore. We have applied our simulations to describe the time-evolution of dG and dS in one HIV patient for a period of approximately 10 years following seroconversion. Our simulations capture the data well (Fig. 7), suggesting that our simulations are representative of the scenario in vivo.
Current population genetics theories provide insights into the influence of recombination elucidated by our simulations (Ewens, 2004; Hartl & Clark, 2007; Kouyos et al., 2007; Otto & Lenormand, 2002; Rice, 2002). According to these theories, recombination acts to reduce the magnitude of linkage disequilibrium (LD). In a two-locus-two-allele model, where gab is the frequency of haplotype ab, LD=gabgAB–gaBgAb measures the extent to which the frequency of double-mutants is different from that expected from the frequencies of single-mutants. In the absence of selection and with large Ne, LD vanishes. Recombination then will not influence viral diversification (Supplementary Figs S3–S5). Random genetic drift generates negative LD – which implies an overrepresentation of single-mutants – according to the well-known Hill–Robertson effect (Hill & Robertson, 1966). Epistasis also introduces LD; then LD has the same sign as E (Eshel & Feldman, 1970). When Ne is small, drift may dominate epistasis and create net negative LD. When recombination lowers negative LD, the frequency of double-mutants and hence viral diversity increases (Hartl & Clark, 2007; Kouyos et al., 2007; Otto & Lenormand, 2002). When Ne is large, drift is reduced. LD is then determined by epistasis. In our simulations, we have assumed a fitness landscape that extends over multiple loci and has mean E>0 (Bonhoeffer et al., 2004). Although LD depends in a complicated manner on the distribution of epistasis and not the mean epistasis alone (Kouyos et al., 2006b), the assumed landscape may be expected to generate positive LD. When recombination lowers positive LD, viral diversity is expected to decrease (Hartl & Clark, 2007; Kouyos et al., 2007; Otto & Lenormand, 2002). Thus, a competition between negative LD introduced by drift and positive LD due to epistasis appears to underlie the effect of recombination and Ne on viral diversity observed in our simulations.
Our simulations also suggest that for small Ne (<103), the enhancement in viral diversity due to recombination increases with increasing Ne (Fig. 6b). For very small Ne, the Hill–Robertson effect may not apply (Otto & Barton, 2001). Thus, the gradual emergence of the Hill–Robertson effect with increasing, yet small, Ne may underlie the observed enhanced effect of recombination. We observe finally that in all our simulations, recombination increases mean viral fitness (Fig. 6) and hence decreases the mutational load, an effect suggested as one of the plausible causes of the evolutionary origins of recombination (Hartl & Clark, 2007; Kouyos et al., 2007; Otto & Lenormand, 2002).
Prediction of the influence of recombination on viral diversification and consequently the emergence of drug resistance has been precluded by the lack of robust estimates of Ne in vivo (Kouyos et al., 2006a). Models based on neutral evolution estimate Ne to be approximately 103 (Achaz et al., 2004; Brown, 1997; Nijhuis et al., 1998; Rodrigo et al., 1999; Seo et al., 2002; Shriner et al., 2004b). HIV evolution in vivo, however, is expected to be driven by selection. A model that assumes viral evolution with selection estimates Ne to be >105–106 (Rouzine & Coffin, 1999). The model, however, is restricted to fitness interactions between pairs of loci and ignores recombination, which may overestimate Ne (Shriner et al., 2004b). In our simulations, we consider fitness interactions between multiple loci and predict the evolution of viral diversity and divergence. The evolution of viral diversity and divergence are sensitive to Ne. Comparison of our predictions with data of the evolution of viral diversity and divergence from patients therefore presents an avenue for obtaining more accurate estimates of Ne in vivo. We demonstrate the applicability of this methodology by analysing data from one patient and estimate Ne to be approximately in the range 1500–5000. Analysis of data from a larger set of patients – a promising potential application of our simulations – would provide robust estimates of Ne in vivo and establish the benefit of recombination to HIV.
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ACKNOWLEDGEMENTS |
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), 0.001 (
), 0.0005 (
), and 0.0001 (
) substitutions per nucleotide per replication. The grey bands represent deviations to the mean (±SD) due to stochastic variations in approximately 1000 realizations. Solid lines are model predictions (Supplementary Information).
