Coalescent estimates of HIV-1 generation timein vivo

Abstract

The generation time of HIV Type 1 (HIV-1) in vivo has previously been estimated using a mathematical model of viral dynamics and was found to be on the order of one to two days per generation. Here, we describe a new method based on coalescence theory that allows the estimate of generation times to be derived by using nucleotide sequence data and a reconstructed genealogy of sequences obtained over time. The method is applied to sequences obtained from a long-term nonprogressing individual at five sampling occasions. The estimate of viral generation time using the coalescent method is 1.2 days per generation and is close to that obtained by mathematical modeling (1.8 days per generation), thus strengthening confidence in estimates of a short viral generation time. Apart from the estimation of relevant parameters relating to viral dynamics, coalescent modeling also allows us to simulate the evolutionary behavior of samples of sequences obtained over time.The integration of mathematical modeling and experimental approaches has led to a deeper understanding of HIV-1 viral dynamics in vivo. In particular, these studies suggest that the viral population in the peripheral blood (and the secondary lymphatics) turns over rapidly, with generation times estimated to be on the order of one to two days on average (ref. 1; A. Perelson, personal communication). However, because these studies are based on abstract and simple models of a complex biological system, it is not obvious how accurate these estimates are. One way to address this is to try to estimate the same parameters by using different methods and different types of data.Here, we apply a new method developed by Rodrigo and Felsenstein (2) which is based on a mathematical construct introduced by Kingman (3, 4) called the n-coalescent (or coalescent for short). The coalescent relies on the fundamental notion that all individuals in a population have a genealogy, so that if we begin with a sample of n individuals, each drawn randomly from a population, and we reconstruct the genealogy of these n individuals, we will begin to see lineages coalescing as we move further back in time. Each coalescent event represents the split of two lineages from a common ancestor. Obviously, if we go back far enough, we arrive at a point where all lineages have coalesced, and this point represents the most recent common ancestor of all sequences in the sample. The mathematics of coalescent theory gives us the distribution of times, measured as the number of generations, between coalescent events, as one moves back in time along the genealogy. The distribution of times itself is contingent on the dynamics of the population in question. For instance, the expected coalescence time of two individuals drawn at random, each from a compartment of a subdivided population, depends on the rate of migration between the compartments. Similarly, two individuals drawn from a growing population will have a different expected time to coalescence than two individuals drawn from a population at e...

Genetic drift and within-host metapopulation dynamics of HIV-1 infection

“…We have demonstrated recombination at the local level, and although it is not known how recombination at a subpopulation level translates to the effective recombination rate in the body as a whole, estimates of N e based on the level of linkage disequilibrium are likely to be overestimates. Nevertheless, metapopulation structure is unlikely to be the sole cause of differences between the actual and effective population sizes as estimates of N e based on the level of diversity (24,36) and the rate of divergence of the C2-V3 region of the env gene (27) are of the order 10 3 -10 4 , which is lower than could realistically be produced under our simple metapopulation model. Other factors, such as the process of ''genetic draft'' (61), where a reduction in effective population size arises because of selection on linked viral mutations, may play an important role.…”

“…Indirect observations of the apparently stochastic way in which multiply resistant mutants emerge during therapy are also consistent with a role of genetic drift (18,24,25). In addition, three studies of the evolution of env gene sequences have found substantially lower genetic variation than expected for a population of the order of 10 7 (24,26,27). These studies estimated the ''effective'' population size to be of the order of 10 3 , reflecting the high relatedness between env sequences sampled at a given time.…”

Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology

“…At least one other study reported similar values (66). However, other lines of evidence, including differences among rates of accumulation in different genes (74) and very high (44,84) or very low (4, 5) ratios of synonymous to nonsynonymous mutations in some genes, imply that HIV populations are subject to significant selective influences.…”

The Dynamics of HIV-1 Adaptation in Early Infection

“…These include acute infection, defined as the first 100 days, and early chronic infection, defined as the next 100 days (McMichael et al 2010). The viral generation length has been estimated as 1-2 days (Perelson et al 1996;Rodrigo et al 1999;Markowitz et al 2003;Murray et al 2011). , also estimated from simulations, underestimates N model because the population is not at mutation-drift equilibrium.…”

“…Together with evidence of strong selection by the immune system (Williamson 2003), this would suggest highly deterministic evolution (Coffin 1995;Overbaugh and Bangham 2001). On the other hand, the within-patient N e during chronic infection has been routinely estimated to be only 10 3 , suggesting that stochastic genetic drift is a powerful force in HIV-1 evolution Nijhuis et al 1998;Rodrigo et al 1999;Drummond et al 2002;Seo et al 2002;Achaz et al 2004;Shriner et al 2004b). In addition, variation among patients in the rate and pattern of the evolution of HIV-1 resistance to antiviral drugs has been attributed to the effects of genetic drift (Leigh Brown and Richman 1997;Nijhuis et al 1998;Frost et al 2000).…”