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Recombination rate and selection strength in HIV intra-patient evolution
Richard A. Neher, Thomas Leitner
TL;DR
HIV evolution is shaped by mutation, selection, recombination, and stochasticity, while standard recombination estimators often assume neutrality. The paper uses longitudinal within-patient sequence data to estimate effective recombination and selection, finding ρ ≈1.4×10^-5 per site and generation and strong selection at about 15% of observed nonsynonymous polymorphisms.
Problem
HIV evolution involves simultaneous mutation, selection, recombination, and stochasticity, limiting traditional estimators that assume one dominant evolutionary force or neutrality.
Method
The study compares longitudinal sequence samples from 11 patients, using temporal haplotype appearance to estimate recombination and allele-frequency changes to estimate selection coefficients.
Results
The effective recombination rate is ρ ≈1.4×10^-5 per site and generation, and 15% of observed nonsynonymous polymorphisms have selection coefficients greater than 0.8% per generation.
Takeaways & Limitations
The estimates provide a basis for more detailed understanding of HIV evolution, including evolution under drug treatment where recombination may facilitate acquisition of multiple resistance mutations.
Takeaways & Limitations
The study is limited by low time resolution and small sequence samples; larger samples could provide more accurate and detailed estimates.
Abstract
from arXiv · showhide
The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Here, we estimate the rate of recombination and the distribution of selection coefficients from time-resolved sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be r=1.4e-5 recombinations per site and generation. Furthermore, we provide evidence that selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible, as soon as data with higher time resolution and greater sample sizes is available.
Introduction
HIV evolves rapidly during chronic infection under substantial mutation, selection, and recombination, making quantitative parameter estimation difficult. This study estimates effective recombination and selection strength from longitudinal sequence data.
- HIV produces and removes approximately 10^10 virions per day, with a generation time slightly below two days and a mutation rate of 2.5×10^-5 per site and generation.
- Recombination may accelerate drug resistance evolution, but its impact depends on population-dynamic parameters that remain insufficiently known.In vitro measurements indicate that reverse transcriptase switches templates about 2–3 times while copying the genome.
- The study estimates an effective recombination rate of ρ ≈1.4×10^-5 per site and generation and finds that about 15% of observed nonsynonymous polymorphisms have selection coefficients above 0.8% per generation.These estimates use longitudinal sequence data from 11 patients sampled at approximately six-month intervals.
- Recombination can generate a previously missing haplotype, and its rate is inferred from dependence on site distance and the interval between observations.The missing haplotype is formed from alleles already present at two polymorphic sites.
Results
Longitudinal HIV sequence data were used to estimate recombination and selection from temporal changes in haplotypes and allele frequencies. The analysis estimated an effective recombination rate and found substantial positive selection among observed non-synonymous polymorphisms.
- Data and approach: Sequence samples from eleven patients, collected over 6–13 years at approximately 6–10 month intervals, provided the time-resolved data for estimating recombination and selection.Each time point contained about 5–20 successfully sequenced viruses.
- Recombination rate: The probability of detecting a previously missing haplotype increased from about 0.1 to about 0.35 as site separation increased to 500 bp, consistent with distance-dependent recombination.The analysis examined biallelic site pairs in which three of four possible haplotypes were observed.
- Recombination rate: The fitted effective recombination rate was 1.4 ± 0.6 × 10^-5 recombinations per site and generation.The uncertainty was estimated by resampling patients with replacement 500 times.
- Recombination rate: The recombination estimate assumes allele frequencies remain constant between samples, but repeated selective sweeps may cause the method to overestimate recombination.Increasing minor-allele frequencies can produce the missing haplotype faster than expected under the assumption.
- Selection: About 15% of observed non-synonymous polymorphisms changed faster than 0.002 per generation, compared with almost none of the synonymous polymorphisms.The analysis used allele-frequency change rates to infer selection while accounting for sampling noise with synonymous polymorphisms.
- Selection: The observed frequency-change distribution implied that about 15% of non-synonymous polymorphisms were positively selected with s > 8 × 10^-3 per generation.The fastest detected changes were about 0.01 per generation, which limited resolution.
Discussion
Longitudinal HIV sequence data enabled direct estimation of population-dynamics parameters despite the virus’s simultaneous mutation, selection, recombination, and stochasticity. The study estimates effective recombination and selection while identifying limits from sampling resolution, sample size, and model assumptions.
- Longitudinal inference: Longitudinal sampling lets researchers trace allele and genotype dynamics directly, simplifying parameter estimation from population data.The study used time-resolved data from 11 patients.
- Recombination: 1.4×10^-5 recombinations per site and generation was estimated as HIV’s effective recombination rate, about 20-fold below template switching.The estimate implies a coinfection probability of about 10%.
- Selection: 15% of nonsynonymous polymorphisms were estimated to have selection coefficients greater than 0.8% per generation.The inference compares allele-frequency change distributions for synonymous and nonsynonymous polymorphisms.
- Selection: The selection estimate assumes each locus changes frequency through its own fitness effect rather than linked selection or epistatic combinations.Rapid synonymous changes near rapidly changing nonsynonymous polymorphisms support hitch-hiking over distances below 100 bp.
- Sweep dynamics: Sweeping loci were estimated to be separated by roughly 400 bp, comparable to s/ρ, suggesting recombination may limit sweep interference.The authors describe this interpretation as conceivable and note substantial uncertainty.
- Limitations: The study is limited by low time resolution and small sequence samples, motivating larger samples and more accurate, detailed analyses.The recombination method also assumes a constant rate across env, although breakpoint distributions vary along the genome.
Methods
The methods infer recombination from the appearance of previously missing haplotypes across successive time slices and infer selection from allele-frequency changes in synonymous versus nonsynonymous polymorphisms. The analyses account for undersampling, uncertainty, and possible hitch-hiking while using longitudinal sequence data.
- Recombination-rate estimation: Recombination was estimated by tracking whether a fourth, previously missing haplotype appeared between successive time slices.The analysis averaged this frequency across patients, time points, and site pairs within distance intervals.
- Recombination-rate estimation: The recombination fit minimized squared deviations weighted by relative uncertainty, with confidence intervals estimated from 500 patient-resampling replicates.The fitting procedure used the distance-time relationship and averaged ⟨Mp_Ap_B⟩ across contributing site pairs.
- Recombination-rate estimation: The method uses biallelic site pairs where three of four possible haplotypes are observed, because rare-allele haplotypes can be missed by undersampling.Skewed allele frequencies make the haplotype formed by the two minor alleles especially difficult to observe.
- Recombination-rate estimation: The missing-haplotype frequency was modeled through recombination-dependent relaxation and evaluated using small-distance behavior where linkage disequilibrium remains largely intact.At small distance-time products, the observed appearance probability measures the missing haplotype’s population frequency.
- Selection-coefficient estimation: Allele-frequency change rates were calculated from successive time slices for biallelic or newly polymorphic sites, including ∆p = 1 for complete state changes.Rare cases involving a third allele contributed both relevant absolute frequency-change rates.
- Selection-coefficient estimation: Selection was tested by comparing cumulative rate-of-change distributions for nonsynonymous and synonymous polymorphisms using a Kolmogorov-Smirnov test.Only consecutive samples with both sample sizes greater than 10 were included.
- Selection-coefficient estimation: Synonymous polymorphisms within 100 bp of rapidly changing nonsynonymous sites were excluded to assess hitch-hiking effects.Rapid nonsynonymous changes were defined as exceeding 0.002 per generation between successive time slices.