HIV recombination: what is the impact on antiretroviral therapy?

Modeling dynamics of acute HIV infection incorporating density-dependent cell death and multiplicity of infection

Understanding the dynamics of acute HIV infection can offer valuable insights into the early stages of viral behavior, potentially helping uncover various aspects of HIV pathogenesis. The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV infection. For instance, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further, when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models-1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)-to investigate acute infection dynamics in 43 people living with HIV very early after HIV exposure. We find that all models qualitatively describe the data, but none of the tested models is by itself the best to capture different kinds of heterogeneity. Instead, different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious across study participants by the corrected Akaike Information Criterion (AICc), we find that viral peaks are better explained by a model allowing for cellular MOI, using a linear regression analysis as analyzed by R2. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model. Depending on the specific aspect of interest, a corresponding model should be employed.

Consequences of Genetic Recombination on Protein Folding Stability

Genetic recombination is a common evolutionary mechanism that produces molecular diversity. However, its consequences on protein folding stability have not attracted the same attention as in the case of point mutations. Here, we studied the effects of homologous recombination on the computationally predicted protein folding stability for several protein families, finding less detrimental effects than we previously expected. Although recombination can affect multiple protein sites, we found that the fraction of recombined proteins that are eliminated by negative selection because of insufficient stability is not significantly larger than the corresponding fraction of proteins produced by mutation events. Indeed, although recombination disrupts epistatic interactions, the mean stability of recombinant proteins is not lower than that of their parents. On the other hand, the difference of stability between recombined proteins is amplified with respect to the parents, promoting phenotypic diversity. As a result, at least one third of recombined proteins present stability between those of their parents, and a substantial fraction have higher or lower stability than those of both parents. As expected, we found that parents with similar sequences tend to produce recombined proteins with stability close to that of the parents. Finally, the simulation of protein evolution along the ancestral recombination graph with empirical substitution models commonly used in phylogenetics, which ignore constraints on protein folding stability, showed that recombination favors the decrease of folding stability, supporting the convenience of adopting structurally constrained models when possible for inferences of protein evolutionary histories with recombination.

Superinfection exclusion: A viral strategy with short-term benefits and long-term drawbacks

Viral superinfection occurs when multiple viral particles subsequently infect the same host. In nature, several viral species are found to have evolved diverse mechanisms to prevent superinfection (superinfection exclusion) but how this strategic choice impacts the fate of mutations in the viral population remains unclear. Using stochastic simulations, we find that genetic drift is suppressed when superinfection occurs, thus facilitating the fixation of beneficial mutations and the removal of deleterious ones. Interestingly, we also find that the competitive (dis)advantage associated with variations in life history parameters is not necessarily captured by the viral growth rate for either infection strategy. Putting these together, we then show that a mutant with superinfection exclusion will easily overtake a superinfecting population even if the latter has a much higher growth rate. Our findings suggest that while superinfection exclusion can negatively impact the long-term adaptation of a viral population, in the short-term it is ultimately a winning strategy.

Viral social behaviour has recently been receiving increasing attention in the context of ecological and evolutionary dynamics of viral populations. One fascinating and still relatively poorly understood example is superinfection or co-infection, which occur when multiple viruses infect the same host. Among bacteriophages, a wide range of mechanisms have been discovered that enable phage to prevent superinfection (superinfection exclusion) even at the cost of using precious resources for this purpose. What is the evolutionary impact of this strategic choice and why do so many phages exhibit this behaviour? Here, we conduct an extensive simulation study of a phage population to address this question. In particular, we investigate the fate of viral mutations arising in an environment with a constant supply of bacterial hosts designed to mimic a “turbidostat,” as these are increasingly being used in laboratory evolution experiments. Our results show that allowing superinfection in the long-term yields a population which is more capable of adapting to changes in the environment. However, when in direct competition, mutants capable of preventing superinfection experience a very large advantage over their superinfecting counterparts, even if this ability comes at a significant cost to their growth rate. This indicates that while preventing superinfection can negatively impact the long-term prospects of a viral population, in the short-term it is ultimately a winning strategy.

ProteinEvolverABC: coestimation of recombination and substitution rates in protein sequences by approximate Bayesian computation

MOTIVATION

The evolutionary processes of mutation and recombination, upon which selection operates, are fundamental to understand the observed molecular diversity. Unlike nucleotide sequences, the estimation of the recombination rate in protein sequences has been little explored, neither implemented in evolutionary frameworks, despite protein sequencing methods are largely used.

RESULTS

In order to accommodate this need, here I present a computational framework, called ProteinEvolverABC, to jointly estimate recombination and substitution rates from alignments of protein sequences. The framework implements the approximate Bayesian computation approach, with and without regression adjustments and includes a variety of substitution models of protein evolution, demographics and longitudinal sampling. It also implements several nuisance parameters such as heterogeneous amino acid frequencies and rate of change among sites and, proportion of invariable sites. The framework produces accurate coestimation of recombination and substitution rates under diverse evolutionary scenarios. As illustrative examples of usage, I applied it to several viral protein families, including coronaviruses, showing heterogeneous substitution and recombination rates.

AVAILABILITY AND IMPLEMENTATION

ProteinEvolverABC is freely available from https://github.com/miguelarenas/proteinevolverabc, includes a graphical user interface for helping the specification of the input settings, extensive documentation and ready-to-use examples. Conveniently, the simulations can run in parallel on multicore machines.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Quantifying the dynamics of viral recombination during free virus and cell-to-cell transmission in HIV-1 infection

Recombination has been shown to contribute to human immunodeficiency virus-1 (HIV-1) evolution in vivo, but the underlying dynamics are extremely complex, depending on the nature of the fitness landscapes and of epistatic interactions. A less well-studied determinant of recombinant evolution is the mode of virus transmission in the cell population. HIV-1 can spread by free virus transmission, resulting largely in singly infected cells, and also by direct cell-to-cell transmission, resulting in the simultaneous infection of cells with multiple viruses. We investigate the contribution of these two transmission pathways to recombinant evolution, by applying mathematical models to in vitro experimental data on the growth of fluorescent reporter viruses under static conditions (where both transmission pathways operate), and under gentle shaking conditions, where cell-to-cell transmission is largely inhibited. The parameterized mathematical models are then used to extrapolate the viral evolutionary dynamics beyond the experimental settings. Assuming a fixed basic reproductive ratio of the virus (independent of transmission pathway), we find that recombinant evolution is fastest if virus spread is driven only by cell-to-cell transmission and slows down if both transmission pathways operate. Recombinant evolution is slowest if all virus spread occurs through free virus transmission. This is due to cell-to-cell transmission 1, increasing infection multiplicity; 2, promoting the co-transmission of different virus strains from cell to cell; and 3, increasing the rate at which point mutations are generated as a result of more reverse transcription events. This study further resulted in the estimation of various parameters that characterize these evolutionary processes. For example, we estimate that during cell-to-cell transmission, an average of three viruses successfully integrated into the target cell, which can significantly raise the infection multiplicity compared to free virus transmission. In general, our study points towards the importance of infection multiplicity and cell-to-cell transmission for HIV evolution.

Effect of synaptic cell-to-cell transmission and recombination on the evolution of double mutants in HIV

Recombination in HIV infection can impact virus evolution in vivo in complex ways, as has been shown both experimentally and mathematically. The effect of free virus versus synaptic, cell-to-cell transmission on the evolution of double mutants, however, has not been investigated. Here, we do so by using a stochastic agent-based model. Consistent with data, we assume spatial constraints for synaptic but not for free-virus transmission. Two important effects of the viral spread mode are observed: (i) for disadvantageous mutants, synaptic transmission protects against detrimental effects of recombination on double mutant persistence. Under free virus transmission, recombination increases double mutant levels for negative epistasis, but reduces them for positive epistasis. This reduction for positive epistasis is much diminished under predominantly synaptic transmission, and recombination can, in fact, lead to increased mutant levels. (ii) The mode of virus spread also directly influences the evolutionary fate of double mutants. For disadvantageous mutants, double mutant production is the predominant driving force, and hence synaptic transmission leads to highest double mutant levels due to increased transmission efficiency. For advantageous mutants, double mutant spread is the most important force, and hence free virus transmission leads to fastest invasion due to better mixing. For neutral mutants, both production and spread of double mutants are important, and hence an optimal mixture of free virus and synaptic transmission maximizes double mutant fractions. Therefore, both free virus and synaptic transmission can enhance or delay double mutant evolution. Implications for drug resistance in HIV are discussed.

The emergence of an unassigned complex recombinant form in a Pakistani HIV-infected individual

In Pakistan, the HIV situation has gone from an outbreak to a concentrated epidemic, and the virus has now crossed into the low-risk population. In addition, several new HIV outbreaks have occurred in different parts of the country. HIV-1 subtype A has been the major epidemic subtype in Pakistan; however, as the epidemic has grown, the emergence of several new subtypes and recombinant forms has been observed. Here, we present the first case and genetic analysis of an unassigned, complex recombinant form in a Pakistani HIV-infected individual with virological failure. Genetic analysis of the sequence indicated that this recombinant form is multi-drug resistant, harboring drug resistance mutations against more than one class of antiretroviral drugs.

Multiple infection of cells changes the dynamics of basic viral evolutionary processes

The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoretical insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.

Pathogen evolution in finite populations: slow and steady spreads the best

The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evolutionary outcome. We discuss the importance of the shape of the pathogen fitness landscape on the balance between mutation, selection and genetic drift. This analysis reconciles Adaptive Dynamics with population genetics in finite populations and provides a new theoretical toolbox to study life-history evolution in realistic ecological scenarios.

Sanger and Next Generation Sequencing Approaches to Evaluate HIV-1 Virus in Blood Compartments

The implementation of antiretroviral treatment combined with the monitoring of drug resistance mutations improves the quality of life of HIV-1 positive patients. The drug resistance mutation patterns and viral genotypes are currently analyzed by DNA sequencing of the virus in the plasma of patients. However, the virus compartmentalizes, and different T cell subsets may harbor distinct viral subsets. In this study, we compared the patterns of HIV distribution in cell-free (blood plasma) and cell-associated viruses (peripheral blood mononuclear cells, PBMCs) derived from ART-treated patients by using Sanger sequencing- and Next-Generation sequencing-based HIV assay. CD4⁺CD45RA⁻RO⁺ memory T-cells were isolated from PBMCs using a BD FACSAria instrument. HIV pol (protease and reverse transcriptase) was RT-PCR or PCR amplified from the plasma and the T-cell subset, respectively. Sequences were obtained using Sanger sequencing and Next-Generation Sequencing (NGS). Sanger sequences were aligned and edited using RECall software (beta v3.03). The Stanford HIV database was used to evaluate drug resistance mutations. Illumina MiSeq platform and HyDRA Web were used to generate and analyze NGS data, respectively. Our results show a high correlation between Sanger sequencing and NGS results. However, some major and minor drug resistance mutations were only observed by NGS, albeit at different frequencies. Analysis of low-frequency drugs resistance mutations and virus distribution in the blood compartments may provide information to allow a more sustainable response to therapy and better disease management.

Dynamics of HIV-1 coinfection in different susceptible target cell populations during cell-free infection

HIV-1 mutations rapidly accumulate through genetic recombination events, which require the infection of a single cell by two virions (coinfection). Accumulation of mutations in the viral population may lead to immune escape and high-level drug resistance. The existence of cell subpopulations characterized by different susceptibility to HIV-1 infection has been proposed as an important parameter driving coinfection (Dang et al., 2004). While the mechanism and the quantification of HIV-1 coinfection have been recently investigated by mathematical models, the detailed dynamics of this process during cell-free infection remains elusive. In this study, we constructed ordinary differential equations considering the heterogeneity of target cell populations during cell-free infection in cell culture, and reproduced the cell culture experimental data. Our mathematical analyses showed that the presence of two differently susceptible target cell subpopulations could explain our experimental datasets, while increasing the number of subpopulations did not improve the fitting. In addition, we quantitatively demonstrated that cells infected by multiple viruses mainly accumulated from one cell subpopulation under cell-free infection conditions. In particular, the frequency of infection events in the more susceptible subpopulation was 6.11-higher than that from the other subpopulation, and 98.3% of coinfected cells emerged from the more susceptible subpopulation. Our mathematical-experimental approach is able to extract such a quantitative information, and can be easily applied to other virus infections.

Mutation and recombination in pathogen evolution: Relevance, methods and controversies

Mutation and recombination drive the evolution of most pathogens by generating the genetic variants upon which selection operates. Those variants can, for example, confer resistance to host immune systems and drug therapies or lead to epidemic outbreaks. Given their importance, diverse evolutionary studies have investigated the abundance and consequences of mutation and recombination in pathogen populations. However, some controversies persist regarding the contribution of each evolutionary force to the development of particular phenotypic observations (e.g., drug resistance). In this study, we revise the importance of mutation and recombination in the evolution of pathogens at both intra-host and inter-host levels. We also describe state-of-the-art analytical methodologies to detect and quantify these two evolutionary forces, including biases that are often ignored in evolutionary studies. Finally, we present some of our former studies involving pathogenic taxa where mutation and recombination played crucial roles in the recovery of pathogenic fitness, the generation of interspecific genetic diversity, or the design of centralized vaccines. This review also illustrates several common controversies and pitfalls in the analysis and in the evaluation and interpretation of mutation and recombination outcomes.

Heterogeneous recombination among Hepatitis B virus genotypes

The rapid evolution of Hepatitis B virus (HBV) through both evolutionary forces, mutation and recombination, allows this virus to generate a large variety of adapted variants at both intra and inter-host levels. It can, for instance, generate drug resistance or the diverse viral genotypes that currently exist in the HBV epidemics. Concerning the latter, it is known that recombination played a major role in the emergence and genetic diversification of novel genotypes. In this regard, the quantification of viral recombination in each genotype can provide relevant information to devise expectations about the evolutionary trends of the epidemic. Here we measured the amount of this evolutionary force by estimating global and local recombination rates in >4700 HBV complete genome sequences corresponding to nine (A to I) HBV genotypes. Counterintuitively, we found that genotype E presents extremely high levels of recombination, followed by genotypes B and C. On the other hand, genotype G presents the lowest level, where recombination is almost negligible. We discuss these findings in the light of known characteristics of these genotypes. Additionally, we present a phylogenetic network to depict the evolutionary history of the studied HBV genotypes. This network clearly classified all genotypes into specific groups and indicated that diverse pairs of genotypes are derived from a common ancestor (i.e., C-I, D-E and, F-H) although still the origin of this virus presented large uncertainty. Altogether we conclude that the amount of observed recombination is heterogeneous among HBV genotypes and that this heterogeneity can influence on the future expansion of the epidemic.

Models of Viral Population Dynamics

Models of viral population dynamics have contributed enormously to our understanding of the pathogenesis and transmission of several infectious diseases, the coevolutionary dynamics of viruses and their hosts, the mechanisms of action of drugs, and the effectiveness of interventions. In this chapter, we review major advances in the modeling of the population dynamics of the human immunodeficiency virus (HIV) and briefly discuss adaptations to other viruses.

The Role of Recombination in Evolutionary Rescue

How likely is it that a population escapes extinction through adaptive evolution? The answer to this question is of great relevance in conservation biology, where we aim at species' rescue and the maintenance of biodiversity, and in agriculture and medicine, where we seek to hamper the emergence of pesticide or drug resistance. By reshuffling the genome, recombination has two antagonistic effects on the probability of evolutionary rescue: it generates and it breaks up favorable gene combinations. Which of the two effects prevails depends on the fitness effects of mutations and on the impact of stochasticity on the allele frequencies. In this article, we analyze a mathematical model for rescue after a sudden environmental change when adaptation is contingent on mutations at two loci. The analysis reveals a complex nonlinear dependence of population survival on recombination. We moreover find that, counterintuitively, a fast eradication of the wild type can promote rescue in the presence of recombination. The model also shows that two-step rescue is not unlikely to happen and can even be more likely than single-step rescue (where adaptation relies on a single mutation), depending on the circumstances.

Clonality and intracellular polyploidy in virus evolution and pathogenesis

In the present article we examine clonality in virus evolution. Most viruses retain an active recombination machinery as a potential means to initiate new levels of genetic exploration that go beyond those attainable solely by point mutations. However, despite abundant recombination that may be linked to molecular events essential for genome replication, herein we provide evidence that generation of recombinants with altered biological properties is not essential for the completion of the replication cycles of viruses, and that viral lineages (near-clades) can be defined. We distinguish mechanistically active but inconsequential recombination from evolutionarily relevant recombination, illustrated by episodes in the field and during experimental evolution. In the field, recombination has been at the origin of new viral pathogens, and has conferred fitness advantages to some viruses once the parental viruses have attained a sufficient degree of diversification by point mutations. In the laboratory, recombination mediated a salient genome segmentation of foot-and-mouth disease virus, an important animal pathogen whose genome in nature has always been characterized as unsegmented. We propose a model of continuous mutation and recombination, with punctuated, biologically relevant recombination events for the survival of viruses, both as disease agents and as promoters of cellular evolution. Thus, clonality is the standard evolutionary mode for viruses because recombination is largely inconsequential, since the decisive events for virus replication and survival are not dependent on the exchange of genetic material and formation of recombinant (mosaic) genomes.

Genetic Consequences of Antiviral Therapy on HIV-1

A variety of enzyme inhibitors have been developed in combating HIV-1, however the fast evolutionary rate of this virus commonly leads to the emergence of resistance mutations that finally allows the mutant virus to survive. This review explores the main genetic consequences of HIV-1 molecular evolution during antiviral therapies, including the viral genetic diversity and molecular adaptation. The role of recombination in the generation of drug resistance is also analyzed. Besides the investigation and discussion of published works, an evolutionary analysis of protease-coding genes collected from patients before and after treatment with different protease inhibitors was included to validate previous studies. Finally, the review discusses the importance of considering genetic consequences of antiviral therapies in models of HIV-1 evolution that could improve current genotypic resistance testing and treatments design.

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

Recombination accelerates adaptation on a large-scale empirical fitness landscape in HIV-1

Recombination has the potential to facilitate adaptation. In spite of the substantial body of theory on the impact of recombination on the evolutionary dynamics of adapting populations, empirical evidence to test these theories is still scarce. We examined the effect of recombination on adaptation on a large-scale empirical fitness landscape in HIV-1 based on in vitro fitness measurements. Our results indicate that recombination substantially increases the rate of adaptation under a wide range of parameter values for population size, mutation rate and recombination rate. The accelerating effect of recombination is stronger for intermediate mutation rates but increases in a monotonic way with the recombination rates and population sizes that we examined. We also found that both fitness effects of individual mutations and epistatic fitness interactions cause recombination to accelerate adaptation. The estimated epistasis in the adapting populations is significantly negative. Our results highlight the importance of recombination in the evolution of HIV-I.

One of the most challenging issues in evolutionary biology concerns the question of why most organisms exchange genetic material with each other, e.g. during sexual reproduction. Gene shuffling can create genetic diversity that facilitates adaptation to new environments, but theory shows that this effect is highly dependent on how different genes interact in determining the fitness of an organism. Using a large data set of fitness values based on HIV-1, we provide evidence that shuffling of genetic material indeed raises the level of genetic diversity, and as a result accelerates adaptation. Our results also propose genetic shuffling as a mechanism utilized by HIV to accelerate the evolution of multi-drug-resistant strains.

Mathematical models of HIV replication and pathogenesis

This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.

Superinfection with drug-resistant HIV is rare and does not contribute substantially to therapy failure in a large European cohort

Background

Superinfection with drug resistant HIV strains could potentially contribute to compromised therapy in patients initially infected with drug-sensitive virus and receiving antiretroviral therapy. To investigate the importance of this potential route to drug resistance, we developed a bioinformatics pipeline to detect superinfection from routinely collected genotyping data, and assessed whether superinfection contributed to increased drug resistance in a large European cohort of viremic, drug treated patients.

Methods

We used sequence data from routine genotypic tests spanning the protease and partial reverse transcriptase regions in the Virolab and EuResist databases that collated data from five European countries. Superinfection was indicated when sequences of a patient failed to cluster together in phylogenetic trees constructed with selected sets of control sequences. A subset of the indicated cases was validated by re-sequencing pol and env regions from the original samples.

Results

4425 patients had at least two sequences in the database, with a total of 13816 distinct sequence entries (of which 86% belonged to subtype B). We identified 107 patients with phylogenetic evidence for superinfection. In 14 of these cases, we analyzed newly amplified sequences from the original samples for validation purposes: only 2 cases were verified as superinfections in the repeated analyses, the other 12 cases turned out to involve sample or sequence misidentification. Resistance to drugs used at the time of strain replacement did not change in these two patients. A third case could not be validated by re-sequencing, but was supported as superinfection by an intermediate sequence with high degenerate base pair count within the time frame of strain switching. Drug resistance increased in this single patient.

Conclusions

Routine genotyping data are informative for the detection of HIV superinfection; however, most cases of non-monophyletic clustering in patient phylogenies arise from sample or sequence mix-up rather than from superinfection, which emphasizes the importance of validation. Non-transient superinfection was rare in our mainly treatment experienced cohort, and we found a single case of possible transmitted drug resistance by this route. We therefore conclude that in our large cohort, superinfection with drug resistant HIV did not compromise the efficiency of antiretroviral treatment.

Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs

Cell-to-cell viral transmission via virological synapses has been argued to reduce susceptibility of the virus population to anti-viral drugs through multiple infection of cells, contributing to low-level viral persistence during therapy. Using a mathematical framework, we examine the role of synaptic transmission in treatment susceptibility. A key factor is the relative probability of individual virions to infect a cell during free-virus and synaptic transmission, a currently unknown quantity. If this infection probability is higher for free-virus transmission, then treatment susceptibility is lowest if one virus is transferred per synapse, and multiple infection of cells increases susceptibility. In the opposite case, treatment susceptibility is minimized for an intermediate number of virions transferred per synapse. Hence, multiple infection via synapses does not simply lower treatment susceptibility. Without further experimental investigations, one cannot conclude that synaptic transmission provides an additional mechanism for the virus to persist at low levels during anti-viral therapy.

Modeling sequence evolution in HIV-1 infection with recombination

Previously we proposed two simplified models of early HIV-1 evolution. Both showed that under a model of neutral evolution and exponential growth, the mean Hamming distance (HD) between genetic sequences grows linearly with time. In this paper we describe a more realistic continuous-time, age-dependent mathematical model of infection and viral replication, and show through simulations that even in this more complex description, the mean Hamming distance grows linearly with time. This remains unchanged when we introduce recombination, though the confidence intervals of the mean HD obtained ignoring recombination are overly conservative.

Virus dynamics in the presence of synaptic transmission

Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become. clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immunodeficiency virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell-cell synaptic transmission. We explore different "strategies" of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.

Accelerated crossing of fitness valleys through division of labor and cheating in asexual populations

Complex traits can require the accumulation of multiple mutations that are individually deleterious. Their evolution requires a fitness valley to be crossed, which can take relatively long time spans. A new evolutionary mechanism is described that accelerates the emergence of complex phenotypes, based on a “division of labor” game and the occurrence of cheaters. If each intermediate mutation leads to a product that can be shared with others, the complex type can arise relatively quickly as an emergent property among cooperating individuals, without any given individual having to accumulate all mutations. Moreover, the emergence of cheaters that destroy cooperative interactions can lead to the emergence of individuals that have accumulated all necessary mutations on a time scale that is significantly faster than observed in the absence of cooperation and cheating. Application of this mechanism to somatic and microbial evolution is discussed, including evolutionary processes in tumors, biofilms, and viral infections.

Circulating virus load determines the size of bottlenecks in viral populations progressing within a host

For any organism, population size, and fluctuations thereof, are of primary importance in determining the forces driving its evolution. This is particularly true for viruses--rapidly evolving entities that form populations with transient and explosive expansions alternating with phases of migration, resulting in strong population bottlenecks and associated founder effects that increase genetic drift. A typical illustration of this pattern is the progression of viral disease within a eukaryotic host, where such demographic fluctuations are a key factor in the emergence of new variants with altered virulence. Viruses initiate replication in one or only a few infection foci, then move through the vasculature to seed secondary infection sites and so invade distant organs and tissues. Founder effects during this within-host colonization might depend on the concentration of infectious units accumulating and circulating in the vasculature, as this represents the infection dose reaching new organs or "territories". Surprisingly, whether or not the easily measurable circulating (plasma) virus load directly drives the size of population bottlenecks during host colonization has not been documented in animal viruses, while in plants the virus load within the sap has never been estimated. Here, we address this important question by monitoring both the virus concentration flowing in host plant sap, and the number of viral genomes founding the population in each successive new leaf. Our results clearly indicate that the concentration of circulating viruses directly determines the size of bottlenecks, which hence controls founder effects and effective population size during disease progression within a host.

Stochastic simulations suggest that HIV-1 survives close to its error threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.

Currently available antiretroviral drugs curtail HIV infection but fail to eradicate the virus. A strategy of intervention radically different from that employed by current drugs has been proposed by the molecular quasispecies theory. The theory predicts that increasing the viral mutation rate beyond a critical value, called the error threshold, would cause a severe loss of genetic information, potentially leading to viral clearance. Several chemical mutagens are now being developed that can increase the mutation rate of HIV-1. Their success depends on reliable estimates of the error threshold of HIV-1, which are currently lacking. The quasispecies theory cannot be applied directly to HIV-1: the theory considers an infinitely large population of asexually reproducing haploid individuals, whereas HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We employed detailed stochastic simulations that overcome the limitations of the quasispecies theory and accurately mimic HIV-1 evolution in vivo. With these simulations, we estimated the error threshold of HIV-1 to be ∼2–6-fold higher than its natural mutation rate, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs.

Suboptimal provirus expression explains apparent nonrandom cell coinfection with HIV-1

Despite the ability of primate lentiviruses to prevent infected cells from being reinfected, cell coinfection has occurred in the past and has shaped virus evolution by promoting the biogenesis of heterozygous virions and recombination during reverse transcription. In vitro experiments have shown that cell coinfection with HIV is more frequent than would be expected if coinfection were a random process. A possible explanation for this bias is the heterogeneity of target cells and the preferred infection of a subpopulation. To address this question, we compared the frequency of double-positive cells measured following coincubation with green fluorescent protein (GFP) and DsRed HIV reporter viruses with that of stochastic coinfection calculated as the product of the frequencies of GFP- and DsRed-positive cells upon incubation with either reporter virus. Coinfection was more frequent than would be expected on the grounds of stochastic infection, due to the underestimation of single-infection frequencies, which mathematically decreased the calculated frequency. Indeed, when cells were incubated with either reporter virus, a fraction of the cells were scored as uninfected yet harbored a silent provirus that was reactivated upon coinfection through cross talk between viral elements. When such cross talk was avoided, experimental and calculated coinfection frequencies matched, indicating random coinfection. The proportion of infected cells harboring a silent provirus was estimated from coinfection experiments and was shown to be cell type dependent but independent of the virus entry route.

The origin of genetic diversity in HIV-1

One of the hallmarks of HIV infection is the rapid development of a genetically complex population (quasispecies) from an initially limited number of infectious particles. Genetic diversity remains one of the major obstacles to eradication of HIV. The viral quasispecies can respond rapidly to selective pressures, such as that imposed by the immune system and antiretroviral therapy, and frustrates vaccine design efforts. Two unique features of retroviral replication are responsible for the unprecedented variation generated during infection. First, mutations are frequently introduced into the viral genome by the error prone viral reverse transcriptase and through the actions of host cellular factors, such as the APOBEC family of nucleic acid editing enzymes. Second, the HIV reverse transcriptase can utilize both copies of the co-packaged viral genome in a process termed retroviral recombination. When the co-packaged viral genomes are genetically different, retroviral recombination can lead to the shuffling of mutations between viral genomes in the quasispecies. This review outlines the stages of the retroviral life cycle where genetic variation is introduced, focusing on the principal mechanisms of mutation and recombination. Understanding the mechanistic origin of genetic diversity is essential to combating HIV.

Viral quasispecies evolution

Evolution of RNA viruses occurs through disequilibria of collections of closely related mutant spectra or mutant clouds termed viral quasispecies. Here we review the origin of the quasispecies concept and some biological implications of quasispecies dynamics. Two main aspects are addressed: (i) mutant clouds as reservoirs of phenotypic variants for virus adaptability and (ii) the internal interactions that are established within mutant spectra that render a virus ensemble the unit of selection. The understanding of viruses as quasispecies has led to new antiviral designs, such as lethal mutagenesis, whose aim is to drive viruses toward low fitness values with limited chances of fitness recovery. The impact of quasispecies for three salient human pathogens, human immunodeficiency virus and the hepatitis B and C viruses, is reviewed, with emphasis on antiviral treatment strategies. Finally, extensions of quasispecies to nonviral systems are briefly mentioned to emphasize the broad applicability of quasispecies theory.

Increased burst size in multiply infected cells can alter basic virus dynamics

BACKGROUND

The dynamics of viral infections have been studied extensively in a variety of settings, both experimentally and with mathematical models. The majority of mathematical models assumes that only one virus can infect a given cell at a time. It is, however, clear that especially in the context of high viral load, cells can become infected with multiple copies of a virus, a process called coinfection. This has been best demonstrated experimentally for human immunodeficiency virus (HIV), although it is thought to be equally relevant for a number of other viral infections. In a previously explored mathematical model, the viral output from an infected cell does not depend on the number of viruses that reside in the cell, i.e. viral replication is limited by cellular rather than viral factors. In this case, basic virus dynamics properties are not altered by coinfection.

RESULTS

Here, we explore the alternative assumption that multiply infected cells are characterized by an increased burst size and find that this can fundamentally alter model predictions. Under this scenario, establishment of infection may not be solely determined by the basic reproductive ratio of the virus, but can depend on the initial virus load. Upon infection, the virus population need not follow straight exponential growth. Instead, the exponential rate of growth can increase over time as virus load becomes larger. Moreover, the model suggests that the ability of anti-viral drugs to suppress the virus population can depend on the virus load upon initiation of therapy. This is because more coinfected cells, which produce more virus, are present at higher virus loads. Hence, the degree of drug resistance is not only determined by the viral genotype, but also by the prevalence of coinfected cells.

CONCLUSIONS

Our work shows how an increased burst size in multiply infected cells can alter basic infection dynamics. This forms the basis for future experimental testing of model assumptions and predictions that can distinguish between the different scenarios.

Impaired immune evasion in HIV through intracellular delays and multiple infection of cells

With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8(+) cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.

The evolutionary epidemiology of multilocus drug resistance

The evolution of resistance to drugs is a major public health concern as it erodes the efficacy of our therapeutic arsenal against bacterial, viral, and fungal pathogens. Increasingly, it is recognized that the evolution of resistance involves genetic changes at more than one locus, both in cases where multiple changes are required to obtain high-level resistance, and where compensatory changes at secondary loci ameliorate the costs of resistance. Similarly, multiple loci are often involved in the evolution of multidrug resistance. There has been widespread interest recently in understanding the evolutionary consequences of multilocus resistance, with many empirical studies documenting extensive patterns of genetic interactions (i.e., epistasis) among the loci involved. Currently, however, there are few general theoretical results available that bridge the gap between classical multilocus population genetics and mathematical epidemiology. Here, such theory is developed to shed new light on these previous studies, and to provide further guidance on the type of data required to predict the evolution of pathogens in response to drug pressure. Our results reveal the importance of feedbacks between the epidemiological and evolutionary dynamics, and illustrate how these feedbacks can be exploited to control resistance. In particular, we show how interventions such as social distancing and isolation can influence rates of recombination, and how this then can slow the spread of multilocus resistance and increase the likelihood of reversion to drug sensitivity once drug therapy has ceased.

Effect of multiple infection of cells on the evolutionary dynamics of HIV in vivo: implications for host adaptation mechanisms

The dynamics between human immunodeficiency virus type 1 and the immune system have been studied both experimentally and mathematically, exploring aspects of host adaptation and viral mechanisms to escape host control. The majority of this work, however, has been performed assuming that any cell can only be infected by one copy of the virus. In recent years, it has become clear that multiple copies of the virus can infect the same cell, a process we refer to as co-infection. Here, we review this topic and discuss how immune control of the infection and the ability of the virus to escape immune control is affected by co-infection.

Population biological principles of drug-resistance evolution in infectious diseases

The emergence of resistant pathogens in response to selection pressure by drugs and their possible disappearance when drug use is discontinued are evolutionary processes common to many pathogens. Population biological models have been used to study the dynamics of resistance in viruses, bacteria, and eukaryotic microparasites both at the level of the individual treated host and of the treated host population. Despite the existence of generic features that underlie such evolutionary dynamics, different conclusions have been reached about the key factors affecting the rate of resistance evolution and how to best use drugs to minimise the risk of generating high levels of resistance. Improved understanding of generic versus specific population biological aspects will help to translate results between different studies, and allow development of a more rational basis for sustainable drug use than exists at present.

The role of recombination for the coevolutionary dynamics of HIV and the immune response

The evolutionary implications of recombination in HIV remain not fully understood. A plausible effect could be an enhancement of immune escape from cytotoxic T lymphocytes (CTLs). In order to test this hypothesis, we constructed a population dynamic model of immune escape in HIV and examined the viral-immune dynamics with and without recombination. Our model shows that recombination (i) increases the genetic diversity of the viral population, (ii) accelerates the emergence of escape mutations with and without compensatory mutations, and (iii) accelerates the acquisition of immune escape mutations in the early stage of viral infection. We see a particularly strong impact of recombination in systems with broad, non-immunodominant CTL responses. Overall, our study argues for the importance of recombination in HIV in allowing the virus to adapt to changing selective pressures as imposed by the immune system and shows that the effect of recombination depends on the immunodominance pattern of effector T cell responses.

Taking multiple infections of cells and recombination into account leads to small within-host effective-population-size estimates of HIV-1

Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, N(e), are widely varying. Models assuming HIV-1 evolution to be neutral estimate N(e)~10²-10⁴, smaller than the inverse mutation rate of HIV-1 (~10⁵), implying the predominance of stochastic forces. In contrast, a model that includes selection estimates N(e)>10⁵, suggesting that deterministic forces would hold sway. The consequent uncertainty in the nature of HIV-1 evolution compromises our ability to describe disease progression and outcomes of therapy. We perform detailed bit-string simulations of viral evolution that consider large genome lengths and incorporate the key evolutionary processes underlying the genomic diversification of HIV-1 in infected individuals, namely, mutation, multiple infections of cells, recombination, selection, and epistatic interactions between multiple loci. Our simulations describe quantitatively the evolution of HIV-1 diversity and divergence in patients. From comparisons of our simulations with patient data, we estimate N(e)~10³-10⁴, implying predominantly stochastic evolution. Interestingly, we find that N(e) and the viral generation time are correlated with the disease progression time, presenting a route to a priori prediction of disease progression in patients. Further, we show that the previous estimate of N(e)>10⁵ reduces as the frequencies of multiple infections of cells and recombination assumed increase. Our simulations with N(e)~10³-10⁴ may be employed to estimate markers of disease progression and outcomes of therapy that depend on the evolution of viral diversity and divergence.

Effect of different modes of viral spread on the dynamics of multiply infected cells in human immunodeficiency virus infection

Infection of individual cells with more than one HIV particle is an important feature of HIV replication, which may contribute to HIV pathogenesis via the occurrence of recombination, viral complementation and other outcomes that influence HIV replication and evolutionary dynamics. A previous mathematical model of co-infection has shown that the number of cells infected with i viruses correlates with the ith power of the singly infected cell population, and this has partly been observed in experiments. This model, however, assumed that virus spread from cell to cell occurs only via free virus particles, and that viruses and cells mix perfectly. Here, we introduce a cellular automaton model that takes into account different modes of virus spread among cells, including cell to cell transmission via the virological synapse, and spatially constrained virus spread. In these scenarios, it is found that the number of multiply infected cells correlates linearly with the number of singly infected cells, meaning that co-infection plays a greater role at lower virus loads. The model further indicates that current experimental systems that are used to study co-infection dynamics fail to reflect the true dynamics of multiply infected cells under these specific assumptions, and that new experimental techniques need to be designed to distinguish between the different assumptions.

Accurately measuring recombination between closely related HIV-1 genomes

Retroviral recombination is thought to play an important role in the generation of immune escape and multiple drug resistance by shuffling pre-existing mutations in the viral population. Current estimates of HIV-1 recombination rates are derived from measurements within reporter gene sequences or genetically divergent HIV sequences. These measurements do not mimic the recombination occurring in vivo, between closely related genomes. Additionally, the methods used to measure recombination make a variety of assumptions about the underlying process, and often fail to account adequately for issues such as co-infection of cells or the possibility of multiple template switches between recombination sites. We have developed a HIV-1 marker system by making a small number of codon modifications in gag which allow recombination to be measured over various lengths between closely related viral genomes. We have developed statistical tools to measure recombination rates that can compensate for the possibility of multiple template switches. Our results show that when multiple template switches are ignored the error is substantial, particularly when recombination rates are high, or the genomic distance is large. We demonstrate that this system is applicable to other studies to accurately measure the recombination rate and show that recombination does not occur randomly within the HIV genome.

A phylogenetic and Markov model approach for the reconstruction of mutational pathways of drug resistance

MOTIVATION

Modern HIV-1, hepatitis B virus and hepatitis C virus antiviral therapies have been successful at keeping viruses suppressed for prolonged periods of time, but therapy failures attributable to the emergence of drug resistant mutations continue to be a distressing reminder that no therapy can fully eradicate these viruses from their host organisms. To better understand the emergence of drug resistance, we combined phylogenetic and statistical models of viral evolution in a 2-phase computational approach that reconstructs mutational pathways of drug resistance.

RESULTS

The first phase of the algorithm involved the modeling of the evolution of the virus within the human host environment. The inclusion of longitudinal clonal sequence data was a key aspect of the model due to the progressive fashion in which multiple mutations become linked in the same genome creating drug resistant genotypes. The second phase involved the development of a Markov model to calculate the transition probabilities between the different genotypes. The proposed method was applied to data from an HIV-1 Efavirenz clinical trial study. The obtained model revealed the direction of evolution over time with greater detail than previous models. Our results show that the mutational pathways facilitate the identification of fast versus slow evolutionary pathways to drug resistance.

AVAILABILITY

Source code for the algorithm is publicly available at http://biorg.cis.fiu.edu/vPhyloMM/

Multiple HIV-1 infection of cells and the evolutionary dynamics of cytotoxic T lymphocyte escape mutants

Cytotoxic T lymphocytes (CTL) are an important branch of the immune system, killing virus-infected cells. Many viruses can mutate so that infected cells are not killed by CTL anymore. This escape can contribute to virus persistence and disease. A prominent example is HIV-1. The evolutionary dynamics of CTL escape mutants in vivo have been studied experimentally and mathematically, assuming that a cell can only be infected with one HIV particle at a time. However, according to data, multiple virus particles frequently infect the same cell, a process called coinfection. Here, we study the evolutionary dynamics of CTL escape mutants in the context of coinfection. A mathematical model suggests that an intermediate strength of the CTL response against the wild-type is most detrimental for an escape mutant, minimizing overall virus load and even leading to its extinction. A weaker or, paradoxically, stronger CTL response against the wild-type both lead to the persistence of the escape mutant and higher virus load. It is hypothesized that an intermediate strength of the CTL response, and thus the suboptimal virus suppression observed in HIV-1 infection, might be adaptive to minimize the impact of existing CTL escape mutants on overall virus load.

Timing the emergence of resistance to anti-HIV drugs with large genetic barriers

New antiretroviral drugs that offer large genetic barriers to resistance, such as the recently approved inhibitors of HIV-1 protease, tipranavir and darunavir, present promising weapons to avert the failure of current therapies for HIV infection. Optimal treatment strategies with the new drugs, however, are yet to be established. A key limitation is the poor understanding of the process by which HIV surmounts large genetic barriers to resistance. Extant models of HIV dynamics are predicated on the predominance of deterministic forces underlying the emergence of resistant genomes. In contrast, stochastic forces may dominate, especially when the genetic barrier is large, and delay the emergence of resistant genomes. We develop a mathematical model of HIV dynamics under the influence of an antiretroviral drug to predict the waiting time for the emergence of genomes that carry the requisite mutations to overcome the genetic barrier of the drug. We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments. Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately. Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments

Growth competition assays have been developed to quantify the relative fitness of HIV-1 mutants. In this article, we develop mathematical models to describe viral/cellular dynamic interactions in the assay system from which the competitive fitness indices or parameters are defined. In our previous HIV-viral fitness experiments, the concentration of uninfected target cells was assumed to be constant (Wu et al. 2006). But this may not be true in some experiments. In addition, dual infection may frequently occur in viral fitness experiments and may not be ignorable. Here, we relax these two assumptions and extend our earlier viral fitness model (Wu et al. 2006). The resulting models then become nonlinear ODE systems for which closed-form solutions are not achievable. In the new model, the viral relative fitness is a function of time since it depends on the target cell concentration. First, we studied the structure identifiability of the nonlinear ODE models. The identifiability analysis showed that all parameters in the proposed models are identifiable from the flow-cytometry-based experimental data that we collected. We then employed a global optimization approach (the differential evolution algorithm) to directly estimate the kinetic parameters as well as the relative fitness index in the nonlinear ODE models using nonlinear least square regression based on the experimental data. Practical identifiability was investigated via Monte Carlo simulations.

Modeling HIV infection dynamics: the role of recombination in the development of drug resistance

The benefit of recombination to HIV remains unclear because just as recombination can induce the association of favorable mutations and accelerate the development of multidrug resistance, it can also dissociate favorable combinations of mutations. The confounding influences of mutation, random genetic drift, selection and epistatic interactions between multiple resistance loci render the role of recombination difficult to unravel experimentally. Mathematical models provide valuable insights into the influence of recombination on the genomic diversification of HIV and the development of drug resistance in patients undergoing therapy, capture several recent experimental observations of HIV recombination quantitatively, and set the stage for the establishment of a robust framework for the identification of improved treatment protocols and guidelines for drug development.

Recombination increases human immunodeficiency virus fitness, but not necessarily diversity

Recombination can facilitate the accumulation of mutations and accelerate the emergence of resistance to current antiretroviral therapies for human immunodeficiency virus (HIV) infection. Yet, since recombination can also dissociate favourable combinations of mutations, the benefit of recombination to HIV remains in question. The confounding effects of mutation, multiple infections of cells, random genetic drift and fitness selection that underlie HIV evolution render the influence of recombination difficult to unravel. We developed computer simulations that mimic the genomic diversification of HIV within an infected individual and elucidate the influence of recombination. We find, interestingly, that when the effective population size of HIV is small, recombination increases both the diversity and the mean fitness of the viral population. When the effective population size is large, recombination increases viral fitness but decreases diversity. In effect, recombination enhances (lowers) the likelihood of the existence of multi-drug resistant strains of HIV in infected individuals prior to the onset of therapy when the effective population size is small (large). Our simulations are consistent with several recent experimental observations, including the evolution of HIV diversity and divergencein vivo. The intriguing dependencies on the effective population size appear due to the subtle interplay of drift, selection and epistasis, which we discuss in the light of modern population genetics theories. Current estimates of the effective population size of HIV have large discrepancies. Our simulations present an avenue for accurate determination of the effective population size of HIVin vivoand facilitate establishment of the benefit of recombination to HIV.

Emergence of recombinant forms of HIV: dynamics and scaling

The ability to accelerate the accumulation of favorable combinations of mutations renders recombination a potent force underlying the emergence of forms of HIV that escape multi-drug therapy and specific host immune responses. We present a mathematical model that describes the dynamics of the emergence of recombinant forms of HIV following infection with diverse viral genomes. Mimicking recent in vitro experiments, we consider target cells simultaneously exposed to two distinct, homozygous viral populations and construct dynamical equations that predict the time evolution of populations of uninfected, singly infected, and doubly infected cells, and homozygous, heterozygous, and recombinant viruses. Model predictions capture several recent experimental observations quantitatively and provide insights into the role of recombination in HIV dynamics. From analyses of data from single-round infection experiments with our description of the probability with which recombination accumulates distinct mutations present on the two genomic strands in a virion, we estimate that approximately 8 recombinational strand transfer events occur on average (95% confidence interval: 6-10) during reverse transcription of HIV in T cells. Model predictions of virus and cell dynamics describe the time evolution and the relative prevalence of various infected cell subpopulations following the onset of infection observed experimentally. Remarkably, model predictions are in quantitative agreement with the experimental scaling relationship that the percentage of cells infected with recombinant genomes is proportional to the percentage of cells coinfected with the two genomes employed at the onset of infection. Our model thus presents an accurate description of the influence of recombination on HIV dynamics in vitro. When distinctions between different viral genomes are ignored, our model reduces to the standard model of viral dynamics, which successfully predicts viral load changes in HIV patients undergoing therapy. Our model may thus serve as a useful framework to predict the emergence of multi-drug-resistant forms of HIV in infected individuals.