Estimation of viral parameters, such as the basic reproductive number (R0) and infected cell life span, is central to the quantitative study of the within-host dynamics of viral diseases such as human immunodeficiency virus, hepatitis B or hepatitis C. As these parameters can rarely be determined directly, they are usually estimated indirectly by fitting mathematical models to viral load data. This paper investigates how parameter estimates obtained by such procedures depend on the assumptions made concerning the viral life cycle. It finds that estimates of the basic reproductive number obtained using viral load data collected during the initial stages of infection can depend quite sensitively on these assumptions. The use of models which neglect the intracellular delay before virion production can lead to severe underestimates of R0 and, hence, to overly optimistic predictions of how efficacious treatment must be in order to prevent or eradicate the disease. These results are also of importance for attempts at estimating R0 from similar epidemiological data as there is a correspondence between within-host and between-host models. Estimates of the life span of infected cells obtained from viral load data collected during drug treatment studies also depend on the assumptions made in modelling the virus life cycle. The use of more realistic descriptions of the life cycle is seen to increase estimates of infected cell life span, in addition to providing a new explanation for the shoulder phase seen during drug treatment. This study highlights the limitations of what can be learnt by fitting mathematical models to infectious disease data without detailed independent knowledge of the life cycle of the infectious agent.
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.
HIV; multiple infection; mathematical model; spatial; virus spread
The spread of epidemics not only depends on the average number of parasites produced per host, but also on the existence of highly infectious individuals. It is widely accepted that infectiousness depends on genetic and environmental determinants. However, even in clonal populations of host and viruses growing in homogeneous conditions, high variability can exist. Here we show that Escherichia coli cells commonly display high differentials in viral burst size, and address the kinetics of emergence of such variability with the non-lytic filamentous virus M13. By single-cell imaging of a virally-encoded fluorescent reporter, we monitor the viral charge distribution in infected bacterial populations at different time following infection. A mathematical model assuming autocatalytic virus replication and inheritance of bacterial growth rates quantitatively reproduces the experimental distributions, demonstrating that deterministic amplification of small host inhomogeneities is a mechanism sufficient to explain large and highly skewed distributions. This mechanism of amplification is general and may occur whenever a parasite has an initial phase of exponential growth within its host. Moreover, it naturally reproduces the shift towards higher virulence when the host is experimenting poor conditions, as observed commonly in host-parasite systems.
The mathematical model for the dynamics of the hepatitis C proposed in Avendaño et al. (2002), with four populations (healthy and unhealthy hepatocytes, the viral load of the hepatitis C virus, and T killer cells), is revised. Showing that the reduced model obtained by considering only the first three of these populations, known as basic model, has two possible equilibrium states: the uninfected one where viruses are not present in the individual, and the endemic one where viruses and infected cells are present. A threshold parameter (the basic reproductive virus number) is introduced, and in terms of it, the global stability of both two possible equilibrium states is established. Other central result consists in showing, by model numerical simulations, the feasibility of monitoring liver damage caused by HCV, avoiding unnecessary biopsies and the undesirable related inconveniences/imponderables to the patient; another result gives a mathematical modelling basis to recently developed techniques for the disease assessment based essentially on viral load measurements.
Coinfection of the same host cell by multiple viruses may lead to increased competition for limited cellular resources, thus reducing the fitness of an individual virus. Selection should favor viruses that can limit or prevent coinfection, and it is not surprising that many viruses have evolved mechanisms to do so. Here we explore whether coinfection is limited in the RNA bacteriophage φ6 that infects Pseudomonas phaseolicola. We estimated the limit to coinfection in φ6 by comparing the frequency of hybrids produced by two marked phage strains to that predicted by a mathematical model based on differing limits to coinfection. Our results provide an alternative method for estimating the limit to coinfection and confirm a previous estimate between two to three phages per host cell. In addition, our data reveal that the rate of coinfection at low phage densities may exceed that expected through random Poisson sampling. We discuss whether phage φ6 has evolved an optimal limit that balances the costly and beneficial fitness effects associated with multiple infections.
The mechanism by which human immunodeficiency virus (HIV)-Mycobacterium tuberculosis coinfection facilitates development of HIV-related tuberculosis is poorly characterized. Macaque models of simian immunodeficiency virus (SIVmac)-Mycobacterium bovis BCG coinfection were employed to explore the pathogenesis of AIDS virus-related tuberculosis. Following BCG coinfection, SIV (SIV)-infected macaques with high viral loads developed an SIV-related tuberculosis-like disease. This disease was characterized clinically by a syndrome of diarrhea, anorexia, weight loss, and altered levels of consciousness and pathologically by the presence of disseminated granulomas. In contrast, SIVmac-infected macaques with low viral loads either showed no evidence of BCG-induced disease or developed focal granulomatous lesions. Pathogenic SIV-BCG interactions appeared to play a critical role in triggering the development of this SIV-related tuberculosis-like disease. BCG coinfection enhanced the destruction of CD4+ T cells in SIVmac-infected macaques whose viral loads were high. Reciprocally, exacerbations of SIV disease led to marked suppression of BCG-specific T-cell responses, persistence of the BCG infection, and development of an SIV-related tuberculosis-like disease. Furthermore, development of this SIV-related tuberculosis-like disease was also seen in naïve macaques simultaneously inoculated with SIVmac and BCG. These results provide in vivo evidence that coinfection of AIDS virus-infected individuals with an avirulent mycobacterium can lead to development of a tuberculosis-like disease.
Currently, little is known about the viral kinetics of influenza A during infection within an individual. We utilize a series of mathematical models of increasing complexity, which incorporate target cell limitation and the innate interferon response, to examine influenza A virus kinetics in the upper respiratory tracts of experimentally infected adults. The models were fit to data from an experimental H1N1 influenza A/Hong Kong/123/77 infection and suggest that it is important to include the eclipse phase of the viral life cycle in viral dynamic models. Doing so, we estimate that after a delay of ∼6 h, infected cells begin producing influenza virus and continue to do so for ∼5 h. The average lifetime of infected cells is ∼11 h, and the half-life of free infectious virus is ∼3 h. We calculated the basic reproductive number, R0, which indicated that a single infected cell could produce ∼22 new productive infections. This suggests that antiviral treatments have a large hurdle to overcome in moderating symptoms and limiting infectiousness and that treatment has to be initiated as early as possible. For about 50% of patients, the curve of viral titer versus time has two peaks. This bimodal behavior can be explained by incorporating the antiviral effects of interferon into the model. Our model also compared well to an additional data set on viral titer after experimental infection and treatment with the neuraminidase inhibitor zanamivir, which suggests that such models may prove useful in estimating the efficacies of different antiviral therapies for influenza A infection.
Cytotoxic T-lymphocyte (CTL) memory to viruses has traditionally been studied in an isolated setting. However, recent experiments have indicated that the presence of antigenically heterologous challenges can result in the attrition of CTL memory. Here we use mathematical models in order to explore the consequence of these dynamics for the ability of the immune system in controlling multiple infections. Mathematical models suggest that antigen-independent persistence of CTL memory is required in order to resolve and clear an infection. This ensures strong immunological pressure at low loads when the virus population declines towards extinction. If the number of antigenic stimuli exposed to the immune system crosses a threshold, we find that immunological pressure is significantly reduced at low loads and this can prevent virus clearance and reduces overall control of viral replication. Hence, exposure to many heterologous challenges reduces the ability of CTL memory to contribute to virus control. The higher the number of infections present in the host, the higher the overall virus load and the higher the total number of memory CTLs. Beyond a given threshold, addition of new viruses to the system results in accelerated loss of virus control which eventually leads to a reduction in the overall memory CTL population. These dynamics might contribute to the progressively weaker immunity observed as a result of ageing. In this context, antigenically variable pathogens expose the immune system to many heterologous challenges within a short period of time and this could result in accelerated ageing of the immune system. These results have important implications for vaccination and treatment strategies directed against viral infections.
Oncolytic viruses are viruses that specifically infect cancer cells and kill them, while leaving healthy cells largely intact. Their ability to spread through the tumor makes them an attractive therapy approach. While promising results have been observed in clinical trials, solid success remains elusive since we lack understanding of the basic principles that govern the dynamical interactions between the virus and the cancer. In this respect, computational models can help experimental research at optimizing treatment regimes. Although preliminary mathematical work has been performed, this suffers from the fact that individual models are largely arbitrary and based on biologically uncertain assumptions. Here, we present a general framework to study the dynamics of oncolytic viruses that is independent of uncertain and arbitrary mathematical formulations. We find two categories of dynamics, depending on the assumptions about spatial constraints that govern that spread of the virus from cell to cell. If infected cells are mixed among uninfected cells, there exists a viral replication rate threshold beyond which tumor control is the only outcome. On the other hand, if infected cells are clustered together (e.g. in a solid tumor), then we observe more complicated dynamics in which the outcome of therapy might go either way, depending on the initial number of cells and viruses. We fit our models to previously published experimental data and discuss aspects of model validation, selection, and experimental design. This framework can be used as a basis for model selection and validation in the context of future, more detailed experimental studies. It can further serve as the basis for future, more complex models that take into account other clinically relevant factors such as immune responses.
HIV can spread through its target cell population either via cell-free transmission, or by cell-to-cell transmission, presumably through virological synapses. Synaptic transmission entails the transfer of tens to hundreds of viruses per synapse, a fraction of which successfully integrate into the target cell genome. It is currently not understood how synaptic transmission affects viral fitness. Using a mathematical model, we investigate how different synaptic transmission strategies, defined by the number of viruses passed per synapse, influence the basic reproductive ratio of the virus, R0, and virus load. In the most basic scenario, the model suggests that R0 is maximized if a single virus particle is transferred per synapse. R0 decreases and the infection eventually cannot be maintained for larger numbers of transferred viruses, because multiple infection of the same cell wastes viruses that could otherwise enter uninfected cells. To explain the relatively large number of HIV copies transferred per synapse, we consider additional biological assumptions under which an intermediate number of viruses transferred per synapse could maximize R0. These include an increased burst size in multiply infected cells, the saturation of anti-viral factors upon infection of cells, and rate limiting steps during the process of synapse formation.
Many studies have shown that vaccines inducing CD8+ T cell responses can reduce viral loads and preserve CD4+ T cell numbers in monkey models of HIV infection. The mechanism of viral control by the vaccine-induced CD8+ T cells is usually assumed to be cytolysis of infected cells. However, in addition to cytolysis of infected cells, CD8+ T cells secrete a range of soluble factors that suppress viral replication. We have studied the dynamics of virus and CD4+ T cells in a successful vaccination-challenge model of SHIV infection. We find that better viral control in the acute phase of infection is associated with slower decay of peak viral load. Comparing viral and CD4+ T cell dynamics in acute infection, we find that a cytolytic mode of viral control with direct killing of infected cells is inconsistent with the observed trends. On the other hand, comparison of the predicted effects of noncytolytic CD8+ effector function with the experimental data shows that non-cytolytic control provides a better explanation of the experimental results. Our analysis suggests that vaccine-induced CD8+ T cells control SHIV infection by non-cytolytic means.
Mathematical models of hepatitis C viral (HCV) kinetics provide a means of estimating the antiviral effectiveness of therapy, the rate of virion clearance and the rate of loss of HCV-infected cells. They have also proved useful in evaluating the extrahepatic contribution to HCV plasma viremia and they have suggested mechanisms of action for both interferon-α and ribavirin. Viral kinetic models can explain the observed HCV RNA profiles under treatment, e.g., flat partial response, biphasic and triphasic viral decay and viral rebound. Current therapy with (pegylated) interferon-α and ribavirin has a poorer success in patients having insulin resistance, hepatic fibrosis, African American ethnicity, HCV/HIV-coinfection, HCV genotype-1 and high baseline viral load. The use of mathematical modeling and statistical analysis of experimental data have been useful in understanding some of these treatment obstacles.
The simulation of the dynamics of viral infections by mathematical equations has been applied successfully to the study of viral infections during antiviral therapy. Standard models applied to viral hepatitis describe the viral load decline in the first 2-4 wk of antiviral therapy, but do not adequately simulate the dynamics of viral infection for the following period. The hypothesis of a constant clearance rate of the infected cells provides an unrealistic estimation of the time necessary to reach the control or the clearance of hepatitis B virus (HBV)/hepatitis C virus (HCV) infection. To overcome the problem, we have developed a new multiphasic model in which the immune system activity is modulated by a negative feedback caused by the infected cells reduction, and alanine aminotransferase kinetics serve as a surrogate marker of infected-cell clearance. By this approach, we can compute the dynamics of infected cells during the whole treatment course, and find a good correlation between the number of infected cells at the end of therapy and the long-term virological response in patients with chronic hepatitis C. The new model successfully describes the HBV infection dynamics far beyond the third month of antiviral therapy under the assumption that the sum of infected and non-infected cells remains roughly constant during therapy, and both target and infected cells concur in the hepatocyte turnover. In clinical practice, these new models will allow the development of simulators of treatment response that will be used as an “automatic pilot” for tailoring antiviral therapy in chronic hepatitis B as well as chronic hepatitis C patients.
Viral hepatitis; Bio-mathematical models; Hepatitis B virus; Hepatitis C virus; Viral dynamics
In rapidly evolving viruses the detection of virally infected cells can possibly be subverted by the production of altered peptides. There are peptides with single amino acid changes that can dramatically change T-cell responses, e.g. a loss of cytotoxic activity. They are still recognized by the T cell, but the signals required for effector function are only partially delivered. Thus, altered peptide presenting cells can act as decoy targets for specific immune responses. The existence of altered peptides in vivo has been demonstrated in hepatitis B and HIV. Using a mathematical model we address the question of how these altered peptides can affect the virus-immune system dynamics, and demonstrate that virus survival is enhanced. If the mutation rate of the virus is sufficient, one observes complex dynamics in which the antagonism acts so as to maintain the viral diversity, possibly leading to the development of a mutually antagonistic network or a continual turnover of escape mutants. In either case the pathogen is able to outrun the immune system. Indeed, sometimes the enhancement is so great that a virus that would normally be cleared by the immune system is able to outrun it.
In contrast to many other virus infections, primary cytomegalovirus (CMV) infection does not fully protect against reinfection. Accordingly, clinical data have revealed a coexistence of multiple human CMV variants/strains in individual patients. Notably, the phenomenon of multiple infection was found to correlate with increased virus load and severity of CMV disease. Although of obvious medical relevance, the mechanism underlying this correlation is unknown. A weak immune response in an individual could be responsible for a more severe disease and for multiple infections. Alternatively, synergistic contributions of variants that differ in their biological properties can lead to qualitative changes in viral fitness by direct interactions such as genetic recombination or functional complementation within coinfected host cells. We have addressed this important question paradigmatically with the murine model by differently designed combinations of two viruses employed for experimental coinfection of mice. Specifically, a murine cytomegalovirus (MCMV) mutant expressing Cre recombinase was combined for coinfection with a mutant carrying Cre-inducible green fluorescent protein gene, and attenuated mutants were combined for coinfection with wild-type virus followed by two-color in situ hybridization studies visualizing the replication of the two viruses in infected host organs. These different approaches concurred in the conclusion that coinfection of host cells is more frequent than statistically predicted and that this coinfection alters virus fitness by functional trans-complementation rather than by genetic recombination. The reported findings make a major contribution to our molecular understanding of enhanced CMV pathogenicity in the multiply infected host.
Mathematical models based on kinetics of HIV-1 plasma viremia after initiation of combination antiretroviral therapy (cART) inferred HIV-infected cells to decay exponentially with constant rates correlated to their strength of virus production. To further define in vivo decay kinetics of HIV-1 infected cells experimentally, we assessed infected cell-classes of distinct viral transcriptional activity in peripheral blood mononuclear cells (PBMC) of five patients during 1 year after initiation of cART
In a novel analytical approach patient-matched PCR for unspliced and multiply spliced viral RNAs was combined with limiting dilution analysis at the single cell level. This revealed that HIV-RNA+ PBMC can be stratified into four distinct viral transcriptional classes. Two overlapping cell-classes of high viral transcriptional activity, suggestive of a virion producing phenotype, rapidly declined to undetectable levels. Two cell classes expressing HIV-RNA at low and intermediate levels, presumably insufficient for virus production and occurring at frequencies exceeding those of productively infected cells matched definitions of HIV-latency. These cells persisted during cART. Nevertheless, during the first four weeks of therapy their kinetics resembled that of productively infected cells.
We have observed biphasic decays of latently HIV-infected cells of low and intermediate viral transcriptional activity with marked decreases in cell numbers shortly after initiation of therapy and complete persistence in later phases. A similar decay pattern was shared by cells with greatly enhanced viral transcriptional activity which showed a certain grade of levelling off before their disappearance. Thus it is conceivable that turnover/decay rates of HIV-infected PBMC may be intrinsically variable. In particular they might be accelerated by HIV-induced activation and reactivation of the viral life cycle and slowed down by the disappearance of such feedback-loops after initiation of cART.
We used vesicular stomatitis virus to test the effect of complementation on the relative fitness of a deleterious mutant, monoclonal antibody-resistant mutant (MARM) N, in competition with its wild-type ancestor. We carried out competitions of MARM N and wild-type populations at different multiplicities of infection (MOIs) and initial ratios of the wild type to the mutant and found that the fitness of MARM N relative to that of the wild type is very sensitive to changes in the MOI (i.e., the degree of complementation) but depends little, if at all, on the initial frequencies of MARM N and the wild type. Further, we developed a mathematical model under the assumption that during coinfection both viruses contribute to a common pool of protein products in the infected cell and that they both exploit this common pool equally. Under such conditions, the fitness of all virions that coinfect a cell is the average fitness in the absence of coinfection of that group of virions. In the absence of coinfection, complementation cannot take place and the relative fitness of each competitor is only determined by the selective value of its own products. We found good agreement between our experimental results and the model predictions, which suggests that the wild type and MARM N freely share all of their gene products under coinfection.
Experimental evidence and mathematical models indicate that CD4+ T-cell help is required to generate memory cytotoxicT-lymphocyte precursors (CTLp) that are capable of persisting without ongoing antigenic stimulation, and that such responses are necessary to clear an infection or to control it in the long term. Here we analyse mathematical models of simian immunodeficiency virus (SIV) replication in macaques, assuming that SIV impairs specific CD4+ T-cell responses. According to the models, fast viral replication during the initial stages of primary infection can result in failure to generate sufficient long-lived memory CTLp required to control the infection in the long term. Modelling of drug therapy during the acute phase of the infection indicates that transient treatment can minimize the amount of virus-induced immune impairment, allowing a more effective initial immune sensitization. The result is the development of high levels of memory CTLp that are capable of controlling SIV replication in the long term, in the absence of continuous treament. In the model, the success of treatment depends crucially on the timing and duration of antiretroviral therapy. Data on SIV-infected macaques receiving transient drug therapy during acute infection support these theoretical predictions. The data and modelling suggest that among subjects controlling SIV replication most efficiently after treatment, there is a positive correlation between cellular immune responses and virus load in the post-acute stage of infection. Among subjects showing less-efficient virus control, the correlation is negative. We discuss our findings in relation to previously published data on HIV infection.
Influenza virus infection remains a public health problem worldwide. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. Here, we developed a mathematical model including both innate and adaptive immune responses to study the within-host dynamics of equine influenza virus infection in horses. By comparing modeling predictions with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. Our results show that the rapid and substantial viral decline (about 2 to 4 logs within 1 day) after the peak can be explained by the killing of infected cells mediated by interferon activated cells, such as natural killer cells, during the innate immune response. After the viral load declines to a lower level, the loss of interferon-induced antiviral effect and an increased availability of target cells due to loss of the antiviral state can explain the observed short phase of viral plateau in which the viral level remains unchanged or even experiences a minor second peak in some animals. An adaptive immune response is needed in our model to explain the eventual viral clearance. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection.
Influenza, commonly referred to as the flu, is a contagious respiratory illness caused by influenza virus infections. Although most infected subjects with intact immune systems are able to clear the virus without developing serious flu complications, the mechanisms underlying viral control are not fully understood. In this paper, we address this question by developing mathematical models that include both innate and adaptive immune responses, and fitting them to experimental data from horses infected with equine influenza virus. We find that the innate immune response, such as natural killer cell-mediated infected cell killing and interferon's antiviral effect, can explain the first rapid viral decline and subsequent second peak viremia, and that the adaptive immune response is needed to eventually clear the virus. This study improves our understanding of influenza virus dynamics and may provide more information for future research in influenza pathogenesis, treatment, and vaccination.
Concurrent infection of cattle with bovine viral diarrhoea virus (BVDV) and Mycobacterium bovis is considered to be a possible risk factor for onward transmission of bovine tuberculosis (BTB) in infected cattle, and is known to compromise diagnostic tests. A comparison is made here of M. bovis shedding (i.e. release) characteristics from 12 calves, 6 experimentally coinfected with BVDV and 6 infected with M. bovis alone, using simple models of bacterial replication. These statistical and mathematical models account for the intermittent or episodic nature of shedding, the dynamics of within-host bacterial proliferation and the sampling distribution from a given shedding episode. We show that, while there are distinct differences amongst the shedding patterns of calves given the same infecting dose, there is no statistically significant difference between the two groups of calves. Such differences as there are can be explained solely in terms of the shedding frequency, but with all calves potentially excreting the same amount of bacteria in a given shedding episode post-infection. The model can be thought of as a process of the bacteria becoming established in a number of discrete foci of colonisation, rather than as a more generalised infection of the respiratory tract. In this case, the variability in the shedding patterns of the infected calves can be explained solely by differences in the number of foci established and shedding being from individual foci over time. Should maximum exposure on a particular occasion be a critical consideration for cattle-to-cattle transmission of bovine tuberculosis, cattle that shed only intermittently may still make an important contribution to the spread and persistence of disease.
mathematical model; bacteria; macrophages; tuberculosis
The dynamics of HIV infection have been studied in humans and in a variety of animal models. The standard model of infection has been used to estimate the basic reproductive ratio of the virus, calculated from the growth rate of virus in acute infection. This method has not been useful in studying the effects of vaccination, since, for the vaccines developed so far, early growth rates of virus do not differ between control and vaccinated animals. Here, we use the standard model of viral dynamics to derive the reproductive ratio from the peak viral load and nadir of target cell numbers in acute infection. We apply this method to data from studies of vaccination in SHIV and SIV infection and demonstrate that vaccination can reduce the reproductive ratio by 2.3- and 2-fold, respectively. This method allows the comparison of vaccination efficacies among different viral strains and animal models in vivo.
Two or more viruses infecting the same host cell can interact in ways that profoundly affect disease dynamics and control, yet the factors determining coinfection rates are incompletely understood. Previous studies have focused on the mechanisms that viruses use to suppress coinfection, but recently the phenomenon of enhanced coinfection has also been documented. In the experiments described here, we explore the hypothesis that enhanced coinfection rates in the bacteriophage Φ6 are achieved by virus-induced upregulation of the Φ6 receptor, which is the bacterial pilus. First, we confirmed that coinfection enhancement in Φ6 is virus-mediated by showing that Φ6 attaches significantly faster to infected cells than to uninfected cells. Second, we explored the hypothesis that coinfection enhancement in Φ6 depends upon changes in the expression of an inducible receptor. Consistent with this hypothesis, the closely related phage, Φ12, that uses constitutively expressed lipopolysaccharide as its receptor, attaches to infected and uninfected cells at the same rate. Our results, along with the previous finding that coinfection in Φ6 is limited to two virions, suggest that viruses may closely regulate rates of coinfection through mechanisms for both coinfection enhancement and exclusion.
bacteriophage; coinfection; complementation; evolution; reassortment; virus
Influenza viruses transcribe and replicate their negative-sense RNA genome inside the nucleus of host cells via three viral RNA species. In the course of an infection, these RNAs show distinct dynamics, suggesting that differential regulation takes place. To investigate this regulation in a systematic way, we developed a mathematical model of influenza virus infection at the level of a single mammalian cell. It accounts for key steps of the viral life cycle, from virus entry to progeny virion release, while focusing in particular on the molecular mechanisms that control viral transcription and replication. We therefore explicitly consider the nuclear export of viral genome copies (vRNPs) and a recent hypothesis proposing that replicative intermediates (cRNA) are stabilized by the viral polymerase complex and the nucleoprotein (NP). Together, both mechanisms allow the model to capture a variety of published data sets at an unprecedented level of detail. Our findings provide theoretical support for an early regulation of replication by cRNA stabilization. However, they also suggest that the matrix protein 1 (M1) controls viral RNA levels in the late phase of infection as part of its role during the nuclear export of viral genome copies. Moreover, simulations show an accumulation of viral proteins and RNA toward the end of infection, indicating that transport processes or budding limits virion release. Thus, our mathematical model provides an ideal platform for a systematic and quantitative evaluation of influenza virus replication and its complex regulation.
Retroviral recombination is a potential mechanism for the development of multiply drug resistant viral strains but the impact on the clinical outcomes of antiretroviral therapy in HIV-infected patients is unclear. Recombination can favour resistance by combining single-point mutations into a multiply resistant genome but can also hinder resistance by breaking up associations between mutations. Previous analyses, based on population genetic models, have suggested that whether recombination is favoured or hindered depends on the fitness interactions between loci, or epistasis. In this paper, a mathematical model is developed that includes viral dynamics during therapy and shows that population dynamics interact non-trivially with population genetics. The outcome of therapy depends critically on the changes to the frequency of cell co-infection and I review the evidence available. Where recombination does have an effect on therapy, it is always to slow or even halt the emergence of multiply resistant strains. I also find that for patients newly infected with multiply resistant strains, recombination can act to prevent reversion to wild-type virus. The analysis suggests that treatment targeted at multiple parts of the viral life-cycle may be less prone to drug resistance due to the genetic barrier caused by recombination but that, once selected, mutants resistant to such regimens may be better able to persist in the population.
drug resistance; recombination; treatment failure; mathematical model
In the course of infection, human immunodeficiency virus type 1 (HIV-1) mutates, diverging into a “swarm” of viral quasispecies, and the predominance of CCR5- or CXCR4-utilizing quasispecies is strongly associated with the pattern of disease progression. Quantification of CCR5- and CXCR4-utilizing viruses in viral swarms is important in the investigation of the mechanisms of this phenomenon. Here, we report on a new real-time PCR-based methology for the evaluation of replication of individual CCR5- and CXCR4-utilizing variants. The assay is highly reproducible, with a coefficient of variation of <3%, and it accurately estimates the numbers of virus-specific RNA copies even when their difference in the mixture is 2 orders of magnitude. We demonstrate that replications of CCR5- and CXCR4-utilizing variants can be evaluated and distinguished in experimentally coinfected human lymphoid tissue. The assay we developed may facilitate study of the mechanisms of the R5-to-X4 switch in viral swarms in human tissues infected with HIV-1.