Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection

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

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 ∼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

Estimating the fraction of progeny virions that must incorporate APOBEC3G for suppression of productive HIV-1 infection

AbstractThe contest between the host factor APOBEC3G (A3G) and the HIV-1 protein Vif presents an attractive target of intervention. The extent to which the A3G–Vif interaction must be suppressed to tilt the balance in favor of A3G remains unknown. We employed stochastic simulations and mathematical modeling of the within-host dynamics and evolution of HIV-1 to estimate the fraction of progeny virions that must incorporate A3G to render productive infection unsustainable. Using three different approaches, we found consistently that a transition from sustained infection to suppression of productive infection occurred when the latter fraction exceeded ~0.8. The transition was triggered by A3G-induced hypermutations that led to premature stop codons compromising viral production and was consistent with driving the basic reproductive number, R0, below unity. The fraction identified may serve as a quantitative guideline for strategies targeting the A3G–Vif axis

Cassava storage : post-harvest deterioration and storage of fresh cassava roots

<p>Sum of squares of the errors (SSE) between data from patients <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone.0014531-Shankarappa1" target="_blank">[36]</a> and our predictions of viral diversity, <i>d_G</i>, and divergence, <i>d_S</i>, for different values of the population size, <i>C</i>, (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone-0014531-g005" target="_blank">Fig. 5</a>) and the viral generation time, τ, shown for each of the nine patients. <i>C</i> and τ that yield the lowest SSE provide the best fit to the data. The best-fit value of <i>C</i> yields <i>N_e</i> (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014531#pone-0014531-t001" target="_blank">Table 1</a>).</p

Modeling viral and drug kinetics: Hepatitis C virus treatment with pegylated interferon alfa-2b

Administration of peginterferon alfa-2b plus ribavirin results in an early hepatitis C virus (HCV) RNA decay followed by an increase as the drug concentration declines between doses. Upon administration of the next dose 1 week later, the same pattern is observed. We have incorporated pharmacokinetic/pharmacodynamic analysis into a model of viral dynamics to describe the effect that changes in drug concentration and effectiveness can have on viral levels. To illustrate the relationship between pharmacokinetics and viral dynamics, we fit the model to data from four HCV/human immunodeficiency virus co-infected patients, and obtained good agreement with the measured serum HCV RNA levels. We were able to account for the observed increases in HCV RNA, and estimate virion and drug half-lives that are in agreement with previous reports. Models incorporating pharmacokinetics are needed to correctly interpret viral load changes and estimate drug effectiveness in treatment protocols using peginterferon alfa-2b

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, Ne, are widely varying. Models assuming HIV-1 evolution to be neutral estimate Ne∼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 Ne>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 Ne∼103–104, implying predominantly stochastic evolution. Interestingly, we find that Ne 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 Ne>105 reduces as the frequencies of multiple infections of cells and recombination assumed increase. Our simulations with Ne∼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

Ribavirin-Induced Anemia in Hepatitis C Virus Patients Undergoing Combination Therapy

The current standard of care for hepatitis C virus (HCV) infection – combination therapy with pegylated interferon and ribavirin – elicits sustained responses in only ∼50% of the patients treated. No alternatives exist for patients who do not respond to combination therapy. Addition of ribavirin substantially improves response rates to interferon and lowers relapse rates following the cessation of therapy, suggesting that increasing ribavirin exposure may further improve treatment response. A key limitation, however, is the toxic side-effect of ribavirin, hemolytic anemia, which often necessitates a reduction of ribavirin dosage and compromises treatment response. Maximizing treatment response thus requires striking a balance between the antiviral and hemolytic activities of ribavirin. Current models of viral kinetics describe the enhancement of treatment response due to ribavirin. Ribavirin-induced anemia, however, remains poorly understood and precludes rational optimization of combination therapy. Here, we develop a new mathematical model of the population dynamics of erythrocytes that quantitatively describes ribavirin-induced anemia in HCV patients. Based on the assumption that ribavirin accumulation decreases erythrocyte lifespan in a dose-dependent manner, model predictions capture several independent experimental observations of the accumulation of ribavirin in erythrocytes and the resulting decline of hemoglobin in HCV patients undergoing combination therapy, estimate the reduced erythrocyte lifespan during therapy, and describe inter-patient variations in the severity of ribavirin-induced anemia. Further, model predictions estimate the threshold ribavirin exposure beyond which anemia becomes intolerable and suggest guidelines for the usage of growth hormones, such as erythropoietin, that stimulate erythrocyte production and avert the reduction of ribavirin dosage, thereby improving treatment response. Our model thus facilitates, in conjunction with models of viral kinetics, the rational identification of treatment protocols that maximize treatment response while curtailing side effects