Hepatitis C viral kinetics with the nucleoside polymerase inhibitor mericitabine (RG7128).

UNLABELLED: Mericitabine (RG7128) is a nucleoside polymerase inhibitor (NPI), which requires intracellular uptake and phosphorylation to two active triphosphates. Mathematical modeling has provided important insights for characterizing hepatitis C virus (HCV) RNA decline and estimating in vivo effectiveness of antiviral agents; however, it has not been used to characterize viral kinetics with NPIs. HCV RNA was frequently measured in 32 treatment-experienced patients infected with HCV genotype 1 during and after mericitabine monotherapy for 14 days with 750 mg or 1500 mg administered once (qd) or twice daily (bid). The initial decline of HCV RNA was typically slower than with interferon-α or protease inhibitors, and 12 patients presented a novel pattern of HCV RNA kinetics characterized by a monophasic viral decline. Viral kinetics could be well fitted by assuming that the effectiveness in blocking viral production gradually increased over time to reach its final value, ε(2), consistent with previous accumulation time estimates of intracellular triphosphates. ε(2) was high with bid dosing (mean 750 mg and 1500 mg: 98.0% and 99.8%, respectively; P = 0.018) and significantly higher than in patients treated qd (mean qd versus bid: 90% versus 99%, P < 10(-7)). Virus rebounded rapidly upon drug discontinuation, which was attributed to the elimination of active drug and the subsequent decline of drug effectiveness, with mean t(1/2) = 13.9 hours in the bid regimens. CONCLUSION: The observed slower initial decline likely represents the time needed to accumulate intracellular triphosphates and is consistent with in vitro data. When administered bid, mericitabine reached a high, dose-dependent, final effectiveness in blocking viral production that rapidly dropped upon treatment cessation. Understanding HCV RNA kinetics with mericitabine could provide valuable insights for combining it with other direct-acting antiviral agents.

CD8+ lymphocytes control viral replication in SIVmac239-infected rhesus macaques without decreasing the lifespan of productively infected cells.

While CD8+ T cells are clearly important in controlling virus replication during HIV and SIV infections, the mechanisms underlying this antiviral effect remain poorly understood. In this study, we assessed the in vivo effect of CD8+ lymphocyte depletion on the lifespan of productively infected cells during chronic SIVmac239 infection of rhesus macaques. We treated two groups of animals that were either CD8+ lymphocyte-depleted or controls with antiretroviral therapy, and used mathematical modeling to assess the lifespan of infected cells either in the presence or absence of CD8+ lymphocytes. We found that, in both early (day 57 post-SIV) and late (day 177 post-SIV) chronic SIV infection, depletion of CD8+ lymphocytes did not result in a measurable increase in the lifespan of either short- or long-lived productively infected cells in vivo. This result indicates that the presence of CD8+ lymphocytes does not result in a noticeably shorter lifespan of productively SIV-infected cells, and thus that direct cell killing is unlikely to be the main mechanism underlying the antiviral effect of CD8+ T cells in SIV-infected macaques with high virus replication.

Modelling hepatitis C virus kinetics: the relationship between the infected cell loss rate and the final slope of viral decay.

BACKGROUND: Patients infected with hepatitis C virus (HCV) who respond to treatment with interferon-alpha plus ribavirin exhibit biphasic or triphasic viral load decreases. While the rapid first phase is indicative of the effectiveness of therapy in blocking viral production (epsilon), the slope of the final phase (lambda), that is, the second phase in biphasic decreases and the third phase in triphasic decreases, depends on the infected cell loss rate (delta). In standard models, lambda is approximately epsilondelta when the viral clearance rate c>>delta, as has been previously estimated. METHODS: The relationship among epsilon, delta, lambda and the baseline fraction of HCV-infected hepatocytes (pi) was investigated in a model that included proliferation of hepatocytes. RESULTS: We found that lambda was not proportional to epsilon, but rather obeyed a complex relationship that could lead to dramatic increases in estimates of delta as epsilon increased. In particular, when epsilon<99%, lambda moderately underestimated delta in patients with a small pi, whereas delta might be up to 10-fold larger than lambda in patients with a large pi. Interestingly, when epsilon>99%, delta approximately lambda regardless of pi. CONCLUSIONS: Our results indicated that in patients undergoing therapy who achieved a 2 log(10) reduction in viral load (epsilon<99%), previously estimated delta values might represent only a minimal estimate of the infected cell loss rate. Moreover, combining interferon-alpha with new antiviral agents to achieve epsilon>99% should allow for a more accurate estimate of delta in HCV RNA kinetic studies. This might be important when using viral kinetics to estimate the effect of the immune response on viral elimination and the attainment of sustained virological response.

Modeling HCV kinetics under therapy using PK and PD information.

BACKGROUND: Mathematical models have proven helpful in analyzing the virological response to antiviral therapy in hepatitis C virus (HCV) infected subjects. OBJECTIVE: To summarize the uses and limitations of different models for analyzing HCV kinetic data under pegylated IFN therapy. METHODS: We formulate mathematical models and fit them by nonlinear least square regression to patient data to estimate model parameters. We compare the goodness of fit and parameter values estimated by different models statistically. RESULTS/CONCLUSION: The best model for parameter estimation depends on the availability and the quality of data as well as the therapy used. We also discuss the mathematical models that will be needed to analyze HCV kinetic data from clinical trials with new antiviral drugs.

Modeling complex decay profiles of hepatitis B virus during antiviral therapy.

UNLABELLED: Typically, hepatitis B virus (HBV) decays in patients under therapy in a biphasic manner. However, more complex decay profiles of HBV DNA (e.g., flat partial response, triphasic, and stepwise), for which we have no clear understanding, have also been observed in some treated patients. We recently introduced the notion of a critical drug efficacy, epsilon(c), such that if overall drug efficacy, epsilon(tot), is higher than the critical drug efficacy (i.e., epsilon(tot) > epsilon(c)) then viral levels will continually decline on therapy, while if epsilon(tot) < epsilon(c), then viral loads will initially decline but will ultimately stabilize at a new set point, as seen in flat partial responders. Using the idea of critical efficacy and including hepatocyte proliferation in a viral kinetic model, we can account for these complex HBV DNA decay profiles. The model predicts that complex profiles such as those exhibiting a plateau or shoulder phase, as well as a class of stepwise declines, occur only in patients in whom the majority of hepatocytes are infected before therapy. CONCLUSION: We show via kinetic modeling how a variety of HBV DNA decay profiles can arise in treated patients.

Mathematical modeling of HCV infection and treatment.

In the last decade, viral kinetic modeling has played an important role in the analysis of HCV RNA decay after the initiation of antiviral therapy. Models have provided a means of evaluating the antiviral effectiveness of therapy and of estimating parameters, such as the rate of virion clearance and the rate of loss of HCV-infected cells, and they have suggested mechanisms of action for both interferon-alpha and ribavirin. The inclusion of homeostatic proliferation of infected and uninfected hepatocytes in existing viral kinetic models has allowed prediction of most observed HCV RNA profiles under treatment, for example, biphasic and triphasic viral decay and viral rebound to baseline values after the cessation of therapy. In addition, new kinetic models have taken into consideration the different pharmacokinetics of standard and pegylated forms of interferon and have incorporated alanine aminotransferase kinetics and aspects of immune responses to provide a more comprehensive picture of the biology underlying changes in HCV RNA during therapy. Here, we describe our current understanding of the kinetics of HCV infection and treatment.

A hepatitis C viral kinetic model that allows for time-varying drug effectiveness.

BACKGROUND: The standard model of hepatitis C virus (HCV) dynamics under high-dose daily interferon (IFN) therapy assumed that the drug effectiveness remains constant. However, for treatment with pegylated (PEG)-IFN-alpha2b dosed weekly, drug levels fall substantially and viral load rebounds have been observed toward the end of the weekly dosing interval, implying non-constant drug efficacy. METHODS: In this paper, we developed the decreasing effectiveness (DE) model, a new mathematical model that allows the drug effectiveness to change with time. RESULTS: The DE model can describe viral load rebounds as well as other viral kinetic patterns observed in clinical practice, such as biphasic viral declines. We applied the DE model to the HCV RNA kinetic data under PEG-IFN-alpha2b therapy. The average drug effectiveness during the first week of therapy estimated in the DE model agreed with the one estimated from HCV RNA kinetic data plus pharmacokinetic data. CONCLUSIONS: We illustrated the usefulness of the DE model by analysing HCV RNA data from patients who received PEG-IFN-alpha2b once weekly plus daily ribavirin.

Impact of early viral kinetics on T-cell reactivity during antiviral therapy in chronic hepatitis B.

BACKGROUND: The patterns of hepatitis B viral dynamics during different antiviral therapies and the associated changes in HBV-specific T-cell reactivity are not well defined. METHODS: We investigated the impact of early viral load decline on virus-specific T-cell reactivity in 30 hepatitis B e antigen (HBeAg)-positive patients with chronic hepatitis B randomized to monotherapy with adefovir dipivoxil (ADV) or in combination with emtricitabine (ADV/FTC). Viral kinetics were analysed by mathematical modelling. T-cell reactivity to HBV core and/or surface antigens and natural killer T cell frequency were tested longitudinally, baseline to week 48, using EliSPOT assays and/or flow cytometry. RESULTS: Mathematical modelling of early HBV kinetics identified two subsets of patients: 11 fast responders (undetectable viraemia by week 12; eight on ADV/FTC three on ADV) and 19 slow responders who remained viremic (six on ADV/FTC 13 on ADV). The rate of infected hepatocyte loss was higher in fast than in slow responders (P = 0.0007), and correlated inversely with pre-treatment levels of intrahepatic covalently closed circular HBV DNA. The frequency of HBV core-specific CD4+ T-cells increased significantly only in fast responders, peaking between week 16 and 24, while the HBV surface-specific CD4+ T-cells increased in both subsets. These changes in CD4+ T-cell reactivity were transient however, and no increase in HBV-specific CD8+ T-cells was observed. By week 48, HBeAg seroconversion occurred only in 3/30 (10%) patients. CONCLUSIONS: Early viraemia clearance facilitates recovery of virus-specific CD4+ T-cell reactivity, but appears insufficient to establish clinically relevant antiviral immunity.

Robustness of the signal transduction system of the mammalian JAK/STAT pathway and dimerization steps.

In the interferon-gamma (IFNgamma)-activated Janus Kinase (JAK)/signal transducer and activator of transcription 1 (STAT1) pathway, multiple steps of STAT1 dimerization are required prior to gene expression that produce antiviral molecules. By interpreting experimental results, an existing mathematical model suggested that only phosphorylated STAT1 dimers could translocate to the nucleus and activate gene transcription. In this paper, we examine the role of STAT1 dimerization steps by studying the dynamic behaviors of four alternative models. By analyzing several system properties at low input IFNgamma signal including the steady-state antiviral molecule production, to the input, the delay of responses triggered by input, and the parameter sensitivity, we found that the mice JAK/STAT1 system identified by experiments (1) suppresses antiviral molecule production at low input signal, (2) has slow kinetics of antiviral molecule production and (3) has low parameter sensitivity of antiviral molecule production at steady state. We conclude that the observed structure of the JAK/STAT1 pathway is responsible for the robust system behavior.

Dynamic optimization of host defense, immune memory, and post-infection pathogen levels in mammals.

When attacked by pathogens, higher vertebrates produce specific immune cells that fight against them. We here studied the host's optimal schedule of specific immune cell production. The damage caused by the pathogen increases with the pathogen amount in the host integrated over time. On the other hand, there is also a cost incurred by the production of specific immune cells, not only in terms of the energy needed to produce and maintain the cells, but also with respect to damages sustained by the host's body as a result of immune activity. The optimal strategy of the host is the one that minimizes the total cost, defined as a weighted sum of the damage caused by pathogens and the costs caused by the specific immune cells. The problem is solved by using Pontryagin's maximum principle and dynamic programming. The optimal defense schedule is typically as follows: In the initial phase after infection, immune cells are produced at the fastest possible rate. The amount of pathogen increases temporarily but is eventually suppressed. When the pathogen amount is suppressed to a sufficiently low level, the immune cell number decreases and converges to a low steady level, which is maintained by alternately switching between fastest production and no production. We examine the effect of time delay required to have fully active immune cells by comparing cases with different number of rate limiting steps before producing immune cells. We examine the effect of the duration of time (time delay) required before full-scale production of active immune cells by comparing cases with different numbers of rate-limiting steps before immune-cell production. We also discuss the role of immune memory based on the results of the optimal immune reaction.

Optimal choice between feedforward and feedback control in gene expression to cope with unpredictable danger.

All organisms face risks of unpredictable danger caused by harmful physical environments, pathogens, parasites or predators. Organisms may have several alternative ways of coping with such dangers. These differ in cost, effectiveness and activation time. We study the conditions under which it is optimal to use different alternatives for damage control. As an example we consider a microbe (such as E. coli), which may experience heat shocks that cause denaturation of proteins in the cell. To restore the denatured proteins the organism produces heat-shock proteins (HSP). There are two different pathways for production of HSP. Some HSP are produced immediately after a heat shock (feedforward control), but additional HSP may be produced thereafter, stimulated by the presence of denatured proteins (feedback control). Feedforward is based solely on heat-shock intensity without accurate information on the resulting amount of denatured proteins. We examine the optimal combination of the two pathways that minimizes the sum of the damage caused by the presence of untreated denatured proteins and the production cost of HSP. The optimal response depends on the time delay for feedback control, the effectiveness of HSP in processing denatured proteins, the production cost of HSP, the severity of damage by denatured proteins and the probability distribution of the abundance of denatured protein conditional on heat-shock intensity. We find that feedforward control should always be used. Additional HSP may be produced by feedback control when the abundance of denatured protein is large whilst no feedback control should be used when it is small. All the HSP are produced by feedforward control when the maximum is close to the mean of denatured protein abundance conditional on the heat-shock intensity.

Optimal defense strategy: storage vs. new production.

If hosts produce defense proteins after they are infected by pathogens, it may take hours to days before defense becomes fully active. By producing defense proteins beforehand, and storing them until infection, the host can cope with pathogens with a short time delay. However, producing and storing defense proteins require energy, and the activated defense proteins often cause harm to the host's body as well as to pathogens. Here, we study the optimal strategy for a host who chooses the amount of stored defense proteins, the activation of the stored proteins upon infection, and the new production of the proteins. The optimal strategy is the one that minimizes the sum of the harm by pathogens and the cost of defense. The host chooses the storage size of defense proteins based on the probability distribution of the magnitude of pathogen infection. When the infection size is predictable, all the stored proteins are to be activated upon infection. The optimal strategy is to have no storage and to rely entirely on new production if the expected infection size n(0) is small, but to have a big storage without new production if n(0) is large. The transition from the "new production" phase to "storage" phase occurs at a smaller n(0) when storage cost is small, activation cost is large, pathogen toxicity is large, pathogen growth is fast, the defense is effective, the delay is long, and the infection is more likely. On the other hand, the storage size to produce for a large n(0) decreases with three cost parameters and the defense effectiveness, increases with the likelihood of infection, the toxicity and the growth rate of pathogens, and it is independent of the time delay. When infection size is much smaller than the expected size, some of the stored proteins may stay unused.