New kinetic models for the hepatitis C virus


  • Alan S. Perelson,

    Corresponding author
    1. Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM
    • MS-K710, T-10, Los Alamos National Laboratory – Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87525
    Search for more papers by this author
    • fax: 505-665-3493.

  • Eva Herrmann,

    1. Saarland University, Faculty of Medicine, Internal Medicine II, Homburg/Saar, Germany
    2. Darmstadt University of Technology, Faculty of Mathematics, Darmstadt, Germany
    Search for more papers by this author
  • Florence Micol,

    1. Saarland University, Faculty of Medicine, Internal Medicine II, Homburg/Saar, Germany
    Search for more papers by this author
  • Stefan Zeuzem

    1. Saarland University, Faculty of Medicine, Internal Medicine II, Homburg/Saar, Germany
    Search for more papers by this author

  • Potential conflict of interest: Dr. Zeuzem has received research grants for clinical trials from, consults with, has an advisory arrangement with, and is on the speakers' bureau for Schering Plough and Hoffmann–La Roche. He also has advisory arrangements with Vertex, Idenix, Human Genome Sciences, Novertis, and Anadys.


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, of estimating parameters such as the rate of virion clearance and the rate of clearance of hepatitis C virus (HCV)–infected cells, and they have suggested mechanisms of action for both interferon and ribavirin. Nevertheless, the models that were originally formulated were unable to explain all of the observed HCV RNA profiles. We provide an update on the state of HCV kinetic modeling and discuss new models that have taken into consideration the different pharmacokinetics of standard and pegylated forms of interferon, allow for changes in drug effectiveness as drug concentrations fall between dosing intervals, and that 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. (HEPATOLOGY 2005;42:749–754.)

Kinetic models of hepatitis C virus (HCV) RNA decay induced by interferon (IFN) therapy have been developed by us and others.1–6 The models, inspired by previous work on HIV and hepatitis B virus kinetics,7–9 stimulated the collection of frequent viral loads and alanine aminotransferase (ALT) measurements after the initiation of therapy that revealed previously unknown kinetic patterns of HCV RNA change. The models have successfully summarized much of these new kinetic data and have given insights into features of HCV biology in vivo, such as the rate of virion clearance and the daily rate of virion production. More importantly from a clinical perspective, the models have allowed quantification of the antiviral effects of therapy and thus have made comparison of the antiviral effectiveness of different drug regimens possible using data collected over short intervals.1, 6, 10, 11 Furthermore, initial viral kinetic parameters play a major role when predicting sustained virologic response. Future challenges of viral kinetic analysis comprise the possibility of rapidly evaluating and comparing relative to existing therapies the in vivo antiviral effects of new compounds such as HCV protease and polymerase inhibitors. We review the current state of viral kinetics in HCV and discuss new work that incorporates ALT, drug pharmacokinetics, and pharmacodynamics; explains viral load rebounds seen toward the end of the dosing interval; and provides insight into the mechanism of ribavirin action.


HCV, hepatitis C virus; IFN, interferon; ALT, alanine aminotransferase; PEG-IFN, pegylated interferon.

During chronic infection, the level of serum HCV RNA is in a steady state with only minor fluctuations in untreated patients.12 This suggests that viral production is in balance with the viral clearance. Interferon alpha (IFNα)–based therapy changes this balance and typically leads to a biphasic decline of the HCV RNA with a rapid first phase lasting for approximately 1 to 2 days during which HCV RNA may fall 1 to 2 logs in genotype 1–infected patients1 and as much as 3 to 4 logs in genotype 2–infected patients.10 Subsequently, a slower second phase of HCV RNA decline ensues (Fig. 1A-B). In some patients, however, a more complex kinetic pattern has been observed with an intermediate increase of HCV RNA,13 further accelerations of the decline after some time,6 or even a rebound (Fig. 1C-D). In nonresponders, there may be no first- or second-phase decline (null response) or a first phase followed by little or no second-phase decline (flat response). In responders, the biphasic HCV RNA decline pattern tends to be seen when high daily doses of IFN are used,1, 3, 10, 14 and more complex patterns tend to be seen when standard thrice-weekly doses or pegylated forms of IFN are used.4, 6, 11, 15, 16

Figure 1.

Viral kinetic pattern in 4 patients receiving peginterferon α2a plus ribavirin. (A and B) Data points and curve fit from a biphasic viral kinetic model for patients infected with HCV genotype 1 and genotype 2, respectively. (C) Data and curve fit from a triphasic viral kinetic model for a patient infected with HCV genotype 1. (D) Viral kinetic data with an intermediate rebound in a patient infected with HCV genotype 2.

When daily doses of IFN are given to chronically infected patients, the magnitude of the first-phase decline depends on the dose of IFN given, with 10-MU and 15-MU doses leading to larger declines than a 5-MU dose. Neumann et al.1 explained both the speed and the magnitude of the first-phase decline by assuming that IFN partially blocks HCV production from infected cells. The fraction of virion production that was blocked was called the effectiveness of therapy, ε. With production partially blocked, normal clearance mechanisms assumed to occur at rate c per virion then cause a decrease in the serum concentration of HCV RNA, with the magnitude of the decline depending on the degree of blockage of virion production. For example, if the effectiveness of therapy, ε, in blocking virion production, is 90%, then during the first phase HCV RNA will decline 1 log10; 99% effectiveness corresponds to a 2 log10 decline. Although directly measuring the rate of virion production in vivo has not been possible, in vitro experiments have confirmed that IFN blocks viral replication in infected cells.17–19 The effectiveness of therapy in blocking virion production depends not only on treatment regimens but also on further factors, such as ethnicity and HCV genotype.10, 13, 14 Results on the effectiveness in blocking virion production in patients co-infected with HCV and HIV from recent viral kinetic studies are problematic because of small sample sizes and complex patterns leading to a lack of model fit in several patients.20–22 Nevertheless, no large differences have been found in the effectiveness of therapy in blocking virion production in patients with HCV and HIV coinfection compared with those in patients with HCV monoinfection.

By fitting first-phase HCV RNA declines, not only ε but also c have been estimated. Estimates of the virion clearance rate c were independent of drug dosage,1 and for genotype 1 virus corresponded to a serum half-life (t1/2) of 2.7 hours. This estimate has been independently confirmed in 2 ways. First, by using plasma apheresis to artificially increase the virion clearance rate, the mean virion t1/2 was estimated in 2 chronically infected HCV/HIV patients as 2.4 hours.23 Second, during the anhepatic phase of liver transplant surgery, HCV RNA was estimated to decay with a t1/2 of 2.2 hours.24 However, when the parameters ε or c are reported for populations of patients, the results have been obtained only from patients who show a first-phase response to therapy. Although this includes most patients, it does exclude patients, “null-responders,” who show less than a half-log drop during the first phase.

The second phase of decline in patients responding well to therapy, according to models, reflects the net loss of infected cells. With viral production, partially blocked viral loads fall (first phase), and with lower viral loads, less de novo infection occurs. Thus, infected cells that are lost are not efficiently replaced, and a net loss of infected cells and a further reduction in overall viral production and HCV RNA occurs. For patients exhibiting low drug effectiveness—low ε—second-phase slope is not a good indicator of infected cell loss, because viral production and de novo infection are continuing and affecting the second phase. Note that the association of the second phase with infected cell loss does not necessitate assuming that drug therapy directly enhances infected cell loss. Furthermore, current models cannot distinguish among various possible mechanisms of infected cell loss, which include immune-mediated mechanisms, natural cell death, and “noncytolytic cure” of the infected cell by loss of HCV RNA. Also, decreases in the rate of de novo infection, as might occur if ribavirin acts as a mutagen,25 can lead to an increased net loss of infected cells. In the case of HIV infection in which models have also predicted loss of infected cells and estimated their rate of loss, δ, direct validation has been possible by measuring the rate of decline of the number of infected cells in vitro26 and in vivo through sequential tonsilar biopsies.27 In the case of HCV infection, such direct observation has not been possible. However, Neumann et al.1 showed that second-phase slope was correlated with baseline ALT and histological activity index, suggesting but not proving a relationship with cell death.

Serum ALT, a surrogate marker for hepatocellular necrosis, usually decreases rather than increases during the second phase. How can this be if the second phase is associated with infected cell loss? Ribeiro et al.,3 modeling both HCV RNA and ALT kinetics in patients treated with high-dose daily IFN, showed that the ALT kinetics are consistent with the assumption of the second phase being attributable to infected cell loss. Intuitively, if infected cells decay during the second phase, then fewer infected cells remain to release ALT, and hence the level of ALT will ultimately decay. Colombatto et al.28 developed a more complex kinetic model incorporating loss of infected cells by immune system activity that can also account for both HCV RNA and ALT changes during therapy.

Models in which infected cells are lost by noncytolytic cure have not been thoroughly analyzed, especially because this leads to changes in uninfected cell numbers that may need to be taken into account. However, if cells are noncytolytically cured without loss of ALT, then by simultaneously modeling ALT and HCV RNA kinetics one should be able to get information about the relative roles of cytolytic and noncytolytic loss of infected cells. One difficulty in this approach is that amount of ALT released on infected cell death and the half-life of ALT are not precisely known. A recent analysis of viral and ALT kinetics in acute HCV infection of chimpanzees has begun to approach these issues.29

The initial mathematical models of HCV RNA decay assumed that after a short delay to account for drug delivery and stimulation of IFN response genes, ε was constant.1, 3, 6 Because some of the antiviral actions of IFN may be delayed and because the pharmacokinetics of 3 times per week standard IFN and once-weekly pegylated interferon are such that a constant IFN action may not occur, more recent models, discussed below, allow ε to vary. These models can explain some of the observed deviations from a biphasic pattern and therefore may be used for a more sensible quantification of treatment effects and a more reliable prediction of virological treatment response.

In some studies on IFN induction therapy, dose reductions can be followed by viral load increases. Because the effectiveness of a drug depends on its dose, a model with variations in the efficiency of blocking viral production is needed. Thus, Bekkering et al.5 introduced a model in which ε was changed starting at the time of dose reduction from a level ε1 to a lower level ε2 with a smooth transition between these values. The model provided a good fit to the viral load data and showed that models are capable of mimicking non-biphasic viral load patterns.

A transient loss of drug efficacy also may occur during phases of low IFN-α serum concentration. Lam et al.30 showed that after a single dose of IFN viral loads that decreased at 24 hours were rebounding at 48 hours. Taking variations of interferon serum concentration into account was initially proposed by Powers et al.4 and followed by a fuller analysis by Ribeiro et al.31 and Talal et al. (unpublished data), who suggested allowing ε to depend on the drug concentration C according to

equation image(1)

where the constant EC50 is the concentration at which the drug's efficiency in blocking viral production is half its maximum, n is a parameter called the Hill coefficient, and the time delay τ takes into account that IFN binds cellular receptors and initiates a signaling cascade before having an intracellular affect (Fig. 2). This model was used to analyze kinetic data from patients co-infected with HCV and HIV who were treated with peginterferon alfa-2b (PEG-IFN) plus ribavirin. Both HCV RNA and PEG-IFN concentration were measured frequently after the first 3 weekly doses. The serum PEG-IFN concentrations were fitted to a pharmacokinetic model and C(t) was estimated. The Neumann et al.1 model with ε chosen as in Eq. (1) was then able to fit the end-of-the week rebounds in HCV RNA seen in patient data. A more extensive kinetic analysis of data from 21 HCV/HIV-coinfected patients in the same clinical study showed that drug concentration per se was not associated with long-term response but that features such as the maximum drug effectiveness computed from Eq. (1) and the weekly average drug concentration divided by the EC50 were correlated with end-of treatment and sustained virological response (Talal et al., unpublished data). Rebounds have also been reported in patients chronically infected with HCV alone and treated with standard interferon, PEG-IFN α-2b, or α-2a13, 15, 16, 32 and may likewise be explained by the pharmacokinetics of the drug. Thus, we believe the approach of incorporating pharmacokinetics and pharmacodynamics into viral dynamic models will also apply to PEG-IFN α-2a and possibly to other compounds.

Figure 2.

Simulated curves from an extreme model with drug efficiency depending on pharmacokinetics. Shown are the (A) simulated drug levels using an elimination-only model4 in which drug absorption is assumed to be instantaneous, (B) respective drug efficiency curve, and (C) corresponding viral kinetic curve using a combined pharmacokinetic and viral kinetic model.

A triphasic viral decay was observed during antiviral treatment in patients chronically infected with HCV.6, 33 In this case, a first phase (1-2 days) with rapid viral decline was followed by a “shoulder phase” of approximately 7 to 28 days in which the virus load declined slowly, remained constant, or even increased, and a third phase of faster viral decay (Fig. 1C). Herrmann et al.6 suggested that the infected cell loss may be enhanced during therapy, with some delay, for example, after the HCV RNA declines below some individual threshold. Furthermore, the third phase was more pronounced in patients treated with PEG-IFN α-2a in combination with ribavirin than in patients treated with PEG-IFN α-2a alone, suggesting a role for ribavirin in either enhancing the immune response or otherwise enhancing the second-phase slope as its serum concentration, which takes 4 weeks to reach steady state, builds up.6 An additional mutagenetic effect of ribavirin was discussed and could not be ruled out. In the triphasic model, the pretreatment infected cell loss rate δ is increased to a treatment-enhanced infected cell loss Mδ at a time t1 that demarks the start of the third phase. The constants δ, Mδ, and the point t1 can be estimated from non-linear fitting of the model to HCV RNA data.

Ribavirin has little or no antiviral activity against HCV in monotherapy,34, 35 although in some patients a transient decline in viral load can be observed.36 However, in combination with interferon-α, end-of-treatment and sustained virological response rates are substantially enhanced.37–39 The antiviral mechanisms of ribavirin when used in combination with an interferon-α are still unknown. Both immunologic and direct antiviral effects, for example, lethal mutagenesis, have been suggested.17, 40–45 To understand how ribavirin can increase response rate, Dixit et al.25 developed a viral dynamic model in which they assumed that in a dose-dependent manner ribavirin (alone or in combination with interferon) causes a fraction ρ of newly produced virions to be non-infectious, presumably through mutagenic action.41, 43–45 Because the concentration of ribavirin increases during the first month of therapy, they also assumed that ρ increases with time on therapy, reaching saturation at 28 days. Analysis of the model then showed that when ε is high, ribavirin has negligible influence on viral load, whereas when ε is low, ribavirin is predicted to enhance viral load decay. This effect is predicted to be entirely in the second-phase decay of HCV RNA. These predictions are in agreement with recent experiments,6, 14, 36 such as those observing that with high daily dosing of IFN, ribavirin addition does not affect first-phase decay (ε),14 and the observation by Hermann et al.6 of an increased infected cell loss rate in patients treated with PEG-IFN α-2a in combination with ribavirin, compared with patients treated with pegylated interferon α-2a alone. Thus, the model reconciles the seemingly conflicting observations that ribavirin addition enhances viral load decline in some cases but not in others. The analysis also ruled out a major antiviral role for the immune modulatory effect of ribavirin, suggested as a key alternative mechanism of ribavirin action against HCV.35 An immune modulatory effect would enhance the second-phase slope regardless of interferon effectiveness, contrary to these observations.6, 14, 36 Lastly, the model predicted long-term response rates that are in good agreement with experiments. This model thus provides a picture of how ribavirin enhances HCV RNA decline and improves the long-term outcome of interferon-based therapy.

How then can one reconcile the Herrmann et al.6 observation of a faster last phase decline with IFN plus ribavirin than with IFN alone, which they interpret as due to an immunomodulatory increase in δ, with the Dixit et al.25 model? Both Herrmann et al. and Dixit et al. found no increased first-phase decline with ribavirin. Thus, both groups agree that ribavirin does not increase antiviral efficacy. Hermann et al. interpret the increased last-phase slope as an immunomodulatory effect, that is, increased infected cell death rate, whereas Dixit et al. interpret the increased slope as attributable to the increased presence of non-infectious particles and hence slowed de novo infection. Because second- or last-phase slope in both models is caused by the net loss of infected cells, where net loss is loss of infected cells minus new production, one can increase this slope by increasing loss or decreasing new infections. Which interpretation is correct remains to be seen, although a recent report provides the first direct evidence of increased in vivo HCV mutagenesis during ribavirin monotherapy.45 In spite of recent advances in the therapy of chronic HCV infection, sustained virological response rates to current treatments with PEG IFN in combination with ribavirin are still unsatisfying in patients infected with HCV-genotypes 1 or 4 or co-infected with HIV. The analysis of new therapies is thus a further challenge of HCV RNA kinetic studies. Several new HCV protease and polymerase inhibitors are under investigation in clinical studies and may become approved in the near future.46–49 Kinetic analyses of monotherapy or combination therapy with new drugs that are designed to specifically inhibit viral enzymes with or without interferon can be used to compare efficacy of these new treatments with that of existing interferon-based treatments. A kinetic analysis of the serine protease inhibitor BILN 2061 demonstrated that the effectiveness in blocking viral production was dose-dependent and high compared with interferon-α.50 Additionally, because the major treatment effects of this enzyme inhibitor are well defined, these results confirmed estimates of viral half-life and infected-cell loss as well as conclusions on treatment effects drawn from prior HCV kinetic analyses.50 In the future, kinetic analysis of HCV RNA decay induced by these new agents also may prove valuable in the search for and quantification of drug resistance in patients treated for several days or weeks.

Although controversy still exists about the interpretation of HCV RNA decays,51, 52 HCV kinetic analyses have provided new insights into the mechanisms of antiviral therapy and provided a means to compare different treatment regimens and responses in different patient populations. In the last 1 to 2 years, new models have been developed that incorporate ALT kinetics,3, 28 pharmacokinetic and pharmacodynamic effects,4 immune modulation,6 and ribavirin activity.25 Models of HCV kinetics during and after liver transplantation also have been developed.53 These models have expanded the set of HCV RNA patterns that can be explained to include the end of the week rebounds seen with PEG IFN and triphasic responses, as well as offering suggestions of how treatment works1, 25 and why some people, such as African Americans, do not respond.14 Nevertheless, patterns such as the hump in the viral load curve seen between 32 and 120 hours by Bekkering et al.13 in hard-to-treat patients have not yet been explained, and even when patterns are “explained” by models, the underlying hypotheses still need to be confirmed experimentally. Models are not static, and new features, such as a more explicit incorporation of immune responses, IFN receptor levels, and downstream effects in the IFN response pathway, need to be incorporated as experimental information becomes available. Analysis of HCV kinetics with mathematical models is an important tool in the assessment and comparison of therapies for HCV and should become an even better one as we learn more about the underlying biology of HCV and the host response to HCV infection.


The authors thank Harel Dahari and Ruy Ribeiro for helpful comments on the manuscript.