Published online 31 August 2012
Using mathematical models to understand the behavior of the deadly hepatitis C virus, Indian scientists have shown that the microbe's sensitivity towards drugs varies in various phases of the disease1. They say early treatment could actually clear the virus entirely from the system for a sustained period.
"There are multiple phases when the sensitivity of the infection to drug treatment varies. We found that early treatment of the infection is likely to result in sustained virological response," says Raghvendra Singh, an assistant professor in the Department of Chemical Engineering at the Indian Institute of Technology Kanpur.
Singh got interested in the area partially from the concern that many victims may neither know of their infection nor when or how they got the virus, and partially while working with retroviruses as a gene delivery vehicle during his doctorate.
A large number of people around the world are infected with hepatitis C, the virus that primarily affects liver cells or hepatocytes. Majority of the newly infected patients become chronic carriers of the virus. Chronic infection progressively causes liver damage, resulting in cirrhosis and liver failure. Some patients also develop liver cancer due to the harmful proteins produced from the HCV genetic material in the infected cells. After the initial infection, the virus enters the blood stream and reaches the target tissues.
Then, the HCV particles attach themselves to the wall of the hepatocytes through receptors and co-receptors and the virus enters the cell. Inside the cell, it uses the host machinery to produce its proteins and replicate its genetic material, needed for the assembly and release of the new viral particles from the cells.
Significant progress has been made towards understanding the pathogenesis of the disease, structure of the virus, finding drug targets and development of drugs as well as understanding their effects on the disease. Yet, in nearly half of the treated patients, the virus persists or rebounds after the therapy.
Singh and his team's mathematical model also showed that the drug, which blocks new infections of the target cells, is more potent in clearing the infection than the drug, which blocks the production of the virus from the infected cells.
Currently, most patients are treated during the late phase of the infection, partly due to the late detection of the disease. "Our finding, on the other hand, recommends treatment during the acute phase and development of more sensitive screening methods to detect the infection early," he says.
Since vaccines for HCV and HIV are not available yet, drugs are the only hope for millions infected with these viruses. "It is encouraging to see that besides the interferon- and ribavirin, many newer drugs are undergoing clinical trial for HCV and there is a sense of optimism that the cure may be in sight," Singh says.
1. Gupta, S. et al. Analysis of the virus dynamics model reveals that early treatment of HCV infection may lead to the sustained virological response. PLoS ONE. doi: 10.1371/journal.pone.0041209 (2012)
Analysis of the Virus Dynamics Model Reveals That Early Treatment of HCV Infection May Lead to the Sustained Virological Response
Saurabh Gupta, Raghvendra Singh*
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, India
Considerable progress has been made towards understanding hepatitis C virus, its pathogenesis and the effect of the drug therapy on the viral load, yet around 50% of patients do not achieve the sustained virological response (SVR) by the standard treatment. Although several personalized factors such as patients' age and weight may be important, by mathematical modeling we show that the time of the start of the therapy is a significant factor in determining the outcome. Toward this end, we first performed sensitivity analysis on the standard virus dynamics model. The analysis revealed four phases when the sensitivity of the infection to drug treatment differs. Further, we added a perturbation term in the model to simulate the drug treatment period and predict the outcome when the therapy is carried out during each of the four phases. The study shows that while the infection may be difficult to treat in the late phases, the therapy is likely to result in SVR if it is carried out in the first or second phase. Thus, development of newer and more sensitive screening methods is needed for the early detection of the infection. Moreover, the analysis predicts that the drug that blocks new infections is more effective than the drug that blocks the virus production.
Hepatitis C, a single stranded RNA virus belonging to flaviviridae family, has a high prevalence rate with an estimated 170 million likely carrier worldwide . Around 4.1 million individuals may be carrying the virus in the U.S. alone, majority developing the chronic infection . Chronic infection may progressively cause liver fibrosis, resulting in cirrhosis in around 20% of the patients , . It has also been linked to development of hepatocellular carcinoma , with likely role of HCV core protein . The antiviral cytokine, interferon-α, had been the corner stone of the chronic HCV treatment for many years. However, treatment with IFN-α was effective in achieving the sustained virological response (SVR) in less than 20% of the patients . The combination therapy, which includes ribavirin along with IFN-a, and replacement of IFN-α by pegylated interferon have further improved the treatment, increasing the SVR rate to more than 50% , , . More recently, a HCV protease inhibitor, telaprevir, has shown potential to improve the SVR rate further , , an inhibitor of HCV NS5A, a protein critical in viral life cycle and a likely drug target, has been identified , and many more drugs are undergoing clinical trials. Thus, considerable progress has been made in treating the infection and identifying newer targets for the drug therapy. Yet, in a significant percentage of the patients, the infection persists or resurges after the completion of the treatment, many developing liver cirrhosis and cancer. Therefore, better understanding of the role of the drugs in achieving SVR as well as the progression of disease is needed.
A model of virus dynamics has been previously described -. It has helped in explaining multiple aspects of HIV , , , HBV , and HCV ,  infections. The in-vivo study on the effect of the IFN-α showed a biphasic response and it was found that IFN-α likely decreases the initial viral load mainly by blocking the virus production from the infected cells . In some patients, besides the two phases of decline of the viral load, an intermediate shoulder phase, in which the viral load remains nearly constant -, has been observed. This triphasic viral load decay has been explained by taking into account the proliferation of hepatocytes , ,  in the original model. Besides explaining many observed viral decay profiles, the model also revealed that for the efficacies of the drug higher than a critical value, the infection will be cleared during the treatment and for efficacies lower than the critical value, a new steady state of infection may be reached , . Thus, the likelihood of achieving SVR as well as development of drug resistance may depend on the efficacy of the drug treatment .
Although a lot is known about IFN-α, its role in modulating immune response, and its antiviral activity, it is not clear why the therapy fails to achieve SVR in around 50% of cases. The response of the therapy may depend on factors such as: the HCV genotype -, level of hepatic fibrosis , , the viral load , body weight and age of the patient , . Besides these variables, it is known that replacing IFN-α with pegylated interferon increases the chances of achieving SVR significantly, likely due to better half life and bioavailability of the drug, and a higher dose of pegylated interferon is more effective in achieving SVR than a lower dose . Moreover, a significant percentage of the patients, who were previously treated with IFN-α and ribavirin combination therapy, achieved SVR when retreated with pegylated interferon and ribavirin . Furthermore, retreating the patients with higher dose of IFN-α for 6 months caused 29% of the patients to achieve SVR  and it has been found that interferon alfa-2b decreases viral load in a dose dependent manner . Thus, the dose of the drug and its bioavailability may be an important factor in determining the outcome of the therapy  and regression analysis based on clinical data has been used to predict the dose of IFN plus ribavirin that may be required to maximize the number of patients who clear the virus during the therapy .
These studies prompted us to look mechanistically into the role of effective dosing of the drug in achieving SVR. We performed the sensitivity analysis on the standard virus dynamics model. The analysis revealed that there are four time periods, in which the sensitivity of the infection to drug treatment varies. Based on this finding, we added a perturbation term in the model to simulate the drug treatment during a specific phase of the infection. The perturbation analysis showed that the first and second phases are the most effective for the antiviral therapy. Further, the study shows that the drug that blocks new infections is more potent in achieving SVR than the drug that blocks the virus production.
Interestingly, the sensitivity analysis of the virus dynamics model with respect to the two efficacy parameters showed multiple phases, suggesting that the time of the start of the therapy may be an important factor in determining the response. The magnitude of the sensitivity coefficient describes how the uninfected, infected cells and the viral load will change at a given time if the efficacy of the drug is varied at that time. On the other hand, the slope of the sensitivity coefficient vs time plot describes how the uninfected, infected cells and the viral load will vary with time if a drug of a fixed efficacy is applied during a time period (equation 11 and 15).
If a 6 month therapy is carried out in the first or the second phase of the infection, the increase in the dose of the drug steadily delays the point of inflection in the dynamics, delaying the approach to the steady state. As the dose is further increased to a certain value, the uninfected, infected cells and the viral load do not reach the same steady state as they did for the lower doses but the infected cells and the viral load decrease to zero while the uninfected cells increase to the same number as the total number of the cells. Thus, the steady state of the infection has been altered from a 31.25% infected cells and 9.4x106 viral load to an uninfected state. It also suggests that a critical efficacy of the drug is needed to achieve the SVR as described by others , . For the same mode of the drug, in the first and second phases, the doses required to achieve the SVR are nearly the same. In addition, in these phases, the alteration of the steady state is very sensitive to the dose and a small increase in the perturbation could change the steady state from the "infected state" to an "uninfected state". These effects are likely due to the early phase of the infection. As the viral load and infected cells decline, the number of uninfected cells increases. When the viral load reaches zero during the therapy, there are no virus particles left to propagate the infection and the cells remain uninfected even after the therapy has been withdrawn. A lower dose of the drug may be needed to achieve SVR if the mode of action of the drug is to block the de novo infections than to block virus production since the former affects the new infections directly while the later affects it indirectly by reducing the plasma virus concentration.
In contrast, in the third phase, due to the positive slope of the sensitivity curve for the viral load and infected cells, the drug serves as an activator of the infection (equation 11 and 15). It causes the viral load and the infected cells to increase. The slopes of the sensitivity curves in this phase gradually changes to zero (Fig. 1 B, C) so is the effect of the drug. When the perturbation is withdrawn, the system returns to the infected state.
In the final phase, the infection has reached the steady state in which the uninfected, infected cells and the viral load have attained equilibrium. Thus, all the sensitivity coefficients have attained constant values (Fig. 1 A, B, C). Since, the slope of the sensitivity coefficient vs time plot is zero in this phase, a drug may not perturb the system either as an activator or a repressor.
Time of start of the therapy is an important factor in determining the outcome. For both modes of action of drugs, there is an optimum time to start the treatment. Since the magnitude of the slope of the sensitivity curve for the infected cells and the viral load progressively increases in the first and second phases, reaching a point of inflection in the second phase (Fig. S2 B, C), a therapy close to this time will be the most effective, giving the lowest dose that could alter the steady state of the infection.
Our analysis shows that blocking new infections is more effective than blocking virus production. Although significant changes in the model will be needed for it to be applicable to direct acting antivirals , its implications to DAAs are interesting. It can be inferred that blocking wild type virus at an early phase of HCV lifecycle is better yet the direct acting antivirals produce drug resistant viral quasispecies, depending on the phase they block. Genetic barrier to resistance of NS3/4A protease inhibitors, which block an early phase of HCV lifecycle, has been shown to be low , . On the other hand, genetic barrier to resistance of nucleoside analog polymerase inhibitors, which block a later phase of the viral lifecycle, have been shown to be high while that of the nonnucleoside polymerase inhibitor is low , . Therefore, there may be optimum phases at which a drug may be highly effective in terms of both blocking the wild type infection and limiting the number of drug resistant viral quasispecies.
From the present study, we conclude that the treatment during the first and second phases of the infection will likely result in SVR, explaining the recent clinical studies -. Therefore, development of better HCV screening tools is needed so that the infection is detected early on. Furthermore, we found that the drug that blocks de novo infections is more effective in achieving the SVR.