Interferon at the cellular, individual, and population level in hepatitis C virus infection: Its role in the interferon‐free treatment era

The advent of powerful direct‐acting antiviral agents (DAAs) has revolutionized the treatment of hepatitis C. DAAs cure nearly all patients with short duration, oral treatments. Significant efforts are now underway to optimize DAA‐based treatments. We discuss the potential role of interferon in this optimization. Clinical studies present compelling evidence that DAAs perform better in treatment‐naive individuals than in individuals who previously failed treatment with interferon, a surprising correlation because interferon and DAAs are thought to act independently. Recent mathematical models explore a mechanistic hypothesis underlying this correlation. The hypothesis invokes the action of interferon at the cellular, individual, and population levels. Strong interferon responses prevent the productive infection of cells, reduce viral replication, and impede the development of resistance to DAAs in infected individuals and improve cure rates elicited by DAAs in treated populations. The models develop descriptions of these processes, integrate them into a comprehensive framework, and capture clinical data quantitatively, providing a successful test of the hypothesis. Individuals with strong endogenous interferon responses thus present a promising subpopulation for reducing DAA treatment durations. This review discusses the conceptual advances made by the models, highlights the new insights they unravel, and examines their applicability to optimize DAA‐based treatments.

Interferon is a central player in our innate immune system. 9,10 It is a cytokine produced by cells in response to viral infections. Following its secretion, it binds cell surface receptors in a paracrine and autocrine manner and triggers a complex series of signaling events involving the JAK-STAT pathway. As a result, several hundred genes, termed interferon-stimulated genes (ISGs), are expressed, which collectively create an antiviral state in cells. Viral replication gets controlled in infected cells. Furthermore, neighboring cells acquire a heightened degree of protection, limiting the spread of the infection. HCV as well as other viruses have evolved sophisticated mechanisms to subvert the interferon response. For instance, HCV can suppress interferon production, interfere with the JAK-STAT pathway, block the translation of ISG mRNA, and inhibit the action of ISGs. 10 regimens. Experiments that establish quantitative links from the cellular to the population level and synthesize the above observations are difficult to conceive and perform. In recent studies, mathematical models have been constructed that quantitatively describe all of the above experimental observations and facilitate the establishment of these links. 12,13 Here, we review the conceptual advances made by these models, highlight the insights they provide, and examine their implications and prospects for optimizing DAA treatments.
The rest of the review is organized as follows. In the next section, we summarize clinical evidence in support of interferon improving the response to DAAs. In the third section, we present an overview of the modeling framework that establishes links between the roles of interferon from the cellular to the population level. In Sections 4, 5, and 6, we describe the components of the framework at the cellular, individual, and population level, respectively, and examine their key predictions. At each stage, we draw links with existing models wherever possible and highlight similarities and differences. We end in Section 7 with an outlook on the key findings and their implications and prospects.

| CLINI C AL E VIDEN CE THAT INTERFERON C AN IMPROVE DA A TRE ATMENT OUTCOME S
Does a better endogenous interferon response translate to better DAA treatment outcomes? To answer this question, a recent study 13 considered all clinical trials involving DAAs and collated those DAA combinations and treatment regimens for which cure rates in both treatment-naive individuals and previous null responders to PR were reported. Null responders to PR are those who experience <2 log 10 viral load decline in 12 weeks of therapy. Cure is assumed when treatment elicits a sustained virologic response (SVR), defined as undetectable plasma viremia 12 weeks after the end of treatment. The strength of the endogenous interferon response is difficult to measure, especially because the dynamics in the liver may be distinct from that in the blood. 14 Individuals who previously failed PR treatment are expected to be less responsive to interferon than typical treatmentnaive individuals. If interferon were to improve DAA treatment outcomes, SVR rates in a previous null responder population would be lower than in a treatment-naive population subjected to the same treatment regimen. From data of over 50 clinical trials,  involving numerous single, pairs, and three drug combinations of about a dozen DAAs, administered with and without interferon, SVR rates in treatment-naive patient populations were found to be significantly higher than in previous null responders to PR (Figure 1; P ≈ 10 −59 overall using the chi-squared test). The difference remained significant when interferon-free regimens alone were considered (P ≈ 0.007) and was starker when interferon formed part of the treatment (P ≈ 10 −65 ).
Patients with liver cirrhosis are considered difficult to treat. The difference was significant when cirrhotic patients alone were considered (P ≈ 10 −5 ) and remained so with noncirrhotic patients (P ≈ 10 −29 ). The difference diminished when powerful DAA combinations were used that elicited nearly 100% SVR. Nonetheless, the clinical evidence in support of the hypothesis that interferon can improve DAA treatment outcomes is overwhelming. Two questions follow: (1) Can the role of interferon in improving DAA treatments be described mechanistically and quantified? This question assumes significance because interferon and DAAs have been thought to act independently; interferon upregulates the innate immune response in a generic manner, 10 whereas DAAs target specific HCV proteins. 66 Ribavirin has been argued to potentiate the activity of interferon. 67,68 In vitro experiments have seen synergy between interferon and some DAAs, 69,70 but the origins of the synergy remain to be fully established. 71 (2) Can the role of interferon be leveraged to personalize and optimize DAA treatments? These questions form the subject of recent mathematical modeling studies, 12,13 which we describe next.

| OVERVIE W OF THE MATHEMATI C AL MODELING FR AME WORK
The models considered the role of interferon at each of the underlying scales, from the cellular to the population level, in independent parts and devised novel ways of integrating them ( Figure 2). 12,13 At each step, quantitative contact was made with experiments. First, a comprehensive model of the intracellular interaction between the interferon signaling network and HCV was constructed to describe the fates of cells infected with HCV in response to stimulation with interferon. The network was found to exhibit bistability, with one steady state where the virus subverted the interferon response and thrived and the second where it was cleared by interferon. Cells in which the former fate was realized predominantly were refractory to interferon. Cells in which the latter fate was predominant were responsive to interferon. Signatures of the underlying bistability were evident in experiments, 72 which the model quantitatively described. The fraction of cells in an individual that was responsive to F I G U R E 1 Interferon improves direct-acting antiviral agent (DAA) treatment outcomes. (A) Sustained virological response rates (SVR) elicited by different drug combinations in treatment-naive individuals (blue) and previous null responders to combination therapy with interferon and ribavirin (red). Data for a given drug combination from all relevant clinical trials (see text) have been combined. SVR rates in treatment-naive individuals are significantly higher than in previous null responders except for the combinations where the SVR rates are nearly 100%, where the differences are not significant. (B) The data in (A) presented as a correlation between SVR rates in treatment-naive individuals and null responders. The datasets are further classified based on whether the populations were cirrhotic and noncirrhotic, the treatments were with or without interferon, and where available based on the hepatitis C virus (HCV) genotype and treatment duration. The black lines indicate model predictions (solid) and their 95% confidence intervals (dashed). The pink dashed line marks the y = x boundary. The acronyms for the drugs are as follows: SOF-sofosbuvir; RBV-ribavirin; BOC-boceprevir; PR-pegylated interferon and ribavirin; TVRtelaprevir; SMV-simeprevir; PTV/r-paritaprevir/ritonavir; DSV-dasabuvir; DCV-daclatasvir; ASV-asunaprevir; BCV-beclabuvir; LDVledipasvir; OBV-ombitasvir; GZR-grazoprevir; EBR-elbasvir; GS-9669-radalbuvir interferon quantified the extent to which interferon could suppress infection in the individual.
Next, standard models of viral kinetics were advanced by incorporating the distinct subpopulations of cells, refractory and responsive to interferon, to elucidate the role of interferon in inducing viral load changes during treatment. 12 The resulting model quantitatively described all the patterns of viral load changes observed in patients treated with PR 73 and explained several confounding observations associated with PR treatment. Third, the model was extended to incorporate the influence of DAAs. 13 DAAs directly suppressed viral replication, controlling the infection, but were susceptible to failure via viral mutation-driven development of drug resistance. 74,75 Interferon was hypothesized to improve DAA treatment by restricting the replication space required for the development of drug resistance. The larger was the fraction of cells responsive to interferon, the smaller was the chance of the emergence of resistance to DAAs. The model thus predicted how an individual with a given degree of responsiveness to interferon would respond to DAAs.
Finally, a distribution of the degree of responsiveness of interferon across individuals in a population was posited in order to predict the fraction of individuals that would respond to a given DAA treatment regimen. 13

| The problem of the response to interferon
Interferon signaling via the JAK-STAT pathway leading to ISG expression is well studied. 9 Of the many hundred ISGs, those that exert a significant antiviral effect against HCV have been identified. [76][77][78][79][80] F I G U R E 2 Schematic of the overall modeling framework. At the cellular level, the interferon signaling network in the presence of hepatitis C virus (HCV) is characterized by a double negative feedback motif, which yields bistability. HCV thrives in one steady state and is cleared in the other. Depending on the strength of the interferon response relative to the strength of its subversion by HCV, cells could admit the first steady state alone, both the steady states or the second steady state alone. They are accordingly termed interferon refractory (blue), bistable (yellow), and interferon responsive (green). At the level of the infected individual, the relative prevalence of these cellular phenotypes defines the outcomes of therapy. Interferon refractory cells continue to get infected and produce virions during therapy with pegylated interferon and ribavirin (PR). Uninfected bistable cells are protected from infection, but infected ones continue viral production. Interferon responsive cells are cured and protected. When the fraction of interferon refractory cells is low, treatment with direct-acting antiviral agents (DAAs) succeeds as both the wildtype and resistance-associated variants (RAVs) are controlled, whereas when the fraction is high, RAVs rise and induce treatment failure. At the population level, a distribution of the latter fraction exists. Individuals with the fraction smaller than a critical fraction (brown region) succeed. The critical fraction increases as more drugs are used in combination, improving sustained virologic response (SVR) rates The levels of their expression in response to stimulation with interferon as well as their effect in blocking HCV replication in infected cells have been quantified. 72,77,81 At the same time, the mechanisms used by HCV in subverting the action of ISGs have been elucidated. 10,11 Chief among them is the translational block induced by HCV via the dimerization and phosphorylation of protein kinase R (PKR) ( Figure 3A). 72,82,83 The HCV genome is a positive-strand RNA molecule, which in infected cells acts as a template to produce negative-strand RNA. [84][85][86][87][88] The negative-strand RNA typically exists complexed with its positive strand counterpart as double-stranded RNA (dsRNA). The negative-strand RNA in turn acts as a template to produce more positive-strand RNA. An infected cell can accumulate many tens to hundreds of positive-strand RNA genomes, 89 which can be packaged and released as progeny virions. In the presence of dsRNA, the enzyme PKR is dimerized and autophosphorylated. 90,91 Phosphorylated PKR phosphorylates the eukaryotic translation initiation factor 2α-GDP (eIF2α-GDP) and prevents F I G U R E 3 Interferon signaling in infected cells. (A) A schematic of the interferon signaling network in the presence of hepatitis C virus (HCV) demonstrating ISG production and HCV-induced translational block via protein kinase R (PKR) (left), which together yield a double negative feedback motif (right). The network includes ISG expression following stimulation of the JAK-STAT pathway with interferon and the resulting control of HCV replication by key ISGs. At the same time, it considers the suppression of ISG translation by HCV via PKR dimerization and autophosphorylation, and the resulting depletion of eIF2α-GTP due to the phosphorylation of eIF2α-GDP and the sequestration of eIF2B. These competing interactions between HCV and interferon give rise to the double negative feedback loop. (B) Model predictions of the steady state expression of HCV RNA levels for fixed ISG levels (blue) and ISG levels for fixed HCV RNA levels (red). The intersections of the curves yield the steady states of the network. The filled circles are stable and the empty circle is unstable. (C) HCV RNA levels measured 20 hours postinterferon exposure as a function of the time of interferon addition postinfection (green) and the corresponding model predictions (purple) without (top) and with PKR silencing (bottom). Note that the switch in the HCV RNA levels is not sharp because the data are averaged across cells and also because the steady states may not be achieved within 20 hours. (D) The steady state HCV RNA levels admitted by the system as ISG-induced control of HCV is repressed by the factor ω. Regions I, II, and III define cells that are interferon refractory, bistable, and interferon responsive, respectively it from acting as a substrate of the enzyme eIF2B, which converts eIF2α-GDP to eIF2α-GTP. 92 eIF2α-GTP is a key factor in protein translation and is hydrolyzed to eIF2α-GDP during translational events. 93 Phosphorylation of eIF2α-GDP prevents its recycling back to eIF2α-GTP. 92,93 Furthermore, phosphorylated eIF2α-GDP sequesters eIF2B and restricts its activity. Consequently, the cell becomes depleted of eIF2α-GTP. ISG translation is halted. HCV protein translation is less sensitive to eIF2α-GTP. 72,94-96 HCV therefore thrives.
The PKR-mediated translational block thus presents a powerful mechanism with which HCV subverts the interferon response. It may underlie the failure of PR in eliciting SVR in all of the patients treated. The puzzle, however, is that PR succeeds in ~50% of the patients treated despite the translational block. The question therefore arises: when does PR succeed and when does it fail? One possibility is that differences in host genetics render individuals more or less responsive to PR. Indeed, whole-genome analyses to define correlates of treatment outcome identified single-nucleotide polymorphisms in the interferon lambda gene locus as strong predictors of treatment response. 97,98 SVR rates could be as high as 80% in individuals with favorable alleles and as low as 25% in individuals with unfavorable alleles at this locus. 99 A significant portion of the differences in the responses of patients to PR was thus attributable to host genetic differences. A significant portion, however, remained unexplained.
Even with favorable alleles, there was a 20% chance of treatment failure. At the same time, with unfavorable alleles, a 25% chance existed of being cured with PR. Factors other than host genetics at the interferon lambda gene locus thus contributed to the response to PR. Could differences in the expression of genes involved in the interferon response explain the remaining differences in treatment outcomes? Intriguingly, studies found pretreatment ISG expression to be higher in individuals who eventually failed treatment than in those who responded. [100][101][102] Furthermore, exposure to interferon as part of treatment did not lead to a significant increase in ISG expression in the former individuals but did in the latter. [100][101][102] The question then arises: when does HCV infection lead to high (pretreatment) ISG expression and why, therefore, to poor response to PR? This puzzle was addressed by a mathematical model constructed recently of the interferon signaling network in the presence of HCV and its blockade of ISG translation. 12

| A systems view of the interferon signaling network
Earlier studies identified the many molecular players and the mechanisms involved in interferon-mediated control of HCV [76][77][78][79][80] and the subversion of these mechanisms by HCV, 10,11 unraveling the many fronts of the battle between HCV and interferon. The individual fronts, however, were inadequate to predict the outcome of the battle. The key insight of the recent study was that the outcome of the battle was not the result of these individual molecular interactions between HCV and interferon but rather a systems-level, emergent property of the interferon signaling network. 12 The model identified The model displayed bistability ( Figure 3B). In one stable steady state, HCV levels were high and ISG protein levels were low. This was the interferon refractory state. In the second stable steady state, ISG protein levels were high and HCV was cleared. This was the interferon-responsive state. Separating the two was an unstable steady state of intermediate ISG and HCV levels. The stability of a steady state is defined classically by its response to perturbations.
Perturbations from an unstable state are spontaneously amplified and drive the system away from the steady state, whereas perturbations from a stable state die down. The system would thus reside in one of the two stable steady states, the chosen one depending on the initial conditions. If the initial conditions were such that a cell had significantly higher virus and/or lower ISG levels than those corresponding to the unstable intermediate state, the cell would eventually reach the interferon refractory steady state. Otherwise, it would be cleared of the infection.
Signatures of this bistable behavior were evident in in vitro interferon time-of-addition experiments ( Figure 3C). 72 Here, cells were infected with HCV and after a certain amount of time exposed to a fixed concentration of interferon. Several hours later, the level of HCV in the culture was measured. As the time when interferon was added was increased, a switch from low-to high-eventual viral levels was observed.
This switch arises from the underlying bistability. When interferon is added before the HCV level in cells crosses the unstable boundary, interferon would eventually clear the infection. When it is added after, however, HCV would thrive and reach the high viral level corresponding to the refractory state. The model quantitatively captured these observations. As further proof, when the experiments were repeated with PKR-silenced cells, the switch was lost. Viral levels remained low regardless of the time of interferon addition, indicating that HCV could no longer subvert the interferon response. The bistability was eliminated and the system could only access the interferon-responsive state, as predicted by the model.

| Implications of bistability in the interferon signaling network
The insights above had several implications. First, the model pre- Consider a cell that admits the interferon-responsive steady state alone. Before exposure to interferon, such a cell is expected to have low ISG mRNA levels and high viral levels. When interferon is added, its ISG levels rise and the virus is cleared. In contrast, consider a cell that admits the interferon refractory state alone.
Following exposure to interferon, the ISG mRNA levels rise but are unable to clear the virus because of the strong translational block. Any further interferon addition is unlikely to alter this state.
An individual with weak endogenous interferon production 110,111 but with a preponderance of cells responsive to interferon is thus typical of those who respond to PR. The individual displays low ISG levels pretreatment, a rise in ISG levels following the start of treatment, and an eventual response to PR. An individual with strong endogenous interferon production but with a preponder- properties of the interferon signaling network and synergize with interferon in effecting viral control. Synergy between DAAs and interferon has been observed in vitro 69,70 and in vivo. [112][113][114][115] Whether the mechanism of synergy underlying the observations is the one suggested here remains to be ascertained. Nonetheless, the model suggested a novel approach to describing within-host viral kinetics, which we review next.

| A bird's-eye view
Modeling viral kinetics within infected individuals has had a rich history. 116,117 This year marks the 20th year since the seminal paper During the short period following the start of therapy, for which data were analyzed, the target cell population was assumed not to change significantly. Before treatment, viral production and clearance were balanced (pI ss = cV ss ), and so were infected cell production and loss (βV ss T ss = δV ss ), yielding a steady viral load, V ss , often referred to as the baseline or set point viral load. (The subscript 'ss' refers to steady-state quantities before the start of treatment.) Treatment with interferon upset this balance and induced a biphasic decline in viral load. The first phase was attributed to the imbalance between viral production and clearance, was fast, and lasted 1-2 days, at which point, the viral load reduced approximately to V ss (1 − ε). The second phase was due to the resulting imbalance between the production and loss of infected cells, was slower, and typically lasted the rest of the treatment duration (many weeks), improving SVR in combination with interferon was described assuming that ribavirin rendered virions noninfectious. 67 Models that suggested optimal ribavirin usage, which kept its key side effect, hemolytic anemia, tolerable, were also constructed. 120,121 Homeostatic proliferation of hepatocytes was incorporated to explain the triphasic decline of viremia observed in some patients. 122 With the advent of DAAs, viral mutation and the development of drug resistance became important and were incorporated to describe the kinetics of resistant strains and to predict the minimum genetic barrier of DAA combinations required to prevent treatment failure. 123 More recently, multiscale models that couple intracellular viral replication with within-host kinetics have been constructed to describe the rapid viral load decline observed with some of the new DAAs. 124 Finally, models are now being constructed that explicitly incorporate the influence of the adaptive immune system to describe the intriguing recent observation of patients achieving SVR despite viremia being detected at the end of treatment with DAAs. [125][126][127] Several excellent reviews have documented these and other advances and highlighted their contributions to our understanding of HCV pathogenesis and the design of improved treatment protocols. 116,117 Here, we focus on a recent model 12,13 that advances the basic model by incorporating the distinct cellular interferon response phenotypes described above and enables a more accurate description of the influence of interferon on HCV kinetics.

| Viral kinetics with distinct cellular phenotypic responses to interferon
Based on the implications of the bistability of the intracellular interferon signaling network elucidated above, the model divides the hepatocyte population in an infected individual into three subpopulations ( Figure 4A). 12 The first comprises those that admit the interferon refractory steady-state alone. These cells are unaffected by

| A mechanistic hypothesis
The motivation for building a model of the response to interferon at the population level arose from the compelling clinical evidence, presented at the start of this review, of a superior response to DAAs in treatment-naive patients than in previous null responders to interferon. Previous models have used empirical arguments to describe this differential response. 133 mechanistic explanation was lacking. The model of interferon action at the individual level described above allowed the construction of a mechanistic hypothesis to explain this differential response. DAAs fail primarily due to the development of drug resistance. 74,75 Viral mutation forms the route through which resistant strains arise. HCV has high mutation 88 and replication 73 rates and exists in infected individuals as a quasispecies. 123,136 Many mutations can give rise to resistance to individual DAAs. 137,138 Thus, the chance that resistant strains exist in infected individuals before the onset of treatment can be high. 123 Previous models that coupled viral kinetics with viral mutation predicted that all single and double mutants are likely to preexist in infected individuals and an additional mutation is likely to arise during therapy, leading to the recommendation of a minimum genetic barrier of 4 for DAA combinations to succeed. 123 Following these arguments, if DAAs work better in individuals with stronger interferon responses, it is likely that interferon compromises the ability of the virus to develop resistance to DAAs. A model that superimposes viral kinetics and evolution on the formalism above of the distinct cellular interferon response phenotypes would help test this hypothesis. Such a model was constructed. 13

| Viral kinetics with interferon and DAAs
The model again divided cells into the three interferon response phenotypes, with the pretreatment fraction of cells refractory to interferon, that is, the pretreatment ϕ 1 , denoted ϕ p ( Figure 5A). 13 Cells could be infected with either the wildtype viral strain, denoted V 0 , or a mutant, denoted V 1 . Cells infected with the wildtype produced a majority of wildtype progeny virions and a small proportion of mutants. The proportion was dictated by the mutation rate, μ. Cells infected with mutant strains would similarly produce a majority of mutant virions. The viral burst size and/or infectivity of the mutant strains was lower (ie, p 0 > p 1 and/or β 0 > β 1 ), representing the fitness cost associated with the resistance mutation. 137 The resulting model equations were as follows.
Here, in addition to distinguishing cell types based on their inter- , against the wildtype and the mutant strains, respectively. 137 The model predicted that given a set of drug effectiveness values, Response to direct-acting antiviral agent (DAA)-based therapy. (A) A schematic of the model in Figure 4 extended to include DAAs and viral mutation and drug resistance. Viruses are now divided into drug sensitive (denoted '0') and resistant (denoted '1') strains. DAAs block the production of these strains with strain-specific effectiveness ε DAA . Mutations occur at the rate μ. Resistant strains are assumed to suffer a cost in the replicative ability resulting in a lower production rate from infected cells. The schematic applies to all the interferon response phenotypes. (B-D) Distributions of the pretreatment fraction of interferon refractory cells, ϕ p , in all infected individuals, chronically infected individuals, and null responders to pegylated interferon and ribavirin (PR), respectively. ϕ c , ϕ DAA , ϕ null , and ϕ PR+DAA represent threshold values of ϕ p that define spontaneous clearers, responders to a DAA, null responders to PR, and responders to PR + DAA, respectively. (E) An illustration of the relationship between the SVR rates in treatment-naive individuals and previous null responders to PR. The areas of the shaded regions are marked with alphabets. For a given drug combination, let sustained virologic response (SVR) be achieved when ϕ p < ϕ drug . SVR in treatment-naive individuals would thus be the area SVR naive = A+B. SVR in null responders would be the ratio SVR null = B/(B + C), because the percentage of null responders to PR is NULL = B + C. Recognizing that A + B + C = 1, it follows that SVR naive = 1 -NULL + NULL × SVR null . The relationship provides the fit in Figure 1B and is also close to predictions of the model above.
Note that when SVR naive < 100%, SVR null is less than SVR naive, whereas when SVR naive approaches 100%, the two become equal.
(F) Viral kinetics illustrating the reduction in the required time for SVR from ~12 weeks (green) to ~8 weeks (blue) as ϕ p decreases. The inset shows the percentage of the population that would respond to a representative treatment regimen as the treatment duration is decreased.
Using the distribution of ϕ p in treatment-naive individuals and SVR rates as a function of treatment duration, it follows that 20% of the patients, with high interferon responsiveness, can afford a reduction in treatment to 8 weeks, and ~50% with intermediate responsiveness to 10 weeks, from the prescribed 12 weeks a critical value of ϕ t existed below which the treatment succeeded.
The critical value was akin to the critical fraction ϕ critical identified above in the absence of DAAs. Thus, greater interferon responsiveness (lower ϕ t ) resulted in improved DAA treatment outcomes.

| The distribution of interferon responsiveness and the success rates of treatments
To examine whether this prediction translated to the SVR rates observed, the following approach was used. ϕ p was assumed to be distributed log normally across individuals in a population. The pretreatment steady state of the model showed that ϕ p was directly linked to the baseline viral load: The model yielded a nonzero baseline viral load only when ϕ p > ϕ c . Individuals with ϕ p < ϕ c thus represented those who spontaneously cleared the infection ( Figure 5B). From the distribution of ϕ p , the percentage of spontaneous clearers was estimated to be ~21%, which was close to the mean of ~26% obtained from 31 longitudinal studies. 140 The distribution of ϕ p truncated below by ϕ c yielded the distribution of ϕ p in chronically infected treatment-naive individuals ( Figure 5C). To compare the response elicited in this population with that in null responders to PR, the distribution of ϕ p in null responders was required.
Null response to PR was defined to occur when ϕ p > ϕ null . To estimate ϕ null , the extent to which interferon increases responsive- The distribution of ϕ p truncated below by ϕ null yielded the distribution of ϕ p in null responders ( Figure 5D). SVR rates in null responders could thus be predicted. Indeed, using the value of ϕ PR+DAA above, the SVR rate elicited by the combination of telaprevir and PR in null responders to PR was estimated to be 26%, again in good agreement with the 32% observed clinically. 15 The model now had all the ingredients required to predict SVR Where the duration predicted may be large with DAAs alone, the addition of interferon may provide an additional option.

| OUTLO O K
Overwhelming clinical evidence points to better responses to DAAs, including to interferon-free combinations, in patients with stronger endogenous interferon responses. Recent mathematical models provide explanations of this intriguing correlation. 12,13 The advance made by these models is the integration of the manifestation of the action of interferon at the cellular, individual, and the population level into a single mathematical framework.
Consequently, the models are able to describe a large body of clinical observations quantitatively, including the percentage of infected individuals that spontaneously clears the infection, the percentage of chronically infected individuals that fails to respond to interferon, and the percentage of the latter that responds to DAAs.
The models and the clinical evidence suggest that interferon could be leveraged to improve outcomes of the new DAA combination treatments. Individuals with strong interferon responsiveness could be a promising subpopulation for reducing treatment durations. The models suggest that short-term viral load decline could provide an estimate of the degree of interferon responsiveness of an individual. Future studies could establish correlations between the short-term viral load decline and the corresponding interferon responsiveness, which could then be exploited to estimate the minimum duration of treatment required to achieve SVR in a potentially personalized manner.
Despite their complexity, the models are restricted to descriptions of the essential roles of interferon. A more comprehensive description of the role of interferon would require addressing several additional issues. The models, for instance, do not present a way to estimate the interferon responsiveness of an individual a priori.
DAAs and interferon have been shown to synergize via multiple mechanisms. Although the models identify a mechanism of such synergy, they neglect its effects in defining treatment outcomes.
While the collated clinical data appear well described despite this simplifying approximation, specific cases where DAAs exhibit strong synergy with interferon may be inadequately captured.
The possibility of synergy implies that the models yield conservative estimates of the required treatment duration. The treatment duration in the models is based on driving viremia below the cure boundary of one virion in the 15 l of fluid volume in a typical individual. Alternative descriptions of the cure boundary have been proposed-for instance, one infected cell in the body instead of one virion-and this can alter the predicted treatment duration. 116 Whether the models can similarly be applied to describe clinical data with these alternative cure boundaries remains to be examined. Furthermore, more recent observations where some patients with detectable viremia at the end of treatment also achieved SVR suggest that the required treatment durations may be shorter than estimated based on the above cure boundaries. 8,[143][144][145][146][147][148][149][150] Indeed, in a recent study, noncirrhotic Chinese individuals infected with HCV genotype 1b who displayed an ultrarapid early response (viremia <500 copies/ml by day 2 of treatment) were found to achieve SVR with just 3 weeks of therapy. 6 The mechanisms underlying the spontaneous achievement of SVR despite detectable viremia at the end of treatment remain to be elucidated. Some studies suggest that DAAs irreversibly diminish the infectivity of the virus [151][152][153] to a point where not enough infectious virions are left at the end of treatment to establish a lasting infection. 125,126 Other studies argue that the reduction in viremia due to DAAs could reverse the exhaustion of cytotoxic T lymphocytes, [154][155][156][157] which then clear the infection. Mathematical models based on both these hypotheses appear to be consistent with patient data. [125][126][127] Interferon has been argued to enhance exhaustion late in infection [158][159][160] and is thus likely to influence outcomes differently depending on which mechanism predominates. Future studies that establish the underlying mechanism would further clarify the role interferon can play and help refine the predictions of the minimum treatment duration made with present models.

ACK N OWLED G EM ENTS
This work was supported by the Wellcome Trust/DBT India Alliance Senior Fellowship IA/S/14/1/501307 (NMD). We thank Pranesh Padmanabhan for help with the figures and for comments.

CO N FLI C T O F I NTE R E S T
The authors declare that they do not have any conflicts of interest.