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Required concentration index quantifies effective drug combinations against hepatitis C virus infection

  • The Correction to this article has been published in Theoretical Biology and Medical Modelling 2021 18:5

Abstract

Successful clinical drug development requires rational design of combination treatments based on preclinical data. Anti-hepatitis C virus (HCV) drugs exhibit significant diversity in antiviral effect. Dose-response assessments can be used to determine parameters profiling the diverse antiviral effect during combination treatment. In the current study, a combined experimental and mathematical approaches were used to compare and score different combinations of anti-HCV treatments. A “required concentration index” was generated and used to rank the antiviral profile of possible double- and triple-drug combinations against HCV genotype 1b and 2a. Rankings varied based on target HCV genotype. Interestingly, multidrug (double and triple) treatment not only augmented antiviral activity, but also reduced genotype-specific efficacy, suggesting another advantage of multidrug treatment. The current study provides a quantitative method for profiling drug combinations against viral genotypes, to better inform clinical drug development.

Introduction

Newly approved antiviral drugs rely upon dosage, treatment period, and drug combinations established during clinical trials. Trials require large cohorts of patients, significant cost, extensive time and strict management of ethics and compliance: Different dose regimens, treatment times and drug combinations are evaluated during trials [1, 2]. Additional trials are needed to establish drug efficacy against different viral genotypes [3,4,5,6]. Despite the significant effort placed in clinical trials, escalation of dosage, increased treatment period, and combination therapy, significant improvement in efficacy have not always been realized.

Drug concentrations which achieve 50% virus reduction (IC50), can be used to characterize drug activity. Lower IC50 means that antiviral effects are achieved with lower concentrations of drug [7]; however, a lower IC50 does not necessarily translate to higher antiviral effect. Antiviral effect depends on the Hill coefficient (m), in addition to IC50. A higher m value exponentially increases antiviral activity at higher doses [8,9,10,11,12,13,14]. We have previously shown that m is unique to each anti-hepatitis C virus (HCV) drug, and that augmentation of antiviral activity with escalation of drug dose is quite diverse among the types of anti-HCV drugs [14]. Multidrug treatments also result in diverse effects depending on the drug combination. In-depth profiling of drug antiviral effects can be useful in designing a treatment protocol with maximal antiviral efficacy. Such profiling could result in significant savings in clinical trials. To date, antiviral efficacy variances between different anti-HCV drugs and drug combinations has not been characterized in detail.

HCV infection is a leading cause of liver cirrhosis and hepatocellular carcinoma, serious public health problems affecting approximately 170 million people worldwide [15]. Recently, the development of new antiviral drugs known as direct acting antivirals (DAAs), have greatly improved treatment outcomes [16, 17]. Commercial interests restrict the combinations which have entered clinical trials as the combinations are all company specific rather than based on any assessment of what would be the best combination for all available agents. Further evaluation of HCV DAA effects could help identify the “best” available therapy and assist with optimizing combination treatments. A new quantitative method could also support evaluation of next generation anti-HCV treatments that could lead to the eradication of HCV. In the current study, we compare antiviral profiles of different classes of anti-HCV drugs to understand diversity of effects.

We recently developed a cell culture system combined with a mathematical model for quantifying anti-HCV drug efficacy at any concentration and multidrug combination [14]. We systematically evaluated and compared the intrinsic anti-HCV activity of 15 antiviral agents and their combinations against HCV genotype 1b. In the current study, we evaluate intrinsic anti-HCV activity in both genotype 1b and 2a. We create an “effectiveness” ranking for HCV replication inhibition in mono- and multi-drug cultures following exposure to high drug dose ranges. Significant diversity was observed between the antiviral activity profiles of different drugs. Thus, it is necessary to carefully select multidrug combinations to increase drug efficacy. We have demonstrated that the developed ranking index is able to delineate the advantages of past first-in-line anti-HCV treatment choices [14]. Thus, in the current study, we use the combined cell culture plus mathematical modeling approach to quantify efficacy of diverse antiviral drug combinations. This framework could be applied to other diseases requiring multidrug treatment, such as tuberculosis and cancer.

Methods

Anti-HCV effect of each drug against genotype 1b or genotype 2a was evaluated with subgenomic replicon systems. As a genotype 1b model, LucNeo#2 (LN2) cells were employed that carry a dicistronic subgenomic replicon including open reading frames (ORFs) for the firefly luciferase-neomycin phosphotransferase fusion protein (translated by HCV 5′-untranslated region) and the NS3–NS5B region of HCV genotype 1b strain NN (translated by encephalomyocarditis virus (EMCV) internal ribosome entry site) [18]. Huh-7.5.1 cells transfected with a subgenomic replicon that included the ORFs for the NS3–NS5B region of HCV genotype 2a strain JFH-1 and the firefly luciferase gene (SGR-JFH1/Luc) were used for a genotype 2a model [19]. These cells were seeded at 7 × 103 cells per well and treated with indicated concentrations of various drugs. Following 72 h of incubation, cells were lysed and cellular luciferase activity was measured to evaluate the HCV replication activity with a Luciferase Assay System (Promega) per manufacturer’s protocol [18].

Fourteen anti-HCV drugs were evaluated as single treatments. Eleven of these were direct-acting antivirals (DAAs) of the following classes: NS3/4A protease inhibitors [PIs: telaprevir (TPV), danoprevir (DPV), simeprevir (SMV), and asunaprevir (ASV)], nucleoside NS5B polymerase inhibitor [NI: sofosbuvir (SOF)], non-nucleoside NS5B polymerase inhibitors [NNIs: VX-222 (VX), dasabuvir (DAS), nesbuvir (NSV), and tegobuvir (TGV)], and NS5A inhibitors [NS5AI: daclatasvir (DCV) and ledipasvir (LDV)]. The other 3 drugs tested were host-targeting agents (HTAs) including interferon-alpha (IFNα) and cyclophilin inhibitors [Cis: cyclosporin A (CsA) and SCY-635. For multidrug studies, cells were treated with combinations of two or three drugs prior to evaluation of activity. All anti-HCV agents were purchased or kindly provided as described [14].

Results

Fig. 1a provides a schematic of the combined experimental and mathematical system that we previously developed for quantifying anti-HCV activity of drug(s) [14]. In the previous study 14 anti-HCV agents were evaluated in mono and combination treatments against HCV genotype 1b [14]. In the current study the same 14 drugs (Table 1) were tested against HCV genotype 1b (Fig. 1b) and HCV genotype 2a (Fig. 1c). Antiviral activity results from mono and combination treatments were used to develop a novel ranking index, the “required concentration index” or RCI (see below). Note that 14 anti-HCV agents include 11 direct-acting antivirals (DAAs) including NS3 protease inhibitors [PIs; telaprevir (TPV), danoprevir (DPV), simeprevir (SMV), and asunaprevir (ASV)], a nucleoside NS5B polymerase inhibitor [NI; sofosbuvir (SOF)], non-nucleoside NS5B polymerase inhibitors [NNIs; VX-222 (VX), dasabuvir (DAS), nesbuvir (NSV), and tegobuvir (TGV)], and NS5A inhibitors [NS5AI; daclatasvir (DCV) and ledipasvir (LDV)] and 3 host-targeting agents (HTAs) included interferon-alpha (IFNα) and cyclophilin inhibitors [CIs; cyclosporin A (CsA) and SCY-635 (SCY)].

Fig. 1
figure1

Experimental and mathematical system for quantifying antiviral activity of hepatitis C virus (HCV) drug(s): a Schematic representation of the method for quantifying HCV replication level. The assay uses HCV subgenomic replicons for genotype 1b and 2a carrying a fusion of the firefly luciferase gene (Luc) with or without the neomycin phosphotransferase (Neor). The replicons autonomously and persistently replicate in Huh-7.5.1 cells [18, 19]. Cells were incubated for 72 h with or without drug(s) then harvested and luciferase activity detected. Inhibition of HCV replication was quantified as the luciferase activity in drug-treated cells, relative to untreated cells. b Log–Log plots of dose-response curves normalized by IC50 (x-axis), determined from HCV genotype 1b subgenomic replicon assay of NS3 protease inhibitors (PIs; TPV, DPV, ASV, SMV), nucleoside-type NS5B polymerase inhibitor (NI; SOF), non-nucleoside-type NS5B polymerase inhibitors (NNIs; VX, DAS, NSV, TGV), NS5A inhibitors (NS5AIs; DCV, LDV), interferon (IFNα), and cyclophilin inhibitors (CIs; CsA, CSY). Each point represents the mean of three experiments. Least-square regression analysis was used to fit Eq.(1) to the corresponding dose-response curve for estimation of IC50 and m value for each drug against HCV genotype 1b. c Log–Log plots of dose-response curves from HCV genotype 2a subgenomic replicon assay of PIs (ASV, SMV), NI (SOF), NNIs (DAS), and NS5AIs (DCV, LDV). Each point represents the mean of three experiments. Least-square regression analysis was used to fit Eq. [1] to the corresponding dose-response curve for each drug against HCV genotype 2a. d Dose-response curves for hypothetical drugs with m = 1 and 5. Drugs with a higher m value show stronger antiviral activity at the same normalized drug concentration

Table 1 Estimated characteristic parameters of the tested antiviral drugs

Ranking anti-HCV mono-drug treatments

As shown in Fig. 1b, c, the antiviral profile of drugs against HCV genotypes 1b and 2a vary widely, suggesting that anti-HCV drugs exhibit strain-dependent effects. The typical dose-response curves of a single antiviral drug can be analyzed using the following hill function [14] (Fig. 1d):

$$ {f}_u=\frac{1}{1+{\left(\frac{D}{IC_{50}}\right)}^m}. $$
(1)

Here, fu represents the fraction of infection events unaffected by the drug (i.e., 1 − fu equals the fraction of drug-affected events). D is the drug concentration, IC50 is the drug concentration that achieves 50% inhibition of activity, and m is the slope of the dose-response curve (i.e., Hill coefficient) [14]. Dose-response curves for drugs with higher m values show stronger antiviral activity at the same normalized drug concentration so long as the drug concentration is higher than IC50 (Fig. 1d). Least-square regression analysis was used to fit Eq.(1) to dose-response curves (Fig. 1b, c) and estimate IC50 and m values. Estimated values for each drug against each HCV genotype are summarized in Table 1. The hill function may not accurately fit the dose-response curve at lower drug concentrations (Fig. 1c, especially for doses lower than IC50). Typical clinical drug concentrations are around 10- to 100-fold of IC50, therefore it is generally possible to quantify effectiveness of anti-HCV drug(s) with this method especially for such a high drug concentration. As discussed in recent publications [8,9,10,11,12,13,14], both IC50 and m values are needed to accurately estimate antiviral drug potency, though only IC50 is widely used in the drug development field. Since estimated values for each drug differ relative to target HCV genotype, it is important to optimize mono and combination therapy against each genotype.

To characterize efficacy of drugs, we calculated a “required concentration index” (RCI) for each anti-HCV drug against genotype 1b and 2a. Assuming 1 − fu = x inhibition of viral replication, the RCIx represents the critical fold increase of IC50 requiring x inhibition of viral replication. Solving Eq.(1) for D/IC50, then RCIx is represented as follows:

$$ {\mathrm{RCI}}_x=\frac{D_x}{I{C}_{50}}={\left(\frac{1}{f_u}-1\right)}^{\frac{1}{m}}={\left(\frac{x}{1-x}\right)}^{\frac{1}{m}}. $$
(2)

Here, Dx is the drug concentration required to suppress x of viral replication. Drugs with small RCIx values are more efficient inhibitors of HCV replication than drugs with high RCIx. Interestingly, high m tends to be associated with smaller RCIx. By substituting estimated IC50 and m parameters and setting x to 0.95 in Eq.(2), we calculated the RCIx required for 95% inhibition of HCV replication (i.e., RCI95). We summarize RCI95 values of each drug against genotypes 1b and 2a in Fig. 2a, b, respectively. It should be noted that SOF, a nucleoside-type polymerase inhibitor used as a key agent in current and past DAA combinations, was effective in both genotype 1b and 2a, which is consistent with SOF’s known clinical pan-genotypic anti-HCV characteristic [20].

Fig. 2
figure2

Ranking anti-HCV mono drug treatments against genotypes 1b and 2a: The critical dose of antiviral drug (i.e., fold increase of IC50) required to inhibit viral replication by 95%, i.e., RCI95, was calculated for HCV (a) genotype 1b and (b) genotype 2a

Ranking anti-HCV multi-drug treatments

Using the replicon system, the antiviral activity of double- and triple-drug combinations (Fig. 3 & Fig. 4) were investigated using consistent ratios of drug concentrations (i.e., 0.25 × IC50, 0.5 × IC50, 1 × IC50, 2 × IC50, and 4 × IC50).

Fig. 3
figure3

Quantification of anti-HCV double-drug combinations against genotype 1b and 2a: Log–log plots of dose-response curves for 43 (a) and 9 (b) double-drug combinations of inter-class (or subclass) antiviral drugs against genotype 1b (a) and genotype 2a (b). Each point represents the mean of four experiments. For comparison of drugs, concentration of each drug was based on a consistent ratio of its IC50 value. (c) Dose-response curve for a hypothetical double-drug combination. RCI95 for (double or triple-) drug combinations can be determined from the point where the curve intersects \( {f}_u^{\mathrm{com}}=0.05 \) (dashed line). (d) and (e) show RCI95 rankings for 43 double-combinations against HCV genotype 1b and 9 double-combinations against HCV genotype 2a, respectively. Combinations with gray bars and black numbers (e.g., ❶) correspond to treatment regimens that include HTAs. Light pink to blue bars and white numbers (e.g., ) correspond to treatment combinations with DAA-only

Fig. 4
figure4

Quantification of anti-HCV triple-drug combinations against genotype 1b and 2a: Log–log plots of dose-response curves for 8 (a) and 6 (b) triple-drug combinations against HCV genotype 1b (a) and 2a (b). Each point represents the mean of five experiments for genotype 1b and four experiments for genotype 2a. For comparison of drugs, concentration of each drug was based on a consistent ratio of its IC50 value. (c) and (d) show RCI95 rankings of the triple-drug combinations against HCV genotype 1b and 2a, respectively

Inhibitory activity was evaluated for 43 double drug combinations against HCV genotype 1b, and, 9 double drug combinations against genotype 2a. Results are shown in Fig. 3a, b, respectively. Here, Da, Db, …, Di are defined as the concentration of drug a, b, …, i and \( I{C}_{50}^a \), \( I{C}_{50}^b \), …, \( I{C}_{50}^i \) refer to the corresponding IC50. Combined drug concentration in these experiments is described as \( {D}^{\mathrm{com}}=\left({D}_a,{D}_b,\dots, {D}_i\right)=\left(\overset{\sim }{D}\times I{C}_{50}^a,\overset{\sim }{D}\times I{C}_{50}^b,\dots, \overset{\sim }{D}\times I{C}_{50}^i\right) \), where \( \overset{\sim }{D}={D}_a/I{C}_{50}^a={D}_b/I{C}_{50}^b=\dots ={D}_i/I{C}_{50}^i \) is the constant ratio to IC50 of each combined drug (x-axis of dose-response curves). As shown in Fig. 3c, a similar hill function can be fit to dose-response curves of drug combinations [14]:

$$ {f}_u^{\mathrm{com}}=\frac{1}{1+{\left(\frac{\overset{\sim }{D}}{I{C}_{50}^{\mathrm{com}}}\right)}^{m^{\mathrm{com}}}}. $$
(3)

Here, \( {f}_u^{\mathrm{com}} \) is the fraction of infection events unaffected by the drug combination, \( I{C}_{50}^{\mathrm{com}} \) is the constant ratio that inhibits HCV replication by 50%, and mcom is the Hill coefficient [14]. In Table 2, we summarize estimated parameters, \( I{C}_{50}^{\mathrm{com}} \) and mcom, for double-drug combinations.

Table 2 Estimated characteristic parameters of the antiviral drug combinations

Similar to mono treatments, the required concentration index for drug combinations is derived as

$$ {\mathrm{RCI}}_x={\overset{\sim }{D}}_c=I{C}_{50}^{\mathrm{com}}{\left(\frac{1}{f_u^{\mathrm{com}}}-1\right)}^{\frac{1}{m^{\mathrm{com}}}}=I{C}_{50}^{\mathrm{com}}{\left(\frac{x}{1-x}\right)}^{\frac{1}{m^{\mathrm{com}}}}, $$
(4)

The RCI95 required for 95% inhibition of HCV replication is extrapolated from the point at which the curve intersects \( {f}_u^{\mathrm{com}}=0.05 \) (dashed line in Fig. 3c). Note that the critical constant ratio, \( {\overset{\sim }{D}}_c \), satisfying Eq.(4) can be uniquely determined. The RCI95 values for double-drug combinations against genotype 1b and 2a are summarized in Fig. 3d, e, respectively. RCI95 varies depending on drug combination. For genotype 1b, RCI95 ranged from 1.56 to 5.14, for genotype 2a RCI95 ranged from 1.05 to 2.28. The drug combination with the best anti-HCV profile against genotype 1b is SMV plus IFNα; Fig. 3d❶. This combination used to be the first-in-line anti-HCV drug prior to the development of DAA treatments [17]. Combinations including a non-DAA are presented as gray bars with black number designations. Combinations with DAA-only double treatments are plotted in light pink to blue and designated with white numbers (Fig. 3d). For the DAA-only combinations, one of the most effective treatments against genotype 1b was the combination of SMV and SOF (Fig. 3d), a primary treatment choice in the early era of DAA-only treatment [16]. A long term first-in-line DAA combination, SOF and LDV (Fig. 3d, e), ranked in the mid-range of efficacy against both genotype 1b and 2a. Most other drug combinations ranked differently against genotype 1b and genotype 2a. ASV plus LDV (Fig. 3d, e) was the least effective DAA-only combination against genotype 1b, but fell in the mid-range for effectiveness against genotype 2a. SOF plus DAS (Fig. 3d, e) ranked in the mid-range against genotype 1b, but ranked lowest against genotype 2a. These trends suggest an overall difference in drug effect depending on the target HCV genotype, and indicate the importance of profiling drugs against each genotype.

Eight triple-DAA treatments were profiled against HCV genotype 1b and 6 triple-combinations were evaluated against genotype 2a (Fig. 4a, b). Triple combination assessments included NS3 protease inhibitor (SMV, ASV) with NS5A inhibitor (DCV, LDV) and NI NS5B polymerase inhibitor (SOF), or NS5A inhibitor with NI NS5B polymerase inhibitor and NNI NS5B polymerase inhibitor (VX, DAS). \( I{C}_{50}^{\mathrm{com}} \) and mcom for triple-drug combinations are summarized in Table 3. We need to note that our experimental assay can detect the range of \( 0.005<{f}_u^{com}<0.01 \) in Fig. 4a, b, whereas it is difficult to measure \( {f}_u^{com}<0.005 \) in areas of higher drug concentration, reaching to the detection limit of the assay. RCI95 values of triple-drug combinations against genotype 1b and 2a are summarized in Fig. 4c, d, respectively. RCI95 values ranged from 1.21 to 2.33 for genotype 1b and 0.58 to 0.98 for genotype 2a. Triple combination treatment with SOF, LDV and SMV was most effective against genotype 1b (Fig. 4c), and least effective against genotype 2a (Fig. 4d). SOF plus DCV and SMV (Fig. 4c) was also significantly effective against genotype 1b, consistent with the reported clinical efficacy of this triple combination [21, 22]. These results show the optimal combination of drugs to suppress viral replication in vitro, and shed light on the promising drug combinations for improving clinical outcome.

Table 3 Estimated characteristic parameters of the antiviral drug combinations

The correlation in ranking between the required concentration index and clinical data suggest that this method could assist with the search for drugs that achieve an efficient antiviral inhibition with different HCV genotypes.

Discussion

Our study shows that the concentration of drug (calculated as fold of IC50), that achieves 95% virus inhibition (RCI95), highly varied depending on the type of drug and combination with other drugs. RCI95 of drugs in mono treatment ranged as much as 4.2 fold in antiviral activity against HCV genotype 1b (Fig. 2a, RCI95 = 5.08–21.4). This diversity in RCI95 indicates the importance of characterizing more than just the IC50 of drugs when predicting antiviral efficacy in clinical settings. In double-drug combinations, RCI95 values decreased (Fig. 3d, e) compared with mono treatments (Fig. 2a, b), indicating elevated antiviral activity resulted from combination treatment. The RCI95 values of DAA-only double combinations ranged from 1.70 (SMV & DAS) to 5.14 (ASV & LDV) in genotype 1b and from 1.05 (SOF & DCV) to 2.28 (SOF & DAS) in genotype 2a. Thus, the diversity in RCI95 is different among genotypes. Genotype differences are probably due differences in replication activity and the varied dependency on target [23, 24].

Triple DAA treatments have become the final strategy for improving treatment outcomes, especially with difficult-to-treat HCV. Triple combinations are also used as a means to shorten treatment periods. Understanding the activity of triple DAA combinations is important in advancing towards worldwide eradication of HCV virus [25,26,27,28]. Consistent with ongoing clinical trials which show higher treatment efficacy of triple-drug combinations, triple combinations reduced RCI95 beyond double-drug combination levels (Fig. 4c, d). RCI95 for triple drug combinations ranged from 1.21 to 2.33 in genotype 1b and from 0.58 to 0.98 in genotype 2a. Interestingly, the RCI95 values of selected drugs (SMV, ASV, DCV, LDV, DAS, VX and SOF) were less variable in triple-drug combinations compared with double combinations. RCI95 ranged 1.9 fold (1.21 for SOF & LDV & SMV to 2.33 for SOF & DCV & ASV) with triple-drug combinations, 3.0 fold (1.70 for SMV & DAS to 5.14 for ASV & LDV) in double-drug combinations, and 4.2 fold (5.08 for VX to 21.4 for LDV) in single-drug treatment against genotype 1b. These data suggest that multidrug treatments such as triple-drug combinations provide more consistent antiviral effect irrespective of the choice of drugs, yet another advantage of triple combinations.

Conclusion

In an era of rapidly progressing anti-HCV treatments, selection of the “best” combination treatment is critical to establishing the next generation of anti-HCV treatments against difficult-to-treat HCV and eventually eradicating HCV. We have developed an integrated experimental and mathematical method to evaluate the efficacy of anti-HCV dugs against HCV genotype 1b and 2a. The method was used to score mono- and multi-drug treatment regimens against HCV. This scoring could be used to optimize multidrug treatment regimens prior to clinical entry.

Availability of data and materials

All data generated or analyzed during this study are included in this published article.

Change history

  • 19 January 2021

    An amendment to this paper has been published and can be accessed via the original article.

Abbreviations

HCV:

Hepatitis C virus

DAA:

Direct acting antiviral

RCI:

Required concentration index

TPV:

Telaprevir

DPV:

Danoprevir

SMV:

Simeprevir

ASV:

Asunaprevir

SOF:

Sofosbuvir

VX:

VX-222

DAS:

Dasabuvir

NSV:

Nesbuvir

TGV:

Tegobuvir

DCV:

Daclatasvir

LDV:

Ledipasvir

IFNα:

Interferon-alpha

CsA:

Cyclosporin A

SCY:

SCY-635

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Acknowledgements

We are grateful to Dr. Kunitada Shimotohno at National Center for Global Health and Medicine for providing LucNeo#2 cells. SCY635 was kindly provided by Scynexis, Inc. We appreciate the editorial assistance provided by Dr. Senko Tsukuda at Department of Virology II, National Institute of Infectious.

Funding

This study was supported in part by Grants-in-Aid for JSPS Scientific Research (KAKENHI) Scientific Research B 18KT0018 (to S.I.), 18H01139 (to S.I.), 16H04845 (to S.I.), 17H04085 (to K.W.), Scientific Research in Innovative Areas 19H04839 (to S.I.), 18H05103 (to S.I.); AMED CREST 19 g1310002 (to S.I.); AMED J-PRIDE 19fm0208006s0103 (to S.I.), 19fm0208014h0003 (to S.I.), 19fm0208019h0103 (to S.I.), 19fm0208019j0003 (to K.W.); AMED Research Program on HIV/AIDS 19fk0410023s0101 (to S.I.); Research Program on Emerging and Re-emerging Infectious Diseases 19fk0108050h0003 (to S.I.); Program for Basic and Clinical Research on Hepatitis 19fk0210036h0502 (to S.I.), 19fk0210036j0002 (to K.W.); Program on the Innovative Development and the Application of New Drugs for Hepatitis B 19fk0310114h0103 (to S.I.), 19fk0310114j0003 (to K.W.), 19fk0310101j1003 (to K.W.), 19fk0310103j0203 (to K.W.); JST MIRAI (to S.I. and K.W.); JST CREST (to S.I. and K.W.); Mitsui Life Social Welfare Foundation (to S.I. and K.W.); Shin-Nihon of Advanced Medical Research (to S.I.); Suzuken Memorial Foundation (to S.I.); Life Science Foundation of Japan (to S.I.); SECOM Science and Technology Foundation (to S.I.); The Japan Prize Foundation (to S.I.); Toyota Physical and Chemical Research Institute (to S.I.); Fukuoka Financial Group, Inc. (to S.I.); Kyusyu Industrial Advancement Center Gapfund Program (to S.I.); Foundation for the Fusion Of Science and Technology (to S.I.); The Yasuda Medical Foundation (to K.W.); Smoking Research Foundation (to K.W.); Takeda Science Foundation (to K.W.); Mochida Memorial Foundation for Medical and Pharmaceutical Research (to K.W.).

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SI and KW designed the experiments. HO and KW conducted the experiments. YK, YK and YI carried out the computational analyses. SI and KW supervised the project. All authors contributed to the manuscript text. The author(s) read and approved the final manuscript.

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Correspondence to Shingo Iwami or Koichi Watashi.

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The original online version of this article was revised: Following publication of the original article , we were notified of a few mistakes in figures 1A, 1C and 3B and tables 2 and 3.

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Kakizoe, Y., Koizumi, Y., Ikoma, Y. et al. Required concentration index quantifies effective drug combinations against hepatitis C virus infection. Theor Biol Med Model 18, 4 (2021). https://doi.org/10.1186/s12976-020-00135-6

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Keywords

  • Mathematical model
  • Dose-response curve
  • Drug combination
  • Hepatitis C virus (HCV)