Understanding the antiviral effects of RNAi-based therapy on chronic hepatitis B infection

Reaching hepatitis B surface antigen (HBsAg) loss (called functional cure) with approved treatment with pegylated interferon-α (IFN) and/or nucleos(t)ide analogues (NAs) in chronic hepatitis B virus (HBV) infected patients is suboptimal. The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum HBV DNA, HBsAg and hepatitis B e antigen (HBeAg) in chimpanzees and small animals. A recent clinical study (Heparc-2001) showed reduction of serum HBV DNA, HBeAg and HBsAg in HBeAg-positive patients treated with a single dose of ARC-520 and daily NA (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a a multi-compartmental pharmacokinetic-pharamacodynamic model and calibrated it with measured HBV data. We showed that the time-dependent ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1-4 months. The combined ARC-520 and entecavir effect on HBV DNA is constant over time, with efficacy of more than 99.8%. HBV DNA loss is entecavir mediated and the strong but transient HBsAg and HBeAg decays are solely ARC-520 mediated. We added complexity to the model in order to reproduce current long-term therapy outcomes with NAs by considering the tradeoff between hepatocyte loss and hepatocyte division, and used it to make in-silico long-term predictions for virus, HBsAg and HBeAg titer dynamics. These results may help assess ongoing RNAi drug development for hepatitis B virus infection. Author summary With about 300 million persons infected worldwide and 800,000 deaths annually, chronic infection with hepatitis B virus (HBV) is a major public health burden with high endemic areas around the world. Current treatment options focus on removing circulating HBV DNA but are suboptimal in removing hepatitis B s- and e-antigens. ARC-520, a RNA interference drug, had induced substantial hepatitis B s- and e- antigen reductions in animals and patients receiving therapy. We study the effect of ARC-520 on hepatitis B s- and e-antigen decline by developing mathematical models for the dynamics of intracellular and serum viral replication, and compare it to patient HBV DNA, hepatitis B s- and e-antigen data from a clinical trial with one ARC-520 injection and daily nucleoside analogue therapy. We examine biological parameters describing the different phases of HBV DNA, s-antigen and e-antigen decline and rebound after treatment initiation, and estimate treatment effectiveness. Such approach can inform the RNA interference drug therapy.

Introduction 1 the dynamics for HBsAg titers. 49

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Patient data. We use published data from five HBeAg-positive, treatment-naive 51 chronic hepatitis B patients (cohort 7 in [19]), which are the ones that best responded 52 to ARC-520 therapy. Moreover, they are the only studied cohort in which HBV DNA 53 integration is not reported as a source of HBsAg production (as opposed to 54 HBeAg-negative and NA-experienced HBeAg-positive patients with low cccDNA), and, 55 thus, it allowed us to exclude integration when developing the mathematical model. 56 Data consists of serum HBV DNA titers (in IU/ml), HBsAg, and HBeAg concentration 57 (in IU/ml) measured at t i = {−8, 0, 2, 7, 14, 21, 28, 42, 56, 84} days, where i = {−1, ..., 8} 58 and t 0 = 0 is the day when both daily NA entecavir (ETV) and a single intravenous 59 ARC-520 injection (inoculum of 4 mg/kg) are administrated. 60 Pharmacokinetics-pharamcodynamics model. We are interested in determining 61 the mechanisms underlying the observed HBV DNA, HBsAg and HBeAg kinetics under 62 combined ETV and ARC-520 therapy. We develop a mathematical model that considers 63 the interactions between infected hepatocytes, I (in cells per ml); total intracellular 64 HBV DNA, D (in copies per ml); serum HBV DNA, V (in IU per ml); serum HBsAg, S 65 (in IU per ml); and serum HBeAg, E (in IU per ml). We assume that infected cells 66 decay at per capita rate δ, and we exclude cell proliferation (we will relax this 67 assumption later on). We assume intracellular HBV DNA is synthesized at rate α and 68 is lost at constant per capita rate c D . The replication rate α summarizes various steps 69 that are not modeled explicitly, such as the transcription of pregenomic RNA (pgRNA) 70 from cccDNA, and the generation of single stranded DNA by reverse transcription. 71 Intracellular HBV DNA is assembled and released into blood as free virions at rate p 72 which are cleared at rate c [40]. To account for the different units of intracellular and 73 serum virus, we use the conversion factor ξ = 1/5.3 IU/copies [41]. Lastly, we assume 74 HBsAg and HBeAg are transcribed from cccDNA inside infected hepatocytes and then 75 released into blood at rates p S and p E , respectively, and are cleared at per capita rates 76 d S and d E , respectively. We have not included HBV DNA integration, which is only a 77 substantial source of HBsAg in HBeAg negative patients and NUC-experienced HBeAg 78 positive patients with low cccDNA [19]. The model is given by the following model: Patients were administered daily nucleoside analogous treatment with entecavir 80 starting at day t 0 = 0. ETV is known to block reverse transcription of HBV DNA, and 81 therefore inhibit HBV DNA synthesis. We model this (see model (5)) as a constant following NA treatment initiation [42]. To account for the biphasic HBV DNA decay in 86 3/23 the absence of infected cell killing, we assume that ETV has additional time-dependent 87 inhibitory effects on intracellular HBV DNA synthesis and model it by decreasing α 88 further to α ET V treat = αe −gt (1 − ), where g ≥ 0 is a constant and t is the time in days 89 post ETV initiation. Moreover, a single ARC-520 dose was administrated at time t 0 = 0. 90 Unlike ETV, which was given daily, we model the build-up and clearance of ARC-520 91 pharmacokinetics over time by considering a two-compartment pharmacokinetic model 92 consisting of drug quantity in the plasma and liver, C p and C e , respectively [43]. The 93 inoculum C p (0) = C 0 decays exponentially at rate d = d + k eo , where d is the plasma 94 drug degradation rate and k eo is the absorption into the liver rate. The drug in the liver 95 decays at rate k eo , identical with the absorption rate [44]. Following these assumptions, 96 the pharmacokinetic model has the form: with initial conditions C p (0) = C 0 and C e (0) = 0. This is a linear model which can be 98 solved to give solutions: Lastly, we assume the relationship between the drug quantity in the liver C e (t) and 100 drug efficacy η i (t) to be given by: where η max = 1 is the maximum drug efficacy, EC 50,i are drug quantities that yield 102 half-maximal effects, and i = {1, 2, 3} are the infectious events that are affected by 103 ARC-520 therapy, i.e., the transcription of HBV DNA, the transcription of HBsAg, and 104 the transcription of HBeAg, respectively. The effects of ARC-520 on intracellular HBV 105 DNA, HBsAg and HBeAg are modeled as the reduction of intracellular HBV DNA 106 synthesis α to α ARC treat = (1 − η 1 )α, HBsAg production from p S to p S,treat = (1 − η 2 )p S , 107 and of HBeAg production from p E to p E,treat = (1 − η 3 )p E , respectively. Considered 108 together, models (1) and (4) give the following pharmacokinetics-pharamcodynamics 109 (PK/PD) model: Data fitting. We used published kinetic HBV DNA, HBsAg, HBeAg data in serum 111 measured from five HBeAg-positive, treatment-naive chronic hepatitis B patients as 112 described in the 'Patient data' section. 113

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Parameter values. We assume that, prior to therapy initiation, model (5)  data prior to the start of therapy, t −1 = −8, (day eight prior to the ARC-520 injection). 118 The percentage of HBV-infected hepatocytes is reported to vary between 18 ± 12% in 119 chronic HBsAg carriers [45,46] and 99% in acute infections [21,47]. Without loss of 120 generality, we arbitrary assume that 50% of hepatocytes are infected at the beginning of 121 treatment. Liver contains approximately 2 × 10 11 hepatocytes, which, when distributed 122 throughout 15 liters of extracellular fluid, gives a total hepatocyte concentration 123 T max = 1.4 × 10 7 cells/ml [48]. We set the initial infected hepatocyte population to 124 I 0 = 0.5T max . Lastly, the pre-treatment level of intracellular HBV DNA in HBeAg 125 positive patients is set to D 0 = 225/(I 0 /T max ) = 450 copies/ infected cell, as in [49]. 126 Since we assume that model (5) is in chronic equilibrium (for the additional 127 assumption δ = 0) before the therapy initiation, parameters α, p, p S , p E are fixed 128 according to the following formulas: We start by ignoring the dynamics of infected cells, such as infection of susceptible 130 cells and/or infected cell proliferation (we will relax this assumption in later sections), 131 and assume that infected cells decay due to natural death and immune mediated killing 132 at per capita rate δ = 4 × 10 −3 per day, corresponding to a life-span of 250 days (we 133 will later investigate the effect of increasing the killing rate, to include increased 134 immune mediated killing or RNAi induced toxicity and death). The estimated half-life 135 of intracellular HBV DNA is 24 hours [40,50], which corresponds to the intracellular 136 HBV DNA decay rate c D = 0.69 per day. ARC-520's half-life has been reported to 137 range between 3 and 5 hours [51], corresponding to decay rates 3.3 < d < 5.5 per day; 138 we fix d = 4 per day. Lastly, we set the initial ARC-520 quantity to the trial dose of 139 C 0 = 4 mg/kg.

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(1 − T ) = (1 − )(1 − η 1 (t)) accounts for the total drug effect on HBV DNA production. 142 Since preliminary simulations (not shown) indicate that η 1 (t) is time independent, we 143 cannot separate the ETV effects 1 − from the ARC-520 effects 1 − η 1 (t). We lump 144 them together, and assume a total drug effect, which ranges between 0.9 < T < 1. The 145 other parameter ranges are found as follows. The time-dependent inhibitory effects of 146 treatment on intracellular HBV DNA production, g, was estimated from HBV infected 147 humanized mice treated with NA to range between 0.059 and 0.42 per day [40]. We 148 expand this range by searching over the parameter space 0 < g < 1. There is a wide 149 range of estimates for the free virus clearance rate in serum: as low as 0.69 per 150 day [20,28,52]; and as high as 21.7 per day [53]; we search the entire 0 < c < 100 151 parameter space. The decay rate of HBsAg is bounded between 0 < d S < 200 per day, 152 containing previous estimates ranging between 0.057 to 0.58 per day [54,55]. In 153 previous modeling work [39,56] HBeAg decay rate d E was set to 0.3 per day. We allow 154 for a larger range 0 < d E < 200 per day, corresponding to half-lives greater than 5 155 minutes. We assume that the drug absorption rate k eo ranges between 0 < k eo < 1 per 156 day. Since ARC-520 was reported to have long lasting effects [51], we assume a large for each patient. Functional SSQ describes the distance between HBV DNA, HBsAg, and E(t i ) as given by model (5) at times t i (i = {1, ..., 8}). As 164 described previously (see eq (6)    4. To obtain confidence intervals for the optimal parameter estimates p opt for each 192 patient, we employ a bootstrapping technique. We assume that the best fit 193 parameters yield the true dynamics, and that any discrepancy from the data is 194 due to measurement errors. First, we calculate the residuals between simulated functions and measured data at times t i (i = {1, ..., 8}). Next, we create 1000 data sets for the HBV DNA , HBsAg, and HBeAg data at times t −1 , ..., t 8 , where data at times t −1 and t 0 are as before and data at the remaining times are obtained by adding a randomly drawn residual (with repetition) to the true value at each time, i.e. log 10 (P new data (t i )) = log 10 (P (p opt , t i )) + r P j P,i , where P ∈ {V, S, E}, i = 1, ..., 8, and j P,i is drawn at random from {1, ..., 8}.

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Lastly, for each data set, we find a new set of optimal parameters by using  Table 2. Estimated parameters, fit errors, and confidence intervals.  Table 3 gives the parameters obtained from 207 equilibrium conditions (6).

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For both HBsAg and HBeAg, the effect of ARC-520 lasts longest in patient 703.
and extracellular HBV DNA: The equations for HBeAg is given by: and for HBeAg is given by: Note that both S(t) and E(t) are independent of T . HBV DNA follows a biphasic

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When we consider that the treatment that blocks intracellular HBV DNA synthesis, 293 T , comes from both ETV and ARC-520, we recover the solutions of model (5) for 294 combination therapy given by η 2 = η 3 = 0, g = 0, and T = both T = 0. Both HBsAg and 295 HBeAg decay at a steep rate during the first 22.7 ± 8.5 and 7.6 ± 4.1 days, respectively. 296 After reaching minimum values, on average 1.5 ± 0.2 and 1.6 ± 0.4 orders of magnitude 297 smaller than their initial levels, HBsAg and HBeAg rebound to their respective ETV 298 monotherapy levels (see Fig 7 and 8, solid curves).

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Sensitivity of model predictions with respect to changes in the infected cell 300 population's initial condition. Previous estimates for the percentage of 301 HBV-infected hepatocytes vary between 18 ± 12% in chronic HBsAg carriers [45,46] and 302 99% in acute infections [21,47]. We have derived our results by assuming that during 303 chronic HBeAg-positive cases half of the liver is infected. Here, we investigate how 304 changes in the size of the initial infected cell population alter our predictions. 305 Analytical investigations show that the dynamics of the viral proteins HBsAg and 306 HBeAg are not influenced by the initial size of the infected cell population, I 0 . After 307 treatment initiation I(t) = I 0 e −δt , and p S = d S S 0 /I 0 and p E = d E E 0 /I 0 (based on the 308 equilibrium assumption (6)). Therefore, the equations for S and E: 10/23 are independent of I 0 . Moreover, for p = cV 0 /(ξD 0 I 0 ) and D 0 = 225/(I 0 /T max ) we find 311 that intracellular HBV DNA D depends on I 0 (see Fig 9) but HBV DNA in serum does 312 not. 313 Long-term predictions and the need for uninfected 314 hepatocyte dynamics 315 We assumed that infected hepatocytes have a life-span of 250 days. In this section, we 316 are relaxing this assumption and investigate long-term HBV DNA and HBsAg dynamics 317 when increased hepatocyte loss (due to either drug toxicity, or immune-mediated killing) 318 is being considered. When we model it by increasing the infected cell death rate δ in (5)  previously [21,34,58]. Note that we ignore the age of the infection and assume that once 329 a cell becomes infected, it is producing virus (for a PDE model extension in a hepatitis 330 C virus infection, see [59]). Both uninfected and infected hepatocytes proliferate 331 according to a logistic term with maximal growth rate r T and r I and carrying capacity 332 T max . In chronic HBV infections, cccDNA persist under long-term nucleoside analogues 333 treatment [60]. Since the average cccDNA number of untreated HBeAg positive patients 334 is 2.58 copies per infected cell [49], infected hepatocytes may have two infected 335 offsprings. On the other hand, it has been suggested that cccDNA is destabilized by cell 336 division or even lost during mitosis [60]. We account for this by assuming that a 337 fraction Φ of proliferating infected hepatocytes have one infected and one uninfected 338 offspring, and the remaining infected hepatocytes have two infected offsprings. The new 339 model is given by: Liver regenerates rapidly after injury. To account for fast proliferation during 341 chronic disease, we assume that hepatocytes' maximum proliferation rate is r T ≤ 1 per 342 11/23 day, and r I = 1 per day, corresponding to doubling time of (up to) 16 hours [21,61].

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The infectivity rate is at the lower end of previously fitted values [11], β = 10 −9 344 IU/(ml× day); we include a death rate for the uninfected hepatocyte population, 345 d T = 4 × 10 −3 per day [62], identical to that in model (5); and set the fraction of 346 infected hepatocytes that have one uninfected and one infected offspring to Φ = 0.05.

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Initial conditions of uninfected and infected hepatocytes are set such that the model is 348 in equilibrium prior to treatment with D 0 = 450 , and V 0 , S 0 , and E 0 as in table 1.

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This leads to almost all hepatocytes being infected.

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Without loss of generality, we investigate the dynamics for patient 703 under 351 combination therapy for a continuum of δ values. Our hypothesis is that NA 352 monotherapy cannot lead to HBsAg loss. In order to obtain infected cell persistence

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(under NA monotherapy), we need to decrease r T (for a fixed r I = 1) as δ increases (a 354 r T − δ threshold required for infected cells persistence is given in Fig 10). Therefore,

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HBsAg persistence under increased infected cell killing (as seen in NA treatment) may 356 be explained by high ratio of infected to uninfected cell proliferation. Other events, such 357 as HBV DNA integration, may also explain HBsAg persistence under infected cell (and 358 potentially cccDNA) loss. This is especially true for HBeAg negative patients and NA 359 experienced, HBeAg-positive patients.

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To help in this endeavor, we developed mathematical models describing the HBV 372 DNA, HBsAg and HBeAg in the presence of a silencing RNAi drug called ARC-520. We 373 used the models and clinical trial data from treatment naive, HBeAg-positive patients 374 that receive a one time ARC-520 injection and daily nucleoside analogue treatment with 375 entecavir [19], to determine the efficacy of ARC-520 and nucleoside therapies on the 376 short and long-term dynamics of HBV DNA, HBsAg, and HBeAg. To the best of our 377 knowledge, we report for the first time that the time-dependent ARC-520 effects on 378 HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% 379 in 1.8-3.4 months and 1.5-3.5 months, respectively. The combined ARC-520 and 380 entecavir effect on HBV DNA is constant over time, with efficacy of more than 99.8%, 381 which is similar to other nucleoside analogues trials.  We modeled limited infected cell loss for the short-term dynamics. In the long-term, 388 however, infected cells may die at faster rates, due to either drug toxic effects or HBsAg and HBeAg persistence under long-term HBV DNA clearance can be explained 400 by high ratios of infected to uninfected division rates. Therefore, high ratio of infected 401 to uninfected division rates, which correspond to the infection of the entire liver and 402 may be indicative of scenarios where HBsAg seroclearance will not happen. 403 Interestingly, us and others have associated high ratios of infected to uninfected division 404 rates to triphasic HBV DNA decay under treatments with nucleoside analogues, a sign 405 of suboptimal drug response [28,30]. Whether infected hepatocytes indeed proliferate 406 faster than uninfected hepatocytes remains under investigation.

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While modeling results suggest that one-dose of ARC-520, in combination of daily 408 entecavir, has limited long-term effects, we did not consider whether a transient HBsAg-specific B cells through persistent stimulation [71]. It has been suggested that 413 therapeutic vaccines containing one (PreS2) or two (PreS1 or PreS2) envelope proteins 414 together with serum HBsAg reducing drug therapies are needed in order to induce high 415 levels of anti-HB antibodies, which may correlate with functional cure [72][73][74]. We 416 ignored the level of immune modulation following RNAi based therapy, which is a model 417 limitation, and therefore, we cannot say whether such effects were induced at higher 418 rates during the transient HBsAg loss.

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Our study has limitations. We only used the data on HBeAg-positive patients 420 (cohort 7 in [19]) because they best responded to ARC-520 therapy and because they 421 are the only studied cohort in which HBV DNA integration is not reported as a source 422 of HBsAg production. Because of that, we excluded integration events from our  In conclusion, we developed a mathematical model and used it together with patient 428 data, to estimate the time-dependent ARC-520 efficacies in blocking HBsAg and HBeAg 429 productions. Additional data and theoretical efforts are needed to determine whether