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Viral Dynamics in Hepatitis B Virus Infection (Lamivudine/Antiviral Treatment/Liver/Viral Turnover/Mathematical Model) MARTIN A

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Viral Dynamics in Hepatitis B Virus Infection (Lamivudine/Antiviral Treatment/Liver/Viral Turnover/Mathematical Model) MARTIN A Proc. Natl. Acad. Sci. USA Vol. 93, pp. 4398-4402, April 1996 Medical Sciences Viral dynamics in hepatitis B virus infection (lamivudine/antiviral treatment/liver/viral turnover/mathematical model) MARTIN A. NOWAK*t, SEBASTIAN BONHOEFFER*, ANDREW M. HILLt, RICHARD BOEHMEt, HOWARD C. THOMAS§, AND HUGH MCDADEt *Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, United Kingdom; tGlaxo Research and Development, Greenford Road, Greenford, Middlesex, UB6 OHE, United Kingdom; and §Department of Medicine, St Mary's Hospital Medical School, Imperial College of Science, Technology, and Medicine, London, W2 1PG, United Kingdom Communicated by Richard Southwood, University of Oxford, Oxford, United Kingdom, December 13, 1995 (received for review October 24, 1995) ABSTRACT Treatment of chronic hepatitis B virus (HBV) for 24 weeks. Again we observe rapid decline in plasma virus infections with the reverse transcriptase inhibitor lamivudine load, which falls below detection limit in almost all patients leads to a rapid decline in plasma viremia and provides estimates within 2-4 weeks, and again in most patients, virus resurges for crucial kinetic constants of HBV replication. We find that in rapidly as soon as the drug is withdrawn. HBeAg is a viral persistently infected patients, HBV particles are cleared from the protein produced by infected cells; its production is not directly plasma with a half-life of -1.0 day, which implies a 50% daily inhibited by lamivudine (7), and changes in the serum con- turnover of the free virus population. Total viral release into the centration can therefore reflect changes in infected liver cell periphery is -1011 virus particles per day. Although we have no mass. ALT is released from damaged liver cells; thus it is an direct measurement ofthe infected cell mass, we can estimate the indicator of the level of cell damage and death. HBeAg and turnover rate ofthese cells in two ways: (i) by comparing the rate ALT decline slowly during longterm lamivudine treatment. of viral production before and after therapy or (ii) from the Therapeutically induced HBeAg seroconversion, seen during decline of hepatitis B antigen during treatment. These two successful interferon a therapy and thought to represent the independent methods give equivalent results: we find a wide lysis of infected cells by the host's immune response, is not a distribution of half-lives for virus-producing cells, ranging from feature of lamivudine treatment. 10 to 100 days in different patients, which may reflect differences For a quantitative analysis of these observations, we design in rates of lysis of infected cells by immune responses. Our a simple but natural mathematical model based on ordinary analysis provides a quantitative understanding of HBV replica- differential equations for uninfected cells, x, infected cells, y, tion dynamics in vivo and has implications for the optimal timing and free virus, v: ofdrug treatment and immunotherapy in chronic HBV infection. dx/dt = A dx - bvx, This study also represents a comparison for recent findings on the dynamics ofhuman immunodeficiency virus (HIV) infection. dy/dt = bvx - ay, The total daily production of plasma virus is, on average, higher in chronic HBV carriers than in HIV-infected patients, but the dv/dt = ky - uv. [1] half-life of virus-producing cells is much shorter in HIV. Most strikingly, there is no indication of drug resistance in HBV- Uninfected, susceptible cells are produced at a rate, A, which infected patients treated for up to 24 weeks. may be constant or depend on the total population size of uninfected and infected cells. Uninfected cells die at rate dx, More than 250 million people worldwide are chronically and become infected at rate bvx, where b is the rate constant infected with hepatitis B virus (HBV), and 25-40% of these describing the infection process. Infected cells are produced at will die from liver cirrhosis or primary hepatocellular carci- rate bvx and die at rate ay. Free virions are produced from noma Chronic HBV infection is often the result of infected cells at rate ky and are removed at rate uv. Strictly (1, 2). rate of virus should also be a function exposure early in life, leading to viral persistence in the speaking, the decay free absence of or cellular immune of the uninfected (and infected) cell population, but we expect strong antibody responses (3). term of viral to be of of HBV carriers can aim to either inhibit viral the leading decay independent changes Therapy in the host cell Therefore it is a reasonable or enhance the population. replication immunological responses against to treat u as a constant. The of the virus, or both assumption magnitude (4). parameters a, b, k, and u will be determined by antiviral The nucleoside analogue, (-)-2'-deoxy-3'-thiacytidine immune In the absence of treatment the as an anti-human immuno- responses. system (lamivudine), originally developed converges to a steady state of persistent infection, provided the deficiency virus (HIV) drug, has potent inhibitory effects on basic reproductive ratio of the virus, Abk/(adu) is greater than HBV replication in vivo (5, 6, 31). Chronic HBV carriers were 1. This condition is likely to be fulfilled if patients have weak treated with various doses of lamivudine. Plasma virus load was immune free virus or infected at times and after treat- responses against (low u) against quantified frequent before, during, cells (low a). Hence, in our simple model weak immune ment using quantitative methods for determining viral DNA. responses predispose to carrier state. In the first study, 45 patients were treated for 28 days; in a In the replication cycle of HBV, the viral reverse tran- subsequent study, 50 patients were treated for 24 weeks. Fig. scriptase is responsible for the synthesis of new HBV DNA 1A shows plasma virus changes in six patients treated for 28 from the pregenomic mRNA template (8, 9). Therefore, days. After onset of therapy viral levels decline rapidly, but as lamivudine can prevent the production of new virus particles soon as is virus returns. 1B shows the drug withdrawn, Fig. from already infected cells (k = 0). But the viral polymerase changes in plasma viremia, hepatitis B antigen (HBeAg), and is also essential for completing the double-stranded circular serum alanine aminotransferase (ALT) in six patients treated Abbreviations: HBV, hepatitis B virus; HIV, human immunodefi- The publication costs of this article were defrayed in part by page charge ciency virus; HBeAg, hepatitis B antigen; ALT, alanine aminotrans- payment. This article must therefore be hereby marked "advertisement" in ferase; cccDNA, covalently closed circular DNA. accordance with 18 U.S.C. §1734 solely to indicate this fact. tTo whom correspondence should be addressed. 4398 Downloaded by guest on September 24, 2021 Medical Sciences: Nowak et al. Proc. Natl. Acad. Sci. USA 93 (1996) 4399 A E cn a) Q. c) Patient 3 I ao 0 E Q_ Un0 0- Time (days) B ( 108 ) ) - 10 L. U) 1 0 Tm 104 / n *, 103; \ ,, i . 4A, --A ............ > 102' P,a 101 Patient 1 Patient 2 & Potient 3 71O m m m m m n - 107 < m 106 ' 104 lo3 D 103 -.'-,-' > 102 A^ ^- A" -'', 1 1010 Patient 4 ,-------, Patient 5 Patient 6 10 20 30 40 10 20 30 40 10 20 0 40 Time (weeks) FIG. 1. (A) Rapid viral decline in response to lamivudine treatment in six patients. In this study, a total of45 patients received lamivudine therapy at various doses (5, 20, 100, 300, and 600 mg per day) for 28 days. Plasma virus was determined at days 0, 2, 7, 14, 21, 28, 35, 42, 56, 70, and 84. Squares indicate virus load below detection limit. (B) Viral load (circles and squares), HBeAg (triangles), and ALT levels (crosses) in six patients treated for 24 weeks. In this study, a total of 50 patients received lamivudine therapy at 25, 100, and 300 mg per day. Plasma virus was obtained at weeks 0, 2, and 4, and subsequently every 4 weeks until week 48. For our analysis we only used patients who received at least 100 mg per day. Serum HBV DNA was quantified using the Abbott Genostics solution hybridization kit. HBeAg was quantified using the Kodak Amerlite kit. DNA before migration to the cell nucleus (10), and hence vudine does not effectively prevent infection of new cells, then there is some evidence that lamivudine can prevent the the above equations are still very good approximations, pro- infection of new cells (b = 0) (11). This implies that during vided u is substantially larger than a (which will be shown treatment free virus is decaying exponentially according to below). Therefore our analysis does not rely on the assumption v(t) = voe-ut. Similarly, infected cells are decaying exponen- that lamivudine also blocks new infection. From the decline of tially according to y(t) = yoe-at. Here vo and yo indicate free free virus we can estimate the decay rate u. Before treatment, virus and infected cells at the beginning of therapy. If lami- steady state of free virus implies kyo = uvo. We know vo, Downloaded by guest on September 24, 2021 4400 Medical Sciences: Nowak et al. Proc. Natl. Acad. Sci. USA 93 (1996) hence we can estimate kyo, which is the total virus production producing) cells, a, and consequently, their half-life. This per day. method requires the initial growth rate of virus after therapy From the 1-month study we can estimate the initial rate of has stopped sincey is treated as a constant. The approximation virus decline during the first 2 days of treatment. We obtain an is accurate if virus load is determined early after the end of average of u = 0.67 per day (o- = 0.32, n = 23), which treatment.
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