Page 1

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 ofZoology, 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, UnitedKingdom

Communicated by Richard Southwood, University of Oxford, Oxford, United Kingdom, December 13, 1995 (received for review October 24, 1995)

ABSTRACT

infections with the reverse transcriptase inhibitor lamivudine

leads to arapiddecline inplasmaviremia andprovidesestimates

for crucial kinetic constants ofHBVreplication.We find that in

persistentlyinfectedpatients,HBVparticlesare cleared from the

plasma with a half-life of -1.0 day, which implies a 50%daily

turnover ofthe free virus population.Total viral release into the

peripheryis -1011 virusparticles per day. Althoughwe have no

direct measurement ofthe infected cell mass,we can estimate the

turnover rate ofthese cells in twoways: (i) by comparingthe rate

of viral production before and after therapy or (ii) from the

decline of hepatitis B antigen during treatment. These two

independent methods give equivalent results: we find a wide

distribution of half-lives forvirus-producing cells, rangingfrom

10 to 100daysin differentpatients,whichmayreflect differences

in rates of lysis of infected cells by immune responses. Our

analysis provides aquantitative understandingofHBVreplica-

tiondynamicsin vivo and hasimplicationsfor theoptimal timing

ofdrugtreatment andimmunotherapyin chronicHBV infection.

This study also represents a comparison for recent findings on

thedynamicsofhumanimmunodeficiencyvirus (HIV) infection.

The totaldailyproductionofplasmavirus is,onaverage, higher

in chronic HBV carriers than in HIV-infected patients, but the

half-life ofvirus-producing cells is much shorter in HIV. Most

strikingly,there is no indication of drug resistance in HBV-

infected patients treated forup to 24 weeks.

Treatment of chronic hepatitis B virus (HBV)

More than 250 million people worldwide are chronically

infected with hepatitis B virus (HBV), and 25-40% of these

will die from liver cirrhosis or primary hepatocellular carci-

noma (1, 2). Chronic HBV infection is often the result of

exposure early in life, leading to viral persistence in the

absence ofstrong antibodyor cellular immune responses (3).

Therapy of HBV carriers can aim to either inhibit viral

replication or enhance immunological responses against the

virus, or both (4).

The nucleoside analogue, (-)-2'-deoxy-3'-thiacytidine

(lamivudine), originally developedas an anti-human immuno-

deficiencyvirus (HIV) drug, haspotent inhibitoryeffects on

HBVreplicationin vivo(5, 6, 31).Chronic HBV carriers were

treated with various doses oflamivudine. Plasma virus load was

quantified at frequent times before, during, and after treat-

mentusing quantitative methods for determiningviral DNA.

In the first study, 45 patients were treated for 28 days; in a

subsequent study, 50 patientswere treated for 24 weeks. Fig.

1A shows plasma virus changes in six patients treated for 28

days.After onset oftherapyviral levels declinerapidly,but as

soon as the drug is withdrawn, virus returns. Fig. 1B shows

changesinplasma viremia, hepatitisBantigen (HBeAg), and

serum alanine aminotransferase (ALT)in sixpatients treated

The publication costs of this article were defrayed inpart by page charge

payment.This article must therefore beherebymarked "advertisement" in

accordance with 18 U.S.C. §1734 solely to indicate this fact.

for 24 weeks.Againwe observe rapid decline inplasmavirus

load, which falls below detection limit in almost all patients

within 2-4 weeks, and again in most patients, virus resurges

rapidly as soon as the drug is withdrawn. HBeAg is a viral

protein produced byinfected cells; itsproductionis notdirectly

inhibited by lamivudine (7), and changes in the serum con-

centration can therefore reflect changes in infected liver cell

mass. ALT is released from damaged liver cells; thus it is an

indicator of the level of cell damage and death. HBeAg and

ALT decline slowly during longterm lamivudine treatment.

Therapeuticallyinduced HBeAg seroconversion, seen during

successful interferon a therapy and thought to represent the

lysis of infected cellsbythe host's immune response, is not a

feature of lamivudine treatment.

For aquantitative analysis of these observations, we design

a simple but natural mathematical model based on ordinary

differential equationsfor uninfected cells, x, infected cells, y,

and free virus, v:

dx/dt=A

dx-bvx,

dy/dt=bvx-ay,

dv/dt=ky

-uv.

[1]

Uninfected, susceptiblecells areproducedat a rate, A, which

may be constant or depend on the total population size of

uninfected and infected cells. Uninfected cells die at rate dx,

and become infected at rate bvx, where b is the rate constant

describingthe infectionprocess.Infected cells areproducedat

rate bvx and die at rate ay. Free virions are produced from

infected cells at rate ky and are removed at rate uv. Strictly

speaking,thedecayrate of free virus should also be a function

of the uninfected(and infected)cellpopulation,but weexpect

the leadingterm of viraldecayto beindependentofchanges

in the host cell population. Therefore it is a reasonable

assumption to treat u as a constant. The magnitude of the

parameters a, b, k, and u will be determined by antiviral

immune responses. In the absence of treatment the system

convergesto asteadystate ofpersistent infection, providedthe

basicreproductiveratio of thevirus, Abk/(adu)isgreaterthan

1. This condition islikelyto be fulfilled ifpatientshave weak

immuneresponses againstfree virus(lowu)oragainstinfected

cells (low a). Hence, in our simple model weak immune

responses predispose to carrier state.

In the replication cycle of HBV, the viral reverse tran-

scriptase is responsible for the synthesis of new HBV DNA

from the pregenomic mRNA template (8, 9). Therefore,

lamivudine canpreventtheproductionof new virusparticles

fromalreadyinfected cells(k

is also essential for completing the double-stranded circular

=0). But the viralpolymerase

Abbreviations: HBV, hepatitis B virus; HIV, human immunodefi-

ciency virus; HBeAg, hepatitisB antigen; ALT, alanine aminotrans-

ferase; cccDNA, covalentlyclosed circular DNA.

tTo whom correspondence should be addressed.

4398

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Medical Sciences: Nowak et al.

A

E

a)

Q.

cn

c)

ao

Q_

Un 0

0

E

0-

Proc. Natl. Acad. Sci. USA 93 (1996)

4399

Patient

3

I

Time (days)

\

,,

Patient

1

A^

^-

Patient

4

1020

30

40

L.

.

A,

4

--A............

Patient2

A"

,

-''

, ,------- Patient

2030

5

10

40

*,

/

P,a

&

Potient

3

mm

mm

mn

-.' -,-'

Patient

6

10

20

0

40

Time (weeks)

FIG. 1.

at various doses(5, 20, 100, 300, and 600mg per day)for 28days. Plasma virus was determined atdays 0, 2, 7, 14, 21, 28, 35, 42, 56, 70, and 84.

Squaresindicate virus load below detection limit.(B)Viral load(circlesandsquares), HBeAg (triangles),and ALT levels(crosses)in sixpatients

treated for 24 weeks. In thisstudy, a total of 50patientsreceived lamivudinetherapyat 25, 100, and 300mg per day. Plasma virus was obtained

at weeks 0, 2, and 4, andsubsequently every4 weeks until week 48. For our analysisweonlyusedpatientswho received at least 100mg per day.

Serum HBV DNA wasquantified usingthe Abbott Genostics solutionhybridization kit.HBeAgwasquantified usingthe Kodak Amerlite kit.

DNA before migration to the cell nucleus (10), and hence

there is some evidence that lamivudine can prevent the

infection of new cells (b=0) (11). This implies that during

treatment free virus is decaying exponentially according to

v(t)=voe-ut. Similarly, infected cells aredecaying exponen-

tially accordingtoy(t)=yoe-at. Herevoandyoindicate free

virus and infected cells at the beginning oftherapy. If lami-

(A)Rapidviral decline inresponseto lamivudine treatment in sixpatients.In thisstudy,a total of45patientsreceived lamivudinetherapy

vudine does noteffectively preventinfection of newcells, then

the aboveequations are stillvery good approximations, pro-

vided u is substantially larger than a (which will be shown

below).Therefore ouranalysisdoes notrelyon theassumption

that lamivudine also blocks new infection. From the decline of

free virus we can estimate thedecayrate u. Before treatment,

steady state of free virus implies kyo=uvo. We know vo,

B

108

- 10

U)

1 0

104

103;

102'

101

m

T

n

>

71O

- 107

<106

m

' 104

lo3

D 103

>102

101

1 0

(

)

i

)

Page 3

4400

Medical Sciences: Nowak et al.

hence we can estimatekyo,which is the total virusproduction

per day.

From the 1-month studywe can estimate the initial rate of

virus declineduringthe first 2daysof treatment. We obtain an

average of u = 0.67 per day (o-=0.32, n =23), which

corresponds to a half-life time(Ti/2)of 1.0 day. Hence, in the

absence of treatment =50% of theplasmavirus isreplenished

every day. The total serum virus load (for 3 liters ofserum)

before treatment varies in differentpatients rangingfrom 1010

to 1012 particles, with anaverageof 2.2 x 1011(o-= 2.6 x 1011,

n =45). Consequently, the total amount of plasma virus

production follows a wide distribution with an average of 1.3

x 101l particles per day (a= 8.2 x 1010, n =23). These

differences are likely to reflect different population sizes of

virus-infected cells in individual patients. Plasma virus levels

usually correlate with abundance of infected cells as deter-

mined by histological examination of the liver (12).

Virus decline during treatment is not strictly exponential

(see Fig. 1).This can be explained bytheassumption that the

efficacy of the drug is not 100%. Assuming a certain efficacy

p,viral decay occurs according to v(t)=vo(l

Fittingthis functionprovidesan estimate for theefficacyofthe

drug at various doses. We find that fordailydoses of 20, 100,

300, and 600mg,viralreplicationis inhibitedby 87, 97, 96, and

99%, respectively.

When therapy is withdrawn, virus resurges according to

dv/dt =ky-uv. Hence, the initial virusgrowthrate can be

approximated by

v(t)=v1e-ut +(ky1/u)(1

p+pe-Ut).

e-Ut),

[2]

where v1 andyi indicate the levels of free virus and infected

cells at the end oftherapy.We know v1bydirectmeasurement,

and we have determined the decay rate, u; hence we can

estimate kyl, which is the rate of virus production from

infected cells at the end oftherapy. Comparing kyo andkyl

gives an estimate for the decay rate of infected (virus-

350-

3001

250

200-

150-

100-

50-

0.000.04 0.08

a

0.12

0.16

producing) cells, a, and consequently, their half-life. This

method requires the initialgrowth rate of virus aftertherapy

hasstoppedsinceyis treated as a constant. Theapproximation

is accurate if virus load is determined early after the end of

treatment. In our study, treatment was withdrawn after 28

days, and virus load was determined at days 28 and 35. We

obtain anaveragedecline of a = 0.043per day (oa=0.036, n

=20) corresponding to aTi/2of 16 days. In differentpatients

half-lives range from about 10 to 100 days.

The broad distribution ofturnover rates ofinfected cellsmay

be a consequence ofheterogeneity of the immune response

against infected cells in different patients (13, 14). Damaged

liver cells release ALT, and henceplasmaALT levels should

providesome crude estimate for the amount ofcell death in the

liver. If most cell damage is caused by immune responses

directed to infected cells(15),then ALT levelsprovide some

estimate for the strength of the immunological response

againstHBV. We find apositivecorrelation between thedecay

rate of infected cells and thepretreatmentALT levelamong

different patients (Fig. 2). This supports our hypothesis that

thevariabilityof celldecayrates reflects differentstrengthsof

anticellular immune responses and is not simply caused by

fluctuations in measurement or inaccurate approximation.

In thesubsequent study, treatment continued for 24weeks,

butsamplingwas lessfrequent (thefirst timepointsafter 2 and

4 weeks, thenevery4weeks), and we cannot obtain accurate

estimates of the viral or cellular decay rates with the above

methods. However, we can obtain anindependent estimate of

the turnover of infected cells from the initialdecayofHBeAg.

Reverse transcriptase inhibitors such as lamivudine have no

direct effect on the synthesis and secretion ofHBeAg, which

is derived from mRNA transcribed from existing covalently

closed circular DNA (cccDNA) molecules of HBV within

infected cells. The capacity of the infected host to synthesize

this protein is dependent on the rate of infection of cells

(inhibited by lamivudine)and the rate oflysisof infected cells

(not inhibited by lamivudine) and dependent on immune

0.00

0.04

0.08

a

0.12

0.16

FIG. 2.

the28-day studythedecay rate, a, was estimatedby comparingthe rate of virusproductionbefore and after treatment(at days0 and28).For the

24-weekstudya was estimated from the initial decline ofHBeAgover the first 2 weeks. ASpearmanrank correlationgivesa correlation coefficient

of r=0.61 (P=0.007) for the28-day study, and r=0.50 (P

rates a suggests that the wide distribution of calculated a values does reflect biological heterogeneity (rather than measurementuncertainty);

different patients appear to have different immune responses againstinfected cells. The symbols reflect patientswith differentdaily dosageof

lamivudine. Squares, 100 mg; circles, 300 mg; triangles, 600 mg.

Correlation between initial serum ALT level before treatment and estimateddecayrate ofvirus-infected cells, a, duringtreatment. For

=0.005) for the 24-weekstudy.The correlation between ALT levels anddecay

(D

A

0

c!)

CD

&

El

0

0

CD

Ep

(D

(Z)

a

o

Proc. Natl. Acad. Sci. USA 93 (1996)

Page 4

Proc. Natl. Acad. Sci. USA 93(1996)

4401

recognitionof these cells. Hence the initialdecayofHBeAgin

patients takinglamivudine should reflect thedecayof infected

hepatocytes. Duringthe first 8 weeks of treatment we observe

anaverage decline of a = 0.053 per day (ao=0.039, n =29),

which corresponds to a T,/2of 13 days. This is in agreement

with ourpreviousestimate.Againthere is a wide distribution

of half-lives and we find astrongcorrelation betweendecayof

infected cells andALT levelsamongdifferentpatients (Fig. 2).

After 24 weeks of treatment, patients were followed for

another 24 weeks. Interestingly, there is a strong capacity in

individual patients to return to the pretreatment steady-state

level after these 48 weeks.Fig.3 showsplasmavirus load, ALT

levels, and HBeAg levels for each patient at time 0 and after

48 weeks. Whatever factors-e.g., efficacy of antiviral and

anticellular immuneresponses-determinetheparticular pre-

treatmentsteady-statelevel ofplasma virus, HBeAg,andALT

in individualpatients,it isinterestingto note that these factors

haveappearentlynotchangedover the time course of48weeks

in most patients.

We also analyzed data from a cohort ofJapanese patients,

where treatment continued for 28 days and serum virus load

03

102-

10

1o

101-

3000

3-

103

300

a)

2-

102~

30

103-

300-

102-

1o 0

30-

lo0-

o-

(D

C3

m

go

C^o

.

[]

,.'(

*' o

(D

'1

a

10

10

I1I0'o

'

2

3

10

10

vo

0

o

o°

o/,o

I,,

o

l l0 ll

"

30

io2300 i3000

eoo

..

o,/

101

30

io2

a0

300

io3

FIG. 3.

chronic HBV infection. Patients were treated for 24 weeks and were

subsequentlyfollowed for another 24 weeks. Thefigureindicates virus

load, HBeAg,and ALT beforetherapy (x axes)versus after 48 weeks

(y axes).In eachdiagram,eachpatientis indicatedbyapoint;different

symbolsreflect differentdaily dosagesof lamivudine(squares,100mg

andcircles, 300mg).Mostpointslie close to thediagonal indicating

thetendencyto return to thepretreatmentlevel. Units: virus load in

particles/ml, HBeAginunits/ml,ALT levels inunits/liter.

Capacityto return topretreatment steady-statelevels in

and ALT levels were determined at days 0, 7, and 14, and

subsequently every14days.For the virus decline as measured

from the decay during the first week of treatment, we obtain

u = 0.56 (a-=0.18, n =67) whichcorresponds to a Ti/2 of

1.2days. Average plasmavirusproductionis about 3 x 1012

(o-= 5 x 1012, n =57) particles per day.For the cellulardecay

rate (determined by comparingvirusproduction at day0 and

28)we obtain a wide distribution with anaverageofa = 0.053

per day (va=0.067, n =46) correspondingto aT/12of 13days.

There is, however, only a weak (not significant) correlation

between a and ALT levels in thesepatients, probablybecause

the estimate of a is problematic in some patients, which is

because viral measurements are often below detection limit

and viral increase aftertherapyis determined from virus titer

at days 28 and 42.

It islikelythat HBV infects andreplicatesat different rates

in a number of celltypes (16, 17).Therefore the estimated viral

productionrates and turnover rates of infected cells have to be

interpretedasaveragevalues.Similarly,the rate ofproduction

ofviralparticlesandHBeAgfrom an infected cellmay depend

on the number of cccDNA molecules of HBV in the nucleus

of an infected cell. During drugtreatment the cccDNAcopy

numberperinfected cellmay decline, which could lead to less

viral andHBeAg production independentof death of infected

cells. Therefore the decline of viral production and HBeAg

could overestimate the actual rate ofclearance ofinfected cells

and rather reflect the decay of cccDNA. But for practical

purposes the most important figure is the decay ofpotential

virus "production units" during treatment, independent of

whether this reflects cell death or decay of viral cccDNA.

However, the observed correlation between ALT and the

death rate of infected cells (as estimated by HBeAg decline)

argues in favor of clearance of infected cells as the major

mechanism. Patients with high ALT levels appear to clear

virus-producing units faster.

A half-life of 10daysfor infected, virus-producing hepato-

cytes impliesthat -7% of this cellpopulationis lostper day.

In a chronic HBV infection, between 5% and 40% of all

hepatocytescan be infected andproducevirus(18). Therefore,

between 0.3% and 3% of allhepatocytes are killed and must

bereplenished every dayto maintain a stable liver cell mass.

Since the liver contains -2 x 1011hepatocytes (19),this comes

to 109 cellsper day. This enormous activityof cell death and

regeneration islikelyto be amajor driving force fordevelop-

ment ofhepatocellular carcinoma (17, 20).

Our data provide an interesting comparison with HIV

dynamics (Table 1). In HIV infections, most patients have a

turnover rate of infected cells of -2 days and free virus is

cleared faster than this (21-24). In HBV infections, decay of

plasmavirus occurs with a half-life of

generallyseem to have noantibody againstfree virus. Inter-

estingly, there is a much wider distribution of half-lives of

virus-producingcells in HBV-infected patients ranging from

1dayinpatientsthat

Table 1. HBV versus HIVdynamics

HBV

HIV

Plasma virus

Half-life

Daily turn-over

Totalproduction (periphery)

Load

Infected cell

Half-life

Daily-turnover

AcomparisonofHBV and HIV in vivodynamics.Both viruses have

arapidturnover and a massiveproductionofplasmavirus.Perhapsthe

mostimportantdifference is in the half-life ofvirus-producing cells,

which is much shorter for HIV. The HIV data are from refs. 21, 22,

and 30.

24 hr

50%

10ll

2 X 1011

6 hr

90%

109

109

10-100 days

1-7%

2 days

30%

Mvedical Sciences: Nowak et al.

,'o

of

x6

0

o

Page 5

4402

Medical Sciences: Nowak et al.

about 10 to 100 days. HBV is believed to be largely noncyto-

pathic,and therefore the turnover rates of infected cells can be

due to different anticellular immune responses. HIV, on the

other hand, canprobablykill an infected cell within a fewdays,

and the rather uniform turnover rate ofproductivelyinfected

cells could be theconsequenceof atight strugglebetween viral

cytopathicityand the strong cytotoxic T-lymphocyte response

found in most HIV patients. The large turnover of infected

CD4 cells in HIV infection ['109 CD4 cells are estimated to

be killed bythe virus and regenerated by the immune system

every day (21, 22)] is matched by an equivalent number of

hepatocytes in HBV infection. The total amount of plasma

virus production is larger for HBV; on average, -109 HIV

particles are generated every day comparedwith -101 HBV

particles.Thus chronic HBV infectionemerges also as arapid

dynamic processwith vast amounts of virus and infected cells

produced and killed every day.

Withrespectto accumulation ofgenetic diversityandescape

from drug treatment and immune responses, the relevant

figureis the viralgeneration time, which islargelydetermined

by the turnover rate of virus-infected cells and is therefore

much shorter in HIV. Another important factor is that the

genome lengthofHBV isonly -3200bp comparedto

bpfor HIV and thatmultiple overlapping readingframesmay

imposemore constraints againstvariation on HBV than HIV.

While there is rapid emergence of drug-resistant strains in

HIV (21, 25), we do not find any indication of resistance in

HBV; in our studies HBV virus loads do not increase aslong

as the drug is given.

Treatment of chronic HBV infections with lamivudine leads

to a rapid and sustained decline of plasma virus levels, but

clinical benefit with a reduced risk of cirrhosis and develop-

ment of liver cancer will greatly depend on the decline of

infected cells (26-28).Inpatientswhere infected cells decline

with a half-life of 10days,treatment for 1yearcouldpotentially

reduce the number of infected cells to -10-l

value (with a 100% effective drug). Eradication of the virus

infection depends on whether the efficacy of the drug is

sufficiently high to reduce the basic reproductiveratio of the

virus belowunity [in analogytoepidemiological theory (29)].

Inpatientswith an infected cell half-life of 100days,1yearof

treatment could reduce the number of infected cells to -8%

of its initial value. Thus lamivudine could be used over a

prolonged period as single-agent therapy or to reduce the

number of infected cells before immunotherapy designed to

eradicate infected cells. Immunotherapy without antiviral

treatment could be problematic because of the very large

number of infected liver cells in the typicalHBV carrier. The

quantitative understandingofHBVdynamicsderived here will

make it possible to devise optimal treatment strategies for

individualpatients.

10,000

of its initial

We are indebted to S. Schalm, D. Tyrell, J. Main, J. Fevery, F.

Nevens, D. Mann, and K. Tanikawa forallowingus to use thehepatitis

B marker data from their patients on which our analysis is based.

M.A.N.

Abraham Junior Research Fellow of Keble College.

is a Wellcome Trust Senior Research Fellow and E.P.

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