Supe in ec ion and cu e o in ec ed cells as
mechanisms o hepa i is C i us adap a ion
and pe sis ence
Ruian Ke
a,b,1
, Hui Li
c,d,1
, Shuyi Wang
c,d
, Wenge Ding
c,d
, Ruy M. Ribei o
b,e
, Elena E. Gio gi
b
,
Tanmoy Bha acha ya
,g
, Richa d J. O. Ba na d
h
, Bea ice H. Hahn
c,d,2
, Geo ge M. Shaw
c,d
, and Alan S. Pe elson
b,g,2
a
Depa men o Ma hema ics, No h Ca olina S a e Uni e si y, Raleigh, NC 27695;
b
Theo e ical Biology and Biophysics G oup, Los Alamos Na ional
Labo a o y, Los Alamos, NM 87545;
c
Depa men o Medicine, Uni e si y o Pennsyl ania, Philadelphia, PA 19104;
d
Depa men o Mic obiology, Uni e si y
o Pennsyl ania, Philadelphia, PA 19104;
e
Labo a o y o Bioma hema ics, Facul y o Medicine, Uni e si y o Lisbon, 1600-276 Lisbon, Po ugal;
Theo e ical
Di ision, Los Alamos Na ional Labo a o y, Los Alamos, NM 87545;
g
San a Fe Ins i u e, San a Fe, NM 87501; and
h
Depa men o In ec ious Disease, Me ck &
Co., Inc., Kenilwo h, NJ 07033
Con ibu ed by Bea ice H. Hahn, June 8, 2018 (sen o e iew Ma ch 28, 2018; e iewed by Alison P. Gal ani and Ma in A. Nowak)
RNA i uses exis as a gene ically di e se quasispecies wi h ex ao -
dina y abili y o adap o ab up changes in he hos en i onmen .
Howe e , he molecula mechanisms ha con ibu e o hei apid
adap a ion and pe sis ence in i o a e no well s udied. He e, we
p obe hepa i is C i us (HCV) pe sis ence by analyzing clinical
samples aken om subjec s who we e ea ed wi h a second-
gene a ion HCV p o ease inhibi o . F equen longi udinal i al load
de e mina ions and la ge-scale single-genome sequence analyses
e ealed apid an i i al esis ance de elopmen , and su p isingly,
dynamic u no e o dominan d ug- esis an mu an popula ions
long a e ea men cessa ion. We i ed ma hema ical models o
bo h he i al load and he i al sequencing da a, and he esul s
p o ided s ong suppo o he c i ical oles ha supe in ec ion and
cu e o in ec ed cells play in acili a ing he apid u no e and
pe sis ence o i al popula ions. Mo e b oadly, ou esul s highligh
he impo ance o conside ing i al dynamics and compe i ion a he
in acellula le el in unde s anding apid i al adap a ion. Thus, we
p opose a heo e ical amewo k in eg a ing i al and molecula
mechanisms o explain apid i al e olu ion, esis ance, and pe sis-
ence despi e an i i al ea men and hos immune esponses.
i us e olu ion
|
i us pe sis ence
|
hepa i is C i us
|
phylodynamic
modeling
|
ma hema ical modeling
Many RNA i uses, including global pa hogens o majo
medical impo ance such as hepa i is C i us (HCV), HIV, and
ebola i us, exis wi hin in ec ed hos s as la ge popula ions o gene -
ically ela ed i al a ian s commonly e e ed o as a quasispecies
(1). The di e se na u e o he i al quasispecies allows i al pop-
ula ions o e ol e apidly o adap o ab up changes in he hos en-
i onmen (2); examples include escape om adap i e immune
p essu es (3, 4) and de elopmen o esis ance o an i i als (5, 6).
Despi e he impo ance o i al adap a ion, ou unde s anding o how
he i al quasispecies esponds o selec ion p essu e and he unde -
lying molecula mechanisms suppo ing i al adap a ion in i o is
limi ed by a lack o equen longi udinal i al sequence da a gen-
e a ed by me hods ha e ain linkage ac oss genes and genomes (7).
P e iously, much a en ion has been de o ed o es ima ing he
e ec i eness o an i i als agains i al a ian s in he quasispe-
cies (8–10); howe e , he mechanisms ha d i e an adap i e/
i e a ian (e.g., a d ug- esis an mu an ) a an ini ially low
equency o a high equency a e less well s udied. Theo e ical
wo k sugges s ha i e a ian s a a low equency canno ex-
pand unless he e a e su icien numbe s o a ge cells, ha is,
“ eplica ion space”(5, 11–14). This is analogous o he concep
o compe i i e elease in ecological “niche” heo y, ha is, a
species is no able o expand unless he e is a niche aca ed by
o he species (15). P e ious models ha e in gene al assumed
ha , once a a ian in ec s a cell, he cell is occupied by he
a ian o i s emaining li e ime, and hus he eplica ion space
is p o ided by gene a ion o new a ge cells (5, 8, 13, 16–18).
Unde his amewo k, i al a ian s compe e o in ec ing newly
gene a ed a ge cells, and hus, he expansion o a low- equency
i e mu an is de e mined by how quickly in ec ed cells die and
a e eplaced by new a ge cells. This amewo k has been suc-
cess ully applied o unde s and HIV d ug esis ance (6, 13, 16, 18).
Howe e , he sou ce o eplica ion space o o he apidly e ol ing
i uses, and in pa icula HCV, is unclea .
HCV is a posi i e-s and RNA i us belonging o he la i-
i idae, a amily o medically impo an single-s and RNA
i uses. HCV in ec s ∼80–170 million people wo ldwide (19).
Ch onic in ec ion can lead o ci hosis and hepa ocellula ca ci-
noma. Cu en ea men s o HCV in ec ion in ol e combina-
ions o di ec ac ing an i i als (DAAs), and hey ha e achie ed
Signi icance
Vi al popula ions exhibi an ex ao dina y abili y o su i e
ab up changes in hos en i onmen by apidly gene a ing
adap i e mu a ions. Howe e , ou unde s anding o how i al
popula ions espond o selec ion p essu e and he unde lying
molecula mechanisms suppo ing i al adap a ion in i o is
limi ed. He e, we epo a se o clinical da a sampled om
subjec s ch onically in ec ed by hepa i is C i us (HCV). The da a
show apid expansion and u no e o d ug- esis an i uses
ollowing ea men wi h an HCV p o ease inhibi o . By i ing
ma hema ical models o he da a, we p opose ha supe in ec-
ion and cu e o in ec ed cells play c i ical oles in acili a ing he
apid expansion and u no e o i al popula ions. Ou esul s
highligh he impo ance o conside ing in acellula i al com-
pe i ion in unde s anding apid i al adap a ion.
Au ho con ibu ions: R.K., H.L., R.M.R., G.M.S., and A.S.P. designed esea ch; R.K., H.L.,
S.W., W.D., R.M.R., E.E.G., T.B., R.J.O.B., B.H.H., G.M.S., and A.S.P. pe o med esea ch;
R.K., H.L., S.W., W.D., R.M.R., E.E.G., T.B., R.J.O.B., B.H.H., G.M.S., and A.S.P. analyzed da a;
and R.K., H.L., R.M.R., G.M.S., and A.S.P. w o e he pape .
Re iewe s: A.P.G., Yale Cen e o In ec ious Disease Modeling and Analysis; and M.A.N.,
Ha a d Uni e si y.
Con lic o in e es s a emen : R.J.O.B. is an employee and sha eholde o Me ck & Co.,
Inc. This wo k was unded by a g an om Me ck Sha p & Dohme Co p., a subsidia y o
Me ck & Co., Inc. ( o G.M.S.). A.S.P. consul ed o Me ck Sha p & Dohme Co p., a sub-
sidia y o Me ck & Co., Inc.
This open access a icle is dis ibu ed unde C ea i e Commons A ibu ion-NonComme cial-
NoDe i a i es License 4.0 (CC BY-NC-ND).
Da a deposi ion: The sequences epo ed in his pape ha e been deposi ed in he GenBank
da abase (accession nos. MF282014–MF284666).
1
R.K. and H.L. con ibu ed equally o his wo k.
2
To whom co espondence may be add essed. Email: [email protected] o
[email p o ec ed].
This a icle con ains suppo ing in o ma ion online a www.pnas.o g/lookup/suppl/doi:10.
1073/pnas.1805267115/-/DCSupplemen al.
Published online July 9, 2018.
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ema kably high cu e a es (20–22). I onically, because o his
clinical e ec i eness, combina ion ea men s canno gene ally
be used o p obe he molecula mechanisms ha con ibu e o i us
pe sis ence. Howe e , his in o ma ion may be c i ical o designing
e ec i e accina ion s a egies o HCV and he apeu ic egimens
and accines o o he membe s o he la i i idae amily. He e, we
analyzed clinical samples collec ed om a phase I/IIa mono he apy
ial (23) o a second-gene a ion HCV p o ease inhibi o , MK-5172
(also called g azop e i ) (22, 24–26), ha is ex emely po en bu
suscep ible o d ug esis ance de elopmen h ough mul iple i al
gene ic pa hways o escape. Measu ing i al loads and analyzing
i al popula ions longi udinally by single-genome sequencing (7)
allowed us o ollow he popula ion dynamics and e olu iona y
esponses o HCV o d ug p essu e and i s emo al in i o a high
esolu ion. We analyzed his unique da ase by combining ma he-
ma ical modeling and phylogene ic analysis [ e med “phylody-
namic”analysis (27)]. We p o ide s ong e idence ha cu e and
supe in ec ion o in ec ed cells con ibu e essen ially o he epli-
ca ion space, allowing esis ance mu an expansion and e olu ion.
Resul s
S udy Subjec s and Single-Genome Sequence Analysis. We s udied eigh
pa icipan s om a dose- anging mono he apy ial o MK-5172
(23). Fi e we e ea ed wi h MK-5172 (50 o 800 mg) once daily o
7 d (subjec s 1–5, geno ypes 1a, n=4; 1b, n=1) and h ee we e
ea ed wi h placebo (subjec s 6–8, geno ypes 1a, n=2; 1b, n=1) (SI
Appendix,TableS1). All o he pa icipan s we e ollowed o 7–8wk
a e ea men cessa ion. We measu ed i al loads longi udinally
and analyzed i al popula ions using single-genome sequencing (7).
Samples aken immedia ely be o e ea men ini ia ion, desig-
na ed as day 0, we e analyzed in all eigh subjec s o geno ypic
complexi y and baseline d ug esis ance mu a ions (DRMs). A
each sampling imepoin , ∼100 i al genomes we e sequenced in
each subjec (Fig. 1 and SI Appendix,Figs.S1–S7). Day 0 se-
quences o each subjec showed pa e ns o i us di e si y ypical
o ch onic in ec ion wi h b oad geno ypic he e ogenei y (SI Ap-
pendix, Table S1). Maximum pai wise di e si y and mean pai wise
di e si y anged om 1.17 o 5.64% and 0.53 o 3.45%, e-
spec i ely. No d ug esis ance-associa ed mu a ions we e iden i-
ied in he p e ea men sequences, al hough a Q80K subs i u ion
was ound in all sequences in subjec s 2 and 3. Q80K is a common
polymo phism ha con e s no esis ance o MK-5172.
In he i e subjec s ea ed wi h MK-5172, i al load dec eased
o e 5 logs and wen below (o close o) he limi o quan i ica ion
(=25 IU/mL) du ing he 7-d ea men pe iod (Fig. 1Aand SI
Appendix,Figs.S1–S4). A he end o his pe iod, i al load was oo
low o pe mi sequencing analyses. By day 27, 20 d a e ea men
was s opped, he i al load ebounded o le els (10
6
o 10
7
IU/mL)
simila o he baseline le el be o e ea men in all ea ed subjec s
and could be quan i ied as ea ly as day 14 (7 d a e s opping
ea men ) in subjec s 1 and 4. Follow-up single-genome se-
quencing analyses we e conduc ed on samples om days 14 o 62.
A e he apy was s opped, he i al popula ions ha eme ged
ca ied d ug esis ance mu a ions. Su p isingly, he dynamics o
mu an i us popula ions exhibi ed s ingen popula ion bo le-
necks and apid u no e o he dominan esis an mu an s du ing
he ollow-up pe iod, e en in he p esence o ela i ely s able i al
load (e.g., subjec 1 be ween days 27 and 56; Fig. 1). Ex emely
apid and con inuous u no e o he esis an mu an s, a e
he apy cessa ion, was obse ed in subjec s 1 and 4 (Fig. 1 and SI
Appendix, Fig. S3). In con as o hese d ama ic changes in
plasma i al RNA ( RNA) load in subjec s ea ed wi h MK-5172,
he h ee subjec s who ecei ed placebo had no changes in plasma
RNA le els and no sequences con aining DRMs. Vi al sequences
om hese indi iduals we e ob ained on days 0 and 27 o 34 (SI
Appendix, Figs. S5–S7). Below, we desc ibe he e olu iona y pa -
e ns in subjec 1 in de ail. The pa e ns in o he ea ed subjec s
a e desc ibed in SI Appendix,SI Me hods and Resul s.
In subjec 1, none o 103 single genome sequences on day
0 con ained d ug esis ance-associa ed mu a ions (Fig. 1C). Con-
e sely, on day 14 (i.e., 7 d a e he apy was s opped), all
111 single-genome sequences analyzed con ained one o mo e d ug
esis ance-associa ed mu a ions. Fi y-six o he 111 sequences
con ained single A156T o V mu a ions lis ed in colo on he igh -
hand side o Fig. 1Cand wo sequences con ained a single R155G
mu a ion. These 58 sequences con aining single d ug esis ance
mu a ions we e widely dispe sed h oughou he phylogene ic ee
o p e ea men sequences (Fig. 1B). This indica es ha nea ly all o
hese d ug- esis an sequences ep esen ed dis inc i al lineages
ha aced back 14 d ea lie o in ec ed hepa ocy es ha ca ied
A156T o A156V mu a ions in widely di e gen gene ic back-
g ounds. In ma ked con as , 51 o 111 sequences (46%) con ained
a R155W-plus-A156G double mu a ion, in a nea ly homogeneous
gene ic backg ound whe e sequence di e si y anged om 0 o
1 nucleo ide subs i u ion o e a span o 2,210 bp (<0.1% di e si y).
This esul sugges s ha ∼46% o hepa ocy es, eleasing HCV i-
ions in o he ci cula ion a 14 d a e he ini ia ion o MK-
5172 ea men (and 7 d a e i s discon inua ion), we e in ec ed
by HCV genomes ha had e ol ed om a single R155W-plus-
A156G d ug- esis an i al sequence lineage. In u n, his lineage
mos likely emana ed om a single o a ew p oduc i ely in ec ed
hepa ocy es ha exis ed be o e ea men ini ia ion (Fig. 1C). This
in e ence is d awn based o he iden i y o nea iden i y (1 mu a ion
in 2,210 n ) o he gene ic backg ound in which he R155W-plus-
A156G d ug esis ance mu a ion expanded. These indings a e
consis en wi h model p edic ions o he expec ed equency o a
single mu a ion o any se o wo mu a ions in an HCV RNA
quasispecies in he absence o selec ion (5, 28). In addi ion, one
sequence wi h Y56H-plus-D168V and one wi h Y56H-plus-D168N
double mu a ions we e also de ec ed. A day 27 when he plasma
i al load had e u ned o baseline (>10
6
RNA/mL), he e was a
s iking con ac ion in bo h he R155W-plus-A156G and A156T o
V popula ions and a ema kable expansion o he disc e e homo-
geneous Y56H-plus-D168V and Y56H-plus-D168N double-mu an
popula ions (al eady de ec ed a day 14). A single dominan Y56H-
plus-D168N double-mu an popula ion and h ee dominan Y56H-
plus-D168V double-mu an popula ions oge he ep esen ed 70%
o he sequences. This inding is all o he mo e ema kable gi en
ha , by his ime, s eady-s a e plasma RNA load had e u ned o
i s p e ea men se poin o >10
6
RNA copies pe mL and d ug
he apy had been s opped 20 d p e iously. Two addi ional mono-
phyle ic lineages, each con aining he double-mu an D168E-plus-
F169I, we e p esen on day 27. By day 56, he D168E-plus-F169I
mu an lineages ( i s de ec ed a day 27) expanded o comp ise
79% o he sequences, whe eas he p e iously dominan Y56H-plus-
D168N and Y56H-plus-D168V lineages con ac ed and now
comp ised only 12% o he sequences. Fou wild- ype sequences,
ha is, sequences wi h no known esis ance mu a ions, we e
de ec ed o he i s ime pos ea men a day 56.
Fi ing a Baseline Vi al Dynamic Model o he Vi al Load and
Sequence Da a. The apid i al load decline du ing ea men
and con inuous u no e o esis an mu an s a e ea men
cessa ion obse ed in he ea ed subjec s aise in iguing ques-
ions, such as how do esis ance clones expand so apidly and how
can esis an mu an s domina e he i al popula ion o such a
long pe iod a e ea men cessa ion wi hou being eplaced by
he non esis an i us? To add ess hese ques ions, we i s con-
s uc ed a “baseline”mul is ain HCV model, simila o a p e ious
s anda d i al dynamic model ha inco po a es compe i ion o
a ge cells (5) (Me hods). The s ains in he model a e g ouped
acco ding o he sha ed d ug esis ance mu a ions in he clinical
samples as desc ibed in he sec ion abo e and as colo -coded in
Fig. 1 and SI Appendix, Figs. S1–S7 (see SI Appendix, Table S2, o
he mu an s modeled). In his model, we assume ha in ec ed cells
a e los a a pe -capi a a e δand ha a ge cells p oli e a e
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ollowing a logis ic g ow h e m o eplace hem. Cu e and su-
pe in ec ion o in ec ed cells a e no included in his model.
We i ed his model o he da a om all i e ea ed subjec s.
This model desc ibes bo h he i al load and he sequence da a
well (SI Appendix,Fig.S8). Howe e , he mean loss a e o in-
ec ed cells, δ, es ima ed ac oss all i e ea ed subjec s was 0.68 d
−1
wi h a SD o 0.09 d
−1
(see SI Appendix,TablesS3–S7, o he
bes - i alues o δ). In ou model, he loss o in ec ed cells
A
C
B
Fig. 1. Sequen ial plasma i us load and sequences om subjec 1. (A) Time cou se o ea men wi h MK-5172 (shaded a ea, days 1–7), i al load de e -
mina ions (blue solid do s), and i al sequence analyses (open ci cles a days 0, 14, 27, and 56). (B) A maximum-likelihood (ML) phylogene ic ee o all i al
sequences sampled om subjec 1 om all ime poin s. T ee ips a e colo coded acco ding o he known esis an mu a ions hey bea . (C) ML phylogene ic
ees o i al sequences sampled om subjec 1 a each ime poin .
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co esponds o dea h o hese cells. A la ge dea h a e is needed o
explain he apid second-phase i al load decline du ing ea men
and apid u no e o dominan mu an s a e ea men . How-
e e , such a la ge dea h a e o in ec ed cells (0.68 d
−1
)doesno
seem physiological, as i implies a hal -li e o in ec ed hepa ocy es
o 1 d. In s a k con as , he dea h a e o in ec ed cells has been
es ima ed as 0.14 d
−1
om IFN he apy (29, 30) and p e iously
used by Guedj e al. (31) and Lau e al. (21) o explain i al de-
clines seen wi h o he DAAs. To con i m he necessi y o a high
loss a e in his model, we e i ed he model ixing δa 0.14 d
−1
and ound his al e na i e pa ame e iza ion explains he da a
poo ly (SI Appendix,Fig.S9). These esul s s ongly sugges ha
o he mechanisms (in addi ion o dea h o in ec ed cells) mus
play essen ial oles in d i ing he pa e ns seen in he da a.
Po en ial Roles o In ec ed Cell Cu e and In acellula Vi al
Compe i ion Th ough Supe in ec ion. We hypo hesize ha cu e o
in ec ed cells is he p ima y cause o he loss o in ec ed cells
du ing he apid second-phase decline obse ed in ou da a and
o he s udies (5, 8, 32). In addi ion, we hypo hesize ha he
con inuous u no e o dominan mu an s in he absence o
ea men is mos ly d i en by in acellula compe i ion among
i al s ains, as a esul o supe in ec ion ( a he han compe i ion
o newly gene a ed a ge cells). P e iously, cu e o in ec ed cells
has been demons a ed in in i o s udies (33–37). In i o, he
apid second-phase i al declines unde ea men we e sugges ed
o be a ibu able o cu e o in ec ed cells (32, 38). Fo supe in-
ec ion, in i o expe imen s showed ha mul iple i uses can
en e he same cell, al hough limi ing hos esou ces necessa y o
i al eplica ion and/o ansla ion may es ic ac i e p oduc ion
o mul iple i uses (39, 40). In e es ingly, a ecen s udy demon-
s a ed ha a i e HCV s ain can en e al eady-in ec ed cells
and ou compe e he esiden s ain (41), sugges ing ha mul iple
HCVs can en e a cell and compe e o in acellula esou ces.
To es hese hypo heses, we ex ended he baseline model by
inco po a ing in ec ed cell cu e and supe in ec ion, and ixing
he a e o in ec ed cell dea h a 0.14 d
−1
as es ima ed unde IFN
he apy (29, 30) (Me hods). He e, we assumed ha in ec ed cells
a e cu ed and become a ge cells again unde MK-5172
ea men a pe -capi a a e kcu e ·ð−log10ð1−«iÞÞ, whe e kcu e
is a a e cons an and «iis he d ug e icacy agains he i h s ain
(see Me hods o de ail). To model he in acellula i al com-
pe i ion due o supe in ec ion, we assume, o simplici y, ha
once an in ec ed cell is supe in ec ed, he i e s ain can ou -
compe e he less i s ain in acellula ly, and he cell becomes a
cell in ec ed by he i e s ain a a e k
supe
.
We used h ee a ia ions o he ex ended model o es he im-
po ance o cu e and supe in ec ion in explaining he kine ic pa e ns
in he da a: (i) we allowed cu e bu no supe in ec ion (deno ed
as he “cu e”model), o (ii) supe in ec ion bu no cu e (deno ed
as he “supe in ec ion”model), o (iii) bo h p ocesses (deno ed as
he “ ull”model) (see SI Appendix, Figs. S10 and S11 and Fig. 2,
espec i ely, o model i s and SI Appendix,TablesS3–S7 o
he bes - i pa ame e alues). To s a is ically es he impo -
ance o cu e o /and supe in ec ion in explaining he clinical
da a, we pe o med model selec ion using he co ec ed Akaike
in o ma ion c i e ion (AICc) (Table 1). The esul s sugges ha
cu e o in ec ed cells is needed o explain he apid second-
phase i al load decline du ing ea men seen in all i e sub-
jec s (SI Appendix,Fig.S12). I also helps o explain he apid
selec ion o he esis an mu an s seen a day 14 in subjec s
1 and 4 (compa e he i s be ween solid lines and dashed lines
o da a in SI Appendix,Fig.S13). Based on he bes - i pa ame e s
in he bes model o each subjec (SI Appendix, Table S8), we
es ima ed he mean a e o cu e o cells in ec ed by baseline
i uses unde MK-5172 ea men [kcu e ·ð−log10ð1−«1ÞÞ], whe e
«1is he d ug e icacy agains he baseline i uses) o be 0.56 d
−1
.
On a e age, i akes abou 1.9 d o cu e a cell unde MK-5172
ea men (SI Appendix, Table S8) and he loss o in ec ed cells is
p ima ily h ough cu e a he han dea h o in ec ed cells (as-
sumed o occu a a e o 0.14 d
−1
).
The AICc esul s sugges ha in acellula compe i ion
h ough supe in ec ion is needed o explain he apid and con-
inuous u no e o dominan esis an s ains a e ea men
s ops in subjec s 1 and 4 (SI Appendix, Fig. S14). This is because
a e ea men cessa ion, d ug is elimina ed and d ug-induced
cu e is no longe possible. As a esul , new a ge cells become
a ailable a a much slowe a e han he a e du ing ea men .
Howe e , supe in ec ion allows i e s ains o en e al eady-
in ec ed cells and compe e in acellula ly, g ea ly inc easing
he a e a which a i e s ain ises o a high equency. In
con as , wi hou supe in ec ion and in acellula compe i ion, a
i e s ain is p edic ed o inc ease in equency a a much lowe
a e (see he changes in he equencies o he mu an in g een
du ing he pe iod o days 30–60 in SI Appendix, Fig. S14A).
We pe o med unce ain y analysis in he bes model o each
subjec using likelihood p o iling (42) (SI Appendix, Tables S3–
S7). These analyses indica ed ha he da a allow us o es ima e
accu a ely he e ec i eness o MK-5172 agains he baseline i-
us, «
1
, he a e o i al clea ance, c, and he cu e a e k
cu e
in all
i e subjec s, and he alue o supe in ec ion cons an k
supe
in
subjec s 1 and 4. In addi ion, we explo ed whe he models wi h
al e na i e assump ions can explain he da a. This included a
model assuming a cons an a e o a ge cell gene a ion and
models assuming a DAA-independen cu e o in ec ed cells (SI
Appendix,SI Me hods and Resul s). Fi ing esul s show ha he
ull model p esen ed in he main ex is he bes model, and he
conclusions abou he ole o supe in ec ion and cu e o in ec ed
cells a e obus agains hese model a ia ions.
Compensa o y Mu a ions, Clonal In e e ence o HCV-Resis an
Mu an s. To unde s and be e he e olu iona y dynamics o he
i al s ains conside ed in ou model, we analyzed how he s ains
a di e en ime poin s a e ela ed o each o he . He e, we de ine
s ains pheno ypically, ha is, each “s ain”consis s o a g oup o
ela ed i al sequences in he clinical samples sha ing d ug e-
sis ance mu a ions. We calcula ed he gene ic dis ances be ween
sequences belonging o di e en g oups a he di e en sampling
ime poin s (see Me hods and SI Appendix, Figs. S15–S17). We
hen combined he mu a ional pa e n de i ed om he sequence
da a wi h he esul s om i ing he dynamical models o gene a e
a diag am ha summa izes he e olu iona y dynamics o he d ug-
esis an s ains o e he pe iod o he s udy (Fig. 3).
The diag am e eals how he HCV popula ion esponds o
MK-5172 ea men . Fi s , i al load ebounded apidly in sub-
jec s 1 and 4 o high le els ha pe mi ed sequencing by day 14,
p esumably because o selec ion o he esis an mu an s bea ing
A156T/V o R155G/W in subjec 1 and A156T/V in subjec 4.
We es ima ed ha hese mu an s a e highly esis an , ye ha e
high i ness cos s (Fig. 3), which is consis en wi h esul s shown
in p e ious in i o s udies (24–26). Because o hei sho gene ic
dis ance o he wild- ype i uses (SI Appendix, Figs. S15 and S17),
hey a e likely p esen a low equencies be o e ea men . Du -
ing and sho ly a e ea men , hey ise o high equencies
ansien ly be o e being eplaced by o he esis an mu an s wi h
highe i ness while d ug is clea ed. Second, mu an s wi h he
Y56H mu a ion a e obse ed ansien ly in subjec s 1, 3, and
4 be ween days 27 and 34. Ou analysis sugges s ha he ansien
appea ance o hese mu an s is due o hei in e media e e-
sis ance and i ness alues. These mu an s ga e way o i e s ains
wi h esis an mu a ions a posi ion 168 (e.g., D168E, D168A, o
D168Y; see e s. 24 and 25) ha domina ed he i al popula ion in
subjec s 1–4 a he end o ollow-up pe iod, ha is, 7–8wka e
ea men cessa ion. These dynamics esemble he classical pa -
e n, e med “clonal in e e ence,”as sugges ed by popula ion
gene ic models o he e olu ion o asexual o ganisms (43, 44).
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The i nesses o he esis an mu an s obse ed a la e ime
poin s a e p edic ed o be close o o highe han hose o he
baseline i uses, which emained a low equencies in subjec s 1–4
(Fig. 3). A likely explana ion o he la e appea ance o hese high-
i ness a ian s is ha mu a ion a posi ion 168 on he baseline
i us backg ound esul ed in low i ness (and hus hese mu an s
a e a low equency be o e ea men ). Howe e , g ow h o hese
low- i ness esis an mu an s gene a ed compensa o y mu a ions
ha inc eased hei i ness, and allowed hei equency o in-
c ease and s abilize a a high le el in he popula ion.
Las , we obse e ha d ug-sensi i e i uses, ha is, i uses
wi h no known d ug- esis an mu a ions, eappea ed in he se-
quences a he las ime poin o ollow-up in subjec s 1, 4, and 5.
S a is ical analysis shows ha hese i uses a e likely o be de-
scendan s o d ug-sensi i e i uses p esen be o e ea men
a he han e e sions om esis an a ian s (SI Appendix,SI
Me hods and Resul s). This sugges s ha he d ug-sensi i e i u-
ses we e supp essed o low equencies unde ea men and only
g ow o high equencies long a e ea men cessa ion.
Discussion
He e, we ha e analyzed he e olu iona y dynamics o he HCV
popula ion in esponse o 7-d ea men wi h he p o ease inhibi o
g azop e i (MK-5172) in i e subjec s using single-genome se-
quencing and phylodynamic modeling. HCV- esis an a ian s un-
de wen apid expansion a e d ug ea men wi h su p isingly as
sequen ial u no e o dominan esis an mu an s in he 7- o 8-wk
ollow-up pe iod, a dis inc ea u e o i al pe sis ence. Using
ma hema ical models, we showed ha supe in ec ion and cu e o
in ec ed cells a e likely o be c ucial mechanisms d i ing he ex-
emely apid expansion and u no e o esis an a ian s obse ed
in he clinical da a. Al hough supe in ec ion and cu e o in ec ed
cells ha e been demons a ed in i o (33–37, 41), ou wo k sug-
ges s ha hesep ocessesoccu andplay impo an oles in d i ing
i al adap a ion and pe sis ence in i o.
We es ima ed he a e o cu e o cells in ec ed by wild- ype
i uses unde g azop e i o be 0.56 d
−1
on a e age. Fu he , i
akes abou 1.9 d on a e age o cu e a cell unde MK-5172
ea men . This high a e o in ec ed cell cu e unde ea men is
consis en wi h he clinical da a in his s udy and om p e ious
s udies (8, 30, 32, 45), whe e apid second-phase i al load de-
clines ha e been obse ed. P e ious ma hema ical models sug-
ges ed ha he second-phase decline e lec s bo h he dea h a e
o in ec ed cells and he a e o in acellula RNA deg ada ion
(31, 32, 38). Thus, his apid cu e o in ec ed cells is likely o be a
esul o he apid loss o in acellula HCV RNAs unde ea -
men . Ou model shows ha , due o he apid cu e, d ug-sensi i e
i uses we e a a much lowe equency han esis an mu an s
AB
CD
E
0 102030405060
1234567
Time (days)
Log10 copies/mL
0 102030405060
0.0 0.2 0.4 0.6 0.8 1.0
Time (days)
Mu an equencies
0 102030405060
1234567
Time (days)
Log10 copies/mL
0 102030405060
0.0 0.2 0.4 0.6 0.8 1.0
Time (days)
Mu an equencies
0 102030405060
1234567
Time (days)
Log10 copies/mL
0 102030405060
0.0 0.2 0.4 0.6 0.8 1.0
Time (days)
Mu an equencies
0 102030405060
1234567
Time (days)
Log10 copies/mL
0102030405060
0.0 0.2 0.4 0.6 0.8 1.0
Time (days)
Mu an equencies
0 102030405060
1234567
Time (days)
Log10 copies/mL
0 102030405060
0.0 0.2 0.4 0.6 0.8 1.0
Time (days)
Mu an equencies
Fig. 2. Bes i o he “ ull”model (lines) o he clinical da a (ci cles) om i e subjec s ea ed wi h MK-5172. (A–E) Schema ic diag ams o he e olu iona y
dynamics in subjec s 1–5, espec i ely. A–E, he da a and simula ion esul s o i al loads a e shown in open ci cles and black lines, espec i ely, on he Le ;
he da a and simula ion esul s o mu an equencies a e shown in colo ed open ci cles and lines, espec i ely, on he Righ . The colo coding o each
mu an conside ed is shown in SI Appendix, Table S2.
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when ea men s opped. Tha coupled wi h he apid expansion o
esis an mu an s and gene a ion o compensa o y mu a ions led o he
disappea ance o a delay in he eappea ance o d ug-sensi i e i us.
Supe in ec ion has been demons a ed in i o indi ec ly by he
iden i ica ion o ecombinan o ms o HCV in pa ien s (46–49).
Al hough ecombina ion be ween HCV genomes is appa en ly
a e (50, 51), his does no mean ha supe in ec ion o hepa o-
cy es is in equen , because he o ma ion o dis inc in acellula
HCV eplica ion complexes and a p ocessi e RNA polyme ase
may p e en ecombina ion. In line wi h a ecen in i o s udy
showing ha a i e HCV s ain can en e al eady-in ec ed cells
and ou compe e he esiden s ain (41), ou esul s sugges ha
supe in ec ion and in acellula compe i ion occu equen ly in
i o, especially when di e en s ains exhibi a di e ence in
in acellula eplica ion i ness.
We a gue ha supe in ec ion and in acellula compe i ion a e
c i ical o he es ablishmen and expansion o adap i e mu an s
and hus o he pe sis ence o HCV unde selec ion p essu es.
Fo i uses ha la gely ansmi by cell- o-cell in ec ion, such as
HCV (52–55), ansmission is o en limi ed om an in ec ed cell
o a ew neighbo ing cells. When mos o he cells a e in ec ed by
esiden i al a ian s, wi hou supe in ec ion, he p obabili y ha
an adap i e mu an inds an unin ec ed cell is low. Thus, adap i e
mu an s would likely be los , and o hose mu an s ha do es-
ablish in ec ion, he a e a which hey expand would be low. In
con as , wi h supe in ec ion and in acellula compe i ion, an
adap i e mu an can en e all neighbo ing cells o compe e wi h
any esiden i us, which subs an ially inc eases he p obabili y o
es ablishmen and he a e a which he adap i e mu an expands.
While p e ious heo e ical wo k discussed he ole o supe in-
ec ion in i al e olu ion a he hos le el (56, 57), ou wo k
highligh s he impo an ole ha supe in ec ion plays in acili-
a ing i al adap a ion a he cellula le el.
By combining phylogene ic analysis and ma hema ical modeling,
we p o ided an in eg a ed unde s anding o he HCV e olu iona y
and popula ion dynamics. Fi s , he HCV wi hin-hos e olu ion o
HCV esembles he classical pa e n o he e olu ion o asexual
o ganisms as sugges ed by popula ion gene ic models, e med clonal
in e e ence (43, 44). This emphasizes he use ulness o popula ion
gene ic models in unde s anding i al e olu iona y dynamics. Sec-
ond, ou esul s sugges ha compensa o y mu a ions a e likely o
be gene a ed a e ea men , allowing o s abiliza ion and pe sis-
ence o esis an mu an s in he i al popula ion long a e ea -
men cessa ion. This highligh s he need o main ain a high le el o
adhe ence o combina ion he apies o DAAs. T ea men in e -
up ion would allow apid expansion o i al mu an s esis an o
one o mo e DAAs and possible gene a ion o compensa o y mu-
a ions ha s abilize he esis an mu a ions a a high equency, and
hus c ea ing oppo uni y o ansmission o esis an mu an s. In
si ua ions whe e ea men is in e up ed equen ly, mul iple mu-
a ions may accumula e such ha he e ol ed i us may become
esis an o all DAAs in he combina ion he apy (12).
Al hough beyond he scope o his wo k, a couple o p edic ions o
ou s udy can be u he es ed expe imen ally. Fi s , ou models
sugges ha supe in ec ion and in acellula compe i ion a e impo -
an mechanisms acili a ing he apid expansion and u no e o
esis an mu an s in i o a e ea men cessa ion. Al hough es ing
his p edic ion in i o is no possible, in acellula i al compe i ion
expe imen s as in e . 41 can be pe o med o compe e pai s o
labo a o y i uses wi h he esis an mu a ions iden i ied in his s udy.
The esul s would econ i m he occu ence o supe in ec ion and
de e mine he ela i e i ness o hose mu an s a he in acellula
scale. Second, ou analysis sugges s ha compensa o y mu a ions a e
in ol ed in s abilizing he esis an mu a ions a amino acid 168 seen
in subjec s 1–4. This can be es ed by i s pe o ming whole-genome
sequencing on he i al isola es and hen iden i ying he sha ed mu-
a ions o he i uses wi h a mu a ion a posi ion 168 in each subjec .
These sha ed mu a ions would be candida e compensa o y mu a ions
o he mu a ion a amino acid 168. In oducing one o a combina ion
o hese mu a ions in o i al eplicons, and hen es ing and com-
pa ing he eplica ion i ness o he eplicons (as shown in e s. 24–
26), would be a means o iden i y compensa o y mu a ions.
To summa ize, he esul s in ou s udy elucida e impo an , ye
p e iously un ecognized, mechanisms ha we sugges ope a e in
i o, d i e wi hin-hos i al e olu ion, and allow he adap a ion
and pe sis ence o HCV in he ace o d ug p essu e and immune
esponse. A p e ious amewo k equen ly used in i al dynamic
models (5, 8, 13, 16–18) assumed ha i uses compe e o he
eplica ion space needed o adap a ion o changing hos en i-
onmen s only h ough in ec ion o newly gene a ed a ge cells
(Fig. 4A). Consequen ly, he a e o adap a ion was limi ed by
he a e o a ge cell gene a ion. In con as , ou amewo k
emphasizes ha bo h supe in ec ion and cu e o in ec ed cells (in
addi ion o in ec ion o new a ge cells) can be impo an
mechanisms con ibu ing o he eplica ion space needed o
mu an i us expansion (Fig. 4B). This mechanism can g ea ly
accele a e he a e o wi hin-hos i al adap a ion beyond he
a e se by he gene a ion o a ge cells. This amewo k may be
impo an in elucida ing he con ibu ions and mechanisms o
HCV con ainmen and/o elimina ion media ed by he hos im-
mune sys em ha occu na u ally o ollowing accina ion (58).
Mo e b oadly, ou wo k poin s owa d he impo an ole mo-
lecula mechanisms play in acili a ing i al e olu ion and pe -
sis ence. F equen cell- o-cell in ec ion and high mul iplici y o
in ec ion, ha is, mechanisms ha p o ide he means o in-
acellula compe i ion, ha e been epo ed ecen ly o HIV,
HCV, in luenza, and o he i uses (54, 59–61). We a gue ha
ou amewo k and he conside a ion o i al compe i ion a bo h
he in acellula and hos le el in pa icula , is c i ical o he
unde s anding o he e olu iona y and adap i e dynamics o i al
popula ion a he wi hin-hos le el (62, 63). Thus, i opens he
doo o he nex gene a ion o i al dynamic models and quan-
i a i e amewo ks o unde s and i al e olu ion, in e p e clin-
ical da ase s, and p edic ea men ou comes.
Table 1. Summa y o he model cha ac e is ics and he i ing esul s (i.e., AICc sco es) o each model o each
subjec
Model
Model
cha ac e is ics Fi ing esul s (AICc)
k
cu e
k
supe
Subjec 1 Subjec 2 Subjec 3 Subjec 4 Subjec 5 To al
Baseline model
wi h δ=0.14 d
−1
0.0 0.0 −16.2 −22.1 −8.1 5.0 −24.9 −66.3
Cu e model Fi ed 0.0 −32.8 −53.2 −47.6 −42.6 −86.5 −262.7
Supe in ec ion model 0.0 Fi ed −12.0 −17.8 −9.5 −5.1 −21.2 −65.6
Full model Fi ed Fi ed −63.8 −51.8 −44.5 −90.6 −83.6 −334.3
Bolded AICc sco es deno e he bes model i among all models o he i e subjec s.
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Me hods
Expe imen al Model and Subjec De ails. Fo his s udy, Me ck Sha p and
Dohme Co po a ion p o ided p eexis ing, deiden i ied human blood
plasma specimens collec ed om a mul iins i u ional expe imen al d ug
ea men p o ocol (MK-5172-004) designed o es he an i i al ac i i y
o he HCV p o ease inhibi o g azop e i /MK-5172 (ClinicalT ials.go
iden i ie NCT00998985). The specimens we e collec ed, s o ed, and in-
en o ied wi h s udy subjec s’in o med consen and app o al o u u e
use in he analysis o he e ec s o g azop e i /MK-5172 on HCV eplica-
ion, al hough he specimens we e no collec ed speci ically o he e-
sea ch p ojec desc ibed he e. Based on hese s ipula ions, he esea ch
desc ibed in he cu en epo was deemed by he Ins i u ional Re iew
Boa d o he Uni e si y o Pennsyl ania no o cons i u e human subjec s
in esea ch.
Single-Genome Sequencing. The pa ial NS2 and comple e NS3 and NS4A
gene sequences om all eigh subjec s we e gene a ed using he single-
genome sequencing me hod p e iously desc ibed (50). The p ime s used o
he nes ed PCR included he ollowing: (i) geno ype 1a: i s - ound sense
p ime 1aNS2.F2, 5′-ACCCGRCTTTGGTATTTGACATCACC-3′(nucleo ides 2983–
3008, H77); i s - ound an isense p ime 1aNS4B.R3, 5′-TATTGTATCCCACT-
GATGAAGTTCCACAT-3′(nucleo ides 5634–5662, H77); second- ound sense
p ime 1aNS2.F3, 5′-AAAGTGCCCTACTTYGTGCGCGT-3′(nucleo ides 3063–3085,
H77); and second- ound an isense p ime 1aNS4B.R4, 5′-AGGGCCTTCTGCTT-
GAACTGCTC-3′(nucleo ides 5517–5539, H77); (ii) geno ype 1b: i s - ound
sense p ime 1bNS2.F2, 5′-GCCCGTCGTCTTYTCTGACATGGA-3′(nucleo ides
3257–3280, H77); i s - ound an isense p ime 1bNS4B.R3, 5′-TTCCA-
CATGTGCTTCGCCCA-3′(nucleo ides 5622–5641, H77); second- ound sense
p ime 1bNS2.F3, 5′-TCATCACCTGGGGGGCAGACA-3′(nucleo ides 3289–3309,
H77); and second- ound an isense p ime 1bNS4B.R4, 5′-CGAGCGCCTTCTGCTT-
GAATTG-3′(nucleo ides 5520–5541, H77).
Vi al Load and Sequence Di e si y Analysis. The RNA measu emen was
done by Me ck and Co., Inc., using he Roche Cobas TaqMAN 2.0 assay wi h
a lowe limi o quan i ica ion o 25 IU/mL and a limi o de ec ion o 10
IU/mL. A o al o 2,755 NS2–NS3–NS4 genomes we e gene a ed and analyzed
om he eigh subjec s. The median numbe o sequences analyzed pe
ime poin was 107 (mean, 106; ange, 43–144) (SI Appendix,TableS1).
Sequences alignmen s we e ini ially made wi h clus alW and hen hand-
checked using Geneious o co ec codon alignmen s. The maximum,
minimum, median, and mean di e si y o each sequence se was calcu-
la ed based on Hamming dis ance (SI Appendix,TableS1). Fo each sub-
jec , phylogene ic ees we e gene a ed by maximum-likelihood me hods
using PhyML. The combined phylogene ic ee and he ee om each
ime poin we e oo ed wi h consensus sequences om day 0.
AB
D
C
E
Fig. 3. E olu iona y dynamics o HCV be o e and a e ea men wi h MK-5172. (A–E) Schema ic diag ams o he e olu iona y dynamics in subjec s 1–5,
espec i ely. Each mu an is deno ed as a colo ed ci cle, and he colo coding is shown a he le -hand side o he yaxis in each panel. The numbe s wi hin he
ci cles deno e he i ness o he mu an ela i e o he baseline s ain in he absence o ea men acco ding o he bes - i pa ame e alues in he bes model
o each subjec . The xaxis shows he ime when sequence da a a e aken. The size o he ci cle is scaled acco ding o he equency o he mu an in a gi en
sample. Solid a ows show he s ain (whe e he a ow s a s; say, s ain a) o which he majo i y o he sequences in a mu an s ain o in e es (whe e he
a ow ends; say, s ain b) a e mos closely ela ed, and he numbe s on each a ow show he numbe o sequences in s ain b ha a e mos ly closely ela ed o
s ain a and he o al numbe o sequences in s ain b.
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Cons uc ion o a Baseline Mul is ain HCV Model. We cons uc a i al dynamic
model o wi hin-hos in ec ion by mul iple s ains o HCV based on p e ious
published models (5, 29, 64). In his model, we keep ack o ndi e en HCV
s ains. The o dina y di e en ial equa ions (ODEs) o he model a e as ollows:
dT
d =ρT·T·0
B
B
B
@
1−
T+P
n
i=1
Ii+N
Tmax
1
C
C
C
A
−d·T−X
n
i=1
β·T·Vi,
dIi
d =β·T·Vi−δ·Ii,
dVi
d =ð1−«iÞ· i·p·Ii−c·Vi,
«i=D·expð−w·maxð −7,0ÞÞ
EC50,i+D·expð−w·maxð −7,0ÞÞ.
Ta ge cells (T), p esumably a subse o hepa ocy es, die a a pe -capi a a e, d.
Exis ing a ge cells can p oli e a e, and his p oli e a ion is modeled using a lo-
gis ic e m, ρT·T·ð1−ðT+Pn
i=1Ii+NÞ=Tmax Þ,asinRonge al.(5),whe eρTis a
p oli e a ion a e cons an , I
i
a e cells in ec ed wi h i us s ain i,Nis he con-
cen a ion o hepa ocy es ha a e no a ge cells, and T
max
is he li e ca ying
capaci y. Ta ge cells a e in ec ed by he i h s ain o HCV (Vi)a a eβ·Vi.In ec ed
cells die a pe -capi a a e, δ. D ug-sensi i e i uses, ep esen ed by s ain i=1, a e
p oduced om in ec ed cells a a e ppe cell in he absence o ea men . We
assume ha he i h s ain has a i ness o
i
ela i e o he d ug-sensi i e i uses
(
1
=1). This di e ence in i ness is e lec ed only in he di e ences in i al p o-
duc ion in ou model. Thus, he p oduc ion a e o he i h s ain is i·pin he
absence o ea men . Unde ea men , we assume ha i al p oduc ion o he i h
s ain is educed by a ac o «i,whe e«i=1 co esponds o a 100% e ec i e d ug.
The d ug e ec i eness «
i
is modeled as a unc ion o he d ug concen a ion and
he EC
50
alue o each s ain (EC
50,i
)acco ding oanE
max
model (65). We assume
ha he d ug concen a ion, D, s ays cons an du ing he i s 7 d o ea men ,
since d ug concen a ion eaches i s maximal concen a ion wi hin 2–4h(23).A e
ea men s ops on day 7, we assume he d ug concen a ion declines exponen-
ially a a e, w, ob ained p e iously (23). All i uses a e clea ed a pe -capi a a e c.
The alues o he pa ame e s a e shown in SI Appendix, Table S9.
Cons uc ion o Models wi h Cu e and Supe in ec ion o In ec ed Cells. We
cons uc ed a model inco po a ing cu e and supe in ec ion o in ec ed cells
by ex ending he basic model. The ODEs o his model a e as ollows:
dT
d =ρT·T·0
B
B
B
@
1−
T+P
n
i=1
Ii+N
Tmax
1
C
C
C
A
−d·T−X
n
i=1
β·T·Vi+X
n
i=1
kcu e ·ð−log10ð1−«iÞÞ ·Ii,
dIi
d =β·T·Vi−δ·Ii+ksupe ·X
n
j=1
Mi,j−kcu e ·ð−log10ð1−«iÞÞ ·Ii,
dVi
d =ð1−«iÞ· i·p·Ii−c·Vi,
A
B
Fig. 4. Concep ual amewo ks o i us e olu ion unde an i i al p essu e. Resis an mu an s expand h ough occupying/compe ing o a ailable eplica ion
space. (A) P e ious modeling mos ly assumed ha , once a cell is in ec ed by a i us, he cell emains in ec ed un il dea h. The eplica ion space a ises h ough
gene a ion o new a ge cells. Unde his amewo k, esis an mu an s expand h ough in ec ion o newly gene a ed a ge cells, and he a e o he inc ease o
mu an equency is mos ly se by he a e a which in ec ed cells die and a e eplaced by newly gene a ed cells. (B) Ou esul s sugges a concep ual amewo k
whe e he eplica ion space a ises om mul iple sou ces. In he p esence o po en an i i als, he le el o in acellula HCV RNAs dec eases, leading o cu e o
in ec ion in some cells. Replica ion space hus a ises om bo h newly gene a ed cells and cu ed cells. In addi ion, supe in ec ion makes eplica ion space a ailable
by allowing esis an i uses o en e an al eady-in ec ed cell and compe e o in acellula esou ces. Thus, cu e and supe in ec ion o cells allow esis an mu an
expansion and u no e o occu a a much as e a e han he a e se by he dea h and eplacemen o in ec ed cells only.
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www.pnas.o g/cgi/doi/10.1073/pnas.1805267115 Ke e al.
Downloaded by gues on No embe 30, 2020
«i=D·expð−w·maxð −7,0ÞÞ
EC50,i+D·expð−w·maxð −7,0ÞÞ,
Mi,j=Δ·β·Ij·ViΔ≥0
Δ·β·Ii·VjΔ<0, whe e  Δ=ð1−«iÞ· i−1−«j· j.
To model cu e o in ec ed cells, we assumed ha he a e o cu e o
in ec ed cells is linea ly dependen on he log
10
o he e icacy o he
d ug, log10ð1−«iÞ, and he a e cons an is k
cu e
. This assump ion is
based on a p e ious inding wi h he p o ease inhibi o elap e i ha
he a e o second phase o i al load decline inc eased linea ly wi h
−log10ð1−«Þ(32).
The supe in ec ion we ack he e includes he in ec ion o a cell al eady
in ec ed wi h s ain iwi h a i us o s ain j, and he subsequen con e sion
o he cell in o a cell ha p oduces i us o s ain j. We assume, o simplici y,
ha , i a i e i us, s ain i, en e s a cell in ec ed wi h a less i s ain, s ain j
(modeled using he e m β·Ij·Vi), i can ou compe e s ain j, and hen he
cell is con e ed o a cell p oduc i ely in ec ed by s ain i. We u he assume
he a e o his con e sion is linea ly dependen on he i ness di e ence (Δ)
o he wo s ains, Δ=ð1−«iÞ· i−ð1−«jÞ· j, and k
supe
is a cons an o he
e iciency o his con e sion.
ACKNOWLEDGMENTS. We hank Ge ald Lea n o assis ance wi h DNA
sequence compila ions. We g a e ully acknowledge Me ck Sha p & Dohme
Co p., a subsidia y o Me ck & Co., Inc., o p o iding he samples analyzed
in his wo k. Po ions o his wo k we e pe o med unde he auspices o
he US Depa men o Ene gy unde Con ac DE-AC52-06NA25396. This
wo k was unded by Na ional Ins i u es o Heal h G an s R01-OD011095,
R01-AI028433, R01-AI078881 ( o A.S.P.), R01-AI116868 ( o R.M.R.), and
U19-AI088791 and P30-AI45008 ( o G.M.S.). The con en o his manusc ip
is solely he esponsibili y o he au ho s and does no necessa ily ep e-
sen he o icial iews o he Na ional Ins i u es o Heal h o o Me ck
Sha p & Dohme Co p., a subsidia y o Me ck & Co., Inc.
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