ORIGINAL RESEARCH
published: 20 June 2018
doi: 10.3389/ micb.2018.01326
F on ie s in Mic obiology | www. on ie sin.o g 1June 2018 | Volume 9 | A icle 1326
Edi ed by:
Lisa Sedge ,
Uni e si y o Technology Sydney,
Aus alia
Re iewed by:
Xin Lai,
Uni e si ä sklinikum E langen,
Ge many
S ephen Woodcock,
Uni e si y o Technology Sydney,
Aus alia
*Co espondence:
Na een K. Vaidya
[email p o ec ed]
Special y sec ion:
This a icle was submi ed o
In ec ious Diseases,
a sec ion o he jou nal
F on ie s in Mic obiology
Recei ed: 10 Feb ua y 2018
Accep ed: 30 May 2018
Published: 20 June 2018
Ci a ion:
Vaidya NK, Ribei o RM, Liu P,
Haynes BF, Toma as GD and
Pe elson AS (2018) Co ela ion
Be ween An i-gp41 An ibodies and
Vi us In ec i i y Decay Du ing P ima y
HIV-1 In ec ion.
F on . Mic obiol. 9:1326.
doi: 10.3389/ micb.2018.01326
Co ela ion Be ween An i-gp41
An ibodies and Vi us In ec i i y
Decay Du ing P ima y HIV-1 In ec ion
Na een K. Vaidya1*, Ruy M. Ribei o2,3, Pinghuang Liu4, Ba on F. Haynes5,
Geo gia D. Toma as 5and Alan S. Pe elson2
1Depa men o Ma hema ics and S a is ics, San Diego S a e Uni e si y, San Diego, CA, Uni ed S a es, 2Theo e ical Biology
and Biophysics G oup, MS K710, Los Alamos Na ional Labo a o y, Los Alamos, NM, Uni ed S a es, 3Labo a ó io de
Bioma emá ica, Faculdade de Medicina, Uni e sidade de Lisboa, Lisboa, Po ugal, 4Ha bin Ve e ina y Resea ch Ins i u e,
Chinese Academy o Ag icul u al Sciences, Ha bin, China, 5Duke Uni e si y School o Medicine, Du ham, NC, Uni ed S a es
Recen expe imen s ha e sugges ed ha he in ec i i y o simian immunode iciency i us
(SIV) and human immunode iciency i us ype-1 (HIV-1) in plasma dec eases o e ime
du ing p ima y in ec ion. Because an i-gp41 an ibodies a e p oduced ea ly du ing HIV-1
in ec ion and o m an ibody- i ion complexes, we s udied i such ea ly HIV-1 speci ic
an ibodies a e co ela ed wi h he decay in HIV-1 in ec i i y. Using a i al dynamic model
ha allows i al in ec i i y o decay and equen ea ly i al load da a ob ained om 6
plasma dono s we es ima e ha HIV-1 in ec i i y begins o decay a e abou 2 weeks
o in ec ion. The leng h o his delay is consis en wi h he ime be o e an ibody- i ion
complexes we e de ec ed in he plasma o hese dono s and is co ela ed (p=0.023,
=0.87) wi h he ime o an ibodies o be i s de ec ed in plasma. Impo an ly, we
iden i y ha he a e o in ec i i y decay is signi ican ly co ela ed wi h he a e o inc ease
in plasma an i-gp41 IgG concen a ion (p=0.046, =0.82) and he inc ease in IgM+IgG
an i-gp41 concen a ion (p=8.37 ×10−4, =0.98). Fu he mo e, we ound ha he
i al load decay a e he peak did no ha e any signi ican co ela ion wi h he a e o
an i-gp41 IgM o IgG inc ease. These esul s indica e ha ea ly an i-gp41 an ibodies may
cause i al in ec i i y decay, bu may no con ibu e signi ican ly o con olling pos -peak
i al load, likely due o insu icien quan i y o a ini y. Ou indings may be help ul o de ise
s a egies, including an ibody-based accines, o con ol acu e HIV-1 in ec ion.
Keywo ds: an ibodies, p ima y HIV-1 in ec ion, i al dynamics model, i al load, i us in ec i i y
INTRODUCTION
P ima y human immunode iciency i us ype 1 (HIV-1) in ec ion is associa ed wi h an ini ial
eclipse phase, du ing which he i al load emains below he limi o de ec ion o con en ional
assays, ollowed by a apid i al load inc ease (Daa e al., 1991; Schacke e al., 1996; Fiebig e al.,
2003; Ribei o e al., 2010; Cohen e al., 2011). A e he i al load eaches i s peak, i declines and
eaches a se -poin le el (i.e., a quasi-s eady s a e). The ea ly e en s du ing p ima y HIV-1 in ec ion
no only ha e pa icula ele ance o accine, mic obicide and p e/pos -exposu e p ophylaxis
(Chun e al., 1998; Pope and Haase, 2003; Sha ock and Moo e, 2003; Haase, 2005), hey a e also
impo an in de ining he se -poin i al load la e in in ec ion (Li son e al., 1997) and he ime
Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
pe iod o e which a success ul accine needs o induce a
p o ec i e esponse p io o es ablishmen o he la en pool
o HIV-1 in ec ed CD4+T cells (Wong and Siliciano, 2003;
Johns on and Fauci, 2007).
Based on a p e ious expe imen in ol ing simian
immunode iciency i us (SIV) in ec ion o macaques ha
e ealed a di e ence in in ec i i y be ween i us in plasma
ob ained 7 days a e in ec ion and se -poin i us (Ma
e al., 2009), we in oduced an SIV dynamic model wi h ime-
dependen i al in ec i i y (Vaidya e al., 2010). Also, p elimina y
da a compa ing he a io o he 50% issue cul u e in ec ious dose
(TCID50) wi h HIV-1 RNA copy numbe sugges s a dec ease in
i us in ec i i y o e ime du ing p ima y in ec ion in HIV-1
in ec ed pa ien s, al hough he magni ude o his e ec a ies
among subjec s (Gene ie e Fouda and Da id Mon e io i, Duke
Uni e si y School o Medicine, unpublished da a). Al hough
he mechanisms esponsible o he decay in i al in ec i i y
ha e no been es ablished, i has been specula ed ha binding
o an ibodies o HIV-1 migh be in pa esponsible (Ma e al.,
2009). Consis en wi h his, du ing ea ly HIV-1 in ec ion i has
been shown ha an i-gp41 an ibodies a e p oduced and o m
i ion-an ibody complexes (Toma as e al., 2008; Liu e al.,
2011).
He e we sough o de e mine whe he hese ea ly an i-gp41
an ibodies in luence HIV in ec i i y by i ing a ma hema ical
model o equen ly measu ed plasma i al loads ob ained om 6
plasma dono s. The model, which inco po a es a ime-dependen
in ec i i y a e, i s he acu e in ec ion HIV-1 da a well. We
show he in ec i i y decay p edic ed by ou model signi ican ly
co ela es wi h he an i-gp41 an ibody esponse obse ed in hese
plasma dono s.
MATERIALS AND METHODS
Expe imen al Da a
Sequen ial HIV-1 i al load da a om 6 plasma dono s was
ob ained as p e iously desc ibed (Gaspe -Smi h e al., 2008;
Toma as e al., 2008; S acey e al., 2009). The s udy was app o ed
by he Duke Heal h Ins i u ional Re iew Boa d, p o ocol numbe
P o00006579. Each indi idual dona ed 600–800 ml o plasma
which was ozen wi hin 8 h o −20◦C o less. The plasma
samples we e s o ed up o 2 mon hs hen sen in pools o
be se ologically sc eened o HIV. Dono s who we e HIV-1
posi i e we e no i ied and de e ed om subsequen dona ion.
HIV-1 posi i e samples we e aliquo ed, and e ozen a −20◦C.
Aliquo ed samples o plasma dono s we e quan i ied wi h
he Roche Amplico e HIV-1 RT PCR Ul a assay by Ques
Diagnos ics (Lyndhu s , NY), wi h a lowe limi o quan i ica ion
o 50 HIV-1 RNA copies/ml (Toma as e al., 2008). The e was a
median o 9 da a poin s pe dono wi h a median o 4 da a poin s
be o e he i al peak. The median peak i al load was 6.0 ( ange
4.5–6.8) log10 i al RNA ( RNA) copies/ml. In hese plasma
dono s, he an i-gp41 IgG and IgM esponses we e also measu ed
and eco ded as op ical densi y (O.D.) (Toma as e al., 2008).
In addi ion, ci cula ing an ibody- i ion immune complexes we e
measu ed (Toma as e al., 2008; Liu e al., 2011). The da a
analyzed below is p o ided in Table S1.
Vi al Dynamic Model
To s udy he e ec o an ibody esponses in dec easing i al
in ec i i y ea ly du ing in ec ion, we use he s anda d model o
i al in ec ion (Phillips, 1996; Nowak e al., 1997; Li le e al.,
1999; Pe elson and Nelson, 1999; S a o d e al., 2000), bu allow
he i us in ec iousness o decay in ime a e a ce ain delay τ,
which accoun s o he ime needed o gene a e an an i-HIV-1
esponse. The model is
dT
d =λ−dT −β( )TV,T(0)=T0,
dI
d =β( )TV −δI,I(0)=I0,
dV
d =pI −cV,V(0)=V0, (1)
whe e
β( )=β0, ≤τ,
β∞+(β0−β∞)e−k( −τ), > τ.(2)
The model consis s o a ge cells (CD4+T cells), T, p oduc i ely
in ec ed CD4+T cells, I, and ee i us, V. We assume ha
a ge cells a e gene a ed a a cons an a e λ, ha e a pe capi a
ne loss a e d, which is he di e ence be ween loss om cell
dea h and gain due o cell di ision, and become in ec ed a a
a e p opo ional o he p oduc o a ge cell densi y and i us
concen a ion wi h a ime-dependen a e β( ). The pa ame e s
δ,p, and ca e he a e cons an s o in ec ed cell loss, i us
p oduc ion by in ec ed cells and i us clea ance, espec i ely. As
in Vaidya e al. (2010), we assume a simple exponen ial decay in
in ec i i y o e ime om he ini ial a e β0 o he inal a e β∞
wi h a decay a e k, bu o a mo e gene al o mula ion he e we
include a ime-delay τbe o e in ec i i y decay begins.
Da a Fi s and Pa ame e Es ima ion
We i he model, Equa ions (1) and (2), o plasma i al load
da a ob ained om 6 HIV-1-in ec ed plasma dono s du ing he
acu e phase o in ec ion. Ea lie s udies ha e shown ha he
pe cen age o p oli e a ing CD4+T cells in he pe iphe al blood
o heal hy indi iduals, as measu ed by Ki-67 an igen exp ession,
is ∼1% (Sachsenbe g e al., 1998). We use Ki-67+CD4+cells as
a su oga e o a ge cells and hus ake he ini ial numbe o
a ge cells, T0, as 104pe ml (1% o 106/ml CD4+T cell coun ).
We no e ha , as in S a o d e al. (2000), he model sys em (1)
becomes independen o T0i he scaling p→p/T0is pe o med.
This shows ha aking he alue o T0di e en om 104pe ml
a ec s he es ima es o only p, no he in ec i i y a e, β( ), and
hus, ou conclusions will emain una ec ed i one uses o he
alues o T0. Assuming CD4+T cells we e a equilib ium be o e
in ec ion, we se λ=dT0. Because he ou e o in ec ion o
he plasma dono s is no known, we i s assumed in ec ion was
ini ia ed by ee i us pa icles a he han in ec ed cells, and hus
we se I0=0 (Pea son e al., 2011). Then we also analyzed he
da a assuming in ec ion was ini ia ed by an in ec ed cell. Recen
es ima es show ha he i ion clea ance a e cons an , c, a ies
be ween 9.1 day−1and 36.0 day−1, wi h an a e age o 23 day−1
F on ie s in Mic obiology | www. on ie sin.o g 2June 2018 | Volume 9 | A icle 1326
Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
(Ram a nam e al., 1999). Thus, we ake c=23 day−1, al hough
o he alues in his ange we e also conside ed in a sensi i i y
analysis.
I is di icul o ob ain in o ma ion abou he ini ial i us
concen a ion ha es ablished in ec ion. A leas one i ion, i.e.,
2 i al RNA ( RNA) copies, is needed o es ablish in ec ion. A
70-kg pe son has abou 15 L o ex acellula body wa e and
abou 3 L o plasma. Thus, he ini ial plasma i al load needed
o es ablish sys emic in ec ion is >2 RNA copies pe 3,000 ml
o >2 RNA copies pe 15,000 ml depending upon whe he
he i us dis ibu es h oughou only he plasma o he o al
ex acellula body wa e be o e ini ia ing in ec ion. He e, we
p esen esul s wi h V0=10−3 RNA copies pe ml assuming ha
he i us dis ibu es in he plasma and hen s udy he sensi i i y
o pa ame e es ima es on he ini ial i al load (V0) by a ying
V0 om 10- old lowe conside ing he possibili y o i us being
dis ibu ed h ough ex acellula body wa e o 1,000- old highe
co esponding o he possibili y o much highe le els o i us
ini ially en e ing he ci cula ion.
The exac ime o ini ial in ec ion is no a ailable o his da a
se . Howe e , he ini ial i al expansion a es o hese subjec s
ha e been es ima ed in a p e ious s udy (Ribei o e al., 2010).
Using he slope o i al inc ease es ima ed in Ribei o e al. (2010)
and he base alue o V0, we calcula ed he ime o in ec ion and
hen he ime o he i s measu ed i al load abo e he de ec ion
limi o each o hese subjec s. This allowed us o associa e a ime
since in ec ion wi h each da a poin . To es ima e τ, we a ied τ
in 1 day inc emen s, and chose he one which p o ided he bes
i o each plasma dono . The o he 6 pa ame e s, β∞,β0,k,δ,
d, and p, we e kep ee and es ima ed by i ing he model o
he da a om each plasma dono . We also pe o med i ing by
making τa ee pa ame e and ob ained app oxima ely he same
alue as he bes es ima e om 1-day inc emen i ing. Since
he i was no imp o ed wi h τas an ex a ee pa ame e , we
ixed τas he bes es ima e ob ained om he 1-day inc emen
i ing.
Pa ame e iden i iabili y in HIV models, including hose wi h
ime- a ying pa ame e s, was discussed in Wu e al. (2008) and
Miao e al. (2011). As shown in Miao e al. (2011) and Wu e al.
(2008), wi h λ ixed as in ou case, all he cons an pa ame e s
a e s uc u ally iden i iable. Miao e al. (2011) showed ha he
ime- a ying pa ame e (β( )in ou case) is also iden i iable i
all he cons an pa ame e s a e iden i iable. The e o e, we expec
ha he pa ame e s o ou model a e iden i iable o he numbe
o da a poin s a ailable in his s udy.
The da a i ing p o ocol used o es ima e pa ame e s was
as desc ibed p e iously in Vaidya e al. (2010). We sol ed he
sys em o o dina y di e en ial equa ions (ODEs) nume ically
using a ou h-o de Runge-Ku a in Be keley Madonna. Using
Madonna’s “cu e i e ” op ion, we ob ain a se o ini ial
pa ame e es ima es. The cu e i ing me hod uses nonlinea
leas -squa es eg ession ha minimizes he ollowing sum o he
squa ed esiduals:
Jβ0,β∞,k,δ,p,d=1
N
N
X
i=1log10 V( i)−log10 V( i)2. (3)
He e, Vand Va e i us concen a ions p edic ed by he model
and hose gi en by he expe imen al da a, espec i ely. Nis he
o al numbe o da a poin s.
Using he se o pa ame e s ob ained om Madonna as
ini ial guesses, we e ined he i s by using “ mincon.m”
and/o “ minsea ch.m” unc ions in MATLAB. Fo each bes i
pa ame e es ima e, we p o ide a 95% con idence in e al (CI),
which was compu ed om 500 boo s ap eplica es (E on and
Toibshi ani, 1986). Since we analyze only 6 subjec s, we p esen
esul s as medians and anges, unless o he wise indica ed.
Sensi i i y Analysis
The i al load es ablishing sys emic in ec ion, V0, is no known.
To s udy he sensi i i y o ou esul s o he choice o V0, we
andomly selec ed 200 di e en V0 om 10- old lowe (i.e., 10−4
RNA copies/ml) o 1,000- old highe (i.e., 1 RNA copies/ml)
and es ima ed pa ame e s o each o he 6 dono s.
S a is ical Analysis
We pe o med linea eg ession o ob ain he slope o he
IgG inc ease, he IgM inc ease and he IgG+IgM inc ease. We
hen ca ied ou co ela ion analyses using Pea son’s co ela ion
be ween hese slopes and he decay slope o in ec i i y es ima ed
by ou model. We also calcula ed he slope o he i al load decay
a e he peak and pe o med co ela ion analyses o he i al
decay a e wi h he an ibody esponse.
To e alua e he s a is ical signi icance o models compa isons,
we pe o med an F- es (Ba es and Wa s, 2007) as he models
conside ed in his s udy wi hou and wi h in ec i i y decay a e
nes ed.
RESULTS
Model Fi ing o Da a
We i ed Equa ions (1) and (2) o he HIV-1 da a. We es ima ed
six pa ame e s β∞,β0,k,δ,d, and p om he da a i ing. The
es ima ed pa ame e s along wi h hei 95% con idence in e als
a e summa ized in Table 1. Using hese es ima ed pa ame e s,
we plo ed he i al load dynamics p edic ed by he model along
wi h he da a o each o he 6 HIV-1 in ec ed plasma dono s in
Figu e 1. The p edic ions o ou ime- a ying in ec i i y delay
model (solid cu e) ag ee well wi h he da a ( illed ci cles).
Fo compa ison, we also i ed hese i al load da a using a
cons an in ec i i y (i.e., β( ) cons an ) model (S a o d e al.,
2000), and ound ha he delay model wi h ime-dependen
in ec i i y p o ides s a is ically signi ican be e i s (p=0.001,
F- es wi h all he subjec s combined as in Vaidya e al., 2010).
Mo eo e , we compa ed he da a i ing using a ime-dependen
model wi hou delay (Vaidya e al., 2010) (i.e., τ=0), and ound
ha including a delay in he model signi ican ly imp o ed he i s
(p=0.008, F- es , Vaidya e al., 2010).
Vi us In ec i i y Decay
We es ima ed he median ini ial and la e i al in ec ion a e
cons an s o be β0=4.20 ×10−7ml RNA−1day−1and
β∞=0.76 ×10−7ml RNA−1day−1, espec i ely (Table 1).
This sugges s ha in ec i i y decays du ing acu e HIV-1 in ec ion
F on ie s in Mic obiology | www. on ie sin.o g 3June 2018 | Volume 9 | A icle 1326
Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
TABLE 1 | Es ima ed pa ame e alues β0,β∞,k,δ,p,d,τ, and ime h o each he mid- alue (β0+β∞)/2.
Pa ien β0(10−6ml/RNA/day) β∞(10−6ml/RNA/day) k(1/day) δ(1/day) p(103RNAs/day) d(1/day) τ(day) h(day)
CHID46 0.409 (0.376–0.441) 0.233 (0.169–0.297) 0.249 (0.234–0.250) 0.775 (0.737–0.814) 14.500 (14.499–14.501) 0.030 (0.023–0.038) 7 2.8
CHID77 0.431 (0.417–0.444) 0.140 (0.129–0.151) 0.077 (0.067–0.093) 0.420 (0.417–0.433) 10.000 (9.999–10.001) 0.021 (0.019–0.025) 24 9.0
CHID79 0.201 (0.195–0.208) 0.001 (0.000–0.027) 0.013 (0.012–0.015) 1.048 (0.992–1.064) 30.172 (30.166–30.178) 0.036 (0.033–0.041) 10 53.3
CHID32 9.203 (4.320–11.011) 0.011 (0.000–0.112) 0.013 (0.011–0.020) 0.851 (0.325–1.360) 0.548 (0.391–0.901) 0.055 (0.048–0.156) 12 53.3
CHID40 0.485 (0.457–0.513) 0.291 (0.161–0.339) 0.096 (0.062–0.103) 0.803 (0.623–0.910) 11.425 (11.422–11.428) 0.033 (0.022–0.037) 5 7.2
CHID08 0.057 (0.050–0.112) 0.004 (0.000–0.019) 0.021 (0.019–0.031) 0.821 (0.491–1.170) 89.892 (48.541–130.952) 0.003 (0.000–0.028) 22 33.0
Median 0.420 0.076 0.049 0.812 12.962 0.032 11 21.0
Numbe s in pa en heses indica e 95% con idence in e als (see Ma e ials and Me hods).
(p=0.031, pai ed Wilcoxon Tes ). Such in ec i i y decay o e
ime was also obse ed p e iously in SIV in ec ion (Ma e al.,
2009; Vaidya e al., 2010). Assuming ha he decay o β( ) occu s
exponen ially wi h a e k, we ound ha HIV-1 in ec i i y decays
wi h a median a e o k=0.049 day−1(Table 1) ( ange: k=0.013
day−1 o k=0.249 day−1). Also, he ime, h, o educe he i us
in ec i i y o i s mid- alue, (β0+β∞)/2, gi en by ln (2)/k, was
ound o be 21 days (Table 1).
Co ela ion o In ec i i y Wi h An ibody
Response
I is known ha an ibodies bind o i ions and o m an ibody-
i ion complexes (Dianzani e al., 2002; Toma as e al., 2008; Liu
e al., 2011). Such an ibodies bound o i ions migh in e e e
wi h he in ec ion p ocess (Ma e al., 2009). The e o e, we
examined i he e is any co ela ion be ween he in ec i i y
decay and he ea lies an ibody esponses de ec ed du ing acu e
in ec ion, i.e., he an i-gp41 IgM and/o IgG esponse (Toma as
e al., 2008; Liu e al., 2011).
While we acknowledge some unce ain y due o spa si y in
ea ly Ab da a, in gene al, as shown in Figu e 2, he an i-gp41
IgM concen a ion (measu ed in op ical densi y. i.e., O.D. uni s)
inc eases app oxima ely linea ly up o a maximum alue and
hen decays, whe eas he an i-gp41 IgG concen a ion inc eases
mono onically o e he ime pe iod s udied. This pa e n o IgM
inc easing and hen dec easing is consis en wi h he known
ea u es o he IgM-IgG iso ype swi ch (Mu phy e al., 2008). We
pe o med a linea eg ession analysis o ind he slope o he IgM
inc ease, o he IgG inc ease and o he IgM+IgG inc ease using
he an ibody da a o he ime poin whe e an ibody le els sa u a e
o s a o decay. The IgM and IgG concen a ions inc ease by a
median a e o 0.19 day−1and 0.09 day−1, espec i ely, while he
median a e o inc ease in he IgM +IgG concen a ion is 0.27
day−1(Table S2).
While he e was a posi i e associa ion be ween he a e o
in ec i i y decay es ima ed by ou model (k) and he slope o
IgM inc ease (Figu e 3), his co ela ion was no s a is ically
signi ican (p=0.33, =0.48). Howe e , we ound ha he
a e o in ec i i y decay has a s a is ically signi ican posi i e
co ela ion wi h he slope o IgG inc ease (p=0.046, =0.82)
and a e y signi ican posi i e co ela ion wi h he IgM+IgG
an i-gp41 concen a ion wi h p- alue =8.37 ×10−4and -
alue =0.98 (Figu e 3). This sugges s ha he an ibody esponse
migh con ibu e o he loss o i us in ec i i y. To check he
obus ness o his inding, we pe o med co ela ion analysis by
i e a i ely excluding each dono one a a ime, and ound ha he
co ela ion o in ec i i y decay wi h slope o inc ease o IgM+IgG
emained s a is ically signi ican (p<0.01 in each case, Table S3).
The Delay Be o e he S a o In ec i i y
Decay Co ela es Wi h he Time Un il he
An ibody Response Is De ec ed
Ou model p edic s ha he i us in ec i i y begins o decay
a e a median ime o 11 days ( ange: 5–24 days) o in ec ion.
The exac delay om he ime o in ec ion o he ini ia ion o
an ibody inc ease is no known. Howe e , om he expe imen al
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Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
FIGURE 1 | Fi ed i al dynamics cu e using he delay model wi h ime- a ying in ec i i y o he obse ed i al load da a ( illed ci cle) du ing p ima y in ec ion o 6
HIV-1 in ec ed plasma dono s.
da a we es ima ed he ime om in ec ion (as es ima ed by ou
calcula ion) o he ime when he ee IgM+IgG le el begin
o inc ease in plasma. In he dona ed plasma, an ibodies we e
measu ed and, in e e y case, O.D. eadings o bo h IgM and IgG
began o inc ease on he same day. Since he an ibodies we e
assayed in e e y sample, we de ined he ime when an ibody
becomes de ec able as he i s ime poin o which he O.D. o
IgM+IgG le el was abo e he limi o de ec ion (i.e., O.D. >0.5).
We ound a s a is ically signi ican co ela ion (p=0.0233,
=0.87) be ween he ime ha an ibody became de ec able in
plasma and he delay be o e in ec i i y decay began p edic ed by
ou model (Figu e 4). Fu he mo e, o h ee dono s (CHID77,
CHID08, CHID79), he imes o an ibody- i ion complexes o
be expe imen ally de ec able in plasma we e epo ed p e iously
as 13, 9, and 6 days, espec i ely, whe e his was measu ed
ela i e o he ime a which he plasma i al load i s eached
100 copies/ml (Toma as e al., 2008). Using he eclipse phase
o acu e in ec ion in hese plasma dono s, calcula ed om he
slope o i al inc ease es ima ed in Ribei o e al. (2010), hese
imes ansla e o 24, 18, and 14 days om he ime o in ec ion.
These alues and hei ank-o de a e consis en wi h he delay
o in ec i i y decay p edic ed by ou model (24, 22, 10 days,
espec i ely, Table 1).
Co ela ion o Pos -peak Vi al Load D op
Wi h An ibody Response
To obse e i an ibodies ha e any signi ican impac on i al
load decay a e he i al load peak, we pe o med a co ela ion
analysis be ween he slope o IgM inc ease, IgG inc ease,
IgM+IgG inc ease and he slope o he i al load d op a e he
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Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
FIGURE 2 | An i-gp41 IgM, IgG and (IgM+IgG) an ibody esponse da a du ing p ima y in ec ion om 6 HIV-1 in ec ed plasma dono s. The lines ep esen he bes i s
used o es ima e he upwa d slope o he an ibody inc ease.
peak (Table S2). We did no ind any signi ican co ela ion wi h
IgM, IgG o IgM+IgG indica ing ha his an ibody esponse
migh no be he p ima y cause o he d op o i al load a e
he peak, consis en wi h p e ious indings (Toma as e al., 2008).
In ou i al dynamic model, Equa ion (1), i al load d op a e
he peak is due o a ge cell limi a ion and dea h o p oduc i ely
in ec ed cells.
Sensi i i y Analysis
Abo e we analyzed he co ela ion o wo pa ame e s, kand τ,
wi h he an ibody esponse. We es ima ed hese pa ame e s by
i ing ou model o i al load da a. Due o lack o in o ma ion
abou he ac ual numbe o i ions ini ia ing in ec ion, V0, we
assumed V0=10−3 RNA copies/ml. To ensu e ha he choice
o V0did no bias ou esul s, we e- i he da a aking 200
di e en alues o V0selec ed andomly om 10- old lowe o
1,000- old highe (i.e., 10−4 o 1) han he base-case. We ind
ha he es ima e o τis no a ec ed a all, and ha he median
change in he es ima es o kis below 5% (Figu e S1). The e o e,
ou esul s a e no sensi i e o he choice o V0.
We assumed ha he in ec ion was ini ia ed wi h ee i us
pa icles. To s udy how he es ima es a e a ec ed i he in ec ion
was ini ia ed wi h in ec ed cells, we compa ed he es ima es
be ween an in ec ion wi h one i us pa icle dis ibu ed in 15 L
body wa e (i.e., V0=2/15000 RNA copies/ml) and an
in ec ion wi h one in ec ed cell dis ibu ed in 15 L body wa e
(i.e., I0=1/15000 cells/ml). We ound ha he es ima es o k
a e essen ially he same in hese wo cases (Figu e S2).
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Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
FIGURE 3 | Co ela ion analysis o he slope o expe imen ally measu ed IgM, IgG and (IgM+IgG) an ibody inc ease wi h he a e o in ec i i y decay p edic ed by ou
model.
FIGURE 4 | Co ela ion analysis be ween he ime o o al an ibody (IgM+IgG)
esponse o be expe imen ally de ec able in plasma and he delay o he s a
o in ec i i y decay p edic ed by ou model.
We chose c=23 d−1based on he a e age o he
expe imen ally es ima ed ange be ween 9 and 36 d−1. To es he
obus ness o ou esul s o his assump ion, we e i ed he da a
wi h di e en alues o c wi hin his ange. The only pa ame e s
ha is mainly a ec ed is he i al p oduc ion a e. The e o e, ou
esul s ega ding kand τa e no a ec ed by he speci ic alue o c.
DISCUSSION
Du ing p ima y HIV-1 in ec ion, a decay o i us in ec i i y
o e ime has been sugges ed by compa ing he a io o issue
cul u e in ec ious dose (TCID50) wi h HIV RNA copy numbe
in sequen ial ea ly i al load samples om a limi ed numbe o
subjec s (Gene ie e Fouda and Da id Mon e io i, unpublished
da a). In addi ion, HIV-1-speci ic an i-gp41 an ibodies ha e been
de ec ed in plasma a median o 13 days a e he i al load eaches
100 RNA copies/ml (Toma as e al., 2008). Mo eo e , an i-gp41
IgM- i ion o IgG- i ion complexes we e ound as ea ly as 5
days a e he i al load became de ec able (Toma as e al., 2008;
Liu e al., 2011). The p esence o such an ibodies migh a ec
he in ec i i y o HIV-1 (Toma as e al., 2008; Ma e al., 2009).
The e o e, one o he main objec i es o his s udy was o ask
i he e is a co ela ion be ween he in ec i i y decay o plasma
i us and he an i-gp41 an ibody esponse in HIV-1 in ec ed
indi iduals.
Since he e a e delays be o e an ibodies and an ibody- i ion
complexes become de ec able in plasma (Toma as e al., 2008),
we ex ended a p e ious in ec ion model (Vaidya e al., 2010)
used o s udy acu e SIV in ec ion by inco po a ing a ime-delay
be o e in ec i i y decay begins. We hen used his delay model o
quan i y he ime- a ia ion o HIV-1 in ec i i y du ing p ima y
in ec ion. Ou da a i ing p ocedu e e eals ha bo h ime-
dependen na u e and delay o in ec i i y decay a e necessa y o
be e desc ibe he i al load da a om p ima y HIV-1 in ec ion.
Acco ding o ou model es ima es, plasma HIV-1 in ec i i y
decays exponen ially wi h a median a e o 0.049 day−1(Table 1),
and he e is a ime delay o abou 2 weeks ( ange 5–24 days)
be o e i us in ec i i y begins o decay. The leng h o his delay
is consis en wi h he pe iod om in ec ion o he ime when
he i ion-an ibody complexes we e de ec ed in plasma (Toma as
e al., 2008), and is signi ican ly co ela ed (p=0.0233, =0.87)
wi h he ime pos -in ec ion o an i-gp41 an ibody (IgG+IgM)
o be de ec able in plasma (Figu e 4).
Ou analyses also showed a s a is ically signi ican and s ong
co ela ion be ween he a e o inc ease o he IgM+IgG an i-
gp41 an ibody concen a ion and he a e o in ec i i y decay
es ima ed by he model (p=0.0008, =0.98) (Figu e 3). On he
o he hand, we did no obse e a signi ican co ela ion be ween
he slope o he IgM, IgG o IgM+IgG inc ease and he slope o
i al load d op a e he i al load peak. Taken oge he , hese
esul s indica e ha he an i-gp41 (IgM+IgG) esponse migh
con ibu e o he educ ion o i us in ec i i y, bu ha hese
an i gp41 an ibodies ha e minimal e ec on con olling pos peak
i al load as seen in Toma as e al. (2008). Thus o he ac o s,
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Vaidya e al. HIV-1 In ec i i y and Speci ic An ibodies
such as a ge cell limi a ion (S a o d e al., 2000) and cy o oxic
T cell esponses (Goone illeke e al., 2009) may be playing a
ole in de e mining he pos -peak i al decline. Because cells
a e no collec ed om plasma dono s quan i ying he change in
a ge cell le els and he magni ude o he CTL esponse was no
possible in his s udy.
A con ibu ion o an ibodies o educing i al in ec i i y was
sugges ed by Ma e al. (2009), and suppo ed by hei obse a ion
ha mixing plasma ob ained a se -poin wi h plasma ob ained
7 days a e SIV in ec ion educed he in ec i i y o he 7-
day plasma. Howe e , ou in e ence ha an ibody a ec s he
in ec i i y o HIV-1 du ing ea ly in ec ion is de i ed om a
co ela ion based on limi ed i al load and an ibody da a om
only 6 indi iduals. We canno ule ou o he possible causes
o in ec i i y decay such as he p oduc ion o non-in ec ious
i al genomes ha educe in ec i i y, as he i us ha ounds
he in ec ion di e si ies due o mu a ion du ing ea ly in ec ion,
o o he plasma p o eins binding o i ions and media ing
in ec i i y decay. Also, he co ela ion be ween he slope o
he in ec i i y decay and he up-slope o an ibody esponses
ob ained in his s udy is o he ea ly s ages pos -in ec ion. Once
a plasma dono was iden i ied as being HIV+dona ions we e
s opped and hence no long- e m da a we e collec ed. La e in he
in ec ion an ibody esponses sa u a e o decay. To cap u e he
long- e m e ec , he model needs o be ex ended o inco po a e
such beha io and longe - e m da a is needed o alida e such
ex ended models.
While his s udy suppo s he hypo hesis ha an ibodies
educe i al in ec i i y, we acknowledge ha an ibodies migh
ha e o he an i-HIV e ec s, such as enhanced i ion clea ance
and/o an ibody-dependen cellula cy o oxici y (Toma as and
Haynes, 2009, 2010). Howe e , hese e ec s we e ound o ha e
negligible con ibu ion o HIV-1 i al dynamics (Toma as e al.,
2008). In ou p e ious s udy, we (Toma as e al., 2008) also
in es iga ed he e ec s o an ibody in neu alizing i us by
educing he in ec i i y a e in a ma hema ical model including
an ibody da a, bu we did no ind a signi ican an ibody e ec
in mos pa ien s. The di e ence wi h he cu en esul s could be
due o di e ences in he wo modeling app oaches: he delay in
he an ibody e ec in Toma as e al. (2008) was en i ely gi en
by he ee an ibody da a, i.e., he delay co esponded o he
ime delay o an ibody o become de ec able in plasma, while
he delay in ou model (es ima ed o be much sho e , Figu e 4)
co esponds o he delay o he o ma ion o an ibody- i ion
complexes. No e ha an ibody- i ion complexes a e de ec able
ea lie han ee an ibodies in plasma (Toma as e al., 2008).
The second di e ence in he wo modeling app oaches is he
unc ional o m o he in ec i i y decay in oduced in o he
models (see Tex S1). A s udy wi h mo e an ibody da a may
help o accu a ely and explici ly inco po a e an ibody e ec s
in o i al dynamic models. While di ec compa ison be ween
hese wo models migh no be app op ia e as ou model does
no ha e explici dynamics o an ibodies, cla i ying hese issues
migh be impo an o u u e de elopmen o models ha ake
explici an ibody esponses in o accoun . We also acknowledge
unce ain y in he ou e o in ec ion and he ac ual ime o
in ec ion; i he ime o ini ial in ec ion is di e en , hen his may
imply a di e en dose o in ec ing i us, o e en di e ences in
hos immune esponse o he i us in ec ion. Howe e , we no e
ha i is e y di icul o ind HIV in ec ed indi iduals so ea ly
in in ec ion. This complexi y makes his da a se unique and
highligh s he impo ance o his s udy.
Al hough ou model canno conclusi ely add ess he causes
o decay in HIV-1 in ec i i y, he quan i a i e ag eemen
be ween ou model’s p edic ions and he measu ed i al
load cu es in all 6 subjec s, and he co ela ion o he
a e o in ec i i y decay wi h he measu ed inc ease in
an i-gp41 an ibody concen a ions s ongly sugges he
ea ly an i-HIV-1 esponse, e en hough non-neu alizing
may s ill p o ide bene i . Mo e da a, especially on ea ly
an ibody esponses (including IgA esponses), he o ma ion
o an ibody- i ion complexes, and he a io o in ec ious
i us o o al HIV-1 RNA a e needed o p o ide a mo e
accu a e pic u e o i us in ec i i y du ing p ima y HIV-1
in ec ion.
AUTHOR CONTRIBUTIONS
NV and AP designed he s udy. NV pe o med ma hema ical
analysis and nume ical expe imen s. NV, RR, and AP analyzed
he da a. PL, BH, and GT p o ided he expe imen al da a. All
au ho s con ibu ed o w i ing he pape .
ACKNOWLEDGMENTS
This wo k was unded by NSF g an DMS-1616299 (NV), DMS-
1836647(NV) and he s a -up und om San Diego S a e
Uni e si y (NV). Po ions o his wo k we e done unde he
auspices o he US Depa men o Ene gy unde con ac DE-
AC52-06NA25396 and suppo ed by NIH g an s R01-AI028433
and R01-OD011095 (AP), R01-AI104373 (RR), and he NIH
CHAVI g an U01-AI067854.
SUPPLEMENTARY MATERIAL
The Supplemen a y Ma e ial o his a icle can be ound
online a : h ps://www. on ie sin.o g/a icles/10.3389/ micb.
2018.01326/ ull#supplemen a y-ma e ial
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The e iewe SW and handling Edi o decla ed hei sha ed a ilia ion.
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F on ie s in Mic obiology | www. on ie sin.o g 9June 2018 | Volume 9 | A icle 1326