Correlation between anti-gp41 antibodies and virus infectivity decay during primary HIV-1 infection

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 F on ie s in Mic obiology | www. on ie sin.o g 4June 2018 | Volume 9 | A icle 1326 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 F on ie s in Mic obiology | www. on ie sin.o g 5June 2018 | Volume 9 | A icle 1326 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). F on ie s in Mic obiology | www. on ie sin.o g 6June 2018 | Volume 9 | A icle 1326 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, F on ie s in Mic obiology | www. on ie sin.o g 7June 2018 | Volume 9 | A icle 1326 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. 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Pa ame e iden i iabili y and es ima ion o HIV/AIDS dynamic models. Bull. Ma h. Biol. 70, 785–799. doi: 10.1007/s11538-007-9279-9 Con lic o In e es S a emen : The au ho s decla e ha he esea ch was conduc ed in he absence o any comme cial o inancial ela ionships ha could be cons ued as a po en ial con lic o in e es . The e iewe SW and handling Edi o decla ed hei sha ed a ilia ion. Copy igh © 2018 Vaidya, Ribei o, Liu, Haynes, Toma as and Pe elson. This is an open-access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (CC BY). The use, dis ibu ion o ep oduc ion in o he o ums is pe mi ed, p o ided he o iginal au ho (s) and he copy igh owne a e c edi ed and ha he o iginal publica ion in his jou nal is ci ed, in acco dance wi h accep ed academic p ac ice. No use, dis ibu ion o ep oduc ion is pe mi ed which does no comply wi h hese e ms. F on ie s in Mic obiology | www. on ie sin.o g 9June 2018 | Volume 9 | A icle 1326