Generalized Theoretical Criteria for Annihilation of HIV-1 Virions during HAART

Transcription

1 Fyvll Unvrsy Unvrsy Mh nd Copr n Worng Pprs Collg of Ars nd ns - nrlzd Thorl Crr for Annhlon of HIV- Vrons drng HAART Frn Nn Fyvll Unvrsy fnn@nfs.d Mngn Jn Fyvll Unvrsy jn@nfs.d Follow hs nd ddonl wors hp//dgloons.nfs.d/s_wp Pr of h Copr ns Coons sss Coons f ns Coons nd h Mhs Coons Rondd Con Nn Frn nd Jn Mngn. nrlzd Thorl Crr for Annhlon of HIV- Vrons drng HAART Brsh Jornl of Mhs Copr n 6-99 Arl no.bjmc..8. IN -8. Prn Ths Arl s rogh o yo for fr nd opn ss y h Collg of Ars nd ns glcoons@fyvll Unvrsy. I hs n pd for nlson n Mh nd Copr n Worng Pprs y n horzd dnsror of glcoons@fyvll Unvrsy. For or nforon pls on png@nfs.d.

2 Brsh Jornl of Mhs Copr n 6-99 Arl no.bjmc..8 IN -8 CIENCEOMAIN nrnonl nrlzd Thorl Crr for Annhlon of HIV- Vrons drng HAART Frn Nn * nd Mngn Jn prn of Mhs nd Copr n Fyvll Unvrsy Mrhson Rod Fyvll NC 8 UA. Arl Inforon OI.97/BJMC//9 Edors Crlo Bn prn of Mhl ns Polyhn Unvrsy of Trn Torno Ily. Tn-Xo H prn of Mhs nd Copr n Illnos Wslyn Unvrsy UA. Rvwrs. Anonyos Moroo. Is on p. of n nd Bsnss Mngn My Unvrsy of n nd Thnology Tnzn. Rhl W Mogo rhor Unv. Cnr for Appld Rsrh n Mhl ns CARM ny. Anonyos Ynhng Unvrsy P.R. Chn. Anonyos X n Joong Unvrsy P.R.Chn. Copl Pr rvw Hsory hp// Rvd My Apd Oor Orgnl Rsrh Arl Plshd Oor Asr As Ths ppr s n lor nd nv p o onsr dlly ppll hl odls nd drv rr for ffos Hghly Av An-Rrovrl Thrpy HAART proool for n AI pn. Th pho-physologl dyns of Hn Ino-dfny Vrs yp HIV- ndd AI drng HAART s odld y sys of non-lnr drns dffrnl ons. Th physologlly rlvn nd lnlly plsl ons dp h dyns of nnfd C T lls HIV- nfd C T lls HIV- vrons n h lood pls HIV- spf C8 T lls nd h onnron of HAART drg olls. Th jor ojv of hs rsrh s o onsr n lor hl odl h dps pho-physodyns of HIV- vrons drng HAART. Th drvd hrp rr r prssd n rs of lnlly srl physologl prrs. Invsgv opr slons whh dsr rn sps of HIV- dyns drng HAART r lso prsnd n h ppr. dy sgn Th hl odl s onsrd sd on onporry rsrh d ondnsd fro h lnl lrr on HAART of AI. A sys of opld non-lnr drns dffrnl ons r sd o hrrz h pho-physodyns of *Corrspondng hor fnn@nfs.d;

3 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 HAART drng h pos hron phs. Th hl nlyss of h odl ons nd h opr slons r prford wh rgrd o HAART proools wh onsn onnos nrvnos nd rnsdrl drg nfsons. A syny r wh sohor offn s nrodd no h odl o on for h foron of lrg lnld gp rng C T lls h r osrvd n so AI pns. By ssgnng zro vl o h sohor offn h rol of syny s rogd. Pl nd ron of dy Ths rsrh ws don Fyvll Unvrsy Norh Croln UA nd s sponsord y h FU Mn-rn Awrd nd h HBCU rd TEM rn. Th rsrh ws ondd drng h prng of. Mhodology Th drns nonlnr dyns of HIV- AI ons r nlyzd sng h hns of dynl sys hory prnpls of lnrzd sly non-lnr sys hory nd ohr rlvn hl hns. Th lnlly dsrl lr ss hr lol sn nd glol sly r nlyzd. Invsgv opr slons r prford llsrng so physologl oos. Rsls Th hrp oos r prsnd n h for of horl rr whh r ond fro hl nlyss of h odl ons. In prlr h rl prrs whh govrn h dyns of HIV- vrons drng HAART r lrly dnfd. o lnl plons of HAART r ldd n h opr slons sng hypohl physologl prr onfgrons. Conlson Ths rsrh hs donsrd h sn of plsl rr ndr whh HIV- vrons n nnhld sng HAART. Th ln HIV- vron rsrvors r pld n nsssfl snros of HAART. I hs lso n donsrd h h r onsns ssod wh von of lyphoys y yon nrln- I- ply sgnfn rol n drnng h ffos oos of HAART. ywords HIV- pho-physodyns hl odlng HAART hrpy AI r rr Mhls-Mnn ns. AM j Clssfon 9A; 9; 9; A; 9C; 9C. Inrodon Hghly Av An-rrovrl Thrpy HAART s rrnly h os hrplly ffos rn proool for rng h Ard Inodfny yndro AI. HIV- vrons nd AI y orhsrng n rrvrsl dsron of h C T lls whh hn prlyz h n sys of h HIV- posv prson. Th jor ojvs of HAART hrpy r h prolongon nd provn of h long-r lf ly of pns; opzon of hrpy sh s o spprss h HIV- vrl lod o low ops of HIV- RNA; ronson of h pns n sys sh h h C T lls prolfr o rryng py; nd nzon of drg oy. HAART rn proool onsss of nlosd rvrs rnsrps nhors non-nlosd rvrs rnsrps nhors pros nhors nfngls /n-rls nd n fr ngrs nhors. Th rvrs rnsrps nhors prvn rvrs rnsrpon of HIV- spf NA. Th pros nhors r ngons o ron nd foron of nw HIV- vrons. Th possl rol of ngrs nhors s o prvn h ngron of HIV- vrl NA no h pns NA. In ordr o hv h hrp gols of HAART s plsl o nvolv h hns of hl odlng. Bfor h dvn of HAART h prry fos of h hl odlrs s o nvly nlyz h osrvd pho-physodyns of HIV- nfon n 6

4 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 h AI pns. Ths rlr rsrh pprs nvolv h ponrng wor of Prlson l. Nowr l. nd ohr onrors 6. A rn ppr y Nn nd Jn 7 provdd so physologl rr ndr whh HIV- vrons n n AI pn n nnhld drng HAART. o of h rlr hl odlng plons fos on sngl-drg AI hrpy sng Zdovdn INN or Azdohydn AZT 8. Thn h dvn of Av Rro-vrl Thrpy ART nd h ssod lnl lon l o h dvlopn of HAART rn proools. In sp of h nl sss of HAART hr r lnlly srl nd osrvl shorongs n h rn of AI 9. In prlr HAART s no sssfl n o % of AI pns s of drg-ndd oy nd oplons of rn. HAART proools hv n lnlly osrvd o hv ld hrp ffy d o ohl/lnl drg rssn shor drg hlf-lf low o-vlly nd lood pls os. Mhl odlng provds nv nd ronl pproh o solv h hrp ffy prols ssod wh HAART. In prlr h odls fosd on fndng opl hrp shdls h rols of ln vrl rsrvors s wll s nzng of o sd ff 68-. Mhl odls whh norpor h pl opon of h r r of HIV- ndd AI drng HAART nld odls y -7. rng HAART h jor osl o ol vrl rdon s h sn of vrl rsrvors nd rrovrl lny 8. Rrovrl lny s dfnd s n ngrd pro-vrs wh no v rnsrpon. Ths s ssod wh low-lvl hron vrl nd prssn ryp HIV- rplon. Ths prosss ld o vrl prssn fr nl sssfl HAART 8. Mhl odls whh donsr prssn d o vrl rsrvors hv n onsrd y Nn nd Jn 6. Ohr odls whh lgnly ddrss h rol of vrl rsrvors n prssn nld pprs y Rong nd Prlson n 9 nd Prlson n nd dgh lno nd Wl n. Opl hrps h wll nz sd ffs hv n nvsgd y ny hors n -78. Zr l. n 998 prsnd odl whh ws fosd on h slon of pros nhors nd rol of drg rssn HIV- vrons. ngl n prsnd hl odl of HIV- nfon nd HAART whh donsrd h ffy of hlly opl hrpy. Cno nd Yony n onsrd HAART odl whh norpord h rols of lnly nfd C T lls nd dsssd how h rvrs rnsrps nd pros nhors ffd HIV- dyns drng HAART sng h QR h. In prlr Hf nd Yosf norpord h s rprodv nr R n drnon of opl HIV hrpy n. In spr ppr h s hors onsrd dlyd dffrnl on odl of HIV- dyns drng hrpy n 6. Thy ployd nrl lgorh nd Ponrygn s M Prnpl n drnon of h opl hrps. In fr ppr w wll s Ponrygn s Mnl Prnpl o onsr dssl opl hrps sh s o nz h oy of h drg z h hrp ffy of HAART. 6

5 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 In hs ppr n lor hl odl wll onsrd whh wll norpor physologlly plsl ffs sh s Mhls-Mnn ns rol of HIV- ln vrl rsrvors onnos rnsdrl drg dlvry nd h pl lyphoy prolfron ndon y h C T lls. Th von nd prolfron s oplshd y prrn nd orn prosss whh r dd y h yon nrln- srd y h C T lls. A spl fr of h rrn ppr s h nlson of h syny prodon r o h HIV- vron oprn. I hs n shown y oo l. 7 n h syny ndng HIV- vrns orrng yrs for progrsson o AI on n vrg sgnfnly nrs h r of C dlns. Th dsron hns of C nd C8 T lls d o syny foron nd ohr hnss hs n dsrd y h l. 8. Ths frs r norpord n h rrn ppr y ssgnng wo spr ll loss rs. Th HIV vrons n lso dsngr y rlsng h soll HIV- nvlop pron gp no h lood pls whh n h o nnfd C T lls sng y nods hry nrsng h r of dln of no-opn C T lls. Mhl srrs r sd n h rrn odl o donsr hs sps of HIV- nd C T ll dyns. vrl hors nvsgd h onsns of srrd long-r nd shor-r rn nrrpons drng HAART 9-. Th rrn odl wll dsss hs onsns y ns of slons. Th rrn ppr wll dvdd no gh sons. Th frs son gvs h nrodon no HAART hrpy nd provds h ss for rrn rsrh. Ths s followd y prsnon nd dssson of h odl prrs n on. In on h hl odl of HAART hrpy wll onsrd. Also h nssry nd sffn rr for nnhlon of HIV- vrons drng HAART wll prsnd n sons nd 6. In on 7 lnlly plsl opr slons wll hd. on 8 wll onld h ppr. Prrs In hs son h physologl vrl nd prrs of h HAART odl ons wll dfnd nd plnd. I s phszd h so of hs prrs r ologlly srl or n sd sng lnl hns. In lnl prn hs prrs r dffrn fro pn o pn dpndng on hr pho-physologl ondons. A ls of odl prrs onsns nd vrls s shown s follows. Th nr dnsy of non-hiv--nfd C hlpr T-lyphoys pr n vol Th nr dnsy of HIV- nfd C hlpr T-lyphoys pr n vol Th nr dnsy of HIV- vrons n h lood pls pr n vol Th nr dnsy of HIV- spf C8 yoo T-lyphoys pr n vol Th onnron of drg olls of h HAART rn proool R of spply of n-nfd C T -lyphoys R of spply of lnly nfd C T -lyphoys R of spply of HIV- vrons fro rophg onoys rogll lls nd ohr lyphod ss dffrn fro T -lyphoys R of spply of C8 T 8 lyphoys fro h hys R of HAART drg nfson y rnsdrl dlvry 6

6 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Consn ssod wh von of lyphoys y yon nrln- I- R of HAART drg dgrdon nd ron Consn ssod wh HIV- nfon of C T hlpr lls Th nr of HIV- vrons prodd pr dy y rplon nd ddng n C T hlpr lls R onsn ssod wh rplon nd ddng of HIV- n syny C T hlpr lls pr dy pr rolr µl nd rlsd no h lood pls Th nr of HIV- vronsprodd pr dy y rplon nd ddng n nonsyny C T hlpr lls nd rlsd no h lood pls Consn dpng h r of whh HIV- vrons np h C8 T 8 yoo lls Mhls-Mnnnonlnr ol r onsns ssod wh HAART drg lnon Mhls-Mnnnonlnr ol r onsns ssod wh HAART drg phrons I Cyoo offn whr Consn dpng opon wn nfd nd n-nfd C T hlpr lls Consn dpng dgrdon loss of lonogny or dh R onsn dpng ponnl drg lnon phrons Consn dpng dh or dgrdon or rovl y poposs progrd ll dh Consn ssod wh h llng r of nfd C T lls y C8 T 8 yoo lyphoys All h prrs r posv. Modl Eons. srpon of h Modl Eons Th HIV- pho-physologl dyns drng HAART hrpy n odld sng h followng sys of non-lnr ordnry dffrnl ons. A dld dsrpon of h dyns of h odl vrls nd n fond n Nn nd Jn. Th odl nlds h followng lnl provns Th drg dlvry ss rnsdrl slh-lposo npsld drg dlvry nsd of h r l for s of provd hrp ffy nd rdd gsronsnl oy. I s lso ssd h ls lposos r forld nd slvly rgd sh s o rd oy o non-hiv--nfd C T lls nd C8 yoo T lls. Th HAART drg s sh h h rnl ron nd ody lrn r follows Mhls-Mnn ns. j g for j j j j 66

7 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc } { sn for n f f Ths fnon dps h pross of lyphoy von whh s dd y C T hlpr lls. Ths lls sr yon lld nrln-. v Th prod np fnon f n dpd y h followng plo for onsn onnos np for prod np.. Bonddnss nd Invrn of Non-ngvy of olons In hs sson horl ondons wll onsrd ndr whh solons o h HAART hl odl ons r wll-posd lly ondd nd h nvrn of nonngvy for ll R T. In hs s nd T r dfnd rspvly s s whh HAART hrpy gns nd rns. Thor. Consdr

8 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc whr nd } n{ δ δ δ δ Thn hr ss T > sh h for T << ll solons o h HAART odl ons. wh nl vls R { R } r lly ondd dsspv nd wll vnlly nr h non-ngvly nvrn rgon Ω. In prlr h solons r rppd n h rgon Ω for ll R > T Proof. Usng h rsl fro Nn nd Jn n 7 l. Th non-lnr sys. n onvrd o h followng non-lnr dffrnl nls } { whr C C C C δ. Thor rf. 9 Thor..6. Consdr h dffrnl nly... n f d d wh R R C f n whr R sp {} sp C j for C T j j T j j {} nf for T δ { } Φ R Ω } { δ C Φ Φ

9 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc ppos... n f d d sh h Thn Applyng hor o h sys. h followng nls hold.. In prlr h followng rsls n ond..6 Ths Ω s non-ngvly nvrn nd h sys s lly ondd dsspv wh h onds dfnd y h followng ons..7 As onsn of.7 h ors of r nforly ondd. Ths opls h proof. Th Elr nd Copon of h Jon Mrs In hs son h odl ons wll rsrd o h s for whh h drg np fnon hs h for f. Ths. rds o sys. of drns non-lnr nd onoos ordnry dffrnl ons. > {} {} nd R nd C whr for C γ γ δ γ δ δ C sp l {} sp l } { sp {} } { sp δ C T T T P

10 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 } { for. Th physologl oos or h lr drng onsn onnos rnsdrl HAART hrpy or whn for.. ol Esn Crr for Clnlly Rlvn dy s of HAART In hs sson ss of lnlly rlvn ss or h possl pho-physologl oos fro onsn onnos rnsdrl HAART hrpy r lsd nd nlyzd. Ths oos r llld E for. Th lol sn rr r llld C. E C Ω { } for Ths lr rprsns h snro n whh HAART nnhls h HIV- vrons h nonnfd C h nfd C nd C8 T lls. Th no-oprosd pn y o npd wh opporns nfons. E C Ω { } for Ths lr s slr o s p h HIV- spf C8 lls r now prsn n h sdy s. E C Ω { } for

11 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 Ths lr orrsponds o snro of sssfl HAART proool n whh h sdy s onsss of so nnfd C T lls HIV- spf C8 T lls nd so drg rsd. v E C Ω { } for Ths lr lso orrsponds o snro of sssfl HAART proool n whh h sdy s onsss of so nnfd C T lls nd so drg rsd no HIV- spf C8 T lls. v E C Ω {} for Ths lr hs flr of HAART proool. In prlr h HIV- nfd C T lls nd HIV- vrons popl h sdy s n ddon o so drg rsd whrs h non-nfd C nd C8 T lls r nnhld. v E 6 C 6 Ω { } for Ths lr lso dps s of hrp flr of HAART s HIV- vrons sll rn n h lood pls of h pn. v E 7 C 7 Ω } { for

12 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 Ths lr rprsns nohr snro of nsssfl HAART proool s HIV- nfd C T lls nd drg rsd popl h sdy s. v E 8 C 8 Ω {} for Ths lr s no lnlly dsrl s of sn of HIV- nfd C T lls. E 9 C 9 Ths lr s nohr snro of hrp flr of HAART proool s HIV- nfd C T lls r ll prsn. E Th sdy s E dps prson who s lvng wh AI. In hs s h odl hs prssn nd h vrl r s no sffn o nnhl h n sys. Th rr for prssn of HIV- AI drng HAART wll dsssd n Thor.. Thr r so ohr sdy ss whh r no lsd s hy r lss lnlly nrsng.. Copon of h Jon Mrs Usng h Hrn-ron hor s possl o nvsg h hrp ffy of HAART nd h physologl sly of HIV- AI dss dyns ssod wh h odl ons y lnrzng h sys. n h nghorhood of h lr. Th Jon r of lnrzon nr ny physologl oo s dnod syollly y { } R M E J j Ω for

13 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 In prlr h j nrs r dfnd s follows. Th Jon rs for h sdy ss E E E r rspvly lsd s follows

14 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 } { E J. } { E J. } { E J. } { E J.6

15 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 7 } { E J.7 7 } { E J.8 9 } { E J.9 Nssry Crr for ol ly of Elr drng HAART E {E E E } dno h s of so lnlly rlvn lr of odl ons.. In hs son h lol sly of E E E nd E wll nlyzd sng h prnpls of lnrzd sly of onoos ordnry dffrnl ons. In prlr h nssry hl rr for rn hrp oos drng HAART r opd nd prsnd n h for of hors.. ol ly of E Th Jon r ssod wh E s dfnd s

16 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc } { E J If h ondon s posd on h Jon r ov hn. Th gnspr ssod wh h Jon r s dfnd s } { } { } { E J whr Thor.. ppos C n on. holds nd > >. < < <. Thn h HAART hrp oo E ss nd s lol ror. Proof. Thgn-vls of } { E J ssfy h drnnl on

17 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 d d J{ E } I Usng h pl pnson hn for opon of drnn h hrrs gnvl polynol s gvn y B p J E d d d d. Th gn-spr s hrfor gvn y whr J{ E } { } { } Th ondons. nd. grn h h gn-vls ssod wh h lr E hv ngv rl pr y vr of Roh-Hrwz rr 7. Hn h lr s lolly sypolly sl nd lol ror s wll s hyprol sn. Ths hor slshs 77

18 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 h lol sn nd lol sly of lnlly dsrl physologl oo of HAART proool. Clnl Iplon.. Th rr. nd. grn porry r for h AI pn. Thr wll fn nrvl drng whh h HIV- vrons wll nnhld fro h pn s lood pls. Ths wll howvr shor-lvd s h rs pon E y o nsl nd h rr for porl r r vold. I s possl for hrp rr o drvd o nn h pn o prnnly fr of AI whh w shll dsss n Thor... ol ly of E In hs sson h lol sn nd sly of E wll nlyzd. Th rsls r srzd n h followng hor. Thor.. ppos Esn rr C for lr E holds.. J{ E } h gn-spr of J{ E } w. wh h j r dpd y.7. sh h J{ E } { } { }.6 Whr Tr d d d d.7 78

19 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Thn h rs pon E s lolly sypolly sl hyprol sn nd lol ror f > >.8 > Proof. Th gn-vls ssod wh E ssfy d J{ E } I Usng h pl pnson hn of drnns lds o.6 wh h Roh-Hrwz offns dpd y.7. Th ondons spfd n.8 grn h h lr s lolly sypolly sl nd lol ror. Clnl Iplon.. Ths hor dps h ondons for on of h wors snros drng AI hrpy sng onnos nfson HAART. If h ondons. nd.8 hold hn h HAART hrpy nnhld ll h nnfd C T lls nd HIV- spf yoo C8 T lls. Consnly h n sys of h AI pn os npd nd h pn os h rg of opporns nfons. Howvr hs son y no ls vry long old fl.. ol ly of E ~ In hs sson h lol sn nd lol sly of h non-lnlly ffos lr E wll dsssd. Thorl rr ndr whh E ~ s lolly sl wll drvd. Th rsls r srzd n h followng hor. Thor.. ppos Th rron C holds for h lol sn of E ~ ~ M ~ ~ ~ ~ ~ ~ ~ h h ~ ~ Tr M ~ ~ ~ d ~ ~ ~ ~ d M ~ ~ ~.9 Thn h lr E s hyprol sn lolly sypolly sl nd lol ror f 79

20 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 ~ > ~ > ~ > ~ ~ > ~ Proof. I for { } dno h gn-vls orrspondng o h Jonr J { E } gvn y.. Thn h orrspondng gn-spr s gvn y h on ~ ~ J{ E } { ~ ~ } { } Whr ~ ~ ~ r spfd n.9. B ~ < nd ~ <. Th onlson of h hor follows dly fr pplon of h Roh-Hrwz rr. Clnl Iplon.. If h HAART proool sd for h AI pn s sh h ondon.9 s ssfd hn h pn prns r n sys yooy n whh h nnfd C T lls HIV- spf yoo C8 T lls HIV- vrons nd HIV- nfd C T lls r ll dd. Ths s no hrplly dsrl lnl oo s h pn y o svrly npd. To vod hs snro h HAART hrpy s plnd n sh wy h rron.9 s vold.. ol ly of E Th lol sn nd lol sly of h lr E wll nlyzd n hs sson. Th lnl rlvn of h horl hrp rr wll dsssd. J{ E } h gn-spr for h Jon r { E } J sh h J{ E } { d J E I } Thor.. ppos Th lol sn rr C holds for E < v M < wh J E 8

21 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 8 whr d d d d < < M M Tr Thn h lr E ss lolly nd s lol ror f > > > >. Proof. Consdr h Jon r. ssod wh h lr E. By posng h ondon of h hor nd opng h gn-vls sng h pl pnson hn n osrvd h h gn-vls ssfy on.. Th Roh-Hrwz rr whn ppld o h r M oghr wh h ondons n. grns h lol sn of E s lol ror.. Prssn Anlyss of HAART Th phophysology of HIV- prssn drng HAART s dsrd lorly n h ppr y Pornz n 8. In hs sson h hl rr for vrl prssn drng HAART wll drvd. Th nror rs pon E ss f nd only f h sys. hs prssn. Ths dsrs son n whh h pn srvvs for long wh AI. I s possl drng HAART h h HIV- vrons nno nnhld nsd h sys prsss n hron onfgron n whh h lood pls lvls of h HIV- vrons o-s wh h ohr lnlly srl prrs sh s nnfd C T lls h HIV- nfd C T lls HIV- spf C8 T lls nd HAART drg olls. Th rr for sn of E r lsd n h followng hor. Thor... { } { } { } { } { } sp sp nf sp sp sp sp {} nf U whr T T T T T T T T

22 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 l l l l l nf nf nf nf nf > U > > > >. Thn h sys wll prss nd h HAART hrp oo E ss. Proof. For proof rfr o Nn nd Jn 76. Clnl Iplon.. If nnfd C T lls nfd C T lls h HIV- vrl RNA ops n h lood pls HIV- spf yoo C8 T lls nd h HAART drg onnron r whn rn hrsholds hn h AI pn wll lv wh AI. If ny of h ondons lsd n. r vold h pn wll prn nprdl hrp oos nldng fll-lown AI or sponnos lnon of HIV- vrons. 6 ffn Crr for Prnn Cr of AI drng HAART In hs son h sffn rr for prnn nnhlon of HIV- vrons drng HAART wll drvd. Th lnlly dsrl physologl oos r E nd E. I s rlld h E orrsponds o h physologl oo n whh HIV- nfd C T lls h HIV- vrons n h lood pls nd HIV- spf C8 T lls r lnd n h lood pls of h AI pn. Th sffn rr for E wll dsssd frs. 6. lol ly of E In hs sson h glol sly of E wll slshd n h sp { R Φ } Ω wh Φ dfnd n.. { R Φ } Ω Th glol sypo sly of E n Ω wll slshd rsp o h flow nng fro n n R. 8

23 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 8 Th odl ons. orrspondngly rd o h followng 6. N nghorhood of pon n Ω n. Choos fnonl V on N sh h V s posv dfn wh rsp o E V s } { R R R C V nd ondd low v V s pnov fnonl for 6. v VE v > sh h > V whrvr E B for whr } { < R B v * V long h solon rjors of 6. Consdr h pnov fnonl 6. Th drvv of V long h solon rjors of h odl ons ylds h rsl * V 6. B sdy s h followng ons hold. 6. fn h followng sg srl fnons whh r of ondd vron } { for } { R nd whr V

24 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc * V 6.6 * V nd 6.9 nd dfn M { j }M X R sh h hn 6. Whr X T dnos h rnspos of X nd * V s ngv dfn f ssfy h ondons of < nd d M >. In prlr h j r dfnd s follows v v R v v X M MX X v v v v v v V T *

25 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc As h flow dyns pprohs h sdy s E h followng ondons hold 6. whr In prlr Th sffn rr for h glol sypo sly of E r spfd n h followng hor. Thor 6. Condons of Thor. holds nd > Thn h lre s glolly sypolly sl wh rsp o h flow nng fro Ω n. Proof. Th ondon of h hor grns h lol sn of E nd slshs h E s lol ror. Th glol sypo sly of E n shown y nvong h nhr rr for ngv dfnnss of r M s dfnd n 6.. In prlr * V s ngv dfn f < nd dm>. B s lss hn zro f ondon of h hor hypohss holds. Howvr dm> sn h prod >. Ths * V < nd hn E s glol ror. Ths opls h proof. l l > > < < > f f f

26 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Cons on Thor 6. If > hn > nd > ons sffn ondon for glol sypo sly of E. If < hn > s sffn ondon for glol sypo sly of E. If hn s sffn ondon for glol sypo sly of E. Clnl Iplon 6. Th fnon s sr of h r whh h C T lls r vd y nrln- I- n n orn pross whn h physologl flow drng HAART nds o E. I s possl o h ohl sr o offn nd of. Ths n don s follows!... V whr s pproly l o h Mhls-Mnn onsn of h C T lls von ron y nrln- nd V rprsns h l vloy of h C T lls I- von ron. No h s h r of dgrdon nd dy of h C T lls drng AI. Ths h hor pls h f h r of dgrdon of C T lls s grr hn h r of I- von of T lls nd f n ddon h nr of h C T lls r sh h hn h pn wll rd of AI. 6. lol ly Anlyss for E < In hs sson h ohr lnl dsrl lr E s nlyzd. Th s o fnd h sffn rr ndr whh h HIV- vrons n h lood pls h HIV- nfd C T lls r nnhld h HIV- spf C8 T lls wll prss s ory T lls s wll s h C T lls nd so drg rsds wll rn n h AI pn. I s pd h h C T lls wll vnlly rpopl o hr rryng py whrs h drg rsds wll lly dssp. Th nlyss wll slr o h prdng on for E. 86

27 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc Th rsron of h odl ons. o h sp { } Ω Φ R lds o h followng ons. } { for 6. Th glol sly of E wll slshd wh rsp o h flow nng fro Ω n. Consdr h pnnov fnonl 6. Th drvv of V long h solon rvs of h odl ons ylds h rsl * V Ths sdy s nd h followng ons hold. 6. Ths 6.6 { } R nd whr V * F whr F F V

28 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc Th fnons F r onnos sg srl nd of ondd vrons. 6.7 whr R X nd 6.8 sh h X T dnos h rnspos of X. fn CM R sh h 6.9 Now 6. Whr h j r dfnd s follows 6. As h flow ssod wh h odl ons pprohs E h r nrs j hv h followng for C * V F F CX X V T *

29 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc d d d < < > > < < or or or 6. B n shown h 6. In prlr f. Nn nd Jn lrly 6. Usng h spfons n. h r C hs h for 6.6 Th r C s ngv dfn f h followng rr hold 6.7 l l l l F > F > < < > f f f F > < < > f f f C

30 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Thor 6. { } E sh h < > > Ω. Consdr h pho-physologl lr Thn E s glolly sypolly sl wh rsp o h flow nng fro Ω. In prlr E s glol ror. Consnly ll h HIV- vrons wll prnnly nnhld n h AI pn. T Proof. Th pho-physologl lr E s glol ror f V X CX s ngv dfn or vlnly f h r C s ngv dfn. BC s ngv dfn f ondons 6.7 hold f. nhr. No h 6.7 holds f > nd <. If hn whh lds o h flflln of 6.7. B < nd whrs >. Ths ondon 6.7 s ssfd. As rsl * V s ngv dfn. Thrfor E os glol ror nd hn h hor follows. Clnl Iplons 6. Thor 6. gvs h sffn horl rr for h HIV- nfd C T lls nd HIV- vrons n h lood pls o rdd drng HAART. Ths hor lso provds h ondons ndr whh HIV- spf C8 T lls wll prss s ory lls fr h HAART hrpy. I s possl o prss h ondons of Thor 6. n rs of lnlly srl ophysl prrs. By sng Tylor pnsons of nd h ondon s pproly vln o h prsson < C8 < C * 6.8 Ths n nrprd o n h HAART wll r h AI pn f h nr dnsy of nnfd C T lls s l o h Mhls-Mnn onsn of h I- von of h C8 T lls whh n rn hs o lss hn w Mhls-Mnn onsn of h I- von of h C T lls. Corollry 6. ppos Thn h physologl sdy s E s glol ror. Proof. Th ondons 6.7 hold f h hor hypohss s ssfd. Ths s h r C n 6.9 ngv dfn. Consnly h lr os glol ror. 9

31 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 9 I s possl o on Thor 6. nd Corollry 6. o on h ond rr 7 lons nd ssson of Rsls Invsgv opr slons wll prsnd nd dsssd. Ths slons r prford sng lnlly plsl hypohl pn pho-physologl prr onfgrons. In prlr h slons d for h non-onoos vrson of h odl ons s dsplyd n Th drg np fnon f s hnl onsr sh s o gnr h rngl pls fnon s shown n on.. I rprsns prodlly lrd rnsdrl or nrvnos or pl drg r np wh prod ω. In prlr f fω whr ω6. dys I shold nod h h sys. rprsns HAART drng onsn onnos pl drg r np whh s dffrn fro h snros sd n h slons of hs son. Th opl hl nlyss of h non-onoos sys 7. sng Flo Thory nd Thory of non-lnr prod ynl yss wll don n fr plon. Th nrl ss sd r vrons of ss plshd n h rfrns 9. o hns for sng HIV-I dynl prrs nldmon Crlo slon nd polynol rgrsson nlyss. Th nvsgv opr slons ld svrl dynl sps of HIV- AI dyns whh r sd on h rspv prr onfgrons. Th -s of h slon grphs s lrd n onhs. 7. lon Rsls for Hypohl AI pn # Th AI pho-physologl prr onfgron of hypohl pn # s dnod y P nd hd n Tl. Th slon rsls show h h HAART proool prs HIV- 8 C C } { sn for f f

32 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 dyns n hs pn ldng o rdon of pls HIV- vr. Th slon rsls for pn # r hd n Fg.. I n osrvd h h HIV- nfd C T lls r rdd n hs pn wh h s of n-ai phro-hrp drg proools. In ddon pn # prns HAART- ndd n sys ronson s h nnfd C T lls nd HIV- spf C8 T lls rpopl. Tl. Hypohl AI pn prr onfgron Ρ 8 /dy/µl. /dy/ll/µl.9 /ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. lls/dy/µl lls/µl 8 /dy/µl. /dy/ll/µl./ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. vrons/c /dy./dy/µl. lls/dy/µl.8 lls/µl /dy/µl. vrons/c /dy/ µl. vrons/c /dy.7 /dy/vron/µl./dy/µl. /dy.. lls/µl /dy/µl. /dy/ll/µl./ll/µl. /dy/µl.8/dy/µl. lls/dy/µl. 7 lls/µl ns. g/dy g/dy g/dy g/ g/. g/ lls/µl. /dy onsn nfson Fg.. lon rsls sng prr onfgron Ρ 9

33 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc lon Rsls for Hypohl AI pn # Th hypohl AI pn # s ssgnd h pho-physologl prr onfgron P s prsnd n Tl. Th slon rsls r hd n Fg.. I n osrvd h hs pn dos hv lnlly fvorl prognoss ndr HAART rn proool. Th AI pho physodyns drng h gvn HAART proool s slr o h for pn # s h pn # lso ndrgos n sys ronson n whh h C T lls rpopl. On h ohr hnd h prolfrv vy of h HIV- spf C8 T lls pprs o downrgld. Tl. Hypohl AI pn prr onfgron Ρ 8 /dy/µl. /dy/ll/µl. /ll/µl./dy/vron/µl./dy/µl./dy/µl/ ll. lls/dy/µl lls/µl 8 /dy/µl. /dy/ll/µl./ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. vrons/c /dy./dy/µl. lls/dy/µl.8 lls/µl /dy/µl. vrons/c /dy/µl. vrons/c /dy.7/dy/vron/µl./dy/µl. /dy.. lls/µl /dy/µl. /dy/ll/µl./ll/µl. /dy/µl.8/dy/µl. lls/dy/µl. 7 lls/µl ns. g/dy g/dy g/dy g/ g/. g/ lls/µl. /dy onsn nfson Fg.. lon rsls sng prr onfgron Ρ 9

34 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc lon Rsls for hypohl AI pn # For hs snro h pho-physologl prr onfgron of hypohl pn # s s shown n Tl. I s nod h HIV- AI dyns drng HAART rn proool n hs pn s rd y onrons fro ln rsrvors n onrs o h ohr hypohl pns. Th rsls of h slon r shown n Fg.. Ths s non-lr AI onfgron slon s s vdn prr onfgron nd y h slon profl. Th slon rsls show h drng h gvn HAART proool h hypohl AI pn # prns nnhlon of nnfd C T lls nd h HIV- spf C8 T lls. Consnly n sys prlyss ors s onsn of h low C Tll nr dnsy ldng o n ponnl nrs of h lood pls HIV- vr. Ths slon rprsns n nfvorl AI oo drng HAART. Tl. Hypohl AI pn prr onfgron Ρ 8 /dy/µl. /dy/ll/µl. /ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. lls/dy/µl lls/µl 8 /dy/µl. /dy/ll/µl./ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. vrons/c /dy./dy/µl. lls/dy/µl.8 lls/µl /dy/µl. vrons/c /dy/µl. vrons/c /dy.7/dy/vron/µl./dy/µl. /dy.. lls/µl /dy/µl. /dy/ll/µl./ll/µl.9 /dy/µl.8/dy/µl. lls/dy/µl. 7 lls/µl ns. g/dy g/dy g/dy g/ g/. g/ lls/µl. /dy Consn Infson Fg.. lon rsls sng prr onfgron Ρ 9

35 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc lon Rsls for Hypohl AI Pn # In hs snro h drg np s onnos for 6 onhs nd off for nohr 6 onhs nl HAART s dsonnd. Fg. prsns n nsssfl HAART hrpy for hypohl AI pn wh h pho-physologl prr onfgron P n Tl. In hs HAART snro h pls HIV- vrons oplly ovrwhld h non-nfd C T hlpr lls nd h HIV- spf C8 yoo T lls. Th HIV- nfd C T lls h prod dyns nd h prognoss for h hypohl pn s nwholso s Nn nd Jn 6. Tl. Hypohl AI Pn Prr Confgron Ρ /dy/µl.9 /dy/ll/µl. /ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. lls/dy/µl 8 lls/µl 8 /dy/µl. /dy/ll/µl./ll/µl./dy/vron/µl./dy/µl./dy/µl/ll. vrons/c /dy./dy/µl. lls/dy/µl.8 lls/µl /dy/µl.vrons/c /dy/µl. vrons/c /dy.7 /dy/vron/µl./dy. /dy.. lls/µl /dy/µl. /dy/ll/µl./ll/µl. /dy/µl.8/dy/µl. lls/dy/µl. 7 lls/µl ns. g/dy g/dy g/dy g/ g/.g/ lls/µl n Fg.. lon rsls sng prr onfgron Ρ 9

36 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 8 Conlson Th rrn ppr s lor nd nv p o onsr dlly ppll h odls nd drv rr for ffos HAART proool for n AI pn. Th hl ons prsnd n on r gnrlzon of h odls y Prlson l. Wodrz nd Now nd Tn l. nd ny ohr hors y norporng or lnlly rlvn prrs of HIV- pho-physodyns. In prlr nrl- von of oh C T lls nd C8 T lls r plly norpord no h odl. In hs ppr hs n donsrd h h prrs nd ply sgnfn rol n drnng h ffos oos of HAART. Clrly h lnlly dsrl oos r h rs pons E nd E. Th rr for h sn of E nd E r lsd rspvly n Thor. nd Thor..Ths hors gv h ondons ndr whh oh E nd E n porrly or rnsnly nd. Th rr for E nd E o o glol rors r lsd n Thor 6. nd Thor 6.. Ths hors prssd n rs of spl lnlly nl nd srl prrs gv h sffn ondons for h r of AI. I wll phszd h hr s ohr hrp rr hs r nrl nd rly rdos o hv n lnl sng. On ssnl fr of hs rsrh s h h HAART proool s plnd y sng h onsn onnos nrvnos nfson or onsn onnos rnsdrl nfson of h drg. As sh h rr drvd n hs ppr r ppls o hs sngs. Th hl odl for nrn pl or r l pr orl drg dnsron n drvd sng h nononoos vrson of h odl ons nvolvng h drg np fnon f dsssd y Nn nd Jn n 7. Th snros for lnl flr drng HAART d o r drg oy r rprsnd y h rs pons E nd E.Th rr for hs hrp oos r dsrd y Thor. nd Thor. rspvly. In onlson s phszd h hs horl rsls do no ons lnl rs nlss h rsls r plnd oghr wh ohr phrologl proools for h AI pns. Thr y s ohr horl rsls whh r no plly dsssd n hs plon. Nvrhlss s ssnl o no h hl odlng hs pl n h s for h rn nd r for HIV- ndd AI. Usng h hns of h hl odlng nd non-lnr sys nlyss w donsrd h h von nd n r onsns s wll s h rs of nfl fro lnly nfd rsrvor r porn fors n h drnon of h prognoss nd hrp ffy of HAART. Th fr wor wll nvolv h onsron of hl odls whh wll dsr n AI hrpy sng HAART n ddon o ACI Av Clllr Inohrpy nvolvng nrl-. Also n h fr h hl odl for HAART wll nld h rols of ons sh s h dl CCR on hrp oos. Copng Inrss Ahors hv dlrd h no opng nrss s. 96

37 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Rfrns Hss C l. HIV- spf C8 T lls wh n ffor phnoyp nd onrol of vrl rplon n. ; Pnlo F A. Nw onps n h nophognss of HIV nfon. Annl Rvw of Inology. 99;87-. Prlson A l. y hrrss of HIV- nfd oprns drng onon hrpy Nr. 997; Now MA Bonhoffr hw M My RM. An-vrl drg rn dyns of rssn of fr vrs nd nfd ll poplon. J Thor Bol. 997;8-7. Wodrz Now MA. pf hrpy rgs old ld o long-r nologl onrol of HIV. Pro Nonl Ad UA. 999; Y P ors AP rshnr E. Ronson of hy fnon n HIV- pns rd wh hghly v nrrovrl hrpy Clnl Inology. ; Nn F Jn M. Copr slon of hl odl of HAART hrpy for HIV- AI n Prodngs of h Inrnonl Confrn on Bo Mdl Engnrng nd Infors BMEI'. hngh Chn;. 8 ow H Prns JM ng JM. An-rrovrl hrpy n prvosly nrd dls nfd wh h hn nodfny vrs yp slshd nd ponl drnns of vrologl oo. Nh J Md. ;6-. 9 opl. Inrnonl HIV/AI rl fnds onnos nrrovrl hrpy spror o psod Thrpy NIH Nws Nonl Ins of Hlh; 6. Avll fro hp// Bjr H W rshnr E. Prdng dffrnl rsponss o srrd rn nrrpons drng HAART. Blln of Mhl Bology. ; Cno MA Yony T. hor nd long prod opzon of drg doss n h rn of AI. Ans d Ad Brslr d Cêns. ; Jn Twry A Jn N. Trnsdrl dlvry of n n-hiv gn sng ls lposos hns of on. Crrn rg lvry. 6;7-66. Jn X l. An ngn hrshold for nnng hn nodfny vrs yp - spf yoo T lyphoys. Mol Md. ; szwz J or F. rrd rn nrrpons n HIV/AI hrpy Mros nd Infon. ;7-. 97

38 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 Nn F Jn M. Crr for nnhlon of HIV- drng HAART hrpy. Prodngs of h Inrnonl Confrn on Bonfors nd Coponl Bology BIOCOMP s Vgs NV;. 6 Nn F Jn M. Thorl Anlyss nd lon of A nd Chron Phs HIV- yns Brsh Jornl of Mhs Copr n. ; Hf Yosf N. yns of HIV nfon odl wh hrpy nd r r. Inrnonl Jornl of Toogrphy nd ss. ;6W Pornz RJ Rsrvors of hn nodfny vrs yp h n osls o vrl rdon. Clnl Infos sss. ; Rong Prlson A. Modlng lny nfd ll von vrl nd ln rsrvor prssn nd vrl lps n HIV-nfd pns on pon hrpy. Po Coponl Bology. 9;. H Prlson A. Vrl nd ln rsrvor prssn n HIV- nfd pns on hrpy. Po Coponl Bology. 6;. dgh AR lno RF Wl CO. ow-lvl HIV- rplon nd h dyns of h rsng C T lls rsrvor for HIV- n h sng of HAART. BMC Infos sss. 8;8. ngl RF. Mon nd onrol of h hn nodfny vrs. Mhl Bosns. 8;9-. Tn WY Xng Z. o s sp odls of HIV phognss ndr rn y nvrl drgs n HIV-nfd ndvdls. Mhl Bosns. 999; Zr Byo AM Brndn M Owns. Effs of pros nhors on h sprd of HIV srns slon sdy. lon. 998;6-7. Hf Yosf N. Two opl rns of HIV nfon odl. World Jornl of Modllng nd lon. ; Hf Yosf N. Opl onrol of dlyd HIV nfon odl wh n rspons sng n ffn nrl hod. IRN Bohs;. 7 oo M PM Vos A od R l. Prognos vl of HIV- syny-ndng Phnoyp for r of C ll dplon nd prognoss o AI. Ann Inrn Md. 99; h C Jnns M Croln EJ plon J nls J nndy RC oll R. T ll syny ndd y HIV rls. Jornl of Cll n

39 Nn nd Jn; BJMC 6-99 ; Arl no.bjmc..8 9 Hs B. Ordnry dffrnl ons wh pplons srs on ppld hs nd don. World nf Prss ondon U. ;-. nhr FR. Th hory of rs. Chls Plshng Co. Nw Yor NY. 99;-8. Nn nd Jn; Ths s n Opn Ass rl dsrd ndr h rs of h Crv Coons Aron ns hp//rvoons.org/lnss/y/. whh prs nrsrd s dsron nd rprodon n ny d provdd h orgnl wor s proprly d. Pr-rvw hsory Th pr rvw hsory for hs ppr n ssd hr Pls opy ps h ol ln n yor rowsr ddrss r 99