Modelling Immunological Memory

5 Mo delling Imm unological Me mo r y Simon Garrett 1 , Mart in Ro bbins 1 , Joa nne W alker 1 , Wi lli am W il so n 2 , and U we Ai c k eli n 2 1 Com puta tional Biology Gr ou p, Dep artm en t of Comp uter Sc ie nc e , U niv ers i t y of W ales, Ab ery stwyth , SY23 3P G. W ales, UK. { smg,mjr0 0 } @a ber.ac.uk 2 Sch o ol of Com puter Science (A SA P), U nivers i t y of Not ti ng ham , Not ti ng h a m , NG8 1BB. Eng lan d, UK. { w.wilson,u we.aickelin } @notts. ac.uk Su mm ar y . Ac cur ate imm unological m o dels offer the p oss i bi li t y o f p erform ing high- throug hput e xp erim en t s in silic o that can pred ict, o r at l ea s t sug gest, in vivo phe- nomena. In this c ha pter , w e com pare v ar ious models of imm unological me mor y . W e first v al idat e an exp eri mental immun ological simula tor, develo p ed by the aut hor s, b y simulating seve ral theor ies of immun ological mem ory w ith k no wn res ult s. W e the n use the same sys tem to ev a luat e the pr edi c te d e ff ects of a theor y of immuno logi- cal me mor y . The res ultin g m o de l has not b een exp l ore d b efore in artifi cial imm une syste ms research, and w e comp are the simulat ed in silic o out put wi t h in vivo mea- sur emen t s . Al t hou gh the the ory app ears v al id, we sug gest t hat th ere are a com mon se t of reaso ns why imm unological memory models ar e a us ef ul sup p or t to ol; no t conc lusive in t hem sel v es . 5.1 In t r o du ct io n One o f the fu nda men t al fea tur es of the nat ural imm une syst em ( NIS) is i ts a bil - i t y to maintai n a memo ry of previo us infec tions, so t hat i n fut ure i t can resp on d more q uic kly to si mil ar i nfe cti ons [ Sa wy er 1931 ]. The me chan isms for i mm unological mem ory are s t ill p o orl y und ersto o d and, as a re sul t , are usu ally highly si mpl ifie d duri ng th e c ons t ructi on of artifi cial immune sys tems ( AIS ). Alth oug h all AIS a re inspir e d by the imm une s ys t e m , see Chapte r 3 of t hi s b o ok, here we stu dy more d etai led immun ological mo dels . Immune sy stem mo d els will be requ ired by t he oreti ca l i mmun ol ogi s t s i f the re is to b e a si gni fic a n t inc rea se in the gen erat ion of new ideas i n the field b ecau se com putat ional simulatio n is con side rably fas ter than lab or ator y exp eri men t s . So fa r, ho w eve r, this has not b een prac ti c al b eca us e the gran ul ari t y of the si mulat io ns has b een far too l arg e, and single sy stem s 84 Garr ett e t al . are able to eithe r g enera te h igh- level, global imm une si m u lations , or de t ai l ed but par tia l s imul atio ns, but not b oth. W e di ff e re n ti a te b etween a mo del an d a m e t aphor . In AIS th ere a re se v eral m e t aph or s , such as clonal sel ect ion m eth o ds, neg at i v e sel ecti on m et ho ds, and ne t - w ork meth o ds tha t prov ide com put ati on al to ols for the AIS prac titio ner. These are not mo del s. Mo de l s a re an atte mpt to cre ate an art ificial s ys t em tha t dis plays the sa m e b ehaviours as ano ther ( norma lly natur al) sys tem. Metaphor s si mply use the natural syst em as ins pir atio n for an al gor i t h m ic dev i ce. Here w e f ocus on the cre atio n and use o f imm unological mo de ls i n imm u no logy . Ther e may b e side- effect b en efits from t he s e mo d els t hat inspir e the disc o very of new co mpu tatio nal meth o ds in AIS, but that is no t our ce n tr al aim here. W e ou tline a sys tem, still under dev el op men t, that can prov id e fas t , de tail ed immune simulation s, and which is b egi nni ng to sugg es t in vivo effects with e nough accu racy to b e useful as an immunology su pp or t tool. W e choose i mm unological memory as ou r appl ication ar ea. This c hapte r: • Pr ovide s a survey of i mm unological me mor y , incl udi ng well -k nown the ories, and a new imm unological memory t heo ry that may b e of inter est to AIS pra ct i ti oner s . • Pr ovide s a surv e y of exis ting imm une si mul ati on sy stem s . • Des crib es ho w w e bu i l t and tes t e d a simple set of i mmuno l ogi c al memor y models, and then expan ded this app roach to a m or e adv anc ed, generic si mul ato r. • Des crib es ho w w e tes ted the v al i di t y of a new t heo ry of i mm unological mem- ory [ Ber nas c oni et al. 2002]. Fir st w e us e d t h e adv ance d imm une simulator to gen er ate in silic o resul ts from the new t heo ry . The n, since this t he o ry was gen- era ted in res p onse to in vivo res ults , w e evalu ated the rel i abi li t y of that the ory b y comp aring our in silic o res ults wi t h the in v ivo resul ts. Our adv anced si m u lator is fast, ev en when si mulat ing 10 8 l ym pho cy tes , the num b er presen t in a m ouse. It also has t h e abi li t y to si mul at e cyt okine con ce n tr at ion s, whic h prov e d vital in simulat ing the w ork of [ Ber na s coni et al. 2002]. The simula tor’ s sp eed and fl exi bi li t y al lo ws i t to be app lied to ta sks th at were pre viou sly imp oss ible . F urthe rm ore, ou r new simulato r is not just a one-off imm une simulation for a si ngl e ta sk, rat her it is des ign ed from the gr oun d-up as a reus able, flexible to ol for res earc h. 5.2 Backg rou nd 5.2.1 Imm une M em or y As with man y asp e cts of immunology , our und erstan ding of the pro ces ses und erly- ing imm unological memory is far from co mpl ete. A s Zi nk er nage l et al say , in the ir se min al pap er on v i ral i mmun ol ogi cal me mor y , “Br o wsi ng thr ough text b o oks and 5 Mo del ling Im munol ogi cal M em or y 85 authoritative texts quickly r eve als that the definition of immunolo gic al memory is not str aightfor war d.” [ Zi nkern agel et a l. 1996]. Man y o f t he q ues t i ons they rai sed are stil l re l ev an t alm os t ten y ear s l at e r. Ther e are sev eral the ories, some of whic h app ear mutually ex cl usi v e, and the re is exp erimen t al evide nce used to sup p or t al- m os t all of th ese t heo ri es . Before exam ining the techniqu es for mo dell ing t he ori es of imm unologica l me mor y , w e need to discuss the theor ies t hem se l v es . It is now widely acce pted tha t h y p er- sens i t i v e memory c el ls ex is t , and res ear ch has b ee n con duc ted in order to de scri b e t hei r att ributes a nd b ehaviours , e.g. [ Mc Heyzer- Wi llia ms & Mc Hey zer- Willi ams 20 05] . Me mo ry cells come in at l ea s t t wo v ari e t ies : mem ory B-cells and mem ory T-ce lls. Th ese cells are forme d du ring (or so on aft er) an imm u ne res p ons e. Ac ute viral inf ect io ns induce t wo t yp es of long -term mem- or y : hum ora l i mmun i t y , in whic h B-cells pro d uce antib o d ies to ta g cells infec ted by viru ses, and cel lul ar i mmun i t y , i n wh ich T-c ells , a ctiv at ed by sp ecific viral an t i ge ns, kill the v i rus- infe ct e d cells and a l so pro du ce cy tokin es that pr even t the growth of vi ru se s an d mak e cells res is t an t to viral infec tion 3 . It has b een est ablis hed tha t a mem ory of an inf ect ion is ret ained for sev eral y ears or ev e n deca des [Sawy er 1931, Paul et al. 1951]. One w a y to measu re the stren gth of t hi s imm une memor y is b y coun ti ng the p op ulat ion of sp ecific memory cells. This figure ten ds to fa ll rap idl y im medi ately a f t er an infe ction, reaching a stab le (but repro du cing) leve l that is mai n t ain ed ov er many y ears or decad es, e v e n in the absen ce of re-exposure to the an t i ge n. The chall enge f ac i ng i mmun o log is t s is to discov er how these cells are mai n tai ne d. Under lying these is sue s, it seems likely that some sort of hom e ost asi s me c h anism maintain s a s t abl e tot al p opul atio n size of memory cell s . Ev ide nc e su gge sts th at the tot al numbe r of memo ry cells in the b o dy mus t re main r oug hly con sta n t, and it has b ee n s h o wn that any i ncre a se rap idly ret urns to this res ting co ncentra tion [ T an c hot & Rocha 1995]; inde ed, it is co mmo n sense that t he n umb er of cells c oul d not incre ase indefi nitely w ithin the fixe d v olume of the i mmun e sy stem ’ s hos t. One p ossible exp la nat ion for th is is that m em or y cell s (p articu larly T-cel ls) release cy t ok i ne s that hav e a n i nh i b i tor y e ff ec t on an y enl arged antib o dy s ub-p op ul at i on. Over all, wha t differs in t h e theor ies of im m un olog ical me mor y is: (i ) how memor y cells are for me d, and wh eth er they are qu al i tat i v el y di ff e ren t to oth er B- and T- cell s, and (ii) ho w memor y cells are mai n t ain ed in the long ter m, so that the memor y of the pri m a ry res pon se is not l o st by cell death. Lo n g-L iv ed Me mory Cel l Th eor y : Give n tha t ly mph o cyt es (b ot h B- and T- cells) di ff eren ti at e i n t o ‘ m em or y c e lls’, and tha t th ese mem ory cells are t he n highly res p on sive to the or iginal an ti ge ni c t ri gge r, the si mpl es t w ay of i mpl em en t i ng this in nature m ig h t b e t o inv oke ve ry long-liv ed memor y cells. I n this case , w e wo uld assu m e that the re is no cell- divisi on, the memor y cells just live a v ery l ong time: mor eo ver they must do so if they ar e to pre serve i mmun i t y for m any years . Is thi s 3 from h tt p: //w ww . em ory . edu /E MO R Y REP OR T/e rarc hive/2000/F ebr uary/ er- feb ruar y .21 /2 21 00m e mor y .h t m l . 86 Garr ett e t al . p ossib le, since the m a jori t y of o ur cells hav e a life -span m uch sho rter than that of the bo dy a s a whole, and so cells are contin ua lly dyin g, and b eing re ne w e d ? Zi nk ern agel et al say tha t t here ’s no convin cing e videnc e for thi s t yp e of phen o- t y p e [Zink ernagel et al. 1996] and cur ren t opin ion, s uc h as Mc Heyz er-W illi ams and Mc H e yzer -Wi lli am s ’ , agree [ Mc Heyz er-W i lli am s & Mc Heyz er- Willi ams 2005]. F ur- therm ore , exp erim en ta l evide nce c on tr adicts the long-liv ed mem ory cell theo ry . A series of e xp erim en t s on mice s h o w ed tha t me mory T-cells ca n conti n u e to divide long aft er any pri mary resp on se [ T ough & Spr en t 1 994, T o ug h et al . 1996 ]. Since a stable p op ulat ion is maintai ned, t hi s me ans th at mem ory cells mus t a lso b e d y i ng at a simi lar r ate, and are the ref ore not as lon g-liv e d as orig ina lly b eli ev ed. F urt her mo re, it has b ee n known for decad es [Sawy er 1931, P aul et a l . 1951] that antib o dy pro duce d in res p ons e to an an t i gen ca n p ers is t at sig ni fica n t leve ls in seru m for ye a rs after the ini tial i nfec tion has o ccurr ed. Antibo d ies c annot surv iv e in the b ody for a par ti cul a rl y lon g len gth of tim e, so we can con cl ude th at pl asm a cells are sus t ain ing t h ese con centrati ons ( the pr imar y source of antib o dy) . The prob lem is tha t pla sma cells, in mice, hav e b een sho wn to hav e a lif e-spa n of just a few mon t hs [Slifk a et al. 1998], and that they are only pro duc ed by differ entiating memory c el ls . This evid enc e sh atters the the ory of long-liv ed memo ry B-cells, and draws us to the conclu sion that m em or y B-cells – li ke t hei r T-cell eq uivalen t s – are b ein g c on t i nual l y cycled l ong aft er any inf ect ion has b een dea l t wi t h. Eme rgen t Memo ry T he ory : T o add ress these i ssue s, a Em er gen t Me mo ry t heo ry sugges ts that t here are no s pecial memory cells as suc h, rat her the effector c ell s nat ural ly evo lve tow ar ds highly s p eci fic cells, and are pre ser v ed from ap op totic dea th via s o me sort o f ‘ pr eserv ase ’ en zym e, such as t el om e ra se [ W eng et a l. 1997]. Alth oug h i t is unl ik ely t hat e m er gen t memo ry is s t abl e in itself [Wilson & G arrett 2004], the pro cess w ould expla in ho w memo ry cells are cre ate d: they are jus t sp ec ial ise d forms of effector cell s. ! T e l o m e r e s p r o t e c t t h e t i p s o f t h e D N A i n o u r c e l l s - - i n c l u d i n g i m m u n e c e l l s … ! W h e n t h e y g e t t o o s h o r t , t h e c e l l c a n n o t r e p r o d u c e f u r t h e r . ! T e l o m e r a s e i n c r e a s e s t h e l e n g t h o f t h e t e l o m e r e s ( a d d s T T A G G G x n ) t e l o m e r e c h r o m o s o m e Fig. 5.1. T elom eres prot ect the t ips of our chrom oso mes , and al low cells to repro- duce suc cessful l y . 5 Mo del ling Im muno log ical Me m or y 87 Each c e ll in o ur b odies can rep ro duc e only a pre def ine d n umb e r of ti m es, as defined by the len gth of its telomer es . T el om eres are DN A se quen ces t hat ‘cap’ and protect the tip s of our chrom oso mes , which are shor ted each t i m e the cell rep ro du ces , i ndee d (Fig. 5.1), “ ... e ach cy cle of c el l division r esults in a loss of 50 - 100 terminal nucl e otides fr om the telo mer e end of e ach chr omosome. ” [De B oer & No es t 1 998] . Wh at if the degree of telo mere shor tening were i n vers el y pr op or tiona l to the a ffi ni t y b etween the cell’s ant ib od ies and an t i ge n? In t hat case s t rongl y matching imm une cells w ould t e nd to sur viv e longer than weakly matching ones . This prin ciple is not new in imm u no logy – de B oer has sugg ested a mo del based on simil ar con cepts [De Bo e r & N o es t 1998]. Dut t on , Bra dley and Swain agree that the dea th rate is a v it al com p onen t req uire d in esta blish ing ro bus t me mor y . “ It stands to r e ason that activate d c el l s must esc ap e c el l de ath if they ar e to go on to b e m emor y . Thus, factor s that pr omot e the survival of otherwise de ath-susc eptib le T c el ls ar e c andida te s for memory factors .” [ Dut ton et al. 19 98] . Con sider th e i mpact of this hyp othesis in the co n te xt of di ff eren t t y p es of imm une cells. Gray son et al sta te tha t, “ ... memory T-c el ls ar e mor e r esistan t to ap optosi s than na ¨ ıve c el ls ... R e-exp osur e of m e m ory c el ls to A g [ a n ti gen ] thr ough vir al infe ction r esulte d in a mor e r apid exp ansion and dimin i she d c o ntr actio n c om p a r ed with th o se of n a ¨ ıve c el ls .” [ G ra y so n e t al. 2002]. This ind ica tes th at memo ry cells w oul d hav e lo w er (but not z ero ) deat h rates, and high er pro l i fer ati on rat e s, so the th e cell p op ula tio n wou ld nat urally contrac t to l ong- l i ved (i.e. hi gh- a ffi ni t y ) cells o ver ti m e. T elo merase ma y not b e the only biol ogical mechani sm tha t c an exp lain the ev olu- tio n of i mm une cells in to lo nger l iv ed, hi ghe r a ffi ni t y memor y cells, a n al t e rna t i v e ex pla nat ion und erp inn ing the longer lif e-spa n of memory cells is provi de d by Zan etti [ Z a ne t ti & Crof t 2 001]: the “ ...sele ction of B-c el ls destine d to b e c ome memo ry c el ls takes plac e in GCs [ ge rm i na l cen t res] and is c ontr ol le d by the ex pr ession of intr acy- toplasmic mole cu les ( Bcl-2 and Bcl-x) which pr event a form of cel l de ath ... to gether with the c onc omitant suppr essi on of signals fr om c el l surfac e pr oteins that l e ad to de ath .” Alth oug h differing from the telom erase h yp othe sis, the imp licatio ns w ould b e the sa m e: m em or y cells app ea r to reflect no rmal immun e cells tha t hav e na tur ally ev ol v e d to dev el op a low er deat h r ate, ens urin g thei r sur viv a l ov er oth er cell s such as e ff ect ors . The pr oble m wit h the Em er gen t Me mory the ory is that it is v e ry cell-sp ecific. Ho w can a con ce n tr at ion of cy t ok i ne s ensur e a h igh a ffi ni t y cell li v es longer than a lo we r a ffi ni t y cell in alm os t the same lo cat i on? Resid ual Antig en Th eor y : Sev era l rep orts sugg es t that prot ein an t i ge n can be ret ained in the lym ph node (e. g . [ P ere l so n & W eis bu c h 1 997]), sugge s t i ng tha t nor- mal l ymp ho cy t e fu nct ion c ann ot rem o v e al l trac es of a par ticul ar class of an t i ge n. This is a nat ural resu l t of t he immune syst em b eing focussed on par ticul ar lo cat ions in the b o dy . Wh i ls t m os t an t i geni c mater ial will b e clear ed by the imm une sy stem , caus ing an imm une res p onse, some antigen ic mate rial will escap e a localised imm u n e res p ons e long enoug h to repr od uce. The i mmun e sys tem th en quic kly esta blish es a 88 Garr ett e t al . stea dy sta te b etw ee n imm une resp onse and antigen ic p opu lation si ze, and the im- m une sy stem ’ s p op ul atio n is s t i mul ate d by the no rmal hyp er muta tio n re s p on se. The refore, it is possible that the immune sys tem does not co mpl e t el y re move all antigen ic mat erial from the ho st, ei the r be cau se s mal l conc en t rat i ons of anti geni c cells ma y re main long en oug h to rep ro du ce , or b ecaus e the imm u n e sys tem itself has ret ained some of the an t i geni c mate rial in folli cular den dr i t ic cells (FD Cs). These FD Cs the n slowl y release the antigen ic mate rial in to the host, to s timulate a low- le v el immune res p on se. Zan ett i et al say , “ The pre vailing view is t h at maintenanc e of B c el l memo ry ... is a function of the p ersistence o f antigen on FDCs ... only a few hundr e d pic o g r ams o f antige n ar e r etaine d in the l o ng term on FDCs, but these smal l amo unts ar e sufficient to sustain dur able and efficient m e m ory r esp o nse .” [ Z a ne t ti & Crof t 2001]. In either case, this would ke ep the i mm une s ys tem acti v e en ough to sus t ai n mem ory cell p op ula tio ns. This idea has b ee n sup p orte d by res earch sug gest ing that B-cell memory is par t i cu l arl y sensi tiv e to res idual an t i ge n [T ew e t al. 199 0] . In rec en t y ears ho wev er, comp elli ng evi dence has b een pr e se n t e d sug ges ting that the cycling of mem ory T-cells conti n u es to occur wi tho ut any of the s pecific antigen b ein g pr esen t [ Lau et al. 1994], whic h w oul d m ean that t he se cells mus t b e res p ondi ng to some oth er sti mulus . Al t hou gh some deb ate has o ccur re d [Manz et al. 2002, Zi nk e rn agel 200 2 ], t hi s view is now widely ac cep ted by i mmun ol ogi s t s [ An ti a et a l . 20 05] . An add ition al ob je ction stems from an ev a lu atio n of the p erfor mance of such a sys tem. How c ou ld it b e e ffi ci en t , from an evolut ion ary p oi n t of view, to exp end res our ces on wh at is ess e n ti al l y a rote learn ing a ppro ac h to mem ory? W e kno w, fro m Ma c hi ne Lea rnin g, that rote lear ning is the le a s t e ffi cie n t me tho d of s t ori ng lear ned inf orm ation , and it does not al lo w for ge n eral i sati on. Al t hou gh, the re is an el em e n t of gen eral isatio n i nh ere n t in the Res idual An t i ge n theor y due to the me mori es of prev ious i nf ect i on s ov e rlap ping wi t h new inf ect io ns, and pr ovidi ng a (we ak) ge ner al i se d res p onse, it is que stiona ble wh e t her the re is enough gen eralisat ion to make this an effectiv e source of imm une m em or y . It may seem tha t an t i ge n p ersi stence is i m p ort an t f o r a model of im mune mem or y , to ens ure tha t the high a ffi ni t y mem ory cells are sus t ain ed ov er long p erio ds, but the re is ano ther, r elat ed p os si bi li t y . Perha ps me mo ry cells do not n e ed sti m ul ation by antigen; they si mpl y prol iferate p erio dically . W ou ld this rep re se n t ano ther evo - l uti on ary s t e p for an immune cell in o rder for it to di ff eren ti ate in to a m em or y cell? Gr ayso n et al ide n t ifie d the discr epancy b et ween the long term b ehaviour of mem ory cells and n a ¨ ı v e cells and sta te that , “ ... m e m ory c el ls u nder go a slow ho meos tati c pr olife ratio n , while na ¨ ıv e c e l l s under g o little or no pr o li fer ation .” [ G ra ys on et al. 2002] (our emp hasis) . If this i s the case, do mem ory cells act ually n eed p ersis tence of the antigen to sur viv e? Ev en if re-exposure is not nec essa ry , An t i a et al con clud e tha t “ ... estimate s for the half-life of immu n e me mory suggest that p ersi sten t antigen or r ep e ate d exposu r e to antigen may not b e re quir e d for the maintenanc e of immu ne mem ory in shor t - 5 Mo del ling I mmu nolo gic al Me m or y 89 live d verte br ates; however , ... r ep e a te d exp osur e ma y play an ad ditiona l r ole in the maintenanc e of mem ory of long-live d verte br ates .” [ An ti a et al. 1998]. W e choose to inc lude antigen p ers isten ce in the m o del pr e se n t e d here . Im m un e Net w or k T heo ry : Network th eory is base d aro und the p oss i bi li t y tha t the immu ne sys tem m ai n t ain s and t ri gger s memor y b y intern al, not exter nal stim- ula tion. It su gges ts tha t imm une cel l s, par ticul arly lym pho cy tes, pr esen t regions of them selv es tha t are anti geni c to ot her imm une cells. This causes cycles of sti m u lat ion an d suppr ession, whic h, while b egun by an exter nal antigenic sour ce, are co ntinued and maintain ed eve n in the ir ab se nc e, and are thus a for m of mem ory [ F ar m er et al. 1986]. A netw or k of interac tions b e t w ee n i mm une cells is widely b eliev e d t o a c - coun t for memo ry p o ol hom eo s t as is [Zeng et al. 2005, Schlu ns & Lef ranc ois 2003], an d cer t ai n imm une cells are ev en able to form physicall y c on nect ed netw orks of tun ne ling nan otu bu les in vitr o [ W at ki ns & Sal t e r 20 05] , but li tt le evide nce has b ee n pub lished recently in the m a jor i mmun ol o gy jou rna ls for a stro ng role of the kind of co- sti mulat ion desc rib ed ab o v e. Hetero logous and P o lyclon al M emory T heor ies : It has b ee n obs erved t hat dur ing an immune resp ons e, p op ulations of m e mor y T-c ells unr elated to the an t i ge n may also exp and [ Ber nas co ni et al . 200 2, T o ug h et al. 1996], sugg es t i ng tha t p erh aps ser olo gic al m em or y could b e het erol ogi cal ly ma i n t ain ed by a degree of p olyclonal stimu lation dur ing all imm une res p o ns es. Ac cor din g to [ An t i a et al. 2005], t wo p ossible mecha nis ms hav e b een sugg es t e d t o expla in these res ult s - Bys tan der Sti m ul atio n an d Cros s-Reac tiv e Sti mul ati on: (i) The Byst ander Stimulat ion theor y sugg ests t hat the an t i ge n-s p eci fic T-c ell s pr o - duce a cytokin e tha t sti m ula tes all near b y ( b ys ta nd e r) memo ry T-cells to div ide. It has been sugg es t e d that b y stande r s t i mul ati on could b e res p ons ible for the co n t inue d cycling of m e mor y B- cells, as w ell as for T-cells [ Ber nas c oni et al. 2002]. The res ult s of thi s high imp act w ork show ed that if memory B-cells are si multa neo usl y exp os ed to a n antige n t hat t hey are not sp ecific to, a nd to the cytoki ne IL-15, the y will und ergo clonal exp ansion. This abi li t y w as shown to be un ique to memo ry B-cells, and could not be rep ea ted wi th their na ¨ ı v e eq ui v al e n ts. (ii) the Cr oss- Rea ctive S timul ation the ory is based on s p ec ul at i on tha t m emo ry cells could be more sens itiv e to sti m ul atio n t han na ¨ ı v e cells, and m ig h t t he ref ore b e sti mula ted by di ff ere n t an t i ge ns, p erh ap s even a self -an tigen . In ei t he r case, it has b ee n sho wn e xp erim en t al l y tha t m emor y T-cells sp ecific to a par tic ul ar antig en can b e di rec tl y s t i mul ate d by a di ff eren t , unrel ated antigen [Selin et al. 19 94] . Bot h of these t heo ri es sugg es t that once memor y T-cells hav e b e en cre ated, t hey can b e sti m u late d dur ing immun e res pon ses to un rel at e d antigen . The difference is that in one case the cells are di rec t l y sti m u late d by antigen , and in the oth er (p oly clo nal sti mulat io n) th ey are s t i mul ate d b y cy t ok i ne s rel eas ed by oth er, a n t i ge n-s p eci fic cell s. 90 Garr ett e t al . 5.2.2 A Brief Survey of Immune Mo dell ing Ma the ma tica l Mo d els: Mat hem ati cal models of i mmun ol ogi cal (su b)s yste ms of- ten use or din ary d i ff eren t i al eq uat ion s ( OD E) or par t i al dif fer ential e qua tio ns (PD E) to enca psul ate the ir cho sen dy namic s ( e.g . [ P ere lso n 2002, Sm ith et al. 1999]). Perel- son’s HIV equ ati on s [ P ere lso n 2 002 ], and Smi th’ s i nflu enz a d yna mic s [ Sm i th e t al. 1999], are illus tration s of models of small part s of the imm une s ys t e m dyna mics that hav e had sig ni fica n t b enefi ts to human h eal t h, but whi c h do not se t out to model the imm une syst em as a whole. In Chapte r 4, we hav e alr eady seen Perelson’s detailed models of B cell and T cell rec ep tors . Wh en one cons ide rs the chem ica l com pl ex i t y of amin o aci d bind ing it is not sur prisin g tha t man y balk at the idea of m o de l li ng the imm une syste m at all. Ho wev er, immuno logical simul ati ons a re p ossible b ecause we observe gro ss-scal e effects (such as prima ry/se condary resp ons es) that are then mo d ulat ed to a grea ter or lesser degree by sma ll-scal e pr oce sses, such as Perel son’ s dis cussi on of B and T cell bin din g. B ot h are vit al for tru ly acc urate mo del s, but larg er scale models can be used suc ce ssf ull y to expla in gro ss -s ca le fe atur es of the i mm une sys tem [ Y at es et al. 20 01] . Immuno logic al m emory has also b een mo del led in a sim ilar m anner — the classic exam ple b ein g F ar mer e t al’s wo rk [ F ar m e r et al. 1986] – but the re are more rec en t at tem pts to model i mm unological m em or y to o [ A h med & Has hish 2003]. Alth oug h these models s a y a lot ab ou t cert ain de t ai ls , they are n ot intended to b e global models of immuno logical mem ory . F or examp le, the i m p ort an t w ork of An t i a et al on un der s t and i ng C D8 + T-cell memory [ An ti a et al. 2005] is based on a few, rel atively simple equ ation s. This is not to s a y that i t is easy to g ener ate such equ ation s (it is not); rathe r , w e are sa ying tha t the appl i cab i li t y of these equ atio ns is li m i t e d. In deed , the di ffi cu l t y i n build ing and man agin g these equ atio ns is pre cisel y the reas on t hat a com puta tiona l simulat ion app roach is so m e t i m es more appr opri ate . Com putati onal Mo dels: Co mputatio nal models a re not as well est ablis hed as math ema tical mo del s. Those that do ex is t are us ual l y eit her p opu lati on- bas ed (en- tities that are t rac k e d a s they fre el y inter act w ith each oth er) , or ce llul ar au to ma ta (en ti t ies that are tra c ked in a dis cre te gri d-li k e s t ructu re, ge ner ally wi t h lo cal- only i n te ract i ons [ W ol fr am 2002]). Ne v e rth eles s, co mpu tatio nal models do hav e some ad- v an t ag es ov er math ematica l m o de ls. Fi rs t l y , it is p ossible to define, infor mally , the b ehaviour of a hi ghl y comp lex sys- tem, wi t hout for ma lly defining it in t e rm s of for m al OD E s or PD Es— we can creat e a p op ulat ion of entitie s by m app i ng from ob jects in nat ure to ob jects in the c o m- putati onal si mul at i on . F u rther mor e, man y ODEs hav e no an alyti cal solu tion and can only b e solv ed by co mpu tatio nal ana lysis , in sof tw ar e such a s Mat lab T M and Ma them atica T M . Sec on dly , some forms of in silic o exp e rim enta tio n may b e di ffi c ul t i n math emat ical mo d els, and inde ed in the i mm unology lab ora tory , such as trackin g a s ing le B -cell or antib o d y ov er i t s lifet ime. It is p oss i bl e, t he ref ore , that com putationa l imm une si m- ula tors will prov ide the onl y mean s of investig ating some imm unological c hal l eng es. 5 Mo del ling I mmu nolo gic al Me m or y 91 In all co mpu tatio nal simul atio ns, we re- iterat e the im p ort anc e of the choice of bind- ing mechanism , the t yp e of cell-cell and cell- an t i ge n interac tion , (see [ G arrett 2003] and Ch apte r 4 of this b ook) , and we note tha t th e few co mpu tatio nal si m u lato rs t hat do exis t are ofte n und erde v elo pe d and ma y not hav e b een p eer- revi ewed by the acad em ic com mun i t y . ImmSim : The work of Seiden et al, on Im mSi m w as the first rea l atte mpt to mod el the imm une sys tem as a whole, and it is s t ill the onl y simulat or to hav e b een fairly widely p eer review ed [ K lei nste in & Sei den 2000, Kl ei ns t ei n et al. 2003]. It is simil ar in style to the w ork o f F arm er et al [ F arm e r et al. 1986], but is a true simulation , not a set of OD Es 4 . Simm une : There are at l eas t t wo “Si mmu ne ” immun ology si mul at or s : Meier- Sc heller- sheim’s versi on [ Me i er- Sc hel l ersh e i m & Mack 19 99] , which was deve lo p ed in the lat e-199 0s, and Sm i t h and P e rel son ’s version. Of the t w o, Mei er-Schell ershei m is the more adv a nce d, imple men ted as a full cel lula r au to ma ta wit h the abi li t y to de fin e alm os t any r ule s that the user des ired, w herea s S mith and Perel son’ s w as a rel atively simple, un pub lished Lisp si mul at i on. Synthetic Immune Sys tem (SIS) : A lthoug h SIS app ea rs to b e si gni fic an t l y fas t er and more p o werf ul, it does muc h less . Si mmu ne c an simu lat e large numb er s of comp lex interaction s, w hereas SIS is de s i gne d on ly to investiga te sel f-non sel f r elati onsh ips. SIS i s a cell ul ar auto mata; it can only be found on the web 5 . Im munoSim : Ubay dli and R as h ba ss ’ s Immunos im set out to prov i de res ear chers wi t h an “Im munol ogic al sa ndb ox” - it w as a cus t om i zab l e mo de lling e n v i ro nm e n t that simulate d cell t yp es, re cep tor s, lig ands , ca sca des, effects, and cell cycles, with exp e rim ents run in silic o . A k ey req uire m e n t w as that i t sho uld hav e a pu rely visual inter face , wi t h no pro gra mmin g n ecess ary . It receiv ed the F u lton Ro bert s Imm unol- og y pr ize (twi ce) from Ca mbri dg e Univers i t y but do e s not app ea r to b e a v a ilable as a publ ic ati on . Other systems: These simu lati ons [ Cas t igl i one et al. 2003, Jacob et a l . 2004] are small er scale tha n th at pr op osed here, but hav e s t ill had b enefi ts to c he mothe rapy and immunology , and /or hi ghl i gh t pr obl em s tha t need to b e ov e rco me. O t her s hav e emph asised the imp ortance of the bind ing me c han ism, the t y p e of cell-cell and c e ll- an ti ge n i n t er a cti on chos en, and the multit ude of oth er p o ssib iliti es that s ho ul d b e co nsid er ed [ G ar ret t 200 3 ] . 5.3 Bas ic Sim ul ati on s Our w ork wi t h a set of Basic Si mulat ion s set out to ex plor e the gross -s ca le b ehaviour of some of the theo ries just studi ed, while k e ep i ng the models as simple as p ossi ble – 4 Im mS im c urre n t ly to b e found a t h tt p: //w ww . cs. pr i nc eto n. ed u/i mm si m /so ft w are. h tm l 5 at: http:/ /ww w. cig.s alk. ed u/pa p ers/ SI S m anual wp M. p df 92 Garr ett e t al . here, the only the intera ction s s im ul ated are t h ose b etw ee n an t i b o di es a n d antigen . This b egs th e qu estio n, “how simple can an eff ecti v e m o del b e?” Ass umi ng O cc am ’ s razor appli es, our answ er is, “ as simple as p ossib le, and no simp ler. ” How ever, the models descr ib ed in t hi s section are del ib erat ely to o s i mple. T his is par tly b ec aus e no one kno ws how co mple x a si m u la tio n mu st b e b efore it can ac cur atel y rep ro du ce in vivo resu lts , p art ly b eca us e by sta rting as simple as p ossible we get a lo w er li m i t on the co mp utat ion al p erf or man ce of sim ple m od els, and par tly ( mor e im p ortantl y) b ec aus e it lets us e xpl or e the dyn amic s un der lying simple imm une simulation s, so that late r ad ditio nal c omp lica tion s can b e viewe d as mo d ulatio ns of this ba s ic model. Note tha t t he lack of com pl ex i t y shoul d not b e seen a s an ind icat ion tha t the models descr ibed in this section are tri vi al . A l t hou gh simple, gr eat care was t aken to ensur e they were as rea l i sti c as p ossi ble, as w e hop e will b ecom e cl ear. The Ba sic Si mulati ons will also act as a pri mar y valid ati on for the underl ying me ch- anism s of the mo re compl ex exp eri ments. They do not v ali date any oth er asp ect of the co mp lex ex p eri me n ts . It is easi er to v erify and v ali date the p erfor mance of a simple mo de l tha n a comp lex model; the n if the comp lex and simple models shar e si m il ar b ehaviour t hi s parti ally v al idates the comp lex model. This rai ses ano the r issue: ho w do we v al idate imm unological mo dels ? If we a p ply stan dard Ma c hin e Lear ning me tho dol ogy , where ‘ m o dels’ are ‘ h y p oth ese s’ , the n w e sho uld do s om e form of k -f o ld cros s-v al i dat i on to obt ain a meas ure of the ac curacy of the defined i mmun ol ogi c al h yp oth eses. But ho w do we do this when we hav e no well- es t abl is hed ‘ corr ect’ dat a? T o some ext en t, w e can assu me t hat if a model i s able to pr e d ict wh at will be obse rved in nat ure, t hen the model is v al idat ed to some ext ent. I nd eed, the abi li t y to p redict is one o f the rea sons fo r build ing models i n the first place. W e will ret urn to t hi s p oi n t l ate r. 5.3.1 Basic Sim ulati ons : Metho d s and Material s Each Basic Si mulati on w as bu i l t from antibo di es and antigen , and no mo de ls w ere allow ed to dire ctly cr eate me mor y; me mory had to ev ol v e. This blurs the di s t i nct i on b etween anti b od ies , B-cells and T-cells i n order to explo re t he effects of imm une cell /antibo d y p rolif eratio n i n res p ons e to antigen . T o ind ica te t hi s blu rri ng, we will call the si mul ate d imm une syst em el ements ‘ rea c ti v e imm une sys tem elemen ts ’, or R ISE s. The RIS Es w ere defin ed as b eing more likely to die as t hey got older; im- ple mented by re movi ng a RISE w hen r nd () .a > r nd () . d r , where rnd () is a unif orm r andom numbe r gen erator , a is the age of the RISE me asured in gen eratio ns from the cur ren t g ener ati o n, an d dr is a deat h r ate i n te ger, whic h was set to 30. A cons tan t 50 RISE s were add ed each gen erat ion. This led to a stabl e p o pu l ati on size, which retu rned t o the sta ble lev el d espit e e xte rnal p ert urb atio ns. Fig. 5.2 demon strates this effect: despi t e a large i nfl ux of new RIS Es (th e large p ea k) and a small cul ling of RIS Es (t he sm al l trou gh) , sta bi li t y is maintain ed. The size of the peaks were al so reverse d, w ith the same resu l t tha t the p op ula tio n size re t urn ed to a stab le leve l – note also the dif fer en ces in scale b etween Fig.s 2 ( a) and 2(b) , whic h sho w tha t the size o f p erturbati on is i rr el ev an t . T hi s i mpl e men t s a simple hom eost ati c p op ulat ion of R ISEs . Number of immune c e l l s 5000 10000 15000 2 0000 25000 3 0 0 0 0 Numb er o f immune c e l l s 0e+00 2e+04 4e+ 04 6e+ 04 8e+04 1 e + 0 5 5 Mo del ling I mmu nolo gic al Me m or y 93 0 100 200 300 400 500 0 100 200 3 00 400 500 Time Time Fig. 5. 2. The res t i ng p o pul atio n of B-cells w as in homeo stasis. T hes e gr aph s show the p op ul atio n s ta bi li t y that unde rlies all models t hat will follo w. Any p ositive or neg ative chang e to the p op ulat ion size is quickly corr ecte d, and stab le p op ulat io n size is res t ored . Antige n p op ulati ons w ere ‘ i nje cted’ i n t o the s ys t e m as a whole, at a pre define d tim es. The pr imar y i nfec tion w as alwa ys at ge ner atio n 70 , and th e sec on dar y inf ecti on w as eith er at g ener atio n 120 (‘s ma l l G ap ’ e xp erim en t s ) , or ge nera tion 420 (‘bigG ap’ exp erim en ts), to test t he short - and long- term memo ry abilities of the p op ulat io n. An an ti gen was remo ved once is was b oun d to an RIS E, and bind ing could onl y occ ur when the si m il ari t y b etw ee n the RISE a n d antigen w as wi t hi n a dis ta nce o f 100. The RIS Es could t ak e any v alue b etween zero a nd 10,000, and the an t i ge n alwa ys had a ran dom ly cho sen v alue of 3.3, f ixe d at t hi s v a lue f or al l test s. In a l l cases we assum e that the stron gest a ffi ni t y RISE will bind with the antigen. W e i mpl e men t t hi s by a form o f tou rna m e n t sel ect ion, whereby t h e stro ngest matching RISE o f te n ran dom ly chosen R IS E s is cho sen t o b e the one tha t actu ally bin ds . O ur more com plex si m u lation , pre sented l ater in t hi s chapt er, uses si mul ate d c hem ota xi s. F or eac h exp er iment, w e meas ured the tot al numb er of RIS Es, th e tot al n u m b er of antigen , and the num b er of RI SEs w ith a ffi ni t y in the ran ges, [0.01-0.1), [0.1-1), [1-10), [ 10-100), [ 100 - 1,0 00) , [ 1, 00 0-1 0, 000) a nd [ 10 ,00 0-10 0,0 00 ). W e rec orded this inf orm ation eve r y gen era tion for 600 gen era ti on s . 5.3.2 Basic Sim ulati ons : Exp erimen ts and T ests W e p erform ed the f o l l o w i n g exp erimen t s and tes ts. 94 Garr ett e t al . Me mo ry B y Ex t ernal Sti mula tion These exp eri ments te sted th e abi li t y of the Basic Si mulati on s to re memb e r i nfe ctio ns ov er a s hort and long p erio d of time , ass umin g the only s t i mul ati on to b e exter nal, i.e. via an t i geni c i n te ract i on: Con t rol /N one : On top of the hom eos t as is mechanism , we tes t e d a standa rd imple- mentatio n of clonal sel ecti on. This is acti v at ed b y t he pre sen ce of antigen , so that a go od -mat ching RISE pr od uc es many c lon es, and a p oor- matching RISE pro duced few cl ones . F u rther more, the go o d- mat chin g clones ar e only sli ghtly m utat ed from thei r par en t cells, via a Gau ssian centred on the par en t, wh ere as the few p o or-matching clones are often highl y m ut ate d, rel ati ve to the ir pare n t s. This app roximate s B urne t’s clonal sel ec tion the ory [ Bur net 195 9 ] and acts as a control for these exp erimen ts. Since mem ory cells w ere not exp lici tly cr eate d, w e wou ld exp ect the RISE p op ul atio n to clear the antigen , and t he n forget the i nf ect i on . Em er gen t M emo ry : In the em erg en t mem ory tests, when a R ISE w as b oun d to antigen , the RISE’s age w as redu ced in pr op orti on to its a ffi ni t y to the antigen , so that b e t ter -fit ti ng RIS Es ten ded t o s urvive l on ger – this i mpl em en t ed the effects of ‘ pr eservas e’ . This shoul d pre se rv e th e high ma tc hi ng RIS Es to some ex t e n t, pr o duci ng a for m of m em o ry . Res idual A n t i ge n : Once the antigen p op ulatio n had b ee n inje cted, a single an ti ge n w as then re-intro duc ed in to the si m u lati on a t ra ndo m ti m e i n terv al s ( on av er- age, ev ery thr ee gen era tio ns). W o uld thi s pr even t the mem ory of the inf ect ion from being lost b ecause thi s v a lue is conside rably sm aller than dr ? If so, unde r wh at co n di ti ons ? It m i gh t b e arg ue d th at this does not really rep re se n t resid- ual antigen , as antigen are b ein g rei n tr o duced rat her th an ma i n t ain ed , how e v er the pur po se of this model is t o show wh eth er a sm a ll am ou n t of sti m u latio n can mai n t ai n me mor y , not to dem on strat e me chani sms by which the an t i gen could b e maintain ed, and th us i n prac tical t erms re i n t ro duct i on p erfor ms the same role i n ou r mo del as mai n t enan ce (keepin g a small, s t abl e p opulat ion of antig en) , wit h the advan t age of allo wing us to simplify the exp erimen t . Bot h E m er gen t M emo ry and Residu al Antigen : Is the re any b enefit i n i mpl em en t- ing b oth the E m erg e n t M emo ry and Res idual An ti ge n the ori es? Me mor y B y Inter nal Sti m u lat io n These exp erim en ts t e sted the e ff ects of ad din g inter nal sti mula tion to the Basic Si mulati on s, so t hat one RISE could i ntera c t wi th ano th er R IS E, eve n in the ab senc e o f antigen . A ltho ugh antib o d y-antib o d y inter - acti on is n ot wi del y thou gh t to be a form of memor y in natu re, it does o ccur, and is li k el y to hav e some fun ction. The se tes t s set out to sug ge st wh at t hat fu nction m i gh t be. The grap hs, d escr ibe d ab ov e, of a ffi ni t y l ev el dist ribu tion are of par ticul ar rel ev an ce to these ex p erim e n ts. It is i m p ort an t to note that w e d o not use par at op e-p ar atop e bin ding here: i .e. w e do not assu me tha t a R ISE / an ti b o dy ’ s li gh t chain wil l bi nd wit h the li gh t chain of ano ther R ISE/ an t i b o dy , f o r reason s ou tlined in [ G arrett 200 3 ] (e.g. the prob lems of p ositive fe edb ac k) . In stead we shift ideal bin ding by 2,500 (in a cir cular range of 10 , 000) so that a R IS E with v al ue 1,000 would b ind m os t s t rongl y wi t h ano ther RISE of v alue 3,500. This me ans th ere wou ld need to b e a cycle of f ou r RI SEs if intern al me mor y were to work. This i mpl e men t s par atop e- epitop e bind i ng, al tho ugh 5 Mo del ling I mmu nolo gic al M em or y 95 w e note that t her e is stil l a fu nction al rel ation ship b etw een the par atop e’s and the ep i t op e’ s shap e s pace, which is l ess than rea l i sti c, but was ne cess ar y to keep th e simulation si mpl e. 5.3.3 Basic Sim ulati ons : R esult s Me mo ry By Ex t ernal S timula t i on The res ult s are pre sented i n Fig. 5.3 and Fig. 5. 4. These ar e a verages of ten ru ns. R em em b erin g that the p opu lation is com- pl e t el y renew ed on a verage every 30 gen erat ions, eve n the s hort gap exp erim en t s (left col um n of gr aph s ; 50 gen erations b etw een inf ections) should not ha v e sho w n an y m em ory of the previo us inf ec ti o n. In the “Non e” gra phs ( top line) we actua lly see a sli gh t inc reas e i n res pon se, but this is not stati s t i ca l l y me ani ngf ul – t her e is no m em or y of prev ious infec tions. The stati s t ics w e used were t he Wilc o x on Si gned Ran k T e st, and the res ults are tab ulated in T a ble 5.1. This test al lowe d us to decide when the dif fer enc e in hei g h t b e t we en the pr imar y an d sec ondar y res po nses w as si gni fic an t , and the ratio expr ess es the ex t e n t of tha t d iffe renc e. This non -param etric test w as c hos en b ecau se it is likely that the seco ndary resp on se is con dition ed by the pr imary resp o nse, and tha t the data are not norm ally d i stri but ed. The a ffi ni t y gr aph s in Fig. 5.4 indi cate th ere is an inc rea se i n R ISE s tha t hav e affin ities in the < 0 . 1, < 1 . 0 and < 10 . 0 rang es, but the re is no me mor y b etwee n i nf ect i ons . The “Em erg en t ” res ult s sho w a dis tinc t se con dar y resp on se in the sho rt gap exp er- i men t , b ecaus e the p opu lati on m emb er s t hat w ere able t o su cce ssf ull y bind were preserv ed b eyon d 30 gen eratio ns; ho weve r, thi s eff e ct is not enough to allow mem- ory to p ers is t ov er the big gap b ecau se the antibo die s that w ere effectiv e again st the pri m ary inf ectio n, ten ded to die o ver tha t time p erio d. Never theles s, the resu l t s ind icate t hat m emor y can b e pre serve d for at least 50 gen era ti o ns . No w the a ffi ni t y g rap hs sho w that high a ffi ni t y RI SEs are mai n tai ned b e t w ee n the inf ect ions tha t are sep arated by a small t i m e gap, and ho w these t y p es of R I SE dr ain aw ay o v er the longer tim e gap s o t hat the simulated imm une sys tem needs to b eg in again to find a high a ffi ni t y res p ons e to the an ti ge n. The “R esid u al A ntige n” te sts hav e a sim ilar patt ern in F ig. 5.3, wi th the p op ula- tio n stimulat ed eno ugh by the on- going, lo w-leve l an ti ge n to pro mot e a se con dar y res p ons e in the s hort gap exp eri ment. In t he bi g gap exp er ime n t , how eve r, the effect is not statis ticall y si gni fic a n t. The a ffi ni t y gr aphs sho w an elevated number of high- t o m i d-r ange a ffi ni t y RIS Es (in the < 1, < 10 and < 100 rang es) but i nd ica tes t he v ery high a ffi ni t y RIS Es ret urn t o lo w er levels by 200 gen era tion s. This expla ins why the seco ndar y res p ons e Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s 10000 14000 18000 22000 10000 1200 0 140 00 16000 18000 10000 12000 14000 16000 1 8 0 0 0 20000 10000 12000 14000 16000 Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s 10000 120 00 14000 16000 18000 20000 2 2 0 0 0 10000 12000 14000 16000 18000 10000 12000 14000 16000 18000 10000 12000 14000 16000 96 Ga rret t e t al . 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0 100 200 300 400 500 0 100 200 300 400 500 Time Time Fig. 5. 3. Graphs of the the ory si m u latio ns, “No ne”, “Em er gen t”, “Re sid ual” and “Both” (top to b ottom , in ord er) for a small tim e g ap ( 50 gen eration s, left colu mn) and a longer tim e gap (350 gen era ti o ns , ri gh t colu mn), a ver aged ov er 2 0 runs . Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s 1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000 Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s Numb er of immune c e l l s 1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000 1 10 100 1000 10000 5 Mo del ling I mmu nolo gic al M em or y 97 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time Fig. 5. 4. Graphs of the the ory si m u latio ns, “No ne”, “Em er gen t”, “Re sid ual” and “Both” (top to b ottom , in ord er) for a small tim e g ap ( 50 gen eration s, left colu mn) and a longer tim e gap (350 gen era ti o ns , ri gh t colu mn), a ver aged ov er 2 0 runs . 98 Garr ett e t al . w as not s u ffi ci en t to b e stat istic ally m eani ngfu l when the an ti ge ni c injec tions were sep arated by a large gap . Wi t h “Bo th” em erg en t and resi dual antigen im plemented, the stor y is di ff ere n t . No w, we see stro ng se conda ry resp on ses for b oth sho rt an d big gaps, alth ou gh t here is a sli gh t sust ained, global inc reas e in R ISE p op ul atio n a f t er the first i nfec tion. The a ffi ni t y gr aph s also sho w that the high a ffi ni t y < 0 . 1 RISE s nev e r retur ned to the zero mark. This app ea rs to hav e been cruci al i n ma intain ing a p ow erful sec ond ary res p ons e, and corresp ond s to the ex iste nce of high a ffi ni t y memo ry cells in nat ure. Some may ask wh y the resid ual an tigen phenom enon does not exp lain imm une mem ory on its o wn. If the am o un t of res idual an ti ge n were high enou gh th en surely the immune resp ons e wou ld be enough t o reme m b er th at i nfectio n? I ndeed, this is tru e, but at the cost of a p erm anently raised antib o dy p op ulati on leve l, whic h i s not seen i n natur e. A t the ex t rem e, if the infe ction were to p ers is t at the same high lev els then it is o bvio us tha t the memo ry w ould not b e los t , b ec aus e the infec tion wou ld b e con t i n uou s and on- going, but this is also not a rea listi c stat e of affairs, exc ept in pat hologi cal cases, such as in el der ly pat ients who are infec ted with cytom egolovirus [ P e rel s on 20 0 2]. The level chosen is o ne that only ve ry sli ghtly raises the an ti b o dy p o pul atio n size: it is enough to mai n ta in memor y ov er a sho rt p eri o d, b u t not in the longer term . F u rth er mor e, R es idu al An t i gen does not expla in why b ette r m at c hing cells ten d to survi v e and w orse ma tchin g cells t e nd to die off; no r d o es it e xplai n how memory cells can nat ural ly emerge as a resul t of immune cell evolution. As a res ult, b oth the ap optos is red uction (o r tel omer ase mem ory m aintena nce m ec h anis m), and the re- stimul at i on me chan ism are requ ired to ev olve an effectiv e imm une res p onse . Me mo ry By In ter na l Sti m u lat io n The resul t s are pr e se n t e d i n Fi g. 5. 5 and Fig. 5.6. F or each run, each RISE att emp ted to bind to the RISE with the hig hest a ffi ni t y out of ten ran do mly c hos en R ISE s. Ther e does not app ea r to hav e b een any mem ory e ff ec t; inde ed, the opp o site seems tru e – as so on a s an y s ubp op ul at i on incre ased in size out of pr op orti on to the p opula tion as a whole, the netw o rk effect red uced the siz e of tha t sub p opu lation . This made the leve ls in F ig. 5.6 more stable than the co mpa ra tive g rap hs in Fig. 5.4. W e concl ude that the memor y effects of imm une ne t wor ks are li m i te d — at least the t yp es of netw or k tha t w e hav e imp lemented here. Si nce our aims in these bas i c exp er iments are to pro d uce simple mod e ls of imm unological i n t era cti on s , we use non- s ymm e t ri c, para t op e-e pi to p e bind ing, in which kno wing that A binds B do es not imply B bin ds A . In c o n t r a s t , AIS ne t w ork alg orith ms ten d to use para to p e- par atop e bind ing b ecau se it is of i nteres t f rom a com putatio nal p oi n t o f view, even if it is less bio lo gica lly t e na bl e. 5 Mo del ling I mmu nolo gic al M em or y 99 Ex p er i men t p- V alu e 99 % Rat io None S m a ll G ap 0. 240 No 0. 948 None Big G ap 0. 955 No 1. 011 Em er gen t Sm a ll G a p 0. 000 0957 Y es 0. 852 Em er gen t Bi g G a p 0. 225 No 1. 067 Res idual Sm al l G ap 0. 003 18 Y es 0. 890 Res idual Bi g G ap 0. 332 No 0. 945 Bot h Small G ap 0. 000 0957 Y es 0. 822 Bot h Big G ap 0. 000 0957 Y es 0. 813 Ne twork S m al l G ap 0. 765 No 0. 999 Ne twork B i g G ap 0. 896 No 1. 001 All Small G ap 0. 000 0942 Y es 0. 850 All B ig G ap 0. 000 315 Y es 0. 832 T a ble 5.1 . R es ul t s of the Wilc o x on Signed Rank T e st for di ff ere nc e b etw ee n the size of the t wo p eaks in each exp erimen t . The p-v a l ue s are sho wn to 3 sig ni fica n t figures and wh eth er or not the difference can b e reg ard ed as si gni fican t at the 99 % confi dence leve l. The sm all er t he p-values the g reate r the degree of con fiden ce t hat ther e is a di ff e renc e b etween the pri mary and se con dar y re sp on ses, wi t h 1.0 being zer o co nfi de nce, and 0.0 b eing 100% confi dence. The ratio giv es the s ize a nd dir ectio n of the difference b etween the t wo p eak s. 5.4 E x p eri m e n t s Usi ng t he Se n t inel Sys tem 5.4.1 Metho d and M ate r i als The si mulat ions th at form the basis of this c hap ter were m o de l le d using our so f t - w are, ‘ Sen ti ne l ’ . Senti ne l is an agen t -b ased com pl ex syst em simulatio n pla tform for immu nology and AIS res ear ch t hat curr ently exists as a proto t y pe. Its design is based largely aro und the prin ciples of cel lula r au tom at a, w ith the en vi ro nmen t di- vi ded i n to a disc rete grid of lo ca tio ns. En ti t ies wi t hi n t he simulati on are fre e t o mov e arou nd in this envir on ment, but are on ly ab le to res p on d to e v e n ts that occ ur wi t hi n closely ne ighb ou rin g cells. ‘ En gi ne s ’ , su c h as those used in co mpu ter games for man aging gra phics , phy sics, etc., man age the phy sic al and chem ica l i n t e ra cti ons that occ ur with in thi s e n v i ro nmen t. The ph ysics engine all o ws acc urat e si m u latio n of the ph ysi cal pr o p erti es of age n t s, res t ri ct i ng t he i r movem ents acc or din g to att ribut es such a s size, mass or energy out put. Wher eas m an y si mula tion s or dif fer entia l eq uat ion models are excl usively based on cells that ex hib i t some form of Brownian motion , en t i ti es (cells) i n Senti nel mo ve accord ing to the chemi cal sti m uli they receiv e, th ei r mo tor c ap abi li t ies , and Numb er of immune c e l l s Numb er of immune c e l l s 10000 14000 18000 22000 10000 12000 14000 16000 Numb er of immune c e l l s Numb er of immune c e l l s 12000 14000 16000 18 000 20000 2 2 0 0 0 10000 12000 14000 16000 100 Ga rret t e t al . 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0 100 200 300 400 500 0 100 200 300 400 500 Time Time Fig. 5.5. Graph s of the the ory simulation s, “N et work” and “All” ( top to b ottom) for a sm all t i m e gap (50 gen eration s, left colu mn) and a longer tim e gap ( 350 gen- erat ions, ri gh t colu mn), av er aged ov er 20 ru ns. ex t e rna l forces act ing upon t hem . The phy sics engine ensur es tha t m o v e men t i s as real is t ic as p ossib le, and is a no v el featu re of ou r sys te m. A c hem is t ry engine is res po nsibl e for mana ging chemica l an d bio c he mical reactio ns, and also the di s t ri but i on of ext ra-ce l l ul ar mo lec ul es thr oughou t t he en vi ro nmen t . F or exam ple, if a cell releases a par ticu lar kind of cyto kine at its lo cation, the chem - istry engine will c ause that cy t ok i ne to gradu ally disp erse across the e n v i ro nm e n t (se e Fig. 5.7, right, for an ex amp le map of den sitie s) by diffu sion. Thi s fea tur e is es se n t i al for the ac curat e simulation of cell m o v em en t b y c he motax is – the pro cess by which immune cells m ov e tow a rds highe r con centra tion s of c he mot actic fact ors, i.e. chemi cals tha t at tract th em. It also enabl es a cell to influ ence a larger e xpanse of its env i ro nmen t than w ould t yp i cal l y b e allo we d in a cellular a uto m a ta. Numb er of immune c e l l s Numb er of immune c e l l s 1 10 100 1000 10000 1 10 100 1000 10000 Numb er of immune c e l l s Numb er of immune c e l l s 1 10 100 1000 10000 1 10 100 1000 10000 5 Mo del ling I mmu nolo gic al M em or y 101 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time 0.1 1 10 10 100 0.1 1 10 10 100 0 100 200 300 400 500 0 100 200 300 400 500 Time Time Fig. 5.6. Graph s of the the ory simulation s, “N et work” and “All” ( top to b ottom) for a sm all t i m e gap (50 gen eration s, left colu mn) and a longer tim e gap ( 350 gen- erat ions, ri gh t colu mn), av er aged ov er 20 ru ns. The im ple me ntati on of c h emotax is is ano ther nov el fea tur e of Sen t i ne l . Cells in vivo are able to resp o nd to v ar i ous chemo tactic m olecules b y det ecting den s i t y grad ients, and mo ving tow ard s the hi ghes t or lowe st de ns i t y of tha t ag e n t [ R a msay 197 2 ]. Th e disp ersa l of c hem ota ct ic mol ecules in Sentin el is calc ulat ed by dis per sing m olec ules from eac h lo cation in the simulation to its nei ghb our s ov er tim e. A cell in the si m - ulatio n is able to access its ei gh t nei ghb our in g lo c atio ns to fi nd out the den si ties ther e, and re t ri ev e th e hi ghes t or low est densi t y of a par ticula r mo lecul e. It can then use this info rma tion to move ac c or di ngl y . Giv en a s e t of en t i ti es and chemi cals ( B-ce lls, a n t ib od ies, m em or y cel l s, cytokin es, etc. ), t he influence of the physics and c hem is t ry engines is defined by a num b er of rules . These rules define when an en ti t y can interact wi t h ano ther cell, and the nat ure of that interacti on; ho w one cell releases chemi ca ls, or oth er en ti t i es, in to i t s near enviro nm ent, and any globa l fea tur es, such as bloo d flow that a ff ect all en t i ti es and chem ica ls. 102 Ga rret t e t al . En titie s Ch emic als Ru les Environ men t Da ta Gra phs An alysis Entities and Chemicals, wit hin the Envi ron me nt, acting ac cord ing to given Rul es Fig. 5.7. (le ft) The struct ure of the Sen t i nel syst em. (rig h t) Sen ti ne l models t h e diffusion of chemi cals to i mpl em en t rea listic c hem ota xi s an d, cruci ally , to model the effects of cy t ok i ne s (see te xt). The mai n figure sho ws the di ff e ren t con centra tions of chemi cals ov er a det ai l ed view of the simu lat or’s si mulat ion envi ron me n t. The inset sho ws the lo ca tio n of the de taile d view in the whole space b ein g m o de l l ed. Hav ing defi n ed the simulation model, by cho osing the en ti t i es, c hem i ca l s and rules, the simulator is run and inf orm ation is o utpu t accord ing to user-d efined data-f eeds. These data can the n b e v iew ed in the form of v ar iou s gr aphs and samp les, or strea med to log fil es for analy sis, all wi t hi n the Sen t i ne l s ys t em . It seems likely that thi s simulator arc hi t ectur e will be useful in oth er areas too, suc h as bi o c hem is t ry and abst rac t w ork in genetic and evolutio nary com put i ng. The simulator is comp lemented by a n In t egra ted Dev el op m e n t En vi ro nmen t (I DE) , th at provi des a set of p o werful tools for the rap id dev el opm e n t of new mo del s. The dr ag-a nd-d rop gr aphi cal i n t e rfac es allows the user to quic kly choose sets of agen t s and es t abl is h the li nk s b etwee n t hem , and to se t u p and con nec t areas of the en - vi ro nm e n t, and des cri be the rules of ph ysics that will op erate wi thi n the m. A code ed i t or allow s users to deve lop Jav a-bas ed ex tension s t o t he se basic mo dels , wi t h the ass is t anc e of aut om ated co de- gen erat ion to ols, and a com preh ensive Ap plicat ion Progr amm ers In t e rfac e (A P I) th at p rovid es ge ner al- pur p os e f unc tion s for man ipu- lati ng ag ents an d the envir on me n t. In many resp ec t s, the sys tem is some what simi lar i n nat ure t o pla tfor ms such as Rob o cod e 6 , but far more p ow erf ul . Sen t i ne l can simu late seve ral million cells, hund red s of millions of antibo di es, and their interacti ons, on a t yp i cal high -end de sk t op . Alth oug h t hi s figure v ar ies de pe nd- ing upon the com pl ex i t y of the mod e l, Se n ti nel a pp ears to b e the most p o we rful simulator c urre n tl y av ai labl e, esp e cial ly in view of the comp lex interaction s that it is simulating . Sen ti ne l ’ s abi li t y to si mulat e diffusion is v ery i m p ort an t – cyto kine 6 See h ttp : //rob o co de . so urc eforg e . net 5 Mo del ling I mmu nolo gic al M em or y 103 sig nalli ng b etwee n cells is a vital par t of immun ology . In deed , one of the follo wing exp er iments could not hav e b een imple men ted wi t hout t hi s abi li t y . 5.4.2 Sen tinel Exp erimen ts and T es t s Se n tine l V al idat ion T est s : Before using Sentin el to ev al uat e Ber nasconi et a l’s the ory , w e v al idated its p erf orman ce. Both t he v a lida tio n and the ev a luat ion models ran with of the orde r of 10 8 B-cells. W e reca pitulate d the “No ne”, “Em er gen t ” and “R esi dua l ” exp er iments, as in the pre vious sec tion, but did not i mpl em e n t “Ne t work” b ecause it had li tt le v alue for o ur goals here. By imp lementin g the s am e test s as the B a sic Si mulat ion s, w e set out t o sho w tha t Sentin el w ould w ork at least as w ell as the Bas i c Si mul ati o ns . If the re sults are qua litatively the same the n w e wil l ha v e demo nstrated that Sen tinel can re pro du ce pre vi ous re su l ts . E a c h of our si mulat ions were run ten tim es, in order to ensur e tha t t he res ult s w ere co ns is t e n tl y re pr od uc e d. Se n tine l ‘The ory Ev a l u atio n’ Exp er ime n t : This exp erimen t is de sign ed to ex- plore the veraci t y of Polyc lon al A ctiv atio n Me m o ry , via simulation – some thin g whic h has not been done b efore. W e coul d not use our Basic Si mulati on to ol be- cause the exp erimen t req uire d i mpl em en t ati on of cytoki ne gr adie n t s (of IL-15), and nee ded to b e p erform ed on a mu ch larg er scale to obta in m eani ngf ul resul ts. Only Sen t i ne l could meet these requ irem en ts. The con str uct ion of Bern asconi et al’s mod el is based on the t heory descr ib ed in [ Be rnas con i et al. 2002]. The y sugg ested t he i r t heo ri es as a resul t of in vi v o ex- p erim en ts, and clai m that the ex p e ri men tal res ults prov ide comp elli ng evid ence for bystan der s t i mul ati on o f memo ry B-cell p op ulat ion s. The co mpr ehe nsi ve set of re- sul ts pub lished in [ Be rnas con i et a l. 2002] w ill b e tes t e d aga ins t the dat a from our simulation , so our aim is to simu late the im pli ca tion s o f Bern asconi et a l’s t heo ry , and assess whet her it could indeed b e res p onsibl e for the in vivo res ults tha t they obs erv ed. Desp ite o ur v a lida tio n efforts, the pro cess describ ed ab o v e is fairly limi ted and t he pro cess of par am ete risi ng any simulation is co mpl ex, th eref ore w e ca n only safely lo ok for q ual i t ati v e sim ilarities in b etween the resul t s of Bern asconi et al and those pro d uce d by Se n ti ne l . 5.4. 3 Ass umpt ions In con str uct ing these Senti nel mo dels, a n umb er of ass ump tion s w er e mad e. These hav e b een kept cons i sten t t hro ugh all the si mul ati on s co ndu cte d. Rep e rtoi re: Sen ti ne l ’ s simulat ion rep e rtoire in clude d B-cells, an t i b o di e s, antigen , as w ell as a sign allin g chem ica l. It w as more comp lex i n t e rm s of the en t i ti es used, and used man y orders of mag ni t ud e mo re a ntib o die s, tha n the RI SEs in the Basic Si mul ati ons . 104 Garr ett e t al . Lon ger- lived m emor y cells: Me mor y B-cells liv e longer tha n t heir na ¨ ı v e eq ui v alen ts. In nature, a na ¨ ı v e B-cell t e nd s to live f o r ab ou t 24 hours un l ess it receiv es sti m u lus , a t which p oi n t it is “res cued , and may go on t o live for a few mon t hs [ B e rnas con i et al. 2002] This is ref lect ed i n ou r m o de ls . Anti ge n: A n t i ge n does not re pro d uce or mutat e duri ng t he si mul ati on. Sim pli fied bin ding : As in the b a sic simulations , and i n order to prov i de the b est p ossible p erforma nce, a si mpl ifie d bin ding me chan ism w as used. A strain of antigen is giv e n a n u m b e r b et w een 0 a nd 20,000, whic h rem ains cons tan t across the p op ul ati on . Ev er y new B -cell is ass igne d a rand om n u m b er with in that rang e, and the bind ing success is meas ured as t he dist ance b etw een the t wo n u m b ers . Clonal sele ctio n: In resp onse to antigen , B-cells underg o clonal sel ecti on and h yp er- mutation, as descr ibed by Bu rnet ’s 1959 theory . [ Bur net 19 59] . C ell s tha t hav e b ee n cloned retai n the bind ing intege r v al ue (se e pr evio us b ull et p oi n t ) of thei r par en t , mutated in inver se prop orti o n to i t s bindin g st rength. Si mpl ifie d Immu ne R ep er toir e: The si mulat ion c ons ists of B- cell s , antib o di es and antigen , plus one sign alli ng cy t ok i ne. B -cell T-cell interac tion is not simulated in these tes ts, but are pl ann ed (see F ur ther W o rk). W e needed to keep the model as sim ilar to ou r prev ious sy stem as p ossible (no pla sma cells) to m ake the v a lida tio n pro cess as me ani ngf ul as p oss i bl e. 5.4.4 Sen tinel R esult s Sen ti nel’s V ali d at ion R es ul ts The res ult s in Fig. 5.8 show that S en t inel c orrectl y p rod uces a secon dary resp ons e to a rep ea t inf ectio n of the same antigen , for b oth memor y t he o ri es . F u rther mor e, Sen t i nel ’ s res ults sho w tha t t he Res idual A n t i gen model mai n t ain ed a consid erably higher p opu l ati on of memory cells and antib odi es – d own to only ab ou t 10 6 anti- b o di es b efore second infec tion, comp ared to of the order of 10 1 for the ot he r memor y models. This rel ates to the B asic Si m u latio ns that sho wed the res idua l anti gen p op- ul atio ns had more an t i b o di e s. In b oth s imul ator s, the mo dels of the Emerg ent, ‘ pr eserv ero n’ t he o ri es sus tai ned goo d sho rt-ter m me mor y , and in b oth si m u lato rs we observe d the mem ories stor ed in this man ner failing when the cel ls carr ying t hem died. Unl ess we acc ept tha t the prima ry i mmun e res p ons e pr od uce s me mo ry cells tha t live for y ears, s uc h models wil l alwa ys re sul t in an i mm u ne mem ory tha t fades o ve r t i m e . The mod el of the Res idu al Antig en theo ry sus tain ed a stab le leve l of memor y cells in b oth simula tors , and was able to pro d uce a sub sta n ti al sec on dary res p ons e reg ardl ess of the len gth of time b e t wee n the fir s t inf ect ion and sub s eq ue n t re- inf ectio n. It app ears to b e a vi abl e m o de l of imm u ne me mor y; ho wev er, the req uirem ents to sust ain su c h a sys tem seem unl ikely to be m e t in na tur e b ec au se the imm une s ys tem w ould hav e to pr o duce such mat eria l ov er a highly ex t e nd ed p eri o d. In deed t hi s p oi n t w as debat ed seve ral y ears a g o [ Mat zi nge r 199 4a] . N u m b e r o f A n t i b o d i e s N u m b e r o f A n t i b o d i e s 5 Mo del ling I mmu nolo gic al M em or y 105 9 . 0 E + 0 8 8 . 0 E + 0 8 7 . 0 E + 0 8 6 . 0 E + 0 8 5 . 0 E + 0 8 4 . 0 E + 0 8 3 . 0 E + 0 8 2 . 0 E + 0 8 1 . 0 E + 0 8 0 . 0 E + 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 1 1 0 0 0 1 1 2 0 0 1 1 4 0 0 1 1 6 0 0 1 1 8 0 0 1 T i m e 9 . 0 E + 0 8 8 . 0 E + 0 8 7 . 0 E + 0 8 6 . 0 E + 0 8 5 . 0 E + 0 8 4 . 0 E + 0 8 3 . 0 E + 0 8 2 . 0 E + 0 8 1 . 0 E + 0 8 0 . 0 E + 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 1 1 0 0 0 1 1 2 0 0 1 1 4 0 0 1 1 6 0 0 1 1 8 0 0 1 T i m e Fig. 5.8. V ali dation grap hs for the n umb er of cells o v er arbi trary t i m e for: (i) the Em er gen t /‘ Pre s erv eron’ mod e l, and ( ii) the R esi dua l Antig en model. A n t i ge n A is inje cted at t=3 000, and t = 13 ,0 00. Alth ough t here are some dif fere nces in the de tails, such a s the m ore pron ounc ed seco ndary p eak in the se con dar y re sp ons e, w e consi der the t wo simulators similar enough to pro ceed with t he q ual i t ati v e comp arison of the in vivo and in silic o resul ts. One adv antage of Sentin el is tha t w e c an now di s t i ng ui s h b et w een the sec on dar y res p ons es from the v ar ious th eorie s: (i) the ‘ Pres erv on’ mo del has a wide resp ons e, but it does not lead to as many a n ti b o di es b eing creat ed, and the after -resp on se is small, and ( i i) the R esi dua l Antigen model has a shar p, me dium he i gh t sec on dar y res p ons e, wi t h a m uc h exten ded, exp on en ti ally decre asing aft er-res p on se. Our previou s exp eriments w ere t oo coars e-graine d to provide res ult s that had mean- ingful dif fer en ces, and t he curves they pr od uce d w ere an alm ost p erfe ct e x pon en ti al 106 Garr ett e t al . follo w ed by a slo wer, alm os t p erf ec t ex po ne n ti al d ecr eas e. Intere s ti ngl y , the re is a sli gh t ‘wobble’ at the end of th e ex p one n t i al de crea se, w hi c h is also cons i sten t with the aft er r esp onse w e see i n th e gr aph s of Fi g. 5.8 . These exp erim en ts sho w that w e can repro du ce the re sults of t he Basic sim ula tions, but with finer re sol uti on. Sen ti nel’s ‘ Th eory Ev aluati on’ R es ul ts Since we sta ted in the ‘ E xp er imen t s and T es ts ’ subs ection th at w e ha v e not v ali dated the fi ner- grai ne d el em ents of Sen ti ne l ’ s resu l t s , we will com pare the res ults, in a qua litati v e w ay . Fig. 5.9 shows t wo pl ots from Se n ti nel – each for di ff ere n t mo del par amet ers – and a prese n t ation of the graph from [ Bern asconi et al. 20 02] . Note tha t the Anti-A plot, cause d by re-inj ected Antigen A, in ( top ) and (mi ddle) has a shall o wer p eak than the pl o t of An t i- TT in t he b ott om pl ot. The par am eter v al ues for t he (top ) g rap h yield p o or re sul ts, but in (mi ddle ) are b ette r, assum ing w e use the se ction of grap h from tim e index one to five . The need to find go od pa r am eter s is disc usse d in the F urt her W ork sect ion b elo w. Bot h par amet er c hoi ces resu l t in some fea tures of t h e Bern asconi et al plot but the r elative inc rea ses seem to in dic ate tha t here is some degree of mat c h b et wee n the simulat ed ( midd le) and in v i vo (b ottom) re su l ts . Alth oug h not p erf ectl y conf irm ed, a simulation of Bern asconi et al ’ s the ory has b ee n sho wn to b e qu alita tively reas ona ble, relat ive to t he in vivo meas ureme n t s. But wh at causes the qua n tita tiv e di ff er e nc e s? The dis par i t ies may be due to: (i ) inc orr e ct mo del ling of the Bern asconi et al t he o ry ; (ii) lack of detail in the model; (iii) inc o rr e ct p ar ameterisation of tha t model, and /or (iv) a fund amental ly faulty the ory und erlyin g the model. The next step is to isol ate the cause of dis par i t y . The fir s t and l as t of these p oi n t s can b e addr essed by op e ning a dia logu e w ith Bernas coni ’ s gro up, but p oi n t s (ii) and (iii) will requ ire si gni fican t fu rth er work, as descr ibed b elow . In co nclus ion, the si m u late d the ory of p oly clona l ac tiv at ion pro duc ed i nteres t i ng results, simil ar to those obt ained by res idual antigen the ory , but with ou t r equ iri ng a long-liv ed sup ply of antigen . The si gna l li ng pr ovide d by IL-15 seems to b e ess ential for this ph eno men on . It a pp e ars consi sten t wi th na tur e’s e ffi ci en t wa ys tha t the b ody w ould use t he const an t atta c k by antigen to stre ngth en itself, and we hav e dem on- str ated a p oly clo nal me mor y effect that is qua litatively s imila r to the exp erimen t al obs erv a tions of [ Bern asconi et al. 20 02] . 5.5 F urth er W o r k The l ogical exten sion of our basic model of p oly clo nal m em ory is t o creat e a more det ailed B -cell /T-c ell and AP C model, a n d the n to use t hat as the basis for a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Memory cells / v o l u m e Plas ma cells / 10 ^6 Blood c e l l s Mem ory cells / v o l u m e 5 Mo del ling I mmu nolo gic al M em or y 107 Anti-A Anti-B 10 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.1 Time after antig en re - injecti on Ant i-A Ant i-B 100 0 100 10 1 0.1 Time after antigen re-infectio n 100 00 100 0 100 Ant i-me asles Ant i- T . Gond i Ant i- TT 10 1 0 5 10 15 20 25 0.1 Day s aft er TT injection Fig . 5.9 . (to p and mi ddl e) Plo ts of the memory cell-lev el s p er v olume for t wo antigens, A and B, which are to o dissim ilar to dir ectly cause a resp onse in each other’ s me mory cells. The i mmu ne s ys t e m has alr eady b een exp ose d to b o th Antigen A and B; An t i gen A is re- i n t ro duc ed at t=0. (top ) and (m iddl e) are for t wo di ff er e n t m o del par ameter isation s (see tex t). B oth cases show an unex pe cted i ncr e a se i n the mem ory cells that are speci fi c to the non -inj ected antigen . Si nce pla sma cells lev els are rough ly lin ear, rel ative to memo ry cell lev els, the in silic o res ults are qual itatively consi sten t with the in v i vo Ber nas c oni ’ s res ults (b ottom ). 108 Garr ett e t al . co m b ined model atte mptin g t o si m ula te the lates t th eorie s of b oth B- and T-cell me mory . Once such a model has b ee n imp lemented, we ca n b eg in to explor e qu estions sp ecifi cally sur roun din g the rel ati ons hi p b etween B- and T-ly mpho cy te memory , and look at new rules for pla sm a cell and memor y cell creat ion, deat h and ho meost asi s. As mentioned ab o v e, the leve l of det ail of a simulation sho uld b e as si m p le as p os- sible, b u t a simulati on t hat is too si m p le will n ot b e as effective. This is a stand ard dilem ma of m a c hine lear ning h yp ot he s is gen erat ion, and w e inten d to add ress this issue by mean s of aut om ati c feedbac k . In oth er w ords, we will gen erat e a p op ulati on of si mul at i ons, a nd the n evo lv e t hem to find t he simp lest, m os t effectiv e ca n di dat e m o del . The ch oice of para met ers for any model is known to b e a hard pr obl em [Ljung 1999], but cre atio n of the mo del is m uch har der [King et a l. 20 05] . W e ar e exam ining sev era l m e t ho ds of ass isted par am e t eri sati on of t he models, so tha t a ‘ b es t -fit ’ can b e found by Sentin el. This wil l al low the res ear ch to fo cus on the scie n t ificall y i nteres t i ng m o del - b ui l ding tas k, ra ther t han the more me chan ical par am e t eri sati on t ask , an d wil l help to re move four of the p oss i bi li t ies for the dif fere nces in b et we en the in silic o and in vivo res ults in the pre vious se ction. One of our long -term goals is to pro d uce an i n t e gr a te d mo de l o f immu nological mem - ory tha t ex plain s the ex pe rim ental e vid enc e used to sup p or t man y of, if not all, the theori es exp lored here. Suc h a m o del could b e used t o explore more det aile d issues in imm unologica l m em or y , such a s the unusua l effects of the SA P gene (wh ic h controls l on g-ter m me mor y , but has no effect on sho rt- ter m me mo ry ) [ Crott y et al. 2003]. F u rther mor e, a gen eral t heory of immu nological memor y w oul d hav e imp licatio ns for machine l ear nin g. The app licatio ns de scrib ed here are mos tly r elate d to i mm unology , a nd indeed that is the main fo cus of our work. No neth ele ss, our Sen ti ne l pl atfo rm is li kely to b e useful in AIS endeavours in the futu re, i n par ticul ar when it comes to un der s t and - ing the dyn amics of AIS alg orithm s that are based on co mpl ex s yste ms of age n t s. In addi ti on , simulatin g t he o ri es f rom i mm unology that hav e ye t to b e adapte d b y AIS res ea rcher s can prov ide ass istan ce in det erm ini ng the min imum s et of featu res requ ired in develo ping an abs trac t rep res entat ion of an immu ne m ec han i s m . As Se n ti nel c ontinu es to develop, and b ecome s eve r m ore sop hi sti cate d, we will b e able to d ev elop lar ger, more comp lex m o del s tha n at pr esent. I t will b e i nteres t i ng to see if the in cre ase i n c om pl e xi t y is imp o rtant, or wh ether there is a lev el of com pl ex i t y that is su ffi ci en t for the m a jori t y of immuno logic al resear c h.