System Dynamics Modelling of the Processes Involving the Maintenance of the Naive T Cell Repertoire

System Dynamics Mo delling of the Pro cesses In v olving the Main tenance of the Naiv e T Cell Rep ertoire Grazz iela P . Fig uered o IMA Research Group Sc ho ol of C om p ut er Sc ienc e University of No tti n gh am Nottin gham, NG 8 1B B UK gzf @cs .no tt.a c.uk Uwe Ai c k e lin IMA Rese arch Gr oup S c ho ol of Co m p ute r Sci ence University of No tti n gh am N ottingham, NG8 1B B UK u xa@c s.n ott.a c.u k Am a nd a Wh it br o ok IMA Resea rch Gr oup S c ho ol of Co m p ute r Sci e nce University of N ott in gh a m N ottingham, N G8 1B B UK a mw@ cs .no tt.a c.uk Abstract The stud y of immune s yste m agin g, i.e. immunose nesce nce, is a rela tively new re- search topic. It de als wit h und ers tand - ing t he pro ces ses of im m un o-d eg ra d atio n th at indic ate s igns of fun ction ali ty loss p ossibl y lea din g to deat h. Even tho u gh it is not p ossi ble t o pr ev en t im m un os e- nesce nce, there is great be nefit in c om- pre hen ding its ca uses, which may he lp to re verse some of the da ma ge d one an d thus im prove life exp ec tanc y . O ne of the main f actors influe ncing the pr o cess of i m- munosenesce nce is the number and ph e- notypical v ariety of naive T cells in an in- dividu al. This w ork pre sents a review o f immunose nesce nce, prop oses syste m dy - nami cs m o dell ing o f the pro cesse s inv olv - ing the maintena nce of the naive T ce ll rep e rtoire an d prese nts some pre lim inary res ult s. 1 In tro duct ion The stu dy of ag ing in human b ei ngs is a r el- atively new resear ch topic and deals with un- der st an d ing the pro cess es of tissue deg ener atio n so tha t the y ca n b e st opp ed or slow ed down . Some st ages of d egr ad at io n indic ate si gns of funct ion ality loss tha t prec ede the end of life. Ev en t houg h it is not p ossible to pr ev en t agin g , there is great b enefi t in und e rst a nd in g its caus es, which may help to re v erse some of the d am ag e done and t h us i mpr ov e life exp ectan cy . This work is c oncer ned wi th the agi ng of the immune s y st em ( IS), kn own as im muno sen es- cence. The IS acts to fi gh t and pr ev en t ma n y kinds of dise ases in an i ndiv idual thro ugh out life. H ow ev er , wit h a ge ther e is a deca y of the IS per forman ce resu lti ng in d egenera tive d isease s, der eg ula ted and ineff ective im m u ne res p ons es . This c an end up in comp lete c ollapse of t he de- fence mechanisms resulti ng in deat h. V ari ou s theorie s h av e bee n prop ose d to e x plain this p he- nome non, i nclud ing the levels of antigenic st ress , oxidatio n, lack of cellular res ources and D NA damage. I n order to inv es tigate how the IS a ge s and fa ils it is necessar y to un de rst and the pr o- cesses b y wh ich the ins tabi li ties ta k e place, de- v el op, pro p ag at e and turn o ut to b e destr uc tiv e. By a cqu iring suc h knowled ge i t woul d b e p os- sible to crea te pr edicti ve mo del s th at can es ti- mate th e immune fitne ss of a pa tien t at a ce r- tain a ge gi v en t heir v ac ci n at io n hist ory , exp o- sure to d ise ases and h emogr ams. M oreove r , th e kno w led ge could b e a pplie d t o any other agin g pro cess, sin ce ther e ar e ma ny scientific, so cial, security , e ngineer ing, ec onomica l an d co mp ut a- tionall y imp ort an t proble ms d eman d in g des ign s with mo re pre dict ab le degener ative a ss o cia te d pro p er ti es. A deg enerati ve system is o ne th at, thr ou g h a series of sequential e v ents, devolves in ti me un t il it re aches a p oin t wher e its fu nctio n ality is compr omise d. T r ying to predict w hen a certai n syste m will n o longe r work p rop erl y to sat isf y its original purp ose ha s great b enefit b eca use th e syste m ca n b e rep laced, u pgr aded or red es igned bef ore t his p oin t is rea ched. Th is has p ote n tia l implicati ons f or the saf ety , sec urity and w el fa re of res ource s such as water, ai r transp ort, energ y , pro duct qua lity , com pu te r netwo r ks and c on tro l. There are many f actor s th at can cause a sys- tem t o dete rior ate. F r om the hardware in ter- acti ons per sp ect iv e a gin g refe rs to progr es siv e per forman ce d egr ad a tio n or a su dden hang or crash of a s ystem due t o ex hau st ion of op er ati ng syste m r esources and ac cu mu la tio n of pr ob le m s. Another ca use is the negli gence of a sys tem’ s o wner s to mo di f y it to meet changin g n ee ds and new dema nds i n the ma r k et, such as ne w so ur ce s of info rm atio n, new pr oce s ses and t ec hn ol og y upgrade s. Ot her ag e- ass o c iat ed proble ms can occ ur a s the r esult o f changes tha t are mad e witho ut prop e r testing, intro duci ng ne w fai lu r es. Someti mes system s manufa ctur ers find it d iffi- cult t o k ee p up wi th the market and to comp ete with new pro du cts . This work prese n ts a re vie w of the immunose nesce nce ph en o m en on and in- cludes a descr ip tion of t he v arious the ories tha t could b e used f or m o delli ng and developing algo - rithms for solvin g deg ener ati on proble ms. Als o, a prop o sal for a f irst simulati on mo del and s ome preli min ary resu lts a re pr es en ted . 2 Imm unos ene sce nc e Accordi ng t o B ulati et a l. [ 2], a ging is a c om - plex pro cess tha t negati v el y im pacts the dev el- op men t of t he im mune s ystem and it s a bility to function . Progress ive cha nges in the innate and adaptive immune syste ms h av e a ma jor im pa ct on t he ca pacity of an ind ividual t o pro duc e ef - fecti v e immune r esp onses . These chan ges tha t c h aract eri ze the a ging of t he immune system ar e called immun osenesce nce. The decre ase of im- m un oc omp e tence in t he e lde rl y c an b e envisag ed as the res ult o f the continuous challen ge of the unav oida ble exp osure to a v ariety of p ot en tia l antigens, i.e. viruse s, bact eria, fo o d an d self- antigens [5] . Antig e ns are the c ause of a p ers is - tent life-l ong antigenic stress , re sp onsible for the filling o f the immunol ogical spa ce by ac cu mu la - tion of ef fect or T c e lls and immunologica l mem - ory [ 5] . With age, the re is a lso a s igni f ica n t re- ducti on of n aive T cells c ause d b y t he inv olut ion of the t hy mus. This situ at ion even tual ly leav es the b o d y m ore susce ptible to infec tious a nd no n- infecti ons dise ase s [8]. I n add it ion , there is e vi- dence tha t cl onotypical immunity de ter io r at es, while an ce st ra l innate or natur al immunity is conserved or ev e n up- reg ul at ed [5, 10] . Acc ording t o F rance schi [5], some facto rs tha t char act eri ze im munosenesce nce are the ac- cu mu lat io n of me mor y T ce lls, the decrease an d exh au sti on of nai v e T cell s a nd a marked r edu c- tion of the T ce ll rep er toire. Bulati [2] , o n the other hand, b eli eves b ot h innate a nd ad apt iv e immunity are usuall y involv ed in the pat hog en- esis o f chronic age-r elated disease s l ike arthri - tis, ath ero sc ler os is, osteop orosis, diab etes, etc. Ho wever, innate im munity app ears t o be the prev al en t mechanism drivi ng tiss ue dama ges as- sociat ed with d iffe re n t age -rela ted disease s [2] . Thus, a ging is ac co m p an i ed by an age-d ep e nd en t up-r egu lation of t he infla m mato ry resp onse, due to the c h roni c anti genic stress th at i mp in g es throu gho ut lif e up on inn ate immunit y , an d has p ot ential im plicati ons for t he onset o f inf lam m a- tory disea ses. B ulati p oints o ut some imp ort an t factors r elated to aging : • Re acti vi ty of de nd ri tic ce lls t o s elf an tig en s can b e c h ar a ct eri st ic of aging . F urt h er mo r e, this over-react ivi ty induce s T lym p ho cyt e prolifera tion with sub seq u e n t highe r risk of auto i mmu ne di se as es. • H yper act ivate d T cel ls are p ossibl y in- v ol v e d in b one loss a sso c iated wit h v ascu lar disease in aged mi ce . • There is a decre ase i n v ac cine r esp on si v e- ness . De Martini s [6] and F rances chi [ 5] state th at the most im p ort an t chara ct eris ti cs of im m un os e- nesce nce a re the ac cu mu la tio n of memor y an d effec tor T cell s, red uc tion of na iv e T c ells, shrin k age o f the T ce ll rep ert oire and a f illin g of i mmunologica l s pace. The y p oin t out tha t: • The filli ng of immun ologica l s pace with mem ory an d e ffect or cell s is a c on se que n ce of exp osu re to a v ariety of antigens o v er ti me. • Clonal expa nsion of p er ipheral T c ells car- rying re cept ors f or single epit op es of b o th herp es v irus Cyto meg alov irus (CMV ) and Ep st ein - B ar r virus ( EBV ) are comm on in the e lderl y a nd are a s so ciate d with t he loss of earl y m em ory cel ls, an incre ase of T cy to - to x ic c ells a nd a gradual filling of im muno - logical sp ace . • With t he dec line of im mune funct ion there is an incr ease in auto antib o d y frequ en cy . An imp or tan t result of this may b e the l oss of ab ility to dis tingu ish b etw een self and nonself mo le c ul es. • The lifel ong re spi r at ory burst, i.e. re- acti v e oxygen sp e cies (ROS ) causes dam - age to imp ort an t cell ular c omp one nts (li- pidic membrane s, e nzymat ic and stru ctura l proteins and nucleic aci ds) during agi ng . ROS dama ge is cou nter ac ted by sev eral genetica lly controlled e nzymatic and non - enz y m atic antio xid an t defe nse s ystem s. A ll these protec tive mechanis ms ten d to b e- come l ess eff ective wi th age. • An el derl y I S b ec omes more pr edisp ose d to chronic infla mmat or y rea ctio ns and less able to re sp o nd to ac ute an d mass ive c h al - lenges by ne w antigens. Inflam m-a ging, the pec uliar chronic inf l am m at or y st at us w hic h charact eriz es agin g, is under g en etic c on tro l and is de tri m ent al to l ongevit y . It leads to long term t issue dama ge and is re lated to an increa sed mo rtal ity ris k. • The chronic ov ere xp osure to st ress ors d et er- mines a h ighl y pat ho gen ic sustai ned act iv a- tion o f the stress-resp ons e s ystem l eadin g to a progre ssively re duced ca pacity to re c o v er from str es s- in d u ced mo d ific atio n s. 3 Ev olution ary-b ased Imm unos ene sce nc e De Martinis [ 6] and F r anc eschi [ 5] st ate tha t h uma n immunose nescenc e can b e env i saged as a situ at ion in whic h t he most evolu ti ona ry re - cent, sop hi sti cat ed defen se mech a nisms det e- riorate wi th a ge, while the most e v o lu tion - ary old a n d gross mechanisms are preser v ed or are neglibl y aff ecte d and, in s ome ca ses, up - reg ula ted . Theref ore, the aging of t he im m une syste m i s not a r andom pro ce ss witho ut ru les or dir ecti ons, b ut rat her is s ub ject to e volu- tionar y con str aints . The antago nisti c pl eiotr op y theory of a ging [4] state s th at natu r al se le ctio n has favoured ge nes confer ring sho rt- term b ene - fits to the or ganism at the c ost o f de ter io r atio n in later life. E v ol utionar y i deas lead t o t he b elief tha t the IS has bee n selecte d t o serve ind ivi du - als only until rep r o du ct io n ceases. This me a ns tha t the o ptimum functi onin g of t he IS is on ly guaranteed for the n u mber of y e ars in which an individua l is capable of rep r o d u ct ion [ 4]. Af- ter tha t, all the bio chemic al pro ce sses pro ce ed freel y witho ut any pa st sele ctiv e pressure t o i m- prov e the lif e of that indi v idu al. The tren d of thy mic on toge nesis and i nv oluti on in earl y a ge supp orts this hy p oth esis. Human s had a life ex - pec tanc y of b etw ee n 30 an d 5 0 y e ars t w o ce n- turies ago. N ow a days the IS must se rve ind iv id - uals l ivin g to b e tw een 8 0 a nd 1 20 years, w hi c h is m uch lon ger tha n pre dicte d by ev olu tio n ary forces. Ther efore, o l d p e opl e hav e to c ope wit h a lifelong antigen ic bu rden enc ompa ssin g se v eral decade s of evolu tionar y un pred ict ed exp osur e. This chronic antigenic str ess a nd sub se qu en t in- flam mato ry burde n hav e a ma jor i mpact on sur - viv al and fr ailt y . 4 Ca ndidat es for Imm unose nescence M o de ls The four most infl uential theor ies fr om the ab o v e are selec ted as p os sible can d id at es for bu ild in g com pu ta tio nal ly predict ive s ystems. These the- ories a re immunolo gical space filling wi th mem - ory ce lls, lack of naive T cel ls, t he innate sys te m up- reg ul ati on , and ac cu mu la tio n of T- re gu l ato ry cells. 4.1 Spa ce F ill ing The immune syste m de ter io r ate s with a ge b y losing fun ction ali ty and im mun o c om p ete n t ce lls. More ov e r, it b ec omes l imit ed in its use of re- sources; there is a f inite num b er of T cells in oper ation at any ti me and t o work prop erl y , th e IS nee ds a re serve of nai ve T cells for new in tr u- sions, a nd memo ry cells f or pre viousl y enco un- tered antigens. Wit h a ge, t he rep ert oire of nai v e T c ells s hri nks pr op o rti on ate ly to faced thr eat s, while memor y increas es [5, 6, 8]. Late in l ife th e T cell p op ula tio n b ec omes l ess diverse an d s ome antigen-sp ec ific t yp es of T cell cl ones can gr o w to a great p erce n ta ge of t he tot al T cell p op ul a- tion, which ta k es u p the s pace needed f or othe r T cells, res ulting in a le ss diverse a nd i nef fe cti v e IS. At some p oin t there are not e n ough nai v e T cells left to mou n t any sort of effec tiv e de- fense and the total re pe rt oire o f T lym ph o cy te s is filled with mem ory ce lls. 4.2 Lack of Nai ve T C ell s Bef ore 20 years of a ge the set of na iv e T cell s is sustaine d pri maril y from thymic out put [ 8]. How e ver, in m iddle age t here is a change i n th e source of naive T cells; a s t he thymus inv olut es, there is a consi derable shrinkage in its T cell out - put, wh ich means tha t new T c ells ar e mo s tly pro duce d by p eri pheral expansi on. There is a ls o a b e lief tha t some me mor y ce lls hav e the ir p he- noty p e re verted back to naive c ells [8]. Th es e t w o ne w met ho ds of naive T cell rep e rtoire ma in - tenance ar e not effe ctive [ 8] as the y do not pr o- duce ne w phen otypic changes on lym ph o cyt es. Ra th er , evide nce sh o w s tha t they k eep fill ing th e naiv e T c ell s pace with cop ies of exi stin g cel ls. Theref ore, the age-r elated loss of c lon es of s ome antigen-sp ec ific T cells c ould b e irre ve r sibl e, b e- cause there are no m ore nai ve T ce lls to ma in tain these clones. The se age- rela ted phen omena le ad to a dec ay of p e rforma nce in fighting aggr esso rs. 4.3 Inna te Up -re gul ati on With age there is a de cay in adequ ate funct io n- ing of the mai n pha go c ytes, i.e . ma cr o p h ag es, neu tro ph ils [3] and de nd ri ti c cell s [ 1]. As a co n- sequence , der eg ul ate d immune an d inf lam m a- tory resp on ses o cc ur in old p eople. Th e inv es- tiga tion in t o t he cel lular and mole cular me c h- anism underl ying these disorder s has pro vid ed comp ell ing e vidence tha t u p-r egu l atio n plays a critical ro le in the age -as so ci at ed prob lems of th e immune a nd infl amm ator y resp onses [10] . Th us, innate immunity and a h igh capac ity f or mo un t- ing a str ong infl amm ato ry resp on se, useful at a y oun ger age ca n b ec ome d et rim e ntal later in life . Inflamm- agin g can thus b e consi dered t he mai n ph en o m en on resp on sible fo r ma jor age-r elat ed diseases a nd the evo lu tio n ary price to pay f or an im mune s ystem th at is full y capable o f de- fendin g a gainst infec tious diseases e arlier in life. 4.4 Accu mulatio n of T r eg Cel ls The indi vidual’s ability t o mo un t an eff ect iv e immune resp onse can b e l im ited by reg ul ator y eleme n ts s uch as si gni fic a n t changes i n th e n u m- ber of T regu la tor y ( T r eg ) cell s [ 9] . T r eg cells act t o suppr ess act ivation of the I S and thereby ma int ain immune s y st em ho m eos tas is and toler- ance. The y can accu mulat e or red u ce with age. The ac cu mu la tio n of T r eg cells in th e old inhi bits or preven ts som e imm une res p on se s, i.e . a nti- tumo ral ones. Also, th e re duc tion of T r eg cells migh t comp rom ise the acti v ati on of immune re- sp onses in t he ag ed . T here fore, an imbala nce in T r eg nor mal functi onin g can predisp ose im- m une dysfuncti on. Th is res ults in a h igher ri sk of im mun e- m edi ate d diseas es, cancer or i nfec- tio ns. 4.5 Discu ss ion A sum mar y of t he main chara ct eris tics of the can d id at e mo del s descr ib ed in the pre viou s sec- tions is pre sented in T able 1. The aim of this wo rk i s to develop a mo de l th at cons iders each of these char act eri sti cs and also defin e more simp le mo dels i n order to inv esti gate i ndivid ual asp e cts of the i mmunosenesc ence p hen o m en o n. In par- ticular, si mulation metho ds such as system dy - namics (S D) a nd ag en t base d simulation (A B S) wou l d b e suita ble f or mo de lling t he ph eno men a. An S D appr oach a ims to un de rst and the b e- havior of comp lex s ystems ov er time. It w ork s with feedback lo ops and st o cks an d flows tha t help de scrib e th e s ystems’ no nlin ea ri t y . A BS is concerned with m o delli ng agents to ob ser v e their be haviors giv en changes to the envir on - ment. The m o del prop o sed in this pap e r is bas ed on ref erence [8] a nd inv olves interact ion s tha t influence the naive T cell p op ulat io ns. It is de- scrib ed i n the next se ct io n. 5 Mo del : Naive T Cell Output Some mar k er s of t hy mi c co ntrib u ti on in an in- dividual throu gho ut life are def ined by lev el s of T ce ll re ceptor exci sion circl e (T R EC ) , which is Theo ries Cha rac te rist ics 4.1 4.2 4.3 4.4 Shrinkage of naive c e l ls × × Diver sity d e c r e as e × × F ew clones taki ng s p a c e × × Ex c essive mem ory c e l ls × L oss of cl o ne s × Inf la mm a t ion × × Ex c essive T supp r ess io n × × D e ge n e r at ion × × × × A uto - immu nit y × × × × L ess va c ci ne r es p on se × × × T a ble 1 : M ain chara ct eris t ics of the can d id at e m o d els. one epis omal circula r DN A for med duri ng th e cod ing of the T-cell recept or. TREC p erce n tag e decays with shrink a ge of thymic out put an d ac- tiv ation of naive T c ells. The mo de l pro p os ed here is ba sed o n th e data and e quatio ns ob- tained in [8] , which is c oncer ned wi th estab lis h- ing a n und ers ta nd in g of naive T cell rep ert oir e dynamic s. The mo del’s ob ject iv e is to de ter - mine the li k el y co ntrib u ti on of e ach o f the nai v e T cell ’s sus tai nin g sources, by c ompar ing es ti- mates of TREC (see Fi gure 1). The dyn am- ics of naive pro lif eratio n, TREC and reversal o f mem ory to na ive T ce lls are mo delled ma th e - maticall y . An SD m o del of the math em atica l mo del de scrib ed in [ 8] is prop ose d i n order to repro d uce and f urther investigate t he pro cesse s inv olvin g the maintenanc e of nai v e T c el l p op- ulation s. The v ariable s involv e d are the th ym ic out put rate, the n umbe r of a ctive cell s, the n um- ber of me mor y cel ls turn in g in t o naive c ells an d the number of nai v e T ce lls obt ai n ed by nai v e per iphera l prol ifer atio n. The numbe r and p he- notypical v ar iety of naive T cells i n an indiv idu al is one of the mai n fac tors inf luencin g t he pro ces s of i mmunose nescence . The simu la tion a ims to inv e stigat e the interact ion s between each v ari- able an d t heir relev ance to the maintenanc e o f the nai v e T cell rep ert oi re. 5.1 The Ma the matic al Mo d e l The mat hem ati cal mo del prop osed in [ 8] i s de- scrib ed by the differ ential equati ons ( 1) t o (3 ) bel ow, wher e N is the total number of nai v e ce lls of d ire ct t hymic origi n, N p is the number o f naiv e cells tha t hav e under gone pro lifer atio n, A is th e n umb er of act ivate d ce lls, M is the numb er of mem ory cell s a nd t is t he time (in y e ars). The first differ ential e quati on i s: N p ‾ . N ‾ N ‾ . µ N Figur e 1: D ynamic s of naive T c ell s. cells to memor y cel ls and µ m is the deat h rat e of me mor y cells ( equal to 0.05 ) . Initial S D simu l at ion s using equ atio n s (1) to (3) and appr o xim ated v alues fo r the i nitia l size of each p o pu la ti on of c ells and the rati os th at ru le the kinetics of e ach p o p ul at io n show ed a d ecay in thymic out pu t after t he a ge of ab out t w en t y that b eca me mo re pron oun ced wit h t ime (s ee Figure 2). This v a lida te the resu lts pres en te d in [8] . F ut ur e work will use v a ri at ion s on th e v al ues for t he ra tio v a ria bles used in [8] in ord er to und e rs tan d the imp o rtan c e of e ach indi vidu al in tegr an t in the s ystem. F or exa mple, it is im- p ort ant to establis h how muc h the re v ers ion of mem ory cell s t o a nai ve p hen oty p e rati o i mp ac ts up on the depletion o f nai ve T cell s wit h ag e, th e d N = s e − λ t t s ( N ) − [ λ + µ g ( N ) ] N , ( 1 ) d t 0 p n n p p oin t in time that the s ystem coul d b e define d as losing fun ctio n ali ty , and t he impact of the nai v e w h e r e s 0 i s t h e t h y m i c o u t p u t ( e q u a l t o 1 . 6 5 ) ; λ t i s t h e t h y m i c d e c a y r a t e ( e q u a l t o pro lifer ation rate on the fina l si mul at ion resu lts . l o g ( 2 ) 1 − λ t t 1 5 . 7 ( y e a r − ) ) ; a n d s 0 e s ( N p ) r e p r e s e n t s t h e n u m b e r o f c e l l s t h a t a r i s e f r o m t h e t h y m u s w h e r e s ( N p ) i s t h e r a t e o f e x p o r t o f t h e t h y m u s d e - f i n e d b y : s ( N p ) = 1 . I n ( 1 ) , λ n N r e p - 1 + s ‾ N p r e s e n t s t h e n a i v e c e l l s ’ i n c o r p o r a t i o n i n t o t h e n a i v e p r o l i f e r a t i n g p o o l a n d λ n i s t h e n a i v e p r o - l i f e r a t i o n r a t e ( w h i c h h a s t h e v a l u e s 0 . 2 2 , 2 . 1 , 0 . 0 0 3 , 0 . 0 0 5 i n [ 8 ] ) . µ n i s t h e t h y m i c n a i v e c e l l d e a t h r a t e ( e q u a l t o 4 . 4 ) ; µ n g ( N p ) N r e p r e - s e n t s t h e n a i v e c e l l d e a t h r a t e a n d t h e f u n c t i o n g ( N p ) i s t h e d e a t h r a t e o f b e t w e e n n a i v e T R E C - p o s i t i v e a n d n a i v e T R E C - n e g a t i v e , d e f i n e d a s : b N p Figure 2: D ecay of naive T cells fr om Th y m us. Studies on age- rela ted declines i n CD 4+ T cell fu nction [7] sh o w that there is a red uced T-cell receptor signalin g intens ity , defects i n ac- tivation , d iff erenti ati atio n and ex pans ion after g ( N p ) = 1 + N ‾ p N p a n d s ‾ a r e e q u i l i b r i u m p 1 + N ‾ p a n d s c a l i n g v a l u e s r e s p e c t i v e l y . T h e s e c o n d d i f - f e r e n t i a l e q u a t i o n i s : stimulati on, reduce d pro d uct ion of inter leuk in-2 and i mpaire d a bility t o provide c ognat e he lp to B cell s aft er immun izat ion. These factor s can b e explaine d by th e fact th at, wi tho ut a c on ti n uo us stream of thymic outp ut, T c ells hav e in cr ea se d d N p = λ d t n N + [ c h ( N , N p ) − µ n ] N p + λ m n M , ( 2 ) longe vity to co m p en s ate for the deplet ion of new incomi ng cel ls. Se v era l studies supp ort the f act w h e r e c i s t h e p r o l i f e r a t i o n r a t e ( w i t h v a l u e 0 ( n o p r o l i f e r a t i o n ) o r e q u a l t o µ n ( 1 + 3 0 0 ) ) ; p c h ( N , N p ) N p r e p r e s e n t s t h e n a i v e p r o l i f e r a t i o n w h e r e h ( N , N p ) i s t h e d i l u t i o n o f t h y m i c - n a i v e t h r o u g h p r o l i f e r a t i o n d e f i n e d b y : h ( N , N p ) = that this f orce d long evity o f T ce lls i s s ufficien t for t he accumu lati on of ag e-rela ted CD4+ T cells defec ts. T herefore , p o pul atio n- ba sed mo d - els of T- cell rep e rtoire e voluti on coul d gui de n ew developments for tre ating disease s such as au- toim munity and helping the recov e ry of t he sys- 1 N + N p n p i s t h e d e a t h r a t e o f p r o l i f e r a t i o n - 1 + N ‾ p o r i g i n a t e d n a i v e c e l l s a n d λ m n i s t h e r e v e r s i o n r a t e f r o m m e m o r y i n t o N p , w h i c h h a s t h e v a l u e s 0 a n d 0 . 5 i n t h e e x p e r i m e n t s p r e s e n t e d i n [ 8 ] . T h e f i n a l d i f f e r e n t i a l e q u a t i o n i s : tem a fter depletion ca used by infections, ra dia - tion and ag e.F ut u re work wi ll aim t o develop the SD mo de l i nto a n ABS mo del to simulate c om- p onents, funct ions and inter acti ons invo l ving th e immunosene scence of T cell s, takin g the asp ect s cited ab ov e into cons id eration . This should p er- mit the rep lic ati on of immuno-re sp onses t o st im- d M d t = λ a A − µ m M − λ m n M , ( 3 ) uli at the cell ular le v e l ov er the c ourse of a life- time a nd the simul ation of thymic recon stit ut ion w h e r e λ a i s t h e r a t e o f r e v e r s i o n o f a c t i v a t e d with b e nefit s and pr oblem s asso cia te d. 6 Con cl usi ons Und er sta nd in g immunose nes cence a nd i ts cau ses may he lp to re verse som e of its c onseq uences an d improv e life e xp ecta nc y . Here, t he imp ort an t factors re late d to im munosenes cence have b ee n identified a s the shrin k a ge of t he naiv e T and B c ell rep e rtoire, d ecrease o f innat e i mmune c ell div er sity , filling of the immunol ogical space b y only a few t yp es of ph en o typi c al cl ones, ac cu- m ulati on of memor y cel ls, los s of c lones, inf l am - mation, e xcessi ve T cel l suppressi on, deg en er a- tion, aut o-im munity and a decrease in res p ons e to v ac ci n at ion . O ne of the main fact ors id en ti- fied as inf l ue n t in the pro c ess of im muno sen es- cence is the number and ph en o typi ca l v ar iet y of nai v e T cells in an indi vidu al, which c h ang es with ag e in qu anti ty and diversity . At the b e gin - ning of life, the thymus is the principa l source of naiv e T ce lls. Wi th age, t here is a decay in th y- m us outp u t and a shift b etween the main sou rce of naive T cel ls. It is b elieved th at the sus tain in g of naive T c ells in the or ganism is pr ovided b y per iphera l expansio n, reversi on f r om a me m or y phenotyp e, an d long-l ived T cell s. This work ha s prese nted a re view of the immunosenesc ence ph en o nm e no n and has pr o- p osed exten ding an exi sting S D mo del of the pro cesse s inv olvin g t he maintenance of the nai v e T cell re p ert oire into an ABS mo del. Th is should pr o vide insig h t into h o w much ea ch of the naive T cell su sta ini ng p os sibilitie s i nf lue nc e s the final p o o l of T c ells. Init ial exp eri ments wit h the SD m o del h av e supp ort ed the t he no tion of thy mic decay b e ginnin g at ab out age t w en t y and bec omin g more p rono unced w ith a ge, but the use o f an ABS m o del would pe rmit th e rep li ca - tion of immuno-resp onse s to stimuli at the cel lu- lar level ov er the c ourse o f a lifetime, pr o v iding further in sights i nto the i mmunosenesc ence ph e- nomen on. T he ul tima te goa l of t he ABS mo d el is t o facilitat e suf fi cien t un d ers ta nd i ng of ag ing pro cesse s so th at b o osti ng te c hni ques f or othe r real-world dege nerati v e systems may b e dev el- op e d. References [1] A . Agraw al, S. A graw al, J . T ay , an d S. Gup ta. Biolog y of d end rit ic cell s in ag- ing. J Cli n I mm uno l , 28 :14– 20, 200 7. [2] M. Bul atti, M. P el lica n, S. V asto, an d G. 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