Therapeutic Potential of Bacteria against Solid Tumors.

In eg a ed Sys ems and Technologies: Ma hema ical Oncology The apeu ic Po en ial o Bac e ia agains Solid Tumo s Ha alampos Ha ziki ou 1,2 , Juan Ca los L opez Al onso 1,2 , Sa a Leschne 3 , Sieg ied Weiss 3,4 , and Michael Meye -He mann 1,5 Abs ac In en ional bac e ial in ec ions can p oduce e ficacious an i- umo esponses in mice, a s, dogs, and humans. Howe e , low o e all success a es and in ense side e ec s p e en such app oaches om being employed clinically. In his wo k, we i e ed bac e ia and/o he p oinflamma o y cy okine TNFain a se o es ablished mu ine models o cance . To in e p e he expe imen s conduc ed, we conside ed and calib a ed a umo –e ec o cell ec ui men model unde he influence o unc ional umo -associa ed ascula u e. In his model, bac- e ial in ec ions and TNFaenhanced immune ac i i y and al e ed ascula iza ion in he umo bed. In o ma ion o p edic bac e ial he apy ou comes was p o ided by p e ea - men umo size and he unde lying immune ec ui men dynamics. No ably, inc easing bac e ial loads did no neces- sa ily p oduce be e long- e m umo con ol, sugges ing ha umo sizes a ec ed op imal bac e ial loads. Sho - e m ea - men esponses we e a o ed by high concen a ions o e ec- o cells pos injec ion, such as induced by highe bac e ial loads, bu in he longe e m did no co ela e wi h an e ec i e es o a ion o immune su eillance. O e all, ou findings sugges ed ha a combina ion o in e media e bac e ial loads wi h low le els TNFaadminis a ion could enable mo e a o able ou comes elici ed by bac e ial in ec ions in umo - bea ing subjec s. Cance Res; 77(7); 1553–63. 2017 AACR. In oduc ion Bac e ia o many species in ade and colonize solid umo s (1–3). In many cases, his leads o g ow h e a da ion o he neoplasia, and in he mos a o able si ua ions o comple e umo clea ance (1, 2, 4). This phenomenon has been desc ibed al eady 200 yea s ago (1813) by A s ene-Hippoly e Vau ie , a F ench physician who obse ed ha he umo s o pa ien s sh ank when hey also su e ed om gas gang ene (3, 5). We now know ha hese symp oms a e due o a Clos idium pe ingens in ec ion. Se e al a emp s ha e been ca ied ou o es ablish bac e ia- media ed an i umo he apy in he clinical p ac ice (3, 4, 6). Mos p ominen we e he a emp s o William B. Coley, an Ame ican su geon who success ully ea ed inope able skin cance s wi h hea -inac i a ed bac e ia (3, 7). Howe e , he se e e side e ec s, as well as unce ain ies on he unde lying mechanisms, p e en ed he gene al use o bac e ia as a he apeu ic agen . Cu en ly, in ace o he ac ha cance is he mos equen cause o dea h in he indus ialized wo ld and he second in economically de eloping coun ies wi h a ising incidence (8), no el s a egies ha e o be 1 Depa men o Sys ems Immunology and B aunschweig In eg a ed Cen e o Sys ems Biology, Helmhol z Cen e o In ec ion Resea ch, B aunschweig, Ge many. 2 Cen e o In o ma ion Se ices and High Pe o mance Compu ing, Technische Uni e si € a D esden, D esden, Ge many. 3 Molecula Immu- nology, Helmhol z Cen e o In ec ion Resea ch, B aunschweig, Ge - many. 4 Ins i u e o Immunology, Medical School Hanno e , Hanno e , Ge many. 5 Ins i u e o Biochemis y, Bio echnology and Bioin o ma ics, Technische Uni e si € a B aunschweig, B aunschweig, Ge many. No e: Supplemen a y da a o his a icle a e a ailable a Cance Resea ch Online (h p://cance es.aac jou nals.o g/). H. Ha ziki ou and J.C. L opez Al onso con ibu ed equally o his a icle. Co esponding Au ho : Michael Meye -He mann, Depa men o Sys ems Immunology and B aunschweig In eg a ed Cen e o Sys ems Biology, Helmhol z Cen e o In ec ion Resea ch, Reben ing 56, 38106 B aunsch- weig, Ge many. Phone: 4905-31391-55210; Fax: 4905-31391-55211; E-mail: [email p o ec ed] doi: 10.1158/0008-5472.CAN-16-1621 2017 Ame ican Associa ion o Cance Resea ch. Majo Findings We p esen he fi s sys ema ic s udy ha combines in i o mu ine expe imen s and ma hema ical modeling owa d he mechanis ic unde s anding o he he apeu ic po en ial o bac e ial in ec ions agains solid umo s. In pa icula , we elucida e he in e play be ween g owing umo s, ascula - iza ion, and immune ec ui men dynamics in esponse o bac e ial in ec ions. This s udy sugges s ha be o e he a- peu ic in e en ions, umo size and immune ec ui men dynamics a e c i ical ac o s o long- e m umo con ol. Mo eo e , an a bi a y inc ease o bac e ial loads can be de imen al o ea men ou comes, which sugges s he exis ence o an op imal bac e ia load depending on umo size. The model p edic s ha in e media e bac e ial loads and adminis a ion o low TNFapo en ially inducing umo ascula iza ion can lead o enhanced he apeu ic ou comes in silico. Cance Resea ch www.aac jou nals.o g 1553 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 explo ed o inc ease he spec um and e ec i eness o he apies agains his de as a ing disease. In acco dance, since wo decades, sys ema ic expe imen a ion has been ca ied ou o unde s and he umo -in asi e p ope ies o bac e ia, as well as he mechan- isms ha lead o bac e ia-induced umo sh inkage o clea ance. Recen p og ess in knowledge o hos bac e ial pa hogen in e - ac ion, ad ances in genome esea ch, as well as he de elopmen o new echnologies o manipula e bac e ia allow now o de elop Quick Guide o Model Equa ions and Assump ions Tumo -E ec o Cell Rec ui men Model We conside a ma hema ical model ha combines adial umo g ow h and immune ec ui men dynamics (9) o ga he in o ma ion abou specific umo esponses o di e en he apeu ic combina ions o bac e ial loads and TNFain mice (Figs. 1A–D and 2A). The p oposed model elies on he ollowing main assump ions: 1 The empo al e olu ion o he a e age umo adius is conside ed, whe e in asi e and di usi e umo g ow h a e no aken in o accoun . 2 The dea h a e l A eflec s he lump e ec o apop o ic and nec o ic p ocesses. 3 Inna e immuni y o base immune su eillance is ep esen ed as a minimum p esence o ac i e e ec o cells a any ime, e en in he absence o umo cells. 4 E ec o cell ec ui men a e is a unc ion o umo cells ollowing Michaelis–Men en dynamics. 5 The e ficacy o immune killing depends on he abili y o e ec o cells o pene a e he umo bulk ia he umo -associa ed ascula u e (10, 11). Wi h be e ascula iza ion, he e ec o cells kill umo cells no only on he su ace o he umo bu also u he inside. 6 E ec o cells die wi h a cons an a e and ge inac i a ed in dependence on hei an i umo ac i i y. The sys em a iables a e he a e age umo adius R( ) and e ec o cell concen a ion E( ) in he umo icini y. The ma hema ical model is o mula ed as a sys em o o dina y di e en ial equa ions (ODE) gi en by dR d ¼1 3lMBlA ðÞR |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} ne ascula umo g ow h þlM1BðÞLD 1 anh R=LD ðÞ LD R  |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} a ascula umo g ow h cER RðB1Þ RðB1Þþ1 |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} dea h due o e ec o cells ðAÞ dE d ¼ R3 KþR3E |fflfflfflfflfflffl{zfflfflfflfflfflffl} ec ui men o e ec o cells d1R3RðB1Þ RðB1Þþ1  E |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} inac i a ion o e ec o cells d0E |{z} dea h o e ec o cells þs |{z} inna e immuni y a e ;ðBÞ whe e he ime coo dina e has been omi ed o sake o no a ion simplici y. L D is an in insic leng h scale esul ing om nu ien dynamics, ha is, di usion, supply, and consump ion. We assume ha Bis a dimensionless pa ame e , whe e 0B 1 ep esen s he deg ee o unc ional umo -associa ed ascula u e, ha is, essels ha allow he flow o blood o he umo . The unc ional ascula ne wo k is assumed o modula e bo h he umo g ow h and umo –immune cell in e ac ions as shown in Eqs. A and B. The pa ame e s l M and l A a e he mi o ic and dea h a es o umo cells, espec i ely. Pa ame e c ep esen s he killing a e o umo cells by e ec o s, is he immune ec ui men a e, and Kis he umo olume a which he ec ui men a e is hal -maximal. d 1 and d 0 a e he inac i a ion and dea h a es o e ec o cells, espec i ely, and sis he backg ound a e o immune e ec o ec ui men . L D ,B,l M ,l A ,c, ,K,d 1 ,d 0 ,andsa e posi i e cons an s. Fu he de ails abou de i a ion, pa ame iza ion, and heo e ical analysis o he umo -e ec o cell ec ui men model can be ound in e . 9. The apeu ic Po en ial Defini ion The apeu ic po en ial TP (p): O p ![0, 1] is in e p e ed as he a e age umo con ol, ha is, a io be ween cases whe e he umo adius s ays bounded o e all he possible cases, wi h espec o a ce ain egime o model pa ame e p2{B, , R 0 } gi en by TPðpÞ¼ Ð Wp HR SðpÞRp;  ðÞ½dp Ð Wp HRp;  ðÞ½dp ;ðCÞ whe e ¼100 days (abou 3 mon hs) is he a ge ime, R S (p)is he umo adiusa hesaddlepoin (Fig.2B),andH()isa Hea iside s ep unc ion (9). We ema k ha mice a e ypically conside ed in a comple e emission s age, ha is, pe manen absence o disease, i hey a e umo - ee a e 100 days o ea men (12, 13). Ha ziki ou e al. Cance Res; 77(7) Ap il 1, 2017 Cance Resea ch1554 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 new bac e ial s ains. They should be me abolically and unc ion- ally a enua ed o ende hem sa e o applica ion in cance pa ien s and a he same ime he apeu ically highly po en (14). In pa allel, a emp s a e made o employ such bac e ia and hei umo - a ge ing ea u es as ca ie s o he apeu ic com- pounds like oxins, which can be exp essed di ec ly in cance ous issues (15–17). Ac i e chemo ac ic mechanisms o bac e ia a ge ing and colonizing solid umo s ha e been sugges ed o Salmonella based on in i o da a (18). Howe e , di e en species o bac e ia ha lack hese p ope ies we e s ill able o a ge cance ous si es in immunocompe en mice (19). A passi e al e na i e has been ecen ly p oposed (20). Namely, upon sys emic applica ion, G am-nega i e bac e ia elici a cy okine s o m ia hei endo oxin. The domina ing cy okine is mos likely he umo nec osis ac o TNFa(20). As a consequence o he cy okine s o m, he leaky pa hologic blood essels o he umo open and a se e e hemo - hage is induced. This lea es a la ge nec o ic egion behind a e he hemo hage has been clea ed. The acul a i e anae obe Sal- monella migh be simply flushed in o he umo du ing he blood influx. Salmonella hen p oli e a e in he immune-p i ileged si es p o ided by he nec o ic and hypoxic egions o he umo , and e en ually sca enge on he dead cells. The hemo hage and induc ion o nec osis also explains he umo g ow h e a da ion ha is obse ed a e applica ion o he bac e ia (20). Final umo clea ance is mos likely due o he induc ion o a specific immune esponse agains umo an igens ha is ac i a ed by he adju an e ec s o he bac e ia (21). Howe e , mos o he umo s eco e om he o iginal a ack by bac e ia and e en ually con inue o g ow. Immune escape mechanisms o he neoplasia migh be esponsible o his phenomenon (22). The e o e, a mechanis ic unde s anding o he biology o bac e ia-media ed he apy is o u mos impo ance o he u he de elopmen o such a high po en ial an icance ea men . In his wo k, we conside in i o mu ine umo s ea ed wi h di e en bac e ial loads and/o TNFa, and eco d he co e- sponding umo olume e olu ions be o e and a e ea men . Then, we use a ma hema ical model ha combines ascula ized umo g ow h and e ec o cell ec ui men dynamics o gain insigh s in o he possible easons o success o ailu e o bac e ial he apies. Ma hema ical models ha e been a he success ul in in es iga ing he biology o cance (23–26) and a e becoming an inc easingly impo an esou ce o add ess immunologic ques ions (27–29), as well as use ul o op imiz- ing and p edic ing an i umo he apy ou comes (9, 27, 30–36). Model analysis no only p o ides a quali a i e and quan i a i e explana ion o expe imen al esul s, bu also allows o no el he apeu ic s a egies. Ma e ials and Me hods Mice, bac e ia, and cell lines BALB/c mice we e pu chased om Jan ie Labs. All ecom- binan mice we e b ed a he Helmhol z-Zen um ü In ek ions- o schung and all expe imen s we e pe o med wi h emale, 8- 12-week-old mice i no s a ed di e en ly and unde app o al o LAVES (Niede s€ achsisches Landesam € u Ve b auche schu z und Lebensmi elsiche hei ); Pe mission: 33.9-42502-04-12/ 0173. S. Typhimu ium SL7207 [hisG46, D407(a oA544::Tn10)] and E. coli TOP10 we e g own on LB aga wi h 30 mg/mL s ep omycin a 37C. CT26 (ATCC CRL-2638) cells we e cul u ed in IMDM supplemen ed wi h 10% FCS, 100 U/mL penicillin, and 100 mg/mL s ep omycin, 50 mmol/L 2-me cap oe hanol, 2 mmol/L L-glu amine, and main ained a 37C and 5% CO 2 . The F1A11 (H-2 d ) cell line is a mu ine fib osa coma ha exp esses b-galac osidase (b-gal) and was ob ained by ansduc ion o spon aneously ans o med BALB/c fib oblas cell line F1 wi h he LBSN e o i al ec o (37). Cell lines used in he s udy we e ob ained in he yea 2000. Tumo g ow h and bac e ial in ec ions Tumo s CT26 and F1A11 we e se by injec ing 5 10 5 cells in 100-mL PBS subcu aneously. G ow h was moni o ed by calipe . Viable umo olume was calcula ed as V¼4/3p(hw 2 )/8, whe e h ¼heigh and w¼wid h. Fo in a enous (i. .) in ec ion, bac e ia om glyce ol s ocks we e cul i a ed on s ep omycin LB pla es o e nigh . Single colonies we e esuspended in PBS and adjus ed o 10 3 o 5 10 6 bac e ia in 100-mL PBS. Bac e ia we e injec ed in o he ail ein o he animals, as soon as he umo had eached a olume be ween 100 and 200 mm 3 . Simila ly, 1 mg o ecom- binan TNFain 100-mL PBS was injec ed in a enously. Fo analysis, o gans we e homogenized in 0.1% ( / ) T i onX-100/ PBS and homogena es we e pla ed on s ep omycin LB pla es. Pa ame e calib a ion o he p einjec ion umo g ow h phase (days 0–9) The p oposed ma hema ical model gi en by Eqs. A and B was fi s calib a ed o he un ea ed phase o umo g ow h (days 0–9). The p einjec ion umo e olu ions in Fig. 1 desc ibe simila g ow h a es han hose obse ed in immunocomp o- mised Rag1 / , which canno p oduce unc ional T cells and B cells, and wild- ype (WT) BALB/c mice expe imen s (9). As he expe imen al p o ocols o un ea ed umo s a e he same, and he umo olume in hese expe imen s was quan ified daily ins ead o e e y wo days (Fig. 1), we expec mo e p ecise pa am- e e es ima es. The e o e, we conside he alues o model pa a- me e s o he un ea ed (p einjec ion) phase o umo g ow h (days 0–9) as hose ha we p e iously es ima ed om Rag1 / and (WT) BALB/c mu ine umo g ow h expe imen s (9). Mo e p ecisely, we calib a ed he in insic umo pa ame e s, ha is, he ne p oli e a ion a e lp, he deg ee o unc ional ascula iza ion B, and he a e age leng h o nu ien g adien L D om immunocomp omised Rag1 / mice expe imen s (9). The con ol immune- ela ed pa ame e s such as he dea h a e o umo cells due o e ec o cells c, he immune cell ec ui men a e , and he ini ial concen a ion o e ec o cells E 0 , we e es ima ed om (WT) BALB/c mice expe imen s (9). The es o pa ame e alues we e aken om ea lie s udies o umo - immune dynamics (30, 38–40) and a e summa ized in Supple- men a y Table S1. Model pa ame e s pos injec ion (days 11–21) we e calib a ed on he basis o expe imen al da a o umo s ea ed wi h di e en combina ions o bac e ial loads and TNFa(Fig. 1A–D). As ini ial condi ions, we conside he umo adius R 0 a day 1 pos injec- ion, and es ima e he concen a ion o e ec o cells E 0 a day 1 pos injec ion, as well as he immune ec ui men a e and deg ee o unc ional o umo -associa ed ascula u e Bpos injec ion. In all cases, we assume ha E 0 and B a y up o 4.0 10 6 cells and 0.20 a day 1 pos injec ion, espec i ely. These anges o alues a e based on he po en ial de ia ions om he p einjec ion pa a- me e s due o he as dynamics aking place du ing he fi s day pos injec ion. Immune– umo dynamics can be also assumed Bac e ial In ec ions agains Solid Tumo s www.aac jou nals.o g Cance Res; 77(7) Ap il 1, 2017 1555 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 di e en be ween indi idual expe imen s, implying a ia ions on he immune ec ui men a e , anging om 0.4 o 0.7 day 1 . The es o pa ame e alues o he model a e conside ed as in Supplemen a y Table S1. To educe he unce ain ies due o he fini e numbe o obse - a ions, a boo s apping p ocedu e was implemen ed o ob ain he pa ame e es ima es o a e age umo esponses (Table 1). The goal was o ob ain eliable es ima es o he summa y s a is ics by means o a esampling p ocedu e. Di e en nonpa ame ic se s o boo s ap samples we e a ificially gene a ed and ep esen he na u al a ia ion o he expe imen al da ase s (41, 42). The esul ing means and s anda d de ia ions o such samples we e conside ed o pa ame e calib a ion. Fi ing p ocedu es o each expe imen al se ing s a om a la ge numbe o di e en an- dom ini ial condi ions, as well as by andomly pe u bing he pa ame e se o be es ima ed, whe e he solu ions wi h lowes esidual a iances we e selec ed in each case. S a is ical analysis We ha e used he nonpa ame ic one- ailed Mann–Whi ney U es o s a is ically es whe he wo expe imen al ea men s come om he same dis ibu ion. A K uskal–Wallis es was conduc ed o compa e whe he mo e han wo expe imen al samples sha e he same dis ibu ion. S a s ep esen compa isons wi h P alue less han 0.01. Resul s T ea men wi h bac e ia and/o TNFahas he po en ial o induce umo clea ance in i o Tumo s de eloped in BALB/c mice un il day 10, ollowed by injec ion o di e en combina ions o bac e ial loads and/o TNFa. The subsequen umo esponses o ea men we e mon- i o ed o he ollowing 11 days, which ep esen s a o al expe - imen al ime o 21 days. Figu e 1 shows he phases o un ea ed umo g ow h and pos injec ion o ou di e en he apeu ic p o ocols. Injec ion o a low bac e ial load was able o con ol umo g ow h in some bu no all cases (Fig. 1A). In wo expe i- men s, umo g ow h showed only a sligh delay in esponse o he he apeu ic in e en ion. Inc easing he bac e ial load induces a mo e homogeneous eac ion (Fig. 1B). All moni o ed umo s we e educed in size, bu none o hem was e adica ed. Injec ion o TNFaalone o in combina ion wi h he low bac e ial load induced a consis en educ ion o umo olume in all mice and e en leading o umo clea ance in some cases (Fig. 1C and D). These expe imen al esul s p o ide in i o e idence ha he impac o bac e ia and p oinflamma o y ac o s on umo g ow h is di e se and depends on he concen a ion o injec ed bac e ia and/o TNFa. While i becomes clea ha pa icula choices o bac e ial loads a o umo bu den educ ion and in he mos a o able si ua- ions induce umo clea ance, his obse a ion lacks any mech- anis ic insigh . Howe e , be e unde s anding o he easons and mechanisms o he di e se ea men ou comes is necessa y o make his he apeu ic echnique use ul o clinical p ac ice. D i en by he di e si y o ou comes o each expe imen al se ing, we hypo hesize ha he s a e o he mice a he ime o injec ion in e ms o umo olume, p eexis ing numbe , and subsequen ec ui men a e o immune e ec o cells, as well as he deg ee o unc ional ascula iza ion, de e mines he e ficacy o bac e ial he apy beyond he expe imen a ion ime. In i o umo esponses can be ep oduced by a ma hema ical model The de eloped ma hema ical model is pa icula ly designed o allow o long- e m mechanis ic insigh s o bac e ial and/o TNFa ea men success e sus ailu e (see Quick Guide o Model Equa ions and Assump ions). Fo ha pu pose adial umo g ow h, e ec o cell dynamics, and unc ional umo ascula iza ion wi h impac on bo h umo g ow h and ec ui - men o e ec o cells a e explici ly conside ed. P e ea men model pa ame e s we e de e mined om he phase o un ea - ed umo g ow h on he basis o mu ine expe imen s (Supple- men a yTableS1; e .9). Figu e 1. Tumo olume e olu ions (6–7 mice expe imen s) wi hou he apeu ic in e en ions un il day 10, and ea men esponses o di e en combina ions o bac e ial loads and TNFa:10 3 bac e ia (A), 5 10 6 bac e ia (B), TNFa(C), and 10 3 bac e ia and TNFa(D). Ha ziki ou e al. Cance Res; 77(7) Ap il 1, 2017 Cance Resea ch1556 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 The e ec s o bac e ial and TNFa ea men s a e implici ly modeled in he p oposed umo –immune sys em in e ac ion, whe e he umo adius R 0 a day 1 pos injec ion defines he model ini ial condi ions o he subsequen long- e m dynam- ics. T ea men - ela ed pa ame e s, ha is, he ini ial concen a- ion o e ec o cells E 0 , he immune ec ui men a e ,and he deg ee o unc ional umo ascula iza ion Ba e es ima ed a day 1 pos injec ion om he expe imen al da a shown in Fig. 1. Expe imen al e idence sugges ha du ing he fi s 24 hou s pos injec ion, a dynamic in e play be ween bac e ia, immune cells, and umo -induced ascula u e akes place (3, 17, 19– 21). A e day 1 pos injec ion, we obse e a elaxa ion o he a o emen ioned dynamics and he nec o ic co e g ow h, whe e bac e ia se le down and a e p o ec ed om immune a acks. Acco dingly, we assumed in he model ha as p ocesses o umo eo ganiza ion a e induced a e ea men a day 10 o umo g ow h and elax by day 11 (3, 17, 19–21). Du ing his ime, ela ed model pa ame e s, ha is, unc ional ascula i- za ion Band ec ui men o e ec o cells a e modula ed and we assume ha hey emain cons an he ea e . The pa ame e quad uple (R 0 ,E 0 ,B, ) is hen associa ed wi h he indi idual s a e o he mice a he ime o ea men o sho ly a e , and will be used as such when mice a e indi idually dis inguished in he model analysis. To gain insigh on he a e age umo esponses o each ea men s a egy, pa ame e s o in e es a e fi s calib a ed o he mean umo empo al ajec o ies pos injec ion (Fig. 2A). The model quan i a i ely eco e s he mean umo esponses o bac e ial and/o TNFa he apeu ical adminis a ions (Fig. 2C–F). The es ima ed concen a ions o e ec o cells E 0 ,immune ec ui men a e , and deg ee o unc ional umo ascula iza- ion Bpos injec ion a e summa ized in Table 1. E en hough mouse-a e aged esponses o di e en ea men s canno be conside ed conclusi e o he success o ailu e o hese he a- peu ic s a egies, hey can s ill p o ide use ul in o ma ion abou he o e all he apeu ic po en ial o bac e ial in ec ions and TNFap o ocols. Bac e ial in ec ions and TNFaenhance he immune ac i i y and al e ascula iza ion in he umo bed The pa ame e calib a ion o a e age umo e olu ion pos in- jec ion (Fig. 2C–F) e eals ha any combina ion o bac e ial in ec ions and TNFa ea men ele a es he ec ui men a e (Table 1), when compa ed wi h he un ea ed con ol cases Figu e 2. A, A e age umo esponses o he di e en ea men s in Fig. 1, whe e bac e ial loads o TNFaadminis a ion ime is indica ed by an a ow a day 10. B, Es ima es o he c i ical umo adius R S o uncon olled umo g ow h depending on he immune ec ui men a e and unc ional ascula iza ion B. C–F, Fi ing esul s o he model o umo esponses in A, whe e he anges o expe imen al obse a ions o each da ase a e ep esen ed by he shadowed egions. Bac e ial In ec ions agains Solid Tumo s www.aac jou nals.o g Cance Res; 77(7) Ap il 1, 2017 1557 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 (Supplemen a y Table S1). In u n, TNFa ea men s imply inc eased when compa ed wi h exclusi e adminis a ion o bac e ia. The e ec o cell concen a ion E 0 pos injec ion in he icini y o umo s is always highe han wi hou ea men . In e es ingly, high bac e ia loads (5 10 6 ) igge highe E 0 bu lowe when compa ed wi h he co esponding alues induced by 10 3 bac e ia. The abo e obse a ions sugges ha bac e ial in ec- ions wi h o wi hou TNFaenhance he immune ac i i y in he umo bed. We also obse e he des uc ion o unc ional umo - associa ed ascula u e Bwhen mice a e ea ed wi h TNFa.In case ha bac e ial in ec ions a e no adminis e ed wi h TNFa, he alue o Bis p edic ed o emain almos in a ian . All he a o emen ioned model-d i en findings can be deduced om Fig. 3A–D. The ob ious ques ion ha a ises is how hese ea - men -induced model pa ame e cons ella ions impac on sho -, ha is, wi hin he expe imen a ion ime, and long- e m umo dynamics. Figs. 4A–D and 5A–D show he model-fi ing o he indi idual sho - e m e olu ion o umo olume and e ec o cell amoun s a e adminis a ion o di e en combina ions o bac e ial loads o TNFa(Fig. 1A–D). Tumo olume is c i ical o long- e m bac e ial he apy ou comes In addi ion o mean umo esponses o di e en he apeu ic s a egies, we in es iga e indi idual mice and whe he di e ences a he ime o injec ion allow o p edic ea men success o ailu e. Ini ially, we ocus on umo esponses o in ec ions induced by 10 3 bac e ia. This is a pa icula ly in e es ing expe - imen al se ing. I can be conside ed on a e age as a ailu e scena io (Fig. 2A). Howe e , a a ie y o ea men esponses was ound (Fig. 1A). To calib a e , E 0 , and Bwi h espec o his ea men s a egy, we s a ed om he umo adius R 0 a day 1 pos injec ion and he p einjec ion es ima es gi en in Supplemen- a y Table S1 o he o he model pa ame e s. Figu e 3 shows he esul ing pa ame e alues ha accu a ely fi he di e en umo esponses (Fig. 4A; Supplemen a y Table S2). Func ional le els o umo -associa ed ascula u e pos injec ion a e simila o hose in he un ea ed umo g ow h phase (Fig. 3C), bu highe concen- a ion o e ec o cells and immune ec ui men a es pos injec- ion a e achie ed when compa ed wi h he p einjec ion es ima es (Fig. 3A and B). Howe e , ea men induces highe e ec o cell ec ui men a es insu ficien o educe, in mos cases, he umo olume by he end o he expe imen a ion ime (Fig. 4A). The di e se ea men esponses can be g ouped in o h ee cases (Fig. 4A): (i) un a o able umo esponses, expe imen s 2 and 6, (ii) almos in a ian umo olumes be o e and a e adminis- a ion o bac e ia, expe imen s 1, 3, and 5, and (iii) umo educ ion as in expe imen 4. Model simula ions suppo ha he ea men esponsi eness o he umo depends on i s size a he ime o injec ion. Only obse ing he expe imen al cu es, we deduced ha o oo big umo s a day 1 pos injec ion his ea men s a egy p o ides no benefi . Howe e , o su ficien ly small umo sizes, he bac e ial ea men –induced immune ec ui men dynamics a e able o keep umo s unde con ol o educe umo olumes du ing he expe imen a ion ime. Indeed, model analysis demons a es he exis ence o a c i ical umo adius R S , abo e which umo s e ade immune su eillance (9, 34). Conside ing he mean alues o he es ima ed pa ame e s (Supplemen a y Table S2), we can calcula e a c i ical umo adius, R S ¼4.1 mm ha co esponds o a c i ical olume V S ¼ 288.82 mm 3 , which co ec ly p edic s umo escape in expe i- men s 2 and 6 as R 0 >R S a he ime o injec ion (Fig. 4A). A dec easing numbe o e ec o cells pos injec ion is p edic ed in bo h cases (Fig. 5A). Figu e 2B shows nume ical es ima es o R S depending on he ec ui men a e and unc ional umo as- cula u e B. The e exis s a c i ical immune ec ui men a e S depending on B, below which umo g ow h con ol is no achie ed (9). Bu , o inc easing and dec easing B, he chance o long- e m umo con ol inc eases as R S acqui es highe alues. The mean alue o p edic ed in esponse o his bac e ial load is highe han he co esponding c i ical immune ec ui men a e S ’0.49 day 1 (Figs. 2B and 3A). Acco dingly, model simula ions indica e long- e m con ol o umo s wi h adii R 0 <R S , ha is, mu ine expe imen s 1, 3, 4, and 5 (Fig. 4A), whe eas o he emaining cases umo s e ade om immune su eillance. Table 1. Immune ec ui men a e , umo ascula iza ion B, and ini ial numbe o e ec o cells E 0 es ima ed om he a e age beha io o he expe imen al da ase s in Fig. 4 Expe imen al se ing B E 0 R 0 10 3 bac e ia 0.52 day 1 0.18 1.30 10 6 cells 3.52 mm 510 6 bac e ia 0.44 day 1 0.17 2.62 10 6 cells 3.40 mm TNFa0.65 day 1 0.04 1.73 10 6 cells 3.32 mm 10 3 bac e ia þTNFa0.56 day 1 0.04 1.71 10 6 cells 3.40 mm Figu e 3. Pa ame e es ima es o he p einjec ion umo g ow h phase and ea men esponses o di e en combina ions o bac e ial loads o TNFa. Immune ec ui men a e (A), numbe o e ec o cells E 0 (B), unc ional ascula iza ion B(C), and umo adius (D; c ossing lines column). P einjec ion pa ame e alues in Supplemen a y Table S1 and mean umo adius a ime o injec ion (Fig. 2A). Solid colo columns: , E 0 ,B,and mean umo adius R 0 a day 1 pos injec ion es ima ed om mu ine expe imen s (Fig. 1). ,significan di e ences and s aigh lines imply no di e ence. Ha ziki ou e al. Cance Res; 77(7) Ap il 1, 2017 Cance Resea ch1558 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 High bac e ial loads esul in sho - e m posi i e he apeu ic esponses bu no in long- e m umo con ol We now conside mu ine expe imen s ea ed wi h 5 10 6 bac e ia (Fig. 1B). I espec i e o umo sizes, we obse e posi i e ea men esponses du ing he expe imen a ion ime. Tumo sizes a e conside ably educed in all expe imen s, bu comple e neoplasia clea ance is no achie ed a day 11 pos - injec ion. In some cases, he ea men esponse cu es e en sugges umo eg ow h. Al hough all ea men s induce la ge nec o ic egions, expe imen al measu emen s include always iable cance cells a he umo bo de allowing o elapse. Pa ame e es ima es o his he apeu ic choice a e ep esen ed in Fig. 3 (Supplemen a y Table S3). Fi ing esul s p edic a simila umo -associa ed ascula u e B o he one es ima ed om he un ea ed umo g ow h phase (Fig. 3C). A a fi s glance, compa ing wi h umo e olu ions upon injec ion o 10 3 bac e ia, we could na€  ely hink ha highe bac e ial loads lead o imp o ed he apeu ic ou comes. Howe e , Figu e 5. Sho - e m e olu ion o e ec o cell amoun s es ima ed om umo esponses o ea men s wi h 10 3 bac e ia (A),510 6 bac e ia (B), TNFa(C), and 10 3 bac e ia þ TNFa; da a as gi en in Fig. 4A–D(D). Figu e 4. Model fi ing o he indi idual sho - e m umo esponses o ea men s a egies wi h 10 3 bac e ia (A), 5 10 6 bac e ia (B), TNFa(C), and 10 3 bac e ia þTNFa; da a as in Fig. 1A–D(D). Bac e ial In ec ions agains Solid Tumo s www.aac jou nals.o g Cance Res; 77(7) Ap il 1, 2017 1559 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 he model p edic s ha long- e m umo con ol is no achie ed wi h his specific ea men choice. The mos s iking di e ence o o he scena ios is ha he numbe o e ec o cells a day 1 pos injec ion is in e sely ela ed o he immune ec ui men a e (Fig. 3A and B). Highe concen a ions o e ec o s a day 1 pos injec ion a e associa ed wi h apid umo educ ion, bu lowe immune ec ui men a es allow umo eg ow h owa d he end o he expe imen a ion ime (Fig. 4B). In ac , long- e m umo e asion is p edic ed as he mean ec ui men a e es ima ed is below he c i ical immune ec ui men h eshold S ’0.49 day 1 (Figs. 2B and 3A). This esul s in a educ ion o he numbe o e ec o cells pos injec ion (Fig. 5B). The e o e, he model p edic s ha umo con ol canno be ob ained by he adminis- a ion o his bac e ial load. These findings e idence ha an a bi a y inc ease o bac e ial loads does no necessa ily imply be e long- e m he apeu ic ou comes. Combined wi h he p e- ious umo esponses o in ec ions induced by 10 3 bac e ia, we conjec u e he exis ence o an op imal bac e ial load o he a- peu ic benefi s. In e media e bac e ial loads induce op imal in silico ou comes Model esul s sugges ha bac e ia di ec ly a ec he immune sys em dynamics wi hou majo damage o he p eexis ing umo - associa ed ascula unc ionali y. Inc easing bac e ial loads a e associa ed wi h highe numbe s o e ec o cells E 0 and lowe immune ec ui men a es a day 1 pos injec ion. While umo e asion is always p edic ed a e adminis a ion o 5 10 6 bac e ia, posi i e long- e m he apeu ic esponses a e ob ained in he majo i y o cases (4/6) ea ed wi h 10 3 bac e ia. Assuming a mono onically dec easing and inc easing dependency o ec ui - men a es and ini ial concen a ions E 0 o e ec o cells on bac e ial loads as shown in Fig. 6A and B, espec i ely, he model can p o ide insigh s in o he he apeu ic po en ial (TP) o in e - media e bac e ial loads as defined in Eq. C (see Quick Guide o Model Equa ions and Assump ions). Figu e 6C shows ha he e exis s a c i ical bac e ial load, a ound 10 5 bac e ia, abo e which he apeu ic benefi s canno be achie ed i espec i e o umo size. In his case, he deg ee o unc ional umo ascula iza ion Bwas fixed o 0.17, which is in he ange es ima ed a e bac e ial ea men s (Supplemen a y Table S2; Supplemen a y Table S3). The he apeu ic po en ial o bac e ial in ec ions is p edic ed o inc ease below his c i ical h eshold (Fig. 6D). Howe e , o su ficien ly la ge umo s, ha is, R 0 >4.4 mm, bac e ial ea men s alone do no p o ide posi i e ou comes and addi ional he apeu ical s a egies a e equi ed. In e es ingly, hese findings indica e ha o he ailu e cases ea ed wi h 10 3 bac e ia (Fig. 4A), ha is, mu ine expe imen s 2 and 6 wi h R 0 ¼ 4.28 and 4.23 mm, espec i ely, an educa ed bac e ial load inc ease could lead o long- e m umo con ol. Thus, model p edic ions suppo ha adminis a ion o an op imal amoun o bac e ia could significan ly imp o e long- e m ea men ou - comes in silico. TNFaaugmen s e ec o ec ui men dynamics and educes umo -associa ed ascula unc ionali y T ea men esponses in Fig. 1C sugges ha an exclusi e admin- is a ion o TNFainduces umo con ol in mice. The umo - associa ed ascula u e is ound o be damaged unde hese con- di ions (Fig. 3C; Supplemen a y Table S4). This model p edic ion is suppo ed by expe imen al e idence in mice demons a ing ha TNFais a po en an i ascula cy okine able o ini ia e apop osis in cance cells (43, 44). TNFa a ge s umo ascula u e by inducing hype pe meabili y and des uc ion o ascula lining, which esul s in he accumula ion o cy os a ic d ugs inside umo s and damage o he ascula s uc u e (45). The c i ical umo adius in his he apeu ic choice, R S ¼ 5.6 mm, is highe han R 0 o all expe imen s, which indeed Figu e 6. Model p edic ions wi h espec o inc easing bac e ial loads. Aand B, Linea in e pola ions o he immune ec ui men a e and numbe o e ec o cells E 0 a day 1 pos injec ion o bac e ial loads anging be ween 10 3 and 5 10 6 bac e ia. C, P edic ed long- e m umo con ol depending on umo size and bac e ial load. D, The apeu ic po en ial (TP) o bac e ial he apies o umo s wi h sizes be ween 3.5 o 4.5 mm. The y-axis ep esen s he ac ion o umo s con olled 100 days a e he adminis a ion o di e en bac e ial loads. Cand D, Simula ions o umo con ol in 100 days (ligh g ay) and uncon olled umo g ow h (da k g ay). Ha ziki ou e al. Cance Res; 77(7) Ap il 1, 2017 Cance Resea ch1560 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621 sugges s long- e m umo con ol (Supplemen a y Table S4). The numbe o e ec o cells a day 1 pos injec ion is on a e age highe han hose es ima ed om in ec ions induced by 10 3 bac e ia, bu lowe han hose wi h 5 10 6 bac e ia (Fig. 3B). Fi ing o umo esponses in hese cases p edic s ha TNFa induces highe e ec o ec ui men a es compa ed wi h all o he he apeu ic s a egies (Fig. 3A). This p edic ion is sup- po ed by ecen expe imen al da a in mice, whe e an inc eased e ec o cell mig a ion owa d umo bulk is obse ed a e TNFaadminis a ion (46). A e comple e umo clea ance, he e ec o cell concen a ionisdec eased(Fig.5C). The apeu ic combina ions o 10 3 bac e ia and TNFa esul in posi i e sho - e m ea men esponses, and e en in some cases comple e umo clea ance (Fig. 1D). The unc ional le els o umo -associa ed ascula u e and numbe o e ec o cells a day 1 pos injec ion a e es ima ed simila o hose by exclusi e adminis a ion o TNFa(Fig. 3B and C). Howe e , ime-e o- lu ion cu es pos injec ion indica e ha some umo s migh escape om immune su eillance and elapse (Fig. 4D). The analysis o he indi idual expe imen s e eals an associa ion be ween success ul he apy ou comes and high immune ec ui - men a es. Fo expe imen s 2 and 3, he es ima ed alues o a e lowe han he co esponding c i ical immune ec ui men a e, S ¼0.48 day 1 (Supplemen a y Table S5). This sugges s umo e asion accompanied by a educ ion in he concen a- ion o e ec o cells pos injec ion (Fig. 5D). In he emaining cases, > S and R 0 <R S ¼5.6 mm sugges long- e m umo con ol. Thus, he combina ion o bac e ial in ec ions wi h adminis a ion o TNFadoes no always imp o e he he a- peu ic success a e when compa ed wi h he exclusi e admin- is a ion o TNFa. Low TNFadosages could imp o e he e ficacy o in e media e bac e ial loads Recen expe imen s in mice e idenced ha sys ema ic admin- is a ion o TNFahas dual e ec s by emodeling umo s oma and enhancing adap i e immuni y (47). Low doses o in a u- mo al TNFas abilize umo blood essels and p omo e an i u- mo immune esponses media ed by inc eased e ec o cell infil- a ion. These findings indica e ha a low dose o TNFacan be a po en adju an o ac i e immuno he apy (47). On he o he hand, la ge dosages ac as an an i- ascula agen as conside ed in he mu ine expe imen s (Fig. 1). TNFa asomodula o y e ec s on umo g ow h dynamics a e in es iga ed in he amewo k o he p oposed ma hema ical model. In ou p e ious wo ks (9, 34), we demons a ed he exis ence o an op imal combina ion o immuno- and aso- modula o y in e en ions o umo sh inkage. These ideas could be ealized by ea men s a egies wi h combina ions o bac e ial loads and TNFa. We quan i y he long- e m umo con ol dependency on unc ional umo ascula iza ion Band immune ec ui men a e , as well as on he ini ial condi ions R 0 and E 0 . Supplemen a y Figu e S1 shows ha o bo h high and low unc ional le els o umo -associa ed ascula u e B,a he apeu ic "window o oppo uni y" a ises o he long- e m umo con ol in mice. Tumo ascula des uc ion, ha is, low B alues, is associa ed wi h high TNFadosage, which a e a he p ohibi i e o humans (48). On he o he hand, o low doses o TNFa, which po en ially lead o high alues o B ia induced ascula no maliza ion, he model simula ions sugges ha he umo con ol p obabili y is in e sely ela ed o he umo size bu a o ed by la ge immune ec ui men a es. This is sup- po ed by p eclinical s udies demons a ing ha ascula no - maliza ion inc eases infil a ion o e ec o cells in o umo s (49–51). In addi ion, Supplemen a y Fig. S2 e idences he exis ence o an op imal amoun o e ec o cells ha maximizes he egime o a o able ou comes ( o al g een a ea) in mice a high unc ional ascula iza ion. This op imal E 0 concen a ion coincides wi h he in e media e bac e ial loads a ound 10 5 bac e ia (Fig. 6). The e o e, an educa ed combina ion o low TNFaand in e media e bac e ia loads is p edic ed o op imize ea men ou comes. Discussion In he cu en s udy, we in es iga ed he he apeu ic po en ial o bac e ial in ec ions agains umo g ow h. We ocused on he in e play be ween g owing umo s, ascula iza ion, and immune ec ui men dynamics a e bac e ial-based he apeu ic in e en ions. We conduc ed in i o umo expe imen s in mice ea ed wi h di e en combina ions o bac e ia loads and/o TNFa. To assess he expe imen al obse a ions, we used a ma hema ical model o umo –e ec o cell in e ac ions, in which he unc ional umo -associa ed ascula u e and induced immune esponses we e p edic ed o play a c ucial ole in long- e m bac e ial he apy ou comes. P e ea men model pa a- me e s we e calib a ed on he basis o un ea ed umo g ow h mu ine expe imen s (9), and compa ed wi h es ima es pos in- jec ion in ea ed mice wi h ou di e en bac e ial and/o TNFa ea men p o ocols. Mice expe imen s show ha umo g ow h e a da ion, and e en e adica ion in he mos a o able si ua ions, can be ob ained wi h bac e ial in ec ions. This s udy sugges s ha umo sizes a he fi s day pos injec ion and he unde lying immune ec ui - men dynamics con ain p edic i e in o ma ion o sho - and long- e m bac e ial ea men ou comes. Model esul s sugges ha an a bi a y inc ease o bac e ial loads does no necessa ily esul in be e long- e m umo con ol. This implies he exis ence o an op imal bac e ial load o umo emission depending on umo size a he ime o injec ion. The adminis a ion o ade- qua e bac e ial loads combined wi h immunos imula o y agen s is p edic ed o enhance he umo con ol p obabili y. These esul s a e alid unde he assump ion ha he immune ec ui - men a e is ime-in a ian du ing he expe imen a ion ime and e en o longe pe iods. Al hough his assump ion is plausible o sho imes, o example, du ing he expe imen a ion ime, o long- e m one may expec he eco e y o ec ui men a es close o he lowe p e ea men con ol alues. This ypically implies an unde es ima ion o umo g ow h o he fi ed model pa ame e alues when compa ed wi h con ol es ima es. Howe e , his ac does no disquali y he umo –e ec o cell ec ui men model p edic ions. Fo ins ance, in he case o 5 10 6 bac e ia, he es ima ed la ge alues o he e ec o ec ui men a e induce a lowe bound o he umo g ow h a es, in compa ison wi h he co esponding con ol alues. E en o hese unde es ima ed umo g ow h a es, he model p edic s e asion, meaning ha o he con ol ec ui men a es, he umo is su ely uncon ol- lable. Finally, conce ning he long- e m con ollable cases, we can be mo e confiden as hey a e e iden om he sho - e m expe - imen al obse a ions. In he mice expe imen s o umo g ow h we conduc ed, he TNFadose adminis e ed was enough o des oy unc ional Bac e ial In ec ions agains Solid Tumo s www.aac jou nals.o g Cance Res; 77(7) Ap il 1, 2017 1561 on Ap il 13, 2017. © 2017 Ame ican Associa ion o Cance Resea ch. cance es.aac jou nals.o g Downloaded om Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621