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
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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.
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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
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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.
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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
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(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.
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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
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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.
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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
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Published OnlineFi s Feb ua y 15, 2017; DOI: 10.1158/0008-5472.CAN-16-1621