Carcinogenesis vol.33 no.2 pp.253–259, 2012
doi:10.1093/carcin/bgr227
Advance Access publication October 31, 2011
Mechanistic modelling suggests that the size of preneoplastic lesions is limited by
intercellular induction of apoptosis in oncogenically transformed cells
Pavel Kundrát, Georg Bauer1, Peter Jacob and
Werner Friedland
Helmholtz Zentrum München-German Research Center for Environmental
Health, Institute of Radiation Protection, Neuherberg, Germany and
1
Universität Freiburg, Institut für Medizinische Mikrobiologie und Hygiene,
Abteilung Virologie, Freiburg, Germany
To whom correspondence should be addressed. Tel: þ49 89 3187 4114;
Fax: þ49 89 3187 3363;
Email: [email protected]
Selective removal of oncogenically transformed cells by apoptosis
induced via signalling by surrounding cells has been suggested
to represent a natural anticarcinogenic process. To investigate its
potential effect in detail, a mechanistic model of this process is proposed. The model is calibrated against in vitro data on apoptosis
triggered in transformed cells by defined external inducers as well
as through signalling by normal cells under coculture conditions.
The model predicts that intercellular induction of apoptosis is capable of balancing the proliferation of oncogenically transformed
cells and limiting the size of their populations over long times, even
if their proliferation per se were unlimited. Experimental research
is desired to verify whether the predicted stable population of
transformed cells corresponds to a kind of dormancy during
early-stage carcinogenesis (dormant preneoplastic lesions), and
how this process relates to other anticarcinogenic mechanisms taking place under in vivo conditions.
Introduction
Oncogenically transformed cells exhibit some of the features involved
in multistep carcinogenesis, such as morphological changes, lack of
contact inhibition, independence of their growth from specific growth
factors, oncogene activation and tumour suppressor gene inactivation
(reviewed in ref. 1–4). They are capable of inducing tumours in syngeneic or immunocompromised animals. However, cells isolated from
such tumours differ from the initially injected transformed cells in two
important ways: (i) much less of these cells, compared with the
original cells transformed in vitro, are required for a new round of
tumour induction, indicating a strongly increased tumorigenicity and
(ii) the cells derived from tumours exhibit a much higher resistance
against exogenous hydrogen peroxide (H2O2) and are capable of
releasing prostaglandin E2 (5). These findings indicate that further
phenotypical changes, crucial for tumour development, occur at later
stages of carcinogenesis. Thus, oncogenically transformed cells represent an in vitro system mimicking the characteristics of early stage
carcinogenesis in vivo; they ‘reflect the cell culture equivalent of
initiation’ in carcinogenesis (6).
Oncogenically transformed cells constitutively produce superoxide
(O
2 ) through membrane-bound NADPH oxidase (nicotinamide adenine dinucleotide phosphate-oxidase). Superoxide is involved in
maintaining their transformed state and in controlling their proliferation (7); normal cells also use reactive oxygen species for the control
of proliferation, but in contrast to transformed cells only in welldefined pulses within short intervals. Superoxide production is, on
the other hand, the basis for a natural anticarcinogenic process potentially limiting the number of transformed cells, namely the induction
Abbreviations: TGF-b, transforming growth factor type-b; NO , nitric oxide;
HOCl, hypochlorous acid; H2O2, hydrogen peroxide; OH, hydroxyl radical;
POD, peroxidase; MPO, myeloperoxidase; LPO, lipid peroxidation; O2,
superoxide; ONOO-, peroxynitrite anion.
of apoptosis in oncogenically transformed cells by signalling through
surrounding cells (intercellular induction of apoptosis; reviewed in
ref. 3,4,8).
Intercellular induction of apoptosis involves signalling by cytokines as well as reactive oxygen and nitrogen species (Figure 1).
Through transforming growth factor type b (TGF-b) signalling,
transformed cells trigger the release of peroxidase (POD) and nitric
oxide (NO ) in neighbour cells (thus triggering in neighbour cells
their ‘effector function’ with respect to intercellular induction of
apoptosis, step 1 in the process; Figure 1A). POD and NO may be
produced also by transformed cells themselves (dashed arrows in
Figure 1A), leading to autocrine apoptotic self destruction (9,10).
Together with O
2 produced by transformed cells, POD and NO
enter into a cascade of biochemical signalling reactions (step 2),
in which apoptosis inducers are produced in the vicinity of
transformed cells. In the hypochlorous acid (HOCl) pathway
(4,8,11; Figure 1B), O
2 dismutates into H2O2, which, using abundant chloride ions, is converted by POD into HOCl. Upon reaction
with O
2 , HOCl yields hydroxyl radicals (OH), potent apoptosis
inducers. In the peroxynitrite pathway (4,8,11,12; Figure 1B), O
2
reacts with NO to produce peroxynitrite (ONOO), whose protonated form, peroxynitrous acid (ONOOH), decays yielding apoptosisinducing OH and nitrogen dioxide. Consumption reactions may
occur between H2O2 and HOCl and between NO and H2O2, leading
to an interplay of the two pathways (4,9,10; schematically depicted
in Figure 1B); POD also consumes H2O2 by converting it into water.
Two further signalling pathways, namely the nitryl chloride pathway
and metal catalyzed Haber–Weiss reaction, are of a minor importance only (4,8) and are not discussed in this work. Finally (step 3 in
intercellular induction of apoptosis, Figure 1A), upon the attacks of
OH, lipids in cell membranes are peroxidized, leading to local
consumption of intracellular glutathione and through a cascade of
further processes to the activation of mitochondrial pathway of apoptosis (8). The selectivity of intercellular induction of apoptosis
with respect to the transformed phenotype is warranted by the short
lifetime of superoxide, limiting the production of apoptosis inducers
to the vicinity of transformed cells (4,8,11,12).
A large variety of oncogenically transformed cells have been shown
to be targets of intercellular induction of apoptosis, including rodent
and human fibroblasts, epithelial, endothelial and haematopoietic
cells, transformed by viruses, oncogene activation, irradiation or
spontaneously (reviewed in ref. 8). Similarly, various cell types of
murine and human origin are able to serve as effector cells in intercellular induction of apoptosis (i.e. release sufficient POD and/or NO
upon TGF-b signalling), including fibroblasts, epithelial and endothelial cells, monocytes, B-cells and other cell types (8). On the other
hand, tumour cells do not possess sensitivity to intercellular induction
of apoptosis due to their expression of membrane-associated catalase,
which inhibits signalling reactions in step 2, namely the HOCl
pathway by removing H2O2 and the peroxynitrite pathway through
decomposing peroxynitrite and oxidizing NO (9,10).
To help quantitatively understand the process of intercellular induction of apoptosis, enable extrapolations of experimental results to
long-term behaviour and physiologically relevant conditions, and in
particular to help estimate the role of this phenomenon as a control
mechanism in carcinogenesis (3,8,13), a series of mechanistic modelling studies has been performed. Based on existing cell culture data,
the model predicts that intercellular induction of apoptosis is capable
of limiting the size of transformed cell population, providing support
for an important anticarcinogenic role of this process. For simplicity,
this paper is focused on the HOCl signalling pathway, the major
pathway of intercellular induction of apoptosis in many transformed
Ó The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
253
P.Kundrát et al.
A
Step 1: Release rates
TRANSFORMED
CELL
TGF-
O2•-
B
EFFECTOR CELL
EFFECTOR
CELL
CONSUMPTION
POD, NO•
REACTIONS
Step 2: Reactiondiffusion equations
OH•
NO•
POD
HOCl
Cl-
Membrane ddamage
GSH consumption
Step 3: Kinetic model
Apoptosis
ONOO-
H2O2
•
OH• O2 -
O2•-
O2•-
O2•-
OH•
TRANSFORMED CELL
Fig. 1. Mechanism of apoptosis induction in oncogenically transformed cells through signalling by surrounding cells (intercellular induction of apoptosis;
reviewed in ref. 8). Panel A: Three steps in the mechanism of intercellular induction of apoptosis and their representation in the model. In step 1, transformed cells
trigger, through TGF-b signalling, the release of POD and NO in neighbour cells, which thus become effector cells with respect to intercellular induction of
apoptosis; also transformed cells themselves may serve as effector cells and release these species (dashed arrows). In step 2, a cascade of biochemical reactions
occur between superoxide (O
2 ) produced by transformed cells and POD and NO released by effector cells, leading to production of OH in the vicinity of
transformed cells. The two major pathways of the biochemical signalling cascade are depicted in detail in panel B; this work is focused on the HOCl pathway,
highlighted in boldface. Finally, in step 3, the attacks of OH damage cellular membrane, which initiates an intracellular signalling pathway leading to apoptosis. In
the model described in this paper, per-cell release rates of signalling species are considered in step 1, a set of reaction–diffusion equations is used to model step 2,
and step 3 is represented by a non-linear kinetic model in which induction of apoptosis competes with cell proliferation.
cell systems (9); an extension to the peroxynitrite pathway will be
discussed elsewhere.
Materials and methods
A multiscale mathematical model of intercellular induction of apoptosis that
follows its three-step mechanism (Figure 1) has been developed. The model
takes into account the release of superoxide by transformed cells (target cells
with respect to intercellular induction of apoptosis) and the release of POD
(and NO ) by their neighbours (this effector function being triggered by
TGF-b signalling). The biochemical reaction cascade between these species
(Figure 1B) is simulated using reaction–diffusion equations. The resulting
yields of apoptosis inducers serve as input for the last module (step 3, Figure
1A), a kinetic model that accounts for the induction of membrane damage, its
repair by the cell and non-linear triggering of apoptosis as a process competing
with proliferation. The model is calibrated against cell culture data on the
response of transformed and normal cells to defined externally added species
involved in the given signalling as well as on induction of apoptosis in transformed cells cocultured with normal cells. The methods are described in detail
below.
Experimental data used
Published data are analyzed on the extent and rate of apoptosis induced in
208F src3 transformed rat fibroblasts challenged by their parental (non-transformed) cell line 208F (11), measured in a coculture system with normal
(non-transformed) cells pretreated with TGF-b and seeded in inserts with
porous membrane 1 mm above transformed cells, excluding potential contribution of gap-junction communication (8). To help estimate model parameters, data on induction of apoptosis in these cells by externally added
signalling species (14) are used. In all the experiments, apoptosis was scored
by phase contrast microscopy using morphological criteria of membrane blebbing, chromatin condensation and fragmentation; correspondence to apoptosis
was benchmarked by detecting free 3# hydroxyl groups of DNA by the TUNEL
assay (12).
Model scheme
Step 1: Triggering of effector function in neighbour cells through TGF-b
released by transformed cells. Pretreatment with TGF-b used in the analyzed
experiments (10–20 ng/ml TGF-b for 1–2 days) significantly enhances cells’
capability to induce intercellular induction of apoptosis (9). Further increase
in the amount or duration of this pretreatment does not enhance its effect (13),
indicating that pretreated cells have already reached their full capacity of
254
POD production. For the analyzed experiments, the model for Step 1 is thus
reduced to considering constant POD release rates per effector cell, independent of additional TGF-b signalling by transformed cells. POD released by
transformed cells (not pretreated with TGF-b) is neglected with respect to that
from TGF-b pretreated normal cells (effector cells). Similarly, constant release
rates of O
2 per transformed cell are assumed; limited O2 production by nontransformed cells is neglected. Potential variations with cell cycle, passage
number, etc are neglected. In the experiments with externally added signalling
species, external species dominate over those released by cells, which are
neglected accordingly.
Step 2: Intercellular signalling leading to the formation of apoptosis inducing
species. For coculture experiments, biochemical reactions involved in the
HOCl pathway (Figure 1B; Supplementary Material, available at Carcinogenesis Online) are represented by standard reaction–diffusion equations. This set
of non-linear partial differential equations accounts for cellular release of
primary species (O
2 and POD), their diffusion, mutual reactions leading to
intermediates (H2O2 and HOCl) and inducers of apoptosis (OH), lifetimes of
all species in medium and absorption of inducers upon attacking cells and
inducing membrane lipid peroxidation (LPO). In this work, a one-dimensional
approximation to the full three-dimensional reaction–diffusion equations is
used, in which temporal development of species concentrations in dependence
only on the distance from the transformed cell plate is considered and individual cells (sources of primary species) are replaced with mean cell densities;
detailed simulations have verified that this approximation represents the major
system characteristics (results not shown).
For a given species (denoted here by A), the one-dimensional kinetic equation reads
2
2
@½Aðz;
P tÞ @t5DA @ ½Aðz; tÞ @z ½Aðz;
P tÞ tA
B kAþB/CþD ½Aðz; tÞ½Bðz; tÞþ C;D kCþD/AþB ½Cðz; tÞ½Dðz; tÞ;
ð1Þ
where [A](z,t) denotes time-dependent local concentration of species A at
distance z from the plane of transformed cells (and analogously for species
B, C and D), tA lifetime of.species A,
.related to its rate of disappearance kA and
A
A
A
lnð2Þ; DA its diffusion coefficient and
by t1=2
51 kA 5t1=2
half-life t1=2
kAþB/CþD and kCþD/AþB rate coefficients of reactions in which species
A is consumed or produced, respectively. Initial conditions for equation (1)
are given by [A](z,t 5 0) 5 0 for all species except those present in medium or
added externally. Boundary conditions are represented by fluxes jA of species
A released from transformed (at zc 5 0) or non-transformed cells (at zc 5 1
mm) and by consumption of apoptosis inducers upon attacking cells,
Preneoplastic lesions limited by apoptosis
NT
j5DA @½Aðz; tÞ=@zjz5zc 5aTA rT ðzc ; tÞ þ aNT
A r ðzc ; tÞ
A
kLPO
nlip ðrT ðzc ; tÞ þ rNT ðzc ; tÞÞ½Aðzc ; tÞ;
ð2Þ
j 5 0 at the medium surface (z 5 3 mm in the given experiments). Here, aTA and
aNT
A denote the release rates of species A per transformed and non-transformed
cell, rT and rNT densities of transformed and non-transformed cells at plane z 5
A
the reaction rate constant for initiation of LPO by inducer A,
zc and time t, kLPO
and nlip denotes the molar amount, per cell, of membrane lipids exposed to these
attacks (1015 mol/cell, ref. 16).
For experiments on cellular response to externally added signalling species,
the model for Step 2 is reduced essentially to spatially homogeneous decay
kinetics of these species, as these dominate over those released from cells
(Supplementary Material, available at Carcinogenesis Online).
During intercellular signalling leading to induction of apoptosis, OH is the
OH
5109 M1 s1 ; ref. 17); the levels of H2O2 and HOCl
relevant inducer (kLPO
are rather low, so that they do not induce apoptosis directly but serve as
intermediates only (14). In experiments with external species, much higher
H2O2 concentrations were achieved at which it does induce apoptosis, presumably via a reaction with intracellular metal ions (e.g. Feþþ) producing OH
which finally induce LPO (17); in this work, the effects of all these processes
H2 O2
in equation (2).
are lumped together into effective rate constant kLPO
Step 3: Triggering and execution of apoptosis. For simplicity, the present
model works with two cellular states only, ‘living’ and ‘apoptotic’ cells, as
also scored in the experiments. Neither the complex intracellular processes
leading from membrane damage to apoptosis nor the detailed time course of
apoptosis triggering and execution are represented. Only living cells (and not
apoptotic cells) are assumed to release species involved in the given signalling
[cf. equation (2)].
Density r of living transformed (T) and non-transformed (NT) cells is
modelled by
drT;NT ðtÞ=dt5 rT;NT ðtÞ tprolif 1 rT;NT ðtÞ rT;NT
max
rT;NT ðtÞ 1 tspont þ pT;NT
ind ðtÞ tind :
ð3Þ
The first term is a logistic model of cell proliferation, with rate 1/tprolif
modified by saturation effects with maximal cell density rmax. The second
term accounts for spontaneous apoptosis with rate 1/tspont and for intercellular
induction of apoptosis at maximal rate 1/tind modified by a factor 0 pind 1
(discussed below). Density rap of apoptotic cells is given by
T;NT
drT;NT ap ðtÞ=dt5rT;NT ðtÞð1=tspont þ pT;NT
ind ðtÞ=tind Þ rap ðtÞ=trm ;
signalling reactions lead to production of apoptosis inducers. In a complex
non-linear way and with some delay, the spatially dependent concentration
of inducers follows the density of transformed and non-transformed cells.
Inducer attacks increase the probability of apoptosis triggering and execution,
thus reducing the density of living cells that contribute to the signalling. This
forms a feedback mechanism in intercellular induction of apoptosis. Within the
model, this is translated into the given coupled set of differential equations.
Model application to experimental data. Reaction rates and diffusion coefficients are taken from literature (Supplementary Material, available at Carcinogenesis Online). Signalling pathways are modelled in intercellular space
only; diffusion of intermediate species across cell membrane is not considered.
For experiments with externally added signalling species, cell-derived species
are neglected accordingly, decay kinetics of added species described analytically and equations (3–6) solved numerically. Using MINUIT optimization tool
(20), model calculations are fitted simultaneously to data for apoptosis
triggered by (donors of) peroxynitrite and H2O2. This procedure enables estimating cellular sensitivity to apoptosis inducers n1 and n2, rate of apoptosis
induction tind and species lifetimes tA under in vitro conditions.
Cellular release rates of O
2 and POD as well as parameters trm and trep
are adapted to the observed kinetics of apoptosis under intercellular signalling
and in cells exposed to H2O2-producing system complemented by myeloperoxidase (MPO) (cf. Results). For these experiments, the full set of partial
differential equations, equations (1–6), is solved numerically.
As both transformed (208F src3) and normal (208F) cells proliferate with
about the same doubling time t222 h (G. Bauer, unpublished data), equal
proliferation rates 1/tprolif 5 1/(t2ln(2)) are used for both phenotypes. However,
the two phenotypes differ in the extent to which their growth is limited by
contact inhibition. While the density of 208F cells is limited by rNTmax200/
mm2 (G. Bauer, unpublished data), transformed cells are even capable of
growing on
top of each other; thus, a higher maximal density
(rTmax 5300 mm2 ) is assumed for 208F src3 cells in this work. Potential differences in tspont, tind and/or trm between transformed and normal cells are neglected; tspont 5 15trm is taken to reflect the 5% fraction of apoptotic cells in
control experiments. Transformed and normal cells respond to defined external
donors of apoptosis inducers almost equally (14); identical sensitivity parameters n1, n2 are thus used for both phenotypes. As the specific POD that
participates in intercellular induction of apoptosis and its reaction kinetics
are unknown, published data for MPO are used as surrogate also for intercellular signalling. Specific information on limited turnover of this enzyme is
lacking; lifetime of 106 s is assumed.
Further details on the methods are given in Supplementary Material,
available at Carcinogenesis Online.
ð4Þ
with rate of removal of apoptotic bodies 1/trm.
The rate of apoptosis induction through intercellular signalling, pind/tind, is
assumed to increase with the amount of LPO damage nLPO caused by inducer
attacks in a sigmoid manner,
T;NT
n1 ;
ð5Þ
pT;NT
ind ðtÞ5exp exp n2 nLPO ðtÞ n1
this Gompertz function accounts for cellular ability to cope with a certain level
of damage. All downstream intracellular processes leading to activation and
execution of mitochondrial pathway of apoptosis are lumped into cell sensitivity parameters, n1 and n2.
The amount of induced damage is modelled by
T;NT
A
ð6Þ
dnT;NT
LPO ðtÞ dt5kLPO ½Ac ðtÞ nlip nLPO ðtÞ trep ;
with [A]c(t) denoting concentration of inducer A ( OH or H2O2 as discussed
above) at outer cell surface, obtained from the reaction–diffusion equations
describing the biochemical signalling scheme. Only LPO initiation events, i.e.
the number of inducer attacks experienced so far, are considered. The propagation and termination phases of LPO reactions (18) are not modelled explicitly, as the resulting amplification of LPO (estimated as 10–15 propagation
steps per initiation event, ref. 19) would lead to a multiplicative factor only,
scaling the actual nLPO and parameters n1, n2 but not influencing the results on
kinetics of apoptosis. Cellular capability to repair lipid peroxides through
glutathione peroxidases at the expense of glutathione (e.g. reviewed in ref.
18) is approximated by a first-order process, with characteristic time trep.
Summarizing the model scheme. Density of living cells at a given time determines the amount of primary signalling species released. The biochemical
Results
Cellular sensitivity to apoptosis inducer
Exemplary results of model calibration against data on apoptosis
induction in 208F src3 transformed and 208F non-transformed fibroblasts by OH from the decay of peroxynitrite and by H2O2 (14) are
shown in Figure 2A and B; further results are reported in Supplementary Material, available at Carcinogenesis Online. These species
possess only small differences in their effects upon transformed
208F src3 and normal 208F cells (14); these are neglected in model
calculations using the same sensitivity parameters, n1 and n2, for both
phenotypes.
On the contrary, the responses of transformed and non-transformed
cells are very different when MPO is added to the H2O2-producing
glucose oxidase (Figure 2C and D); this system closely resembles the
HOCl pathway of intercellular signalling. MPO converts H2O2 partly
into HOCl (and partly into water). In the low concentrations produced,
HOCl does not affect cell survival by itself (14) but yields apoptosisinducing OH upon reaction with transformed cell-derived superoxide. Compared with the fast effect of the high levels of H2O2 produced
at this glucose oxidase concentration (Figure 2C, dashed line), apoptosis in transformed cells is induced less quickly by the HOCl pathway (Figure 2C, solid line), as only a part of H2O2 is converted into
HOCl which has to react with superoxide and consumption reactions
between H2O2 and HOCl occur (Figure 1A). Scavenging HOCl by
taurine or OH by terephthalate inhibits the induction of apoptosis in
transformed cells (Figure 2C, dash-dotted lines). As non-transformed
cells do not produce sufficient superoxide, addition of MPO inhibits
255
P.Kundrát et al.
the induction of apoptosis due to removal of H2O2 and synthesis of
HOCl, without subsequent superoxide–HOCl interaction (Figure 2D).
Model parameters describing cellular sensitivity to apoptosis inducers and lifetimes of signalling species in vitro, estimated by fitting
the data on apoptosis induction by defined externally added species
Table I. Model parameters estimated from a simultaneous analysis of
experiments on apoptosis induction in rat fibroblasts by externally added
signalling species (Figure 2 and Supplementary Material, available at
Carcinogenesis Online) and from model adaptation to intercellular induction
of apoptosis by the HOCl pathway in the coculture system with transformed
and non-transformed cells (Figure 3)
Parameter
n1
n2
tind
trm
trep
tO
2
tH2O2
tOH
tHOCl
aO
2
aPOD
Value
1017
Characteristic level of membrane LPO leading to
apoptosis induction (mol/cell)
Rate of change in apoptosis induction probability with
increasing LPO (1)
Characteristic time of apoptosis induction (h)
Characteristic time of removal of apoptotic bodies (h)
Characteristic time of LPO repair (h)
O
2 lifetime (s)
H2O2 lifetime (h)
OH lifetime (ls)
HOCl lifetime (ms)
Release rate of O
2 per transformed cell (mol/cell/s)
Release rate of POD per TGF-b pretreated normal cell
(mol/cell/s)
3.5
1.7
15
15
1.7
2.7
3.4
38
1016
1021
Parameters relevant for model calibration only are reported in Supplementary
Material, available at Carcinogenesis Online.
500 M
A
100
250 M
SIN-1
80
Induction of apoptosis in transformed cells through signalling by
normal cells
Due to their limited time span, the aforementioned reconstitution
experiments provide no specific information on the characteristic
times for the removal of apoptotic bodies trm and for the repair of
peroxidative damage to membrane lipids trep, values .12 h yielding
equally good results (trm 5 trep 5 15 h used in Figure 2). These
particular values and the release rates of POD per effector cell and
of superoxide per transformed cell (1021 and 1016 mol/s, Table I)
have been obtained by adjusting model calculations for the HOCl
pathway (Figure 3A) to measured kinetics of apoptosis induced in
208F src3 cells by their parental cell line 208F. Experimentally, the
release of NO and hence the peroxynitrite pathway of intercellular
signalling were inhibited by two inhibitors of NO synthesis (11).
Compared with apoptosis induction by externally added species
(Figure 2), apoptosis induced by intercellular signalling (Figure 3A)
is characterized by a rather long, 2 days delay. The model predicts
that this period corresponds primarily to the need for sufficient POD
and H2O2 to accumulate in the system, as needed for optimal HOCl
production. The prerequisite of sufficient H2O2 production translates
into requiring a certain density of transformed cells that produce
enough superoxide; dismutation of superoxide into H2O2 takes two
O
2 molecules, so that H2O2 production scales roughly quadratically
with cell density. This non-linear nature of the HOCl pathway is
further amplified by the need for another O
2 molecule reacting with
HOCl to yield apoptosis-inducing OH. As illustrated in detail in
Supplementary Material, available at Carcinogenesis Online, the
apoptotic cells (%)
apoptotic cells (%)
100
(Figure 2 and Supplementary Material, available at Carcinogenesis
Online), are listed in Table I.
60
125 M
40
20
B
GOX
80
4 U/l
2 U/l
1.5 U/l
60
40
1 U/l
20
0.5 U/l
0
0
apoptotic cells (%)
100
1
2
3
4
time (h)
5
6
7
100
C
GOX+MPO
60
40
+Ter
+Tau
20
0
2
4
D
GOX
208F
src3
80
0
apoptotic cells (%)
0
6
8
time (h)
10
12
GOX
208F
80
60
40
20
GOX+MPO
0
0
5
10
15
20
time (h)
25
30
0
5
10
15
20
25
30
time (h)
Fig. 2. Apoptosis induced in 208F src3 transformed (A–C) or 208F non-transformed rat fibroblasts (D) by external donors of key signalling species involved in
intercellular induction of apoptosis: selected examples illustrating the calibration of model calculations (lines) against data (points, error bars denoting standard
errors of the mean from several repeats of the experiment, from (ref. 14); where not shown, were the errorbars smaller than the symbols). Additional results are
reported in Supplementary Material, available at Carcinogenesis Online. (A) Kinetics of apoptosis induction by OH generated by decay of peroxynitrite produced
from 0.125 to 0.5 mM 3-morpholino-sydnonimine (SIN-1). (B) Effect of H2O2 continuously produced by 0.5–4 mU/ml glucose oxidase (GOX) from glucose
abundant in medium. (C) In transformed 208F src3 cells, apoptosis induced by H2O2 generated from 4 mU/ml GOX (dashed line) is delayed by adding 200 mU/ml
MPO (GOX þ MPO, solid line). Addition of HOCl scavenger taurine (Tau) or OH scavenger terephthalate (Ter) inhibits apoptosis induction. (D) In nontransformed 208F cells, the apoptosis-inducing effect of H2O2 from GOX is about the same as in 208F src3 cells, but addition of MPO completely abrogates
apoptosis, as superoxide is not produced.
256
apoptotic cells (%)
2
50
A
NMMA
NAME
no inhibitor
40
30
20
10
0
0
transformed cell density (1/mm )
Preneoplastic lesions limited by apoptosis
0.5
1
1.5
2
2.5
3
1000
B
100
10
0
time (d)
2
4
6
8
time (d)
10
12
14
Fig. 3. (A) Kinetics of apoptosis induced by the HOCl pathway in transformed fibroblasts 208F src3 upon coculture with non-transformed 208F cells.
Model calculation (line) compared with data (triangles, ref. 11) obtained when the peroxynitrite pathway was inhibited by NO synthesis inhibitors N-omega-Nitro-Larginine methylester hydrochloride (NAME) or N6-Methyl-L-arginine (NMMA); 40000 transformed cells per well (9.6 cm2) cocultured with the same number of nontransformed cells pretreated with 20 ng/ml TGF-b for 2 days. Data on apoptosis induction without inhibitors (squares) are also shown, although the present calculations
are limited to the HOCl pathway only (cf. Discussion). Error bars were estimated from assays performed in duplicate (ref. 11). (B) The model predicts the existence of
a stable long-term limit to the growth of transformed cell population, approached in a damped-oscillatory mode (solid line). Even if unlimited exponential growth of
transformed cells and a reduced superoxide lifetime of 100 ms (21) are considered, limited population size is predicted (dashed line).
density of transformed cells first increases by proliferation, leading to
increasing superoxide release and enhanced production of H2O2
and in turn also of HOCl and OH. As soon as the amount of LPO
or rate of its induction exceeds the levels that cells can cope with,
apoptosis starts to be triggered. The density of living superoxideproducing transformed cells is thus reduced. Consequently, also the
production of H2O2, HOCl and apoptosis-inducing OH diminishes,
giving cells a chance to repair the LPO damage induced so far. Fewer
cells are sent to apoptosis, and cell density increases by proliferation.
Together with the removal of apoptotic bodies, this may lead to a reduction in the percentage of cells that exhibit apoptotic features, as
shown in Figure 3A, in agreement with the data at 3 days coculture.
The model reproduces the observed selectivity of intercellular
induction of apoptosis to the transformed phenotype (8): due to the
short lifetime and hence diffusion length of superoxide, the majority
of OH are formed in a close vicinity to transformed cells; the model
predicts that the OH levels produced by the HOCl pathway decrease
with distance from transformed cells by factors of 2–4 per 100 lm
(Supplementary Material, available at Carcinogenesis Online).
The model also predicts the dependence of the extent and rate of
intercellular induction of apoptosis via the HOCl pathway on initial
cell densities, distance between transformed and non-transformed cell
populations or the amount of medium (Supplementary Material,
available at Carcinogenesis Online). Measurements addressing these
issues could help verify model assumptions and the derived parameter
values.
Predicted long-term behaviour
In Figure 3B, the long-term behaviour of transformed cell density,
predicted based on the above-mentioned experimental data, is plotted.
The model predicts the existence of a long-term stable state at which
proliferation of transformed cells is counterbalanced by their apoptosis induced through signalling by neighbour normal cells. This steady
state is approached in a damped oscillatory mode, based on the abovediscussed feedback loop between transformed cell density and
concentration of apoptosis inducers.
The equilibrium density as well as the amplitude and frequency of
damped oscillations are given by system parameters, in particular by
the release rates of signalling species, their lifetimes in the medium,
cell sensitivities to inducers and rates of proliferation and apoptosis
induction. To investigate the potential implications of intercellular
induction of apoptosis for carcinogenesis under conditions closer to
in vivo, the influence of larger parameter variations on the existence
of a density limit and its value has been studied. The model predicts
that intercellular induction of apoptosis is capable to balance the
proliferation of transformed cells even if contact inhibition and
other growth limitations are completely abolished and/or the lifetimes of signalling species shortened. This is illustrated in Figure 3B
by a calculation with completely unlimited exponential growth of
transformed cells (rTmax /N), distance between transformed
and non-transformed cells reduced to 0.1 mm and superoxide lifetime reduced to 0.1 s as estimated in blood (21). Although the extent
of intercellular induction of apoptosis is reduced, the density of
transformed cells is still limited; for the given parameter values
the predicted limit amounts to 600 cells/mm2 (Figure 3B).
Discussion
A detailed mechanistic model of intercellular induction of apoptosis
has been developed. For the analyzed experiments, triggering of effector function in normal cells is approximated by constant release
rates of signalling molecules. Detailed reaction kinetic model is used
for the intercellular signalling reactions. Triggering of apoptosis increasing non-linearly with the amount of inducers attacking cells is
considered. Although this apoptosis execution module is relatively
simple and intracellular mechanisms of mitochondrial pathway of
apoptosis are not represented explicitly, the assumed sigmoid response agrees with the behaviour predicted by detailed models of this
apoptosis pathway (e.g. refs. 15,22). The model reproduces the kinetics of apoptosis as well as the dependence on the amounts of donors
added or exposure duration (Figure 2 and Supplementary Material,
available at Carcinogenesis Online).
Despite using data for a particular cell system, namely transformed
208F src3 cells derived from 208F rat fibroblasts, the model as well as
qualitative features and conclusions discussed here are not cell-type
specific, as qualitatively similar behaviour has been observed also
with other cell systems (8,10,13).
By using literature-based reaction kinetics data, the model has
verified the experimentally deduced intercellular signalling mechanism leading to apoptosis. The model confirms the critical role of
superoxide production by transformed cells for both selectivity and
efficiency of this process, pointed out in earlier experimental work
(11,12,14; reviewed in refs. 4,8): Short lifetime of superoxide
limits the production of apoptosis inducers to the vicinity of transformed cells, ensuring selectivity of intercellular induction of apoptosis to transformed phenotype. The efficiency of the HOCl pathway,
which represents a dominant contribution to intercellular induction
of apoptosis (cf. Figure 3), is driven by superoxide production:
enough superoxide is needed for sufficient H2O2 formation and also
for production of apoptosis-inducing OH through HOCl–superoxide
interaction.
Unfortunately, although the model works with mechanistically
distinct parameters, not all of them could have been determined
unambiguously from the limited data available; changes in some parameters can be compensated by adjusting others, as complex largely
competing processes are involved (correlated parameters in terms
of data analysis; cf. Supplementary Material, available at
257
P.Kundrát et al.
Carcinogenesis Online). The characteristic time for the removal of
apoptotic bodies, for instance, can be compensated by characteristic
time for the repair of lipid peroxidative damage, as both processes
tend to reduce the number of apoptotic cells scored, though by very
different mechanisms. This uncertainty in parameter determination
could be reduced if some parameters were directly measured; e.g.
the characteristic time for the removal of apoptotic bodies could be
determined by recording the fate of individual apoptotic cells.
Measuring local concentrations of diverse signalling species would
be extremely challenging due to their large spatial variations. However, methods have been developed for single-cell measurements of
superoxide release (23); peak values of 2 fmol/s and total releases of
50–100 fmol per non-transformed human fibroblast per burst (lasting
over .2 min) after mechanical stimulation were reported (23). These
values indicate that the release of 0.1 fmol/s O
2 per 208F src3 transformed fibroblast estimated here (Table I) is not unrealistically high;
direct single-cell measurements of superoxide release by transformed
cells would benchmark this important model parameter.
The model calibration procedure is also hampered by the fact that
the analyzed data correspond to a few (typically two to three) replicate
experiments scored at a few time points only; improved statistics
would help obtain more reliable parameter estimates. However,
the lack of knowledge on specific parameter values is not critical
for the present study. Although somewhat different parameter sets
are consistent with the analyzed data, they lead to similar results for
the equilibrium transformed cell density as well as the predicted
damped oscillations (Supplementary Material, available at Carcinogenesis Online), as the main characteristics of the long-term behaviour are dictated by the observed onset of apoptosis at 2 days and
reduction at 3 days of coculture.
The predicted long-term behaviour of the system represents the
major result of the reported studies. A long-term stable limit is predicted for the density of transformed cells, i.e. a limited growth of
preneoplastic lesions, due to the capability of intercellular induction
of apoptosis to counterbalance the proliferation of transformed cells
even if their proliferation per se were unlimited (exponential). This
prediction extends the experimental results beyond the 3–5 days, after
which the analyzed experiments with the transformed–non-transformed
coculture system are spoilt by nutrient deprivation and/or build-up of
toxic products. The present work has been limited to the HOCl pathway of intercellular induction of apoptosis; nevertheless, although in
principle, a complex interplay of the two pathways may occur due to
consumption reactions (Figure 1B), the data (cf. Figure 3A) as well
as first calculations (24) including the peroxynitrite pathway show
an enhanced percentage of apoptotic cells, i.e. a further strengthened
density limit.
This long-term density limit is approached by the system in
a damped oscillatory mode. Phenomenological description of the process using damped oscillations theory could be beneficial if only the
kinetics of apoptosis or the resulting transformed cell density are of
interest, e.g. for implementing intercellular induction of apoptosis
into existing mechanistic models of carcinogenesis. Compared with
the present model, such description would require four parameters
only, namely lag time before apoptosis onset (period of undisturbed
proliferation), equilibrium cell density (or percentage of apoptotic
cells), damping ratio and period of oscillations. An approximate description of the predicted sizes of transformed cell populations could
be based on sigmoid or step functions or even just the density limit,
further reducing the number of parameters needed. The detailed
model presented here relates these phenomenological parameters to
mechanistic systems parameters describing experimental setup, initial
cell densities, cellular sensitivity to inducers and release rates and
lifetimes of signalling species.
To address potential implications of intercellular induction of apoptosis under conditions closer to in vivo, model calculations have been
performed with an unlimited growth of transformed cells and lifetime
of superoxide reduced from 1.7 s (derived for in vitro experiments) to
0.1 s estimated in blood (21). The model indicates (Figure 3B) that
even in this case, intercellular induction of apoptosis is capable of
258
limiting the size of transformed cell population. Note that this result
still concerns the coculture geometry with transformed cells seeded in
wells (i.e. in a plane) and effector cells on membrane inserts (i.e. in
another plane, 1 mm separated). To model physiological conditions
more realistically, spheroids or even irregular-shaped transformed cell
populations surrounded by normal cells should be considered, and the
signalling scheme (step 2) modelled in three-dimensional setup; these
generalizations are straightforward though computationally expensive. Furthermore, a detailed representation of the TGF-b signalling
(step 1) is necessary. A corresponding module is under development,
considering TGF-b autoinduction, signal lifetime and a sigmoid increase in release rates of POD (and NO ) with the amount of TGF-b
signals; unfortunately, detailed experimental information on this
process is still lacking.
Nevertheless, already the present results indicate a potentially important role of intercellular induction of apoptosis in carcinogenesis
and enable understanding the key processes deciding on its relevance.
Triggering of effector function in surrounding cells by TGF-b released by the transformed cells decides on when the signalling reactions involved in intercellular induction of apoptosis become
operational. In fact, gradually increasing release rates of primary
species should be considered (contrary to constant releases assumed
in this work), as the surrounding cells gradually respond to TGF-b
released and/or activated by transformed cells. This would lead to
time-dependent limits to cell densities; typically signalling would
increase with time, leading to more stringent density limits. On the
other hand, the system of intercellular induction of apoptosis is not
active in tumour cells, as they express membrane-bound catalase,
inhibiting the given signalling (9,10). Physiological relevance of intercellular induction of apoptosis thus critically depends on the time
window available before membrane-associated catalase expression
occurs as a phenotypical change in the transformed cell population
(Figure 4). If catalase expression appears faster than triggering of
effector function in surrounding cells by TGF-b from transformed
cells, then there is no ‘window of opportunity’ for intercellular induction of apoptosis. However, if the onset of catalase expression
needs longer time, e.g. several weeks or longer, then the present
results suggest that intercellular induction of apoptosis probably represents a crucial anticarcinogenic process limiting the number of
oncogenically transformed cells. Such a stable population of
Fig. 4. Potential physiological relevance of intercellular induction of
apoptosis as an anticarcinogenic mechanism. Following their oncogenic
transformation, cells start TGF-b signalling, which in turn triggers the
release of POD and NO in neighbour cells. These species together with
superoxide produced by transformed cells undergo a cascade of biochemical
reactions (Figure 1B). This intercellular signalling is rendered inactive when
the transformed cells acquire further phenotypical change characteristic for
tumour cells, the production of membrane-bound catalase, which removes
H2O2 and peroxynitrite, key species in this signalling process. If catalase
expression occurs with sufficient delay after the activation of intercellular
signalling that leads to apoptosis induction, a dormant state results in which
further growth of the transformed population is inhibited. This dormant state
represents a window of opportunity for the action of other anticarcinogenic
mechanisms.
Preneoplastic lesions limited by apoptosis
transformed cells (preneoplastic lesion with limited growth) resembles many features of dormant tumours (reviewed e.g. in ref. 25).
Experimental research is needed to verify whether intercellular induction of apoptosis indeed contributes to the mechanism preventing
their growth or whether its potential to specifically induce apoptosis in
malignant cells is not effective under in vivo conditions.
Supplementary material
Supplementary Material can be found at http://carcin.oxfordjournals.
org/
Funding
The research leading to these results has received funding from the
European Atomic Energy Community’s Sixth Framework Programme
(FP6/2002-2006) under grant agreements FI6R-CT-2003-508842
(RiscRad) and FI6R-036465 (NOTE); and Seventh Framework Programme (FP7/2007-2011) under grant agreement no. 249689 (DoReMi).
Conflict of Interest Statement: None declared.
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Received April 22, 2011; revised September 14, 2011;
accepted October 13, 2011
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