Cancer Stem Cell Tumor Model Reveals Invasive Morphology and Increased Phenotypical Heterogeneity
The recently developed concept of cancer stem cells (CSC) sheds new light on various aspects of tumor growth and progression. Here, we present a mathematical model of malignancies to investigate how a hierarchical organized cancer cell population affects the fundamental properties of solid malignancies. We establish that tumors modeled in a CSC context more faithfully resemble human malignancies and show invasive behavior, whereas tumors without a CSC hierarchy do not. These findings are corroborated by in vitro studies. In addition, we provide evidence that the CSC model is accompanied by highly altered evolutionary dynamics compared with the ones predicted to exist in a stochastic, nonhierarchical tumor model. Our main findings indicate that the CSC model allows for significantly higher tumor heterogeneity, which may affect therapy resistance. Moreover, we show that therapy which fails to target the CSC population is not only unsuccessful in curing the patient, but also promotes malignant features in the recurring tumor. These include rapid expansion, increased invasion, and enhanced heterogeneity.
Integrated Systems and Technologies: Mathematical Oncology
Cancer Stem Cell Tumor Model Reveals Invasive Morphology
and Increased Phenotypical Heterogeneity
, Joost J.C. Verhoeff
, Tijana Borovski
, Shannon K. McWeeney
, Jan Paul Medema
, Peter M.A. Sloot
, and Louis Vermeulen
The recently developed concept of cancer stem cells (CSC) sheds new light on various aspects of tumor
growth and progression. Here, we present a mathematical model of malignancies to investigate how a hier-
archical organized cancer cell population affects the fundamental properties of solid malignancies. We estab-
lish that tumors modeled in a CSC context more faithfully resemble human malignancies and show invasive
behavior, whereas tumors without a CSC hierarchy do not. These findings are corroborated by in vitro studies.
In addition, we provide evidence that the CSC model is accompanied by highly altered evolutionary dynamics
compared with the ones predicted to exist in a stochastic, nonhierarchical tumor model. Our main findings
indicate that the CSC model allows for significantly higher tumor heterogeneity, which may affect therapy
resistance. Moreover, we show that therapy which fails to target the CSC population is not only unsuccessful
in curing the patient, but also promotes malignant features in the recurring tumor. These include rapid
expansion, increased invasion, and enhanced heterogeneity. Cancer Res; 70(1); 46–56. ©2010 AACR.
Malignancies arise after sequential accumulations of
mutations in oncogenes and tumor suppressor genes (1).
During the process of malignant transition, fundamental
regulatory mechanisms are lost. The cancerous cell popula-
tion has unlimited growth potential, evades the immune
system and apoptosis, and often acquires the ability to
breach tissue boundaries and expand into foreign environ-
ments (1). The cancer stem cell (CSC) concept sheds new
light on all of these features (2, 3). In this study, we investi-
gate the influence of a hierarchical organization of malignant
clones on tumor growth, evolution, invasion, and morpholo-
gy using a multi-scale cellular automaton–based computer
CSCs. Malignancies are highly heterogeneous tissues con-
taining largely diverse cancer cell populations as well as other
cells such as fibroblasts and macrophages (1). The dominant
genetic view of malignancies explains the heterogeneity in
cancer cells with the presence of genetically diverse clones
emerging from the continuous acquiring of additional genetic
lesions by cancer cells. Such clones compete for resources,
resulting in a highly dynamic process known as Tumor Dar-
winism (5). In this article, we refer to this view of malignan-
cies as the classical model. Although this model greatly
contributes to our understanding of malignancies, recent ex-
perimental evidence suggests an additional layer of complex-
ity. The heterogeneity present in tumors could, in part, be the
result of the diversity in differentiation grade of genetically
identical cells (3, 6). For example, in glioblastoma multiforme,
cells with an immature phenotype expressing the cell surface
marker AC133 are the cells that fuel tumor growth and have
the exclusive capacities to self-renew, differentiate, and trans-
plant the malignancy into severe combined immunodeficien-
cy mice (7). Self-renewal and spin-off of differentiated cells
are features shared with normal stem cells, and therefore,
cells with such features in malignancies are defined as CSCs
Computational Science, Faculty of Science,
University of Amsterdam and
Laboratory for Experimental Oncology
and Radiobiology (LEXOR), Center for Experimental Molecular
Medicine, Academical Medical Center, Amsterdam, the Netherlands;
Division of Bi ostatistic s, Department of Public Health and Preventive
Medicine, Oregon Health and Science University, and
Cancer Institute Portland, Portland, Oregon
Note: Supplementary data for this article are available at Cancer
Research Online (http://cancerres.aacrjournals.org/).
Current address for A. Sottoriva: Department of Oncology, University of
Cambridge, CRUK Cambridge Research Institute, Li Ka Shing Centre,
P.M.A. Sloot and L. Vermeulen share senior authorship.
Corresponding Author: Louis Vermeulen, Academic Medical Center,
Meibergdreef 9, 1105AZ, Amsterdam, the Netherlands. Phone:
31-20566-4777; Fax: 31-20697-7192; E-mail: firstname.lastname@example.org.
©2010 American Association for Cancer Research.
This research shows that the hierarchical organi-
zation of malignant clones, as advocated in the CSC
concept, has major implications for tumor biology.
CSC-driven tumor growth intrinsically orchestrates
tumor invasion, influences clonal selection, and
has crucial consequences for the development of
successful cancer treatments.
Cancer Res; 70(1) January 1, 201046
growth is generally ac-
cepted to be the result
of several highly com-
plex interacting pro-
such as genetic and
transduction route ac-
tivities that in turn
control cellular func-
tions such as mitosis,
apoptosis, and cell mi-
gration. In addition,
and growth factor con-
with these processes.
To study the emergent
properties of such
systems regarding pro-
liferation speed, infil-
trative growth, and
tion of cancer, ad-
models have been de-
veloped (9–11). Here,
we apply computa-
tional modeling tech-
niques to investigate
the consequences of
nized cancer cell po-
pulations on solid
tumor growth dynam-
ics and progression.
We describe that
developing concept of
CSCs in a mathemati-
cal tumor growth
model directly results
in an invasive mor-
we found that hierar-
chical organized ma-
lignant clones have
highly altered evolu-
Most strikingly, the
cal heterogeneity, a
Quick Guide to Equations and Assumptions
The stem cellular automaton (SCA) model is a hybrid cellular automaton (4) in which a
biological cell is a point (10 × 10 μm) in a lattice. Each point can be a normal cell, a cancer
cell, or a necrotic cell, and has the attributes in Table 1. After a cell division, an empty place is
created by shifting the surrounding cells outward.
Major Assumptions. Proliferation concentrates in the proximity of the tumor borders
where oxygen levels are higher, the pH is more normal, and the pressure is lower (12–14).
To model this, we assume the probability of a cell to divide to be linear, from 1 at the tumor
edges to 0 at a distance λ= 600 μm (60 cells) from the tumor margins.
Oxygen is critical for cell survival, it diffuses into the tumor and it is consumed by cancer
cells. Upon discretization of Eq. (A), cancer cells nconsume oxygen at rate κ.
Major Assumptions. Oxygen around the tumor is kept constant by the vascular
system. Cell quiescence occurs below an oxygen threshold κ
and necrosis below an oxygen
During tumor progression, cancer cells lose cell-to-cell attachment and invade the sur-
rounding tissues (15). This process is modeled using the Hybrid Discrete-Continuum Tech-
nique (16), in which cancer cells ndisperse with coefficient D
. To simulate adhesion, we
allow cell movement if the number of neighboring tumor cells g≥α, where αis the adhesion
coefficient of the cell in the range 0 to 4.
Major Assumptions. Cells move according to a random motion coefficient D
adhesion coefficient α.
CSCs divide symmetrically with probability P
and asymmetrically with probability 1 −P
Two new CSCs result from the former, a differentiated cancer cell (DCC) and a CSC from the
latter. CSCs possess unlimited replicative potential and self-renewal whereas DCCs can divide
up to Htimes. A CSC growth model has small P
values, whereas for P
= 1, we simulate the
classical model of malignancies.
Major Assumptions. We fix H= 5 and vary P
to simulate different CSC frequencies. As
suggested experimentally for both CSCs and normal stem cells, we have restricted migration to
We introduced tumor phenotypical heterogeneity in some experiments by assuming that
every CSC self-renewal division has a chance P
for the new CSC to acquire a different phe-
notype (see Supplementary Materials and Methods).
Major Assumptions. Only CSCs contribute to tumor evolution in the long run.
Cancer Stem Cell–Driven Tumor Growth
Cancer Res; 70(1) January 1, 2010www.aacrjournals.org 47
feature that could have immediate consequences for therapy
Materials and Methods
SCA model. We developed a hybrid tumor growth model
based on cellular automata (4) and partial differential equa-
tions. We refer to this model as the SCA model. In the SCA
model, the individual cancer cell is the fundamental unit of
the tumor, we simulate its proliferation, metabolism, migra-
tion, stemness, and differentiation (see Quick Guide and
Supplementary Materials and Methods).
Implementing the CSC model of malignancies means to
simulate cancer cells with different replicative potential with-
in the tumor. For simplicity, we assume that in our model
there are only two types of cells: CSCs and DCCs. CSCs possess
unlimited replicative potential and could either generate new
CSCs (with a probability P
) or DCCs. DCCs can divide for a
maximum of Hgenerations before stopping to proliferate irre-
versibly. This method yields a hierarchy with CSCs at the top
and DCCs at the bottom. We simulate the classical model
of malignancies, in which all cells possess tumor growth–
promoting capacities, by simply setting P
= 1. In such a situ-
ation, all cells possess stem cell characteristics. Using this
method, we have an intuitive way to compare the flat, classical
tumor model with the hierarchically organized CSC model.
Emergent invasive morphology. Computational modeling
allows the exploration of highly complex systems, such as tu-
mor growth. In this study, we have used a computational tu-
mor growth model to test the consequences of hierarchical
organized clones on a vast range of areas of tumor biology.
These include tumor growth dynamics and morphology, but
also tumor evolution and therapeutic effects. The applied
computational modeling technique allows us to get more in-
sight into the underlying dynamics of these aspects of cancer
growth and progression that would be impossible in a con-
ventional experimental biological setting.
First, we investigated how tumor growth dynamics are al-
tered upon varying the CSC fraction. In the SCA model, this cor-
responds to changing the variable P
. For high values of P
expect to model the classical interpretation of tumors because
all cell divisions are symmetrical and all cells are therefore
clonogenic. In contrast, low values of P
CSC model. We simulated the growth of tumors with P
= 0.1, and P
= 0.03 with the variables described in Table 1.
Figure 1Ashows the fraction of CSCs on the total amount of
tumor cells for different values of P
. The selected P
correspond to CSCs populations comprising roughly 100%,
1%, or 0.1% of the total tumor volume and therefore cover
mainly the CSC fractions observed in a variety of solid malig-
nancies (2). In the CSC model (P
= 0.1 and P
= 0.03), small
(early) lesions have relatively high fractions of CSCs, although
this number decreases and tends to stabilize when the tumor
progresses. This observation is supported by in vivo studies
that find increased numbers of CSC marker–bearing cells in
micrometastases compared with larger tumors (21). This indi-
cates that even with fixed self-renewal rates (P
), this phenom-
enon is intrinsic to lesions initiated by a single CSC although
environmental factors influencing self-renewal frequencies
are also likely to contribute. Tumor growth curves for various
values all display the classical Gompertzian-like growth ki-
netics. However, as expected with equal cell cycle durations,
the self-renewal rates of the stem cell fraction influences pro-
liferation rate greatly, hence, low self-renewal rates (small P
correspond to slow tumor growth (Fig. 1B). Interestingly, the
decrease in accumulation of tumor volume is accompanied by
a stabilization of the fraction of CSCs, suggesting an intimate
relationship between these two processes.
Spatially, all experiments display a three-layered structure
consisting of an external proliferative area, an inner senes-
cent layer, and a necrotic core. However, tumor morpholo-
gies for different P
values are remarkably dissimilar
(Fig. 1D). For P
= 1, in which there is no hierarchy, a sym-
metrical, sphere-like tumor morphology is generated that
closely resembles early tumor growth models (22, 23). In
contrast, the shape of the tumors generated with low P
values is highly irregular (especially P
= 0.03). CSC-driven
Table 1. Cellular and microenvironmental variables in the SCA model
Variables Symbol Value Reference/justification
Proliferation speed (average cell cycle duration) T20 h (44)
diffusion coefficient D
concentration, healthy tissue ω10
consumption, proliferative cells κ
consumption, senescent cells κ
concentration resulting in necrosis θ5×10
Senescent consumption as minimum
concentration for cell survival
Random mobility D
Maximum number of generations generated by DCCs H5 We choose to fix Hto 5 and vary P
generate various CSC fractions (3)
NOTE: Variables used in the SCA model. See the Quick Guide and Materials and Methods for details.
Sottoriva et al.
Cancer Res; 70(1) January 1, 2010 Cancer Research48
tumors yield highly invasive morphologies with fingering
fronts and clusters of cancer cells beyond the tumor mar-
gin, driven by the mobility and the exclusive proliferative
properties of CSCs (Movies S1 and S2).
From Fig. 1C, it is evident how hierarchically organized
= 0.03 and P
= 0.1) generate a higher degree of
invasiveness (see Supplementary Materials and Methods),
compared with tumors in the classical model (P
= 1). It is
important to note that the intrinsic properties of the cells
in the classical tumor and the stem cells in the CSC-driven
tumor are completely identical.
Magnification of a tumor border in a CSC-fueled tumor
growth model (P
= 0.03) shows how CSCs migrate beyond
the margins of the tumor mass. CSCs colonize the surround-
ing tissue and expand locally, forming small satellites that
grow back into, and are engulfed by, the main tumor mass
(Fig. 2A). This is accompanied by the observation that the in-
vasive behavior of individual experiments that make up Fig. 1C
occurs in a wave-like fashion (Supplementary Fig. S1). These
results are paralleled by recent findings in a different model
system in which high migration levels in a small subset of
cells give rise to small proliferating extratumoral lesions and
Figure 1. Emergent invasive behavior in the CSC model. A, different P
values result in different CSC fractions. B, growth curves for different P
C, quantitative measure for invasiveness shows increasing invasive behavior with declining P
.Ato C, bars, SD (n= 16). D, hierarchical organization in the
SCA model affects tumor morphology. Tumors for different values of self-renewal probability (P
) and different volumes. Dark blue, cells which have
divided within the last 48 h (depicted larger); light blue, nondividing cells; brown, necrotic center. Right, localization of CSCs in the tumor mass. Gray, tumor
mass; red, CSCs (depicted larger). In all figures, 6 × 6 mm of tissue are represented. See also Movies S1 and S2.
Cancer Stem Cell–Driven Tumor Growth
Cancer Res; 70(1) January 1, 2010www.aacrjournals.org 49
therefore tumors are “conglomerates of self-metastasis”as
the authors propose (24).
In an endeavor to validate these observations from our
computational model, we investigated human tumor speci-
mens. Close examination of the histology of different highly
diverse human malignancies displayed a relatively confined
large tumor mass with clearly detached tumor cells forming
small lesions in the surrounding normal tissue (Fig. 2B). This
exemplifies that human tumor histology contains indications
of a stepwise infiltration and colonization of the surrounding
tissue as our model predicts would follow from a hierarchical
organized malignancy. Next, we attempted to determine the
relationship between CSC fraction and invasive properties, as
predicted by the model, using in vitro cell culture (Fig. 2C;
Figure 2. Invasive behavior in silico, in vivo,
and in vitro. A, close-up of tumor border
showing invasive behavior for P
CSCs (red) infiltrate surrounding tissue and
spin-off DCCs that proliferate (dark blue).
Small satellites are formed in the
surrounding normal tissue (white) and grow
back to and are engulfed by the main
tumor mass. Nondividing cells (light blue).
B, representative figures of various
malignancies. All images reveal island-like
formations at the rim of the main tumor
mass (T). These findings are in line with
tumor expansion as predicted by the SCA
model that implements a CSC hierarchy.
C, cell lines (n= 24) have been plated at
clonal density in Matrigel. Simultaneously,
the clonogenic fraction of the lines has
been determined by limiting dilution
analysis. A significant (P= 0.02) inverse
relationship exists between clonogenicity
and invasion as quantified by the measure
of invasiveness we defined. Two examples
of cell lines are shown and invasiveness
(IM) and clonogenicity are indicated (right).
See Supplementary Figs. S2 to S5 and
Supplementary Table S1 for details.
Sottoriva et al.
Cancer Res; 70(1) January 1, 2010 Cancer Research50
Supplementary Figs. S2–S5 and Table S1). We determined the
clonogenicity of a set of various cell lines (n= 24) as a sur-
rogate for their CSC fraction. Additionally, we quantified the
invasive properties of clonally derived structures with our
measure of irregular morphology both on adherent plates
and in Matrigel for all these lines. A significant inverse rela-
tionship between clonogenic fraction and the invasive prop-
erties of these lines exists. This implicates that tumor
structures driven by a small fraction of clonogenic cells tend
to generate a more irregular and invasive morphology, a find-
ing that corroborates the predictions of our model. Com-
bined, we take this as evidence that the SCA model based
on the CSC concept closely resembles tumor growth patterns
Expansion of the model in three dimensions retains in-
vasive morphology. To show that our results are not limited
to two dimensions only, we expand the SCA model to three
dimensions (see Supplementary Materials and Methods).
The three-dimensional SCA model reproduces the invasive tu-
mor morphology induced by the hierarchical organization,
yielding three-dimensional fingering tumor fronts and clusters
of cancer cells beyond the borders of the main tumor mass
(Fig. 3A; Movie S3). On the contrary, again a classical model
with equal volume does not display any apparent invasive pat-
tern and instead exhibits a spherical morphology (Fig. 3B;
Movie S4). We therefore propose that the CSC model, in con-
trast to the flat model, more faithfully reproduces the human
tumor morphology for both the two-dimensional and the
CSC organization stimulates tumor heterogeneity. The
dominant model evoked to explain the advancement of
malignancies is clonal evolution, as was first proposed by
Nowell (5). The term effective population size is used in pop-
ulation genetics to indicate the fraction of total individuals
in a population that effectively contributes to the next gen-
eration and are therefore evolutionarily relevant. Hence, the
effective population size in a CSC-driven malignancy is smal-
ler than in the classical model because only mutations in the
CSC compartment contribute to the evolutionary process (2).
To implement clonal evolution in our model, we assume
that, at each symmetrical division a CSC has a probability
to acquire a genetic hit and generate a daughter cell
with a different phenotype selected from a randomly gener-
ated pool of 30 phenotypes (Table S2 and S3; see Supplemen-
tary Materials and Methods). Under an equal mutation rate
= 0.1), the CSC model exhibits a slower acquisition of
new phenotypes due to its smaller effective population size
(Fig. 4A), but also shows a radically different selection
Figure 3. Expansion of the model
in three-dimensions retains
of CSC-driven tumor growth
= 0.03) and of the classical
tumor model (B, P
= 1). Aand B,
cells are represented. Inset,
region that is enlarged in the right
image. Normal tissue (black)
and tumor cells (white). Cube
cell lattice. See
also Supplementary Movies S3
Cancer Stem Cell–Driven Tumor Growth
Cancer Res; 70(1) January 1, 2010www.aacrjournals.org 51
process. Strikingly, although the rate of emergence of new
phenotypes is much lower than observed in the classical
model, a wide range of newly acquired phenotypes expands
and contributes to the malignancy (Supplementary Fig. S6A
To compare the phenotypical selection more closely, we
synchronize the pace at which new traits emerge. Evolution-
arily, a CSC model with P
= 0.03 and P
= 0.5 corresponds
to a classical model with P
= 1 and P
= 0.001 (Fig. 4B).
Intriguingly, despite this adaptation of the mutation pace,
the two models differ substantially in the way they exercise
clonal selection. From a representative example in Fig. 4C,it
is evident that the CSC model allows for a much higher phe-
notypical heterogeneity whereas the classical model seems to
select for a small number of aggressive clones (average result
in Supplementary Fig. S6C). Quantification of the heterogene-
ity clearly underscores this (Supplementary Fig. S7Aand Sup-
plementary Materials and Methods). It is important to realize
that the selective pressure from the environment is equal in
both models. This, combined with the equal rate of new
phenotype occurrence, suggests that the geometric proper-
ties of the CSC model promote heterogeneity. We argue
that the intrinsic properties of the CSC model might propel
an alternative process to natural selection, referred to as
genetic drift (25). In populations with small effective popu-
lation sizes, sampling errors are frequent and might allow
for the expansion of clones with no clear survival benefit.
Interestingly, the invasive properties of the CSC model
might fuel such a sampling error promoting mechanism.
The phenomenon we observe at the tumor margins during
invasion: a CSC migrating out of the tumor initiating a
small satellite lesion, resembles the Founder Effect (26).
The Founder Effect occurs when a new population is estab-
lished by a low number of individuals from a larger popu-
lation, this process is often accompanied by a loss of
phenotypical variation in the new population due to sam-
pling errors. In such a scenario, the new generation can
differ substantially from the previous and is not in direct
competition for nutrients and space. This implies that the
pattern of tumor growth in the CSC model stimulates
genetic drift at the infiltrative edges of the tumor and
therefore promotes phenotypical heterogeneity.
Figure 4. Tumor evolution and phenotypical selection in a cancer stem cell context. Phenotypes are randomly generated and possess traits listed in
Supplementary Table S3. A, with equal mutation rates (P
= 0.1), the cumulative amount of phenotypes that emerge is higher in the classical model
= 1) compared with the CSC model (P
= 0.03). B, we adapted P
to obtain an equal rate of emergence of phenotypes. C, under equal conditions,
the phenotypes in the CSC model are more diverse compared with the classical model. A representative example is shown, see also Supplementary
Movies S5 and S6. Aand B, bars, SD (n= 8). C, fraction of cells for each newly generated phenotype. The original phenotype “1”is ignored. For an average
of eight experiments, see Supplementary Figs. S6Band S6C.
Sottoriva et al.
Cancer Res; 70(1) January 1, 2010 Cancer Research52
Dynamics of therapeutic interventions in hierarchical
organized malignancies. After having established the effects
of CSC-driven tumor growth on the invasion and evolution of
malignancies, we now explore the crucial topic of therapeutic
intervention and tumor relapse. CSCs have been suggested to
be more resistant to therapeutic interventions such as che-
motherapy or irradiation compared with their differentiated
counterparts (27, 28). Also tumors that relapse after seeming-
ly successful therapy are believed to regrow from the CSC
that survived the therapeutic regimen (27). Here, we investi-
gate the dynamics associated with therapeutic interventions
that are either selective for non-CSCs or equally efficient
against both cell types. We find that the morphology and
growth kinetics of relapses for both types of therapeutic in-
terventions are very much different (Fig. 5; see Supplementa-
ry Materials and Methods). Regrowth after therapy that
specifically targets DCCs is accompanied by enhanced inva-
sive growth patterns whereas relapsing tumors after stochas-
tic tumor cell killing are similar to the malignancy before
treatment (Fig. 5A). Simultaneously, in case CSCs are resis-
tant to therapy, the pace at which the malignancy relapses
is greatly enhanced due to the relatively high fraction of
CSCs directly following therapy (Fig. 5B). Also, the invasive-
ness of the recurrent tumors is markedly increased following
Figure 5. Dynamics of therapeutic
intervention in hierarchical organized
malignancies. A, effects of therapy
in simulated tumors considering
CSCs to be resistant to treatment
(top) or sensitive to treatment
(bottom). Left, pretreated tumor at
= 25,000 cells. Right, after
treatment and relapsed tumor for
of tumor relapse. Whereas
therapy-sensitive CSCs recapitulate
the initial growth pace, resistant
CSCs yield a faster growth at
relapse. C, a marked increase of
invasive morphology just after
treatment occurs particularly in the
case of resistant CSCs. Band C,
arrows, therapy (n= 8). D, phenotype
distribution in the two cases of
therapy response assuming no
further mutation to occur after
therapy (see Supplementary Fig. S8
for an average of eight experiments).
Although a treatment-resistant
CSC-driven tumor is able to
recapitulate the clonal features of
the initial malignancy by conserving
the initially developed heterogeneity,
for therapy-sensitive CSCs, the
recurrent tumor is highly altered in
terms of phenotypes.
Cancer Stem Cell–Driven Tumor Growth
Cancer Res; 70(1) January 1, 2010www.aacrjournals.org 53
intervention which is not effective against CSCs (Fig. 5C).
These findings are in line with a range of clinical observa-
tions describing increased growth speed and enhanced inva-
sion in the relapsing malignancy that are mostly attributed to
the selection of more aggressive clones by the drug (29–31).
However, our data now indicate that these observations
could be partially explained by the failure of conventional
therapies to eradicate the CSC compartment and the subse-
quent relapse dynamics in CSC-driven tumors. Evaluation of
evolutionary dynamics during relapse after both types of in-
tervention revealed significant differences as well. Following
therapy which is ineffective against CSCs, relapsing tumors
display a marked increase in heterogeneity, whereas therapy
that does target CSCs results in a dramatic decrease of het-
erogeneity (Supplementary Fig. S8). This latter scenario is re-
lated to the fact that relapses are very much different
compared with the primary malignancy with respect to the
clonal lineages that contribute to the relapse of the tumor
(Fig. 5D). Combined, this implicates that applying therapy
that is ineffectively targeting the CSC population is not only
unsuccessful in curing the patient but also promotes malig-
nant features including rapid expansion, increased invasion,
and stimulates heterogeneity directly after therapy.
We have applied a computational tumor growth model to
investigate the effects of hierarchical organization on a range
of areas in tumor biology. The obtained results provide novel
insights into the influence of CSC-driven tumor growth on tu-
mor morphology and invasion. Importantly, we have been able
to partially validate these findings in a biological experimental
setting. We have also established a significant effect of hierar-
chical organized malignant clones on tumor evolution, and
consequently, on tumor progression and relapse after therapy.
Our results stress the need to develop therapeutic interven-
tions that efficiently target the CSC compartment because
drugs that fail to do so are not only unable to cure the pa-
tient—but even enhance the malignant properties of tumors.
Therefore, we conclude that computational oncology has the
potential to greatly enhance our understanding of fundamen-
tal cancer biology and improve future therapeutics.
CSC-Driven tumor growth. The capacity to display infil-
trative growth is a pathognomic feature of malignant cells
(1). Crossing tissue boundaries is the first step in the process
of metastasis and is therefore of special interest. Surprisingly,
this aspect of tumor growth has rarely been investigated in
mathematical models. However, recent important work of
Anderson and colleagues (11) and Bearer and colleagues
(32) illuminate how selective pressure, applied by the micro-
environment, in combination with tumor cell heterogeneity,
could result in an invasive morphology. Here, we report how,
in the SCA model, invasion emerges from the hierarchical
organization of malignant clones and need not be driven
by external interaction with a heterogeneous microenviron-
ment. Hence, invasive morphology is an intrinsic feature of
CSC-driven malignancies and has to be considered when
studying tumor invasion.
Simultaneously, high levels of clonal heterogeneity within
malignancies are associated with rapid progression of the dis-
ease (33), poorer survival (34), and occurrence of therapy resis-
tance (35). Understanding this phenomenon in more detail
might improve the design of more effective treatments and che-
mopreventives. Our results show how CSC-driven tumor
growth stimulates heterogeneity in malignancies. This is related
to the reduced effective population size in these malignancies
and the typical growth pattern that results in the segregation of
clones by formation of small invasive lesions. These satellite
structures are not in direct competition with the dominant
clone, allowing suboptimal clones to expand. We speculate that
interfering with these dynamics, for example by inhibiting mi-
gration, and thereby segregation, might be a potent means by
which reduced heterogeneity accompanied by the slower pro-
gression of the disease and better response to therapy can be
achieved either in a chemopreventive or therapeutic setting.
Additionally, our results underlie the need to develop ther-
apeutic modalities that successfully eradicate the CSC com-
partment. We show how therapeutic interventions that do
not target CSCs efficiently are not only ineffective as a cure,
but might even contribute to an increase in malignant prop-
erties of the relapsing tumor. We find, for example, enhanced
heterogeneity and invasion in the relapsing tumors that are
treated with interventions that are only directed against the
differentiated cells. This is not due to the selection of the most
malignant clones present in the cancer tissue but are intrinsic
to the dynamics of regrowth in CSC-driven malignancies.
Experimental validation and future directions. The
model presented provides a range of predictions and implica-
tions regarding CSC-fuelled tumor growth that can be tested
and exploited to investigate the propertiesof hierarchical orga-
nized malignancies. Here, we report that the clonogenicity of
cell lines is connected with the invasive properties of these lines
in vitro as suggested by our model. In future research, it would
be interesting to expand this finding to human tumor speci-
mens or in established CSC lines in which the CSC fraction
can be manipulated. Additionally, our model illuminates how
tumor features, such as clonal heterogeneity, are related to the
CSC fraction (Supplementary Fig. S7B). Therefore, we speculat-
ed that careful analysis of these tumor properties might lead to
optimized techniques that establish the CSC fraction in malig-
nancies without the need for transplantation studies which are
currently highly disputed (36, 37).
The current version of the SCA model clearly shows the dy-
namics of CSC-driven tumor growth and its consequences for
tumor morphology and evolution. However, further research
efforts will undoubtedly lead to increased insight into the na-
ture of the hierarchical organization of tumor cells. If so, the
SCA model can be easily adapted to implement potential new
information and subsequently come to even more accurate
description of tumor growth. For instance, we have assumed
several variables such as CSC self-renewal frequency, muta-
tion rate, and migration speed to be constant. However, in
in vivo tumors, these variables might be more dynamic both
throughout tumor progression and as a consequence of
microenvironmental interactions. For example, CSCs have
been suggested to reside in a so-called “CSC niche”that is
Sottoriva et al.
Cancer Res; 70(1) January 1, 2010 Cancer Research54
formed by secreted factors and direct cell-cell interactions
(38, 39). This niche is believed to protect CSC from differen-
tiation and to promote CSC self-renewal and therefore intro-
duces dynamic P
values. Moreover, physical circumstances
such as oxygen concentration might have differential effects
on CSCs and DCCs, and therefore, might play a role in dynam-
ic CSC functions (40). In addition, mutation rates are poten-
tially subject to changes during tumor development (41) and
intriguingly, might even be influenced by environmental con-
ditions, such as that reported for bacteria (42). Currently, it
remains elusive as to what extent this latter phenomenon,
which is referred to as “adaptive mutation,”is involved in
human malignancies (43). All these considerations justify
further investigations, but will be dependent on thorough
experimental examination of the variables involved.
Importantly, from the current formulation of the SCA
model, it is indisputable that hierarchical organization of ma-
lignancies significantly contributes to the invasive morphol-
ogy and increased heterogeneity of tumors and is therefore a
crucial issue for better understanding tumor biology and to
improve current anticancer treatments.
Disclosure of Potential Conflicts of Interest
No potential conflicts of interest were disclosed.
We thank M.R. Sprick, D.J. Richel, and F. de Sousa Mello
for useful comments and R. Belleman and J.H. de Jong for
Academic Medical Center (J.J.C. Verhoeff, J.P. Medema,
and L. Vermeulen), ZonMW VICI program (J.P. Medema),
and the Faculty of Science of the University of Amsterdam
(A. Sottoriva, L. Naumov, and P.M.A. Sloot).
The costs of publication of this article were defrayed in part
by the payment of page charges. This article must therefore
be hereby marked advertisement in accordance with 18 U.S.C.
Section 1734 solely to indicate this fact.
Received 6/15/09; revised 10/20/09; accepted 10/20/09.
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