This document describes a mathematical model that was developed to test the hypothesis of tumor self-seeding. Specifically: 1) The model represents the human circulatory system as a directed network with organs as nodes and arteries/veins as edges. 2) Circulating tumor cells are introduced into the model, with heterogeneity defined by phenotypes from the primary tumor. 3) The model incorporates the biological processes of shedding rate from the primary tumor, CTC heterogeneity, organ-specific filtration fractions, and clearance rates from blood and organs. 4) The goals of the model are to define CTC concentrations and phenotypes over time, calculate the average CTC lifespan in circulation, and better understand metastasis patterns based

1. Primary Seeding
Testing the self-seeding hypothesis
with a mathematical model
Jacob G Scott1,2, David Basanta1, Philip Gerlee3,4 & Alexander RA Anderson1
1. Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, USA 2. Centre for Mathematical Biology, Oxford University, UK
3. Sahlgrenska Cancer Center, University of Gothenburg, Sweden 4.Mathematical Sciences, Chalmers University of Technology, Sweden
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Jacob G. Scott, David Basanta, Alexander R. A. Anderson and Philip G
growth
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A mathematical model of tumour self-seedin
on March 11, 2013rsif.royalsocietypublishing.orgDownloaded from
Unifying metastasis — integrating
intravasation, circulation and
end-organ colonization
Jacob Scott1,2
, Peter Kuhn3
and Alexander R. A. Anderson1
Abstract|Recenttechnologicaladvancesthathaveenabledthemeasurementofcirculating
tumourcells(CTCs)inpatientshavespurredinterestinthecirculatoryphaseofmetastasis.
Techniquesthatdonotsolelyrelyonabloodsampleallowsubstantialbiologicalinterrogation
beyondsimplycountingCTCs.
1
Integrated Mathematical
Oncology, Moffitt Cancer
Center, Tampa,
Florida 33612, USA.
2
Oxford University Centre for
Mathematical Biology,
Mathematical Institute,
Oxford OX1 3LB, UK.
3
Department of Cell Biology,
The Scripps Research
Institute, La Jolla,
California 92037, USA.
Correspondence to A.R.A.A.
and J.S.
e-mails: alexander.
anderson@moffitt.org;
jacob.scott@moffitt.org
doi:10.1038/nrc3287
Published online 24 May 2012
In patients with advanced primary cancer, circulating
tumour cells (CTCs)1
can be found throughout the entire
vascular system2
. When and where these CTCs form
metastasis is not fully understood, and is currently the
subject of intensive biological study. Paget’s well-known
seed–soil hypothesis3
suggests that the ‘soil’ (the site of
a metastasis) is as important as the ‘seed’ (the metastatic
cells) in the determination of successful metastasis. The
mechanism by which seeds are disseminated to specific
soil has, to date, been a ‘known unknown’. We think that
it is during this poorly understood phase of metastasis
that we stand to answer important questions4
.
We hypothesize that the rich variety of possible meta-
static disease patterns not only stems from the physical
aspects of the circulation but also from CTC hetero-
geneity (FIG. 1). These seeds represent many different
populations that are derived from a diverse population
of competing phenotypes within the primary tumour5
.
Because such seeds need to pass through a system of
physical and biological filters in the form of specific
organs, the circulatory phase of metastasis could be
modelled as a complex deterministic filter. In theory,
until the evolution of a suitable seed, any number of
CTCs could flow through the circulation and arrest
at end organs without metastases forming. As tumour
heterogeneity is thought to expand as the tumour pro-
gresses, it follows that at some point a seed will come
into existence that is suited to a specific soil within that
patient’s body. If this seed is to propagate it must find
its soil, a process that we hypothesize is governed by
solvable physical rules that relate to the dynamics of
the circulatory flow between different organs and how
these organs filter (not only by size, but probably also by
other biological mechanisms). Although these biologi-
cal mechanisms are not yet known, we might be able to
infer their existence by finding out which measurements
do not fit a model that is defined only by physical flow
and filtration.
To begin the process of physical interrogation, we
propose a model that represents the human circulatory
system as a directed and weighted network, with nodes
representing organs and edges representing arteries and
veins.The novelty is only fully realized when combined
with a heterogeneous CTC population (driven by primary
tumour heterogeneity) modulated by the complex organ
filter system (with physiologically relevant connections)
under dynamic flow. Four important biological processes
emerge from this representation. First, the shedding rate,
which is defined as the rate at which the tumour sheds
CTCs into the vasculature. Second, CTC heterogeneity,
which is defined as the distribution of CTC phenotypes
present in the circulation. Third, the filtration fraction,
which is defined as the proportion (and type) of CTCs
that arrest in a given organ. Fourth, the clearance rate,
which is defined as the rate at which cancer cells are
cleared from the blood and/or organ after arrest. Each of
these biological processes is probably disease- and even
patient-specific, and each is extremely poorly understood.
Using this representation to motivate the develop-
ment of a mathematical model we can define both the
concentration of CTCs and their phenotypic distribu-
tion at any given point in the network, as well as organ-
specific filtration values. To parameterize this model,
characterization and enumeration of CTCs taken from
a single patient at different time points and from differ-
ent points in this network will need to be undertaken.
A complete understanding of the model will also pro-
vide information about the behaviour of the system as
a whole. Specifically, the average lifespan of a CTC in a
patient’s circulation will be able to be calculated with only
a minimum of measurements. Although this seems to
be a simple calculation, the scientific literature on this
NATURE REVIEWS | CANCER VOLUME 12 | JULY 2012 | 445
astasis — integrating
n, circulation and
olonization
and Alexander R. A. Anderson1
ladvancesthathaveenabledthemeasurementofcirculating
havespurredinterestinthecirculatoryphaseofmetastasis.
elyonabloodsampleallowsubstantialbiologicalinterrogation
ncer, circulating
ughout the entire
hese CTCs form
d is currently the
get’s well-known
‘soil’ (the site of
d’ (the metastatic
l metastasis. The
nated to specific
wn’. We think that
ase of metastasis
stions4
.
of possible meta-
rom the physical
m CTC hetero-
many different
verse population
rimary tumour5
.
ugh a system of
form of specific
astasis could be
filter. In theory,
any number of
ation and arrest
ming. As tumour
the tumour pro-
a seed will come
c soil within that
gate it must find
e is governed by
he dynamics of
organs and how
probably also by
gh these biologi-
might be able to
h measurements
do not fit a model that is defined only by physical flow
and filtration.
To begin the process of physical interrogation, we
propose a model that represents the human circulatory
system as a directed and weighted network, with nodes
representing organs and edges representing arteries and
veins.The novelty is only fully realized when combined
with a heterogeneous CTC population (driven by primary
tumour heterogeneity) modulated by the complex organ
filter system (with physiologically relevant connections)
under dynamic flow. Four important biological processes
emerge from this representation. First, the shedding rate,
which is defined as the rate at which the tumour sheds
CTCs into the vasculature. Second, CTC heterogeneity,
which is defined as the distribution of CTC phenotypes
present in the circulation. Third, the filtration fraction,
which is defined as the proportion (and type) of CTCs
that arrest in a given organ. Fourth, the clearance rate,
which is defined as the rate at which cancer cells are
cleared from the blood and/or organ after arrest. Each of
these biological processes is probably disease- and even
patient-specific, and each is extremely poorly understood.
Using this representation to motivate the develop-
ment of a mathematical model we can define both the
concentration of CTCs and their phenotypic distribu-
tion at any given point in the network, as well as organ-
specific filtration values. To parameterize this model,
characterization and enumeration of CTCs taken from
a single patient at different time points and from differ-
ent points in this network will need to be undertaken.
A complete understanding of the model will also pro-
vide information about the behaviour of the system as
a whole. Specifically, the average lifespan of a CTC in a
patient’s circulation will be able to be calculated with only
a minimum of measurements. Although this seems to
be a simple calculation, the scientific literature on this
VOLUME 12 | JULY 2012 | 445
d into one mammary gland in mice to form
or mass. Unlabeled MDA231-LM2 cells were inoc-
ontralateral mammary gland to form a ‘‘recipient’’
ame tumor (Figure 1A). After 60 days, the recipient
xcised and examined for the presence of seeding
ns of ex vivo bioluminescence imaging (BLI).
%) of the recipient tumors showed extensive seed-
31-LM2 cells (Figure 1B and Table 1). Tumors
more indolent MDA231 parental population were
s MDA231-LM2 tumors at capturing seed cells
Table 1). No seeding was observed in mock-inoc-
ary glands within the same time period (Figure 1C).
ce microscopy analysis of MDA231 recipient
med the presence of numerous GFP+ MDA231-
cells as distinct patches typically encompassing
uarter of a tumor section (Figure 1D and data not
n recipient tumors were generated using red-
otein (RFP)-labeled cells, the infiltrating GFP+ cells
were observed intermingling with resident RFP+ cancer cells and
with unlabeled areas of presumptive tumor stroma (Figure 1E).
Quantitative RT-PCR analysis of firefly-luciferase mRNA level
in seeded recipient tumors revealed that seeder cells accounted
for 5%–30% of the recipient tumor mass (data not shown).
To establish the generality of this seeding phenomenon, we
performed similar experiments with different cancer cell lines.
Recipient mammary tumors became seeded with high frequency
(53% to 100% of mice) by donor tumors that were formed with
bone-metastatic (MCF7-BoM2), lung-metastatic (MDA231-
LM2), or brain-metastatic (CN34-BrM2) cells from different sub-
types of breast cancer (basal, estrogen receptor-negative
MDA231 cells versus luminal, estrogen receptor-positive MCF7
cells) or patient-derived malignant cell cultures (CN34 cells)
(Figure 1B and Table 1). Seeding of a recipient tumor by its own
aggressive progeny was also observed between subcutaneous
tumors formed by the human colon carcinoma line SW620 and
its lung-metastatic derivative SW620-LM1, and between the
ing of Established Tumors by CTCs
ontralateral seeding experiment. Unlabeled and GFP/luciferase-expressing breast cancer cells were injected into contralateral No. 2 mammary
pient tumor’’ and a ‘‘donor tumor,’’ respectively.
t tumors extracted from mice bearing the indicated GFP/luciferase-expressing donor tumors. Color-range bars: photon flux. LM2: a lung-meta-
of MDA231. MCF7-BoM2: a bone-metastatic derivative of MCF7. CN34-BrM2: a brain-metastatic derivative of pleural effusion CN34. PyMT:
m mammary tumors developed in MMTV-PyMT transgenic mice.
ree and tumor-bearing mammary glands from mice bearing GFP/luciferase-expressing donor tumors. n = 9–18. Error bars represent SEM.
ns of seeded MDA231-LM2 tumors were visualized by fluorescence microscopy. An entire tumor section and a higher-magnification image (310)
d are shown.
al seeding experiment was performed with RFP- and GFP-expressing MDA231-LM2 cells. Frozen sections from RFP-labeled tumors were
confocal microscopy at 320.
test mammary tumor seeding from lung metastases. GFP/luciferase-expressing MDA231-LM2 cells were injected intravenously. Once lung
established, unlabeled MDA231 cells were injected into a mammary gland No. 2.
f CTCs derived from lung metastases in mice described in (F). Relative levels of CTC were plotted against the luminescent signals of recipient
LI of three representative recipient tumors (i, ii, and iii) identified in the graph.
, 1315–1326, December 24, 2009 ª2009 Elsevier Inc.
CTCs to infiltrate tumors in response to this attraction (Fig-
ure 3E).
To gain further insight into these attraction and infiltration
functions, we performed a trans-endothelial migration assay in
which tumor cell-conditioned media were placed in the bottom
well of the chamber (Figure 4A). Media conditioned by MDA231
breast carcinoma or A375 melanoma cells were several-fold
more active at stimulating the trans-endotheilal migration of
MDA231-LM2 cells than were media conditioned by MCF10A
cells, a human breast epithelial cell line derived from untrans-
formed tissue (Figure 4B). Similarly, A375-BoM2 melanoma cells
migrated through endothelial cell layers more actively inresponse
to these cancer cell-conditioned media than to media condi-
tioned by HaCat cells (Figure 4B), a human keratinocyte cell line
representing the most abundant cell type in skin epidermis.
Media from MDA231 and MDA231-LM2 cultures were equivalent
as a source of attraction in these experiments (Figure 4C), which
is consistent with the equivalent ability of these two cell lines to
act as recipient tumors in self-seeding assays (refer to Figure 1B
and Table 1).
MDA231 cells further stimulated the trans-endothelial migration
of MDA231-LM2 cells (Figure 4C). Parental MDA231 cells
showed low trans-endothelial migration activity even in the pres-
ence of media conditioned by tumor cells (Figure 4C). Similarly,
the migration of A375-BoM2 cells through endothelial layers
was several-fold more efficient than that of the parental A375
cells in the presence of conditioned media from A375 or A375-
BoM2 (Figure 4C). These results demonstrated that cancer cells
release signals that attract their progeny across endothelial
layers. In addition, these results suggest that aggressive cancer
cells are superior to their more indolent counterparts in their
ability to migrate in response to these signals.
Tumor-Derived Mediators of Cancer Cell Attraction
To identify candidate tumor-derived attractants for CTCs, we
compared the secreted levels of 180 cytokines in conditioned
media. This analysis uncovered several cytokines whose
production was higher (IL-6, IL-8, oncostatin M, and vascular
endothelial growth factor [VEGF]) or lower (CCL2) in MDA231
and its derivatives than in MCF10A cells (Figures 5A, S2A, and
Figure 3. Tumor Attraction and Infiltration Functions
(A) Unlabeled MDA231 cells were injected into a mammary gland No. 2. When tumors became palpable, LacZ/GFP/luciferase-expressing MDA231-LM2 cells
were introduced into the circulation by intracardiac injection.
(B) BLI of mice with seeded and unseeded tumors. Arrow, recipient tumor.
(C) Comparative tumor-seeding ability of MDA231 and MDA231-LM2 cells from the circulation. Luminescent signals from recipient tumors at the indicated time
points are shown.
(D) Luminescent signals of recipient tumors from mice injected with indicated cell lines were quantified 10 (MDA-231) and 5 (A375) days after injection. n = 6–10.
(E) A diagram summarizing two functions involved in tumor self-seeding.
Error bars in all cases represent SEM and p values were based on two-tailed Mann-Whitney test.
Kim et al. (2009) Cell
and inoculated into one mammary gland in mice to form
a ‘‘donor’’ tumor mass. Unlabeled MDA231-LM2 cells were inoc-
ulated into a contralateral mammary gland to form a ‘‘recipient’’
mass of the same tumor (Figure 1A). After 60 days, the recipient
tumors were excised and examined for the presence of seeding
cells by means of ex vivo bioluminescence imaging (BLI).
A majority (85%) of the recipient tumors showed extensive seed-
ing by MDA231-LM2 cells (Figure 1B and Table 1). Tumors
formed by the more indolent MDA231 parental population were
as effective as MDA231-LM2 tumors at capturing seed cells
(Figure 1B and Table 1). No seeding was observed in mock-inoc-
ulated mammary glands within the same time period (Figure 1C).
Fluorescence microscopy analysis of MDA231 recipient
tumors confirmed the presence of numerous GFP+ MDA231-
LM2 seeding cells as distinct patches typically encompassing
less than a quarter of a tumor section (Figure 1D and data not
shown). When recipient tumors were generated using red-
fluorescent protein (RFP)-labeled cells, the infiltrating GFP+ cells
were observed intermingling with resident RFP+ cancer cells and
with unlabeled areas of presumptive tumor stroma (Figure 1E).
Quantitative RT-PCR analysis of firefly-luciferase mRNA level
in seeded recipient tumors revealed that seeder cells accounted
for 5%–30% of the recipient tumor mass (data not shown).
To establish the generality of this seeding phenomenon, we
performed similar experiments with different cancer cell lines.
Recipient mammary tumors became seeded with high frequency
(53% to 100% of mice) by donor tumors that were formed with
bone-metastatic (MCF7-BoM2), lung-metastatic (MDA231-
LM2), or brain-metastatic (CN34-BrM2) cells from different sub-
types of breast cancer (basal, estrogen receptor-negative
MDA231 cells versus luminal, estrogen receptor-positive MCF7
cells) or patient-derived malignant cell cultures (CN34 cells)
(Figure 1B and Table 1). Seeding of a recipient tumor by its own
aggressive progeny was also observed between subcutaneous
tumors formed by the human colon carcinoma line SW620 and
its lung-metastatic derivative SW620-LM1, and between the
Figure 1. Seeding of Established Tumors by CTCs
(A) A diagram of contralateral seeding experiment. Unlabeled and GFP/luciferase-expressing breast cancer cells were injected into contralateral No. 2 mammary
glands as a ‘‘recipient tumor’’ and a ‘‘donor tumor,’’ respectively.
(B) BLI of recipient tumors extracted from mice bearing the indicated GFP/luciferase-expressing donor tumors. Color-range bars: photon flux. LM2: a lung-meta-
static derivative of MDA231. MCF7-BoM2: a bone-metastatic derivative of MCF7. CN34-BrM2: a brain-metastatic derivative of pleural effusion CN34. PyMT:
cells derived from mammary tumors developed in MMTV-PyMT transgenic mice.
(C) BLI of tumor-free and tumor-bearing mammary glands from mice bearing GFP/luciferase-expressing donor tumors. n = 9–18. Error bars represent SEM.
(D) Frozen sections of seeded MDA231-LM2 tumors were visualized by fluorescence microscopy. An entire tumor section and a higher-magnification image (310)
of a selected field are shown.
(E) A contralateral seeding experiment was performed with RFP- and GFP-expressing MDA231-LM2 cells. Frozen sections from RFP-labeled tumors were
visualized under confocal microscopy at 320.
(F) A diagram to test mammary tumor seeding from lung metastases. GFP/luciferase-expressing MDA231-LM2 cells were injected intravenously. Once lung
metastases were established, unlabeled MDA231 cells were injected into a mammary gland No. 2.
(G) Left: burden of CTCs derived from lung metastases in mice described in (F). Relative levels of CTC were plotted against the luminescent signals of recipient
tumors. Right: BLI of three representative recipient tumors (i, ii, and iii) identified in the graph.
1316 Cell 139, 1315–1326, December 24, 2009 ª2009 Elsevier Inc.
Metastatic disease accounts for the
lion’s share of cancer deaths, yet it is
a process that remains poorly
understood. Many theories of
metastasis have been posited in
‘cartoon’ form. These include the
well known ‘seed soil’ hypothesis, the
idea that removal of the primary
tumor somehow increases the
growth of metastasis and most
recently, the ‘self-seeding’ hypothesis
(right). In this work, we aim to test
the ‘self-seeding’ hypothesis with a
theoretical construct we recently
posited (below).
Evidence for ‘self-seeding’?
Models of metastasis should not ignore known vascular connectivity
Scott et al.
Scott et al.
A simple model derived from
Norton et al. (Nature Med 2006)
iterated on the vascular network
Data on CTC prevalence in vascular
network taken from literature: an
opportunity for future personalization?
Results suggest Secondary Seeding is
more likely the mechanism behind ‘self-
seeding’. This suggests that treatment
of subclinical micromets in specific
organs (organ directed therapy) could
be predicted to have clinical utility given
patient specific parameters.
Tumor simulation dynamics
pp λλ
shedding rate
λ
return rate
p