Classification: Biological Sciences – Applied Biological Sciences
Role for Stromal Heterogeneity in Prostate Tumorigenesis
Maria A. Kiskowski,1* Roger S. Jackson 2nd,2,3* Jheelam Banerjee,2,3 Minchul Kang,5 Omar E.
Franco,2,3 Simon W. Hayward,2,3,4 and Neil A. Bhowmick2,3,4**
1
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688.
2
Vanderbilt-Ingram Cancer Center, Departments of 3Urologic Surgery, 4Cancer Biology, and
5
Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, TN
37232.
* Both authors contributed equally.
**Address correspondence to:
Neil A. Bhowmick
Department of Urologic Surgery,
A-1302 Medical Center North
1161 21st Avenue South
Nashville, TN 37232-2765
Tel.; 615-343-7140
Fax: 615-322-5869
neil.bhowmick@vanderbilt.edu
Manuscript Information: # Text pages = 6, # Figures = 5
ABSTRACT
Targeted knockout of the type II TGF-ß receptor in mouse prostate stroma is
known to yield prostatic intra-epithelial neoplasia, a non-invasive pre-malignant
phenotype. A mathematical model was developed to elucidate the counterintuitive experimental result that the receptor knockout stroma resulted in more
advanced invasive tumors when mixed with normal healthy stromal cells in tissue
recombination allografts. The computational model investigates a hypothetical
mechanism in which invasion develops in two independent tumorigenic steps.
Each step is facilitated by a different stromal component resulting in stromal
heterogeneity generating the maximal tumorigenesis. This mechanism can be
generalized for other contexts in which a morphogen may be abundant in healthy
tissue, but is identified as tumorigenic in transformed tissue. The computational
model is biologically intuitive, extremely flexible, and has been refined by
successive input of biological data. Complex spatial relationships, environmental
context, and cell differentiation can be incorporated into the model at the level of
experimental detail. Further, simulation response variables can be measured in
ways that are analogous to experimental protocols. Informed by biological
parameters, the computational model implicates a role for stromal heterogeneity
in prostate tumorigenesis.
2
INTRODUCTION
Organ development and epithelial tumor progression are the result of stromalepithelial interactions that are both reciprocal and sequential. Organ development is the
result of the interaction of multiple tissue groups and often depends on the prior state of
the tissue (1). Prostate cancer (PCa), the most common non-cutaneous cancer in men,
is initiated by the transformation of luminal epithelial cells that line the prostatic ducts.
These cells begin dividing abnormally and result in carcinoma in situ [or prostatic intraepithelial neoplasia (PIN)] (2). The transformed epithelia can further lose their polarity
and invade through the basement membrane into the surrounding prostatic stroma. The
sequential progression of epithelial differentiation to adenocarcinoma is dictated by its
intrinsic genetic stability as well as the microenvironment (3-5). Tgfbr2fspKO mice, with a
conditional knockout of the TGF-ß type II receptor (TßRII) in stromal fibroblasts, develop
PIN lesions and subsequently prostate adenocarcinoma (6, 7). Human PCa is
analogously associated with the loss of TßRII expression in the stromal compartment
(7, 8).
We used a flexible, biologically intuitive, hybrid computational model to
investigate mechanisms for cell-cell communication in stromal and epithelial
compartments on tumor initiation and progression. Hybrid mathematical modeling has
developed into a means of explaining biologic mechanisms that span a range of spatial
scales (for example, macro-scale cellular interactions with micro-scale morphogen
diffusion). Cancer invasion and angiogenesis are important elements of tumorigenesis
and have been modeled using hybrid approaches (9-11). Cell-based models in which
individual cells are explicitly represented are well-suited to modeling cancer since they
3
describe individual cell behaviors and easily account for spatial cell heterogeneity (12,
13). Hybrid models combine explicit representation of cells with continuum descriptions,
for example, of nutrient and waste diffusion (11, 14-16). Our hybrid model combines a
discrete model for the differentiation of individual cells with a continuum model of
morphogen diffusion. In vivo tissue recombination, in vitro biological models, and
mathematical modeling together test and support hypotheses for inter-cellular signaling
within a heterogeneous stromal compartment and cancer progression. Biological and
computational modeling data indicate the role of stromal heterogeneity in the
development of prostate adenocarcinoma.
RESULTS AND ANALYSIS
Stromal heterogeneity: a two-step mechanism for paracrine signaling-mediated
tumor progression. Previous studies have suggested CD90 to be a marker
heterogeneously expressed in PCa associated stromal cells (17). To further explore the
role of stromal TGF-ß signaling in PCa progression, we co-localized CD90 and
phosphorylated-Smad2 expression by immunofluorescence in human PCa associated
and non-cancer associated stromal fibroblastic cells. Interestingly, CD90 and
phosphorylated-Smad2 expression was heterogeneous in the stromal cells of human
PCa tissues (Fig 1A). CD90 expression was generally limited to cancer associated
stromal
cells
compartments
lacking
associated
phosphorylated-Smad2
with
benign
expression.
epithelia
However,
expressed
both
stromal
CD90
and
phosphorylated-Smad2. Tgfbr2fspKO mice were also found to have a heterogeneous
loss of downstream Smad2 activation in stromal fibroblasts (Fig. 1B).
4
To determine the biological ramification of the observed stromal heterogeneity in
TGF-ß signaling, tissue recombination allografting experiments were conducted.
Prostatic stromal cells from control Tgfbr2floxE2/floxE2 mice (Tgfbr2-flox), and those from
Tgfbr2fspKO (Tgfbr2-KO) were cultured. The culturing of prostatic stromal cells from
Tgfbr2fspKO mice beyond six passages results in Tgfbr2 knockout in 100% of the cells,
as the knockout cells proliferate much more rapidly (18). The recombination of wild-type
(WT) prostatic epithelial organoids with Tgfbr2-flox stroma under the renal capsule of
syngeneic mice for 12 weeks yielded recombinants with morphologically normal
prostatic growth (Fig. 2). In contrast, recombination of WT prostatic epithelial organoids
with Tgfbr2-KO stromal cells resulted in PIN development in the same time period.
However, prostatic recombinants resulting from the equal mixture of Tgfbr2-KO and
Tgfbr2-flox stromal cells resulted in prostatic adenocarcinoma. This striking observation
suggested
that
a)
Tgfbr2-KO
stromal cells contribute
to initiating epithelial
transformation and b) the progression to a more aggressive phenotype (invasion) was
the result of the addition of the Tgfbr2-flox stroma. Thus, we hypothesized that the
normal (TGF-ß responsive) stroma contributed to cancer progression. This in vivo
stromal heterogeneity experiment supporting cancer progression yielded a two-step
paracrine model of tumorigenesis.
In step 1, Tgfbr2-KO stromal cells produce a
diffusive signal, morphogen-1 (M1), which causes epithelial cells to transform from
normal to proliferative. And in step 2, Tgfbr2-WT stromal cells produce a diffusive
signal, morphogen-2 (M2), which supports the progression of proliferative epithelial cells
to invade through the ductal basement membrane.
5
Tumorigenesis computational model.
A spatially explicit mathematic model that
describes morphogenetic interactions of the epithelial and stromal fibroblastic cells was
developed to test and simulate the proposed hypothetical mechanism for tumor
progression. We modeled the transformation of epithelial cells in response to steadystate concentrations of morphogens secreted by stromal cells. The model was spatially
explicit, based on tissue geometry of a histologic section of mouse prostate, where
epithelial cells line the ducts and stromal cells are scattered at a lower density in the
region between ducts. Although the experimental system is 3-dimensional (3-D), as a
first approximation we modeled a 2-dimensional (2-D) cross-section of the allograft (SI
Fig. 1A). Stromal cells located at discrete locations were randomly labeled as point
sources (SI Figure 1B) for either morphogen M1 or M2 with probabilities depending
upon the fraction of Tgfbr2-KO and Tgfbr2-WT stromal fibroblasts, respectively.
Morphogen diffusion of stromal products occurred throughout a domain defined as the
area between and around the ducts (such that the basement membrane limited random
diffusion). Epithelial cells, initially non-transformed, responded to (steady-state)
morphogen levels by transforming if they were coincident with threshold morphogen
levels. Epithelial cells transformed from normal to proliferative at threshold levels of M1
(secreted by Tgfbr2-KO stromal cells), and transformed from proliferative to invasive at
threshold levels of M2 (secreted by Tgfbr2-WT stromal cells). Cell division, cell
apoptosis, and cell movement were not simulated. In particular, the model is not
explicitly time resolved as we consider the response of cells to steady state morphogen
concentrations. This was reasonable, as steady state morphogen concentrations
establish at time scales that are fast compared to cell responses (19, 20).
6
Implementation of the two-step mechanism in a computational model yielded
results that reproduced experimental observations. In simulations, the ratio of Tgfbr2KO and Tgfbr2-WT stromal cells was varied from 0 to 1. The measured response
variable for all simulations was the fraction of epithelial cells that transformed (step 1
proliferative or step 2 invasive). The fraction of transformed epithelial cells for a typical
set of simulation parameters is shown in (Fig. 3A). For 100% Tgfbr2-WT stromal cells
(fraction altered stroma, FAS=0.00), there were no associated proliferative or invasive
epithelial cells. For 100% Tgfbr2-KO stromal cells (FAS=1.00), there were only
proliferative epithelia (Step 1). The computational model yielded the greatest invasion at
heterogeneous mixtures of stromal cells. Key model parameters could be varied to tune
the fraction of epithelial cells that became proliferative or invasive; however, all
parameters yielded results that were either identically zero (no proliferative or invasive
epithelial cells) or qualitatively similar to those shown in Fig. 3A, in which the fraction of
proliferative epithelial cells increased monotonically from zero with the fraction of
Tgfbr2-KO stroma (Step 1) and the fraction of invasive epithelia was non-zero only for
intermediate fractions of Tgfbr2-KO stroma (Step 2).
Key simulation parameters (see Methods for details) included: the diffusion
length L of each morphogen, defined as the average distance diffused by a morphogen
in its lifetime; the abundance A of each morphogen, defined as the total steady state
amount of morphogen contributed by a single stromal cell; and the threshold level T at
which an epithelial cell responds and transforms to each morphogen. By varying these
parameters, we found three distinct simulation outcomes: 1) no epithelial cells became
proliferative or invasive, 2) some epithelial cells became proliferative but none became
7
invasive, or 3) some epithelial cells became proliferative and some subset of the
proliferative cells also became invasive; for example, as a function of the abundance A
of each morphogen (Fig. 3B). The morphogen abundance was normalized by the
threshold level TM1 and TM2 required for epithelial response to M1 and M2. For low
abundance levels of M1 (e.g., for A1/T1 < 200) no epithelial transformation occurred.
For higher M1 abundance, cells became proliferative. Finally, cells became invasive
only if both M1 and M2 abundance levels were sufficiently high.
It was experimentally observed that at a 1:1 Tgfbr2-KO:Tgfbr2-WT stromal
fibroblastic cell ratio, the majority of epithelial cells became proliferative while a minority
of epithelial cells became invasive. Model parameters could be tuned to match
experimental epithelial transformation rates. Since increasing the diffusion length L,
increasing the abundance A, and decreasing the threshold level T all had the effect of
increasing the fraction of cells that transform; this tuning was non-unique. In the
Supplemental Information (SI), we describe how we tuned the parameters to find a nonunique set that generated and matched experimental results for the fraction of
proliferative and invasive epithelial cells (SI Figure S2-S3), and that the model
predicted tissue morphology and stromal cell density influence upon epithelial
progression toward cancer (SI Figure S4).
Computational Model Accommodation of Experimentally Measured Production of
Putative Morphogens. In vitro experiments were performed to test the biologic viability
of the modeling assumption that each stromal cell type uniquely produces a morphogen
that acts on the other cell type. Candidate secreted factors dominantly expressed by
8
stromal cells that support proliferation and/or invasive cancer progression, include Wnt3a and SDF1, respectively (7, 18, 21, 22). Initially, Tgfbr2-WT and Tgfbr2-KO stromal
cells were grown in co-culture and analyzed as a mixture. SDF1 mRNA levels
decreased in a linear manner with increasing percentage of Tgfbr2-KO prostate stromal
cells in the mixture (SI Figure S5). Together with previously published Wnt-3a data, this
suggested that Tgfbr2-KO stroma were dominant producers of Wnt-3a and the Tgfbr2WT cells were the dominant producers of SDF1 (7, 23). Notably, non-dominant
production of morphogen was not negligible as was assumed initially in the model. The
production of Wnt-3a by Tgfbr2-WT stromal cells was 20% that of Tgfbr2-KO stromal
cells (7), and the production of SDF1 by Tgfbr2-KO stromal cells was 25% that of
Tgfbr2-WT stromal cells (SI Figure S5). In our original computational model of
tumorigenesis, there was no production of M1 by Tgfbr2-WT stromal fibroblasts and no
production of M2 by Tgfbr2-KO stromal cells. Here, we modified the computational
model to reflect the measured levels of Wnt-3a and SDF1 as putative morphogens M1
and M2, respectively.
The first step of tumorigenesis is independent of the second step.
Our
computational model was first modified to reflect the measured levels of Wnt-3a as a
putative morphogen M1. In the modified model, Tgfbr2-WT stromal cells produced M1
at basal levels that were one fifth the level produced by Tgfbr2-KO stromal cells and we
interrogated whether model parameters could be found for M1 (diffusion rate, decay
rate, and thresholds for transformation) such that 80% of the epithelial cells would
become proliferative at the 50/50 mixture of stromal cell types but 0% would become
proliferative when the stromal cells are 100% normal. We found that over a large
9
parameter range (e.g., diffusion lengths  5000 m), the model could not accommodate
this level of M1 production by Tgfbr2-KO stromal cells. This was demonstrated (SI
Figure 6A) by the observation for any diffusion length L  800 m, a threshold cannot
be found such that 80% of epithelial cells would become proliferative at the 50/50
mixture but 0% of epithelial cells would become proliferative at 100% Tgfbr2-WT
stroma. This was not surprising, as a straightforward calculation showed that at 0%
Tgfbr2-KO stroma the levels of M1 in the tissue due to basal production by Tgfbr2-WT
cells would be equal to 40% of the levels of M1 in the mixed state (SI Table 1).
Secondly, our computational model was modified to reflect the measured levels
of SDF1 as putative morphogen M2. In the modified model, Tgfbr2-KO stromal cells
produced M2 at basal levels that were one fourth the level produced by Tgfbr2-WT
stromal cells. We found that for diffusion lengths greater than 24 m (SI Figure 6A), a
threshold can be found (gray region, SI Figure 6B) for which at least 20% of the
epithelial cells became invasive in the mixed stromal case but no epithelial cells became
invasive in the 100% Tgfbr2-KO stromal case.
Cooperativity of Morphogen M2. To quantify the expression of SDF1 by the individual
cell types cultured in a mixture, stromal cells were co-cultured, followed by FACS
sorting based on CMFDA (green) dye labeling of the Tgfbr2-KO cells. The co-cultures
were designed at the previously described ratios of Tgfbr2-KO and Tgfbr2-WT stromal
cells (see Fig. 2). SDF1 expression of the sorted cells was measured by qRT-PCR. As
before, SDF1 mRNA levels for Tgfbr2-WT prostate stromal cells were 4-fold greater
than Tgfbr2-KO prostate stromal cells when grown alone in culture (Fig. 4B). However,
10
FACS sorting of Tgfbr2-WT stromal cells grown in 75%:25% and 50%:50% co-culture
with Tgfbr2-KO stromal cells revealed an approximately 8-fold increase in SDF1 mRNA
expression compared to Tgfbr2-KO cells grown alone. Interestingly, SDF1 mRNA levels
of the Tgfbr2-KO stromal cells were elevated 2-fold as a result of co-culture over Tgfbr2KO cells grown alone. The results suggested that both Tgfbr2-WT and Tgfbr2-KO
stromal cells may cooperatively induce production of one or more factors resulting in
increased SDF1 mRNA expression. Inputting the experimentally measured relative
production rates of SDF-1 for the production levels of morphogen M2 in the
computational model results in the experimentally observed rate of epithelial
transformation (SI Figure S7).
The up-regulation of SDF1 by Tgfbr2-WT stromal cells in the case of a mixed
stromal cell population indicates that the presence of Tgfbr2-KO cells is communicated
in some way to the Tgfbr2-WT cells, suggesting, for example, that there is a morphogen
secreted by the Tgfbr2-KO cells that Tgfbr2-WT stromal cells respond to by upregulating SDF1 expression. Simulations tested the hypothesis that an M3 could result
in the cooperativity of SDF1 (Fig. 4B). In these simulations, we assumed a geometry of
cells in which stromal cells were confluent and arranged on a 2-D plate, as in the the coculture experiments. We modeled the production and diffusion of an M3 expressed by
Tgfbr2-KO cells that would cause the up-regulation of SDF1 in Tgfbr2-WT cells at
threshold levels. We identified rates of up-regulation and threshold levels that would
result in experimentally measured production rates of SDF1 for 0%, 25%, and 50%
fraction of Tgfbr2-KO stroma. While we were able to find a fit within simulation error for
the lowest fractions of Tgfbr2-KO stroma (gray line, Fig. 4B), these model assumptions
11
could not account for the decrease in SDF1 production for higher levels of Tgfbr2-KO
stroma. In the same way the increase in SDF1 in the heterogeneous stromal mixtures
logically argued for a threshold response to a factor produced by the Tgfbr2-KO stroma,
the subsequent decreases in SDF1 production for higher fraction of Tgfbr2-KO cells
suggested a threshold response to a factor produced by the Tgfbr2-WT stromal cells.
Assuming that SDF1 was up-regulated in response to simultaneous threshold levels of
an additional M3 secreted by the Tgfbr2-KO stroma and even an M4 secreted by the
Tgfbr2-WT stroma allowed finding a set of parameters that resulted in SDF1 production
levels that exactly matched experimentally measured levels within simulation error
(dashed black line, Fig. 4B).
Tgfbr2-WT stromal cells were cultured with a candidate M3, based on previous
reports on factors that induce SDF1 and additionally found to be expressed by Tgfbr2KO stroma. Those Tgfbr2-KO stromal-derived factors that could up regulate SDF1,
included IL-1, IL-1ß, and IL-6 (24-26). Therefore, we tested the expression of SDF1 by
Tgfbr2-WT stromal cells when cultured in the presence of these factors. IL-1ß increased
SDF1 expression over untreated Tgfbr2-WT cells by two-fold (Fig. 5A). Treatment of
Tgfbr2-KO stromal cells with IL-1ß increased SDF1 mRNA levels nine-fold by qRTPCR. Thus, IL-1ß can be a candidate M3 in the mechanism of cooperativity between
heterogeneous TGF-ß responsive prostate stromal cells.
CONCLUDING DISCUSSION
12
Stromal cells underlying epithelia provide instructive paracrine signals to promote
proper epithelial development and maintain homeostasis (5). The step-wise nature of
progression for human carcinomas is widely recognized since the proposal of the
Knudson “Two Hit Hypothesis” (27). Recent work by several labs support that
alterations in the stroma alone, independent of genetic events in the epithelium, can
promote progression of neighboring epithelium to cancer (6, 28-32).
Paracrine-
mediated cancer initiation and progression likely involves at least two distinct steps
perpetuated by two or more morphogens produced by at least two independent cell
types. Among the multiple prostatic stromal cell lineages, at least two sub-populations
of fibroblastic stromal cells could be distinguished by CD90 expression (17).
Interestingly, CD90 expression coincided with heterogeneous loss of Tgfbr2 expression
in human PCa associated stroma. Similar stromal heterogeneity occurs in Tgfbr2 fspKO
mouse prostates and is likely functionally essential for the ensuing cancer progression.
A computational model was established based on tissue recombinant allograft
results indicating a dual requirement for the presence of Tgfbr2-KO stromal cells,
capable of inducing PIN lesions, and Tgfbr2-WT stromal cells to promote progression to
adenocarcinoma.
A
two-step
stromal
instructed
mechanism
for
prostate
carcinogenesis, where Tgfbr2-KO stromal cells locally secrete a morphogen (M1) and
the Tgfbr2-WT stromal cells produce a different morphogen (M2) was postulated. While
the respective candidate morphogens (Wnt-3a and SDF1) helped to provide biologic
relevance to the model, the model was independent of specific morphogen production.
The cooperation or synergism of morphogen production by stromal cells was predicted
by the pattern of SDF1 mRNA expression from co-cultured Tgfbr2-WT and Tgfbr2-KO
13
stromal cells, and SDF1 with this cooperativity was confirmed through modeling to be
consistent with being a M2 morphogen. This potential cooperativity was tested
biologically for Tgfbr2-KO stroma produced factor(s) that act in either an autocrine or a
juxtacrine manner upon neighboring Tgfbr2-WT stroma (morphogen M3). It is possible
that Tgfbr2-WT stroma also produce one or more secreted factors that can act upon the
KO stroma (morphogen M4).
Wnt-3a was not consistent with being a morphogen M1 according to the
assumptions of the computational model that morphogen M1 is a single diffusing
chemical that causes epithelial cells to become proliferative at threshold levels. While
experimental data suggests that Wnt-3a is involved in step 1 epithelial transformation,
the modeling suggests that the interaction is more complex than postulated in the
computation model. For example, multiple diffusing signals may be required
simultaneously for epithelial transformation or there might be additional mechanisms
involved including cell positional information and (anything else you want to throw in?).
Extension of the model from a 2-D to 3-D representation of prostatic tissue, inclusion of
bi-directional stromal-epithelial signaling, and addition of data regarding yet to be
elucidated aspects of stromal-stromal juxtacrine signaling will allow for future refinement
of this computational model of prostatic cancer progression.
The ubiquitous growth factor, TGF-ß, has often been characterized to be tumor
suppressive
in
un-initiated
epithelial
cells,
yet
supports
tumor
invasion
as
carcinogenesis progresses. TGF-ß is tumor suppressive in Tgfbr2-WT stromal cells
since it represses the secretion of Wnt-3a (and other paracrine factors) (6, 7, 33).
Tgfbr2-KO stromal cells produce Wnt-3a as a result of the knockout of TGF-ß
14
responsiveness, promoting epithelial proliferation (18). Fascinatingly, once the system
has reached this state, TGF-ß becomes cancer promoting as it a) stimulates WT
stromal cells to produce SDF1 driving initiated epithelial cells towards primary invasion
and b) TGF-ß promotes the expression of the cognate SDF1 receptor, CXCR4, in
epithelial cells (34). The Tgfbr2-KO stroma further contribute to a cooperative induction
of SDF1 by the expression of IL-1ß (M3). Such TGF-ß responsive stromal juxtacrine
and stromal-epithelial paracrine signaling would support the onset and progression of
prostate cancer (Fig. 5B).
The data from our computational modeling, as well as biological experiments
used to confirm and extend the model, delineate the necessity for stromal heterogeneity
for the progression from benign lesions to prostate adenocarcinoma. Within a
heterogeneous stromal compartment, stromal cells communicate with each other and
can cooperate in stromal-epithelial signals to initiate and promote epithelial tumor
progression. While previous studies have emphasized the critical role of carcinomaassociated fibroblasts, our data suggest that WT stroma are not merely benign
witnesses but contribute to pro-carcinogenic stromal cues to initiated epithelia and the
establishment of a stromal field effect (35). Cooperativity of paracrine signaling within a
heterogenous stromal compartment would provide a mechanism whereby one could
explain the multi-focal and polyclonal progression of PCa (35, 36). This can be
envisioned where an initiating event in a particular duct confined prostatic epithelial cell
causes a change in the neighboring stroma and in turn potentiating initiating change(s)
in the adjacent epithelia at a somewhat distant ductal site(s).
15
MATERIALS & METHODS
Computational Hybrid Model. Our computational model couples a discrete, stochastic
description of cells at the macroscopic scale with a continuous, deterministic description
of morphogen diffusion at the microscopic scale. The (x,y) position of stromal cell
centers are locations for morphogen point sources. In cases of mixed morphogen
production, the labeling of stromal cells as Tgfbr2-WT or Tgfbr2-KO was determined
stochastically. Diffusion occurs in a diffusive region between and surrounding the
prostate ducts. Boundary conditions for the diffusive lattice area are reflective, so that
morphogen could not diffuse beyond the duct boundary. Epithelial cells respond to
morphogen by transforming if they are co-local with threshold steady state levels.
Morphogen production, diffusion and response, steady state analyses and the
numerical scheme are described in Supplemental Methods. Quasi-steady state
morphogen levels were solved using the finite element method using the MATLAB PDE
toolbox.
Defining cell positions and diffusive region. Our computational model approximates
a section of mouse prostate in which morphogen interactions are occurring as a finite,
rectangular 2-D region. The diffusion region and cell positions were defined using a 250
m x 400 m experimental image (SI Figure 1A). Cell and duct positions in this
experimental figure determined cell and duct positions in silico. 209 epithelial cells and
44 stromal cells were identified by hand in the experimental figure depending upon the
intensity of blue and red dye, respectively, and ducts were identified using an image
16
processing algorithm that identified the ductal boundary. Identified cells and ducts are
shown in (SI Figure 1B).
Correspondence of Model and Physical Parameters. The PDE model generates
steady state morphogen levels as a function of the diffusion rates D1, D2, production
rates k1, k2 and decay rates kd1, kd2 of each morphogen. In this manuscript, we
equivalently describe these parameters in more physically useful terms as the diffusion
rates D1, D2, diffusion lengths L1, L2 and abundance A1, A2. The diffusion length L is
defined from the diffusion rate D (m2/s) and the decay rate kd (s-1) as L 
4D
.
kd
Physically, it corresponds to the average distance diffused by a morphogen during its
average lifetime. Here, it is more useful than the decay rate it replaces because it does
not depend explicitly on time. The total abundance of each morphogen produced per
source (per cell) is defined from the production rate k (s-1) and the decay rate kd (s-1) as
A
k
. Physically, it corresponds to the average steady state amount of morphogen
kd
contributed by a single morphogen-producing cell. Here, it is again more useful than the
production rate it replaces because it does not depend explicitly on time. In all
simulations, the diffusion rate was fixed at D = 0.19 m2/s and in all simulations where
the production was not explicitly varied, we fixed the abundance for both morphogens at
A=10,000 morphogen units by varying the production P as a function of the decay rate
(A=P/kd). The diffusion length L for each morphogen was a free parameter in our model.
17
Additional information, regarding mathematical and biological methods, is available in
supplemental information (SI Methods 1-4).
ACKNOWLEDGMENTS. The authors wish to thank the members and advisors of the
Vanderbilt University Tumor Microenvironment Network (VUTMEN) for helpful
discussions throughout the course of this work. This work has been supported
financially by NIH/NCI grant CA108646 (to N.A.B.), the NIH/NCI U54-CA126505
program grant supporting the VUTMEN, a DOD PRCP postdoctoral training grant
W81XWH-08-1-0542 (to R.S.J.), and the assistance of Minchul Kang on this project has
been supported by NIH RO1-GM073846 (to Anne Kenworthy).
18
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FIGURE LEGENDS
Figure 1. Stromal heterogeneity of human and mouse prostate tissues. A)
Immunofluorescent staining demonstrating focal areas of increased stromal CD90
expression in human PCa concurrent with loss of stromal phosphorylated Smad2
expression as compared to benign prostate (BPH) tissue samples. B) Reduction in
phospho-Smad2 staining in stroma (S) associated with adenocarcinoma in Tgfbr2-KO
versus Tgfbr2-flox control mouse prostate.
Figure 2. Percentage of WT and KO stroma in prostate tissue recombinant
allografts promotes cancer progression. A) Normal glandular architecture observed
by H&E of graft of WT prostatic epithelial organoids recombined with 100% normal
Tgfbr2-flox prostate stromal cells. B) Progression to adenocarcinoma in grafts of WT
prostatic epithelial organoids recombined with a 50/50 mixture of Tgfbr2-flox and
Tgfbr2-KO prostate stromal cells. C) Only PIN lesions developed in grafts of WT
prostatic epithelial organoids recombined with 100% Tgfbr2-KO prostate stromal cells.
Figure 3. Prostate epithelial progression to adenocarcinoma is dependent on
morphogen production and response thresholds. A) Simulation results indicated
that stromal heterogeneity alters the proliferative and invasive potential of the prostate
epithelial cells, where greatest invasion occured at heterogeneous mixtures of stromal
cells and the extent of epithelial proliferation and invasion depends on the ratio of
morphogen production and threshold response. The number of cells that became
proliferative (Step 1, dashed line) and invasive (Step 2, solid line) when the morphogen
diffusion lengths of M1 and M2 were 200 m and 300 m, respectively, and the
threshold T required for transformation in response to M1 and M2 were 0.0453 and
0.3432 morphogen units, respectively. The total abundance of each morphogen
produced per source (per cell) was fixed at A=10,000 morphogen units. Error bars
indicate the standard error of 100 simulations. B) The phase diagram shows the final
tissue classification as a function of M1 production by Tgfbr2-KO stromal cells (y-axis)
and M2 production by normal stromal cells (x-axis) in a tissue that is a 50/50 mix of
Tgfbr2-WT and Tgfbr2-KO stroma. If the production rate of both morphogens is low
relative to the threshold needed for transformation, the cells remain normal. Morphogen
diffusion lengths and thresholds for M1 and M2 are as in 3B.
Figure 4: Computational modeling predicts cooperativity of morphogen M2
production. A) Expression of mRNA for SDF1, a candidate M2 morphogen, was
measured by qRT-PCR (normalized to ß-actin) from FACS sorted unlabeled Tgfbr2-flox
and CMFDA (green) dye labeled Tgfbr2-KO prostate stromal cell co-cultures. B)
Simulation of SDF1 production cooperativity using assumptions of morphogens M3 and
M4 in a confluent array of Tgfbr2-WT and Tgfbr2-KO stromal cells. First, best fit
parameters were found to match data (4A) assuming morphogen M3 secretion by the
Tgfbr2-KO stroma that results in SDF1 induction by Tgfbr2-WT cells (gray line). Tgfbr2WT cells increased SDF1 production by 1.8 fold in response to threshold M3 levels (6.5
units), and were assumed to produce SDF1 in the absence of Tgfbr2-KO stroma at 4.8
fold greater than Tgfbr2-KO cells (per data in 4A). Second, best fit parameters were
found to match data (4A) with the added assumption of morphogen M4 secretion by the
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Tgfbr2-WT stroma that is required for Tgfbr2-KO cells to respond to M3 (dashed black
line). Tgfbr2-WT cells increased their SDF1 production by 1.7 fold and 3.1 fold,
respectively, in response to threshold M4 level (6.75 units) and simultaneous threshold
levels of M3 and M4 (6.5, 6.75 units). SDF1 production by Tgfbr2-WT cells in the
absence of Tgfbr2-KO stromal cells was assumed to be 2.8 times greater than that of
Tgfbr2-KO cells, as this resulted in the best fit of all the data points. For all simulations,
the diffusion length was 10 m and the decay rate was 0.02.
Figure 5. Paracrine signaling between stromal sub-types drives carcinogenesis.
A) Assessment of SDF1 mRNA expression by WT and KO prostate stromal cells in
response to treatment with the candidate M3 morphogen, IL-1ß. B) Revised model of
TGF-ß signaling in driving prostate carcinogenesis. Loss of stromal responsiveness to
TGF-ß, results in increased production of TGF-ß and Wnt-3a by the stroma. While
increased Wnt-3a paracrine signaling promotes epithelial proliferation, the increase in
TGF-ß in the microenvironment results in induction of CXCR4 expression by the
epithelium, subsequently increasing its sensitivity to SDF1. WT and KO stroma
cooperate by paracrine signaling to produce increased levels of SDF1, driving the
vicious cycle of prostatic carcinogenesis.
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