Supplemental Figure Legends & Methods
A list of all files in supplemental information:
Figure S1. The rate of epithelial transformation increased with responsiveness to
steady state morphogen levels.
Figure S2. Epithelial responsiveness to morphogen levels can be tuned to
experimental results.
Figure S3. Role of tissue position in determining epithelial exposure to diffusive
morphogens and altering proliferative and invasive potential.
Figure S4. Input of experimentally measured relative production rates of SDF1
(M2) results in a rate of epithelial transformation in the computational model.
Table 1. Morphogen M1 production by stromal cell type
Method 1. Biological Methods
Method 2. Cell Positions, Diffusive Region, and Correspondence of Model and
Physical Parameters Defining cell positions and diffusive region.
Method 3. Steady State Analysis
Method 4. Numerical Scheme
Supplemental Figure Legends
Figure S1. The rate of epithelial transformation increased with responsiveness to
steady state morphogen levels. (A) Steady-state morphogen levels of M1 for a
random pattern of 50% mixed Tgfbr2-WT and Tgfbr2-KO stromal cells that result when
the diffusion length LM1 is 200 m and the abundance AM1 is 10,000 morphogen units.
The intensity scale bar on the right indicates that brighter colored pixels correspond to
higher morphogen concentrations. The large white circular areas are luminal spaces
that lie outside the diffusion space of the morphogens. (B) The state of epithelia cells
(normal = yellow, proliferative = red) when the threshold TM1 required for transformation
is (i) 20 morphogen units, (ii) 10 morphogen units or (iii) 1 morphogen unit. As the
threshold of M1 decreases, epithelia transform in response to lower morphogen levels
resulting in an increase in the number of transformed cells. When the threshold level
required for transformation TM1 is 20 morphogen units, 14% of the epithelial cells
transform. When TM1 is lowered to 10 or 1 morphogen units, the fraction of epithelial
cells that transform increases to 24% and 74%.
Figure S2. Epithelial responsiveness to morphogen levels can be tuned to
experimental results. In experiments, approximately 80% of epithelial cells became
proliferative and 20% became invasive at a 50/50 mixture of Tgfbr2-WT and Tgfbr2-KO
stromal cells. In order to find a set of model parameters (for A, L, and T) that simulated
transformation rates that matched these experimental rates, we fixed the value for the
abundance of each morphogen A (AM1=AM2=10,000 morphogen units) and solved for
the threshold T that gave the experimental rate of transformation as a function of the
diffusion length L. This threshold varies with the diffusion length of morphogen M1 and
morphogen M2. A) The threshold of M1, TM1, that results in 80% transformation of
epithelial cells (Step 1) at a 50/50 mixture of Tgfbr2-WT and Tgfbr2-KO stromal cells is
shown as a function of the morphogen diffusion length LM1. For a diffusion length of 200
m, the threshold yielding experimental proliferation rates is 0.045 morphogen units
(star). B) The threshold of M2 TM2 that results in 20% transformation of epithelial cells
(Step 2) at a 50/50 mixture of Tgfbr2-WT and Tgfbr2-KO stromal cells when parameters
for morphogen M1 are LM1=200 m and TM1=0.045 morphogen units is shown as a
function of the morphogen diffusion length LM2. For a diffusion length of 300 m, the
threshold yielding experimental proliferation rates is 0.343 morphogen units (star). Error
bars indicate the standard error of 100 simulations.
At higher threshold levels, fewer epithelial cells would transform; and at lower
threshold levels, more epithelial cells would transform. Note, that in this basic two-step
model for tumorigenesis, epithelial transformation to the proliferative state (Step 1) is
independent of epithelial transformation to the invasive state (Step 2), so that the
fraction of epithelia that becomes proliferative is independent of morphogen M2
parameters.
Figure S3. Role of tissue position in determining epithelial exposure to diffusive
morphogens and altering proliferative and invasive potential. Averaging results
over multiple simulations (a fixed pattern of stromal cell locations with different random
assignments for which stromal cells are Tgfbr2-WT and Tgfbr2-KO) yields predictions
about which epithelial cells are most vulnerable to proliferative and invasive
transformation. Stromal cells are blue and epithelial cells are black (normal), gray (never
transform), or red (transform). A) Highest epithelial cell transformation rates in 50/50
mixed population. Red epithelial cells show cells that transform more than 9 out of 10
simulations. B) Epithelial cell transformation rates with exactly one Tgfbr2-KO stromal
cell (which is expected in vivo at early stages of cancer progression). Red epithelial
cells indicate cells that transform more than 1 out of 10 simulations. Gray epithelial cells
indicate cells that never transform. Simulation parameters are as in Figure 3B and
statistics for coloring are averaged over 100 simulations. The epithelial cells most likely
to transform were located near areas of high stromal density.
Figure S4. Input of experimentally measured relative production rates of SDF1
(M2) results in a rate of epithelial transformation in the computational model.
Relative production levels of SDF1 were experimentally measured for Tgfbr2-WT and
Tgfbr2-KO stromal cells in 5 ratios that varied from 100% Tgfbr2-WT to 100% Tgfbr2KO (Fig. 4C). In order to test whether SDF1 could be a putative morphogen, M2 in our
model, the experimentally measured production rates of SDF1 were used in the
computation model as production levels of M2. Here, the fraction of proliferative
epithelia (dashed line) and invasive epithelia (solid line) is a factor of Tgfbr2-KO stroma.
The parameters for morphogen M1 were chosen as in Fig. 3B, and where diffusion
length LM2 of M2 was 300 and the threshold TM2 was 3.0.
In these simulations, the abundance of morphogen M2 produced by a single cell
was set to be 10,000 units for a Tgfbr2-WT stromal cell in the case of 100% Tgfbr2-WT
cells (the amount assigned a value of 1 in Fig. 3B). The abundance of morphogen M2
for all other cells were altered to reflect the data in Fig. 3B by multiplying 10,000 by the
relative fold production of each cell for that fraction of altered cells. Then, a range of
diffusion lengths was identified (Figs. 4A, 4B) that resulted in simulation of epithelial
invasion rates that matched experimental epithelial invasion rates. In experiments,
approximately 80% of epithelial cells became proliferative and 20% became invasive at
a 50/50 mixture of Tgfbr2-WT and Tgfbr2-KO stromal cells.
Method 1. Biological Methods
Immunofluorescence. Paraffin-embedded tissue sections from human prostate cancer
or benign (BPH) tissue specimens were immunofluorescently stained using either CD90
(1:250, Cat. # 14-0909-82, eBioscience, San Diego, CA) primary antibody with goatanti-mouse Alexa Fluor 594 secondary antibody (1:250, Invitrogen, Carlsbad, CA) or
phospho-Smad2 (1:500, Cat. # 3101L, Cell Signaling Technologies, Danvers, MA)
primary antibody with goat-anti-rabbit Alexa Fluor 488 secondary antibody (1:500,
Invitrogen). Slides were co-stained with DAPI (Vectashield mounting media with DAPI,
Vector Laboratories, Burlingame, CA). All the prostate samples from patients were from
radical prostatectomy performed at Vanderbilt University. These patients received no
documented treatment before surgery. All procedures for human tissue acquisition and
processing were approved by the Vanderbilt University Institutional Review Board.
Immunohistochemistry.
Paraffin-embedded
tissue
sections
were
immunohistochemically stained. 1% antigen unmasking solution (Vector Laboratories)
was used for antigen retrieval according to manufacturer’s instructions. PhosphoSmad2 antibody (1:1000, Cell Signaling Technologies) and appropriate HRPconjugated secondary antibody and DAB incubation (Dako North America, Carpinteria,
CA) was used for visualization.
Primary Stromal Cell Culture. Tgfbr2-flox and Tgfbr2-KO mouse primary prostate
stromal cell cultures were established from 6-8 week old mouse prostates essentially as
previously described (1, 2) by growing in Dulbecco’s Modified Eagle’s Medium/Ham’s F12 (DMEM/F12) media supplemented with 5% fetal bovine serum (HyClone, Fisher
Scientific, Pittsburgh, PA), 5% NuSerum-I (BD Biosciences, San Jose, CA), 5 µg/mL
insulin (Invitrogen), 10-8 M testosterone (dissolved in ethanol at 10-5 M and added fresh
at 1:1000), and 0.1% penicillin/streptomycin (Invitrogen, Carlsbad, CA)(2)(2). Cultures
were incubated at 37C/5% CO2 and the stromal cell media was changed every 3-4
days.
Isolation of prostatic epithelial organoids.
Epithelial organoids were derived by
cutting prostates of 6-12 week old WT C57BL/6 mice to 1mm3 and digesting in 675
units/mL collagenase with 0.04% DNase-I at 37ºC for 1 hour. The organoids were
washed extensively before being combined with the stromal cells and rat-tail collagen
prior to overnight incubation at 37oC.
Allografting
of
tissue
recombinants
to
the
sub-renal
capsule.
Tissue
recombinations were performed as previously described (3). WT epithelial organoids
isolated from prostates from 6-12 week old WT C57BL/6 mice were recombined in 50
µL rat tail collagen with a total of 3x105 Tgfbr2-flox or Tgfbr2-KO stromal cells and
allowed to incubate overnight in a 37oC incubator. The tissue recombinants were then
allografted under the renal capsule of syngenic adult C57BL6 mice for 12 weeks. Grafts
were harvested and fixed in 4% paraformaldehyde, processed for tissue embedding in
paraffin, and sectioned for histologic analysis by hematoxylin and eosin (H&E) staining.
All animal procedures were approved by the Vanderbilt Institutional Animal Care and
Use Committee.
Co-culture and FACS sorting of mouse prostate stromal cells. Tgfbr2-flox and
Tgfbr2-KO prostate stromal cells were grown in primary culture as stated in Materials &
Methods. Viability and cell density was determined by using a hemocytometer and
trypan blue exclusion. To enable FACS-sorting of individual cell populations from cocultures, Tgfbr2fspKO prostate stromal cells were washed with PBS and stained with 2
M CMFDA CellTracker Dye (Molecular Probes, Invitrogen). Labeled cultures were
washed three times with PBS and returned to prostate stromal cell culture media and
incubated 3 hr to O/N. Tgfbr2-WT and CMFDA-labeled Tgfbr2fspKO prostate stromal cells
were plated together as co-cultures in 100 mm tissue culture dishes at 2x106 cells per
dish and incubated for 20 hours. Cells were then trypsinized, neutralized with serumcontaining media, washed once with PBS, and resuspended in PBS-2% FBS to < 5x106
cells/mL, sorted on a BD FACS Aria II (Becton Dickerson, San Jose, CA). Cells were
sorted (negative vs. CMFDA-positive) directly into 3 mL cold RNA extraction buffer.
Total RNA was isolated (Qiagen) following manufacturer instructions. Following DNase-I
treatment, RNA was quantitated for real-time PCR analysis.
Details regarding primary culture, immunofluorescence, immunohistochemistry,
RNA isolation, and real-time PCR are provided in the supplemental information (SI
Method 1).
Quantitative Real-Time PCR. RNA samples were transcribed into cDNA per
manufacturer instructions using the iScript cDNA Synthesis Kit (Bio-Rad, Hercules, CA)
with a 40 L reaction volume and 1 g RNA as template. Quantitative real-time PCR
reactions were carried out using an iCYCLER MyiQ Real-Time PCR thermocycler (BioRad) and contained the following: 12.5 L iQ-SYBR Green Supermix (Bio-Rad), 1.0 L
of each forward and reverse primer [50 ng/L], and 2 µl of 2.5 ng/L RT template with a
total reaction volume of 25 µL. Assays were conducted using the following transcript
specific primer pairs:
mSDF1-upV1: 5'-GCAGAGGGAGGCTCCTTTAT-3'
mSDF1-dnV1: 5'-CATCACTCTCCTCCCTTCCA-3'
-Actin-up: 5’-GTGGGCCGCTCTAGGCACCA-3’
-Actin-down: 5’-CGGTTGGCCTTAGGGTTCAGGGGGG-3’
mGAPDH-F: 5’-AGTGGGAGTTGCTGTTGAAGTC-3’
mGAPDH-R: 5’-CGTGCCGCCTGGAGAAAC-3’
Conditions for the real-time PCR amplification were denaturation at 95C for 3 min, and
45 cycles of 95C 10 sec followed by 52C 45 sec.
Amplification specificity was
confirmed by melt-curve analysis and agarose gel visualization.
were normalized for relative expression using the ∆∆CT method.
Expression values
Method 2. Cell Positions, Diffusive Region, and Correspondence of Model and
Physical Parameters 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
(Fig. 3 part A). 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 processing algorithm that
identified the ductal boundary. Identified cells and ducts are shown in (Fig. 3 part B).
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
L
defined from the diffusion rate D (m2/s) and the decay rate kd (s-1) as
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
k d . Physically, it corresponds to the average steady state amount of morphogen
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.
(I moved this to the Quick Guide, but it can be the first thing to be moved back here if
the space is needed.)
Method 3. Steady State Analysis
Here we provide a steady state analysis for the transformation of different cell types based on the
equilibrium states of the PDE solutions. The results are identical to those obtained in simulations.

Eq. 4 defined point wise depending on the concentration of m1 and

*

*

*

*

*

*

*

*
m2 :
Case1: m1  m1 and m2  m2
Case2: m1  m1 and m2  m2
Case3: m1  m1 and m2  m2
Case4: m1  m1 and m2  m2
In each case, the steady state solutions are computed as


Case 1 ( m1  m1 and m2  m2 ): Only normal cells exist
den
0
dt
dea
0
dt
dec
0
dt
*
en  en (0)
*
en  C0
 ea  ea (0)  ea  0
ec  ec (0)


ec  0
Case 2 ( m1  m1 and m2  m2 ): Only altered cells exist
*
*
den
 k N  m1  en
dt
en  0
en  0
0  k N  m1  en
dea
 k N  m1  en  0  k N  m1  en  ea  C 0  ec (0)  ea  C0
dt
ec  ec (0)
ec  0
ec  ec (0)
dec
0
dt


Case 3 ( m1  m1 and m2  m2 ): Only normal cells exist
*
*
den
0
dt
en  en (0)
en  C 0
dea
 k A  m2  ea  ea  0
 ea  0
dt
ec  0
ec  0
dec

 k A  m 2  ea
dt


Case 4 ( m1  m1 and m2  m2 ): Only cancerous cells exist
*
*
d en
  k N  m1  en
dt
en  0
0  k N  m1  en
d ea
  k A  m2  ea  k N  m1  en  0  k A  m2  ea  k N  m1  en  ea  0
dt
ec  C0
0  k A  m2  ea
d ec

 k A  m 2  ea
dt
This result indicates that depending on k1 and k2, at a specific location, in a single cell level, cell types are
determined as follows:


*

2
*
2

Case3: m1  m1 and m2  m2
k2
*
Normal cell

1
Case1: m
*
*

*
Cancerous cell
 m and m  m
*
1

Case4: m1  m1 and m2  m2

Case2: m1  m1 and m2  m2
Normal cell
*
Altered cell
k1


However, since the steady state levels of m1 and m2 (the solution of Eq. 2) are different from one
location to another and cells are transformed [Normal cell]  [Altered cell]  [Cancerous cell]
sequentially, at the population level we have:


Case3: m1  m1 and m2  m2
k2
*
*
Normal cells

*

*
Normal, Altered and Cancerous
cells

Case1: m1  m1 and m2  m2
*

Case4: m1  m1 and m2  m2
*


Case2: m1  m1 and m2  m2
Normal cells
*
Normal and Altered cells
k1
*
Method 4. Numerical Scheme
Here we briefly describe the numerical scheme used to solve the PDEs.
First we solve Eq. 2 using the finite element method. If we let the inter-ductal area be , the weak forms
of Eq. 2 are
   ( D  m
2
)  j  k d 1 m 1 d
 xk1 
    ( D1 m 2 )  j  k d 1m 2 d
 xk1 
1


1
i1
2
i1

0

 (x
i
,y i )
 jd
x
i
,y i )
 jd
x
0
(x
for basis functions (tent functions) associated with the triangulation of . From the choice of the basis


functions, we have
By integrations by parts
 (D m

1
1

 (D m
2

)   j  k d1m1 dx 

2
20

n  (m1 ) j ds  k1 (x i ,y i )

n  (m2 ) j ds  k2 (x i ,y i )

)   j  k d 2 m2 dx 
i1
20

i1
where n are the outer normal vectors on .
Considering the representation of the solution by a linear combination of the basis functions
(linear interpolation of the solutions) as

n
m1  U k  k
k1
n
m  Vk  k

2
k1
we then obtain an Eq 2–equivalent linear system in (Uk; Vk) as
n
 (D  )  

k
1
n
k

 (D  )  

k
With the solutions m1 


n
2
k
20
 k d1 k dx 

n  ( k ) j ds U k  k1 ( x i ,y i )
j
 k d 2 k dx 

n  (m ) j ds Vk  k 2 ( x i ,y i )



2

i1
20
i1
Ukk andm2   Vkk on the boundaries of ducts, we can find
k1
the steady state solution for Eq. 3 by 4.


j
n
k1
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3.
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