Identifying therapeutic targets in a combined EGFR-TGF R signalling cascade using a multiscale agent-based cancer model

Complex Biosystems Modeling Laboratory, Harvard-MIT (HST) Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital-East, 13th Street, Charlestown, MA 02129, USA.
Mathematical Medicine and Biology (Impact Factor: 1.66). 12/2010; 29(1):95-108. DOI: 10.1093/imammb/dqq023
Source: PubMed
ABSTRACT
Applying a previously developed non-small cell lung cancer model, we assess 'cross-scale' the therapeutic efficacy of targeting a variety of molecular components of the epidermal growth factor receptor (EGFR) signalling pathway. Simulation of therapeutic inhibition and amplification allows for the ranking of the implemented downstream EGFR signalling molecules according to their therapeutic values or indices. Analysis identifies mitogen-activated protein kinase and extracellular signal-regulated kinase as top therapeutic targets for both inhibition and amplification-based treatment regimen but indicates that combined parameter perturbations do not necessarily improve the therapeutic effect of the separate parameter treatments as much as might be expected. Potential future strategies using this in silico model to tailor molecular treatment regimen are discussed.

Full-text

Available from: Zhihui Wang, Jan 16, 2015
Mathematical Medicine and Biology (2012) 29, 95108
doi:10.1093/imammb/dqq023
Advance Access publication on December 8, 2010
Identifying therapeutic targets in a combined EGFR–TGFβR signalling
cascade using a multiscale agent-based cancer model
Z
HIHUI
W
ANG
Complex Biosystems Modeling Laboratory, Harvard-MIT (HST) Athinoula A. Martinos
Center for Biomedical Imaging, Massachusetts General Hospital-East, 2301 Building 149,
13th Street, Charlestown, MA 02129, USA
V
ERONIKA
B
ORDAS
Department of Applied Mathematics, Harvard University, Cambridge, MA 02138, USA
J
ONATHAN
S
AGOTSKY AND
T
HOMAS
S. D
EISBOECK
Complex Biosystems Modeling Laboratory, Harvard-MIT (HST) Athinoula A. Martinos
Center for Biomedical Imaging, Massachusetts General Hospital-East, 2301 Building 149,
13th Street, Charlestown, MA 02129, USA
Corresponding author: deisboec@helix.mgh.harvard.edu
[Received on 20 October 2009; revised on 5 August 2010; accepted on 26 October 2010]
Applying a previously developed non-small cell lung cancer model, we assess ‘cross-scale’ the thera-
peutic efficacy of targeting a variety of molecular components of the epidermal growth factor receptor
(EGFR) signalling pathway. Simulation of therapeutic inhibition and amplification allows for the rank-
ing of the implemented downstream EGFR signalling molecules according to their therapeutic values or
indices. Analysis identifies mitogen-activated protein kinase and extracellular signal-regulated kinase as
top therapeutic targets for both inhibition and amplification-based treatment regimen but indicates that
combined parameter perturbations do not necessarily improve the therapeutic effect of the separate pa-
rameter treatments as much as might be expected. Potential future strategies using this in silico model to
tailor molecular treatment regimen are discussed.
Keywords: agent-based model; multiscale; non-small cell lung cancer; epidermal growth factor receptor;
transforming growth factor
β; signalling pathway.
1. Introduction
Epidermal growth factor receptor (EGFR) is a transmembrane signalling receptor that is frequently over-
expressed in many cancers, including non-small cell lung cancer (NSCLC) (Hirsch et al., 2003). Ligand
binding to EGFR leads to receptor tyrosine kinase activation as well as a series of downstream signalling
events that stimulate cell proliferation, motility, adhesion and invasion, and the overexpression of EGFR
causes cell apoptosis inhibition and resistance to chemotherapy (Mendelsohn & Baselga, 2000). Tyro-
sine kinase inhibitors (TKIs) of EGFR, such as erlotinib and gefitinib, have thus emerged as therapeutic
option for patients with advanced NSCLC (Siegel-Lakhai et al., 2005). Although treatment with these
drugs so far has resulted in significant tumour regressions in only 10–20% of NSCLC patients (Janne
et al., 2005), the development of novel therapeutic targets continues to be a very active topic in current
cancer research.
c
The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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Z. WANG ET AL.
In recent years, interdisciplinary cancer systems biology has drawn much attention in exploring
the quantitative relationship between complicated intra- and intercellular signalling processes and the
behaviour they trigger on the microscopic and macroscopic scales (Anderson & Quaranta, 2008; Sanga
et al., 2007; Wang & Deisboeck, 2008). Many data-driven mathematical and computational models
and analysis methods have been developed, but so far the focus is still mostly on the single-cell level
(Aldridge et al., 2006). As demonstrated elsewhere in systems biology (Swameye et al., 2003), sensi-
tivity analysis has been widely accepted as a useful tool for studying pathway parameters and signalling
events, which have significant effects on system behaviour. Such in silico methods are especially useful
when it is not possible or practical to conduct experiments on the living system itself (van Riel, 2006).
However, different sensitivity analysis methods may produce different parameter rankings for a spe-
cific system outcome (Zhang & Rundell, 2006). Moreover, it is quite common that a parameter that is
significant to one specific system outcome may not be significant to others. For example, in a mitogen-
activated protein kinase (MAPK) signalling pathway study, MAPK kinase (MEK) dephosphorylation
was found to have significant impact on the duration and integrated output, but not the amplitude, of
extracellular signal-regulated kinase (ERK) activation (Hornberg et al., 2005). Hence, in some cases,
an evaluation function that creates a ‘composite ranking’ indicating the importance of parameters in
multiple system outcomes at one time would be more appropriate. In the case of molecular oncology
therapy, we believe that the optimal target should lead to tumour control; i.e. it should reduce the ability
of cancer cells to grow (and/or cause them to die) as well as diminish cancer cell motility (i.e. reduce
invasion and contain metastasis) as much as possible.
We have previously developed a set of multiscale agent-based lung cancer models integrating both
molecular and microscopic levels to examine NSCLC growth dynamics in 2D and 3D microenviron-
ments (Wang et al., 2007, 2009). Using the 2D model as the computational platform, we also presented
a novel ‘cross-scale’ sensitivity analysis method to identify model parameters that have significant effect
on the tumour’s expansion rate (Wang et al., 2008). Here, we introduce a new evaluation measure,
termed the ‘therapeutic index (TI)’ function. The main purpose of this formula is to help identify key
parameters that are critical in affecting the two main tumour phenotypic traits or ‘outcomes’: on-site
tumour growth and spatiotemporal expansion. We employed the 3D model as the simulation platform
to evaluate the TI function and then compared current results with those from the previously developed
sensitivity analysis. Analysis and comparison results showed that the TI function allows for the ranking
of the critical parameters according to their therapeutic values by assessing the influence of changes in
parameters on multiple tumour outcomes and thus demonstrate that this function is a more powerful tool
for target evaluation.
2. Methods
2.1 Multiscale cancer model
We briefly reintroduce the main features of the multiscale 3D agent-based NSCLC model (Wang et al.,
2009), which encompasses both molecular (signalling pathway) and microscopic (multicellular) scales.
At the molecular level, two stimuli, epidermal growth factor (EGF) and transforming growth factor β
(TGFβ), trigger downstream signalling through different routes but converge at the activation of the Raf
signal. This process then initiates the ERK signalling cascade. Figure 1 shows, in brief, the implemented
signalling scheme (see Wang et al., 2009 for detailed pathway kinetics). At the microscopic level, we
construct a 3D microenvironment consisting of a discrete cube with 200 × 200 × 200 grid points
(Fig. 2); a single distant nutrient source representing a blood vessel is located at grid point (150, 150,
150). A heterogeneous biochemical environment is attained by normally distributing external diffusive
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ANALYSIS OF A MULTISCALE CANCER MODEL
97
F
IG
. 1. Signalling schematic of the integrated pathway, with EGF and TGFβ as the two external stimuli.
F
IG
. 2. Setup of the 3D virtual biochemical microenvironment.
chemical cues (EGF, TGFβ, glucose and oxygen tension) throughout the 3D microenvironment. The
assigned initial values of these chemical cues are weighted by the distance of a grid point from the
nutrient source. Hence, the nutrient source is the most attractive location for the chemotactically acting
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Z. WANG ET AL.
tumour cells because it maintains the highest weight for each of the aforementioned four cues. Moreover,
throughout the simulation, the concentrations of these four chemical cues are continuously updated at a
fixed rate (see Wang et al., 2009 for corresponding equations).
Each cell (agent) carries a self-maintained signalling network, and the computer model records
the molecular profile for each cell at every time step. In an earlier work, we proposed an experi-
mentally supported molecularly driven cellular phenotypic decision algorithm (Wang et al., 2007). In
brief, phospholipase Cγ (PLCγ ) and ERK (two downstream signalling molecules of EGFR) are used to
determine the emergence of two important phenotypic traits: migration and proliferation, respectively.
Experimental studies have shown that transient acceleration of accumulating PLCγ levels leads to cell
migration (Dittmar et al., 2002), while that of ERK leads to cell replication (Santos et al., 2007). There-
fore, in our model, the rate of change of PLCγ determines the cellular migration decision, and the rate
of change of ERK dictates a cellular proliferation fate. If a cell decides to migrate or proliferate, it will
search for a neighbourhood location to move to or for its offspring to occupy. If there are two or more
locations available, the cell will select the one with the highest glucose concentration (this location is
referred to as the appropriate location); if there are two or more appropriate locations available, the cell
will simply randomly pick one. Generally, tumour cells expand towards the nutrient source since these
sites are more permissive with regard to the chemical cues. A simulation run is terminated when the first
cell reaches the nutrient source since at this point a tumour is able to metastasize (as the nutrient source
represents a blood vessel) and consequently is more difficult to contain and treat. Tumour growth and
invasion patterns due to cell proliferation and migration are neither predefined nor intuitive: they emerge
as a result of intracellular signalling of individual cells and the dynamic cellular interactions within the
framework of the 3D biochemical microenvironment.
2.2 Sensitivity analysis and TI function
In a previous cross-scale sensitivity analysis study (Wang et al., 2008), we used a sensitivity coefficient
as an index to evaluate how a change in a single sub-cellular model component affects the overall system
response at the microscopic level. This coefficient is calculated by the following equation:
S
M
p
=
(M
i
M
0
)/M
0
(p
i
p
0
)/ p
0
, (1)
where p represents the parameter that is varied in a simulation and M the response of the system; M
0
is obtained by setting all parameters to their reference values, and thus (M
i
M
0
) is the change in M
due to the change in p, i.e. (p
i
p
0
). It is worth noting that this type of sensitivity analysis belongs to
the ‘local’ sensitivity analysis category (Rabitz et al., 1983), i.e. quantifying the influence of individual
parameters by varying only one parameter at the same time. Equation 1 will be used here again for
our sensitivity analysis in this study. The system response M now corresponds to either tumour volume
(indicated by the final number of viable cancer cells at the time of termination of the simulation run) or
tumour expansion rate (represented by the total simulation steps; however, a simulation that terminates
after a greater number of time steps has a slower tumour expansion rate).
There are, however, some drawbacks in applying this local sensitivity analysis to target discovery
since (1) can show a parameter’s sensitivity to only ‘one’ tumour outcome at a time, i.e. either tumour
volume or tumour expansion rate. The equation therefore has to be revised especially with respect to
the system output term, M, to concurrently evaluate ‘two or more’ tumour outcomes. Moreover, the
sensitivity coefficient is a relative value showing the correlative relationship between changes in param-
eters and tumour outcome, which means that this value cannot be independently used to evaluate tumour
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ANALYSIS OF A MULTISCALE CANCER MODEL
99
outcomes (in our case, to determine the final number of alive cells and simulation steps). We thus seek
to solve this problem and present here a TI function that incorporates tumour outcome terms directly:
TI(x
i
, y
i
) = k
x
(x
i
/x
0
) k
y
(y
i
/y
0
), i = 1, . . ., n, (2)
where x and y represent the two tumour outcomes, i.e. simulation steps and the final number of alive
cells, respectively; x
i
and y
i
indicate their corresponding values for the ith simulation run; x
0
and y
0
are their corresponding values for the ‘standard’ simulation (when all model parameters are set to their
reference values); k
x
and k
y
are weights for x and y and are both greater than or equal to 0. Hence, the
value of TI increases with x
i
and decreases with y
i
; k
x
and k
y
simply indicate which tumour outcome
(simulation steps or cell number) is more important for the evaluation. In the absence of specific data,
we set k
x
= k
y
= 1, meaning that the two types of tumour outcome are equally important. Future works
can specify these coefficients with regard to tumour type, grade and stage or potentially account for the
particular strengths and weaknesses of the drug under consideration.
The goal of our simulations, aimed at uncovering high-value therapeutic targets, is clear: by chang-
ing parameters separately, we attempt to reduce the cell number (corresponding to tumour growth inhi-
bition) while increasing the number of simulation steps (corresponding to tumour expansion inhibition).
Parameters that produce high TIs merit particular attention since, generally, they will produce favourable
anti-tumour outcomes and hence will be valuable therapeutic targets. However, when changing a param-
eter leads to a simulation result with (x
i
> x
0
and y
i
> y
0
) or (x
i
< x
0
and y
i
< y
0
) and thus a large
value of TI, the particular parameter does not produce a desirable therapeutic outcome because the
tumour still grows in cell number in the former case or spreads faster in the latter. Hence, we further
distinguish between the following two groups:
Group I: (x
i
, y
i
) {x
i
> x
0
, y
i
6 y
0
, (x
i
, y
i
) 6= (x
0
, y
0
)} and
Group II: (x
i
, y
i
) / {x
i
> x
0
, y
i
6 y
0
, (x
i
, y
i
) 6= (x
0
, y
0
)}.
Figure 3 schematically shows the distribution of the two groups. Tumour outcome values in Group
I fulfill the requirements that we set for a therapeutic target. Using these definitions, parameters (along
with their variations) will first be classified into these groups before a parameter ranking is produced
through (2) for each group. The evaluation process also implies that a parameter that produces an (x, y)
pair in Group II with a large TI value cannot be accepted as a promising therapeutic target because
changing the component either decreases simulation steps, increases cell number or both.
3. Results
The 3D agent-based model was implemented in C/C++. A total of 27 seed cells arranged in a 3 × 3 × 3
cube were initially positioned in the center of the 3D environment. Due to computation intensity, the
maximum number of simulation steps for all runs is set to 250, with each time step corresponding to
2.4 h. It takes 10–12 steps for a cell to complete a proliferation process, which is in agreement with
experimental data (Hegedus et al., 2000). The diameter of each cell is 10 μm, and in our model, the cell
shape has been approximated as a cube so that the volume of each cell is 1000 μm
3
. For the standard
simulation case (the final cell number = 16773; the number of elapsed time steps = 222), the resultant
volume (made up of live tumour cells, dead tumour cells and interstitial fractions within the tumour
mass) is approximately 3.75 × 10
2
mm
3
. The variation ranges for individual parameters were set to
(1) [0.1–0.9]-fold for parameter inhibition and (2) [1.1–2, 3–10]-fold for parameter amplification of
their corresponding reference values. Note that we only considered variations of pathway component
concentrations in this study. Each of the variations in the parameters was used as the only change of
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Z. WANG ET AL.
F
IG
. 3. Distribution of Group I and Group II. Only parameter variations resulting in a larger simulation step and a smaller cell
number, when compared to standard simulation results, belong to Group I.
input when running a simulation, and all other parameters were held fixed at their reference values. This
process was repeated for all parameter values, and the resulting tumour growth indices (i.e. simulation
steps and the final number of live cells) were compiled for further analysis.
3.1 Parameter sensitivity rankings
Using (1), we calculated sensitivity coefficients for all of the pathway components over the entire prede-
fined variation range for each of the two tumour growth indices. Table 1 shows the parameter sensitivity
rankings. As described before, a sensitivity coefficient value only reports how sensitive the system out-
come is to a particular parameter and is a relative measure. From Table 1, one cannot determine what
variation of which parameter produces a particular tumour outcome because a coefficient value is cal-
culated specific to only one tumour outcome, ignoring others. For example, although EGFR is the most
sensitive parameter in both simulation steps and cell number, a 0.9-fold variation in EGFR concentration
results in an increase in both tumour outcomes, which does not qualify it to be a therapeutic target. Note
that the same 0.9-fold variation in EGFR results in distinct sensitivity coefficient values for different
tumour outcomes.
3.2 Parameter TI rankings
The parameter rankings based on the value of TI for parameter inhibition and amplification are pre-
sented in Tables 2 and 3, respectively. Under parameter inhibition, MEK with a 0.5-fold variation re-
sults in the maximum value in TI, and thus MEK emerges as the number one therapeutic target for this
treatment strategy. However, further decreasing the MEK concentration fails to add therapeutic value.
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101
T
ABLE
1 Sensitivity rankings with respect to simulation step and cell number; SC standards for
sensitivity coefficient (calculated according to (1)); * indicates that multiple values exist. For a spe-
cific parameter, only the variation resulting in the maximum absolute value of SCs with respect to
simulation step and cell number, respectively, is listed
Rankings Parameter Variation SC Cell number Simulation
step
Tumour output: simulation step
1 EGFR 0.9 0.8108 20102 240
2 ERK 0.9 0.6306 15079 208
3 PLCγ 0.7 0.4054 17449 240
4 MEK 1.2 0.3153 11417 208
4 TGFβR 0.8 0.3153 15224 208
6 Raf 0.5 0.1261 14787 208
7 PKC 3 0.018 19058 230
8 Ras 0.1–10.0 0 * * 222
Tumour output: cell number
1 EGFR 0.9 1.9847 20102 240
2 ERK 1.1 1.8428 13682 222
3 PLCγ 1.4 1.662 5,622 188
4 TGFβR 1.1 0.6296 17829 222
5 MEK 0.7 0.5678 13916 220
6 Raf 0.9 0.4561 17538 222
7 PKC 3 0.0681 19058 230
8 Ras 0.2 0.0581 17552 222
For example, while a variation of 0.4-fold in MEK (Group II section in Table 2) results in an even
smaller cell number, it is also accompanied by the ‘adverse effect’ of faster tumour expansion (a smaller
number of simulation steps in the standard simulation). Under parameter amplification, ERK with a
1.1-fold variation results in the maximum TI, which implies that increasing the concentration of ERK
contributes to an increase in the number of simulation steps and a reduction in the cancer cell num-
ber. However, similar to the result for MEK inhibition, further increasing the ERK concentration (e.g.
to 1.2-fold) causes faster tumour expansion, thus putting ERK with a 1.2-fold variation into Group II.
Figure 4 displays the overall change in TI values for MEK and ERK and depicts a series of selected
simulation snapshots for the standard simulation, with MEK set to a variation of 0.4-fold and ERK to
a variation of 1.1-fold. As can be seen, the MEK treatment simulation takes longer to finish, and both
MEK and ERK treatment cases exhibit a smaller tumour volume than that produced by the standard
simulation.
3.3 Combined parameter perturbations
We next sought to gain an understanding of the influence of combined parameter perturbations on
tumour outcome, using our cross-scale computer simulation and applying the TI method. The param-
eters and their variations that we use for this analysis are those in Group I of Tables 2 and 3 for a
total of eight parameter variation elements. There are 26 combinations of these elements (note: varia-
tion pairs of Ras (0.4-fold) and Ras (4.0-fold), and PKC (0.7-fold) and PKC (2.0-fold) are impossible,
and thus are eliminated). Table 4 shows the analysis results. It is somewhat surprising that only 15 out
of the 26 variation pairs (about 58%) show a therapeutic gain. Of these 15 pairs, the variation pair of
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Z. WANG ET AL.
T
ABLE
2 Rankings with respect to TI for parameter inhibition ([0.1–0.9]-fold of each parameter’s
reference value)
Rankings Parameter Variation TI Cell number Simulation
step
Group I
1 MEK 0.5 0.1308 15184 230
2 PLCγ 0.8 0.1004 16449 240
3 Ras 0.4 0.0138 16542 222
4 PKC 0.7 0.0007 16762 222
Group II
1 ERK 0.1 0.7517 1444 186
2 MEK 0.4 0.252 11413 207
3 EGFR 0.1–0.5 0.1142 16897 249
3 PLCγ 0.1–0.4 0.1142 16897 249
5 TGFβR 0.1 0.0874 14249 208
6 Raf 0.1 0.0805 14365 208
7 PKC 0.9 0 16773 222
8 Ras 0.8 0.0002 16777 222
TGFβR (3.0-fold) and PKC (2.0-fold) results in the biggest TI value. More surprisingly, only in two of
the variation pairs, PLCγ (0.8-fold) and Ras (0.4-fold), and PLCγ (0.8-fold) and Ras (4.0-fold), does
the simulation obtain a greater TI value than when the parameters of the variation pair were varied
individually.
4. Discussion
Despite advances in molecular therapies, only modest improvements have been made in the treatment
of patients with advanced NSCLC (Horn & Sandler, 2009). We have presented here a new method for
evaluating therapeutic NSCLC targets by applying a previously developed multiscale model. Because
this computational model links molecular and microscopic scales, we are able to assess the influence of
parameters at the molecular level on the tumour’s spatiotemporal behaviour at the microscopic and mul-
ticellular level. The most important feature of the method is that it takes both tumour growth measures
(simulation steps and cell number) into account, while general local sensitivity analysis only focuses on
one system output (Rabitz et al., 1983). Hence, the model presented in this paper is more appropriate
for evaluating therapeutic targets when two or more tumour outcomes are involved (as is realistic) than
is the general sensitivity analysis method, which only yields the relative information between the sys-
tem input and output. The comparison results confirm the effectiveness of the new method in yielding
parameter rankings based on both main tumour features (growth and motility), which is a significant
improvement over local sensitivity analysis.
Since PLCγ and ERK have been experimentally proven to play significant roles in cancer cell
growth and invasion (Dittmar et al., 2002; Santos et al., 2007), they have been implemented as ‘de-
cision’ molecules in determining a cell’s migration and proliferation fates in this 3D model (Wang
et al., 2009). It is thus reasonable to expect them to be more prominent than other parameters in the
therapeutic value rankings. Indeed, based on our analysis, PLCγ is a therapeutic target under parame-
ter inhibition strategy (Table 2), while ERK qualifies as a valuable target in an amplification regimen
(Table 3). What is unexpected, however, is that MEK exceeds PLCγ as the most important parameter in