=Paper=
{{Paper
|id=None
|storemode=property
|title=Studying Prostate Cancer as a Network Disease by Qualitative Computer Simulation with Petri Nets
|pdfUrl=https://ceur-ws.org/Vol-852/paper9.pdf
|volume=Vol-852
}}
==Studying Prostate Cancer as a Network Disease by Qualitative Computer Simulation with Petri Nets==
https://ceur-ws.org/Vol-852/paper9.pdf
Proc. BioPPN 2012, a satellite event of PETRI NET 2012
Studying prostate cancer as a network disease
by qualitative computer simulation with
Stochastic Petri Nets
Nicholas Stoy1 Sophie Chen2 Andrzej M. Kierzek3
1
St Georges University of London, Cranmer Terrace, London SW17 0RE,
nicholasstoy@Yahoo.co.uk,
2
OPCaRT, Surrey Research Park, Guildford, GU2 7AF, UK
s.chen@opcart-lab.org
3
Faculty of Health and Medical Sciences, University of Surrey, Guildford, GU2 7XH,
UK
a.kierzek@surrey.ac.uk
Abstract. Despite increased understanding of cancer pathogenesis, trans-
lating this knowledge into therapy remains challenging. Radical progress
depends on utilizing molecular biology knowledge to understand pro-
cesses by which genetic information is executed in response to microen-
vironmental perturbations. Understanding of the molecular machinery of
the cell requires computer simulation of the complex network of molecu-
lar interactions and Petri net offers ideal framework. Lack of quantitative
data about molecular amounts and transition rates necessitates devel-
opment of qualitative methods providing useful insight with minimal
knowledge on quantitative parameters. Here we show work in progress
on the modeling of molecular interaction network involved in the evolu-
tion of prostate cancer. We use statistical model checking of qualitative
model and show that the effects of genetic and pharmacological pertur-
bations on prostate cancer evolution can be predicted by the number
of token game trajectories reaching nodes representing proliferation and
cell death events.
Keywords: Stochastic Petri net, statistical model checking, Prostate
cancer
1 Introduction
Despite increased understanding of cancer pathogenesis, translating this knowl-
edge into therapy remains challenging. Radical progress depends on utilizing ad-
vances in both DNA sequencing technology and molecular biology to understand
processes by which genetic information is executed in response to microenviron-
mental perturbations. However, the expression of genetic information in response
to environmental signals is performed by complex molecular machinery involving
hundreds of thousands of components influencing each other through non-linear
interactions. While the century of biochemistry and molecular biology resulted
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Proc. BioPPN 2012, a satellite event of PETRI NET 2012
in accumulation of voluminous data on molecular components and their inter-
actions the size and complexity of the system makes it impossible to use this
knowledge without computer models. This situation motivated intense research
towards reconstruction or reverse engineering the network of interacting cellular
components in the form of computer simulation capable of predicting effects of
genetic and environmental perturbations on cellular behavior [1-4]. The major
bottleneck in this effort is the lack of quantitative parameters describing molecu-
lar interactions. The existence and sign (activation, inhibition) of the molecular
interaction are much more amenable to experimental studies than quantitative
measurements of molecular amounts or transition rates. This encourages de-
velopment of qualitative simulation approaches where valuable insight can be
provided by analysis of molecular interaction network connectivity, with very
limited quantitative data. In this contribution we present the Petri Net model of
the molecular interaction network involved in the evolution of prostate cancer.
We show that statistical model checking of the qualitative model, with discretized
molecular activities and uniform transition rates provides valuable predictions of
the effects of genetic and pharmacological perturbations on cancer progression.
2 Petri Net model of Prostate Cancer Network.
Molecular species were represented as places and interactions were represented
by transitions. Edges and read edges were used to represent activation interac-
tions whilst inhibitory interactions were represented by molecular state-change
transitions rather than by inhibitory edges, as compiled from research data. Our
model building started from interactions involved in the control of the PTEN
gene. Subsequently, we have included transitions involving molecules controlling
PTEN and proceeded until major inputs for environmental signals were covered.
The model, which is still very much ’work in progress’, currently includes growth
factors, insulin, Wnt and androgen receptors activating the signaling networks
of PI3K-PTEN-Akt, Ras-Raf MEK-ERK, beta-catenin, c-Myc, mTor, p53 and
p27. The intrinsic apoptotic pathway and a very basic representation of the cell
cycle was included in the network. Two special places were introduced into the
network to represent biological outcomes of cell death and proliferation. The
model has been build using a Snoopy Petri Net tool [5] in Extended Petri Net
mode. The final Petri Net model contains 251 nodes and 195 transitions.
3 Statistical Model Checking.
Cancer develops when the cell escapes the cell death program and starts prolif-
erating out of the control of growth factor signals. Thus in our simulations we
investigated reachability of the places representing cell death and proliferation.
In particular, we were interested in whether the proliferation place is reached
before the cell death place is reached. Since, we do not know molecular amounts
and transition rates in the system we have attempted qualitative simulation.
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Proc. BioPPN 2012, a satellite event of PETRI NET 2012
We allowed the state of each place to vary between 0 and 2 tokens, thus repre-
senting absent, low activity and high activity states of molecular components.
Even with this radical discretization the model was still too large to determine
reachability of proliferation place by analysis of full reachability graph. We have
therefore used a statistical model checking approach. For each simulation we
have generated ensemble of token game trajectories starting from the same ini-
tial conditions and determined the number of trajectories in which the marking
of Proliferation place changed from 0 to 1 while the marking of Cell Death place
remained at initial value of 0. In short, we determined the number of token game
trajectories in which proliferation occurred before cell death. We decided to use
Gillespie algorithm [6] numerical simulation of Continuous Time Markov Chain
dynamics to generate trajectory samples. Since, we have no knowledge of rate
constants we have assumed that all transitions are equally likely to occur and
set their rate constants to 1. This implies that we did not interpret Gillespie
algorithm time as a real time, with physical time units. We used it exclusively
to order the sequence of transitions and to limit the maximal trajectory length.
The stochastic Petri net with Gillespie algorithm allowed perturbing the system
by adjusting rates and thus altering probability of the occurrence of selected
events. This is advantageous over similar approach previously used in biological
context [7]. Trajectories were run until the cell death place changed its state
or simulation time reached 100 arbitrary time units. For each of the numerical
experiments we have run 10000 independent trajectories. The numbers of tra-
jectories reaching proliferation before cell death were expressed as fractions and
the 99% binomial probability confidence intervals (99% CI) were calculated to
establish significance of the differences between simulation outcomes. The frac-
tions which were outside of their 99% CIs were considered to be significantly
different.
Simulations were performed by the extended version of SurreyFBA software
[8], which allows statistical model checking in general molecular interaction net-
works. The Python script has been written to automatically convert Petri Nets
in Snoopy file format to simulation software files. Confidence intervals were cal-
culated by binconf() function of Hmisc R package using Wilsons method.
4 Results
We have first run 10000 token game trajectories for the original model. Within
the simulation time of 100 arbitrary time units, the proliferation place has been
reached before the cell death place in 4779 of trajectories. The 99% CI of the
binomial probability was (0.4650524, 0.490777). Subsequently, we have inacti-
vated p53 gene in the model by removing all tokens from the node representing
p53 DNA. The number of token game trajectories in which proliferation was
observed before cell death was 7223 and the 99% CI was (0.7106193, 0.7336859).
Therefore, inactivation of p53 gene resulted in the significant rise of the prolif-
eration. This is in agreement with voluminous experimental data on p53 gene
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Proc. BioPPN 2012, a satellite event of PETRI NET 2012
showing that inactivation of p53 results in the increased chances of proliferation
and cancer. Motivated by this result we have investigated other perturbations.
Simulation of the network where the state of testosterone input node was set
to 0 tokens resulted in proliferation probabilities in the 99% confidence interval
of (0.2349789, 0.2571581). Therefore, removal of testosterone input resulted in
decreased chances of cell proliferation happening before cell death. This result
is also in agreement with experimental data. Next, we tested whether our model
reproduces the effect of GSK-3B enzyme inhibitors of potential use in cancer
chemotherapy [9, 10]. As these drug decrease nuclear stability of an AR-GSK-
3B complex and increase (deactivating) nuclear export of the AR, we modeled
its effect by increasing the rate of transition removing tokens from the place rep-
resenting the phosphorylated AR-GSK-3B nuclear complex. In the perturbed
system the rate of inactivation transition was set to 1000, while all other tran-
sition rates were set to 1. The proliferation probability estimated by running
10000 trajectories was in the 99% CI of (0.3255304, 0.349885). Thus, the sim-
ulation reproduced the action of the drug. While numerical experiments shown
above provide encouraging validation for the model, we have obtained quite dis-
appointing results in simulation of the PTEN gene inactivation. The 99% CI of
proliferation probability was (0.4678475, 0.4935781) i.e. there was no significant
difference between the number of trajectories reaching proliferation in original
wild type model and PTEN knock-out. There are cogent reasons why this may
be the case because the network control of PTEN has been shown in another
systems biology study to be different in the basal state than in the insulin-
stimulated state [10] and so more sophisticated dynamic Petri net modeling is
likely to clarify the situation, particularly as the present result is in contradiction
to experimental data indicating an important role for loss of PTEN activity in
the evolution of prostate cancer. The qualitative balance of PTEN versus PI3K
sensitivity is another area that may also require adjustment in our model to
fit data from the literature. Thus, although the simplified Petri net model of
prostate cancer presented here highlights gaps in current knowledge and the re-
quirement for meticulous incorporation of static and dynamic network behaviour
from the literature, the success of this qualitative approach nevertheless demon-
strates that it is useful to focus experimental effort on determination of a full set
qualitative interactions, before proceeding to difficult quantitative experiments.
5 Conclusions
In this contribution we show preliminary results that demonstrate the applica-
bility of Stochastic Petri nets for qualitative modeling of molecular interaction
networks involved in cancer. We discretize molecular activities to 3 levels, set all
transition rates to 1 and used Gillespie algorithm simulation to generate a sam-
ple of transition sequences leading to alternative biological outcomes of death
and proliferation. We show that despite this radical qualitative approximation
the method captures the effects of best studied perturbations on these key bio-
logical behaviours. The method is computationally efficient and allows accurate
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Proc. BioPPN 2012, a satellite event of PETRI NET 2012
determination of probabilities for large-scale models. Our test shows that it is
possible to perform qualitative simulations of the numerous large-scale network
reconstructions that were so far investigated exclusively by calculation of network
connectivity statistics [1, 2], which does not allow prediction of perturbation ef-
fects. We believe that Stochastic Petri nets can be used to reconstruct genome
scale models of molecular interaction networks and apply them to prediction of
the effects of gene polymorphism and pharmacological interventions in complex
network diseases such as prostate cancer.
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