=Paper=
{{Paper
|id=None
|storemode=property
|title=Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway
|pdfUrl=https://ceur-ws.org/Vol-988/paper4.pdf
|volume=Vol-988
|dblpUrl=https://dblp.org/rec/conf/apn/CetinBT13
}}
==Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway==
https://ceur-ws.org/Vol-988/paper4.pdf
Petri net based modelling and simulation of
p16-Cdk4/6-Rb pathway
Nimet İlke Çetin,1 Rza Bashirov,1 Şükrü Tüzmen2
1
Department of Applied Mathematics and Computer Science
2
Department of Biological Sciences,
Eastern Mediterranean University, Famagusta, North Cyprus, Mersin-10, Turkey
{ilke.cetin;rza.bashirov;sukru.tuzmen}@emu.edu.tr
Abstract. Tumor suppressor gene p16 is of utmost interest in investi-
gation of signal transduction pathways due to its gatekeeper role at the
G1/S checkpoint of the cell cycle. Defects in p16 result in uncontrolled
cell division which leads to progression of malignancy in an organism.
In the present research we focus on p16-Cdk4/6-Rb pathway which is a
cornerstone of G1 phase of the cell cycle. We implement Pet net formal-
ism and Cell Illustrator software tool to create model of p16-Cdk4/6-Rb
pathway and perform a series of simulations to validate the model.
Keywords: Replicative senescence, Cell cycle, p16-Cdk4/6-Rb path-
way, Hybrid functional Petri net, Cell Illustrator
1 Introduction
1.1 Biological context
Cell division is a fundamental biological process that is essential to continuity
of all living organisms. Cell replication or growth is controlled by a complex
network of signals, that control the cell cycle. During the cell cycle cells grow to
twice their size, copy their chromosomes, and divide into two new cells. The cell
cycle is composed of four distinct phases: G1-phase (gap 1), S-phase (synthesis),
G2-phase (gap 2) and M-phase (mythosis) [14]. Cell cycle checkpoints are used
between neighboring phases to monitor and regulate the progress of the cell cycle.
A cell cannot proceed to the next phase until otherwise checkpoint requirements
have been met.
Tumor suppressor gene p16 plays important role in regulating cell grows
and division at checkpoint G1/S [34]. The p16 gene is major tumor suppres-
sor gene that is responsible for replicative senescence. Cell division is not an
infinitely continuous process as cells undergo a finite number of cumulative pop-
ulation doublings [17]. Most human normal cells permanently stop dividing after
a 50-75 cell divisions and enter a state termed cellular or replicative senescence
[17]. Most tumors contain cells that appear to have bypassed this limit and
evaded replicative senescence. Immortality, or even an extended replicative lifes-
pan, greatly increases susceptibility to malignant progression because it permits
G. Balbo and M. Heiner (Eds.): BioPPN 2013, a satellite event of PETRI NETS 2013,
CEUR Workshop Proceedings Vol. 988, 2013.
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 31
the extensive cell divisions needed to acquire successive mutations. Thus, cellular
senescence may act as a barrier to cancer and play an important role in tumor
suppression [8]. Inactivation of tumor suppressor gene p16, which in fact keeps
track of replicative senescence, results in uncontrolled cell division, which leads
to cancer [4].
During G1 phase, proteins Cdk4 and Cdk6 form complex with protein CycD,
which in turn phosphorylates the Rb protein family. When Rb is phosphorylated
by Cdk4/6 it loses its function and releases its target, the E2F family transcrip-
tion factors, resulting in the initiation of DNA replication [31, 32]. Otherwise
Rb inhibits transcription factor E2F [36]. E2F is a transcription factor which
initiates transcription of genes required for S phase [5]. In the case of malignant
progression action of p16 inhibits binding of Cdk4/6 with CycD which leaves Rb,
and other Rb related proteins [25, 35]. The p16 targets Cdk4 and Cdk6, rather
than the CycD, and actually competes with CycD for Cdk binding. Binding
of p16 results in changes in conformation of Cdk proteins so that they can no
longer bind CycD [29]. The p16 may also deactivate preassembled Cdk4/6 CycD
complex blocking their function [29].
The proteins and their complexes are involved in natural degradation. In ad-
dition, the CycD protein is also tightly regulated by ubiquitin-dependent degra-
dation [2, 13, 23].
1.2 Related work
Over the past two decades considerable efforts have been directed towards Petri
net based investigation of biological systems. A series of biological phenomena
modelled and simulated in terms of Hybrid Functional Petri Net (HFPN) in-
clude molecular interactions in the flower developmental network of Arabidopsis
thaliana [19], lac operon gene regulatory mechanism in the glycolytic pathway
of Escherichia coli [9], cell fate specification during Caenorhabditis elegans vul-
val development [21], antifolate inhibition of folate metabolism [3], validation
of transcriptional activity of the p53 [12], glycolytic pathway controlled by the
lac operon gene [11], apoptosis signalling pathway [26], circadian rhythms of
Drosophila [26], switching mechanism of λ phage [26].
In [16] the authors proposed a hybrid Petri net model of cell cycle. The model
comprises both stochastic and deterministic approaches. In this model, stochas-
ticity is used to capture change of the cell size and effect of noises. This model
is centered upon interactions between complexes CycB-Cdk1, Cdh1-APC, and
monomers Cdc14 and Cdc20 [33]. The study expands macro-level understanding
of cell cycle control. However, this study does not provide any insights into un-
derstanding quantitative behavior of biological components involved in the cell
cycle regulation. Indeed, cell cycle regulation is a complex biological mechanism
that consists of hundreds of biological components, processes and pathways. It
is hard if not impossible to perform quantitative analysis of cell cycle regulation
based on modest size model.
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
32 Çetin, Bashirov, Tüzmen
1.3 Contributions
The present research exploits HFPN to create a model of p16-Cdk4/6-Rb path-
way, which is a cornerstone of cell cycle regulation at G1/S checkpoint. We
combine biological facts described in Subsection 1.1 and quantitative knowledge
on reaction rates provided in [11, 12] in a HFPN model. Then we use Cell Il-
lustrator software to perform simulation-based model checking to validate the
HFPN model. Simulation-based model checking in general provides interesting
biological insights which could be used for future wet-lab experiments [22]. Once
the model validated it can be used for obtaining broader understanding of cell
cycle regulation.
The manuscript is organized as follows. Section 2 provides a succinct back-
ground on HFPN. In Section 3 we develop a HFPN model of p16-Cdk4/6-Rb
pathway, and explain relationship between HFPN objects and their biological
counterparts. Section 4 presents and analyzes the simulation results. Finally,
conclusions are outlined in Section 5.
2 Hybrid Functional Petri Net
Biological systems are characterized by interaction of different structured pro-
cesses. A continuous process is used to represent a biological reaction, at which
a real number called the reaction speed or reaction rate is assigned as a param-
eter. Concentration change of the biological components or substrates after the
biological reaction is completed is also represented as a real number. Promo-
tion/inhibition mechanisms and checking for presence of this or that biological
component or phenomenon are typical discrete processes. Change of quantity in
a discrete process is usually expressed by integers or Boolean values.
When modelling biological pathways it is desirable to use a modelling frame-
work that combines both continuous and discrete processes. Related software
tools are consequently expected to comprise different structured data types in-
cluding real numbers, integers, Boolean, etc. HFPN [26, 21] was originally pro-
posed for modelling and simulating biological systems employing hybrid struc-
ture and dedicated software Cell Illustrator [11, 27] provides suitable platform
for visualization and simulation of HFPN models.
While modelling with HFPN, the researchers prefer to use terminology that
is slightly different than the traditional one [28]. In order to ensure compliance
with the biological content Petri net objects such as place, transition, arc and
token are respectively renamed as entity, process, connector and quantity. To
increase the readability of the paper below we provide a brief description of
HFPN model elements. For more detailed information on this issue the readers
are referred to [10].
In context of HFPN an entity is an abstract object that represents biolog-
ical component or substrate such as DNA, mRNA, protein, enzyme, complex
of proteins, etc. Each entity is assigned a numeric value called quantity, which
stands for concentration of related substrate. Variables are used to carry con-
centration values. A process is another abstract object that is used to model
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 33
biological reaction or phenomenon like transcription, translation, binding, nu-
clear export/import, ubiquitination and natural degradation. A process defines
the change rate of entity value and establishes interactions among entities. Rate
of change is expressed as a formula.
Table 1. Correspondence between biological components and HFPN entities.
Entity name Entity type Variable Initial value Value type
p16mRNA Continuous m1 0 Double
p16(C) Continuous m2 0 Double
p16(N) Continuous m3 0 Double
CDK4mRNA Continuous m4 0 Double
CDK4(C) Continuous m5 0 Double
CDK4(N) Continuous m6 0 Double
CDK6mRNA Continuous m7 0 Double
CDK6(C) Continuous m8 0 Double
CDK6(N) Continuous m9 0 Double
CycDmRNA Continuous m10 0 Double
CycD(C) Continuous m11 0 Double
CycD(N) Continuous m12 0 Double
CDK4 CDK6 Continuous m13 0 Double
CDK4 CDK6 CycD Continuous m14 0 Double
Phosphate Continuous m15 100 Double
RB DP E2F Continuous m16 100 Double
nr div Discrete m17 0 Integer
RB P Continuous m18 0 Double
DP E2F Continuous m19 0 Double
Mutation Generic m20 true/false Boolean
p16mutated Continuous m21 0 Double
G1-dysfunction Generic m22 true/false Boolean
p16 CDK4/6(N) Continuous m23 0 Double
p16 CDK4/6(C) Continuous m24 0 Double
Ubiquitin Continuous m25 100 Double
CycD[Ub] Continuous m26 0 Double
S phase genes Continuous m27 0 Double
The entities and processes are classified as being discrete, continuous and generic.
A discrete entity is quantified by integers. A discrete process causes integer-
valued change of a quantity. A continuous entity is quantified by real numbers,
and consequently continuous process causes change of a quantity according to
reaction rate formula, which is also represented by real numbers. A generic en-
tity contains structured data type composed of different structured data such as
Boolean, double and integer. A generic process handles structured data assigned
to associated entities. In HFPN we distinguish between process connector, in-
hibitory connector and association connector. A process connector is adjacent
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
34 Çetin, Bashirov, Tüzmen
from input entity to a process or from process to its output entity. Weight pa-
rameter is used to specify an activation threshold. Process connectors ensure
flow of tokens in the model. An inhibitory connector is used to inhibit a process.
Inhibitory connectors are integral elements of biological models with competing
processes. An association connector establishes adjacency relation between spec-
ified entity and process under circumstance that occurrence of related process
does not cause concentration change. An association connector is often used in
modelling of enzymatic and catalytic reactions.
Table 2. Correspondence between biological phenomena and HFPN processes.
Biological phenomenon Process Process type Process rate
Transcription of p16mRNA T1 Continuous 1
Translation of p16 T2 Continuous m1*0.1
Nuclear import of p16 T3 Continuous m2*0.1
Transcription of CDK4mRNA T4 Continuous 1
Translation of CDK4 T5 Continuous m4*0.1
Nuclear import of CDK4 T6 Continuous m5*0.1
Transcription of CDK6mRNA T7 Continuous 1
Translation of CDK6 T8 Continuous m7*0.1
Nuclear import of CDK6 T9 Continuous m8*0.1
Transcription of CycDmRNA T 10 Continuous 1
Translation of CylinD T 11 Continuous m10*0.1
Nuclear import of CycD T 12 Continuous m11*0.1
Binding of CDK4 and CDK6 T 13 Continuous m6*m9*0.01
Binding of CDK4 CDK6 and CycD T 14 Continuous m12*m13*0.01
Phosphorylation of RB T 15 Continuous m14*m15*m16*0.1
Mutation of p16 T 16 Generic m2*0.1
Binding of p16(N) and CDK4 CDK6 T 17 Continuous m3*m13*0.01
Nuclear export of p16 CDK4 CDK6 T 18 Continuous m23*0.1
Ubiquitination of CycD T 19 Continuous m11*m25*0.01
Degradation of CycD[Ub] T 20 Continuous m26*0.5
Transcription of S phase genes T 21 Continuous m19*1
Table 3. Natural degradations in the HFPN model.
Biological phenomenon Process Process type Process rate
Degradation of proteins d2, d3, d5, d6, d8, d9, Continuous mi*0.01
d11 − d18
Degradation of mRNAs d1, d4, d7, d10 Continuous mi*0.05
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 35
Fig. 1. A Cell Illustrator screen snapshot of p16-CDK4/6-RB HFPN model.
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
36
RB_DP_E2F
nr_div
0 100
m17 m16 Phosphate
c29
threshold 100
c30 c28
RB_P m15
m14*m15*m16*0.1 threshold
T15
0 c31
Çetin, Bashirov, Tüzmen
c27 m14
m18
c32 m8*0.01
m19 threshold
m12*0.01 c59
c65 0
0
d14
d18 DP_E2F CDK4_CDK6_cyclinD
Places Transitions
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
RB_DP_E2F CDK4_CDK6_cyclinD DP_E2F RB_P phosphorylated Cell division Natural
Phosphate Phosphorylation
complex complex complex protein counter degradation
Fig. 2. A Petri net fragment illustrating phosphorylation of RB and natural degradation of the components involved into the process.
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 37
Table 4. Connectors in the HFPN model.
Connector Firing style Firing script Connector type
c4 Rule m20==1 Input process
c25 Rule (m20==0 && m22==0) || Input process
(m20==1 && m22==0) ||
(m20==1 && m22==1)
c34 Rule m22==1 Input association
c36 Rule m20==0 Input process
c2,c7,c12,c20,c28,c29 threshold 0 Input association
c43,c63
c9,c14,c16,c17,c22,c24 threshold 0 Input process
c25,c27,c33,c37,c38,c40
c42,c45-c62,c65
c1,c3,c5,c6,c8,c10 threshold 0 Output process
c11,c13,c15,c18,c19,c21
c23,c26,c30,c31,c32,c35
c39,c41,c44,c64
3 Model Development
In this section we provide step-by-step explanation on how HFPN model of
p16-Cdk4/6-Rb pathway is created according to the biological facts provided
in Subsection 1.1, and describe relationship between HFPN objects and their
biological counterparts.
The entities used in the model are detailed in Table 1. The entities represent
mRNAs, nuclear and cytoplasmic proteins, protein complexes, phosphate, ubiq-
uitin, mutation and G1-dysfunction. A variable associated with a continuous
entity quantifies concentration of specified substrate. To ensure continual phos-
phorylation of Rb we assume that there exist sufficient amount of phosphate and
Rb DP E2F concentration. This is why variables m15 and m16 are initially
set to 100. Likewise, m25 is set to 100 to guarantee continual ubiquitination of
CycD. The initial concentration of mRNAs and consequently protein monomers
and their complexes are set to 0 since simulation starts with transcription of re-
lated mRNAs. The entities G1-dysfunction and mutation are used to indicate
boolean status or presence/absence of corresponding events. The entity nr div
counts the number of cell divisions.
The processes used in the present research include transcription, transla-
tion, nuclear import/export, binding, ubiquitination, phosphorylation and nat-
ural degradation. Relationship between processes and biological phenomena are
illustrated in Table 2 and Table 3. It was reported that mutations in the p16
binding site result in diminished capability of p16 binding to Cdk4/6. This par-
ticularly leads to loss of function of p16 as an inhibitor of Cdk4/6-CycD complex.
In this model, boolean status of mutation is controlled by T16 and m20. As-
signment m20==1 constitutes presence of mutation, consequently leading to
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
38 Çetin, Bashirov, Tüzmen
occurrence of T16 which in deed arrests p16 in cytoplasm. Otherwise T3 occurs
generating nuclear import of p16. Likewise, the presence/absence of dysfunction
in the G1 phase is controlled by entity G1-dysfunction and variable m22. As-
signment m22==1 indicates the presence of dysfunction in the G1 phase. Next
p16 acts as inhibitor of Cdk4/6-CycD complex. We use two Boolean variables
with total of four distinct combinations. The rules set for associated connectors
and processes depend on four distinct combinations of two Boolean variables
m20, which represents the mutation in p16, and m22, which stands for the
dysfunction in G1 phase. Occurrence of transitions T3, T14, T16, and T17
respectively depend on the rules on connectors c4, c25, c34, and c36. For in-
stance, T3, nuclear import of p16, occurs if there is no mutation in p16. That
is, T3 can fire only if m20==0. All connectors together with their firing styles,
firing scripts, and connector types are described in Table 4. A snapshot of HFPN
model is illustrated in Fig. 1.
A net fragment bound to T15 is shown in Fig. 2. This fragment reveals
the structural basis for phosphorylation of Rb. Other than connector rules, the
phosphorylation of Rb (T15) has its activity rule as: (m20==0 && m22==0 ||
(m20==1 && m22==0) || (m20==1 && m22 ==1). Here, the first statement
part is for the case when p16 is not mutated, and there is no dysfunction in
the G1 phase. It is known that replicative senescence should occur if there is no
mutation and dysfunction in a cell, which means that the cell stops dividing after
50 divisions [17]. In our model, the m17 is defined as a counter which keeps track
the number of divisions, and in the case of no mutation and no dysfunction, it is
checked whether the counter is less than 50 or not. If it is not, the cell should stop
dividing, which means that RB should not be phosphorylated after 50 divisions.
The other two statement parts in the activity rule of T15 are the cases when
p16 is mutated. If p16 is mutated, then the replicative senescence will not occur
and the cell will divide continually leading to progression of malignancy.
Process rates are chosen in accordance with the reaction speeds for specific
reaction types adopted in [11, 12]. Process rate for transcription is set to 1 to
ensure continual mRNA production. The process rates are listed in Table 2.
4 Simulations and Results
In this research, simulations were carried out using Cell Illustrator 5.0 (profes-
sional version) that is licensed to Eastern Mediterranean University. Simulation
results for concentration behaviour of nuclear and cytoplasmic proteins and their
complexes are illustrated in Fig. 3-5. We performed simulations for the following
four cases:
1. The p16 is not mutated and there is no dysfunction in the G1 phase (m20==0
&& m22==0).
2. The p16 is not mutated and there is dysfunction in the G1 phase (m20==0
&& m22==1).
3. The p16 is mutated and there is no dysfunction in the G1 phase (m20==1
&& m22==0).
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 39
4. The p16 is mutated and there is dysfunction in the G1 phase (m20==1 &&
m22==1).
It is generally assumed that p16 is transported to the nucleus and acts as a
CKI to regulate the G1/S cell cycle checkpoint. This phenomenon has been
reported in normal cells where the protein was mainly found in the nucleus but
not in the cytoplasm [5]. This fact is supported by the simulation results that
are illustrated in Fig.3. For all four cases the concentration of p16(C) is at level
17.5 after almost 50 pt (Petri net time), at which the steady state starts. On
the other hand, if there is no dysfunction in the G1 phase (m22==0) and if p16
is not mutated (m20==0) p16(N) is at level 175, that is, almost 10 times more
than that of in cytoplasm. It should be noticed that small oscillations in the
p16(C) graphs are result of natural degradation which is 10 times slower than
the translation process. Mutation in p16 arrests it in cytoplasm. This is why
when p16 is mutated its concentration in nucleus is constantly 0.
Healthy and functioning p16 protein forms a complex with Cdk4/6 if it de-
tects a dysfunction. Simulation results, that are illustrated in Fig. 3 and Fig. 4,
have shown that p16 Cdk4/6 concentration in cytoplasm and nucleus are respec-
tively at level 125 and 15, i.e. p16 Cdk4/6 concentration in cytoplasm is almost
8 times more than that in nucleus, indicating that p16 Cdk4/6 is accumulated
in cytoplasm rather than in nucleus. We were not able to find an experimental
result to compare this finding with. The reasonable explanation for this fact
however could be the difference between reaction rates of nuclear export and
binding, i.e., the former is 10 times faster than the latter.
It was reported in [24] that levels of Cdk proteins in cells vary little through-
out the cell cycle. Simulation results for change of Cdk4 and Cdk6 concentrations
in nucleus and cytoplasm are shown in Fig. 4-5. These results fully agree with
this fact, in sense that concentration of Cdk4 and Cdk6 in nucleus and cyto-
plasm are respectively at the level 12 and 17 throughout the simulations. This
fact remains true even for Cdk4/6 (Fig. 5).
5 Conclusions
The present research explores interaction between HFPN and biological pro-
cesses, to the benefit of both fields. On the one hand we adopt HFPN for mod-
elling and simulation of specific biological pathways, and consequently expand
the list of HFPN applications. On the other hand, through modelling and sim-
ulating with HFPN we obtain broader understanding of cell cycle regulation.
The fact that in normal cells p16 protein is mainly accumulated in the nucleus
but not in the cytoplasm [5] is confirmed by simulation results. The simulation
results have shown that the p16 CDK4/6 protein complex is accumulated in
cytoplasm rather than in nucleus. We were not able to find an experimental
result to compare this finding with. The simulation results are in agreement
with the fact that levels of Cdk proteins in cells vary little throughout the cell
cycle [24].
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
40
m20==0 && m22==0 m20==0 && m22==1 m20==1 && m22==0 m20==1 && m22==1
Çetin, Bashirov, Tüzmen
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
Fig. 3. Simulation results for p16(C), p16(N) and p16 CDK4/6.
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 41
m20==1 && m22==1
m20==1 && m22==0
Fig. 4. Simulation results for CDK4(C) and CDK4(N).
m20==0 && m22==1
m20==0 && m22==0
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
42
m20==0 && m22==0 m20==0 && m22==1 m20==1 && m22==0 m20==1 && m22==1
Çetin, Bashirov, Tüzmen
Proc. BioPPN 2013, a satellite event of PETRI NETS 2013
Fig. 5. Simulation results for CDK6(C), CDK6(N) and CDK4/6.
Petri net based modelling and simulation of p16-Cdk4/6-Rb pathway 43
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Proc. BioPPN 2013, a satellite event of PETRI NETS 2013