MULTI-LEVEL DYNAMIC MODELING IN BIOLOGICAL SYSTEMS

Application of Hybrid Petri Nets to Network Simulation

Rafael S. Costa

1,3

, Daniel Machado

, A. R. Neves

and Susana Vinga

3,4

IBB-Institute for Biotechnology and Bioengineering, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal

ITQB/UNL, R. Qta Grande 6, 2781-901 Oeiras, Portugal

Instituto de Engenharia de Sistemas e Computadores, Investigac¸

ao e Desenvolvimento (INESC-ID),

R. Alves Redol 9, 1000-029 Lisboa, Portugal

FCM-UNL, C. Martires P

atria 130, 1169-056 Lisboa, Portugal

Keywords:

Systems biology, Integrated dynamic modelling, Hybrid Petri net, Approximate rate laws, Streptococcus

pneumoniae.

Abstract:

The recent progress in the high-throughput experimental technologies allows the reconstruction of many bi-

ological networks and to evaluate changes in proteins, genes and metabolites levels in different conditions.

On the other hand, computational models, when complemented with regulatory information, can be used to

predict the phenotype of an organism under different genetic and environmental conditions. These computa-

tional methods can be used for example to identify molecular targets capable of inactivating a bacterium and

to understand its virulence factors. This work proposes a hybrid metabolic-regulatory Petri net approach that

is based on the combination of approximate enzyme-kinetic rate laws and Petri nets. A prototypic network

model is used as a test-case to illustrate the application of these concepts in Systems Biology.

1 INTRODUCTION

Living cell systems are complex networks with dif-

ferent kinds of interacting chemical compounds (e.g.

genes, small molecules and proteins). The interac-

tions with each other propagate through the global

network and the understanding of how a system be-

havior emerges is a major aim of the recent ﬁeld of

science called Systems Biology (Kitano, 2002). Un-

derstanding the mechanisms of the cell is essential for

research in several areas such as drug design with ap-

plications to personalized medicine (Zhu et al., 2008),

identiﬁcation potential drug targets (Lee et al., 2009)

and metabolic engineering (Park et al., 2007).

By using mathematical models of cellular

metabolism, it is possible to systematically test and

predict the optimal environmental and genetic manip-

ulations (Di Ventura et al., 2006). The availability

of genome sequences for many microorganisms has

allowed the development of constraint-based models

representing the global network of metabolic reac-

tions (Price et al., 2003). However, while captur-

ing most mass balance effects, those models ignore

regulation and cannot be used for dynamic simula-

tions. Moreover, applying constraint based methods

directly to integrated networks is challenging (Covert

et al., 2008). Ideally, the models would comprise

different levels of knowledge, from reactions stoi-

chiometry to reactions kinetics and regulatory infor-

mation (e.g. transcriptional and enzymatic regulation)

(Klipp, 2007). This is the basis of the E-Cell project

(Tomita et al., 1999), that uses an approach to repre-

sent the dynamic state inside the whole cell. Although

until recently most cellular components have been

studied individually, the behavior of the cell emerges

at the network-level interactions and requires an inte-

grative analysis. Several models and analysis focused

primarily on isolated network models rather than in-

tegrated systems. Examples of this are the analy-

sis of signaling (Hoffmann et al., 2002), metabolic

(Chassagnole et al., 2002) and regulation (Lee et al.,

2002) systems. Thus, it is highly desirable that in-

formation obtained from genome annotation, together

with kinetic and regulatory information can be used

for the construction of integrated models that account

for various interactions at diverse temporal and spatial

scales.

Petri nets are a mathematical formalism that have

been applied in the modeling of several biological

pathway systems (Chaouiya et al., 2004; Chen et al.,

2007; Zevedei-Oancea et al., 2003). Hybrid Petri

nets are a particular type of Petri net extension devel-

317

S. Costa R., Machado D., R. Neves A. and Vinga S..

MULTI-LEVEL DYNAMIC MODELING IN BIOLOGICAL SYSTEMS - Application of Hybrid Petri Nets to Network Simulation.

DOI: 10.5220/0003785503170321

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2012), pages 317-321

ISBN: 978-989-8425-90-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

oped to accomodate discrete and continuous elements

within the same formalism. This makes them spe-

cially appealing for the integration of gene regulatory

and metabolic networks, that are more commonly rep-

resented as Boolean networks and differential equa-

tions, respectively. This idea was explored in (Chen

and Hofestadt, 2003) to build a regulated metabolic

model of the urea cycle, and also in (Doi et al., 2004)

to reconstruct the glycolytic pathway controlled by

the lac operon.

The recent advent of so-called genome-wide high-

throughput methods have generated the called omics

data (e.g. metabolomics, proteomics, transcriptomics

and genomics) of bio-molecules like mRNA, proteins

and metabolites, the detection of molecular interac-

tions, such as, protein-DNA and protein-metabolite

(Nielsen and Olsson, 2002). This has allowed a bet-

ter understanding of the regulation of metabolism at

a global scale (Lee et al., 2005). However, in spite

of the great advances in the area, we are still far from

a whole-cell computational model that integrates dif-

ferent omics data, as there exists a few approaches

for the model-driven interpretation of these data and

models that couple enzymatic and transcriptional reg-

ulation (Bettenbrock et al., 2006; Kotte et al., 2010;

Tenazinha and Vinga, 2011; Usuda et al., 2010; Patil

and Nielsen, 2005).

The main aim of this work is the creation of an

integrating framework for metabolic and regulatory

modeling of biological systems, including how we ad-

dress some challenges in integrated systems. This pa-

per is organized as follows: Section 1 explores the

state of the art and the motivation for the work; Sec-

tion 2 presents a hybrid kinetic modeling framework

and Section 3 discusses their application to a proto-

typic small network. Section 4 discusses remaining

challenges and our future directions.

2 METHODS

2.1 Model Topology

In order to evaluate the proposed approach we used as

an example the model topology shown in Figure 1. It

comprises some of the glycolysis reactions for Strep-

tococcus pneumoniae retrieved from the draft model

reconstruction using the SEED web-tool (Henry et al.,

2010) and information from KEGG (Ogata et al.,

1999) database. The biochemical interactions of these

reactions have been translated into the Petri net model

used in this work. The network consists of 5 contin-

uous transitions representing the reactions; 8 continu-

ous places representing 8 metabolites; and 2 discrete

places and 2 discrete transitions were used to create

the regulatory components (on/off switch).

Figure 1: Hybrid Petri net representation of the prototypic

metabolic-regulatory network buit with the Snoopy sofware

tool (Rohr et al., 2010). The metabolites are represented

by circles (places) and the enzymes by squares (transi-

tions). Metabolites abbreviations: pyr, pyruvate; pep, phos-

phoenolpyruvate; glc, glucose; g6p, glucose-6-phosphate;

f6p, fructose-6-phosphate; fdp, fructose-1,6-bisphosphate;

gly, glycine; g3p, glucose-3-phosphate. Enzymes abbre-

viations: GLCpts, phosphotransferase of PTS system (EC

2.7.3.9); PGI, glucose-6-phospate isomerase (EC 5.3.1.9);

PFK, phosphofructokinase (EC 2.7.1.11); FBA, fructose-

bisphosphate aldolase (EC 4.1.2.13); G3PI, triosephosphate

isomerase (EC 5.3.1.1).

2.2 Modeling Process

The overall idea of the modeling method is depicted

in Figure 2. After the model topology construction,

it is necessary to translate into mathematical differen-

tial equations and introduce the control of regulatory

events. In this study, we use an extension of the orig-

inal formalism known as hybrid Petri nets (Hassane

and David, 1998) that accounts for metabolite dy-

namics coupled gene regulation and enzyme kinetics

to construct the hybrid metabolic-regulatory model.

The metabolic network is represented with continu-

ous places and continuous transitions. Genes are rep-

resented by discrete places. Each gene is represented

by two places (on and off), which are connected to

transitions that activate and inactivate the gene, ensur-

ing that the activation of both places is mutually ex-

clusive. The connection between both layers is made

by means of activation arcs between the reactions and

the respective genes. The Petri net model of the net-

work was drawn using the graphical editor of the Petri

BIOINFORMATICS 2012 - International Conference on Bioinformatics Models, Methods and Algorithms

318

net tool Snoopy (Rohr et al., 2010). Snoopy is a gen-

eral purpose software application for design and sim-

ulation of graph-based formalisms and is freely avail-

able.

Recently, we have studied several types of approx-

imate enzyme-kinetic rate laws (Costa et al., 2010).

In this study, approximate kinetics lin-log representa-

tions are used for the rate equations, but alternatively

other approximate rate laws (e.g convenience kinet-

ics) can be also integrated. Lin-log kinetics (Visser

and Heijnen, 2003) are formulated based on a refer-

ence rate r

, and given by:

r = r

1 +

∑





∑





(1)

where the superscripts (

) denote the reference

state (e.g. wild type at steady-state), r

is the refer-

ence reaction rate value, e/e

represent the relative

enzyme activities, S

and P

are the relative

concentrations that inﬂuence the kinetics of the reac-

tion.

The negative of the corresponding stoichiometric

coefﬁcients were set as the initial guesses for the elas-

ticities parameter values as suggested by (Smallbone

et al., 2007). The initial concentrations of metabo-

lites were taken as arbitrary values and are assuming

that the reference steady-state is known (pyr = 0.02

mM; pep = 0.2 mM; glc, = 1 mM; g6p = 0.5 mM;

f6p = 0.3 mM; fdp = 0.02 mM; gly = 0.3 mM; g3p

= 0.1 mM). The simulation process of the metabolic-

regulatory model performed in this study, were car-

ried out using the Snoopy tool (Rohr et al., 2010).

3 ILLUSTRATION OF A

PROTOTYPIC NETWORK

Computational models are very useful for exploring

the effects of manipulating pathways through drugs.

The aim of this study was to present an approach to

construct a hybrid mathematical kinetic model that

accounts for the metabolic and regulatory events.

This approach was applied by taking the small pro-

totypic integrated system of S. pneumoniae (shown in

Figure 1) as an example.

In Figure 3a and 3b simulation time courses of

all the metabolite concentration show the effect of a

gene activation with and without the regulation part,

respectively.

We demonstrated how inclusion of regulatory

events may affect the phenotype behavior. As an ex-

ample of this changes, at time = 600 seconds the pgi

Figure 2: Overview of the modeling process from the con-

struction of a biochemical reaction network to conversion

into a mathematical format. (1) SEED web-based soft-

ware is used to reconstruct the metabolic network includ-

ing the metabolic part and the regulatory information are

based on existing biological knowledge. (2) Conversion of

the metabolic network to a computational model. Combin-

ing the regulatory events and the metabolic information in

a hybrid Petri net modeling framework. (3) Modeling and

simulation in Snoopy tool (Rohr et al., 2010). (4) Model

application example: identify essential genes encoding new

targets for antibacterial drugs that can be tested in vitro for

reduction of pathogenicity.

gene is activated and the affect on the dynamical be-

haviour of the g6p, f6p, fdp, gly and g3p metabolites

are shown, reaching a new steady state a time = 1100

seconds (3a). Our results show that regulation has

inﬂuence on the steady-state distribution obtained in

comparison with the model without the regulation ef-

fect. Accounting for these regulations may have a sig-

niﬁcant impact in the phenotype predictions and can

reveal new therapeutic targets.

MULTI-LEVEL DYNAMIC MODELING IN BIOLOGICAL SYSTEMS - Application of Hybrid Petri Nets to Network

Simulation

319

Figure 3: Simulation of the dynamics for the prototypic S.

pneumoniae model with the pgi gene activation after 600s

(a) and without accounting regulatory effects (b). The inte-

grated system, comprise metabolic and regulation events.

4 CONCLUSIONS AND FUTURE

WORK

This work presents a strategy to build a hybrid

metabolic-regulatory model based on a Petri net

framework. This work addresses also the impact of

accounting of a kind of regulation which comes from

gene regulation. This approach has signiﬁcant advan-

tages, because the model design and analysis is easily

connected between the continuous and discrete fea-

tures that would otherwise be unforeseen. Moreover,

it can reveal insights into disease mechanism and pos-

sible therapeutic targets with applications to health.

On the other hand, there are still some current

problems in our proposed modeling approach that

need to be addressed. The kinetic parameter val-

ues estimation is a signiﬁcant bottleneck. Here we

use the negative of the stoichiometry from each reac-

tion for the parameters as suggested by (Smallbone

et al., 2007). However a natural attempt is to distin-

guish kinetic parameters for the discrete and continu-

ous events of the hybrid model. In order to estimate

the kinetic parameters of the metabolic reactions, the

proposed procedure is to isolate the metabolic net-

work and perform parameter ﬁtting using experimen-

tal data (metabolites and ﬂuxes time course data) on

a short time scale for which the genetic part can be

considered constant. For this purpose, in the future it

is intended to use experimental steady-state and time-

course metabolomic and ﬂuxomic data from S. pneu-

moniae that will be generated by other participants

in the PneumoSyS project. This experimental data

will be also used for model validation. Another lim-

itation is that the metabolic reconstructions obtained

from the SEED tool do not account for the regulatory

interactions. Therefore, it will be necessary to anno-

tate the model topology reconstruction with such in-

formation, which can be obtained from available liter-

ature and web-databases. An additional challenge of

integrated modeling approaches are time scales. For

example, metabolic reactions occur on the order of

seconds. By contrast, regulatory reactions can take

several minutes to hours.

In future work, we intend develop and vali-

date a complete dynamic hybrid metabolic-regulatory

model of S. pneumoniae using the proposed approach

to predict disease-related metabolic states, which is of

major bio-medical interest.

ACKNOWLEDGEMENTS

This work was partially supported by post-doctoral

grant by Fundac¸

ao para a Ci

encia e a Tecnolo-

gia (FCT) (SFRH/BPD/80784/2011), project Pneu-

moSyS - A Systems Biology approach to the role

of pneumococcal carbon metabolism in colonization

and invasive disease (FCT contract: PTDC/SAU-

MII/100964/2008) and by FCT (INESC-ID multian-

nual funding) through the PIDDAC Program funds.

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