Int. J. Modelling, Identification and Control, Vol. X, No. Y, XXXX 1

Multiagent modelling and simulation ofcarbohydrate oxidation in cell

Nicola Cannata, Flavio Corradiniand Emanuela Merelli*

Dipartimento di Matematica e Informatica,Università di Camerino,Camerino 62032, ItalyFax: +39-073-740-2561E-mail: nicola.cannata@unicam.itE-mail: flavio.corradini@unicam.itE-mail: emanuela.merelli@unicam.it*Corresponding author

Abstract: A cell consists of a large number of components interacting in a dynamic environment.The complexity of interactions among cell components makes design of cell simulation achallenging task. Multiagent systems can be considered a suitable framework for modelling andengineering complex systems organised as autonomous interactive components. The multiagentparadigm proved natural and useful not only in building simulations, but also for devising anengineering methodology. To evaluate the proposed approach, we constructed a multiagent modelof cell components involved in the metabolic pathways of Carbohydrate Oxidation (CO).

Keywords: agent technology; multiagent systems; systems biology; simulation; complex systems;model validation.

Reference to this paper should be made as follows: Cannata, N., Corradini, F. and Merelli, E.(XXXX) ‘Multiagent modelling and simulation of carbohydrate oxidation in cell’, Int. J.Modelling, Identification and Control, Vol. X, No. Y, pp.XXX–XXX.

Biographical notes: Nicola Cannata received the Computer Science degree from the Universityof Pisa and his PhD in Biotechnology from the University of Padova. Currently, he is aPostDoc Researcher in the Complex Systems research group, Department of Computer Scienceand Mathematics at the University of Camerino, Italy. His research interests include bioinformaticsand systems biology.

Flavio Corradini received the Computer Science degree from the University of Pisa and his PhDin Computer Science from the University of Rome. He is a Full Professor of Computer Science inthe Department of Computer Science and Mathematics at the University of Camerino, Camerino,Italy. He is the Leader of the Complex Systems research group. His research interests includeformal methods and software engineering.

Emanuela Merelli received the Computer Science degree from the University of Pisa and her PhDin Artificial Intelligent Systems from the University of Ancona. She is an Assistant Professor inComputer Science in the Department of Computer Science and Mathematics at the University ofCamerino, Italy. She is Member of the Complex Systems research group. Her research interestsinclude agent-based computing and computational systems biology.

1 Introduction

A biological cell is a complex system. It consists of alarge number of components interacting with each other toperform cell functions. Each cell is a self-contained andself-maintaining entity. It can take in nutrients, convertthese nutrients into energy, carry out specialised functionsand reproduce itself. The modelling and simulation ofcell behaviour (Chiarugi et al., 2004; Gonzalez et al.,2003; Loew and Schaff, 2001; Tomita et al., 1999)belongs to an emerging research area, systems biology

(Kitano, 2002), whose aim is to understand how biologicalsystems function. Systems Biology studies at differentabstraction levels the relationships and interactions betweenthe various parts of a biological system (e.g. molecules,organelles, cell compartments, cells, organs, physiologicalsystems, organisms and communities). Mathematical orcomputational models, trying to capture the existentbiological knowledge, are the most utilised instruments in thiseffort. The modelling of complex systems, as suggested inKitano (2002), implies a deep understanding of the biologicalsystem both in terms of its structure and its behaviour.

Copyright © XXXX Inderscience Enterprises Ltd.

2 N. Cannata, F. Corradini and E. Merelli

Cells grow through the functioning of cell metabolism. Cellmetabolism is the process by which individual cells processnutrient molecules. In particular, Carbohydrate Oxidation(CO) is the process by which a cell produces energythrough chemical transformation of carbohydrates (Garretand Grisham, 1995). In biochemistry, those cell processes,which imply a series of chemical reactions within a cell,are called metabolic pathways. In this paper, we proposea Multi-Agent System (MAS) (Jennings and Wooldridge,1998) to model and simulate a biological system as asociety of autonomous components interacting to performa set of system functions (Jennings, 2001). The approachsuggests the main steps that could characterise a methodologyto automatically generate models and simulation systemsfrom available biological knowledge resources. Themultiagent approach allows to design systems very closeto the user’s mental model. The resulting MAs is veryflexible. It supports changes to the model during simulationtime, by adding and removing components by changingthe behaviour of components and by moving, cloning andconsuming components as it happens naturally in the cell.Furthermore, the agents’ autonomy and proactivity allow toeasily represent the non-deterministic behavioural model ofthe cell as in nature. Thus, one is allowed to progressivelyrefine components and develop the simulation system.Then, novel knowledge concerning emerging behavioursof the modelled biological system can be acquired.Next section of this paper summarises the cell processof CO. Section 3 describes the process of engineeringbiological system simulation. Section 4 introduces AgentOriented Software Engineering (AOSE) and describes theProcess forAgent Societies Specification and Implementation(PASSI) methodology. Section 5 presents a MAS formodelling CO. Section 6 discusses the validation issue ofthe MAS model. Section 7 concludes.

2 CO in the cell

The cell consists of a large number of components interactingin a dynamic environment. We study the process of CO,that is, the energy production process, that happens insidea cell through the transformation of carbohydrates (Garretand Grisham, 1995).

We have considered the case of fructose, glucose,mannose, maltose, lactose, saccharose, glycogen andstarch. Each kind of carbohydrate follows its own metabolicpathway, that is, a series of chemical reactions transformingit. These can happen in presence of oxygen (i.e. aerobicrespiration in mitochondria) or in its absence (i.e. anaerobicmetabolism – fermentation). Since each of the carbohydratesis transformed into glucose or a derivate of it, in the following,we focus on glucose. Once inside the cell, glucose isbroken down to make Adenosine Triphosphate (ATP), an‘energy packet’ of the cell, via two main different pathwaysand several minor processes (Figure 1). The first pathway,Glycolysis, occurs inside the Cytoplasm, requires no oxygenand is referred to as anaerobic metabolism. Each reaction isdesigned to produce some hydrogen ions that can then beused to make ATP. The second pathway, called the Kreb’sCycle occurs inside the Mitochondrion and is capable of

generating enough ATP to run all the cell functions. Wemodel the glycolysis and then the destination of pyruvatedepends on the presence of oxygen (aerobic respiration inthe Mitochondrion) or its absence (fermentation).

Figure 1 Oxidative process for one molecule of glucose

G

M

Cytoplasm is the viscid, semifluid component between thecell membrane and the nuclear envelope, where the firststage of carbohydrate molecule transformation takes place. Itconsists primarily of water.It also contains various organelles (e.g. mitochondria) as wellas salts, dissolved gases and metabolites.

The first stage of the CO process, Glycolysis, converts onemolecule of glucose into two molecules of pyruvate.

A graphical description of this pathway is shown inFigure 2 extracted from the Pathway Database of the KyotoEncyclopedia of Genes and Genomes (KEGG (Ogata et al.,1999)). The pathway can be summarised in the followingformula

glucose + 2ATP + 4ADP + 2Pi + 2NADox→ 2 pyruvate + 2ADP + 4ATP + 2NADrid +2H2O

where ATP, ADP, Pi, NADox and NADrid are energypackets. Under anaerobic conditions, the pyruvate isprocessed differently by Lactic Fermentation or by AlcoholicFermentation, depending on the cell typology.

In absence of oxygen, Lactic Fermentation reduces thepyruvate to Lactate. It occurs in anaerobic microorganisms(e.g. sour milk) and animal cells (e.g. muscle pain).In the absence of oxygen, Alcoholic Fermentation reducespyruvate to Ethanol. It occurs in yeast (Saccharomyces)causing the transformation of carbohydrates present in grapesand malted barley into Ethanol.

In presence of oxygen, pyruvate enters into Mitochondrionand undergoes the Kreb’s Cycle.

Mitochondrion consists of two subcomponents, the InnerMitochondrial Membrane (IMM) and the MitochondrialMatrix (MM), where the aerobic respiration takes place viafour processes. In IMM, Transportation process transportspyruvate from the Cytoplasm to MM. In IMM, ElectronTransport Chain transfers electrons from reduced NADand FAD (energy packets) to the final electron acceptor,molecular oxygen. The function of this chain is to permitthe controlled release of free energy to drive the synthesis of

Multiagent modelling and simulation of carbohydrate oxidation in cell 3

ATP (oxidative phosphorylation). In MM, Partial Oxidationof pyruvate degrades the pyruvate w.r.t.

2pyruvate + 2NADox + 2CoA → 2acetylCoA

+ 2NADrid + 2CO2

Figure 2 KEGG’s diagram for the Glycolysis

In MM, Kreb’s Cycle forms part of the breakdown ofcarbohydrates, fats and proteins into carbon dioxide andwater in order to generate energy. It is a series of chemicalreactions of central importance in all living cells that utiliseoxygen as part of cellular respiration. The Kreb’s cycle issummarised in the following formula

acetylCoA + 3NADox + FADox + GDP + Pi → CoA

+ 3NADrid + FADrid + GTP + 2CO2

Following the Kitano suggestion (Kitano, 2002), to model abiological system, we need to identify (1) the cell structure –topological relationship of the network of cell components,as well as the parameters for each relation –, analyse (2)the cell behaviour – understand the processing of metabolicpathways –, control (3) the system simulation and designsystems. In the next section, we introduce a generalmethodology to model and simulate a biological system.

3 Engineering biological system simulations

The use of models to represent a biological system atdifferent abstraction levels helps us to understand thebiological system itself. The specification model can helpby identifying the system structure, critical component rolesand responsibilities, functions and interactions (which aregenerally poorly identified). Of course, to create models,

we need languages and suitable notations. In the literature,a wide range of formal and semiformal languages andnotations can be found. These depend on the level considered,on the properties in which the designer is interested, andon the tools available to perform the analysis and verifyproperties. Proving properties in biological models can meanverifying properties related to the system/process behaviour(e.g. safety properties, liveness properties, simulations ofsystem dynamics, checking for causal relationships). Anyproperty can be formally proved by using well-knownmethods such as equivalence checking, model checking,simulation and model synthesis.

“If in computer science we have studied manyformal and semiformal methods, why not applyour experience to the design of new tools forsystems biology? Computer scientists couldlearn something new.”

In a very simple scenario, a semiformal notation, based onPetri Nets (Peleg et al., 2002) and UML activity diagrams(Cacciagrano et al., 2004), is used to graphically describethe workflow activities for a biological process. In particular,Figure 3 shows engineering life cycle for the simulation ofour biological system. Four different models represent theCO system at different levels of abstraction using differentformalisms. Bold arrows indicate the steps (modelling,verification, simulation and validation) to derive one modelfrom another.

Starting from the existing knowledge of a biologicalsystem, a graphical (semiformal) description can be derived.An example of semiformal description is that adopted in theKEGG (Ogata et al., 1999) pathway diagrams (in Figure 3 onthe upper-right corner). Then, on one hand, this semiformalmodel can be translated into a formal specification(e.g. using a process algebra notation (Milner, 1989), Figure 3left in the middle). For formal models, a wide rangeof methods is available to verify the model’s properties(Peleg et al., 2002; Regev, 2001). On the other hand,the graphical description can be compiled into a low-levelspecification (in an agent-oriented language, in Figure 3 onthe down-right corner) to generate the agent-based simulation(Figure 3 on the down-left corner) of the biological system.The last step, the software validation of the MAS, can giverise to an enrichment of the formal model by includingproperties to make the model more faithful to the biologicalsystem (Merelli and Young, 2005). We can understand thedifference between verification and validation consideringthe aphoristic formulation of Boehm (1981). Verification asks‘Did we build the system right?’ and validation asks ‘Did webuild the right system?’

3.1 Modelling biological systems as MAS

Agents have been described in several ways in literature(Jennings, 2000; Jennings andWooldridge, 1998;Wooldridgeand Jennings, 1995), with different acceptation accordingto the research field where they have been considered.Agent metaphor is successfully adopted in a plethora offields: from Distributed Artificial Intelligence (DAI) tosoftware engineering and concurrent/distributed systems,from social/psychological/economic sciences to Computer

4 N. Cannata, F. Corradini and E. Merelli

Figure 3 Engineering biological system simulation

≥≥

x(z)Q’{u/y}|xv P’ |x(y)x(z)R’x(z)Q’{u/y}|P’ |x(z)R’{v/y}

x(y)x(z).Q’|xu xv P’ |x(y)x(z)R’

Supported Cooperative Work (CSCW). For the purpose ofmodelling biological systems, we focus on autonomy andinteraction properties of agents. As an autonomous entity, anagent encapsulates the execution of independent activities ortasks within its environment. From the software engineeringpoint of view, agents have full control of their state andbehaviour. Also objects encapsulate an internal state and abehaviour but they cannot control their behaviour. Therefore,agents operate by autonomously executing their tasks,concurrently to the work of other agents. An agent interactswith its environment by means of actions and perceptions,which enable the agent to partially observe and control itsenvironment. Biological systems are typically characterisedby a number of complex and concurrent activities. So,in biological system simulation, agents can be suitablyadopted for modelling at the appropriate level of abstractionssuch activities or better the biological components thatare responsible for them. Agent abstraction makes itpossible to model directly reactive and proactive behaviourof biological components, both considering internal andinteractive activities. Besides individual biocomponents, akey aspect for our simulations is modelling the environmentwhere the biocomponents are immersed, and more generally,the biological system, overall. By exploiting the MASparadigm, such aspects can be modelled with abstractionsthat have been introduced to model agent environment and,in particular, the environmental structures or artefacts whichmediate agent interaction. Agent interaction can be modelledboth as direct communication among agents using somekind of Agent Communication Language (ACL), and asmediated interaction exploiting the mediating artefacts whichare part of their environment (Ricci et al., 2005). Mediatingartefact can range from a simple communication channelto a shared data structure, from a shared blackboard toa scheduler, useful for agents to synchronise their tasksand coordinate. Therefore, MASs provide the appropriate

abstraction level to model a biological system overall. If anagent represents an individual component of the systems, theoverall MAS including environmental abstractions capturesthe overall set of the biological components and theirenvironment, including also the structures involved intheir interaction. Mediating and coordination artefacts, inparticular, can be adopted to model the various patterns ofinteraction that can be found in biological processes. Finally,the agent society notion can be used here for defining anensemble of agents and the mediating/coordination artefactsinvolved in the social task characterising the society. Thenotion of agent society can be suitably adopted also forscaling with complexity, identifying different levels ofdescriptions of the same system. What can be describedat one level as an individual agent, at a more detailedlevel, can be described as a society of agents (zooming in)– so an ensemble of agents plus their mediating artefacts– and vice-versa (zooming out). These modelling featurescan be exploited then for simulation of biological systemsinvolving different description levels, each one characterisedby different kind of emerging phenomena.

In this work, we assume the first two steps (processmodelling and model verification) of the above describedmethodology as already executed. Thus, in the sequel, weexploit the agent-oriented technology for modelling andengineering of CO in a cell system. Adopting a AOSEmethodology to specify the MAS, we implemented thecorresponding system simulator. The fidelity of obtainedMAS model with respect to the real biological process wasvalidated (Merelli and Young, 2005) by using a techniquebased on mutation testing (Budd et al., 1980). As result,we obtained that the cell-MAS model was not designed tosupport changes in the biological system and we identified acharacteristic of the model that should be refined to improvethe correspondence between software model and naturalsystem.

Multiagent modelling and simulation of carbohydrate oxidation in cell 5

4 Agent-oriented software engineering

AOSE is a new discipline (Ciancarini and Wooldridge,2001; Gervais et al., 2004; Zambonelli and Omicini, 2004)which provides development methodologies and modellingtechniques to support MAS engineering. Based on the agentcomputing paradigm, it represents a guide for softwareengineers whose aim is to analyse, model and implement acomplex system. In fact, by a MAS, we can simulate complexsystems whose modelling becomes almost impossiblewithout a rigorous guide. Several methodologies havebeen proposed in literature (Bresciani and Giorgini, 2002;Omicini, 2001; Padgham and Winikoff, 2002; Wooldridgeet al., 2000). Among these, we chose the PASSI methodology(Cossentino and Potts, 2002) because it was supportingmany models, concerning different design levels. It supports,by means of domain ontologies, the identification of ahuge amount of variables, different systems componentsbehaviours and the definition of different communicationsprotocols. Furthermore, the PASSI ToolKit provides all thesystem specification by means of UML diagrams.

4.1 PASSI methodology

PASSI (Cossentino and Potts, 2002) is a step-by-steprequirement-to-code methodology for designing anddeveloping MAS. It integrates design models and conceptsfrom object-oriented software engineering using the UMLnotation. PASSI is made up of five models (Figure 4)concerning different design levels, and several steps inthe process of building MAS. For our purposes, we haveconsidered the two following design models:

1 The System Requirements Model is an anthropomorphicmodel of the system requirements in terms of systemfunctionalities and system actors. It is specified throughfour steps:

a Domain description: a functional description of thesystem, using conventional UML use-case diagrams.

b Agent identification: separation of responsibilitiesamong actors (agents), represented by UMLstereotypes.

c Role identification: a functional description of agentroles with respect to the system functionalities andagents responsibilities, using UML sequencediagrams.

d Task specification: specification of the agentbehaviour, using UML activity diagrams.

2 The agent society model is the social organization interms of interactions and dependencies among agents.It is specified by three further steps:

e Ontology description: a description of the knowledgegiven to individual agents and of the high-levellanguage for their interactions, using UML classdiagrams and Object Constraint Languageconstraints.

f Role description: a description of agent roles andtasks, using UML class diagrams.

g Protocol description: communication protocols interms of performative speech-act, using UMLsequence diagrams.

5 Modelling CO with a MAS

In modelling the CO, the PASSI methodology naturally leadsto the identification of structure and behaviour of the cell andits components (Corradini et al., 2005). In fact, the SystemRequirements Model provides the functional view (steps 1and 2), the dynamic view (steps 3 and 4) and the structuralview (steps 5–7) of the cell system. The model is summarisedbelow. A full detailed description can be found in Corradiniet al. (2004).

5.1 Functional view of the cell system

The functional view highlights the cell functionalities and theactors that perform each function of the system. This imply

Figure 4 The five models of PASSI methodology: System Requirements Model, Agent Society Model, Agent ImplementationModel, Code Model and Deployment Model

ur

6 N. Cannata, F. Corradini and E. Merelli

to identify the cell components, their roles and their tasksspecification. The functional view consists of the domaindescription and agent identification diagrams.

Domain description diagram: we identified sevenfunctions that the cell system performs during thecarbohydrate oxidation (Section 2). Therefore, it is naturalto describe the cell functions through seven use cases,as Figure 5 shows: Glycolysis, Lactic Fermentation,Alcoholic Fermentation, Transportation, Partial Oxidationof Pyruvate, Kreb’s Cycle and Electron TransportChain.

Figure 5 shows four further functionalities not related tothe cell system, but concerning the execution environmentand the user interface: Data Updating, Initialisation, ATPQuantitative Analysis and Environment.

We used the metabolic pathways names to identify thecell functionalities. Being the diagrams part of the realimplementation (in Italian Language), to help readers, weprovide the following legend:

Glicolisi GlycolysisFermentazioneLattica Lactic FermentationFermentazioneAlcolica Alcoholic FermentationTrasporto TransportationCatenaRespiratoria Electron Transport ChainCicloAcidoCitrico Kreb’s CycleOssidazioneParzialeAcido Partial Oxidation ofPiruvico PyruvateINIZIALIZZAZIONE InitialisationAggiornaDatiCondivisi Data UpdatingMostraATPCitosol ATP Quantitative AnalysisMostraQuantitaAttuali EnvironmentUtente User

Agent identification diagram: the agent-based simulationsystem aims to be close as much as possible to themental model of its user. We decided that every reactivecell component is represented as an agent. The sevencell functionalities are performed by Cytoplasm andMitochondrion. The latter consists of two subcomponentsIMM and MM. Since each cell functionality is in charge of

one cell component, it is natural to associate agents to cellcomponents.

Figure 6 highlights the association of cell components toagents. Note that a cell component can be responsible formore functionalities. This leads to the definition of differentroles for the corresponding agent.

The agents can communicate with each other through ahigh-level communication protocol. They can also change theenvironment state by modifying the environmental variables.Hence, beside the three cell agent components, we havedefined two further system agents.

AgCytosol: simulates Cytoplasm, playing the AlcoholicFermentation, Lactic Fermentation and Glycolysis roles.

AgMembranaMitocondrialeInterna: simulates the IMM,playing the Transport and Electron Transport Chain roles.

AgMatriceMitocondriale: simulates the MM, playing thePartial Oxidation of Pyruvate and Citric Acid Cycle, that is,the Kreb’s cycle roles.

AgStatoAttuale: simulates the execution environment.AgInterfaccia: is the user assistant agent. It embodies the

interface between the user and the cell simulation system.

5.2 Dynamic view of the cell system

The dynamic view describes the behaviours of cellcomponents during the CO process. It shows how theactivities related to every functionality are ordered over time.It consists of two diagrams: role identification and taskspecification diagrams.

Role identification diagram: describes the order ofsuccession of agents activities.

Each cell functionality is described by a sequencediagram of the communication acts occurring amongdifferent agent roles.

Figure 7 shows only the diagram related to the LacticFermentation (the remaining ones are available inCorradini et al. (2004)). It can be noticed that the

Figure 5 The cell description diagram

Multiagent modelling and simulation of carbohydrate oxidation in cell 7

AgCitosol agent undertakes two different roles in thisfunctionality (i.e. Glycolysis and Lactic Fermentation).

Task specification diagrams: in the cell system, eachcomponent behaves differently with respect to itsfunctionalities. Thus, the behaviour of each agent ofthe model is specified by an activity diagram withrespect to its roles.

Figure 8 shows the behaviour of theAgMitocondrialInnerMembrane agent that simulates

the MM component. On the right hand side of thefigure, we can notice the tasks related to the Kreb’sCycle. The other activities are related to PartialOxidation of Pyruvate.

5.3 Structural view of the cell system

The structural view is a conceptual model of the cell system.Following the PASSI methodology, it corresponds to theontological description of the cell components and their

Figure 6 Agent identification: the cell components stereotypes

Figure 7 Roles identification: the Lactic Fermentation sequence diagram

8 N. Cannata, F. Corradini and E. Merelli

interaction language. It gives rise to the agents’ knowledgeand agents’ communication language. We have defined ourcell ontology in terms of concepts, attributes (variables),relations, actions and predicates. In the future, we aim toinclude the standard notation provided by KEGG and SBMLspecification (Hucka et al., 2003).

The structural view consists of three diagrams: ontology,role and protocol description diagrams.

Ontology description diagram: our domain is the cell.Thus, the ontology description relates to the metabolicpathways and substances involved within the CO process.A metabolic pathway (i.e. Lactic Fermentation) can bedescribed in terms of the quantities of chemical speciesinvolved in it. A substance (i.e carbohydrate) is describedboth in terms of its attributes and its predicates. Figure 9shows a partial view of the ontology.

The communication ontology diagram describes thecomponents interaction, that is, the agents communicationlanguage. The communication language consists of aset of primitives. Each primitive specifies the senderand its role, the receiver and its role and the type ofmessage. Figure 10 shows part of the communicationlanguage that occurs between two agents, AgStatoAttualeand AgMatriceMitocondriale. The communication primitiveidentified by AgMatriceMitocondriale-AgStatoAttuale, itis sent by the agent AgMatriceMitocondriale in its roleof ‘CicloAcitiCitrico’ (i.e. Kreb’s Cycle), to the agentAgStatoAttuale in the role of ‘AggiornaDatiCondivisi’. Themessage is described w.r.t the Gruppo Dati Ciclo Krebontology (see Figure 9) and it is coded by XML. The FIPAcommunication protocol (http://www.fipa.org) is adopted inthe actual implementation.

Figure 8 Task specification: the MM activity diagram

Figure 9 Ontology description: the cell conceptual model class diagram

Multiagent modelling and simulation of carbohydrate oxidation in cell 9

Roles description diagram: allows to define, for everyagent w.r.t. its roles, the set of tasks and communicationsprimitives. The example in Figure 11 shows the tasksassociated the AgCytosolagent within its three roles.

Protocol description diagram: describes the communicationprotocol shared among agents during the ontologicalcommunication at higher level. The system has beenimplemented by using the FIPA request protocol.

Figure 10 Communication ontology: the cell relationship model class diagram

Figure 11 Role description: the Cytoplasm roles diagram

10 N. Cannata, F. Corradini and E. Merelli

6 Validating a carbohydrate oxidationMAS model

The CO is a complex function of the cell system. As aconsequence, the complexity of interactions is far to be fullycomprehended by the human mind. Therefore, computersimulation can be a useful tool for testing and refiningour understanding of emerging system behaviour. But, thesystem’s model must be a ‘good’ model, that is a modelwhose structure and function reflects the biological system.The MAS model we have developed intends to imitate thebiological system in structure and behaviour. Therefore, it isimportant to validate the MAS model.

First of all, we analysed if the system behaves as the user(a biochemist in our experiments) required. The implementedsimulation system takes in input a carbohydrate amongfructose, glucose, mannose, maltose, lactose, saccharose,glycogen and starch and the environmental condition (aerobicor anaerobic). The interface, shown in Figure 12, supportsquery as ‘How much ATP is formed when an enzyme isinhibited or is absent from the system?’, ‘What are thelevels of intermediate metabolites during execution ofa metabolic pathway?,’ ‘Which carbohydrate source ismost efficient for ATP production?’ and ‘What is theratio of NADrid/NADox and FADrid/Fadox during theoxidation process?’ Table 1, summarises some experimentalcases in the presence or in the absence of oxygen.

It is important to observe as maltose, lactose and saccharoseare very more energetic than the other carbohydrates; alsoglycogen and starch should be considered because they arepolysaccharides; they are quantified in table with the quantityof Polysaccharides (length of each polysaccharide). It canalso be noticed that there is always equilibrium amongATP and ADP; NADox and NADrid, FADox and FADridbecause the use of one provokes the creation of the otherand vice versa. The pyruvate and Acetyl-CoA are importantintermediate substances that are created and used during theprocess. The value zero of those substances means that theyare completely consumed. We could deduce that the systemapparently behaves correctly w.r.t user expectations.

Then, we validated the fidelity of carbohydrateoxidation MAS model, according to the approach discussedin Merelli and Young (2005), by adding variations inenvironmental conditions. We have used scenarios thatinclude modifications of the system, that is, models of knownand hypothetical mutations. In Merelli andYoung (2005), theauthors propose that the validation should also check whetherthe model keeps going correctly also in presence of changes inthe natural system (i.e. mutations). If we can identify simplechanges to the software system that correspond to knownmutations, and, if this change to the simulation model resultsin behavioural changes, then we gain considerable confidencein model fidelity. Such behavioural changes correspond toknown mutations of the biological system.

Figure 12 Agent identification: the cell components stereotypes

Table 1 Cell-MAS simulation results for the oxidation of carbohydrate. Note that, for each listed carbohydrate, there isalways equilibrium among ATP and ADT as it happens in the real system

Carbohydrate Quantity Oxygen Fermentation ATP ADP NA NA FA FA Acetil Pyruvate CO2 Ethanol LacticDrid Dox Drid Dox CoA Acid

Glucose 1 Yes / 38 −38 0 0 0 0 0 0 6 0 0Fructose 1 Yes / 38 −38 0 0 0 0 0 0 6 0 0Mannose 1 Yes / 38 −38 0 0 0 0 0 0 6 0 0Maltose 1 Yes / 76 −76 0 0 0 0 0 0 12 0 0Lactose 1 Yes / 77 −77 0 0 0 0 0 0 12 0 0Saccharose 1 Yes / 76 −76 0 0 0 0 0 0 12 0 0Glycogen 1(1) Yes / 39 −39 0 0 0 0 0 0 6 0 0Starch 1(1) Yes / 39 −39 0 0 0 0 0 0 6 0 0Glycogen 3(2) Yes / 234 − 234 0 0 0 0 0 0 36 0 0Glucose 3 No Lactic 6 −6 0 0 0 0 0 0 0 0 6Lactose 1 No Lactic 5 −5 0 0 0 0 0 0 0 0 4Glucose 1 No Alcoholic 2 −2 0 0 0 0 0 0 2 2 0

Multiagent modelling and simulation of carbohydrate oxidation in cell 11

Thus, our validation approach imposes a new requirementon the model. It is not sufficient that the output of theabove described queries is accurate. We should, in addition,obtain reasonable results when the model is perturbedin ways corresponding to known or plausible mutations.As noted, carbohydrate oxidation can take place withintwo different environmental conditions, in presenceof oxygen (aerobic) or in its absence (anaerobic).The former takes place in the mitochondria, the latter in theCytoplasm. There are some cases where as consequenceof malfunction due to DNA mutation in theMitochondrion, the aerobic pathway is blocked andmetabolism is forced to change behaviour with respect tothe new condition.

A mutation in the Mitochondrion can lead to a lack ofan enzyme involved in a metabolic pathway. It can providedifferent ATP or in the worst case, block the process. Innature, an aerobic microorganism can become anaerobic as aconsequence of a mutation which prevents use of cellularrespiration in mitochondria. As an example, we considera mutation of the gene that produces one of the enzymesinvolved in the partial oxidation of pyruvate, that is, itallows the passage of pyruvate from the Cytoplasm to theMitochondrion, through the mitochondrial membrane, byallowing the aerobic respiration. If the mutation provokesthe disappearance of an involved enzyme, the microorganismis forced to adapt to a new context by using the anaerobicpathway. In this case, the pyruvate is transformed in lactate byproducing NADox, allowing the cell to maintain glycolysisand to produce ATP.

The cell-MAS model was not designed with the possibilityto support mutations. Therefore, the correspondence betweenthe software system and components in the biological systemwas imperfect. In fact, to simulate the mutation describedabove, we need the enzyme to be explicitly represented.That leads to think that MAS model described the biologicalsystem at too coarse a grain level. As we mentioned inSection 3.1, the notion of agent society can be suitablyadopted for scaling with complexity. What can be describedat one level as an individual agent,can be described as asociety of agents at a more detailed level. It is the case ofIMM agent, which at a more detailed level, contains a societyof enzymes. Among them the specific enzyme that allowsthe passage of pyruvate from Cytoplasm to Mitochondrionmight exist.

A refining of the system implied a further modelling ofthe Mitochondrion as a MAS system itself. The fine grain(at enzyme level) design of the Inner MitochondrionMembrane has been done in a natural way by substitutingan agent with a society of agents (MAS) and maintainingconsistent the communications among other agents whosediagrams we omit for lack of space. This modification to theMAS system induced also a refinement of the MitochondrionMatrix and the Cytoplasm.

Furthermore, the activation of the anaerobic pathway mustarise from chemical conditions, and the anaerobic pathwaycould be activated by failure of the aerobic pathway. Thesystem being under validation, was instead implementedallowing the user to select the aerobic and anaerobic pathwayscondition, as shown in Figure 12. This implementation choicewas suggested by user requirements addressed to the usability

more then to the fidelity of the system. This weakness hasbeen overcome by allowing aerobic and anaerobic pathwaysto be executed in parallel.

7 Conclusion and future work

A key reason for choosing agent-based simulation of abiological system over other kinds of simulation models is thepotential for establishing strong structural and behaviouralcorrespondence.

Our experience in modelling carbohydrate oxidation leadsto conclude that agent technology is an appealing approachto building models that are as close as possible to the mentalmodel of the bioscientist. The model consists of softwarecomponents that correspond closely with the componentsof the biological system, at whatever level of granularity isappropriate to understanding.

We implemented the cell system simulator for carbohydrateoxidation, and we validated the MAS model fidelity byusing a technique based on mutation testing. As a result,we concluded that the cell-MAS model was not designedto support changes in the biological system. We identified acharacteristic of the model that has been refined to improvethe correspondence between software model and naturalsystem. The redesigning of the system was facilitated by thesemiformal notation used to model the system.

Following this experience, as a future work, we aimto automatically generate domain description models andformal descriptions directly from the Pathway Databaseof KEGG. We will also exploit mobility to simulate cellcomponents movement (Cardelli, 2005), which will bepossible because the system has been implemented withHermes middleware for mobile computing (Corradini andMerelli, 2005).

Acknowledgements

The authors are grateful to Marco Vita, Eleonora Paganelliand Dario Santarelli for the first implementation of the cellmodel and to Eleonora Berluti and Stefano Leli for the secondimplementation. This work was supported by the ItalianMinistry of Education, University and Research (MIUR),projects ‘Laboratory of Interdisciplinary Technologies inBioinformatics (LITBIO)’.

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