Systems BiologyLooking at opportunities and challengesin applying systems theory to molecular

and cell biology.

Systems theory or systems science has nevermanaged to achieve widespread and inde-pendent status in curricula, departments, andjournals but instead acts as an umbrella for anumber of research activities across the physi-cal and engineering sciences. Now, with revolu-

tionary developments in the life sciences, there is renewedinterest in systems thinking. In this article, we survey op-portunities and challenges for the application of systemstheory to biology in the postgenomic era—a new area of re-search also referred to as systems biology.

With the sequencing of DNA for a number of genomes,scientists now have an inventory of genes available to em-bark on the study of the organization and control of geneticpathways. This new phase in the biological revolution, thepostgenomic era, is closely associated with the fields“genomics, transcriptomics, proteomics,” and “metabolo-

mics” (called “the omics” for short). These fields take usfrom the DNA sequence of a gene to the structure of theproduct for which it codes (usually a protein) to the activityof that protein and its function within a cell, the tissue, andultimatively the organism. A series of articles in Nature [1]are recommended for an introduction to these research ar-eas of the biomedical sciences.

With the emergence of “the omics,” molecular biologycurrently witnesses a shift of focus from molecular charac-terization to the understanding of functional activity. Thetwo central questions scientists investigate are “What arethe genes’ functional role?” and “How do genes and/or pro-teins interact?” Answering these questions has become pos-sible with new high-throughput technologies to takemeasurements at the molecular level. In the past, singlegenes were studied, but with DNA microarray technologywe can now measure the activity levels of thousands of

38 IEEE Control Systems Magazine August 20030272-1708/03/$17.00©2003IEEE

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By Olaf Wolkenhauer, Hiroaki Kitano, and Kwang-Hyun Cho

genes at the same time. Thus it becomes possible to identifyinterrelationships between groups of genes (with respect totheir functional role) and to analyze dynamic interactionsamong genes (gene networks). Similarly, proteomics re-search shows that most proteins interact with several otherproteins, and it is increasingly understood that the functionof a protein is appropriately described in the context of itsinteractions with other proteins.Most of these interactions are theconsequence of dynamic and con-trolled processes, and it is not sur-prising that there is renewed interestin the application of systems think-ing to biology.

The rest of this article is orga-nized as follows. We first introduce systems biology in thecontext of the study of complex systems, reviewing a num-ber of related and relevant areas of research and define com-plexity in the context of biological systems. Systems biologyhas a history, and its early stages in the 1960s involved emi-nent researchers, including Wiener, Kalman, Bertalanffy,Rosen, and Mesarovic. We discuss why these attempts dis-appeared from the research agendas and why there is re-newed interest in the postgenomic era of the life sciences.We then follow with two examples of systems biology beforeoutlining current activities from groups around the world.We conclude by listing some of the challenges and hurdlesfor this (re)emerging field.

Genomic CyberneticsThe understanding of causality and coping with complexityis not the holy grail of science but part of its very essence.Not surprisingly then, complexity studies have remained aselusive as inconclusive.

Weaver [2] defined “disorganized complexity” as a prob-lem in which the number of variables is very large and any ofthese variables is best described as a random process. Herewe are at the “molecular level,” and the most successful for-mal methods for representing phenomena at this level de-rive from statistical considerations. In the context of thecell, at the “cellular level,” matters are complicated by thefact that organization becomes an essential feature of theprocesses under consideration. Weaver referred to prob-lems in which a large number of factors are interrelated intoa whole as “organized complexity.” The number of variablesis too large to be dealt with in the Newtonian realm of phys-ics and mathematical modeling, and the systems are too or-ganized to allow statistical techniques. At the time, Weaverdescribed organized complexity as the challenge for sci-ence in the coming 50 years. The enthusiasm he expressedin 1948 is very similar to how one feels today in thepostgenomic era of the life sciences: “It is doubtless truethat we are only scratching the surface of the cancer prob-lem, but at least there are now some tools to dig with and

there have been located some spots beneath which almostsurely there is pay-dirt” [2].

Following Haken’s synergetics, chaos theory, and frac-tals, the science of self-organized criticality [3], nonequili-brium physics, power laws, and emergent phenomenarenewed the interest in complexity studies over the last de-cade or so. These studies developed mostly within the areas

of physics and mathematics. They are seeking general prin-ciple of phenomena that can be observed in a wide range ofdisciplines. Kauffman’s work on genetic networks [4] pavedthe way for complexity studies in biology. The work ofGoodwin [5], [6], Harrison [7], and Meinhardt [8] marked atrend toward an approach more focused on specific organ-isms but continued to investigate cellular processes andmorphological development in evolutionary terms. As Har-old pointed out in his recent book: “Complexity studies is afresh label for a well-known pigeonhole: general systemstheory, that was pioneered by Ludwig von Bertalanffy in the1930s” [9, p. 222]. Systems biology is an emerging field thatcontinues this research into the postgenomic era of the lifesciences [10]-[12]. Complexity studies and systems biologyare different in that the latter takes a signal- and sys-tems-oriented approach to describe the dynamic processeswithin and between biological cells. As we shall see later,systems biology has more to do with the application of sys-tems and control theory to cellular systems than with theapplication of physics to biology.

Systems biology provides a vital interface between cellbiology and biotechnological applications. Before we dis-cuss this area in greater detail in subsequent sections, wenote that complexity in the context of biological systemscan be defined as

• a property of an encoding (mathematical model) (e.g.,its dimensionality, order, or number of variables)

• an attribute of the natural system under consider-ation (e.g., the number of components, descriptiveand organizational levels that ensure its integrity)

• our ability to interact with the system and to observeit (i.e., to make measurements and generate experi-mental data).

On all three accounts, genes, cells, tissues, organs, organ-isms, and populations are individually and as a functionalwhole a complex system. It is the availability of experimen-tal techniques, modern microscopy, laser tweezers, andnanotechnology, as well as DNA microarrays, gel technol-ogy, and mass spectrometry that drives this renewed inter-est in complexity studies and systems biology. While the

August 2003 IEEE Control Systems Magazine 39

Systems biology—applyingsystems theory to biology

in the postgenomic era.

technology to generate and manage data races ahead, it be-comes apparent that methodological advances in the analy-sis of data are urgently required if we want to turn the newlyavailable data into information and knowledge. This needfor research into new methodologies and the developmentof novel conceptual frameworks has been neglected in theeuphoria about new technology. Problems in the post-

genomic era of the life sciences will not only be experimen-tal or technical, but also conceptual. The interpretation ofdata, turning information into knowledge, is as importantfor scientific and biotechnological progress as the possibil-ity of generating and managing data.

With the generation of vast amounts of data, computerscientists have been the natural allies of biologists in themanagement of these data. The growth of bioinformaticsparallels the exciting developments in biology. However theavailability of genome sequence data has led to a focus shiftfrom molecular characterization and sequence analysis toan understanding of functional activity and now interac-tions of genes and proteins in pathways. Gene expressionand regulation, i.e., to understand the organization and dy-namics of genetic, signaling, and metabolic pathways, is thechallenge for the next 50 years. The nature of the experi-ments and the data thereby generated requires an allianceof the biological and biomedical sciences with physical sci-entists (engineers, mathematicians, and physicists). Thefollowing discussion on the challenges and hurdles will clar-ify why such an alliance is so important.

(Not) A New Kid on the BlockAlthough generally considered to be a new area of research,systems biology is not without history, and as early as the1960s the term was used to describe the application of sys-tems and control theory to biology [12]. At the time,Mesarovic wrote: “In spite of the considerable interest andefforts, the application of systems theory in biology has notquite lived up to expectations. ... one of the main reasons forthe existing lag is that systems theory has not been directlyconcerned with some of the problems of vital importance inbiology.” Today, scientists in this field are motivated by theavailability of experimental data, including, for example,DNA microarray time series, and interdisciplinary collabo-rations are widely supported. In fact, the importance of in-terdisciplinary research and close collaborations betweenbiologists and physical scientists is evident in the many

multidisciplinary research centers that are being builtaround the world, gently forcing researchers to interact byconfining them into purpose-built housing.

Mesarovic further suggested that progress could bemade by more direct and stronger interactions of biologistswith system scientists: “The real advance in the applicationof systems theory to biology will come about only when the

biologists start asking questionswhich are based on the system-theo-retic concepts rather than usingthese concepts to represent in stillanother way the phenomena whichare already explained in terms of bio-physical or biochemical principles.... then we will not have the ‘applica-tion of engineering principles to bio-logical problems’ but rather a field of

systems biology with its own identity and in its own right.”Molecular characterization has led to very accurate spatialrepresentations of cellular components, and biochemicalmodeling has been the main approach to studying cellularprocesses. However, the future lies in extending this knowl-edge to observations at higher organizational levels. Thereare few examples of a concerted effort to “translate” biologi-cal representations of gene expression and regulation intothe language of the system scientist [13], [14], and all indica-tions are that the field is going to provide the vital interfacebetween basic cell biology, physiology, and biotechnologi-cal applications such as in metabolic engineering.

Systems biology has new technologies available to gen-erate data from the genome, transcriptome, proteome, andmetabolome, in addition to the physiome. However, whilebioinformatics is usually associated with vast amounts ofdata available in databases, the systems-biological descrip-tion of cellular processes often suffers from a lack of data.

Gene Expression and RegulationEach cell of a (multicellular) organism holds the genomewith the entire genetic material, represented by a large dou-ble-stranded DNA molecule with the famous double-helixstructure. Cells are therefore the fundamental unit of livingmatter. They take up chemical substances from their envi-ronment and transform them. The functions of a cell are sub-ject to regulation such that the cell acts and interacts in anoptimal relationship with its environment. The “centraldogma” of biology describes how information, stored inDNA, is transformed into proteins via an intermediate prod-uct, called RNA. Transcription is the process by which cod-ing regions of DNA (called “genes”) synthesize RNAmolecules. This is followed by a process referred to as“translation,” synthesizing proteins using the genetic infor-mation in RNA as a template. Most proteins are enzymes andcarry out the reactions responsible for the cell’s metabo-lism—the reactions that allow it to process nutrients, tobuild new cellular material, to grow, and to divide.

40 IEEE Control Systems Magazine August 2003

Systems biology has more to do withthe application of systems and controltheory to cellular systems than with theapplication of physics to biology.

Research conducted in the 1960s showed that most basiccellular processes are dynamic and feedback regulated.While investigating regulatory proteins and the interactionsof allosteric enzymes, Jacob and Monod introduced the dis-tinction between “structural genes” (coding for proteins)and “regulatory genes,” which control the rate at whichstructural genes are transcribed. This control of the rate ofprotein synthesis was the first indication that such pro-cesses are most appropriately viewed as dynamic systems.Figure 1 illustrates the processes of gene ex-pression and regulation in bacterial cells.

Although bacterial cells are capable of pro-ducing several thousand different proteins, notall are produced at the same time or in the samequantity. The energy consumption for proteinsynthesis and the relatively short half-life of theRNA molecules are reasons for the cell to con-trol both the types and amounts of each protein.One example of a global regulatory network isthe heat-shock response. When proteins are ex-posed to extremes of heat, they are said to un-dergo “denaturation.” Denaturation is thedestruction of the folding properties of a pro-tein leading (usually) to loss of biological activ-ity. To counteract possible toxic effects frominsoluble aggregates in the cell, the change intemperature and the quantity of denatured pro-teins are “sensed” by the cell and specific heat-shock proteins are produced. Figure 2 illus-trates heat-shock regulation of the DnaK operonin the bacterium Bacillus subtilis. The proteinDnaK is such a “chaperone,” one of a group ofproteins called “molecular chaperones,” whichhelp other proteins to fold properly. These spe-cialist proteins produce barrel-like structures,providing an environment for the denaturedproteins to refold. The described mechanism isreferred to as “negative control” throughrepressor deactivation. A repressor protein is aregulatory protein that binds to a specific siteon the DNA and thereby blocks transcription.

Drawings like Figure 1 are frequently used inbiology textbooks to illustrate structural as-pects and the spatial organization of compo-nents in the cell. Figure 2, on the other hand,also shows the signal flow and temporal effectscomponents have. The next section introducesan area in which signal- and systems-orientedrepresentations play an even greater role.

Intra- and IntercellularDynamics: CellularWeather ForecastingThe previous example described how genes actand interact within the context of the cell. Bio-

logical cells are not running a program but rather continu-ally sensing their environment and making decisions on thebasis of that information. To determine how cells act and in-teract within the context of the organism to generate coher-ent and functional wholes, we need to understand howinformation is transferred between and within cells. Cell sig-naling, or “signal transduction,” is the study of the mecha-nisms that enable the transfer of biological information.Signaling impinges on all aspects of biology, from develop-

August 2003 IEEE Control Systems Magazine 41

Figure 1. Gene expression and regulation in bacteria. Information, stored inthe DNA, is transformed into proteins via an intermediate product called mRNA.The short half-life of mRNA and the energy consumption of protein synthesis formthe basis for a sophisticated hierarchy of a control mechanism.

Figure 2. Negative regulation of the dnaK and GroESL operons in Bacillussubtilis. The HrcA repressor is a regulatory protein that binds at specific sites onDNA and blocks transcription. In the absence of stress, the GroESL co-repressorbinds with HrcA and thereby increases repression of the dnaK operon genes. Uponheat shock, the transcription rate of a group of heat shock proteins, calledchaperones, is increased. They build barrel-type structures, which help denaturedprotein to refold and regain its function.

ment to disease. Many diseases, such as cancer, involve mal-function of signal transduction pathways. Downward [15]provided an excellent account of this field.

Figure 3 illustrates a very basic signaling model. As indi-cated in the previous section, bacteria regulate cell metabo-lism in response to a wide variety of environmental

fluctuations, including the heat-shock example above.Thus, there must be mechanisms by which the cells receivesignals from the environment and transmit them to the spe-cific target to be regulated. Receptors are proteins that spanthe membrane, with a site for binding the signaling com-pound on the outer surface. Binding of the extracellular sig-naling compound to the outer surface of the receptorresults in an activation of an intracellular protein (the “re-sponse regulator”), for example, by phosphorylation. Signaltransduction pathways commonly consist of many morecascaded modules between receptor and genome. Therecan be numerous intermediate steps before the signaltransduction process ends, often with a change in the geneexpression program of the cell. In the figure, the phos-phorylated response regulator is a DNA binding protein,which serves as a repressor, preventing the RNA polymer-ase from transcribing the adjacent gene(s).

In addition to crosstalk between pathways, negativefeedback systems can occur, and the time course of a signaltransduction pathway can be critical. It is therefore impor-tant to develop experimental techniques that allow quanti-tative measurements of proteins and protein interactions.Mathematical modeling and simulation in this field has thepurpose to help and guide the biologist in designing experi-ments and generally to establish a conceptual framework inwhich to think. The article by Hasty [16] provides a surveyof such in numero molecular biology (see also [17]). Smolen[18] surveys mathematical modeling of transcriptional con-trol and future directions. The signal-oriented approach tocellular models by Kremling et al. [13] is an example of sys-tems and control theory bridging the gap between cellularbiology and metabolic engineering. Progressing frommerely descriptive models to predictive models will requirethe integration of data analysis and mathematical modeling

with information stored in biologicaldatabases. The data we currently haveavailable do not allow parametric sys-tems identification techniques to buildpredictive models. Instead, it is thesystems thinking, the modeling pro-cess itself, that often proves useful.

Example: Modeling ofRas/Raf-1/MEK/ERKSignal TransductionPathwayThe Ras/Raf-1/MEK/ERK module inFigure 4 is a ubiquitously expressedsignaling pathway that conveys mito-genic and differentiation signals fromthe cell membrane to the nucleus[19]-[22]. This kinase cascade appearsto be spatially organized in a signalingcomplex nucleated by Ras proteins.The small G protein Ras is activated by

42 IEEE Control Systems Magazine August 2003

EnvironmentalSignal Cell Surface Receptor

(Sensor Kinase)

IntracellularProtein

Cell Membrane

Phosphatase

ResponseRegulator

PhosphorylatedProtein

RNAPolymerase

Promoter Operator Gene(s)

P

P

DNA

Figure 3. Cell signaling (signal transduction). Intracellulardynamics (gene expression) can be affected by extracellular signals.Receptors spanning the cell membrane receive signals and transmitthe information to activate intracellular proteins (the responseregulator). In the figure, the response regulator binds to the operatorregion of a gene and prevents the RNA polymerase fromtranscription of the adjacent gene. A phosphatase ensures that theprocess is continuous.

Figure 4. Biologist’s drawing for the Ras/Raf-1/MEK/ERK signal transduction pathway.

many growth factor receptors and binds to the Raf-1 kinasewith high affinity when activated. This induces the recruit-ment of Raf-1 from the cytosol to the cell membrane. Acti-vated Raf-1 then phosphorylates and activates MAPK/ERKkinase (MEK), a kinase that in turn phosphorylates and acti-vates extracellular signal regulated kinase (ERK), the proto-typic mitogen-activated protein kinase (MAPK). ActivatedERKs can translocate to the nucleus and regulate gene ex-pression by the phosphorylation of transcription factors.This kinase cascade controls the proliferation and differen-tiation of different cell types. The specific biological effectsare crucially dependent on the amplitude and history of ERKactivity. The adjustment of these parameters involves theregulation of protein interactions within this pathway andmotivates a systems biological study. Figures 5 and 6 de-scribe the “circuit diagrams” of the biokinetic reactions forwhich a mathematical model is used to simulate the influ-ence of ligand variations on the pathway

S E SE E Pk

k

k+ →← → +

1

2

3 .

Signal transduction pathways can be represented as se-quences of enzyme kinetics reactions which turn a sub-strate S into a product P via an intermediate complex SEand regulated by an enzyme E . The rate by which the en-zyme- substrate complex SE is formed is denoted by k1. Thecomplex SE holds two possible outcomes in the next step. It

can be dissociated into E and S with a rate constant k2 or itcan further proceed to form a product P with a rate constantk3. It is required to express the relations between the rate ofcatalysis and the change of concentration for the substrate,the enzyme, the complex, and the product. Based on this re-action kinetics [23], we first consider a basic modeling block

August 2003 IEEE Control Systems Magazine 43

Figure 5. Basic pathway modeling block. The pathway model isconstructed from basic reaction modules like this enzyme kineticreaction for which a set of four differential equations is required.

Figure 6. Graphical representation of the Ras/Raf-1/MEK/ERK signal transduction pathway (the shadowed part represents thesuppression by RKIP): a circle represents a state for the concentration of a protein and a bar a kinetic parameter of the reaction to beestimated. The directed arc (arrows) connecting a circle and a bar represents a direction of a signal flow. The bidirectional thick arrowsrepresent an association and a dissociation rate at the same time. The thin unidirectional arrows represent a production rate of products.

of signal transduction pathways. This basic modeling blockis illustrated in Figure 5 and can be described by the follow-ing set of nonlinear ordinary differential equations:

dm tdt

k m t m t k m t

dm tdt

k m t m

11 1 2 2 3

21 1 2

( )( ) ( ) ( )

( )( ) (

= − +

= − t k m t k m t

dm tdt

k m t m t k m t k

) ( ) ( )

( )( ) ( ) ( )

+ +

= − −

2 3 3 3

31 1 2 2 3 3m t

dm tdt

k m t

3

43 3

( )

( )( ).=

From these we have

m t m t C

m t m t m t C2 3 1

1 3 4 2

( ) ( ) ,

( ) ( ) ( ) .

+ =+ + =

Hence we can describe the basic reaction module by twononlinear equations subject to two algebraic conditions.

In general, for a given signal transduction system, thewhole pathway can be modeled by a set of nonlinear dif-ferential equations and a set of algebraic conditions in thefollowing form:

d tdt

t t

m t Cii p

j

mf m k

( )( ( ), ( )),

( ) ,{ , }

=

=∈∑

1

where m( ) [ ( ), ( ), , ( )]t m t m t m tp= 1 2 K , k( ) [ ( ), ( ), ,t k t k t= 1 2 K

k tq ( )], p is the number of proteins involved in the pathway,qis the required number of parameters, and j J∈{ , , }1 K withthe number of algebraic conditions J p< .

Parameter estimation is widely regarded as a major prob-lem in dynamic pathway modeling [25], [26]. A simplemethod first discretizes the nonlinear differential equationsinto algebraic difference equations that are linear with re-

44 IEEE Control Systems Magazine August 2003

Figure 7. Illustration of parameter estimation from time series data: Each parameter is determined from the value to which the estimatesconverge (shown by the horizontal line). (Note that any experimental noise can be further eliminated by regression techniques if multipleexperimental replicates at each time point are available.)

spect to the parameters and then solve the transformed lin-ear algebraic difference equations to obtain the parametervalues at each sampling time point. We can then estimatethe required parameter values by employing curve fitting,calculation of steady state values, and regression tech-niques. For this purpose of parameter estimation, the previ-ous equations are transformed into

k g mm

( ) ( ),( )

t td t

dt=

,

and this can be further transformed into a set of algebraicdifference equations by approximating the differential oper-ator vector g via a difference operator vector h as

k h m m m( ) ( ( ), ( ), , ( ))t t t t r≅ − −1 K

where r depends on the order of approximation. Withoutloss of generality, k( )t can be approximated by k since most

of the signal transduction systems can be regarded asslowly time varying systems compared with the measure-ment windows in time scale. Hence we have

k h m m m≅ − −( ( ), ( ), , ( ))t t t r1 K ,

which implies the parameter estimates based on timecourse measurements.

The entire model, as shown in Figure 6, is constructed inthis way, leading to what usually becomes a relatively largeset of differential equations for which parameter valueshave to be identified. As illustrated in Figure 7, in the estima-tion of parameters from western blot data, the parameter es-timates usually appear as a time dependent profile since thetime course data include various uncertainties. However,since the signal transduction system itself can be consid-ered as time invariant, the estimated parameter profileshould converge to a constant value at steady state. Figure 7illustrates this estimation procedure.

August 2003 IEEE Control Systems Magazine 45

Figure 8. The simulation results for fixed initial conditions: (a) shows the binding of RKIP to Raf-1*, (b) shows the binding of MEK-PP toERK-P, (c) shows the binding of ERK-PP to Raf-1*/RKIP, and (d) shows the binding of RP to RKIP-P.

If a reasonable model is constructed, this can then beused in a variety of ways to validate and generate hypothe-ses, or to help experimental design [22], [24]. Based on themathematical model illustrated in Figure 6 and the esti-mated parameter values as, for example, obtained using adiscretization of the nonlinear ordinary differential equa-tions (as illustrated in Figure 7), we can perform simulationstudies to validate the signal transduction mechanism as il-lustrated in Figure 5 and also to analyze the signaltransduction system with respect to the sensitivity for theligand (via simulation of variable initial conditions) as illus-trated in Figure 9.

Current Research:An International PerspectiveThe interest in systems biology is documented by the in-creasing number of conferences, research groups, and insti-tutes dedicated to this area. Funding initiatives in the UnitedStates, Japan, South Korea, and Germany provide new op-portunities to the engineering sciences. Systems biologyprovides evidence of the growing involvement of control en-gineers, not just at the technological level, but also playing avital role in the development of novel methodological ap-

proaches in mathematical modeling, simulation, and dataanalysis [27]. To allow large scale simulations, internationalprojects are developing a systems biology markup language(SBML) [28] and “Systems Biology Workbench” to allow theintegration of models and simulation tools (visithttp://www.sbw-sbml.org for further information).

The principal challenge for the biomedical sciences is toanswer the following questions [6]:

• How do cells act and interact within the context of theorganism to generate coherent and functional wholes?

• How do genes act and interact within the context ofthe cell to bring about structure and function?

For systems biology we can summarize the challenges asfollows:

• methodologies for parameter estimation• experimental and formal methods for model valida-

tion• identification of causal relationships, feedback, and

circularity from experimental data• modular representations and simulation of large scale

dynamic systems• investigations into the stability and robustness of cel-

lular systems

46 IEEE Control Systems Magazine August 2003

Figure 9. The simulation results for variable initial conditions: (a) shows the variation of Raf-1*, (b) shows the variation of ERK, (c)shows the variation of RKIP, and (d) shows the variation of RKIP-P.

• visualization and fusion of information, integration ofmodels and simulators

• scaling models across time scales and description lev-els (from genes, transcripts, and proteins to cells andorganisms).

Gene expression takes place within the context of a celland between cells , organs, and organisms. Thereductionist approach is to “isolate” a system, conceptu-ally “closing it off” from its environment through the defini-tion of inputs and outputs. We inevitably loose informationusing this approach since conceptual closure amounts tothe assumption of constancy for the external factors andthe fact that external forces are described as a function ofsomething inside the system. Different levels of cellularsystems may require different modeling strategies, and ul-timately we require a common conceptual framework thatintegrates different models, for example, differential (massaction or rate) equations provide a realistic modeling para-digm for a single-gene or single-cell representation, butcell-to-cell and large-scale gene interaction networkscould, for example, be represented by finite-state modelsor using agent-based simulation.

One should not jump to the conclusion, however, thatsystems and control theory could provide all answers tothe challenges given by dynamic systems in molecular bi-ology. In dynamic systems theory, one can often ignorespatial aspects. However, time and space are essential forexplaining the physical reality of gene expression. Thesame component of a pathway may have a different func-tional role depending on its location within the cell. Al-though components of cells have specific locations, theselocations lack exact coordinates. Not only signals are beingtransmitted but components also move around in a non-random fashion. Without spatial entailment there can be noliving cell, and for systems biology it is thus necessary to in-tegrate a topological representation of this organizationwith models of the dynamic behavior.

The biologist Frank Harold presented an excellent dis-cussion of the complexity of cellular processes and pro-vided a compelling argument for the need for moreresearch in complexity studies: “From the chemistry ofmacromolecules and the reactions that they catalyze, lit-tle can be inferred regarding their articulation into physi-ological functions at the cellular level, and nothingwhatever can be said regarding the form of developmentof these cells. It therefore seems to me self-evident thatthe quest for the nature of life cannot be conducted exclu-sively on the biochemist’s horizon. We must also inquirehow molecules are organized into larger structures, howdirection and function and form arise, and how parts areintegrated into wholes” [9].

In general, causation is a principle of explanation ofchange in the realm of matter. In systems biology causationis defined as a (mathematical) relationship, not betweenmaterial objects (molecules), but between changes of states

within and between elements of a system. Instead of tryingto identify genes as causal agents for some function, role, orchange in phenotype we relate these observations to se-quences of events. In other words, instead of looking for agene that is the reason, explanation, or cause of some phe-nomenon we seek an explanation in the dynamics (se-quences of events ordered by time) that led to it. “It issystems dynamics, not a genetic program that gives rise tobiological forms and function” [9, p. 199].

In analyzing experimental data, we usually rely on as-sumptions made about the ensemble of samples. A statisti-cal or “average perspective,” however, may hide short-termeffects that are the cause for a whole sequence of events in agenetic pathway. What in statistical terms is considered anoutlier may just be the phenomenon the biologist is lookingfor. It is very difficult to obtain sufficiently large and reliabledata sets for pathway modeling; it is therefore important tocompare different methodologies, their implicit assump-tions, and the consequences of the biological questionsasked. To allow reasoning in the presence of uncertainty, wehave to be precise about uncertainty, and if we cannot beprecise about uncertainty, modeling (generating hypothe-ses), and model validation (for hypothesis testing) becomecomplementary aspects of an iterative process. It is thus ofparamount importance that we strive to bridge the gap be-tween data and models. In the words of Bertalanffy: “Thuseven supposedly unadulterated facts of observation al-ready are interfused with all sorts of conceptual pictures,model concepts, theories, or whatever expression youchoose. The choice is not whether to remain in the field ofdata or to theorize; the choice is only between models thatare more or less abstract, generalized, near or more remotefrom direct observation, more or less suitable to representobserved phenomena” [29].

ConclusionsSystems biology marks a shift away from an often obses-sively reductionist (molecular) approach to providing acausal and dynamic account of cellular form and function.The biggest if not the principal hurdle for the systems ap-proach is “Zadeh’s uncertainty principle,” which statesthat as the complexity of a system increases, our ability tomake precise and yet significant statements about its be-havior diminishes until a threshold is reached beyondwhich precision and significance (or relevance) become al-most exclusive characteristics.

The cell is a self-controlled and self-regulating dynamic sys-tem consisting of components that are interacting in spaceand time. The relationships that prevail between structure,function, and regulation in cellular networks are still largelyunknown. Systems biology aims to identify and explain theserelationships through an integrated effort of both experimen-tal and theoretical methodologies. For this we require scien-tists who are prepared to invest time and effort into more thanone discipline and scientific culture. This will necessitate a

August 2003 IEEE Control Systems Magazine 47

change in the education, training, and career prospects of in-terdisciplinary scientists. For those who persist, the reward isa better understanding of life itself.

References[1] O.G. Vukmirovic et al., “ Insight—Functional genomics,” Nature, vol. 405,no. 15, pp. 819-846, June 2000.[2] W. Weaver, “Science and complexity,” Amer. Scientist, vol. 36, pp. 536-544,Oct. 1948.[3] P. Bak, How Nature Works: The Science of Self-Organized Criticality. Oxford,U.K.: Oxford Univ. Press, 1997.[4] S. Kauffman, At Home in the Universe: The Search for Laws ofSelf-Organization and Complexity. Oxford, U.K.: Oxford Univ. Press, 1995.[5] B. Goodwin, How the Leopard Changed Its Spots: The Evolution of Complex-ity. Princeton, NJ: Princeton Univ. Press, 2001.[6] R.V. Sole and B.C. Goodwin, Signs of Life: How Complexity Pervades Biology.New York: Basic Books, 2002.[7] L.G. Harrison, Kinetic Theory of Living Pattern, Cambridge, U.K.: Cam-bridge Univ. Press, 1993.[8] H. Meinhardt, The Algorithmic Beauty of Sea Shells. Berlin, Germany:Springer-Verlag, 1988.[9] F.M. Harold, The Way of the Cell: Molecules, Organisms and the Order of Life.Oxford, U.K.: Oxford Univ. Press, 2001.[10] H. Kitano, Ed., Foundations of Systems Biology. Cambridge, MA: MIT Press,2000.[11] H. Kitano, “Systems biology: A brief overview,” Science, vol. 295, no. 5, pp.1662-1664, Mar. 2002.[12] O. Wolkenhauer, “Systems biology: The reincarnation of systems theoryapplied in biology?,” Briefings Bioinform., vol. 2, no. 3, pp. 258-270, 2001.[13] A. Kremling, K. Jahreis, J.W. Lengeler, and E.D. Gilles, “The organization ofmetabolic reaction networks: A signal-oriented approach to cellular models,”Metabolic Eng., vol. 2, no. 3, pp. 190-200, July 2000.[14] Caltech ERATO Kitano, “Systems Biology Workbench,” [Online].http://www.cds.caltech.edu/erato/[15] J. Downward, “The ins and outs of signaling,” Nature, vol. 411, no. 14, pp.759-762, June 2001.[16] J. Hasty, D. McMillen, F. Isaacs, and J.J. Collins, “Computational studies ofgene regulatory networks: In numero molecular biology,” Nature Reviews Ge-netics, vol. 2, no 4, pp. 268-279, Apr. 2001.[17] J.J. Tyson and M.C. Mackey, “Molecular, metabolic, and genetic control,”Chaos, vol. 11, no. 1, pp. 81-282, Mar. 2001.[18] P. Smolen, D.A. Baxter, and J.H. Byrne, “ Modeling transcriptional controlin gene networks—Methods, recent results, and future directions,” Bull.Math. Biol., vol. 62, pp. 247-292, 2000.[19] K. Yeung, P. Janosch, D.W. Rose, H. Mischak, J.M. Sedivy, and W. Kolch,“Mechanism of suppression of the Raf/MEK/Extracellular Signal-RegulatedKinase pathway by the Raf Kinase Inhibitor Protein,” Mol. Cell. Biol., vol. 20,pp. 3079-3085, May 2000.[20] K. Yeung, T. Seitz, S. Li, P. Janosch, B. McFerran, C. Kaiser, F. Fee, K.D.Katsanakis, D.W. Rose, H. Mischak, J.M. Sedivy, and W. Kolch, “Suppression ofRaf-1 kinase activity and MAP kinase signaling by RKIP,” Nature, vol. 401, pp.173-177, Sept. 1999.[21] C.J. Marshall, “Specificity of receptor tyrosine kinase signaling: Tran-sient versus sustained extracellular signal-regulated kinase activation,” Cell,vol. 80, pp. 179-185, Jan. 1995.[22] K.-H. Cho, S.-Y. Shin, H.-W. Kim, O. Wolkenhauer, B. McFerran, and W.Kolch, Mathematical Modeling of the Influence of RKIP on the ERK SignalingPathway (Lecture Notes in Computer Science). Milan, Italy: Springer-Verlag,2003.[23] D.P. Robert and M. Tom, “Kinetic modeling approaches to in vivo imag-ing,” Nature Rev.: Molecular Cell Biol., vol. 2, pp. 898-907, Dec. 2001.[24] K.-H. Cho, S.-Y. Shin, H.-W. Lee, and O. Wolkenhauer, “Investigations intothe analysis and modeling of the TNF α mediated NF-κ B signaling pathway,”in Proc. 3rd Int. Conf. Systems Biology, Stockholm, Sweden, p. 87, 2002 and Ge-nome Research (Special Issue on Systems Biology), to be published.[25] H.G. Bock, “Numerical treatment of inverse problems in chemical reac-tion kinetics,” in Modeling Chemical Reaction Systems, K.H. Ebert, Ed.Springer-Verlag: New York, vol. 18, pp. 102-125, 1981.

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Olaf Wolkenhauer received the Dipl.-Ing. and BEng. degreein control engineering in 1994 from the University of AppliedSciences, Hamburg, Germany and the University ofPortsmouth, U.K., respectively. He received the Ph.D. fromthe University of Manchester Institute of Science and Tech-nology (UMIST). From 1997 to 2002 he held a research lec-tureship at the Control Systems Centre, UMIST, and since2002 he has held a joint senior lectureship between the De-partment of Biomolecular Sciences and the Department ofElectrical Engineering and Electronics. In 1999 and 2000 hewas a visiting research fellow at Delft University of Technol-ogy, The Netherlands. He has authored two books, Possibil-ity Theory with Applications to Data Analysis (RSP, 1998) andData Engineering (Wiley, 2001). His research interest is in theapplication of systems and control methodologies to molec-ular and cell biology. Since July 2003 he has held the chair inBioinformatics and Systems Biology at the University ofRostock. He can be contacted at the Department ofBiomolecular Sciences and Department of Electrical Engi-neering and Electronics, Control Systems Centre, Universityof Manchester Institute of Science and Technology , P.O. Box88, Manchester M60 1QD, U.K., o.wolkenhauer@umist.ac.uk.

Hiroaki Kitano is a director at Sony Computer ScienceLaboratories, Inc., director of ERATO Kitano Symbiotic Sys-tems Project, JST, and president of The Systems Biology In-stitute. He received his B.A. in physics from InternationalChristian University, Tokyo, in 1984 and a Ph.D. in com-puter science from Kyoto University in 1991. He receivedthe Computers and Thought Award in 1993 and the Prix ArsElectronica in 2000.

Kwang-Hyun Cho received his B.S., M.S., and Ph.D. degreesin electrical engineering from the Korea Advanced Instituteof Science and Technology in 1993, 1995, and 1998, respec-tively. He joined the School of Electrical Engineering at theUniversity of Ulsan, Korea, in 1999 as an assistant professor.From 2002 to 2003, he was a research fellow at the ControlSystems Centre, Department of Electrical Engineering andElectronics at the University of Manchester Institute of Sci-ence and Technology, U.K. His research interests cover theareas of systems science and control engineering includinganalysis and supervisory control of discrete event systems,nonlinear dynamics, hybrid systems, and applications tocomplex systems such as communication networks and bio-logical systems.

48 IEEE Control Systems Magazine August 2003