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//-->Identifying Constraints that Govern CellBehavior: A Key to Converting Conceptualto Computational Models in Biology?Markus W. Covert, Iman Famili, Bernhard O. PalssonDepartment of Bioengineering, University of California, San Diego, 9500Gilman Drive, La Jolla, California 92093; telephone: 858-534-5668;fax: 858-882-3120; e-mail: palsson@ ucsd.eduPubilshed online 24 November 2003 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.10849Abstract:Cells must abide by a number of constraints. Theenvironmental constraints of cellular behavior and phys-icochemical limitations affect cellular processes. To regu-late and adapt their functions, cells impose constraintson themselves. Enumerating, understanding, and applyingthese constraints leads to a constraint-based modelingformalism that has been helpful in converting conceptualmodels to computational models in biology. The continuedsuccess of the constraint-based approach depends uponidentification and incorporation of new constraints tomore accurately define cellular capabilities. This reviewconsiders constraints in terms of environmental, physico-chemical, and self-imposed regulatory and evolutionaryconstraints with the purpose of refining current constraint-based models of cell phenotype.B2003 Wiley Periodicals, Inc.Keywords:systems biology; flux balance analysis (FBA);extreme pathway analysis; constraints; computationalmodelingINTRODUCTIONThe complex composition of a biological system requires theuse of computational tools to describe its integrated func-tion. As a result, more biologists are turning to engineers,physicists, and mathematicians, who in turn are scramblingto learn biological fundamentals. Such cross-disciplinaryfertilization has led to important studies on regulation ofgalactose utilization in yeast (Ideker et al., 2001), control ofthe InB – NF –nBsignaling module (Hoffmann et al., 2002),and mammalian cell cycle regulation (Qu et al., 2003),among others. Taken together, these developments signal animportant shift in biology fromconceptual modelingtocomputational modeling.Conceptual models describe asystem in qualitative terms, whereas computational modelscan quantitatively simulate systemic properties to ana-lyze, interpret, and predict cell behavior. Thanks to the high-Correspondence to:B. PalssonContract grant sponsors: National Science Foundation; National Insti-tutes of HealthContract grant numbers: BES 01-20363; GM 57089throughput generation of ‘‘omics’’ data (Blaine-Mettingand Romine, 1997), biologists find themselves well posi-tioned to reconstruct fairly complicated conceptual modelsof metabolic, regulatory, and signaling networks (in order ofdifficulty) (Davidson et al., 2002a, 2002b; Karp et al., 2002;Salgado et al., 2001), culminating in the development ofdatabases such as KEGG and MetaCyc (Kanehisa and Goto,2000; Karp et al., 2000).One current challenge in systems biology is to translatethese conceptual models into genome-scale computationalmodels. It is clear that the complexity of biological systems,the difficulty of obtaining kinetic parameters, and the enor-mous generation of data will require the development of newanalytical methods inin silicobiology (Bailey, 2001; Kitano,2002) (Fig. 1). The constraint-based approach (Palsson,2000) to the deduction of phenotype from the genotype andenvironment directly addresses these challenges. In theconstraint-based approach to analyzing metabolic networks,all possible behaviors of a system (e.g., flux distributionsthrough the metabolic network) are considered, as shown inFigure 2. Although cellular behavior may not be completelyspecified at this point, it is known that cells behave in waysthat reflect the constraints imposed by their environments, byphysicochemical laws, and by themselves. By successivelyimposing constraints on conceptual models, as illustrated inFigure 2, the allowable range for each flux in the network isreduced dramatically. The problem of modeling complexbiological systems shifts from experimental determination ofkinetic and other fundamental parameters—as mentioned,currently an intractable problem—to continued identifica-tion of constraints that allow a more specific description ofthe system—a challenge that is successfully being addressed,as discussed in what follows.Current constraint-based computational models have fo-cused on microbial organisms. These models are at the‘‘genome-scale’’—referring simply to the amount of genesaccounted for in the model, which has now reached approx-imately 30% to 35% of the annotated genes in an organism(Price et al., 2003). Genome-scale models have focusedprimarily on metabolism and associated transcriptionalB2003 Wiley Periodicals, Inc.Figure 1.The shift from studying components to studying systems requires the use of computational tools to integrate conceptual data and simulatesystemic behavior. The importance of computation has become apparent in the biological sciences, wherein generation of experimental data far outpacesefforts to reconcile these data in terms of a comprehensive model. New mathematical approaches will be required to describe such systems. Such achallenge is not new; the development of statistical mechanics originated as an attempt to integrate the known chemical properties of molecules to simulatethe properties of a bulk fluid.Escherichia coliimage courtesy of www.denniskunkel.com.regulation, but are aimed at a complete representation of anorganism and have already been used to simulate cellbehavior under a variety of conditions (Reed and Palsson,2003). In addition, because these models attempt to capturesystems-level behaviors as completely as possible, they areinstrumental in identifying and characterizing emergentproperties of biological networks, where an observedbehavior has been difficult or even impossible to interpretfrom the cellular ‘‘parts list’’ alone (Papin et al., 2003; Priceet al., 2003).The success of the constraint-based approach dependsupon identification and incorporation of new constraints todefine the cellular capabilities more accurately. This reviewconsiders constraints in terms of environmental, physico-chemical, and self-imposed regulatory and evolutionaryconstraints with the purpose of refining current constraint-based models of cell phenotype. Some of the constraints mayseem intuitive or basic; however, we aim to illustrate howtheir consideration leads to nonintuitive modeling conse-quences (Fig. 3, Table I).ENVIRONMENTAL CONSTRAINTSThe constraints imposed on cells by their environments—both external and internal—have a major influence on cellbehavior. External environments impose constraints on cellsin terms of nutrients, physical factors, and neighboring influ-ences. Whether a cell can grow in a given environmentdepends in part on its ability to obtain or synthesize all nec-essary biomass components (Neidhardt et al., 1990). Thepresence or absence of necessary compounds thus representsan environmental constraint on the cell. As an example,development of a ‘‘minimal gene set’’ to sustain life must bekept in the context of environmental constraints, as theminimal gene set for life in a complex medium would differsignificantly from that required for life in glucose minimal764BIOTECHNOLOGY AND BIOENGINEERING, VOL. 84, NO. 7, DECEMBER 30, 2003Figure 2.The constraint-based approach applied to metabolic networks. A small network with only two chemical reactions (fluxv1: A!B; fluxv2:A!C) and two transport processes (metabolite A enters the cell with fluxvinand B and C exit together via fluxvout) is depicted together with the allowablerange of each reaction/transport flux. Initially, the flux ranges are unbounded. By incorporating characteristics of the system, such as reactionthermodynamics, maximum enzyme turnover rates, and metabolite mass balance, in terms of constraints, the allowable ranges are reduced significantly. Ifthe system is characterized completely, the ranges are reduced to a single point.medium (Burgard et al., 2001; Koonin, 2000). The impor-tance of the nutrient constraints imposed by the externalenvironment also underscores the importance of definedmedia in mathematical simulation of cell behavior. WithoutFigure 3.Perspectives generated using the constraint-based approach.The phenotypic potential (set of all behaviors that can be exhibited by abiological system) can be represented as a solution space (shown as anellipse for simplicity). The identification of constraints that the cell mustobey, such as conservation of mass and energy, survivable temperatureranges, etc., further constrain this space (e.g., solutions that violateconservation laws are excluded from the space). Depending on the objectiveof the cell, it may exhibit a variety of behaviors. Although the cell isconstrained by its solution space at one point in time, it is also able to controlits behavior over time via processes such as evolution and regulation.Escherichia coli:image courtesy of www.denniskunkel.comadequate knowledge of the nutritional content of the exter-nal environment, significant constraints must be ignored orgrossly approximated, resulting in incorrect or misleadingpredictions of cell behavior. The development of high-throughput phenotyping technologies has addressed theinadequacies of studies on undefined media, enabling char-acterization of the environmental effects on organism growthunder thousands of well-defined conditions (Bochner et al.,2001). Physical characteristics of the external environment,such as temperature, pressure, pH, and exposure to light orwater, can also limit possible cell behavior and survival.Physical environmental constraints have been used to inves-tigate the possibility of life on Mars (Cockell et al., 2000).The environmental conditions experienced by a cell gen-erally change over time. They may change by the presenceof new harmful products (such as the cell’s own waste),depletion of nutrients (by the cell itself or by competitors), orother dynamic forces. A tightly packed cellular communitynecessitates competition for, or exchange of, nutrients andadhesion sites, evolving mechanisms to survive toxin expo-sure or to move toward scarce nutrients, but also raises thepossibility of obtaining new cellular capabilities via genetransfer, or of cooperation and specialization, such as in atissue, where signaling molecules allow cells to communi-cate and cooperate (DeLisa et al., 2001). To account for suchinteractions in a model, the cellular community must there-fore be accurately represented (Tsuchiya et al., 1966). Forcessuch as fluid flow (wind on a plant leaf, juices through theintestines) necessitate that cells adhere to their chosen envi-ronments or develop systems that are resilient to changingenvironments (sporulation, broad substrate utilization). Thecell is therefore constrained to the development of biologicalfunctions that allow it to thrive in a dynamic environment.The intracellular environment of a cell also imposes con-straints on cellular behavior, notably in terms of its internalcomponents and the physical properties of its interior. Cellsare obviously limited by the biochemical components ofCOVERT ET AL.: CONSTRAINT-BASED MODELING765Table I.Some biological constraints with important modeling consequences. The constraints listed at the left may seem intuitive, but the consideration ofsuch constraints in modeling biological systems can be vital in terms of correct prediction and simulation.which they are comprised; the glycolytic genes must notonly be located in the genome but also must be expressed asfunctional proteins for glycolysis to occur in an organism.The components may be thought of as a ‘‘toolbox’’ that thecell requires to use the resources found in the environmentto perform necessary functions (growth, signaling, chemo-taxis, etc.). This toolbox constantly changes over time,either enabling or limiting the function of the cell. Forexample, the maximum transport rate of a particular cellmoiety will be determined in part by the number of transportproteins specific to that moiety located in the cellmembrane. The total number of components that can becontained in the cell are limited by a generalized boundingconstraint, cell volume (i.e., the toolbox is also quite small).The last several decades of biological research has focusedon identifying cellular components, culminating in the dev-elopment of high-throughput methods to study the genome(Gaasterland and Oprea, 2001), transcriptome (Devauxet al., 2001), proteome (Naaby-Hansen et al., 2001), andmetabolome (Raamsdonk et al., 2001) of organisms undervarious conditions. Because cell function depends on theaction and interaction of various components, the ‘‘omics’’data are of fundamental importance in the effort to modelcell behavior.Physical factors of the cellular interior also imposeconstraints on the cell. Pictorial models of the interior ofE. colidepict a crowded, tightly packed, nonhomogeneouscytoplasm (Ellis, 2001; Goodsell, 1993). Such a denseenvironment has a constraining effect on solute and macro-molecular diffusion. One way in which cells may overcomediffusion-related constraints in a crowded environment isvia compartmentalization of major cell processes andmetabolic channeling (Verkman, 2002). Furthermore, thecrowded internal environment of the cell creates an osmoticpressure in relation to the often aqueous external environ-ment that must be balanced. Cells achieve this balance byexchanging molecules with the external environment. Thebalance of osmotic pressure must be achieved whilemaintaining an electroneutral environment on both sidesof the membrane. Osmotic and electroneutrality constraintscan affect the total volume of the cell, and the need to meetthese constraints imposes significant energy demands onthe cell.PHYSICOCHEMICAL CONSTRAINTSPhysicochemical laws place demanding constraints on cel-lular behavior (see examples in Appendix). Cells balance766BIOTECHNOLOGY AND BIOENGINEERING, VOL. 84, NO. 7, DECEMBER 30, 2003mass and energy, conform to the laws of thermodynamicsand kinetics, and operate under limited enzyme turnoverrates and activity of gene products. Physicochemical con-straints are generally considered to be ‘‘hard’’ constraintsand are thought to remain unchanged.Mass and energy are never created or destroyed in thecell. Elements entering the cell are either incorporated intobiosynthetic material for cell growth and replication,utilized to generate energy required for cellular functions,or secreted into the extracellular environment. Excessbiochemical byproducts that remain internal to the cellmay accumulate over time and result in cellular toxicity anddeath. Complex systems have evolved to sense and respondto imbalances of mass within the cell. Energy imbalancealso has detrimental consequences. Eukaryotic loss ofmitochondrial function to generate energy prohibits the cellfrom driving cellular functions and causes death (Scheffler,1999). The balance of mass and energy thus poses criticalconstraints on how the cell must allocate its resources. Massbalance of reactions also imposes stoichiometric constraintson the network. The stoichiometric coefficients of anybiochemical reaction are such that the number of elementsand charge is conserved in a conversion. Stoichiometricconstraints impose restrictions on the network that, apartfrom the nature of kinetics, define what combinations ofspecies must be present or absent in a steady state (Feinberg,1987). For example, for a set of compounds with zeroconcentrations, it is possible to determine which reactionshave zero rates (i.e., ‘‘switched off’’) and which havepositive rates (i.e., ‘‘switched on’’) (Feinberg, 1987). Therequirement of mass balance exerts such a strong constrainton metabolic network function that flux balance analysisrequires virtually only these constraints, with only a handfulof strain-specific parameters, for detailed qualitative sim-ulations (Edwards et al., 2002).The thermodynamics of internal reactions can signifi-cantly affect the overall capability and phenotypic propertiesof the cell. The direction in which reactions proceed is afunction of energetic properties of the biochemical conver-sions and may determine the ability of the cell to reachdiverse metabolic states in a variety of internal and externalconditions. Furthermore, chemical turnover of uncatalyzedreactions is often very slow. In the presence of enzymes,however, substrates are quickly converted into products.Enzymes also provide means for fast-responding controlmechanisms. Feedback and feedforward control mecha-nisms, including inhibition and activation, and effect of pHand temperature on enzyme activity can influence the rate ofbiochemical reactions, either linearly or nonlinearly (Bailey,1998; Desai et al., 1999; Lee et al., 1999; Savageau, 1998).Kinetic constraints are especially important in cells withlittle or no other means of regulation. Upon maturation, thered blood cell loses its DNA and, consequently, lacks anymeans of transcriptional regulation. The sole form of regu-lation in the red cell is thus kinetic regulation, which makesthe red cell a suitable model for studying kinetics (Jamshidiet al., 2001).The maximum throughput or enzyme capacity of bio-chemical reactions can also force the cell to exhibit morelimited behaviors than otherwise. The enzyme turnover rateof reactions in biochemical pathways can impose ‘‘bottle-neck’’ constraints on the maximum allowable flow achievedin a pathway (Bailey, 2001). Such bottlenecks have beenidentified and analyzed using metabolic flux analysis andmetabolic control analysis (Stephanopoulos et al., 1998).Metabolic engineering of microbial organisms has centeredaround the premise of removing such bottleneck constraintsand achieving a higher production rate of desirable com-pounds. Such efforts have been successful in a number ofcases (Stephanopoulos et al., 1998).The balance of osmotic pressure and maintenance ofelectroneutrality also impose constraints on cells. For exam-ple, the constraints of osmotic pressure and charged mole-cule requirements (e.g., nutrients) were found to be drivingforces in evolution of cell walls in bacteria (Koch, 2000).Although cell volume regulation is relatively well charac-terized (Hallows and Knauf, 1994), it is routinely ignored bymost models. The consequences of such constraints havebeen studied in detail in the human red blood cell, becausesuch cells are relatively simple, lacking chromosomes, andare therefore not capable of replication (Joshi and Palsson,1989; Werner and Heinrich, 1985). Initial assessment ofthe importance of these constraints using metabolic controlanalysis shows that they represent dominant regulatory ef-fects (Lee and Palsson, 1991). Clearly, much work is re-quired to ascertain the importance of these constraints andimplement them in mathematical models.SELF-IMPOSED CONSTRAINTSWe have previously discussed the environmental and phys-icochemical constraints imposed on cells, which are beyondthe cells’ direct control. To respond to these constraints andstill carry out their desired functions (e.g., growth, nitrogen/carbon dioxide fixation, development), cells must imposeconstraints upon themselves to direct their behavior, select-ing the ‘‘best’’ or most suitable option from a range of al-lowable alternatives. Self-imposed constraints are differentfrom other constraints because they respond to—and oftenchange—internal or external environments. Unlike physico-chemical constraints, they are time-dependent. Such adap-tive constraints may entail regulation in the short term andevolution over longer time scales.Evolutionary ConstraintsAlthough cells are constrained by the contents of their ge-nome, they are able to change their genome sequence viaevolution. The evolutionary process is associated with cer-tain constraints. For example,E. coli’soverall error rate forDNA replication is between 1 in 1010and 1 in 1011basepairs(Neidhardt et al., 1990); this error rate may change some-COVERT ET AL.: CONSTRAINT-BASED MODELING767
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