Biological role of noise encoded in a genetic network motif

Biological role of noise encoded in agenetic network motifMark Kittisopikul and Gürol M. Süel1

Green Center for Systems Biology and Department of Pharmacology, University of Texas Southwestern Medical Center, Dallas, TX 75390

Edited* by José N. Onuchic, University of California at San Diego, La Jolla, CA, and approved June 4, 2010 (received for review March 25, 2010)

Genetic circuits that regulate distinct cellular processes can differ intheir wiring pattern of interactions (architecture) and susceptibilityto stochastic fluctuations (noise). Whether the link between circuitarchitecture and noise is of biological importance remains, how-ever, poorly understood. To investigate this problem, we per-formed a computational study of gene expression noise for allpossible circuit architectures of feed-forward loop (FFL) motifs. Re-sults revealed that FFL architectures fall into two categories de-pending on whether their ON (stimulated) or OFF (unstimulated)steady states exhibit noise. To explore the biological importanceof this difference in noise behavior, we analyzed 858 documentedFFLs in Escherichia coli that were divided into 39 functional cate-gories. The majority of FFLs were found to regulate two subsetsof functional categories. Interestingly, these two functional cate-gories associated with FFLs of opposite noise behaviors. This oppo-site noise preference revealed two noise-based strategies to copewith environmental constraints where cellular responses are eitherinitiated or terminated stochastically to allow probabilistic sam-pling of alternative states. FFLs may thus be selected for theirarchitecture-dependent noise behavior, revealing a biological rolefor noise that is encoded in gene circuit architectures.

gene expression bursts ∣ stochastic simulation ∣ design principles ∣demand theory ∣ shot noise

Cellular processes are typically regulated by genetic circuitswith particular architectures of interactions among genes and

proteins. However, it is not well understood whether different ar-chitectures of genetic circuits generate distinct properties thatcan be subject to selective pressures. For example, selection ofcircuit architectures can be driven by the requirement to generatebiologically important dynamic behaviors such as oscillations (1).However, other selective pressures must also exist becausenatural genetic oscillators, such as circadian clocks and cell cyclecircuits, can differ in architecture (2–6). Furthermore, a recentstudy in Bacillus subtilis showed that the dynamics of a naturalcellular differentiation circuit could be reconstituted by a syn-thetic circuit with an alternative architecture but with differencesin variability (noise) and physiology (7). These and other studiessuggest that gene circuit architectures can encode distinct proper-ties such as susceptibility to noise that could be critical to the phy-siological process that they implement (3, 8–13). Systematiccomparisons of alternative architectures could therefore revealdifferent properties supported by distinct topologies and helpuncover the biological importance of gene circuit architecture.

Feed-forward loops (FFLs) constitute an ideal gene circuitmotif for studying the relationship between circuit architectureand biological function because of their simple architectureand well characterized functional roles in organisms such as Es-cherichia coli (2) and Saccharomyces cerevisia (14). In a FFL cir-cuit, a transcription factor A regulates a second transcriptionfactor B and both can regulate expression of the output geneC (Fig. 1 A and E). Therefore, expression of the FFL output geneC represents the integration of the activities of A and B transcrip-tion factors. There are a total of eight possible FFL architecturesbecause the regulatory links among A, B, and C can either bepositive (activation) or negative (repression). Examples of all

possible FFL architectures have been identified and shown toregulate a multitude of cellular processes in a diverse range oforganisms ranging from bacteria to human cells (15, 16). Thelarge body of knowledge on FFLs makes this motif an appropriatemodel system to study the link between circuit architecture andbiological function (4).

Continuous simulations based on ordinary differential equa-tions have suggested that distinct FFL architectures can differin their dynamics. In particular, differences have been observedbetween two types of architectures classified as coherent andincoherent FFLs based on whether the net sign of direct and in-direct (through B) regulatory links from A to C are the same or

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Fig. 1. Stochastic simulations reveal two noise behaviors in incoherentFFLs. A–D and E–H pertain to the FFL circuits 011 (A) and 101 (E), respectively.The logic of integration for the regulation of the output node C is a BooleanAND gate. B, C, F, and G show time traces of C molecule numbers expressedfrom the C output promoter as obtained from stochastic simulations basedon the Gillespie algorithm (SI Appendix Section 4.1.1) (30). B and F show datafor C expression obtained in the OFF steady state (unstimulated state of A).C and G depict data for the ON steady state (stimulated state of A). D and Hshow the mean durations of high gene expression bursts of C obtainedfrom simulations and precisely defined by the time (seconds) the C promoterremains in the high expression state as determined by the binding state oftranscription factors A and B.

Author contributions: M.K. and G.M.S. designed research; M.K. performed research; M.K.and G.M.S. analyzed data; and M.K. and G.M.S. wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.

See Commentary on page 13197.1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1003975107/-/DCSupplemental.

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opposite, respectively (2). For example, it has been shown thatcoherent FFL architectures can serve as delay elements wherethe expression of the output gene C is delayed with respect tothe activation of the input transcription factor A (2). Comparedto coherent FFLs, incoherent circuits in turn have been shown tohave an accelerated output response to input, where the maxi-mum expression of the output gene C is lower and thus reachedsooner upon activation of A (17). Therefore, continuous simula-tions have revealed that differences in the architectures and logicsof FFLs can give rise to divergent dynamics.

While continuous simulations can predict gene circuit dy-namics, they do not account for the stochastic behavior that isinherent to the biochemical reactions comprising FFLs. Stochas-tic fluctuations can alter the dynamics of genetic circuits and eveninduce qualitatively distinct behaviors (6, 18–20). For example,probabilistic interactions among small numbers of molecules cangenerate stochastic bursts of gene expression. Single-cell andsingle-molecule measurements have characterized these burstsand implicated transcription and translation processes as possiblesources (21–23). Perhaps more importantly, recent studies haveshown that gene expression bursts can serve a biological function(13, 24, 25). Stochastic fluctuations have also been shown todepend on the architecture of genetic circuits (7, 26, 27). Addi-tionally, recent studies have begun to show that distinct FFL ar-chitectures can differ in behavior at the stochastic regime (28).For example, it has been suggested that coherent FFLs amplifycircuit-extrinsic noise at the C output, while incoherent FFLsattenuate such noise (27). Furthermore, an analytical study hasshown that the most abundant coherent FFL exhibits the lowestnoise amplitudes of all FFL architectures (28). In contrast, themost abundant incoherent FFL architecture exhibits the highestnoise amplitudes (28). It is however unclear if all possible FFLarchitectures differ in stochastic behavior and, more importantly,if differences in noise behavior are of biological importance.

To systematically investigate the relationship between FFL ar-chitecture, noise, and function, we performed discrete stochasticsimulations for all possible three-component circuit architecturesand three logic gates (AND, OR, and XOR). We found that allFFL circuit architectures could be classified into two categoriesaccording to how susceptible their ON and OFF steady stateswere to noise, independent of their logic gates. This noise beha-vior of FFL architectures is coupled to circuit function. In parti-cular, these data show that FFLs with high noise in their OFFstate preferentially regulate rare stochastic processes in E. colisuch as the generation of antibiotic-resistant persister cells (29).In contrast, cellular processes that are typically in high demand,such as anaerobic respiration, are found to be regulated byFFLs with high noise in their ON state. While FFLs with highernoise in their OFF state can stochastically initiate rare cellularresponses, FFLs with higher noise in their ON state can stochas-tically terminate cellular processes that are in high demand.These results suggest that specific FFL architectures may beselected based on their distinct noise behaviors to allow samplingof alternative cellular states and cope with environmentalconstraints.

ResultsTwo Incoherent FFLs Differ in Their Susceptibility to Gene ExpressionBursts. We began by investigating a pair of FFL circuits with si-milar architecture (Fig. 1 A and E). In both circuits, the inputnode A transcriptionally activates output node C directly and alsorepresses C indirectly through node B. Because the direct andindirect regulatory pathways have opposite signs (direct activat-ing and indirect repressing), both circuits are traditionally classi-fied as incoherent FFLs (2). The difference in architecturebetween these circuits is the opposite order of sequential activa-tion and repression reactions comprising their indirect pathways.We refer to circuits with such alternative architectures as “isocir-

cuits.” For easier comparison, we adopt here a three-digit binarynomenclature that classifies FFL circuits based on the signs ofinteractions among A–B, B–C, and A–C nodes, respectively,where 1 ¼ activating and 0 ¼ repressing (Fig. 1A and E). Despitesimilarities between the isocircuits, circuit 101 occurs more fre-quently in E. coli than its isocircuit partner 011 (165 versus 53circuits, respectively). Therefore, a systematic comparison ofisocircuits could reveal the biological importance of the architec-tural difference between them.

To investigate the differences between these isocircuits, weconstructed discrete stochastic models and simulated them usingthe Gillespie algorithm (30, 31). Simulations described produc-tion and degradation of proteins of A, B, and C species as discretereactions and also accounted explicitly for the stochastic behaviorof binding and unbinding events of A and B transcription factorsto the C promoter. For simplicity, we first considered here anAND logic for the regulatory input of A and B into the C pro-moter. Using these simulations, we studied the behavior of theincoherent FFL isocircuits 011 and 101. The dynamics of the iso-circuits during transitions between ON and OFF steady states (asdefined by whether input A was absent or present, respectively)are consistent with previous literature and ordinary differentialequation based simulations (2, 14, 16, 17). However, when thecircuits remained at OFF (Fig. 1 B and F) or ON (Fig. 1 Cand G) steady states, stochastic simulations revealed that bothcircuits were subject to stochastic bursts in C promoter expression(Fig. 1 B, C, F, and G). These bursts are particularly prominentwith slow binding kinetics of transcription factors to C promoter,but also occur with fast binding kinetics (see SI AppendixSection 4.5). Simulations allowed us to determine the amountof time each circuit resides stochastically in the C promoterstate(s) that gives rise to high expression bursts. Therefore, wedefine here burst noise as the amount of time spent in the highexpression state, which in turn determines the duration and am-plitude of the observed C promoter expression bursts. We notethat multiple binding or unbinding events of A and B to the Cpromoter can lead to the high expression state from severalequivalent low expression states. Therefore, C promoter expres-sion bursts do not necessarily correspond to a single binding/un-binding event, but rather transitions between different expressionlevels. Even though each isocircuit displayed gene expressionbursts, circuit 011 displayed burst noise in both the ON and OFFstates, whereas circuit 101 exhibited higher noise, but only in theOFF state (Fig. 1 D and H).

What causes differences in C promoter expression burstsbetween the isocircuit steady states? In both circuits, bursts aregenerated by transient access to a high expression state of the Cpromoter due to stochastic binding and unbinding events ofA andB transcription factors to the C promoter (SI Appendix Fig. S1).However, the amount of time spent in the high expression state ofthe C promoter is dictated by circuit architecture and is thus dis-tinct between the two circuits. For example, in circuit 011, exitfrom the high expression state occurs by unbinding of either Aor B. However, in circuit 101, exit from the high expression stateoccurs either by unbinding of A or binding of B. Binding reactionsdependent on the concentration of the transcription factor andthus their rates can differ in ON and OFF steady states. Unbind-ing reactions, on the other hand, are concentration independent.Therefore, differences in circuit architectures give rise to differ-ences in noise behavior that can be defined by the mean durationsof C promoter expression bursts in the ON and OFF steady statesas described above (Fig. 1 D and H). Global parameter sensitivityanalysis showed that these differences in noise behavior betweenisocircuits are consistently observed for a broad range of para-meter values (2-fold change) as long as high concentrations ofA and B transcription factors can effectively repress C promoterexpression (SI Appendix Figs. S13–S16).

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All Possible FFL Architectures Fall into Two Distinct Categories of NoiseBehavior.Do architecture-dependent differences in noise profilesobserved among isocircuit members 101 and 011 generally holdfor all possible FFL architectures and even different logic inputsinto the C promoter? To address this question we systematicallyperformed discrete stochastic simulations for all eight FFL archi-tectures and three binary input logics (AND, OR, and XOR) for atotal of 24 systems (SI Appendix Section 4.1). Together, these si-mulations showed that the difference in noise profiles, taken asthe proportion of mean burst duration in the ON state, observedbetween isocircuits 101 and 011 exists for all isocircuit pairs(Fig. 2). The percent noise of C promoter gene expression in theON state appears to depend on circuit architecture, but surpris-ingly does not correlate with logic gates (Fig. 2). Regardless of lo-gics, each isocircuit pair contains one circuit that has higher noisein its OFF steady state and one that does not. Together, these datasuggest that architecture, but not logics at theC promoter, dictatesthe steady state noise profile of the output node C of FFLs.

The steady state noise behavior of FFLs was observed to cor-relate with whether node A activates or represses node B. Spe-cifically, simulations of all possible FFL circuits showed thatwhen B is activated by A, noise in the OFF state is higher (Fig. 2).In contrast, for FFL circuits where B is repressed noise is similarin both the ON and OFF states. These results reveal a simpleprinciple in steady state noise behavior of isocircuits and FFLsin general. When node A activates node B, the concentrationsof A and B are correlated. Therefore, when the circuit is inthe OFF steady state, both A and B are at low molecule numbersand thus subject to stochastic fluctuations. High noise in A and Bin the OFF state in turn gives rise to higher noise in C promoterexpression (Fig. 1F). Concurrently, when the circuit is in the ONstate, A and B are at high concentrations and thus both are lessnoisy (Fig. 1G). Therefore, in these circuits the OFF state will benoisy and the ON state will be quiet. However, in circuits wherenode A represses B, the concentrations of A and B vary oppo-sitely. This inverse correlation in concentrations gives rise toan inverse correlation in noise of A and B. As a result, whenthe circuit is either in the ON or OFF state, only one of thetwo regulatory inputs into the C promoter is noisy. This inversecorrelation distributes the noise across the ON and OFF statessuch that both states exhibit noise (Fig. 1 B and C). Therefore,the mode of regulation of node B by A and not logics of C pro-

moter regulation appears to dictate noise behavior at steady state,emphasizing the importance of FFL architecture.

Functional Profiles Discriminate Among FFL Architectures with Oppo-site Noise Behaviors. To determine if the distinct noise profiles ofFFL isocircuits are of biological importance, we analyzed the wellcharacterized and extensive dataset of E. coli FFLs associatedwith various functional categories. This functional dataset is com-prised of 858 examples of FFLs grouped into 39 functional cate-gories, obtained from the publicly available E. coli databasesEcoCyc (32) and RegulonDB (33) (SI Appendix Section 2.2). Thisdataset contains examples of functional categories such as DNAsynthesis that are regulated by all FFL architectures, as well asexamples such as biotin synthesis where only a specific FFLarchitecture (000) is assigned to it. Another difference among dis-tinct FFL architectures and isocircuit members is that they vary inabundance (SI Appendix Fig. S18). For example, whereas circuit101 is more common (n ¼ 164) and regulates a larger number offunctional categories (n ¼ 25), its isocircuit counterpart 011 isless abundant (n ¼ 53) and regulates fewer distinct functionalcategories (n ¼ 15) (Fig. 3). Therefore, each FFL architecturehas a unique functional profile based on the number and cate-gories of cellular functions assigned to it. Differences in thesefunctional profiles suggest a relationship between FFL architec-tures and their biological functions.

Next we asked if the differences in functional profiles of FFLarchitectures are related to the differences in their steady statenoise behavior. Specifically, we clustered all eight FFLs by func-tional categories (rows) and circuit architectures (columns) to de-termine which FFL architectures have similar functional profiles(Fig. 3). Hierarchical clustering segregated FFL architecturesinto two groups with four circuits each (p < 0.001 by PearsonG test of independence) using complete linkage and a Euclideanmetric. Interestingly, FFLs within the same group exhibited simi-lar noise behavior in stochastic simulations (Fig. 3). In particular,FFLs with higher noise in the OFF state were grouped into onecluster and circuits with noise in their ON state formed the other.Therefore, clustering of functional profiles discriminated FFLsaccording to their architectures, since FFLs where node A acti-vates B generate higher noise in the OFF state compared to thosewhere A represses B (Fig. 2). These results suggest that the func-tional profiles of FFLs contain information about the architec-ture-dependent noise behavior of these circuits at steady state.

Clustering of the functional dataset did not discriminatecircuits according to the coherent/incoherent classification. To in-vestigate this issue further, we tested the robustness of clusteringby analyzing how random perturbations to FFL functional pro-files affect clustering (Fig. 4A). Specifically, we repeatedly elimi-nated random subsets of functional categories and measuredaverage clustering distances (linkage) among FFLs with oppositenoise behavior and compared them to average distances amongcircuits with similar noise behavior (Fig. 4A). A ratio greater than1 was obtained 81% of the time, which indicated that distancesamong FFLs with similar noise profiles were consistently closer.Clustering of FFL circuits according to noise appears to be robustto random elimination of functional categories (Fig. 4A). Func-tional profiles systematically failed to cluster coherent/incoherentFFLs, as only 35% of iterations gave a ratio greater than 1(Fig. 4A). These data show that functional profiles reliablysegregate FFLs according to architecture-dependent noise, sug-gesting that this property is of biological importance.

Demands on Biological Processes Correlate with FFL Noise Behaviors.Cluster analysis more specifically revealed three groups of func-tional categories that diverged in their preference for FFL archi-tectures with distinct noise profiles (p < 0.001) (Figs. 3 and 4B):Group1wasenriched forFFLarchitectureswithhighnoise in theirON states. Group 2 did not display a preference based on noise

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Fig. 2. FFL architecture determines noise behavior. Shown are results fromdiscrete stochastic simulations for all possible FFL circuit architectures andthree Boolean logic gates (AND, OR, and XOR) for the regulation of the C out-put promoter. Each FFL is labeled according the three-digit binary nomencla-ture described in the main text as well as the standard classification. FFLarchitectures are paired as isocircuits and grouped according to the standardcoherent and incoherent FFL classification (2). Rectangles above each FFLcircuit depict the proportion (%) of mean noise in the ON state divided bythe total noise in the ON plus OFF states color coded according to the scaleon the right. The amount of noise in ON and OFF states corresponds to dura-tions of C promoter expression bursts as defined in Fig. 1. The noise patterncorrelates withwhether nodeB is activated or repressed by nodeA. Activationof B byA is associated with higher noise in the OFF state (left member of eachpair), whereas repression of B by A is associated with higher noise in the ONversus OFF state (right member of each pair).

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behavior. Finally, group 3 preferred FFL architectures that gener-ate higher noise in their OFF state. Even though groups 1 and 3combined constitute only 18% of all functional categories, theyare associated with 70% of the categorized FFLs. Therefore, wefind that the number of FFLs is not evenly distributed across func-

tional categories. Together, these results show that most of theFFLs identified in E. coli are involved in the regulation of a fewfunctional categories that in turn appear to select for circuits basedon their architecture-dependent noise properties.

What accounts for the enrichment of FFL architectures withspecific noise profiles in functional groups 1 and 3? Many FFLsassociated with these functional groups contain an interactingpair of global and functionally specific transcription factors, con-sistent with the hierarchical organization of gene regulatorycircuits (4). Specifically, many FFLs in group 1 contain the globalregulator fnr (fumarate nitrate reductase) as their A node and amore specific transcription factor narL (nitrate reductase) astheir B node, that together regulate E. coli metabolism underanaerobic conditions (34, 35). An example of such a FFL circuitis shown in Fig. 4C, where fnr regulator is active in the absence ofoxygen and represses narL, and these transcription factorsregulate dcuB, the C4-dicarboxylate transporter necessary foranaerobic growth. Discrete stochastic simulations predict thatthe repression of narL (node B) by fnr (node A) gives rise toa noisy ON state expression of dcuB (node C) (Fig. 4C). Noisein the ON state can result in the stochastic termination of dcuBexpression during anaerobic growth (Fig. 4C). This propensity forstochastic termination could permit occasional sampling of aero-bic respiration that could be beneficial if environmental condi-tions unexpectedly change. Additionally, the noisy ON state ofFFLs associated with group 1 could provide a mechanism tomodulate the expression level of downstream targets of fnrand narL possibly through frequency modulation of stochasticbursts (36). Therefore, enrichment of FFL architectures that giverise to noisy ON states may be a result of functional requirements

Fig. 3. Functional profiles segregate FFLs according to architecture-dependent noise behavior. Matrix representation of the abundance (log color scale) ofeach FFL architecture for a given functional category in E. coli arranged according to two-dimensional hierarchical cluster analysis. Columns represent distinctFFL architectures, whereas functional categories are shown in rows. The dataset is comprised of a collection of 858 FFLs identified in E. coli and categorized into39 distinct classes of biological functions according to the publicly available E. coli databases EcoCyc and RegulonDB. Dendrograms obtained from clusteringwere color coded to emphasize distinct clusters of FFL architectures (red and green) and three distinct groups of functional categories, orange (group 1), gray(group 2), andmagenta (group 3). The FFL architecture clusters correspond to the predicted noise profiles shown in Fig. 2 and are accordingly colored green andred. For easier comparison, the noise results shown in Fig. 2 are depicted underneath respective circuit architectures.

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Fig. 4. Robust clustering of FFL functional profiles reveals two noise-basedcellular strategies. (A) Barchart of the percent of bootstrap samples (total ¼100;000) that cluster according to noise (blue) or the traditional coherent/incoherent classification (gray) (SI Appendix Section 2.2.7). (B) Reducedmatrix representation of the cluster analysis result and color coding depictedin Fig. 3. (A). Shown are themean abundances of the two clusters of FFL circuitarchitectures and the three clusters of functional categories indicated in Fig. 3.Functional group 1 (orange) is comprised of categories associated with anae-robic metabolism and contains 30% (259∕858) of FFLs. Functional group 2(gray) contains, among others, housekeeping genes and the most numberoffunctional categories (32∕39),butcontainsonly54%(467∕858)ofFFLs. Func-tional group 3 (magenta) contains 5∕39 functional categories and 62%(477∕858) of FFLs that are in general related to stress responses. (C) Represen-tative time traces from simulations depicting predicted stochastic terminationand initiation expression patterns of genes dcuB (Top) and glpT (Bottom),respectively, according to the FFL architecture shown (Right).

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associated with anaerobic respiration processes that make upfunctional group 1.

Most FFLs in group 3 are associated with known stochasticprocesses in E. coli that respond to stress and give rise to hetero-geneity. Although group 1 and group 3 both exhibit a preferencefor FFL architectures based on noise, they do so in an oppositemanner. In particular, the functional categories comprisinggroup 3 are enriched for FFL architectures where node A acti-vates node B and thus gives rise to high noise in the OFF stateof node C. Concurrently, group 3 FFLs share a pattern where aglobal regulator such as IHF (integrative host factor) positivelyregulates a more functionally specific transcription factor such asfis (factor for inversion stimulation). Together, IHF (node A) andfis (node B) regulate genes such as glpT (glycerol-3-phosphatetransporter) (nodeC) that have been implicated in the generationof resistance to antibiotics such as fosfomycin (Fig. 4C) (37). IHFhas also been identified in a screen for genes involved in the sto-chastic generation of antibiotic-resistant persister cells (29). InFFLs with this architecture, expression of glpT is predicted tobe noisy in the OFF state, giving rise to stochastic bursts of glpTexpression. These data reveal that group 3 is comprised ofbiological processes associated with stress responses that canbe initiated in a stochastic manner even in the absence of stressstimuli. Consistent with this finding, the architecture of FFLsenriched in group 3 exhibit higher noise in their OFF state thatcan facilitate stochastic activation and thus sampling of alterna-tive stress responses at the single-cell level. Such probabilisticbehavior at the single-cell level has been shown to be a beneficialstrategy under unpredictable environmental conditions and maythus explain the preference of group 3 functions for FFLs withhigh noise in the OFF state (7, 13, 38–40).

Functional categories comprising group 2 exhibit a lack of pre-ference for FFLs architectures according to noise. Even thoughgroup 2 contains 82% of functional categories, only 54% of FFLsare associated with this group. FFLs within group 2 may of coursehave been selected for based on properties other than noise.However, the low number of FFLs contained within group 2suggests that noise behavior is at least one of the importantproperties underlying FFL function. If noise behavior is not cri-tical for the operation of biological processes contained withingroup 2, perhaps FFLs are a less preferred circuit motif. Inter-estingly, the functional categories comprising group 2 are amongothers, associated with housekeeping processes such as celldivision and amino acid synthesis. These basic biological pro-cesses are not known to benefit from stochastic behavior. Thethree groups of functional categories suggest that most FFLsare selected based on their noise properties by cellular processesthat may benefit from stochastic fluctuations.

DiscussionThe comprehensive analysis presented here reveals a generaltrend regarding the preference of biological processes for FFLarchitectures based on their noise profiles. However, the follow-ing points have to be considered: (i) There may be additional un-accounted regulatory inputs into FFLs other than the three nodesconsidered here, possibly altering the noise behavior. (ii) It is im-portant to note that FFLs do not exist in isolation. Genes can beshared among FFLs and there can be cross-regulation betweenindividual circuits. (iii) Robust clustering of FFLs according tonoise does not imply that other differences among FFL architec-tures cannot be of functional importance. It is therefore strikingthat functional profiles containing information on biologicallyrelevant properties robustly cluster FFLs consistent with architec-ture-dependent noise behavior. Stochastic behavior thus appearsto be at least one of the important biological properties of FFLs.

Many gene regulatory circuits contain pathways comprised ofconsecutive activation and repression reactions similar to those inFFLs. Therefore, the noise behavior of other gene regulatory

circuits may also be determined by the order of regulatory linkswith opposite actions. Specifically, noise in target gene expressionthat is governed by a net negative linear cascade of transcriptionfactors will depend on whether this regulation is mediated by therepression of an activator or the activation of a repressor. Reg-ulation will therefore either be mediated by a high concentrationof repressor, or a low and thus noisy concentration of activator.For example, the order of activation and repression reactionscomprising a net negative feedback loop of a bacterial differen-tiation circuit has been shown to dictate stochastic fluctuations incircuit dynamics (7). Therefore, in instances where gene expres-sion is regulated by a net negative cascade of transcription factorswith opposite regulatory modes, noise of gene expression maydepend on the order of activation and repression reactions.

Susceptibility to stochastic bursts of gene expression may, ofcourse, not be the only functionally relevant property of FFLsthat gives rise to clustering according to architectures. We con-sidered another possible explanation for the observed clusteringpattern known as demand theory (41, 42). Demand theory pre-dicts that depending on the organism’s native environment, genesin high demand are regulated by activators, whereas genes in lowdemand are regulated by repressors. Because functional groups 1and 3 display opposite clustering preferences where node A eitherrepresses or activates B, respectively, demand theory would pre-dict that node B is in low demand in group 1, whereas it is in highdemand in group 3. Group 1 FFLs are involved in anaerobicmetabolism and thus are expected to be in high demand in thenative environment of E. coli such as the mammalian colon. How-ever, transcriptional regulators corresponding to node B such asnarL and nikR are more often repressed than activated in group 1FFLs. FFLs in group 3, on the other hand, are involved in stressresponses and thus expected to be in low demand assuming thatE. coli is well adapted to its environment. In particular, stress re-sponse regulators that correspond to node B such as baeR, HN-S,and fis should be in low demand and thus expected to berepressed according to demand theory. However, these transcrip-tional regulators are found to be activated in group 3 FFLs.Therefore, rather than demand theory, the noise behavior ofcircuit architectures is more consistent with clustering of FFLs.

Stochastic bursts of gene expression have been demonstratedto be physiologically important for the many systems such aslambda and Lac repressors as well as the differentiation ofB. subtilis cells into the state of competence (6, 20, 25, 43–46).Consistent with these findings, FFL architectures that generatestochastic bursts of gene expression appear to be favored byE. coli stress responses such as the stochastic generation of anti-biotic-resistant persister cells (29, 47). In addition to stochasticinitiation, our results also suggest that some cellular processes,such as anaerobic metabolism of E. coli, may prefer the abilityto stochastically terminate their response. These data indicatea possible relationship between the default state of a cellular pro-cess and the noise behavior of the associated FFLs. Depending onwhether the default state of the cellular process is active (ON) orinactive (OFF), FFLs with higher noise in ON or OFF steadystates can enable sampling of alternative states by stochastic ter-mination or activation, respectively. These findings suggest a pos-sible link between the demand on a cellular process and the typeof noise generated by the associated FFL architecture. Further-more, these results suggest that particular architectures of FFLsmay have been selected for their inherent noise properties tocope with distinct environmental constraints. It may thus be pos-sible to decode functional properties and selection pressuresfrom architectures of gene regulatory circuits.

MethodsProgramming Language and Statistical Computing Environment R. Version 2.9.1of R from The R Foundation for Statistical Computing ISBN 3-90051-07-0 wasused as distributed in the Debian GNU/Linux package r-base version 2.9.1-2.R was used to run stochastic simulations and analyze data.

13304 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1003975107 Kittisopikul and Süel

Stochastic Simulation Software: GillespieSSA. Version 0.5–3 of the GillespieSSApackage for R by Mario Pineda-Krch was used for stochastic master equationsimulations (48).

Feed Forward Loop Simulations. The simulation environment was constructedin R as a wrapper around GillespieSSA. The three components of the FFLs, A,B, and C, each were modeled as genes with corresponding transcriptionalpromoters and translated protein species. The protein products for A andB then served as transcription factors for downstream genes as shown inFig. 1. Transcription and translation were modeled explicitly as a single stepwith propensity determined by the binding state of transcription factors tothe promoter as opposed to using a cis regulatory input function. Transcrip-tion factor binding was modeled with a Hill coefficient of 2.

Databases: RegulonDB and EcoCyc. Genetic transcriptional network informa-tion was downloaded from RegulonDB (33) from the Regulatory NetworkInteractions section of datasets as NetWorkSet.txt, Version 6.3, releasedon January 30, 2009. Genetic regulatory interactions were consistent withEcoCyc (32) due to data sharing between the two databases. We excludedambiguous or unknown interactions from our analysis, but did not excludemicroarray or electronically inferred interactions.

Gene Annotation. Genes in FFLs were identified using FANMOD (49). Func-tional annotation and grouping was based on that of Ma et al. (50). Furthergene classification was done with the assistance of EcoCyc. All genes involvedin a feed-forward loop were annotated, and analysis was done both by con-sidering three annotations per feed-forward loop (Fig. 3).

Cluster Analysis. With R, hierarchical clustering was applied to both func-tional categories and FFL types using a Euclidean distance metric and com-plete linkage based on the abundance of the number of FFLs. Bootstrapresampling analysis was done using the boot package available fromCRAN (51).

ACKNOWLEDGMENTS. We thank S. Altschuler, L. Avery, R. Hiesinger,R. Ranganathan, E. Ross, K. E. Süel, L. Wu, and members of the Süellaboratory for critical manuscript reading. M.K. is supported by Mol.Biophysics Training Grant GM T32008297, NIH-NIGMS MSTP Grant 5 T3208014, and the Perot Foundation. This research was supported by grantsNIH NIGMS RO1 GM088428, Welch Foundation (I-1674) and JamesS. McDonnell Foundation (220020141). G.M.S. is a W. W. Caruth, Jr. Scholarof Biomedical Research.

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