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Proc Natl Acad Sci U S A. Jul 27, 2010; 107(30): 13300–13305.
Published online Jun 28, 2010. doi:  10.1073/pnas.1003975107
PMCID: PMC2922135
From the Cover
Biophysics and Computational Biology

Biological role of noise encoded in a genetic network motif

Abstract

Genetic circuits that regulate distinct cellular processes can differ in their wiring pattern of interactions (architecture) and susceptibility to stochastic fluctuations (noise). Whether the link between circuit architecture and noise is of biological importance remains, however, poorly understood. To investigate this problem, we performed a computational study of gene expression noise for all possible circuit architectures of feed-forward loop (FFL) motifs. Results revealed that FFL architectures fall into two categories depending on whether their ON (stimulated) or OFF (unstimulated) steady states exhibit noise. To explore the biological importance of this difference in noise behavior, we analyzed 858 documented FFLs in Escherichia coli that were divided into 39 functional categories. The majority of FFLs were found to regulate two subsets of functional categories. Interestingly, these two functional categories associated with FFLs of opposite noise behaviors. This opposite noise preference revealed two noise-based strategies to cope with environmental constraints where cellular responses are either initiated or terminated stochastically to allow probabilistic sampling of alternative states. FFLs may thus be selected for their architecture-dependent noise behavior, revealing a biological role for noise that is encoded in gene circuit architectures.

Keywords: gene expression bursts, stochastic simulation, design principles, demand theory, shot noise

Cellular processes are typically regulated by genetic circuits with particular architectures of interactions among genes and proteins. However, it is not well understood whether different architectures of genetic circuits generate distinct properties that can be subject to selective pressures. For example, selection of circuit architectures can be driven by the requirement to generate biologically important dynamic behaviors such as oscillations (1). However, other selective pressures must also exist because natural genetic oscillators, such as circadian clocks and cell cycle circuits, can differ in architecture (26). Furthermore, a recent study in Bacillus subtilis showed that the dynamics of a natural cellular differentiation circuit could be reconstituted by a synthetic circuit with an alternative architecture but with differences in variability (noise) and physiology (7). These and other studies suggest that gene circuit architectures can encode distinct properties such as susceptibility to noise that could be critical to the physiological process that they implement (3, 813). Systematic comparisons of alternative architectures could therefore reveal different properties supported by distinct topologies and help uncover the biological importance of gene circuit architecture.

Feed-forward loops (FFLs) constitute an ideal gene circuit motif for studying the relationship between circuit architecture and biological function because of their simple architecture and well characterized functional roles in organisms such as Escherichia coli (2) and Saccharomyces cerevisia (14). In a FFL circuit, a transcription factor A regulates a second transcription factor B and both can regulate expression of the output gene C (Fig. 1 A and E). Therefore, expression of the FFL output gene C represents the integration of the activities of A and B transcription factors. There are a total of eight possible FFL architectures because the regulatory links among A, B, and C can either be positive (activation) or negative (repression). Examples of all possible FFL architectures have been identified and shown to regulate a multitude of cellular processes in a diverse range of organisms ranging from bacteria to human cells (15, 16). The large body of knowledge on FFLs makes this motif an appropriate model system to study the link between circuit architecture and biological function (4).

Fig. 1.
Stochastic simulations reveal two noise behaviors in incoherent FFLs. AD and EH 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 Boolean AND gate. B ...

Continuous simulations based on ordinary differential equations have suggested that distinct FFL architectures can differ in their dynamics. In particular, differences have been observed between two types of architectures classified as coherent and incoherent FFLs based on whether the net sign of direct and indirect (through B) regulatory links from A to C are the same or opposite, respectively (2). For example, it has been shown that coherent FFL architectures can serve as delay elements where the expression of the output gene C is delayed with respect to the activation of the input transcription factor A (2). Compared to coherent FFLs, incoherent circuits in turn have been shown to have an accelerated output response to input, where the maximum expression of the output gene C is lower and thus reached sooner upon activation of A (17). Therefore, continuous simulations have revealed that differences in the architectures and logics of FFLs can give rise to divergent dynamics.

While continuous simulations can predict gene circuit dynamics, they do not account for the stochastic behavior that is inherent to the biochemical reactions comprising FFLs. Stochastic fluctuations can alter the dynamics of genetic circuits and even induce qualitatively distinct behaviors (6, 1820). For example, probabilistic interactions among small numbers of molecules can generate stochastic bursts of gene expression. Single-cell and single-molecule measurements have characterized these bursts and implicated transcription and translation processes as possible sources (2123). Perhaps more importantly, recent studies have shown that gene expression bursts can serve a biological function (13, 24, 25). Stochastic fluctuations have also been shown to depend on the architecture of genetic circuits (7, 26, 27). Additionally, recent studies have begun to show that distinct FFL architectures can differ in behavior at the stochastic regime (28). For example, it has been suggested that coherent FFLs amplify circuit-extrinsic noise at the C output, while incoherent FFLs attenuate such noise (27). Furthermore, an analytical study has shown that the most abundant coherent FFL exhibits the lowest noise amplitudes of all FFL architectures (28). In contrast, the most abundant incoherent FFL architecture exhibits the highest noise amplitudes (28). It is however unclear if all possible FFL architectures differ in stochastic behavior and, more importantly, if differences in noise behavior are of biological importance.

To systematically investigate the relationship between FFL architecture, noise, and function, we performed discrete stochastic simulations for all possible three-component circuit architectures and three logic gates (AND, OR, and XOR). We found that all FFL circuit architectures could be classified into two categories according to how susceptible their ON and OFF steady states were to noise, independent of their logic gates. This noise behavior of FFL architectures is coupled to circuit function. In particular, these data show that FFLs with high noise in their OFF state preferentially regulate rare stochastic processes in E. coli such 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 by FFLs with high noise in their ON state. While FFLs with higher noise in their OFF state can stochastically initiate rare cellular responses, FFLs with higher noise in their ON state can stochastically terminate cellular processes that are in high demand. These results suggest that specific FFL architectures may be selected based on their distinct noise behaviors to allow sampling of alternative cellular states and cope with environmental constraints.

Results

Two Incoherent FFLs Differ in Their Susceptibility to Gene Expression Bursts.

We began by investigating a pair of FFL circuits with similar architecture (Fig. 1 A and E). In both circuits, the input node A transcriptionally activates output node C directly and also represses C indirectly through node B. Because the direct and indirect regulatory pathways have opposite signs (direct activating and indirect repressing), both circuits are traditionally classified as incoherent FFLs (2). The difference in architecture between these circuits is the opposite order of sequential activation and repression reactions comprising their indirect pathways. We refer to circuits with such alternative architectures as “isocircuits.” For easier comparison, we adopt here a three-digit binary nomenclature that classifies FFL circuits based on the signs of interactions among AB, BC, and AC nodes, respectively, where 1 = activating and 0 = repressing (Fig. 1 A and E). Despite similarities between the isocircuits, circuit 101 occurs more frequently in E. coli than its isocircuit partner 011 (165 versus 53 circuits, respectively). Therefore, a systematic comparison of isocircuits could reveal the biological importance of the architectural difference between them.

To investigate the differences between these isocircuits, we constructed discrete stochastic models and simulated them using the Gillespie algorithm (30, 31). Simulations described production and degradation of proteins of A, B, and C species as discrete reactions and also accounted explicitly for the stochastic behavior of binding and unbinding events of A and B transcription factors to the C promoter. For simplicity, we first considered here an AND logic for the regulatory input of A and B into the C promoter. Using these simulations, we studied the behavior of the incoherent FFL isocircuits 011 and 101. The dynamics of the isocircuits during transitions between ON and OFF steady states (as defined by whether input A was absent or present, respectively) are consistent with previous literature and ordinary differential equation based simulations (2, 14, 16, 17). However, when the circuits remained at OFF (Fig. 1 B and F) or ON (Fig. 1 C and G) steady states, stochastic simulations revealed that both circuits were subject to stochastic bursts in C promoter expression (Fig. 1 B, C, F, and G). These bursts are particularly prominent with slow binding kinetics of transcription factors to C promoter, but also occur with fast binding kinetics (see SI Appendix Section 4.5). Simulations allowed us to determine the amount of time each circuit resides stochastically in the C promoter state(s) that gives rise to high expression bursts. Therefore, we define here burst noise as the amount of time spent in the high expression state, which in turn determines the duration and amplitude of the observed C promoter expression bursts. We note that multiple binding or unbinding events of A and B to the C promoter can lead to the high expression state from several equivalent low expression states. Therefore, C promoter expression bursts do not necessarily correspond to a single binding/unbinding event, but rather transitions between different expression levels. Even though each isocircuit displayed gene expression bursts, circuit 011 displayed burst noise in both the ON and OFF states, whereas circuit 101 exhibited higher noise, but only in the OFF state (Fig. 1 D and H).

What causes differences in C promoter expression bursts between the isocircuit steady states? In both circuits, bursts are generated by transient access to a high expression state of the C promoter due to stochastic binding and unbinding events of A and B transcription factors to the C promoter (SI Appendix Fig. S1). However, the amount of time spent in the high expression state of the C promoter is dictated by circuit architecture and is thus distinct between the two circuits. For example, in circuit 011, exit from the high expression state occurs by unbinding of either A or B. However, in circuit 101, exit from the high expression state occurs either by unbinding of A or binding of B. Binding reactions dependent on the concentration of the transcription factor and thus their rates can differ in ON and OFF steady states. Unbinding reactions, on the other hand, are concentration independent. Therefore, differences in circuit architectures give rise to differences in noise behavior that can be defined by the mean durations of C promoter expression bursts in the ON and OFF steady states as described above (Fig. 1 D and H). Global parameter sensitivity analysis showed that these differences in noise behavior between isocircuits are consistently observed for a broad range of parameter values (2-fold change) as long as high concentrations of A and B transcription factors can effectively repress C promoter expression (SI Appendix Figs. S13–S16).

All Possible FFL Architectures Fall into Two Distinct Categories of Noise Behavior.

Do architecture-dependent differences in noise profiles observed among isocircuit members 101 and 011 generally hold for all possible FFL architectures and even different logic inputs into the C promoter? To address this question we systematically performed discrete stochastic simulations for all eight FFL architectures and three binary input logics (AND, OR, and XOR) for a total of 24 systems (SI Appendix Section 4.1). Together, these simulations showed that the difference in noise profiles, taken as the proportion of mean burst duration in the ON state, observed between isocircuits 101 and 011 exists for all isocircuit pairs (Fig. 2). The percent noise of C promoter gene expression in the ON state appears to depend on circuit architecture, but surprisingly does not correlate with logic gates (Fig. 2). Regardless of logics, each isocircuit pair contains one circuit that has higher noise in its OFF steady state and one that does not. Together, these data suggest that architecture, but not logics at the C promoter, dictates the steady state noise profile of the output node C of FFLs.

Fig. 2.
FFL architecture determines noise behavior. Shown are results from discrete stochastic simulations for all possible FFL circuit architectures and three Boolean logic gates (AND, OR, and XOR) for the regulation of the C output promoter. Each FFL is labeled ...

The steady state noise behavior of FFLs was observed to correlate with whether node A activates or represses node B. Specifically, simulations of all possible FFL circuits showed that when 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 similar in both the ON and OFF states. These results reveal a simple principle in steady state noise behavior of isocircuits and FFLs in general. When node A activates node B, the concentrations of A and B are correlated. Therefore, when the circuit is in the OFF steady state, both A and B are at low molecule numbers and thus subject to stochastic fluctuations. High noise in A and B in the OFF state in turn gives rise to higher noise in C promoter expression (Fig. 1F). Concurrently, when the circuit is in the ON state, A and B are at high concentrations and thus both are less noisy (Fig. 1G). Therefore, in these circuits the OFF state will be noisy and the ON state will be quiet. However, in circuits where node A represses B, the concentrations of A and B vary oppositely. This inverse correlation in concentrations gives rise to an inverse correlation in noise of A and B. As a result, when the circuit is either in the ON or OFF state, only one of the two regulatory inputs into the C promoter is noisy. This inverse correlation distributes the noise across the ON and OFF states such 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 promoter regulation appears to dictate noise behavior at steady state, emphasizing the importance of FFL architecture.

Functional Profiles Discriminate Among FFL Architectures with Opposite Noise Behaviors.

To determine if the distinct noise profiles of FFL isocircuits are of biological importance, we analyzed the well characterized and extensive dataset of E. coli FFLs associated with various functional categories. This functional dataset is comprised of 858 examples of FFLs grouped into 39 functional categories, obtained from the publicly available E. coli databases EcoCyc (32) and RegulonDB (33) (SI Appendix Section 2.2). This dataset contains examples of functional categories such as DNA synthesis that are regulated by all FFL architectures, as well as examples such as biotin synthesis where only a specific FFL architecture (000) is assigned to it. Another difference among distinct FFL architectures and isocircuit members is that they vary in abundance (SI Appendix Fig. S18). For example, whereas circuit 101 is more common (n = 164) and regulates a larger number of functional categories (n = 25), its isocircuit counterpart 011 is less abundant (n = 53) and regulates fewer distinct functional categories (n = 15) (Fig. 3). Therefore, each FFL architecture has a unique functional profile based on the number and categories of cellular functions assigned to it. Differences in these functional profiles suggest a relationship between FFL architectures and their biological functions.

Fig. 3.
Functional profiles segregate FFLs according to architecture-dependent noise behavior. Matrix representation of the abundance (log color scale) of each FFL architecture for a given functional category in E. coli arranged according to two-dimensional hierarchical ...

Next we asked if the differences in functional profiles of FFL architectures are related to the differences in their steady state noise behavior. Specifically, we clustered all eight FFLs by functional categories (rows) and circuit architectures (columns) to determine which FFL architectures have similar functional profiles (Fig. 3). Hierarchical clustering segregated FFL architectures into two groups with four circuits each (p < 0.001 by Pearson G test of independence) using complete linkage and a Euclidean metric. Interestingly, FFLs within the same group exhibited similar noise behavior in stochastic simulations (Fig. 3). In particular, FFLs with higher noise in the OFF state were grouped into one cluster and circuits with noise in their ON state formed the other. Therefore, clustering of functional profiles discriminated FFLs according to their architectures, since FFLs where node A activates B generate higher noise in the OFF state compared to those where A represses B (Fig. 2). These results suggest that the functional profiles of FFLs contain information about the architecture-dependent noise behavior of these circuits at steady state.

Clustering of the functional dataset did not discriminate circuits according to the coherent/incoherent classification. To investigate this issue further, we tested the robustness of clustering by analyzing how random perturbations to FFL functional profiles affect clustering (Fig. 4A). Specifically, we repeatedly eliminated random subsets of functional categories and measured average clustering distances (linkage) among FFLs with opposite noise behavior and compared them to average distances among circuits with similar noise behavior (Fig. 4A). A ratio greater than 1 was obtained 81% of the time, which indicated that distances among FFLs with similar noise profiles were consistently closer. Clustering of FFL circuits according to noise appears to be robust to random elimination of functional categories (Fig. 4A). Functional profiles systematically failed to cluster coherent/incoherent FFLs, as only 35% of iterations gave a ratio greater than 1 (Fig. 4A). These data show that functional profiles reliably segregate FFLs according to architecture-dependent noise, suggesting that this property is of biological importance.

Fig. 4.
Robust clustering of FFL functional profiles reveals two noise-based cellular strategies. (A) Barchart of the percent of bootstrap samples (total = 100,000) that cluster according to noise (blue) or the traditional coherent/incoherent ...

Demands on Biological Processes Correlate with FFL Noise Behaviors.

Cluster analysis more specifically revealed three groups of functional categories that diverged in their preference for FFL architectures with distinct noise profiles (p < 0.001) (Figs. 3 and and44B): Group 1 was enriched for FFL architectures with high noise in their ON states. Group 2 did not display a preference based on noise behavior. Finally, group 3 preferred FFL architectures that generate higher noise in their OFF state. Even though groups 1 and 3 combined constitute only 18% of all functional categories, they are associated with 70% of the categorized FFLs. Therefore, we find that the number of FFLs is not evenly distributed across functional categories. Together, these results show that most of the FFLs identified in E. coli are involved in the regulation of a few functional categories that in turn appear to select for circuits based on their architecture-dependent noise properties.

What accounts for the enrichment of FFL architectures with specific noise profiles in functional groups 1 and 3? Many FFLs associated with these functional groups contain an interacting pair of global and functionally specific transcription factors, consistent with the hierarchical organization of gene regulatory circuits (4). Specifically, many FFLs in group 1 contain the global regulator fnr (fumarate nitrate reductase) as their A node and a more specific transcription factor narL (nitrate reductase) as their B node, that together regulate E. coli metabolism under anaerobic conditions (34, 35). An example of such a FFL circuit is shown in Fig. 4C, where fnr regulator is active in the absence of oxygen and represses narL, and these transcription factors regulate dcuB, the C4-dicarboxylate transporter necessary for anaerobic growth. Discrete stochastic simulations predict that the repression of narL (node B) by fnr (node A) gives rise to a noisy ON state expression of dcuB (node C) (Fig. 4C). Noise in the ON state can result in the stochastic termination of dcuB expression during anaerobic growth (Fig. 4C). This propensity for stochastic termination could permit occasional sampling of aerobic respiration that could be beneficial if environmental conditions unexpectedly change. Additionally, the noisy ON state of FFLs associated with group 1 could provide a mechanism to modulate the expression level of downstream targets of fnr and narL possibly through frequency modulation of stochastic bursts (36). Therefore, enrichment of FFL architectures that give rise to noisy ON states may be a result of functional requirements associated with anaerobic respiration processes that make up functional group 1.

Most FFLs in group 3 are associated with known stochastic processes in E. coli that respond to stress and give rise to heterogeneity. Although group 1 and group 3 both exhibit a preference for FFL architectures based on noise, they do so in an opposite manner. In particular, the functional categories comprising group 3 are enriched for FFL architectures where node A activates node B and thus gives rise to high noise in the OFF state of node C. Concurrently, group 3 FFLs share a pattern where a global regulator such as IHF (integrative host factor) positively regulates a more functionally specific transcription factor such as fis (factor for inversion stimulation). Together, IHF (node A) and fis (node B) regulate genes such as glpT (glycerol-3-phosphate transporter) (node C) that have been implicated in the generation of resistance to antibiotics such as fosfomycin (Fig. 4C) (37). IHF has also been identified in a screen for genes involved in the stochastic generation of antibiotic-resistant persister cells (29). In FFLs with this architecture, expression of glpT is predicted to be noisy in the OFF state, giving rise to stochastic bursts of glpT expression. These data reveal that group 3 is comprised of biological processes associated with stress responses that can be initiated in a stochastic manner even in the absence of stress stimuli. Consistent with this finding, the architecture of FFLs enriched in group 3 exhibit higher noise in their OFF state that can facilitate stochastic activation and thus sampling of alternative stress responses at the single-cell level. Such probabilistic behavior at the single-cell level has been shown to be a beneficial strategy under unpredictable environmental conditions and may thus explain the preference of group 3 functions for FFLs with high noise in the OFF state (7, 13, 3840).

Functional categories comprising group 2 exhibit a lack of preference for FFLs architectures according to noise. Even though group 2 contains 82% of functional categories, only 54% of FFLs are associated with this group. FFLs within group 2 may of course have been selected for based on properties other than noise. However, the low number of FFLs contained within group 2 suggests that noise behavior is at least one of the important properties underlying FFL function. If noise behavior is not critical for the operation of biological processes contained within group 2, perhaps FFLs are a less preferred circuit motif. Interestingly, the functional categories comprising group 2 are among others, associated with housekeeping processes such as cell division and amino acid synthesis. These basic biological processes are not known to benefit from stochastic behavior. The three groups of functional categories suggest that most FFLs are selected based on their noise properties by cellular processes that may benefit from stochastic fluctuations.

Discussion

The comprehensive analysis presented here reveals a general trend regarding the preference of biological processes for FFL architectures based on their noise profiles. However, the following points have to be considered: (i) There may be additional unaccounted regulatory inputs into FFLs other than the three nodes considered here, possibly altering the noise behavior. (ii) It is important to note that FFLs do not exist in isolation. Genes can be shared among FFLs and there can be cross-regulation between individual circuits. (iii) Robust clustering of FFLs according to noise does not imply that other differences among FFL architectures cannot be of functional importance. It is therefore striking that functional profiles containing information on biologically relevant properties robustly cluster FFLs consistent with architecture-dependent noise behavior. Stochastic behavior thus appears to be at least one of the important biological properties of FFLs.

Many gene regulatory circuits contain pathways comprised of consecutive activation and repression reactions similar to those in FFLs. Therefore, the noise behavior of other gene regulatory circuits may also be determined by the order of regulatory links with opposite actions. Specifically, noise in target gene expression that is governed by a net negative linear cascade of transcription factors will depend on whether this regulation is mediated by the repression of an activator or the activation of a repressor. Regulation will therefore either be mediated by a high concentration of repressor, or a low and thus noisy concentration of activator. For example, the order of activation and repression reactions comprising a net negative feedback loop of a bacterial differentiation circuit has been shown to dictate stochastic fluctuations in circuit dynamics (7). Therefore, in instances where gene expression is regulated by a net negative cascade of transcription factors with opposite regulatory modes, noise of gene expression may depend on the order of activation and repression reactions.

Susceptibility to stochastic bursts of gene expression may, of course, not be the only functionally relevant property of FFLs that gives rise to clustering according to architectures. We considered another possible explanation for the observed clustering pattern known as demand theory (41, 42). Demand theory predicts that depending on the organism’s native environment, genes in high demand are regulated by activators, whereas genes in low demand are regulated by repressors. Because functional groups 1 and 3 display opposite clustering preferences where node A either represses or activates B, respectively, demand theory would predict that node B is in low demand in group 1, whereas it is in high demand in group 3. Group 1 FFLs are involved in anaerobic metabolism and thus are expected to be in high demand in the native environment of E. coli such as the mammalian colon. However, transcriptional regulators corresponding to node B such as narL and nikR are more often repressed than activated in group 1 FFLs. FFLs in group 3, on the other hand, are involved in stress responses and thus expected to be in low demand assuming that E. coli is well adapted to its environment. In particular, stress response regulators that correspond to node B such as baeR, HN-S, and fis should be in low demand and thus expected to be repressed according to demand theory. However, these transcriptional regulators are found to be activated in group 3 FFLs. Therefore, rather than demand theory, the noise behavior of circuit architectures is more consistent with clustering of FFLs.

Stochastic bursts of gene expression have been demonstrated to be physiologically important for the many systems such as lambda and Lac repressors as well as the differentiation of B. subtilis cells into the state of competence (6, 20, 25, 4346). Consistent with these findings, FFL architectures that generate stochastic bursts of gene expression appear to be favored by E. coli stress responses such as the stochastic generation of antibiotic-resistant persister cells (29, 47). In addition to stochastic initiation, our results also suggest that some cellular processes, such as anaerobic metabolism of E. coli, may prefer the ability to stochastically terminate their response. These data indicate a possible relationship between the default state of a cellular process and the noise behavior of the associated FFLs. Depending on whether the default state of the cellular process is active (ON) or inactive (OFF), FFLs with higher noise in ON or OFF steady states can enable sampling of alternative states by stochastic termination or activation, respectively. These findings suggest a possible link between the demand on a cellular process and the type of noise generated by the associated FFL architecture. Furthermore, these results suggest that particular architectures of FFLs may have been selected for their inherent noise properties to cope with distinct environmental constraints. It may thus be possible to decode functional properties and selection pressures from architectures of gene regulatory circuits.

Methods

Programming Language and Statistical Computing Environment R.

Version 2.9.1 of R from The R Foundation for Statistical Computing ISBN 3-90051-07-0 was used 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.

Stochastic Simulation Software: GillespieSSA.

Version 0.5–3 of the GillespieSSA package for R by Mario Pineda-Krch was used for stochastic master equation simulations (48).

Feed Forward Loop Simulations.

The simulation environment was constructed in R as a wrapper around GillespieSSA. The three components of the FFLs, A, B, and C, each were modeled as genes with corresponding transcriptional promoters and translated protein species. The protein products for A and B then served as transcription factors for downstream genes as shown in Fig. 1. Transcription and translation were modeled explicitly as a single step with propensity determined by the binding state of transcription factors to the promoter as opposed to using a cis regulatory input function. Transcription factor binding was modeled with a Hill coefficient of 2.

Databases: RegulonDB and EcoCyc.

Genetic transcriptional network information was downloaded from RegulonDB (33) from the Regulatory Network Interactions section of datasets as NetWorkSet.txt, Version 6.3, released on January 30, 2009. Genetic regulatory interactions were consistent with EcoCyc (32) due to data sharing between the two databases. We excluded ambiguous or unknown interactions from our analysis, but did not exclude microarray or electronically inferred interactions.

Gene Annotation.

Genes in FFLs were identified using FANMOD (49). Functional annotation and grouping was based on that of Ma et al. (50). Further gene classification was done with the assistance of EcoCyc. All genes involved in a feed-forward loop were annotated, and analysis was done both by considering three annotations per feed-forward loop (Fig. 3).

Cluster Analysis.

With R, hierarchical clustering was applied to both functional categories and FFL types using a Euclidean distance metric and complete linkage based on the abundance of the number of FFLs. Bootstrap resampling analysis was done using the boot package available from CRAN (51).

Supplementary Material

Supporting Information:

Acknowledgments.

We thank S. Altschuler, L. Avery, R. Hiesinger, R. Ranganathan, E. Ross, K. E. Süel, L. Wu, and members of the Süel laboratory for critical manuscript reading. M.K. is supported by Mol.Biophysics Training Grant GM T32008297, NIH-NIGMS MSTP Grant 5 T32 08014, and the Perot Foundation. This research was supported by grants NIH NIGMS RO1 GM088428, Welch Foundation (I-1674) and James S. McDonnell Foundation (220020141). G.M.S. is a W. W. Caruth, Jr. Scholar of Biomedical Research.

Footnotes

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.

See Commentary on page 13197.

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

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