S. Mangan and U. Alon ^@

Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

^@ To whom correspondence should be addressed. E-mail:  urialon@weizmann.ac.il

Engineered systems are often built of recurring circuit modules that carry out key functions. Transcription networks that regulate the responses of living cells were recently found to obey similar principles: they contain several biochemical wiring patterns, termed network motifs, which recur throughout the network. One of these motifs is the feed-forward loop (FFL). The FFL, a three-gene pattern, is composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene. The FFL has eight possible structural types, because each of the three interactions in the FFL can be activating or repressing. Here, we theoretically analyze the functions of these eight structural types. We find that four of the FFL types, termed incoherent FFLs, act as sign-sensitive accelerators: they speed up the response time of the target gene expression following stimulus steps in one direction (e.g., off to on) but not in the other direction (on to off). The other four types, coherent FFLs, act as sign-sensitive delays. We find that some FFL types appear in transcription network databases much more frequently than others. In some cases, the rare FFL types have reduced functionality (responding to only one of their two input stimuli), which may partially explain why they are selected against. Additional features, such as pulse generation and cooperativity, are discussed. This study defines the function of one of the most significant recurring circuit elements in transcription networks. 

Cells contain networks of biochemical transcription interactions. These networks have evolved to perform
information-processing functions (1, 2). The inputs to the network, such as external nutrients and stresses, affect the activity of transcription factor proteins. The transcription factors bind regulatory regions of specific genes and activate or repress their transcription. As a result, cell processes are modulated to fit the environmental conditions. Transcription networks can be described as directed graphs, in which the nodes are genes (3–12). Directed edges represent transcription interactions, where a transcription factor encoded by one gene modulates the transcription rate of the second gene.

It is of interest to understand the dynamic behavior of transcription networks (2, 3, 5, 7–10). It was recently found that these networks contain significantly recurring wiring patterns termed "network motifs" (6, 11, 12). Network motifs are patterns that occur in the network far more often than in randomized networks with the same degree sequence (6, 11). The transcription networks of the bacterium Escherichia coli (6, 11) and the yeast Saccharomyces cerevisiae (11, 12) were found to contain the same small set of highly significant motifs. The significance of these structures raises the question of whether they have specific information-processing roles in the network. If they do, they might be used to understand the network dynamics in terms of elementary computational building blocks.

One of the most significant network motifs in both E. coli and yeast is the feed-forward loop (FFL) (6, 11). The FFL is composed of a transcription factor X, which regulates a second transcription factor Y (Fig 1a). X and Y both bind the regulatory region of target gene Z and jointly modulate its transcription rate. The FFL has two input signals, the inducers, Sx and Sy, which are small molecules, protein partners, or covalent modifications that activate or inhibit the transcriptional activity of X and Y (Fig. 1a). The FFL has three transcription interactions. Each of these can be either positive (activation) or negative (repression). There are therefore eight possible structural configurations of activator and repressor interactions (6) (Tables 1 and 2). Four of these configurations are termed "coherent" (Table 1): the sign of the direct regulation path (from X to Z) is the same as the overall sign of the indirect regulation path (from X through Y to Z) (6). The other four structures are termed "incoherent" (Table 2): the signs of the direct and indirect regulation paths are opposite.

Fig. 1.
(a) FFL. Transcription factor X regulates transcription factor Y, and both jointly regulate Z. Sx and Sy are the inducers of X and Y, respectively. The action of X and Y is integrated at the Z promoter with a cis-regulatory
input function (7, 14), such as AND or OR logic.
(b) Simple regulation of Z by X and Y.

Here we use mathematical modeling to study the function of the eight FFL structural configurations, with AND- and OR-gate logic. This work extends our previous study that was limited to only one FFL type with three activators and AND logic (6). We find that incoherent FFLs can serve as a novel mechanism for accelerating the expression of the target genes. Both coherent and incoherent FFL behavior is sign sensitive: they accelerate or delay responses to stimulus steps, but only in one direction. The FFL functions are essentially the same with either AND- or OR-gates, but with reversed sign sensitivity. These results directly suggest experiments that can test the function of this network motif.
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Discussion:

We theoretically analyzed the functions of the eight FFL structural configurations. We find that the incoherent FFLs act as sign-sensitive accelerators: they provide a mechanism for speeding up the responses of the target genes. In addition, some incoherent FFL types can act as pulsers. Coherent FFLs act as sign-sensitive delays. These functions are carried out with either AND- or OR-gate regulation in the Z promoter, with reversed sign sensitivity. The results are summarized in Table 3.

Why Do Some FFL Configurations Occur More Often than Others in Transcription Networks?

We find that in transcription databases of E. coli and yeast coherent type 1 FFLs occur far more often than the other three coherent types. Similarly, incoherent type 1 occurs much more often than the other incoherent types. Type 2 coherent and type 2 incoherent FFLs appear to be the next most selected configurations in yeast.

Can the difference in the abundance of the FFL types be simply explained by the relative numbers of repressor and activator interactions in the network? In the E. coli database, there are ~2/3 activator and 1/3 repressor interactions (6). This finding would naively mean that there should be a total of ~18 coherent FFLs of types 2–4, which is much more than observed. Similarly, in the yeast database, ~80% of the interactions are activators (11). Yet type 1 and types 3 and 4 incoherent FFLs occur in very different numbers, despite the fact that they have one repressor and two activator interactions. Thus, the difference in the frequencies of the FFL types is not simply explained by the relative abundances of repressor and activator interactions in the network.

Are all types of FFLs biologically feasible? In FFL types 3 and 4, the protein X has regulations of different signs for Y and Z (one repression and one activation), whereas in types 1 and 2 the regulation is of the same sign (both activation or both repression). It is well established that many transcription activators act to repress a subset of their downstream genes (24, 25). Hence, types 3 and 4 FFLs are, in principle, biologically feasible. What, then, might underlie their relative scarcity?

Our analysis suggests that AND-gate FFLs of types 3 and 4 have reduced functionality relative to types 1 and 2. Types 3 and 4 respond at most to one of their input stimuli (Sx) at steady state, whereas types 1 and 2 respond to both stimuli (Sx and Sy). This reduced functionality might be part of the reason that types 3 and 4 appear to be selected against during evolution of transcription networks. Furthermore, type 1 coherent FFL benefits from increased cooperativity. This reasoning does not apply to FFLs with OR-gate logic, and additional reasons may underlie the observed bias in FFL types.

Coherent FFLs as Persistence Detectors.

An equivalent way to describe the sign-sensitive delay function of the coherent FFL is sign-sensitive persistence detection (6): it responds only to persistent Sx stimuli and rejects short Sx pulses. Short pulses are rejected, however, only in one direction. For example, type 1 AND-gate FFLs (Fig. 1a) reject short on pulses of Sx (in these simulations, the input Sy is on throughout). On the other hand, Z responds strongly even to short off
pulses of Sx. Similar persistence detection can be performed by all four coherent FFL types.

Incoherent FFLs as a Mechanism for Speeding Response Times in Transcription Networks.

The response time of transcription networks is generally slow (16, 17). Although it takes only a few minutes for the first protein products to appear, the response time (time to reach half-steady-state level) is governed by the lifetime of the protein product (9, 16, 17), which is often on the order of hours. One way to speed up the response time is to increase the degradation rate of the protein product (16, 17). This has the cost of requiring increased production to achieve a given steady-state level. An additional solution is to implement negative autoregulation, in which a transcription factor represses its own transcription. This negative feedback loop has been shown both theoretically (17, 26) and experimentally (17) to speed the response. Negative autoregulation, however, can only work for transcription factors (or genes on an operon that encodes a transcription factor). Genes that are not transcription factors cannot negatively autoregulate their own transcription.

The present study suggests a mechanism for speeding transcriptional responses. We find that the incoherent FFL can greatly reduce the response time relative to simple regulation designs with the same steady state (Fig. 4). The incoherent FFL mechanism can in principle apply to any gene, not only to transcription factors, because the acceleration is carried out by the two transcription factors upstream of the target gene.

In E. coli, several key global regulators play the role of X in coherent type 1 FFLs, including regulators that respond to glucose starvation (CRP), nitrogen limitation (rpoN), and noxious drugs (rob). Interestingly, nonhomologous yeast systems that respond to these key stimuli also display coherent FFLs, with X transcription factors such as MIG1, GLN3, and PDR1 that respond to glucose, nitrogen, and drugs, respectively. Incoherent type 1 FFLs in yeast include anaerobic metabolism (HAP1 as X) and nitrogen starvation (DAL80 or GLN3 as X) systems. One pair of transcription factors in E. coli that respond to anaerobic conditions (fnr as X and arcA as Y) show four different types of FFLs with different operons: coherent type 1 for Z = focA, coherent type 3 for Z = cyoABDCE, incoherent type 1 for Z = glpACB, and incoherent type 3 for Z = cydAB. This diversity suggests an intricate kinetic regulation of different anaerobic metabolism systems, possibly some with sign-sensitive delays, others with sign-sensitive acceleration and others with pulses, with respect to oxygen availability (27, 28). Often, several FFLs share the same X, e.g., 16 for CRP, a property that should not affect any of the present conclusions. Tables 4 and 5, which are published as supporting information on the PNAS web site, www.pnas.org, show all FFLs in the E. coli and S. cerevisiae databases, respectively.

The present study suggests a defined experimental program to test the functions of the FFL types. We found experimentally that the ara system in E. coli, which is a type 1 AND-gate coherent FFL, acts as a sign-sensitive delay with respect to cAMP signals (34). Similar experiments on other natural systems can help establish the function of the FFL in its various structural configurations. In addition, all of the FFL types may be synthetically built out of characterized components (16, 17, 29–33), allowing construction of pulsers and other useful circuit elements. This article focused on kinetic behavior and steady-state logic. The FFL may have been selected to perform additional functions, including functions associated with intermediate steady-state levels. Some of the characteristics of FFLs can be carried out by simpler circuits; for example, AND-like and OR-like steady-state logic can be carried out by simple regulation, and cooperativity increase can be carried out by cascades. However, FFLs have some unique features, such as acceleration and pulse generation that cannot be carried out by cascades or simple regulation. It would be interesting to map additional functions that can be performed by
FFLs, in particular functions that cannot be carried out by simpler circuits.

New network motifs are likely to emerge as our knowledge of biological networks becomes more complete. It would be fascinating to study the function of additional network motifs to determine whether biological networks can be understood in terms of recurring circuit elements, each with a defined information-processing role.

Acknowledgements:

We thank S. Shen-Orr for discussions, and the Israel Science Foundation, the National Institutes of Health, and Minerva for support.
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