Structure and function of the feed-forward loop network motif

Abstract

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.

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.

Fig. 2.

Kinetics of coherent type 1 (Left) and type 4 (Right) FFLs with AND regulatory logic, in response to on and off steps of Sx. Note that the delayed response to on steps of the FFLs (thick, medium lines) compared to a corresponding simple system (thin line). Note that FFLs can behave as simple regulation for nonfunctional parameter domains (see Materials and Methods). Simulation parameters: K_xz = K_xy = 0.1; for type 1, K_yz = {0.5, 5}; for type 4, K_yz = {0.6, 0.3}; all others are as stated in Materials and Methods.

Fig. 3.

Kinetics of incoherent type 1 (Left) and type 4 (Right) FFLs with AND regulatory logic and no basal activity of Y, in response to on and off steps of Sx. Note that type 4 FFLs can produce a strong pulse that is enabled by Sy. Type 1 can produce only a weak pulse when Sy = 1, and the pulse-like nature of the response is lost when Sy = 0. Simulation parameters: K_xz = K_xy = 0.1; for type 1, K_yz = {0.01, 0.1, 0.3}; for type 4, K_yz = {1, 0.3, 0.1} (thick, medium, thin lines); all others are as stated in Materials and Methods.

Fig. 4.

Kinetics of incoherent type 1 (Left) and type 4 (Right) FFLs with basal Y activity and AND regulatory logic, in response to on and off steps of Sx. Note that the response of the FFL to on steps (thick, medium lines) is faster than that of a corresponding simple system (thin line). Simulation parameters: for type 1, K_xz = 1, K_xy = 1, K_yz = 0.5, B_y = {0.5, 0.3}; for type 4, K_xz = 1, K_xy = 0.1, K_yz = 0.5, B_y = {0.45, 0.35}; all others are as stated in Materials and Methods.

Fig. 5.

Kinetics of coherent type 1 with AND (Left) and OR (Right) regulatory logic at Z promoter. Note that the AND FFL has delayed response to on steps, whereas OR FFL has delayed response to off steps. FFL: thick, medium lines; simple system: thin line. Simulation parameters: K_xz = 0.1, K_xy = 0.5; for AND, K_yz = {0.5,5}; for OR, K_yz = {0.7,0.3}; all others are as stated in Materials and Methods.

Fig. 6.

Apparent cooperativity of steady-state Z response as a function of X activity. The graph shows the z(x) response curve for type 1 (thick line), type 4 (thin line) FFLs, and a simple regulation system (○), for H_zx = H_yx = H_zy = 2. Simulation parameters: α_i = 1, β_i = 1, K_ij = 1, B_i = 0. Type 1 coherent FFL (thick line) has an effective cooperativity of H_eff = H_xz + H_xy*H_yz, where H_ij is the Hill coefficient of the regulation reaction of protein j by protein i. Other coherent FFL types have H_eff = H_zx.