Topological units of environmental signal processing in the transcriptional regulatory network of Escherichia coli

Abstract

Recent evidence indicates that potential interactions within metabolic, protein-protein interaction, and transcriptional regulatory networks are used differentially according to the environmental conditions in which a cell exists. However, the topological units underlying such differential utilization are not understood. Here we use the transcriptional regulatory network of Escherichia coli to identify such units, called origons, representing regulatory subnetworks that originate at a distinct class of sensor transcription factors. Using microarray data, we find that specific environmental signals affect mRNA expression levels significantly only within the origons responsible for their detection and processing. We also show that small regulatory interaction patterns, called subgraphs and motifs, occupy distinct positions in and between origons, offering insights into their dynamical role in information processing. The identified features are likely to represent a general framework for environmental signal processing in prokaryotes.

Fig. 1.

Definition and characteristics of transcriptional subnetworks. (A) Schematic representation of the E. coli TR network. Nodes are genes/operons and their protein products, and links are TR interactions between them. White nodes represent TF-encoding operons in the input layer (layer 0); they are not regulated transcriptionally by any other TFs. Nodes located farther from the input layer are increasingly darker. The color of the links indicates activation (green), repression (red), or both activation and repression (yellow). Nodes marked by purple circles of larger size within the light-purple shaded area form a signal-affected transcriptional subnetwork, or origon, rooted at the node in layer 0. The numbers on the right indicate the number of nodes in the corresponding layers of the E. coli TR network. (B) The rob origon is shown as an example from the E. coli TR network. (C) The origon network. Circles represent origons labeled by their root node, which directly or indirectly regulates all other nodes in the origon. The radius of circles is proportional to the base-2 logarithm of the number of operons (nodes) in that origon. Black circles represent origons with tree topology, and red circles represent origons with FFL-tree topology, an example of the latter being shown in B. Two origons are connected if they share at least one node, with the thickness of links being proportional with the number of nodes in common.

Fig. 2.

Validation of the origon concept by microarray data. (A) Definition of node–signal covariance (cov_NS) and node–node cross-correlation (cor_NN). The quantity cov_NS characterizes the impact of the changes in environmental oxygen concentration (39 binary values of [O₂] in the top graph) on the intracellular mRNA expression [log ratios (LRs): vertical axes in the bottom three graphs] of three representative single-gene nodes (sodA, adhE, and cpxP). The z score, z_NS, measures how different the cov_NS value of a node is from other nodes in the network. The quantity cor_NN characterizes the similarity between the mRNA expression profiles of the different genes. (B) Histograms of cov_NS (Left) within the crp and fnr origons (red bars) versus equal number of nodes chosen randomly (black bars) for FNR-specific (aerobic-shift) perturbation. The corresponding z_NS histograms are shown (Center), as are the double z scores, Z_NS, for all origons (Right) (the Z_NS values for the fnr and crp origons are circled). The dashed black line corresponds to a cutoff of Z_NS = 2. (C) Histograms of z_NN within the crp and fnr origons (red bars) versus equal number of nodes chosen randomly (black bars) for FNR-specific (aerobic-shift) and nonspecific perturbation. The Z_NN values for all origons are shown (Right)(fnr and crp origons are circled, and the dashed black line corresponds to a cutoff of Z_NN = 2). (D) The predicted binary node–node correlation (within the narL origon) between two nodes is equal to the product of link types along any path connecting the two nodes in a nondirectional version of the origon. Link types are considered as follows: +1, activating; –1, repressing; 0, dual. (E) Predictions are only indicative of measured node–node cross-correlations in the fnr origon for FNR-specific stimulus. Along the horizontal and vertical axes are operons within the crp or fnr origon so that the diagonal contains values calculated for an operon with itself. The agreement between predicted binary (Left) and measured (Center) cross-correlations is calculated as the product of the predictions and measurements (Right) and the corresponding averages 〈P × M〉. All values in the right column are between –1 and 1, and correct predictions result in positive values, as indicated by the color scale shown at the bottom.

Fig. 3.

Filtering properties and dynamics of small subgraphs. (A) Directed small subgraphs: SRI, DIV, CNV, CAS, and FFL are shown. The nodes are labeled by X, Y, and Z progressively, depending on their distance from the input layer of the subgraph (layer 0). (B) Schematic illustration of SRIs, the basic building unit of all three-node subgraphs, reflecting the mechanism considered in our modeling. The signal S_X activates the input TF, P_X. Once activated, binds to the operator region of gene Y and allows binding of RNA polymerase P_R to its promoter region. The polymerase–operator complex initiates transcription, resulting in the synthesis of an mRNA molecule R_Y after a delay τ_R, which, bound by a ribosome P_P, is translated into the output protein P_Y after a delay τ_P. (C) Time courses of output protein levels after a periodic perturbation for SRIs and DIVs (black line), CASs (blue line), and FFLs (red line). The amplitude of fluctuations at the output of the FFL is nearly the same as at the output of the SRI, although it is substantially reduced because of the stronger filtering properties of CAS. (D) Frequency response of SRI and DIV (black circles), CAS (blue squares), and FFL (red triangles) showing the amplitude of fluctuations at the output of subgraphs (vertical axis) versus the frequency of the signal applied to their input (horizontal axis). All subgraphs are low-pass filters, but CAS has a much stronger filtering effect than either the SRI (DIV) or FFL.