Functions of bifans in context of multiple regulatory motifs in signaling networks

Abstract

Representation of intracellular signaling networks as directed graphs allows for the identification of regulatory motifs. Regulatory motifs are groups of nodes with the same connectivity structure, capable of processing information. The bifan motif, made of two source nodes directly crossregulating two target nodes, is an overrepresented motif in a mammalian cell signaling network and in transcriptional networks. One example of a bifan is the two MAP-kinases, p38, and JNK that phosphorylate and activate the two transcription factors ATF2 and Elk-1. We have used a system of coupled ordinary differential equations to analyze the regulatory capability of this bifan motif by itself, and when it interacts with other motifs such as positive and negative feedback loops. Our results indicate that bifans provide temporal regulation of signal propagation and act as signal sorters, filters, and synchronizers. Bifans that have OR gate configurations show rapid responses whereas AND gate bifans can introduce delays and allow prolongation of signal outputs. Bifans that have AND gates can filter noisy signal inputs. The p38/JNK-ATF2/Elk-1bifan synchronizes the output of activated transcription factors. Synchronization is a robust property of bifans and is exhibited even when the bifan is adjacent to a positive feedback loop. The presence of the bifan promotes the transcription and translation of the dual specificity protein phosphatase MKP-1 that inhibits p38 and JNK thus enabling a negative feedback loop. These results indicate that bifan motifs in cell signaling networks can contribute to signal processing capability both intrinsically and by enabling the functions of other regulatory motifs.

FIGURE 1

The JNK1/p38 – ATF2/Elk-1 bifan motif configuration and its immediate environment. (a) The basic motif is in the shaded area. (b) The shaded area is the bifan motifs with an adjacent link from JNK to c-Jun. JNK phosphorylates and activates c-Jun. (c) The shaded area includes a positive feedback loop involving the immediate early gene c-Jun. (d) The shaded area includes a negative feedback loop involving the immediate early gene MKP-1.

FIGURE 2

(a) Truth table and diagram of the OR gate. (b) Truth table and diagram of the AND gate. (c) Concentration of free active ATF2 as a function of time for various configurations of the bifan motif shown in Fig. 1 a. Stimulus was given at time 0 < t < 5. The initial condition was: [p38] = [JNK] = 10 μM, [ATF2] = [ELK1] = 30 μM. (d) Concentration of free active ATF2 as a function of time for various configurations of the bifan motif shown in Fig. 1 a. Stimulus was given for 1 minute every 5 min (periodically). The initial conditions were the same as in (c). (e) Concentration of free active ATF after a single 1-min pulse.

FIGURE 3

Effect of increasing the initial concentration of Elk-1 on ATF2 homodimers production. Elk-1 “trapping” of JNK1 and p38α, leaving less free p38* (a), results in a decrease in the production of activated ATF2 homodimers (b). Nonordered AND gate was assumed, initial condition: [p38] = [JNK] = 10 μM, [ATF2] = 30 μM. Initial concentration of Elk-1 varies between 0 and 50 μM, as indicated by the curves. The figure presents the concentration of produced homodimers disregarding reactions such as degradation, dissociation, etc.

FIGURE 4

The bifan motif as a filter for fluctuating signals. Time course of ATF2 homodimers is the output. (a) An example of random pulse series as input. (b) Filtering periodic signal. The power spectrum of the output from oscillating signal to the OR gate motif (thick dashed line, right panel) deviates from the response to the nonoscillating input (thin dashed lines). The deviation at the AND gate configuration (solid lines, left panel) is much smaller. (c) Oscillation filtering index (see text for definitions) of various configurations as a function of time period.

FIGURE 5

Dynamics of activated transcription factors in a bifan motif configuration with an additional arm from JNK to c-Jun. The original configuration as shown in Fig. 1 b (top panel); after eliminating the links from p38 to ELK1 and from JNK1 to ATF2 (middle panel); and without the links from p38 to ATF2 and from JNK1 to ELK1 (bottom panel). The initial conditions were: [p38] = [JNK] = 3 μM, [ATF2] = [ELK1] = 30 μM, and [c-Jun] = 10 μM. OR gates were assumed for all substrate activations. Cartoons of the network are presented in each panel. The signal inputs are presented at the most upper panel.

FIGURE 6

Deviation from synchronization of bifan motif and nonbifan circuits for a range of initial conditions. Deviation from synchronization was calculated as the root mean-square of the difference between normalized concentrations (see text for details). The network is the same as in Fig. 5 and the initial conditions are: [ATF2] = [ELK] = 20 μM, [c-Jun] = 10 μM, [p38] = 3 μM, and [JNK] was varying from 0.3 to 30 μM. As an example, time course of free ATF2* and ELK* is presented in the inset for the case p38:JNK = 1:10. In the full bifan configuration (solid lines) the two lines coincide, whereas without the cross links (dotted line) the two TFs are not synchronized.

FIGURE 7

Deviation from synchronization of bifan motif and nonbifan circuits for a range of initial conditions. The network is the same as in Fig. 5. The initial conditions are: [p38] = [JNK] = 3 μM, [ATF2], [ELK], and [c-Jun] varying between 10 μM to 50 μM, yielding TF/kinase ratios between 3 and 17.

FIGURE 8

Dynamics of free monomeric activated transcription factors (TF) in a bifan motif configuration adjacent to a positive feedback loop. The full bifan configuration as shown in Fig. 1 c (top panel); after eliminating the links from p38 to ELK1 and from JNK1 to ATF2 (middle panel); and without the links from p38 to ATF2 and from JNK1 to ELK1 (bottom panel). The initial conditions were: [p38] = [JNK] = 3 μM, [ATF2] = [ELK1] = 30 μM, and [c-Jun] = 10 μM. OR gates were assumed for all substrate activations. Cartoons of the network are presented by each panel. The signal inputs are presented at the most upper panel.

FIGURE 9

Dynamics of free monomeric activated transcription factors (TF) in a bifan motif configuration adjacent to a positive feedback loop and nested in a negative feedback loop. The full bifan configuration as shown in Fig. 1d (top panel); after eliminating the links from p38 to ELK1 and from JNK1 to ATF2 (middle panel); and without the links from p38 to ATF2 and from JNK1 to ELK1 (bottom panel). The initial conditions were: [p38] = [JNK] = 3 μM, [ATF2] = [ELK1] = 30 μM, and [c-Jun] = 10 μM. OR gates were assumed for all substrate activations. Cartoons of the network are presented by each panel. The signal inputs are presented at the most upper panel.

FIGURE 10

Coupling of two motifs. (a) Nesting of a bifan motif in a negative feedback loop. (b) Serial combination; the output of the bifan is the input for the positive feedback loop

FIGURE 11

Effect of initial condition of MKP1 levels on the feedback loop dynamics. When the bifan synchronizes the dynamics of the transcription factors, the feedback loop is highly active (upper panel). However, after eliminating the links from p38 to ELK1 and from JNK1 to ATF2 there is no more synchronization, and thus no transcription of MKP1 observed (lower panel).