Fig. 4: Comparing the E. coli transcriptional regulatory network with random networks of the same density.
a The actual E. coli network does not become unstable even when the maximum regulation strength \({{{\Omega }}}_{\max }\) is increased (blue stars). In contrast, as \({{{\Omega }}}_{\max }\) increases, the probability P(stable) of the system having a stable fixed point decreases for scrambled networks of the same interaction density ρ = 0.0011, regardless of whether the number of transcription factors (TFs) q = 211 is kept fixed (yellow circles) or not (red squares). However, scrambling the network while maintaining the same number of TF-other TF, TF-nonTF, and self interactions can significantly enhance the probability of the system is stable (green triangles). Each of the data points represents an average over 15 sets of 10 regulatory networks, with error bars indicating the interquartile range. [Other parameters: h = 2]. b A typical example of oscillatory dynamics in protein concentrations c when the system no longer has a stable fixed point. [Parameters: \({{{\Omega }}}_{\max }=1585\), h = 2]. c An example of the system going unstable and exhibiting chaotic behavior when the real network is scrambled at time t = 5 × 106 marked by the dashed vertical line. [Parameters: \({{{\Omega }}}_{\max }=1000\), h = 5]. In both (b) and (c), time t is in units of 1/kp.
