Figure 3. Critical dynamics in E. coli using canalizing functions.

Derrida map M(x) for the E. coli network with different fractions f_c of canalizing functions. To compute f_c we took into consideration only the genes for which K≥2. For fully random Boolean functions f_c = 0.51. (a) We increased the value of f_c by adding canalizing functions to the 230 genes with K≥4. Note that M(x) remains critical even for f_c≈0.66, but it starts to deviate from criticality towards the ordered region for f_c>0.7 (dotted dashed curves). (b) We decreased the value of f_c by removing canalizing functions from the 421 genes which originally are regulated by canalizing functions just by chance (most of them with K = 2 and K = 3). In this case the curve deviates from criticality towards the chaotic region only for f_c<0.4. Each point in the curves is the average over 5000 initial conditions randomly chosen.