Figure 1

Mass action kinetics predict that 3-gene repression-based transcriptional circuits are generic oscillators. ( A ) A generic transcriptional circuit with three components and circular repression. G _i , M _i and P _i refer to the gene, mRNA and protein, respectively, of components i∈{0,1,2}. ( B ) Bifurcation diagram of the mass action kinetics approximation of the model of (A) ((2)) in the (T _P -α) plan. Two Hopf-Bifurcation branches (full lines) separate a region of spontaneous oscillatory behavior (grey area) from stable steady state behavior. ( C ) Bifurcation diagram along T _P for α=0.1 (green dashed line in B). Full thick black lines locate stable steady-states, the dashed black line locates unstable steady-states, and thick green lines show minimal and maximal values (envelope) of limit cycle oscillations. ( D ) Spontaneous oscillations of the three proteins for α=0.1 and T _P =3 × 10⁵ (green star in B). All other parameters were according to the standard set defined in the Methods section.