English: a | A network of three genes is modelled using ordinary differential equations (ODEs). Reaction rate constants are denoted by 'k'. b | The regulatory relations are depicted graphically. c | The trajectories of the model. Each equation shows the change in the level of a gene as a difference of its synthesis and degradation. Gene 1 is constitutively expressed, and is repressed by gene 3. Therefore, its level may reach a maximal rate of increase (k1,s; 's' stands for synthesis) when the level of gene 3 is 0, in which case k1,s will be multiplied by 1. When the level of gene 3 is non-zero, the level of gene 1 rises slower than k1,s. Transcription of gene 2 is activated by gene 1. This is expressed in the second equation of panel a, in which gene 2 level rises as a Michaelis–Menten function of the level of gene 1. Similarly, transcription of gene 3 is activated when both gene 1 and gene 2 levels are non-zero, and this relationship is given in the third equation of panel a. Degradation is modelled as a first-order reaction with rate constants ki,d (in which 'i' can be 1, 2 or 3). This formulation assumes that every transcript is immediately translated, and therefore the synthesis constants ki,s refer to both transcription and translation. According to simulation (bottom), the system stabilizes in a steady state at about 4.5 time units. The values of the rates in the simulations were: k1,s=k2,s=2; k3,s=15; k1,d=k2,d=k3,d=1; k2,1=k3,1=k3,2=1; and k1,3=100. The initial levels were all zero. Equations were solved using DESSolver v1.7 and the fourth order Runge–Kutta method.