Sketch of a bistable switch with reciprocal transcriptional repression between genes a and b.

Three obtained bistable switches. Each diagram represents a network composed from individual reactions drawn from those listed in Fig. 2. In A and B, the values of the kinetic constants of all elementary reactions are provided together with the range of variation in which the network keeps its bistable character (a range of x–y means that the corresponding constant can be multiplied by any number between x and y, maintaining all others fixed). For instance, in A, the evolution of protein A concentration reads, d[A]/dt = 0.20–0.0085[A]–0.72 [A] [B]–0.19 [A]+0.42[b:A]. The different states of a gene (without or with proteins bound on its promoter) are assumed to sum to one (thus [b] + [b:A] = 1). The kinetic constants for the network shown in C are provided in Fig. 12.

The “core” oscillating network extracted from the evolutionary process shown in Fig. 4. The kinetic constants for this network are provided in Fig. 15. In Fig. 4, the rapid score decrease and emergence of oscillations at generation 260 are associated with the creation of the complex ABCC.

List of possible reactions. The schematic representations are used to represent the reactions in Figs. 3, 4, 5. In the allied rate equations, Greek letters (τ, δ, γ, θ) denote kinetic constants; A:B denotes the bound complex of protein A and B; and a:P denotes gene a with protein P bound on its promoter. Reaction ii is illustrated here only for the case of an already existing bound complex between a protein P and the promoter of a gene a. The same reaction is also possible between a protein and a “naked” promoter (i.e., without P). Only the term corresponding to the displayed reaction has been written on the right side of the equations, giving the evolution of protein concentrations. In a given network of reactions, all such terms should be added to obtain the evolution of a particular species (e.g., the evolution of a protein A produced from gene a and only undergoing a posttranscriptional modification would be obtained by combining i and iii: d[A]/dt = τ_A[a] – δ_A[A] – τ_M[A]).

Dynamics of six networks at different stages in the evolutionary process leading to the creation of an oscillatory network. The score evolution is shown (Bottom).