Network interaction examples and mutational operators. a(i) shows an example 3-gene regulatory network, indicating protein–DNA interactions, where rectangles represent binding sites (+ activating; − inhibitory), triangles represent genes. The greyscale fill of each binding site and gene represents its ‘shape’. Unbroken lines represent strongest binding affinity, whilst dashed lines represent a weaker binding affinity. a(ii) shows the same 3-gene network visualised as a graph. Nodes represent genes; → are positive interaction; —| are negative interaction and weighting of line again represents binding affinity. b shows several of the mutational operators in diagrammatic form: (i) gene duplication, (ii) gene loss, (iii) protein shape mutation, (iv) binding site duplication, (v) binding site loss, (vi) binding site shape mutation and (vii) binding site regulation type ‘flip’

Different network topologies evolve in different environments. Populations evolved in environments with stresses (starvation and heat-shock-like stresses) have networks with a wide variety of all possible sub-systems a(i–ii). A similar functional structure is observed, consisting of a large energy regulation system (pink), two stress response systems (yellow) and growth systems (blue). Global regulators are evident in each example (Rsp1 and Fod6 in a(i); Nrg2 in a(ii)), each performing only repression. Populations evolved in a stress-less environment do not show as much variety of sub-systems b(i–ii). Energy regulation is on a smaller scale than in stressed populations, but growth systems are more heavily utilised, usually consisting of at least three growth systems. Global regulators are also present in all examples, but have a different structure to those found in the stressed populations. The global regulators perform the energy regulation, but are also incorporated into the growth systems, meaning the global regulators are dual-function

Robustness and fragility to mutations in network components. Wild-type (WT) model is evolved network from Fig. 3h and each strain is simulated 1000 times. The WT consistently reaches the termination criteria of 2,000 simulation steps, indicating a robust and efficient network. Removing the global regulators (nrgKO) governing the energy regulation system reduces survival rate to 0, but is able to survive around 150 time-steps. Removal of the first stress response system (str1KO) also reduces the survival rate to 0, and can survive only tens of time-steps. A similar result is observed removing the second stress response system (str2KO), but survives around 100 time-steps. The mutants, str1KO and str2KO, cause the network to die at different points in simulation, due to the additional global regulator activity of elements of the str1 system. Removal of the independent growth system (grwKO) has a positive effect on survival rate, reaching nearly 100%. Therefore, certain sub-systems are pre-requisites for survival, whilst others can be lost with little effect on survival rate. Perturbing the global regulator, Rsp1, also dramatically affects survival rate. Halving the protein stability (HALF-STAB) causes the network to die at any point, but mostly replicates. Reducing the protein production rate also has a large impact on survival, indicating the highly tuned state of the network

Incremental evolution of a functionally complex gene regulatory network. The network initially starts with each type sub-system, yet is unable to survive more than a few tens of time-steps (a). After 100 generations the network structure has changed dramatically, losing the growth system, but gaining an efficient stress response system (b). By 250 generations a second stress response system has evolved, and also the energy regulation system has continued to grow (c). By 500 generations a number of small global regulators have evolved, further increasing the energy regulation system (d). The network also has a number of redundant regulators each performing identical roles. A growth system has also re-emerged which is interacting with stress and energy regulation systems. The first replication event after 1,166 generations shows the network has a very efficient set of stress response systems, and also the emergence of just two co-regulating global regulators performing the majority of the energy regulation (e). The different systems have become increasingly interconnected. After 1,500 generations only a single global regulator now performs the key role in global regulation (f). An independent growth system has also emerged, which is now viable due to efficient energy regulation and stress systems. Network functionality remains similar after 5,000 generations, with the global regulator increasing the number of pathways regulated, and recruitment of another gene as a transient global regulator (g). The growth system has increased in efficiency, now utilising the energy signals. After 10,000 generations network structure and function is again similar (h). The energy regulation system is still controlled by the same global regulator, and a secondary weaker connected regulator. The main growth system is now independent of other systems, and a second has evolved within the energy regulation and stress systems. The network functionality is evolved in stages, with certain systems as prerequisites for the sustainability of others