Fig. 3: Behaviour of a minimal interaction motif.

a The motif includes the unbound state of A (A--0), the unbound state of B (B--0) and the bound state (A--B). As in Fig. 2, the motif contains four different reaction types: component A can be synthesised (in its neutral state A--0) or degraded (in either state), and Component A and Component B can bind (ppi+; consumes A--0 and B--0, produces A--B) or dissociate (ppi- consumes A--B, produces A--0 and B--0). Not that degradation of A in the A--B dimer releases B--0, hence this reaction is a degradation reaction of A and conditional production reaction for B--0. The regulatory and elemental species-reaction graphs of the motif can be found in Supplementary Fig. 1. b–d Initial conditions, expectations and simulation results. Each line correspond to the simulation of one or more model variants, and visualise which reactions are active, which states are initiated, which behaviour we expect, and the behaviour we observed. b To define the desired behaviour of the motif, we create 128 variants of the motif with each of the four reactions constitutively ON (true) or OFF (false) (columns 1–4), and each of the elemental states initially true or false (columns 5–7), and define the expected steady state as a function of initial state and active reactions (“Expected attractor”; columns 8 and 9). As in Fig. 2, the initial state is preserved when no reaction is active. However, the steady state in the presence of active reactions is more complex, as both unbound states are necessary for the reaction to fire—which affects both the generation of the A--B state and the depletion of the unbound states. With degradation and without synthesis, A--0 and A--B is removed, releasing B--0 in the latter case. Finally, synthesis of A only leads to A--B in the presence of the forward reaction, in which case B--0 is depleted unless A--B is turned over by degradation or dissociation. c The attractors reached after simulation with the update rules in the original ansatz. The attractors correspond to the expected attractors (see B), except when either component is present in only one state (unbound or bound). This happens in the analogous case to the spurious oscillations in the modification motif in Fig. 2, but also when A is synthesised if B is only present in one form. d The attractors reached after simulation with the smoothed update rules. The attractors are identical to the expected attractors in all cases.