Figure 1

State complexity and parameter complexity. A: Schematic representation of a hypothetical regulatory biological network. A transcription factor TF (striped circle) interacts with either one of two competing co-activators (CA1, CA2) to drive expression of one of two target genes (triangles T1, T2). Presence of an inhibitor (grey, rounded rectangle) blocks TF. B: In the absence of detailed knowledge of the underlying interactions, the network from A can be simplified into this diagram, with the state complexity translated into parameter complexity as shown in C. C: For the 2⁴ possible activation patterns of the 4 input nodes in B, logical functions for the two targets T1 and T2 are specified. The only knowledge is about the activating or inhibiting influence of the input nodes on the targets. For the logical functions, we use the convention introduced by Thomas et al. [6], i.e. parameter K_TF,R,CA2 stands for the value (either 0 or 1) to which the target node tends under the positive influence (i.e., presence of activators, absence of inhibitors) of the input nodes mentioned as subscripts. For lnet, only two of the logical parameters for every node are pre-defined (values assigned in bold). Two additional columns, Ex1 and Ex2, specify the concrete values of all parameters for the system as depicted in A.