Evolutionary simulation scheme, and definition of model.

<p>(<b>A</b>) Simulation was initiated by randomly choosing population members each consisting of 2 matrices and . The next steps were repeated at each generation until the stopping condition was satisfied: the population was duplicated, one copy was kept unchanged and the other was mutated with probability . Mutation could be either sum-rule or product-rule. Fitness of all members (original and mutated) was evaluated by the distance of the product from a desired goal matrix , , where denotes the sum of squares of terms which is the square of (Frobenius) norm. individuals were selected according to their fitness. Several selection methods were employed (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070444#pone.0070444.s001" target="_blank">Text S1</a> for details). The simulation was stopped when the mean population fitness reached a value which was within a preset difference from the optimal fitness (usually 0.01). (<b>B</b>) Model represents a three layer network with a linear transformation function. Input signals are transformed to intermediate layer activities (transcription factors) with . The intermediate layer is then transformed to output layer (gene expression) . Modularity means block or diagonal structure of the matrices, corresponding to signals that affect only subsets of intermediate and output nodes.