First step: definition of the expression profiles

In the first step the positive Boolean functions $\varphi _1$ and $\varphi_2$ associated with the two expression profiles are to be defined. To this aim, for each of them the following parameters must be selected:

1. The number $h$ of expression signatures (ES);
2. A range $[l_{\min},l_{\max}]$, inside which the procedure randomly chooses (with uniform distribution) the number of genes $l_i$ belonging to each of the $h$ expression signatures.
3. The minimum fraction $d$ of genes that have to be modulated to make the ESs active, for each signature.
4. The minimum number $s$ of ESs that have to be active to make the function assume value $1$.

Then, the sign (over or under-expression) of the modulated genes and a range $[t_{\min},t_{\max}]$, where the procedure chooses the modulation thresholds $t_i$, are selected, in order to properly define the mappings $\beta_1$ and $\beta_2$ for the model (see the main paper). The procedure allows also to establish whether, inside the same ES, the genes are modulated when over (or under) expressed or if both types of modulation can coexist in the same ES. To control this step, three parameters for each EP are required:

• Number of positive (overexpressed) ESs in the EP;

• Number of negative (underexpressed) ESs in the EP;

• Number of heterogeneous ESs in the EP.

Furthermore, the procedure allows to define the number of mandatory ESs in each EP. These ESs are such that their activation is a necessary condition for the EP is verified.

Finally, the procedure permits to share some ESs between the EPs. When two EPs are to be constructed, four parameters can be set to distinguish different cases:

• Number of common ESs that are mandatory for both EPs;

• Number of common ESs that are not mandatory for both EPs;

• Number of common ESs that are mandatory for the first EP and are not mandatory for the second one;

• Number of common ESs that are not mandatory for the first EP and are mandatory for the second one.