Simulation
Melanoma Application
Data (31 samples and 7 genes)
The 7 genes are WNT5A, pirin, S100P, RET1, MART1, HADHB and STC2.
Procedure to select the 10 attractor sets
At first 150( a large number compared to 31 samples) attractor sets (each set containing a random number of attractors between 2 and 5) are selected. From these 150 attractor sets, all those sets which are subsets of other sets are removed. From the remaining sets, we randomly select 10 sets and find the MSE between the original distribution and the overall distribution of these 10 attractor sets. This procedure is performed 10,000 times and the one with the lowest MSE is selected.
Algorithm 1 is used to generate 100 Boolean Networks for each attractor set. We randomly select one BN from each attractor set and form a PBN assuming equal probability for each BN. We compute the Mean Square Error between the Original Distribution of the data and the distribution of the data states in the PBN. As the BNs do not contain any cycles, the frequency corresponding to a particular state is the sum of the basin sizes for which that state is an attractor divided by the total number of states. This procedure is performed around 10,000 times and the PBN with the lowest MSE is selected.
The generated PBN is then run with the following values
Perturbation probability = .001,
Transition probability between networks = .001
Number of runs = 250,000.
