Supplemental Document Cod-based Stationary Control Policy for Intervening in Large Gene Regulatory Networks " By

The current paper uses a 17-gene real-world derived network for comparing the performance of the CoD-CP with MFPT-CP and SSD-CP. The CoD-CP can be used for directly designing the stationary control policy on the 17-gene network and only need the SSD of the network. To compare the performance of the CoD-CP designed on the 17-gene network with the MFPT-CP and SSD-CP, we had to reduce the size of the network before being able to design the latter two intervention policies. We used the gene reduction method introduced in [2] and deleted genes consecutively until 10 genes were left in the network. At that point it was possible to design MFPT-CP and SSD-CP; then those policies were induced back to the original 17-gene network. The steady state distribution of the original 17-gene network is needed for designing the CoD-CP and also for reduction of the network. Due to the large size of the network it is computationally impossible to analytically derive the SSD of the network. We estimated the SSD of the network using the method proposed in [3]. The intuition behind the algorithm is to let the network transition for a long time and then use the Kolmogorov-Smirnov test to examine if the network reached its steady state. The method for deciding state transitions of the Markov Chain in the current paper differs slightly from the method which is used in [2]. The 17-gene network used in two papers are the same, but it is noted that the SSD shift toward Desirable states using induced MFPT-CP is different. The two different state transition methods led to both different steady-states of the networks and differences in the SSD shift after applying a control policy. In this section we describe these two state transition methods. The main assumption in [2] is that the decision to use either gene perturbation or the network's transition function for the next network transition is made with a probability of 0.5. Such an interpretation leads to using the network transition function approximately half of the time.