Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited

In biology, there are numerous examples where the (in)activation of one gene or protein can lead to a certain cellular functional state or phenotype. For instance, in a stable cancer cell line, the reproductive cell cycle is repeated, and cancerous cells proliferate with time in the absence of intervention. One can use the p53 gene if the intervention goal is to push the cells into apoptosis, or programmed cell death, to arrest the cell cycle. The p53 gene is the most well-known tumor suppressor gene, encoding a protein that regulates the expression of several genes such as Bax and Fas/APO1, which function is to promote apoptosis [1, 2]. In cultured cells, extensive experimental results indicate that when p53 is activated, for example, in response to radiation, it leads to cell growth inhibition or cell death [3]. The p53 gene is also used in gene therapy, where the target gene (p53 in this case) is cloned into a viral vector. The modified virus serves as a vehicle to transport the p53 gene into tumor cells to generate intervention [4, 5]. As this and many other examples suggest, it is prudent to use gene regulatory models to design therapeutic interventions that expediently modify the cell's dynamics via external signals. These system-based intervention methods can be useful in identifying potential drug targets and discovering treatments to disrupt or mitigate the aberrant gene functions contributing to the pathology of a disease.The main objective of intervention is to reduce the likelihood of encountering the undesirable gene-activity profiles associated with aberrant cellular functions. Probabilistic Boolean networks (PBNs), a class of discrete-time discrete-space Markovian gene regulatory networks, have been used to derive such therapeutic strategies [6]. These classes of models, which allow the incorporation of uncertainty into the inter-gene relationships, are probabilistic generalizations of the standard Boolean networks introduced by Kauffman [7–9]. In a P