Control theory is a well-established approach in network science, with applications in bio-medicine and cancer research. We build on recent results for structural controllability of directed networks, which identifies a set of driver nodes able to control an a-priori defined part of the network. We develop a novel and efficient approach for the (targeted) structural controllability of cancer networks and demonstrate it for the analysis of breast, pancreatic, and ovarian cancer. We build in each case a protein-protein interaction network and focus on the survivability-essential proteins specific to each cancer type. We show that these essential proteins are efficiently controllable from a relatively small computable set of driver nodes. Moreover, we adjust the method to find the driver nodes among FDA-approved drug-target nodes. We find that, while many of the drugs acting on the driver nodes are part of known cancer therapies, some of them are not used for the cancer types analyzed here; some drug-target driver nodes identified by our algorithms are not known to be used in any cancer therapy. Overall we show that a better understanding of the control dynamics of cancer through computational modelling can pave the way for new efficient therapeutic approaches and personalized medicine.
Computational analysis of the structure of intra-cellular molecular interaction networks can suggest novel therapeutic approaches for systemic diseases like cancer. Recent research in the area of network science has shown that network control theory can be a powerful tool in the understanding and manipulation of such bio-medical networks. In 2011, Liu et al. developed a polynomial time algorithm computing the size of the minimal set of nodes controlling a linear network. In 2014, Gao et al. generalized the problem for target control, minimizing the set of nodes controlling a target within a linear network. The authors developed a Greedy approximation algorithm while leaving open the complexity of the optimization problem. We prove here that the target controllability problem is NP-hard in all practical setups, i.e., when the control power of any individual input is bounded by some constant. We also show that the algorithm provided by Gao et al. fails to provide a valid solution in some special cases, and an additional validation step is required. We fix and improve their algorithm using several heuristics, obtaining in the end an up to 10-fold decrease in running time and also a decrease in the size of solutions.
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