Graph-theoretic topological control of biological genetic networks

The control of biological genetic networks is an important problem. If the system is abstracted into a graph, then the affect of drugs, pharmaceuticals, and gene therapy can be abstracted as changing the topology of the graph. We consider the control objective of removing the stable oscillations of the genetic network. This control is done using several theorems relating the topology of the network to the dynamics of the system. These theorems suggest that the controller should remove all the negative feedback in the networks.We prove that the problem of minimizing the edges and vertices to remove, in order to remove negative feedback, is NP-hard. In light of this result, a heuristic algorithm to solve this graph problem is presented. The algorithm is applied to several genetic networks, and it is shown that the heuristic gives reasonable results. Additionally, we consider the p53 network and show that the algorithm gives biologically relevant results.