2010 Research Summary

Topology Based Control of Genetic Regulatory Networks

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Anil Jayanti Aswani and Claire Tomlin

National Science Foundation CCR-0225610

The traditional control scheme has been to input a signal into a plant, where the signal is derived from either an open-loop or a closed-loop. This control strategy requires that the plant be able to accept inputs or can be modified to do so. However, this situation is not always true in biological genetic networks; in these systems, there is often no input or obvious modification to allow inputs. We believe that they require a new paradigm for control. Biotechnology techniques are such that it is easier to make topological changes to a genetic network than it is to either change the states of the pathway or add more elements to the pathway. Thus, for such genetic networks it is important to develop a theory of control based on making large- scale changes (e.g. genetic mutations) to the topology of the network; we provide steps towards such a theory. We highlight some useful results from monotone and hybrid systems theory, and show how these results can be used for such a topological control scheme. We consider the cancer-related p53 pathway as an example; we analyze this system using control theory and devise a controller.

Figure 1: The time course plots for the different pathways display the effect of the abnormality and the controller. Note that p53 is solid, cyclin A is dashed, and MDM2 is dash- dotted.

[1]

A. Aswani and C. Tomlin, “Topology based control of biological genetic networks,” In Proceedings of 47th IEEE CDC: 781-786.

[2]

Graph-theoretic topological control of biological genetic networks, In Proceedings of the ACC 2009: 1700-1705.