Relating cross Gramians and sensitivity analysis in systems biology.
Streif, Stefan and Findeisen, Rolf and Bullinger, Eric (2006) Relating cross Gramians and sensitivity analysis in systems biology. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), July 24-28, 2006, Kyoto International Conference Hall, Kyoto, Japan.
One of the key challenges in systems biology is the analysis of often complex biochemical reacation networks which contain many uncertain parameters. Typically, the dynamics of these systems strongly depends on a significant amount of parameters, hampering the analysis significantly as even the small changes in the value of the parameters can have significant influences on the overall behaviour of the entire network. Thus one of the key problems in systems biology is to analyse the influence of parameters on the steady state and transient behaviour. In the first part of this work we derive links between first order sensitivity analysis as typically employed in systems biology and the concepts of controllability and observability of systems theory. Specifically we establish a close connection between cross Gramians and the so called response coefficients as used in Metabolic Control Analysis. In a second part we outline an expansion of this approach using empirical cross Gramians, allowing to overcome some of the limitations of first order sensitivity methods such as local validity.
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