|In metabolic reaction networks, the analysis of enzyme levels yielding a desired phenotype is an interesting problem for 1. fundamental understanding how biological systems are constructed, and 2. re-designing such systems for industrial (e.g. improved product formation) or medical applications (e.g. finding new drug targets).
Recently, the concept of feasibility space has been developed in our group in order to analyze the design space of metabolic reaction networks . Since the dynamics of metabolic reaction networks are highly complex and non-linear, it it is of great value to determine the set of regulatory states (enzymes) that achieve a set of desired physiological states (metabolites, fluxes) under a number of thermodynamic and physiological constraints.
The recently-developed concepts of nonlinear inversion and of flatness [2,3], both developed within systems theory, extend the known notion of controllability to nonlinear dynamical systems.
The fundamental goal of controllability is that to explicitly express all states and inputs as a function of a desired output of the model.
Inspired by an application to study general trajectory planning problems for nonlinear models,
we plan to employ the aforementioned techniques to formally devise enzyme profiles that steer the model dynamics according to certain phenotypes.
This will allow us to find out the set of feasible regulatory states (enzymes) controlling desired outputs (physiological states), under dynamic physiological constraints.
 E. Nikerel et al., 2010, ``Understanding regulation via feasibility spaces,'' under review.
 S. Devasia, D. Chen and B. Paden ``Nonlinear Inversion-Based Output Tracking,'' IEEE Transactions on Automatic Control, Vol. 41 (7), pp. 930-942, July 1996.
 R. Fliess et al., 1995, ``Flatness and defect of non-linear systems: Introductory theory and examples'' International Journal of Control 61(6), pp. 1327-1361.