Piecewise synergetic systems and applications in biochemical systems theory

Abstract

We study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.

The best models of metabolism

“…As a compromise, piecewise S-system formulations have been proposed, which improve accuracy, but require more parameters. [174][175][176] Furthermore, Löwe et al 177 proposed a BST model reduction based on hierarchies of time-scales, which indeed can span several orders of magnitude in actual applications. 178 An entirely different type of metabolic model makes use of typical control strategies in cybernetics.…”