Abraham van der Schaft

Complex and detailed balancing of chemical reaction networks revisited

The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff’s Matrix Tree theorem for directed weighted graphs. This yields an elucidation of previously obtained results, in particular with respect to the Wegscheider conditions, and a new necessary and sufficient condition for complex balancing, which can be verified constructively.

Integral regulation mechanism in phosphorylation cycles

In this paper, we study integral regulation mechanism in a class of phosphorylation cycles where we consider enzyme regulation by an intermediary metabolite. Using chemical reaction network framework, we prove that the network dynamics is (locally) asymptotically stable for sufficiently small integral gain. Furthermore, we show that the integral regulation ensures the absolute concentration robustness (ACR) property of the network.

Stability analysis of networked systems containing damped and undamped nodes

This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the damped nodes will always converge to a steady-state value, the convergence of the undamped nodes is much more delicate and depends on the parameter values of the network as well as on the topology of the graph. A complete stability analysis is presented based on an eigenvector analysis involving the system parameters and the topology of both the original graph and the reduced graph obtained by a Kron reduction that eliminates the damped nodes.