In this chapter, we present a theoretical framework for the analysis, synchronization and control of biochemical circuits and systems modeled by means of ODEs. The methodology is based on the use of contraction theory, a powerful concept from the theory of dynamical systems, ensuring convergence of all trajectories of a system of interest towards each other. After introducing contraction theory, we present some application to biochemical networks. Specifically, we introduce a graphical approach to verify if a system is contracting and apply it to synthesize networks of self-synchronizing Repressilators. We then present a more general analysis of quorum sensing networks and discuss the role of symmetry to explain the dynamics of incoherent feedforward loops common in biological networks.
|Translated title of the contribution||Design and Analysis of Biomolecular Circuits|
|Volume||1st Edition., 2011, XIII|
|Publication status||Published - 2010|