## Abstract

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 |
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Original language | English |

Publisher | Springer |

Volume | 1st Edition., 2011, XIII |

ISBN (Print) | 9781441967657 |

Publication status | Published - 2010 |