Mogens Høgh Jensen
Genetic circuits have been studied quite intensively in recent years. In particular, we have focussed on oscillatory patterns related to negative feed-back loops inside single cells in eucaryotic systems [1,2]. In many cases, however, it is of interest to study how cells communicate with each other when cells are arranged in certain spatial structures, like biofilms and tissues. We have attacked this problem by means of a repressor-lattice where single repressilators (closed feed-back loops) are placed on a hexagonal lattice . Such systems can be build without any internal frustration and can in most cases exhibit stable, oscillating states. Commensurability effects however play a role and may lead to internal frustration causing breaking of symmetries and solutions of many different phases. Eventually, also chaotic solutions may be present . We discuss both situations of directed and bi-directed interactions on the repressor-lattice.  S. Pigolotti, S. Krishna and M.H. Jensen, "Oscillation patterns in negative feedback loops", Proc.Nat.Acad.Sci. 104, 6533-6537 (2007).  S. Pigolotti, S. Krishna and M.H. Jensen, "Symbolic dynamics of biological feedback networks", Phys. Rev. Lett. 102, 088710 (2009).  M.H. Jensen, S. Krishna and S. Pigolotti, "The Repressor-Lattice: Feedback, Commensurability, and Dynamical Frustration, Phys. Rev. Lett. 103, 118101 (2009).