Genetic circuits have been studied quite intensively in
recent years. We have focused on oscillatory
patterns in eucaryotic systems related to negative
feed-back loops inside single cells [1,2,3]. In many cases
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 [4]. 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 [3].
With bi-directed interactions the tissues locally
exhibit switch-like behavior. During growth the tissues may
develop ‘defects’ and we have found that mutations have
a larger effect in such cases than in ordered tissues.
[1] S. Pigolotti, S. Krishna and M.H. Jensen,
“Oscillation patterns in negative feedback loops”,
Proc.Nat.Acad.Sci. 104, 6533-6537 (2007).
[2] S. Pigolotti, S. Krishna and M.H. Jensen,
“Symbolic dynamics of biological feedback networks”,
Phys. Rev. Lett. 102, 088710 (2009).
[3] B. Mengel, A. Hunziker, L. Pedersen, A. Trusina,
M.H. Jensen and S. Krishna, “Modeling oscillatory control
in NF-kB, p53 and Wnt signaling”, Current Opinion in Genetics
and Development, doi:10.1016/j.gde.2010.08.008 (2010).
[4] M.H. Jensen, S. Krishna and S. Pigolotti,
“The Repressor-Lattice: Feedback, Commensurability,
and Dynamical Frustration, Phys. Rev. Lett. 103, 118101
(2009).
Niels Bohr Institute, Copenhagen, Denmark