We model ultradian oscillations in four different eucaryotic systems: Hes1, p53-mdm2, NF-kB and Wnt-Notch. In each of the systems we identify the feed-back loops for the genetic regulations. Oscillations are possible when time delays are present, either by directly introducing a delay, by many steps in the loops or by saturated degradation. The oscillations are important for apoptosis and control of inflammation. The Wnt-Notch system is essential in embryo segmentation and we introduce a model in which the Wnt oscillates by itself but drives the Notch cycle out of phase with the Wnt cycle, in good agreement with experimental observations.
 

S. Krishna, M.H. Jensen and K. Sneppen, "Spiky oscillations in NF-kappaB signalling", Proc.Nat.Acad.Sci. 103, 10840-10845 (2006). S. Pigolotti, S. Krishna and M.H. Jensen, "Oscillation patterns in negative feedback loops", Proc.Nat.Acad.Sci., 104, 6533-6537 (2007). G. Tiana, S. Krishna, S. Pigolotti, M.H. Jensen and K. Sneppen, "Oscillations and temporal signalling in cells", Physical Biology 4, R1-R17 (2007).