Coupled Oscillators and Arnold Tongues in Cell Dynamics !!!!!!!!AV60,!Rome!,!22!Sep!20140 !Mogens!H.!Jensen,!Niels!Bohr!Institute0 1.  Two oscillators couple: One internal to one external: Arnold tongues or entrainment ! 2. Biological oscillations: Cell cycle, circadian, calcium, embryos, proteins (DNA damage) 3. Oscillations of a protein density inside a cell: regulated by negative feed-back loops (NF-κB, p53, Wnt proteins): DNA damage, inflammation, embryo segmentation. 4. An external (cytokine or protein) oscillation coupled to internal oscillation: Oscillations synchronize (entrain) Arnold tongues → Chaotic attractors 5. Pulsatile extracellular signaling: A way to control cell dynamics ? A way to control embryo segmentation ? 6. Distinguish a non-linear from a linear, noisy systems: Occurrences of Arnold tongues ? Collaborators: •  Sandeep Krishna, Uri Alon, Namiko Mitarai, Leo Kadanoff, M.H. Jensen and S. Krishna, “Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli”, FEBS Letters 586, 1664-1668 (2012). N. Mitarai, U. Alon and M.H. Jensen, “Entrainment of linear and non-linear system under noise”, Chaos, 23, 023125 (2013) Leo Kadanoff and M.H. Jensen, “Global and Local: Synchronization and Emergence”, Review (2012) Oscillations:!S.!PigoloFi,!L.!Pedersen,!B.!Mengel,!A.!Trusina,!P.!Jensen,!P.!Yde,0 !!!!!!!!!!!!!!!!!!!!!!!S.!Chakraborty,!S.!Semsey,!A.!Hunziker,!K.!Moss,!J.!Juul…….0 Congratulations Angelo !! It has been a FANTASTIC experience to collaborate with you Yours knowledge about dynamical systems and physics is truly amazing You are a true scholar ! !!Synchronization!of!two!oscillators0 !!!!!!!!!!!!!!Huygens’!clocks!16650 Three!different!nonWlinear!dynamics0 Two!coupled!oscillators:!Arnold!tongues0 Examples!of!Arnold!tongues!!0 Examples!of!Arnold!tongues!!0 Chicago!basement!convection!!0 Stavans,!Heslot,!Libchaber0 Glazier,!Jensen,!Libchaber,!Stavans0