Type I Type II, PRCs and Coupling

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Presentation transcript:

Type I Type II, PRCs and Coupling Daniel Forger

Through what mechanism do oscillations appear? 2

Type 1 Integrator 3

4

With such a mechanism Oscillations abruptly start or stop The period changes drastically when parameters are changed The system does not resonate, instead it needs to get kicked 5

Type 2 Resonator 6

With such a mechanism Oscillations switch from decaying very slowly to growing very slowly The period of the oscillations barely changes when going through the bifurcation The system “resonates” 7

Chaotic Entrainment 8

Type I vs. Type II PloS Computational Biology 2:e30

Design I

Design II

Coupling by sharing a protein

Coupling by sharing a protein

Coupling by extracellular signaling Garcia-Ojalvo et al. PNAS 101:10955

Order Parameter

Coupling can reduce noise

Phase Shifting Glass and Winfree AJP 246:R251

PRC Atlas

Formula for the PRC Point D is on a limit Cycle We perturb in the positive horizontal direction

0-D phaseless region

1-D phaseless region

2-D Phaseless Region 28

29

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Ukai, Nature Cell Biology 9:1327