Organizational Remarks: PS #2, 1b: Correction: Plot k a and k b for L = 0...2/K L (NOT: Plot k a and k b for L = 0...2K L ) Tomorrow’s recitation topic: ‘PS #2 support’ 1 Dynamical response of switches, chemotactic network and oscillators ‘switch’ adaptation (differentiator, at least for small frequencies) oscillator 2 Dynamical response of switches, chemotactic network and oscillators two stable fixed points one stable fixed point unstable fixed point 3 nullclines: γ u1 2 α v β v1 1 α u + = + = Image removed due to copyright considerations. v γ u1 2 α dt dv u β v1 1 α dt du ? + = ? + = 4 y x ineffpt ineffeffpt rykxky rykxkkx +?= +++?= 2 24 )( & & 0=y & 0=x & ? ? ? ? ? ? ? ? + = )( 2 , 2 ),( 24 4 4 ** Lkk krkr k r yx effeff ptineffin eff in Adaptation (one stable fixed point) sfp 5 Oscillator (unstable fixed point) 0 0 > > y x & & 0 0 > < y x & & 0 0 < > y x & & 0 0 < < y x & & 0=x & 0=y & ufp y x 6 Oscillators continued .... yxayby yxayxx 2 2 ??= ++?= & & model for glycolysis 2 2 xa b y xa x y + = + = nullclines: 2 * * ba b y bx + = = fixed point: stable or unstable ? 7 0 0 > > y x & & 0 0 > < y x & & 0 0 < > y x & & 0 0 < < y x & & 0=x & 0=y & y x 8 9 limitcycle x x time y 10 Image removed due to copyright considerations. See figures 1, 2, 3 in Elowitz, M. B., S. Leibler. "A synthetic oscillatory network of transcriptional regulators." Nature 403, no. 6767 (Jan 20, 2000): 335-8. 11