l10_notes

l10_notes - Organizational Remarks: PS #2, 1b: Correction:...

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Unformatted text preview: Organizational Remarks: PS #2, 1b: Correction: Plot ka and kb for L = 0...2/KL (NOT: Plot ka and kb for L = 0...2KL ) 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: α u= 1 1 + vβ α 2 v= 1 + uγ Image removed due to copyright considerations. α du 1 −u = dt 1 + vβ α dv 2 −v = dt 1 + uγ 4 Adaptation (one stable fixed point) & y=0 y sfp ⎛ 2rin rin keff 4 + 2rin k pt (x , y ) = ⎜ , ⎜k ⎝ eff 4 keff 4 keff 2 ( L) * * ⎞ ⎟ ⎟ ⎠ & x=0 x & x = −(k pt + keff 4 ) x + keff 2 y + rin & y = k pt x − keff 2 y + rin 5 Oscillator (unstable fixed point) & y=0 y & x>0 & y<0 & x=0 & x>0 & y>0 ufp & x<0 & y>0 & x<0 & y<0 x 6 Oscillators continued .... & x = − x + ay + x 2 y & y = b − ay − x y 2 model for glycolysis nullclines: x y= a + x2 b y= a + x2 x* = b stable or unstable ? fixed point: b y= a + b2 * 7 & y=0 y & x>0 & y<0 & x=0 & x>0 & y>0 & x<0 & y>0 & x<0 & y<0 x 8 9 limitcycle y x x time 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 ...
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l10_notes - Organizational Remarks: PS #2, 1b: Correction:...

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