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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): 3358. 11 ...
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.
 Spring '08
 BobSauer

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