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August 2006 Half Adder - Modelling ETH Zürich | iGEM team 2006

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August 2006 ETH Zurich iGEM team 2006 2 ODE’s: Constitutive A u·k A A k A-Deg d[A ]/dt= u· k A - [A]· k A-Deg simplified: d[A ]/dt= 0 [A] = const. (high/low dep. on input u)

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August 2006 ETH Zurich iGEM team 2006 3 ODE’s: Induction kIkI I A d[A ]/dt= [I·DNA]·k A d[I ]/dt= [I·DNA]·k -I – [I]·[DNA]·k I d[DNA ]/dt= [I·DNA]·k -I – [I]·[DNA]·k I d[I·DNA ]/dt= [I]·[DNA]·k I – [I·DNA]·k -I [I·DNA]+[DNA]= const. [I·DNA]+[I]= const. I + DNA k -I I · DNAI · DNA + A kAkA

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August 2006 ETH Zurich iGEM team 2006 4 ODE’s: Repression kRkR R + DNA k -R R · DNA R A DNADNA + A kAkA d[A ]/dt= [DNA]·k A d[R ]/dt= [R·DNA]·k -R – [R]·[DNA]·k R d[DNA ]/dt= [R·DNA]·k -R – [R]·[DNA]·k R d[R·DNA ]/dt= [R]·[DNA]·k R – [R·DNA]·k -R [R·DNA]+[DNA]= const. [R·DNA]+[R]= const.

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August 2006 ETH Zurich iGEM team 2006 5 AND – 1 E1 E2 PoPS a b A B e1 e2 E1-active

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August 2006 ETH Zurich iGEM team 2006 6 AND – 1 (ODE’s) A B E2E2 E1E1 E 1 -act Out uAuA uBuB d[A]/dt= k A u A d[B]/dt = k B u B d[E 1 ]/dt= k E1 [A] - k E [E 1 ][E 2 ] + k -E [E 1 E 2 ] d[E 2 ]/dt= k E2 [B] - k E [E 1 ][E 2 ] + k -E [E 1 E 2 ] + k E1-act [E 1 E 2 ] d[E 1 E 2 ]/dt= k E [E 1 ][E 2 ] - k -E [E 1 E 2 ] - k E1-act [E 1 E 2 ] d[E 1 -act]/dt= k E1-act [E 1 E 2 ] d[Out]/dt= k out [E 1 -act] E2E2 E1E1 kAkA kBkB kEkE k -E k E1-act k Out k E1 k E2

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August 2006 ETH Zurich iGEM team 2006 7 AND – 2 E1 E2 PoPS a b A B i1 i2 E1 E2

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August 2006 ETH Zurich iGEM team 2006 8 AND – 3

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August 2006 ETH Zurich iGEM team 2006 9 uBuB k I1 A B I2I2 I1I1 Out uAuA k’ Out k I2,deg k I1,deg k I2 k Out,deg k’’ Out AND – 3 (ODE’s) d[A]/dt= k A u A d[B]/dt = k B u B d[I 1 ]/dt= k I1 m1 /([A] m1 - m1 ) – k I1,deg [I 1 ] d[I 2 ]/dt= k I2 m1 /([B] m1 - m1 ) – k I2,deg [I 1 ] d[Out]/dt= k’ Out m3 /([I 1 ] m3 - m3 ) k’’ Out m4 /([I 2 ] m4 - m4 ) – k Out,deg [Out] [X] m /([X] m - m ) 1 only qualitative!

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August 2006 ETH Zurich iGEM team 2006 10 AND – 4

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August 2006 ETH Zurich iGEM team 2006 11 XOR – 1

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August 2006 ETH Zurich iGEM team 2006 12 XOR – 1 (ODE’s) I1I1 Out uAuA d[I 1 ]/dt= k A1 u A – k I1I’1 [I 1 ][I’ 1 ] – k I1,deg [I 1 ] d[I’ 1 ]/dt= k A2 u A – k I1I’1 [I 1 ][I’ 1 ] – k I’1,deg [I’ 1 ] d[I 2 ]/dt = k B1 u B – k I2I’2 [I 2 ][I’ 2 ] – k I2,deg [I 2 ] d[I’ 2 ]/dt= k B2 u B – k I2I’2 [I 2 ][I’ 2 ] – k I’2,deg [I’ 2 ] d[I 1 I’ 1 ]/dt= k I1I’1 [I 1 ][I’ 1 ] d[I 2 I’ 2 ]/dt= k I2I’2 [I 2 ][I’ 2 ] d[Out]/dt= k I1 (1- m1 /([I 1 ] m1 - m1 )) + k I2 (1- m2 /([I 2 ] m2 - m2 )) – k Out,deg [Out] I’ 2 I2I2 I’ 1 I’ 2 uBuB I2I2 I’ 1 I1I1 k A1 k I1I’1 k A2 k B2 k B1 k Out,deg k I1,deg k I’1,deg k I’2,deg k I2,deg k I2I’2 k I1 k I2 Question: Should k I1I‘1 and k I2I‘2 be modelled as reversible reactions? OR

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August 2006 ETH Zurich iGEM team 2006 13 XOR – 2

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August 2006 ETH Zurich iGEM team 2006 14 XOR – 2 (ODE’s)

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August 2006 ETH Zurich iGEM team 2006 15 XOR – 3

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August 2006 ETH Zurich iGEM team 2006 16 XOR – 3 (ODE’s)

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