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Half Adder - Modelling

Half Adder - Modelling. ETH Zürich | iGEM team 2006. ODE’s: Constitutive. A. A. u·k 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). ODE’s: Induction. I. A. k I. k A. I + DNA. I · DNA. I · DNA + A. k -I.

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Half Adder - Modelling

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  1. Half Adder - Modelling ETH Zürich | iGEM team 2006

  2. ODE’s: Constitutive A A u·kA kA-Deg d[A]/dt = u·kA - [A]·kA-Deg simplified: d[A]/dt = 0  [A] = const. (high/low dep. on input u)

  3. ODE’s: Induction I A kI kA I + DNA I · DNA I · DNA + A k-I d[A]/dt = [I·DNA]·kA d[I]/dt = [I·DNA]·k-I – [I]·[DNA]·kI d[DNA]/dt = [I·DNA]·k-I – [I]·[DNA]·kI d[I·DNA]/dt = [I]·[DNA]·kI – [I·DNA]·k-I [I·DNA]+[DNA] = const.[I·DNA]+[I] = const.

  4. ODE’s: Repression kR R R + DNA R · DNA A k-R kA DNA DNA + A d[A]/dt = [DNA]·kA d[R]/dt = [R·DNA]·k-R – [R]·[DNA]·kR d[DNA]/dt = [R·DNA]·k-R – [R]·[DNA]·kR d[R·DNA]/dt = [R]·[DNA]·kR – [R·DNA]·k-R [R·DNA]+[DNA] = const.[R·DNA]+[R] = const.

  5. AND – 1 a PoPS E1-active A E1 PoPS e1 e2 E2 B PoPS b

  6. A B E2 E1 E2 E1 Out AND – 1 (ODE’s) uA kA k-E kE1-act E1-act kE1 kE kE2 kOut kB d[A]/dt = kAuA d[B]/dt = kBuB d[E1]/dt = kE1[A] - kE[E1][E2] + k-E[E1E2] d[E2]/dt = kE2[B] - kE[E1][E2] + k-E[E1E2] + kE1-act[E1E2] d[E1E2 ]/dt = kE[E1][E2] - k-E[E1E2] - kE1-act[E1E2] d[E1-act]/dt = kE1-act[E1 E2] d[Out]/dt = kout[E1-act] uB

  7. AND – 2 a PoPS A E1 PoPS i1 E1 E2 i2 E2 B PoPS b

  8. AND – 3

  9. m/([X]m-m) A B I2 I1 only qualitative! 1 Out [X]  AND – 3 (ODE’s) uA kI1,deg kI1 k’Out kOut,deg kI2 k’’Out kI2,deg uB d[A]/dt = kAuA d[B]/dt = kBuB d[I1]/dt = kI1 m1/([A]m1-m1) – kI1,deg[I1] d[I2]/dt = kI2 m1/([B]m1-m1) – kI2,deg[I1] d[Out]/dt = k’Outm3/([I1]m3-m3) k’’Outm4/([I2]m4 - m4) – kOut,deg[Out]

  10. AND – 4

  11. XOR – 1

  12. I’2 I2 I1 I’1 I1 I’1 I’2 I2 Out XOR – 1 (ODE’s) kI1,deg kI1 kA1 Question: Should kI1I‘1 and kI2I‘2 be modelled as reversible reactions? uA kI1I’1 kA2 kI’1,deg kOut,deg d[I1]/dt = kA1uA – kI1I’1[I1][I’1] – kI1,deg[I1] d[I’1]/dt = kA2uA – kI1I’1[I1][I’1] – kI’1,deg[I’1] d[I2]/dt = kB1uB – kI2I’2[I2][I’2] – kI2,deg[I2] d[I’2]/dt = kB2uB – kI2I’2[I2][I’2] – kI’2,deg[I’2] d[I1I’1]/dt = kI1I’1[I1][I’1] d[I2I’2]/dt = kI2I’2[I2][I’2] d[Out]/dt = kI1(1- m1/([I1]m1-m1)) + kI2(1- m2/([I2]m2 - m2)) – kOut,deg[Out] kI’2,deg kB2 uB kI2I’2 kI2 kB1 kI2,deg OR

  13. XOR – 2

  14. XOR – 2 (ODE’s)

  15. XOR – 3

  16. XOR – 3 (ODE’s)

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