Modelling Biochemical Reaction Networks Lecture 20: A genetic - - PowerPoint PPT Presentation

Modelling Biochemical Reaction Networks Lecture 20: A genetic toggle switch

Marc R. Roussel Department of Chemistry and Biochemistry

Recommended reading

◮ Lepzelter et al., J. Phys. Chem. B 111, 10239 (2007).

Genetic toggle switches

◮ There are many examples in biology of genes which should

not both be transcribed at the same time.

◮ Various solutions to this problem, including genetic toggle

switches, where one gene turns the other off, and vice versa (bistability).

◮ Synthetic toggle switches have been made.

Model for a genetic toggle switch

Oon

A + 2B hA

− ⇀ ↽ −

fA

Ooff

A

Oon

B + 2A hB

− ⇀ ↽ −

fB

Ooff

B

Oon

A gA

− → Oon

A + bAA

Oon

B gB

− → Oon

B + bBB

A k − → B k − →

Differential equation model

◮ Equations and parameters are given in the xppaut input file

toggle.ode.

◮ Look at what happens when you vary gA:

0.2 0.4 0.6 0.8 1 OONA 50 100 150 200 250 300 350 400 450 500 gA

Differential equation model

◮ Set hA = hB = 0.0005, fA = fB = 0.5, bA = bB = 1,

gA = gB = 100, and obtain the following by varying k:

0.2 0.4 0.6 0.8 1 OONA 1 2 3 4 5 k

Stochastic model

◮ Should in principle calculate stochastic rate constants, but

rate constants given above are not in any particular units, so just use them as is.

◮ File stoch_toggle.ode ◮ Stochastic switching in bistable regime:

20 40 60 80 100 120 140 160 180 molecules 100 200 300 400 500 600 700 time

Red=A Black=B