= Genetic toggle switch
A \b[<genetic toggle switch>] is a <gene regulatory network> designed to retain one of two alternative expression states and to switch between them after an appropriate input. A common architecture uses <mutual repression>: each arm suppresses production from the other. Two inhibitory interactions can sustain the alternatives “high first arm, low second arm” and “low first arm, high second arm”. Memory requires <bistability> under the same continuing conditions, rather than two different steady responses forced by two different inputs.
In 2000, <Timothy S. Gardner>, <Charles R. Cantor> and <James J. Collins> constructed such a network in <Escherichia coli>. They used transient chemical or thermal induction to change the expression state.<Construction of a genetic toggle switch in Escherichia coli by Timothy S. Gardner and others>[Nature 403, pp. 339–341, Figure 4]{ref} Their <green fluorescent protein> readout was measured with a FACSCalibur <flow cytometer>, using 488 nm excitation and a 515–545 nm emission filter. Individual-cell <fluorescence> distributions distinguished high and low expression populations, including a bimodal distribution near the switching threshold.<Construction of a genetic toggle switch in Escherichia coli by Timothy S. Gardner and others>[p. 341, Figure 5; p. 342, Methods, Assay of gene expression]{ref} A population average alone could conceal two distinct subpopulations.
An original illustrative model uses dimensionless concentrations and time:
$$
\dot x=\frac3{1+y^2}-x,\qquad
\dot y=\frac3{1+x^2}-y.
$$
For an asymmetric <equilibrium>, subtraction of the equilibrium equations gives $xy=1$, and substitution gives $x+y=3$. Thus the two alternatives are
$$
(x,y)=\left(\frac{3+\sqrt5}{2},\frac{3-\sqrt5}{2}\right)
\quad\text{or their interchange},
$$
approximately $(2.618,0.382)$ and $(0.382,2.618)$. The <quadratic-Hill mutual repression switch> analysis gives <eigenvalues> $-1\pm2/3$ at either alternative, so small disturbances decay. These stipulated numbers illustrate the mechanism; they are not fitted parameters from the original constructs.
A transient perturbation can move the system across the boundary between the two <basins of attraction>, after which the other state persists without that perturbation. The <genetic toggle switch stability margin> measures one aspect of local return toward a state. Local attraction alone does not establish a second stable state, immunity to molecular noise, or indefinite cellular memory.
Back to article page
