Genetic toggle switch

A 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.^[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.^[ref] A population average alone could conceal two distinct subpopulations.

An original illustrative model uses dimensionless concentrations and time:For an asymmetric equilibrium, subtraction of the equilibrium equations gives $xy=1$, and substitution gives $x+y=3$. Thus the two alternatives areapproximately $(2.618,0.382)$ and $(0.382,2.618)$. The quadratic-Hill mutual repression switch analysis gives eigenvalues $-1\pm 2/3$ 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.

Mutual transcriptional repression is a gene regulatory network arrangement in which each of two gene products inhibits transcription of the other arm. A transcriptional repressor can bind a regulatory DNA region associated with the opposing promoter, reducing production of the other repressor. This is a mechanistic instance of mutual repression; it differs from suppressing an already made protein's activity.

Two inhibitory links can reinforce an imbalance: more of the first repressor reduces the second, releasing the first arm from inhibition. In a genetic toggle switch, this arrangement can support bistability. The 2000 experimental construction by Timothy S. Gardner, Charles R. Cantor and James J. Collins used opposing repressible promoters in Escherichia coli and demonstrated persistent expression alternatives after transient inputs.^[ref]

Repression alone does not guarantee two stable states. An original dimensionless model with weakly cooperative repression isAt an equilibrium, $x+xy=a=y+xy$, hence $x=y=r$, with $r^2+r=a$. The product of the two local repression slopes isThe mutual repression stability criterion therefore makes this unique positive equilibrium attracting. For $a=2$, $r=1$ and the Jacobian matrix has eigenvalues $-1\pm 1/2$. This circuit represses in both directions but has no alternative stable expression states in the stated model.

Stronger nonlinear responses, asymmetric production strengths and removal rates change the analysis. The quadratic-Hill mutual repression switch provides a contrasting cooperative model. Experimentally, measuring promoter output and protein turnover separately helps distinguish repression from changes in protein degradation. A reporter time course is evidence about a readout chain; it does not by itself locate the inhibited step.