Bistable system

A biological toggle switch can be formed by two mutually cooperatively repressing gene products. Left: suppose that initially, the number of molecules of one of the species dominates the other species. Then the production of that species is inhibited and the system finds a stable state. However, by a certain small probability the stochastic noise can make the system switch and due to this 'tunneling' effect, the roles of the two species suddenly change. Right: here the system starts with the same number of molecules of both kinds and the system becomes symmetric; this example demonstrates the sensivity with respect to the initial configuration.

Toggle switches are interesting entites because they can be though of as a biological transistor. Not much effort needs to be spent in switching the state of the system ("1" or "0") and, depending on the parameters of the reactions, the switch will with high probablity remain in its state.

(Plot info: each axis tick is 25 molecules and the contour levels have been chosen by Matlab)


  • S. Engblom: Spectral Approximation of Solutions to the Chemical Master Equation, in J. Comput. Appl. Math. 229(1):208--221, 2009: (doi)
  • S. Engblom: Galerkin Spectral Method applied to the Chemical Master Equation, in Commun. Comput. Phys. 5(5):871--896, 2009: (abstract), (pdf).

  • Stefan Engblom
    Last modified: Thu May 10 11:04:19 MEST 2007