Saint Petersburg/AlgebraJQ

From 2007.igem.org

Bistable behaviour of two repressors, mutually repressing each other

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Bifurcation set in (J, Q) cross section is given by the following parametric equations:

Spb eqn 030.gif

To obtain the bifurcation curve one should plot the second parameter versus the first, varying X from 0 to P+J. The cusp is located as shown in the figure below. While Q is increasing the cusp tip moves right and upwards.

Bifurc JQ1.gif

Figure. Cross section of bifurcation set by (J, Q) plane. The case with m=2, n=2, P=10 is shown.

Important findings:

The cusp in this cross-section is located as shown in fig XXX. While Q is increasing the cusp tip moves right and upwards.

Important findings:

At constant value of P and increasing values of Q the behaviour changes in the following way:

  • Small Q – monostable behaviour
  • Intermediate Q – full trigger
  • Large Q – Shmitt trigger/comparator (threshold level increase, while hysteresis width decrease as Q increase)
  • Very large Q – monostable behaviour

See also:

(P,Q)-Cross Section - analysis of hysteresis existense

(J,P)-Cross Section - type of responce at various values of P