Saint Petersburg/AlgebraJP

From 2007.igem.org

< Saint Petersburg(Difference between revisions)
m (Bistable behaviour of two repressors, mutually repressing each other)
 
Line 1: Line 1:
==Bistable behaviour of two repressors, mutually repressing each other==
==Bistable behaviour of two repressors, mutually repressing each other==
-
[[Saint_Petersburg|Main page]] [[Saint_Petersburg/Algebra|Back to Main Algebra page]]
+
[[Saint_Petersburg|Main page]]  
 +
 
 +
[[Saint_Petersburg/Algebra|Back to Algebra page]]
Bifurcation set in (''J'', ''P'')  cross section is given by the following parametric equations:
Bifurcation set in (''J'', ''P'')  cross section is given by the following parametric equations:
-
+
[[Image:spb_eqn_028.gif]]
-
 
+
-
The cusp is located as shown in the figure below. While Q is increasing the cusp tip moves right and upwards.
+
 +
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.
 +
 +
[[Image:bifurc_JP1.gif]]
Important findings:
Important findings:
-
At constant value of Q and increasing values of P the behaviour changes in the following way:
+
At constant value of ''Q'' and increasing values of P the behaviour changes in the following way:
*Small ''P'' – monostable behaviour
*Small ''P'' – monostable behaviour
Line 24: Line 27:
See also:
See also:
-
[[Saint_Petersburg/Algebra|(''P,''Q'')-Cross Section]]
+
[[Saint_Petersburg/Algebra#The results|(''P,''Q'')-Cross Section]] - analysis of hysteresis existense
-
[[Saint_Petersburg/AlgebraJQ|(''J,''Q'')-Cross Section]]
+
[[Saint_Petersburg/AlgebraJQ|(''J,''Q'')-Cross Section]] - type of responce at various values of ''Q''

Latest revision as of 08:53, 22 October 2007

Bistable behaviour of two repressors, mutually repressing each other

Main page

Back to Algebra page

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

Spb eqn 028.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 JP1.gif

Important findings:

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

  • Small P – monostable behaviour
  • Intermediate P – Shmitt trigger/comparator
  • Large P – true trigger (sensitivity increase as P increase)
  • Very large P – monostable behaviour

See also:

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

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