McAdams and Arkin report the following synthetic biology oscillator circuit in their paper “Gene regulation: Towards a circuit engineering discipline” :
The circuit works by having gene R1’s protein inhibit production of R3, who’s protein inhibits production of R2, which in turn inhibits production of R1. Delays in the inhibition processes cause sufficient expression of each gene to allow the amounts of each protein present to oscillate.
I took a crack at simulating such a system with Vensim, a system dynamics software package:
Here the boxes represent the amount of the given protein in the cell. The inward flows model gene expression, the rate of which is modulated by the amount of their associated protein. I also made the assumption that the proteins degrade or are otherwise removed from the cell, which I modeled with first-order dynamics (the outward flows). I set the initial values of R1, R2, and R3 to 10, 0, and 0, respectively. The Vensim model file is attached to the bottom of this post.
Simulating this system shows the expected steady-state oscillation:
- McAdams, Harley, and Arkin, Adam. Gene regulation: Toward a circuit engineering discipline. Current Biology, 2000.