A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML version of the model has been checked in COR and OpenCell and the model runs to replicate the results in the original published paper. The units have been checked and are consistent.
Model Structure
ABSTRACT: Many organisms display rhythms of physiology and behavior that are entrained to the 24-h cycle of light and darkness prevailing on Earth. Under constant conditions of illumination and temperature, these internal biological rhythms persist with a period close to 1 day ("circadian"), but it is usually not exactly 24 h. Recent discoveries have uncovered stunning similarities among the molecular circuitries of circadian clocks in mice, fruit flies, and bread molds. A consensus picture is coming into focus around two proteins (called PER and TIM in fruit flies), which dimerize and then inhibit transcription of their own genes. Although this picture seems to confirm a venerable model of circadian rhythms based on time-delayed negative feedback, we suggest that just as crucial to the circadian oscillator is a positive feedback loop based on stabilization of PER upon dimerization. These ideas can be expressed in simple mathematical form (phase plane portraits), and the model accounts naturally for several hallmarks of circadian rhythms, including temperature compensation and the per(L) mutant phenotype. In addition, the model suggests how an endogenous circadian oscillator could have evolved from a more primitive, light-activated switch.
model diagram
Schematic diagram of a simple molecular mechanism for the circadian clock in Drosophila PER and TIM proteins are synthesised in the cytoplasm where they may either be degraded by proteolysis or alternatively they may combine to form relatively stable heterodimers. These complexes are then transported to the nucleus where they act to inhibit the transcription of per and tim mRNA.
The original paper reference is cited below:
A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM, John J. Tyson, Christian I. Hong, C. Dennis Thron, and Bela Novak, 1999,Biophysical Journal, 77, 2411-2417. PubMed ID: 10545344
M
mRNA concentration
$\frac{d M}{d \mathrm{time}}=\frac{\mathrm{vm}}{1.0+\left(\frac{\mathrm{Pt}(1.0-q)}{2.0\mathrm{Pcrit}}\right)^{2.0}}-\mathrm{km}Mq=\frac{2.0}{1.0+\sqrt{1.0+8.0\mathrm{Keq}\mathrm{Pt}}}$
Pt
total protein concentration
$\frac{d \mathrm{Pt}}{d \mathrm{time}}=\mathrm{vp}M-\frac{\mathrm{kp1}\mathrm{Pt}q+\mathrm{kp2}\mathrm{Pt}}{\mathrm{Jp}+\mathrm{Pt}}+\mathrm{kp3}\mathrm{Pt}$
circadian rhythms
oscillator
TIM
PER
72
c.lloyd@auckland.ac.nz
The University of Auckland, Auckland Bioengineering Institute
Catherine Lloyd
10545344
The University of Auckland
The Bioengineering Institute
This is a CellML description of Tyson et al.'s 1999 simple mathematical model of circadian rhythms based on dimerisation and proteolysis of PER and TIM.
keyword
Catherine Lloyd
C
Thron
Dennis
A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM
77
2411
2417
2007-10-03T00:00:00+00:00
Catherine
Lloyd
May
Bela
Novak
This CellML version of the model has been checked in COR and PCEnv and the model runs to replicate the results in the original published paper. The units have been checked and are consistent.
1999-11-00 00:00
John
Tyson
J
Tyson et al.'s 1999 simple mathematical model of circadian rhythms based on dimerisation and proteolysis of PER and TIM.
Biophysical Journal
Christian
Hong
I