Model Status
This CellML model runs in both OpenCell and COR to recreate the published results. The units have been checked and they are consistent. This particular version of the model describes the second control system with interactions between non-linear oscillations.
Model Structure
ABSTRACT: THE demonstration of negative feedback control processes operating at the molecular level in cells is one of the most significant developments in modern biology. The phenomena of feedback inhibition and feedback repression, whereby enzymatic activities are controlled at the level of the enzyme and the gene, respectively, provide a firm experimental basis for the construction of dynamic models which represent the fundamental regulatory activity of cells. The behavior of these and other molecular control circuits thus constitutes the basis of cell physiology, and in effect provides the physiologist with his elementary units of function. The purpose of this paper is to illustrate the type of periodic behavior which can arise in model systems incorporating the essential control features of enzymatic regulatory processes, and to discuss the significance of oscillatory motion in relation to the organization of cellular processes in time.
The complete original paper reference is cited below:
Oscillatory behavior in enzymatic control processes, Brian C. Goodwin, 1965, Advances in Enzyme Regulation
, 3, 425-438. (An abstract and a PDF version of the article are available to subscribers on the journal website.) PubMed ID: 5861813
cell diagram
Schematic diagram of the second control system modelled in this study. It is to be expected from the complexity of intracellular processes that control circuits will interact in some manner. One type of interaction which seems very probable is for the repressor of one genetic locus to have a repressive effect on another locus. This situation can be represented schematically here.
X1
concentration of mRNA of the 1st species
$\frac{d \mathrm{X1}}{d \mathrm{time}}=\frac{\mathrm{a1}}{\mathrm{A1}+\mathrm{k11}\mathrm{Y1}+\mathrm{k12}\mathrm{Y2}}-\mathrm{b1}$
Y1
concentration of protein of the 1st species
$\frac{d \mathrm{Y1}}{d \mathrm{time}}=\mathrm{alpha\_1}\mathrm{X1}-\mathrm{beta\_1}$
X2
concentration of mRNA of the 2nd species
$\frac{d \mathrm{X2}}{d \mathrm{time}}=\frac{\mathrm{a2}}{\mathrm{A2}+\mathrm{k21}\mathrm{Y1}+\mathrm{k22}\mathrm{Y2}}-\mathrm{b2}$
Y2
concentration of protein of the 2nd species
$\frac{d \mathrm{Y2}}{d \mathrm{time}}=\mathrm{alpha\_2}\mathrm{X2}-\mathrm{beta\_2}$
1965-00-00 00:00
Brian
Goodwin
C
2008-09-26T00:00:00+00:00
This CellML model runs in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. This particular version of the model describes the second control system with interactions between non-linear oscillations.
5861813
Catherine Lloyd
keyword
circadian rhythms
The University of Auckland
Auckland Bioengineering Institute
Advances in Enzyme Regulation
Oscillatory behavior in enzymatic control processes (Model 2)
This CellML model runs in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. This particular version of the model describes the second control system with interactions between non-linear oscillations.
Oscillatory behavior in enzymatic control processes
3
425
438
Catherine Lloyd
80
false
0.1
10000
true
0.01
c.lloyd@auckland.ac.nz
Catherine
Lloyd
May