Model Status
This CellML model runs in both OpenCell and COR, however it does not recreate the published results - the CellML model does not oscillate. The units have been checked and they are consistent. This particular version of the model describes the third control system of a circuit with limit cycles. We suspect the CellML model does not oscillate because it does not include time delays. These are mentioned in the main body of text in the published paper, but they are not descibed mathematically in the model equations.
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 third control system modelled in this study: a control circuit with limit-cycle characteristics.
X1
concentration of the nuclear messenger
$\frac{d \mathrm{X1}}{d \mathrm{time}}=\frac{\mathrm{a1}}{\mathrm{A1}+\mathrm{k1}\mathrm{Z1}}-\mathrm{b1}\mathrm{X1}$
Y1
concentration of the active cytoplasmic messenger
$\frac{d \mathrm{Y1}}{d \mathrm{time}}=\mathrm{alpha\_1}\mathrm{X1}-\mathrm{beta\_1}\mathrm{Y1}$
Z1
concentration of the active enzyme
$\frac{d \mathrm{Z1}}{d \mathrm{time}}=\mathrm{gamma\_1}\mathrm{Y1}-\mathrm{delta\_1}\mathrm{Z1}$
This CellML model runs in both PCEnv and COR, however it does not recreate the published results - the CellML model does not oscillate. The units have been checked and they are consistent. This particular version of the model describes the third control system of a circuit with limit cycles. We suspect the CellML model does not oscillate because it does not include time delays. These are mentioned in the main body of text in the published paper, but they are not descibed mathematically in the model equations.
Oscillatory behavior in enzymatic control processes (Model 3)
Catherine
Lloyd
May
Oscillatory behavior in enzymatic control processes
3
425
438
Brian
Goodwin
C
c.lloyd@auckland.ac.nz
2008-09-26T00:00:00+00:00
keyword
circadian rhythms
Advances in Enzyme Regulation
The University of Auckland
Auckland Bioengineering Institute
5
1965-00-00 00:00
Catherine Lloyd