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 first control system with non-interacting oscillations.
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 s, 3, 425-438. (An abstract and a PDF version of the article are available to subscribers on the journal website.) PubMed ID: 5861813
|Schematic diagram of the first control system modelled in this study. Here Li is a genetic locus which produces messenger dbonudeic acid (mRNA) in quantities denoted by Xi. This mRNA then combines with ribosomes to form active protein-synthesizing aggregates (polysomes) designated by R, producing protein in quantity Yi. This protein assumed to be an enzyme then directs a metabolic transformation giving rise to a metabolic species M, which passes through a cellular pool, Pi. A fraction of the metabolite in the pool feeds back to the genetic locus where it serves to repress the activity of the gene, presumably in association with a macromolecule, the aporepresser.|