A refined mathematical model (N2) was developed and analyzed; the model describes the generation of relaxation auto-oscillations in the open reaction E(A,B) -S,-S,- in which the enzyme E(A, B) is covalently modified by the modifying enzymes EA and EB such a way that the active A form of enzyme is converted to the inactive B form by enzyme EA, and the B form in reactivated to the A form by enzyme EB. The M2 model assumes that the substrate S1 and the product S2 competitively inhibit the inactivating enzyme EA. The system described by M2, like the previously described phenomenological model M1 (E. E. Sel'kov and I. I. Goryanin, Mol. Biol., 20, 1550-1562 (1986)), was shown to be able to undergo relaxation auto-oscillation. Asyptotic equations for the quasi-stationary rate of the reaction S1 → S2 were derived, taking all enzyme-ligand complexes of enzymes E, EA, and EB into consideration, and asymptotic expressions for the period and amplitude of the relaxation oscillations were also deduced. Good qualitative and quantitative agreement was demonstrated between experimentally measured oscillation periods for the M1 and M2 models and values obtained by numerical integration of the M2 model in conditions in which the total enzyme concentration E(A, B) was significantly greater than the total concentrations of enzymes EA and EB.
|Number of pages||13|
|Publication status||Published - 1992|