Mathematical models of the prokaryotic control systems of tryptophan biosynthesis (both normal and with cloned blocks) and arabinose catabolism have been built using the method of generalized threshold models. Kinetic curves for molecular components (mRNAs, proteins, metabolites) of the systems considered are obtained. It has been shown that the method of generalized threshold models gives a more detailed qualitative picture of the dynamics of the molecular genetic control systems in comparison with the heuristic method of threshold models. The qualitative analysis of the functioning of the following mechanisms of control of the tryptophan biosynthesis: (1) inhibition of the activity of anthranilate synthetase by tryptophan, (2) repression and (3) attenuation of transcription of the tryptophan operon on the basis of the mathematical model of the control system of the tryptophan biosynthesis demonstrates that feedback inhibition is the most operative of the considered mechanisms while repression allows the bacterium to economize intracellular resources. As regards the control system of the arabinose catabolism the results of modelling enable us to state the following. The induction by arabinose within a wide range of parameter values causes two subsystems (araBAD and transport operons) of the arabinose regulon with a low rate of arabinose utilization to pass into a stationary regime and one subsystem (araC operon) to pass into a stable periodical regime. A study of the system characterized by the effective utilization of arabinose has shown that under induction by arabinose stable oscillations with small amplitudes of the concentration of regulatory protein and oscillations with large amplitudes of the concentrations of arabinose-isomerase and transport protein may occur. The period of the oscillation depends on the mean lifetime of the "activator-DNA" complex and on the rate constant of arabinoseisomerase degradation.
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