Abstract
The paper is devoted to the extension of Brown’s model of enzyme kinetics to the case with distributed delays. Firstly, we construct a multi-substrate multi-inhibitor model using discrete and distributed delays. Furthermore, we consider simplified models including one substrate and one inhibitor, for which an experimental study has been performed. The algorithm of parameter identifications was developed which was tested on the experimental data of solution conductivity. Both the model and Kohlrausch’s law parameters are obtained as a result of the optimization procedure. Comparison of plots constructed with the help of the estimated parameters has shown that in such case the model with distributed delays is more chemically adequate in comparison with the discrete one. The methods of generalization of the results to the multi-substrate multi-inhibitor cases are discussed.
Highlights
Delayed systems play an important role in chemical kinetics [1,2]
Even for the complex network of the first order reactions, it can be described by relatively simple system of delayed differential equations, in which the effects of intermediates are replaced by time lags [3,4]
Since delay τ is rather a random variable than a deterministic one and can accept various values according to some distribution laws, here, we offer a considerably more advanced model which includes continuously distributed delays, which can be described by the differential equation with distributed delay: creativecommons.org/licenses/by/
Summary
Delayed systems play an important role in chemical kinetics [1,2]. Even for the complex network of the first order reactions, it can be described by relatively simple system of delayed differential equations, in which the effects of intermediates are replaced by time lags [3,4].The interaction between two chemicals A and B, forming the product C, is not instant but is during some time interval τ > 0. Delayed systems play an important role in chemical kinetics [1,2]. Even for the complex network of the first order reactions, it can be described by relatively simple system of delayed differential equations, in which the effects of intermediates are replaced by time lags [3,4]. The law of mass action as the fundamental law of chemical kinetics should be reformulated schematically as: Publisher’s Note: MDPI stays neutral k. Which is called the law of delayed mass action. Since delay τ is rather a random variable than a deterministic one and can accept various values according to some distribution laws, here, we offer a considerably more advanced model which includes continuously distributed delays (or distributed delays), which can be described by the differential equation with distributed delay: creativecommons.org/licenses/by/
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