The classical Michaelis‐Menten model is widely used as the basis for modeling of a number of biological systems. As the model does not consider the inhibitory effect of endproducts that accumulate in virtually all bioprocesses, it is often modified to prevent the overestimation of reaction rates when products have accumulated. Traditional approaches of model modification use the inclusion of irreversible, competitive, and noncompetitive inhibition factors. This article demonstrates that these inhibition factors are insufficient to predict product inhibition of reactions that are close the dynamic equilibrium. All models investigated were found to violate thermodynamic laws as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. For modeling of biological processes that operate close to the dynamic equilibrium (e.g., anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached the dynamic equilibrium. This can be achieved by using a reversible kinetic model. However, the major drawback of the reversible kinetic model is the large number of empirical parameters it requires. These parameters are difficult to determine and prone to experimental error. For this reason, the reversible model is not practical in the modeling of biological processes. This article uses the fundamentals of steady‐state kinetics and thermodynamics to establish an equation for the reversible kinetic model that is of practical use in bio‐process modeling. The behavior of this equilibrium‐based model is compared with Michaelis‐Menten‐based models that use traditional inhibition factors. The equilibrium‐based model did not require any empirical inhibition factor to correctly predict when reaction rates must be zero due to the free energy change being zero. For highly exergonic reactions, the equilibrium‐based model did not deviate significantly from the Michaelis‐Menten model, whereas, for reactions close to equilibrium, the reaction rate was mainly controlled by the quotient of mass action ratio (concentration of all products over concentration of all substrates) over the equilibrium constant K. This quotient is a measure of the displacement of the reaction from its equilibrium. As the new equation takes into account all of the substrates and products, it was able to predict the inhibitor effect of multiple endproducts. The model described is designed to be a useful basis for a number of different model applications where reaction conditions are close to equilibrium.

No abstract

For modeling of biological processes that operate close to the dynamic equilibrium (eg. anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached dynamic equilibrium. Traditional Michaelis-Menten based models were found to violate the laws of thermodynamics as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. The inclusion of empirical “product inhibition factors” as suggested by previous work could not prevent this problem. This paper compares the predictions of the Michaelis-Menten Model (with and without product inhibition factors) and the Equilibrium Based Model (which has a thermodynamic term introduced into its rate equation) with experimental results of reactions in anaerobic bacterial environments. In contrast to the Michaelis-Menten based models that used traditional inhibition factors, the Equilibrium Based Model correctly predicted the nature and the degree of inhibition due to endproduct accumulation. Moreover, this model also correctly predicted when reaction rates must be zero due to the free energy change of the conversion reaction being zero. With these added advantages, the Equilibrium Based Model thus seemed to provide a scientifically correct and more realistic basis for a variety of models that describe anaerobic biosystems.

No abstract