A practical kinetic model that considers endproduct inhibition in anaerobic digestion processes by including the equilibrium constant

Abstract

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.

Kinetic study of biogas production from energy crops and animal waste slurry: Effect of organic loading rate and reactor size

“…Furthermore, high-energetic substrates raise the danger of overloading. Several models and reactor configurations have been developed in recent years which make it possible to predict real process response to specific operation conditions [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For example, a simple model has been developed to describe the relation between the hydraulic retention time and methane yield in the digestion of animal waste [12,13].…”

Performance of a commercial-scale DiCOM™ demonstration facility treating mixed municipal solid waste in comparison with laboratory-scale data

“…6A). In-line with thermodynamic theory, propionate degradation required low hydrogen and 12 acetate concentrations, the precise inhibiting concentrations being able to be calculated 13 from the mole fraction of end products and substrates and the equilibrium constant of 14 the propionate degradation reaction (Hoh and Cord-Ruwisch, 1996). 15 …”

Modeling Microbial Communities: A Call for Collaboration between Experimentalists and Theorists

“…Thus, the incorporation of thermodynamic considerations is essential for achieving a precise characterization of low-abundance compounds. The aforementioned work by Hoh [33] made a significant contribution in this direction.…”

“…In order to rectify the limitations of these equations, Hoh and colleagues designed a kinetic model which takes into consideration rate-limiting factors and thermodynamic theory [33]. The model requires the following assumptions: (1) a reaction that has reached equilibrium cannot proceed in any direction due to the lack of a driving force (change in Gibbs free energy); (2) a reaction that is only slightly displaced from its equilibrium will proceed at a reduced rate compared to a reaction that is further away from equilibrium; (3) the model is free of any additional empirically measured parameters, excluding the organism-specific reaction rates incorporated into the original Michaelis-Menten kinetic equations.…”