Abstract
The specific consumption rate of substrate, as well as the associated specific growth rate, is an essential parameter in the mathematical description of substrate-limited microbial growth. In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails. Additionally, our model converges asymptotically to Michaelis-Menten predictions as substrate concentration increases. Instead of the single active site enzymatic reaction of Michaelis-Menten type, the proposed model assumes a multi-site kinetics, simplified as an apparent all-or-none mechanism for the transport, which is controlled by means of the local substrate concentration in the close vicinity of the transport protein. Besides, the model also assumes that this local concentration is not equal to the mean substrate concentration experimentally determined in the culture medium. Instead, we propose that it fluctuates with a mostly exponential distribution of Weibull type.
Highlights
Due to the microscopic nature of single microbial cells, the knowledge and mathematical modelling of the mechanisms controlling growth of microbial populations is considered essential to analyze, predict, and control the effect of microbes in nature and industry
In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails
Considering fixed amount of substrate, fixed external conditions, and no volume limitations, it is assumed that the specific growth rate is a function μ(C) of the substrate concentration C, and that the specific consumption rate is likewise a function q(C) of the substrate concentration
Summary
Due to the microscopic nature of single microbial cells, the knowledge and mathematical modelling of the mechanisms controlling growth of microbial populations is considered essential to analyze, predict, and control the effect of microbes in nature and industry. Among the factors controlling microbial growth, its dependence on the concentration in the medium of the carbon and energy source is recognized as one of the most relevant ones. The equation developed by Monod [1], which describes a hyperbolic dependence of the specific growth rate on the external concentration of the carbon source, continues to be the most widely used model in biotechnology and applied microbiology. Stochastic model for the specific consumption rate in microbial growth meaning. For this reason, many attempts have been developed to give a mechanistic structure to the hyperbolic Monod equation. Liu [2] revised these attempts, concluding that “no universal physical meaning of the Monod constant can be revealed”
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