An official website of the United States government
Abstract Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth‐inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic‐Monod growth model, which accounts for multiple growth‐dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic‐Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Yx/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic‐Monod equation represents the cell growth transition from substrate‐limiting condition to growth‐inhibiting condition, which could be adopted to accurately describe the multi‐phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale‐up in industrial biotechnology.
more »
« less
Limited Mechanistic Link Between the Monod Equation and Methanogen Growth: a Perspective from Metabolic Modeling
ABSTRACT The Monod equation has been widely applied as the general rate law of microbial growth, but its applications are not always successful. By drawing on the frameworks of kinetic and stoichiometric metabolic models and metabolic control analysis, the modeling reported here simulated the growth kinetics of a methanogenic microorganism and illustrated that different enzymes and metabolites control growth rate to various extents and that their controls peak at either very low, intermediate, or very high substrate concentrations. In comparison, with a single term and two parameters, the Monod equation only approximately accounts for the controls of rate-determining enzymes and metabolites at very high and very low substrate concentrations, but neglects the enzymes and metabolites whose controls are most notable at intermediate concentrations. These findings support a limited link between the Monod equation and methanogen growth, and unify the competing views regarding enzyme roles in shaping growth kinetics. The results also preclude a mechanistic derivation of the Monod equation from methanogen metabolic networks and highlight a fundamental challenge in microbiology: single-term expressions may not be sufficient for accurate prediction of microbial growth. IMPORTANCE The Monod equation has been widely applied to predict the rate of microbial growth, but its application is not always successful. Using a novel metabolic modeling approach, we simulated the growth of a methanogen and uncovered a limited mechanistic link between the Monod equation and the methanogen’s metabolic network. Specifically, the equation provides an approximation to the controls by rate-determining metabolites and enzymes at very low and very high substrate concentrations, but it is missing the remaining enzymes and metabolites whose controls are most notable at intermediate concentrations. These results support the Monod equation as a useful approximation of growth rates and highlight a fundamental challenge in microbial kinetics: single-term rate expressions may not be sufficient for accurate prediction of microbial growth.
more »
« less
- PAR ID:
- 10346208
- Editor(s):
- Gralnick, Jeffrey A.
- Date Published:
- Journal Name:
- Microbiology Spectrum
- Volume:
- 10
- Issue:
- 2
- ISSN:
- 2165-0497
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Kinetic modeling of microbial reactions is a common tool for addressing the central environmental questions of our time, from contaminant remediation to the global carbon cycle. This review presents an overview of trait-based frameworks for modeling the kinetics of microbial reactions, with an emphasis on environmental application. I first highlight two key model assumptions: the simplification of microbial communities as ensembles of microbial functional groups and the description of microbial metabolism at a coarse-grained level with three metabolic reactions – catabolic reaction, biomass synthesis, and maintenance. Next, I aim to establish a connection between microbial rate laws and the mechanisms of metabolic reactions. For metabolic reactions limited by single substrates, the widely used rate law is the Monod equation. However, in cases where substrates are solids or nonaqueous phase liquids (NAPLs), the Contois equation and the Best equation may offer better alternatives. In microbial metabolisms limited by multiple nutrients simultaneously, two competing rate laws exist: the multiplicative rate law and Liebig’s law of the minimum. Then I present two strategies for extending the modeling framework developed for laboratory cultures to natural environments. One strategy follows the multiplicative rate law and incorporates dimensionless functions to account for pH, temperature, salinity, cell density, and other environmental conditions. The other strategy focuses on the physiology of natural microbes, explicitly considering dormancy, biomass decay, and physiological acclimation. After that, I highlight recent improvements enabled by the application of molecular biology tools, ranging from functional gene-based models to metabolic models. Finally, I discuss the inherent limitations of trait-based modeling frameworks and their implications for model development and evaluation, including the gap between functional groups represented in silico and microbial communities found in natural environments, as well as the requirement of internal consistency in microbial parameter sets.more » « less
-
Kamerlin, Lynn (Ed.)Abstract Millions of years of evolution have optimized many biosynthetic pathways by use of multi‐step catalysis. In addition, multi‐step metabolic pathways are commonly found in and on membrane‐bound organelles in eukaryotic biochemistry. The fundamental mechanisms that facilitate these reaction processes provide strategies to bioengineer metabolic pathways in synthetic chemistry. Using Brownian dynamics simulations, here we modeled intermediate substrate transportation of colocalized yeast–ester biosynthesis enzymes on the membrane. The substrate acetate ion traveled from the pocket of aldehyde dehydrogenase to its target enzyme acetyl‐CoA synthetase, then the substrate acetyl CoA diffused from Acs1 to the active site of the next enzyme, alcohol‐O‐acetyltransferase. Arranging two enzymes with the smallest inter‐enzyme distance of 60 Å had the fastest average substrate association time as compared with anchoring enzymes with larger inter‐enzyme distances. When the off‐target side reactions were turned on, most substrates were lost, which suggests that native localization is necessary for efficient final product synthesis. We also evaluated the effects of intermolecular interactions, local substrate concentrations, and membrane environment to bring mechanistic insights into the colocalization pathways. The computation work demonstrates that creating spatially organized multi‐enzymes on membranes can be an effective strategy to increase final product synthesis in bioengineering systems.more » « less
-
Zhou, Ning-Yi (Ed.)ABSTRACT We used time-resolved metabolic footprinting, an important technical approach used to monitor changes in extracellular compound concentrations during microbial growth, to study the order of substrate utilization (i.e., substrate preferences) and kinetics of a fast-growing soil isolate, Paraburkholderia sp. strain 1N. The growth of Paraburkholderia sp. 1N was monitored under aerobic conditions in a soil-extracted solubilized organic matter medium, representing a realistic diversity of available substrates and gradient of initial concentrations. We combined multiple analytical approaches to track over 150 compounds in the medium and complemented this with bulk carbon and nitrogen measurements, allowing estimates of carbon use efficiency throughout the growth curve. Targeted methods allowed the quantification of common low-molecular-weight substrates: glucose, 20 amino acids, and 9 organic acids. All targeted compounds were depleted from the medium, and depletion followed a sigmoidal curve where sufficient data were available. Substrates were utilized in at least three distinct temporal clusters as Paraburkholderia sp. 1N produced biomass at a cumulative carbon use efficiency of 0.43. The two substrates with highest initial concentrations, glucose and valine, exhibited longer usage windows, at higher biomass-normalized rates, and later in the growth curve. Contrary to hypotheses based on previous studies, we found no clear relationship between substrate nominal oxidation state of carbon (NOSC) or maximal growth rate and the order of substrate depletion. Under soil solution conditions, the growth of Paraburkholderia sp. 1N induced multiauxic substrate depletion patterns that could not be explained by the traditional paradigm of catabolite repression. IMPORTANCE Exometabolomic footprinting methods have the capability to provide time-resolved observations of the uptake and release of hundreds of compounds during microbial growth. Of particular interest is microbial phenotyping under environmentally relevant soil conditions, consisting of relatively low concentrations and modeling pulse input events. Here, we show that growth of a bacterial soil isolate, Paraburkholderia sp. 1N, on a dilute soil extract resulted in a multiauxic metabolic response, characterized by discrete temporal clusters of substrate depletion and metabolite production. Our data did not support the hypothesis that compounds with lower energy content are used preferentially, as each cluster contained compounds with a range of nominal oxidation states of carbon. These new findings with Paraburkholderia sp. 1N, which belongs to a metabolically diverse genus, provide insights on ecological strategies employed by aerobic heterotrophs competing for low-molecular-weight substrates in soil solution.more » « less
-
Specialized metabolites are structurally diverse and cell‐ or tissue‐specific molecules produced in restricted plant lineages. In contrast, primary metabolic pathways are highly conserved in plants and produce metabolites essential for all of life, such as amino acids and nucleotides. Substrate promiscuity – the capacity to accept non‐native substrates – is a common characteristic of enzymes, and its impact is especially apparent in generating specialized metabolite variation. However, promiscuity only leads to metabolic diversity when alternative substrates are available; thus, enzyme cellular and subcellular localization directly influence chemical phenotypes. We review a variety of mechanisms that modulate substrate availability for promiscuous plant enzymes. We focus on examples where evolution led to modification of the ‘cellular context’ through changes in cell‐type expression, subcellular relocalization, pathway sequestration, and cellular mixing via tissue damage. These varied mechanisms contributed to the emergence of structurally diverse plant specialized metabolites and inform future metabolic engineering approaches.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1128/spectrum.02259-21
