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 (
- 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
-
more » « less
Abstract Y x/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. -
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
-
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
-
more » « less
Abstract Background Quantification of individual species in microbial co-cultures and consortia is critical to understanding and designing communities with prescribed functions. However, it is difficult to physically separate species or measure species-specific attributes in most multi-species systems. Anaerobic gut fungi (AGF) (Neocallimastigomycetes) are native to the rumen of large herbivores, where they exist as minority members among a wealth of prokaryotes. AGF have significant biotechnological potential owing to their diverse repertoire of potent lignocellulose-degrading carbohydrate-active enzymes (CAZymes), which indirectly bolsters activity of other rumen microbes through metabolic exchange. While decades of literature suggest that polysaccharide degradation and AGF growth are accelerated in co-culture with prokaryotes, particularly methanogens, methods have not been available to measure concentrations of individual species in co-culture. New methods to disentangle the contributions of AGF and rumen prokaryotes are sorely needed to calculate AGF growth rates and metabolic fluxes to prove this hypothesis and understand its causality for predictable co-culture design.
Results We present a simple, microplate-based method to measure AGF and methanogen concentrations in co-culture based on fluorescence and absorbance spectroscopies. Using samples of < 2% of the co-culture volume, we demonstrate significant increases in AGF growth rate and xylan and glucose degradation rates in co-culture with methanogens relative to mono-culture. Further, we calculate significant differences in AGF metabolic fluxes in co-culture relative to mono-culture, namely increased flux through the energy-generating hydrogenosome organelle. While calculated fluxes highlight uncertainties in AGF primary metabolism that preclude definitive explanations for this shift, our method will enable steady-state fluxomic experiments to probe AGF metabolism in greater detail.
Conclusions The method we present to measure AGF and methanogen concentrations enables direct growth measurements and calculation of metabolic fluxes in co-culture. These metrics are critical to develop a quantitative understanding of interwoven rumen metabolism, as well as the impact of co-culture on polysaccharide degradation and metabolite production. The framework presented here can inspire new methods to probe systems beyond AGF and methanogens. Simple modifications to the method will likely extend its utility to co-cultures with more than two organisms or those grown on solid substrates to facilitate the design and deployment of microbial communities for bioproduction and beyond.
-
more » « less
Abstract Anaerobic fungi and methanogenic archaea are two classes of microorganisms found in the rumen microbiome that metabolically interact during lignocellulose breakdown. Here, stable synthetic co-cultures of the anaerobic fungus
Caecomyces churrovis and the methanogenMethanobacterium bryantii (not native to the rumen) were formed, demonstrating that microbes from different environments can be paired based on metabolic ties. Transcriptional and metabolic changes induced by methanogen co-culture were evaluated inC. churrovis across a variety of substrates to identify mechanisms that impact biomass breakdown and sugar uptake. A high-quality genome ofC. churrovis was obtained and annotated, which is the first sequenced genome of a non-rhizoid-forming anaerobic fungus.C. churrovis possess an abundance of CAZymes and carbohydrate binding modules and, in agreement with previous studies of early-diverging fungal lineages, N6-methyldeoxyadenine (6mA) was associated with transcriptionally active genes. Co-culture with the methanogen increased overall transcription of CAZymes, carbohydrate binding modules, and dockerin domains in co-cultures grown on both lignocellulose and cellulose and caused upregulation of genes coding associated enzymatic machinery including carbohydrate binding modules in family 18 and dockerin domains across multiple growth substrates relative toC. churrovis monoculture. Two other fungal strains grown on a reed canary grass substrate in co-culture with the same methanogen also exhibited high log2-fold change values for upregulation of genes encoding carbohydrate binding modules in families 1 and 18. Transcriptional upregulation indicated that co-culture of theC. churrovis strain with a methanogen may enhance pyruvate formate lyase (PFL) function for growth on xylan and fructose and production of bottleneck enzymes in sugar utilization pathways, further supporting the hypothesis that co-culture with a methanogen may enhance certain fungal metabolic functions. Upregulation of CBM18 may play a role in fungal–methanogen physical associations and fungal cell wall development and remodeling.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1128/spectrum.02259-21
