Microbial energetics should be considered in manipulating metabolism for biotechnological purposes

The conversion of substrates into products and biomass in a microbial culture is a chemical reaction, albeit a complicated one. The stoichiometry and kinetics of this reaction provide information which can be useful in demonstrating how the intrinsic properties of microorganisms or the conditions imposed on them influence productivity in bioreactors. Microbial energetics can be used to guide the selection of production strains both by culture screening and recombinant DNA techniques, to predict the maximum yield of a product from a particular organism, and to explain the influence of culture conditions on productivity.     

Predicting microbial growth dynamics in response to nutrient availability

Developing mathematical models to accurately predict microbial growth dynamics remains a key challenge in ecology, evolution, biotechnology, and public health. To reproduce and grow, microbes need to take up essential nutrients from the environment, and mathematical models classically assume that the nutrient uptake rate is a saturating function of the nutrient concentration. In nature, microbes experience different levels of nutrient availability at all environmental scales, yet parameters shaping the nutrient uptake function are commonly estimated for a single initial nutrient concentration. This hampers the models from accurately capturing microbial dynamics when the environmental conditions change. To address this problem, we conduct growth experiments for a range of micro-organisms, including human fungal pathogens, baker’s yeast, and common coliform bacteria, and uncover the following patterns. We observed that the maximal nutrient uptake rate and biomass yield were both decreasing functions of initial nutrient concentration. While a functional form for the relationship between biomass yield and initial nutrient concentration has been previously derived from first metabolic principles, here we also derive the form of the relationship between maximal nutrient uptake rate and initial nutrient concentration. Incorporating these two functions into a model of microbial growth allows for variable growth parameters and enables us to substantially improve predictions for microbial dynamics in a range of initial nutrient concentrations, compared to keeping growth parameters fixed.     

Kinetic modeling of microbial growth,enzyme activity,and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. This integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.     

Evaluation of growth yield of Spirulina (Arthrospira) sp. in photoautotrophic, heterotrophic and mixotrophic cultures

In microbial cultures, both cellular growth rate and yield (defined as the degree of substrate conversion into the biomass) are important. Although effect of culture conditions on growth kinetics has been well documented for various microbial strains, there is almost no literature concerning the effect of environmental conditions on growth equilibrium, expressed as biomass yield coefficients from substrate. The present paper discusses the effect of culture conditions: irradiance (physical substrate) and glucose concentration (chemical substrate) on biomass yield coefficients from two chemical substrates: glucose and nitrate-nitrogen in photoautotrophic, heterotrophic and mixotrophic culture of blue-green alga Spirulina (Arthrospira) sp. The efficiency of substrates incorporation into the biomass can be precisely determined only if the elemental composition of the biomass is known. The experimental results showed that culture conditions had a substantial influence on biomass yield coefficients (biomass yield from glucose and nitrate-nitrogen). It was found that, the increase of irradiance favoured increase of biomass yield coefficient from both, glucose and nitrate-nitrogen. However, in the case of yield from nitrogen in mixotrophic culture, the effect was opposite. The effect of glucose concentration was different: the higher the initial glucose concentration, the lower the biomass yield coefficients from chemical substrates.     

Experimental simulation of oxygen profiles and their influence on baker's yeast production: I. One-fermentor system

In production-scale bioreactors microorganisms are exposed to a continually changing environment. This may cause loss of viability, reduction of the yield of biomass or desired metabolites, and an increase in the formation of by-products. In fed-batch production of baker's yeast, profiles may occur in substrate and oxygen concentrations and in pH. This article deals with the influence of a periodically changing oxygen concentration on the growth of baker's yeast in a continuous culture. Also, influences on the production of ethanol, glycerol, acetic acid, and on the composition of the cells were investigated. It was found that relatively fast fluctuations between oxygen-unlimited and oxygen-limited conditions with a frequency of 1 or 2 min had a distinct influence on the biomass and metabolite production. However, RNA, protein, and carbohydrate contents measured in cells exposed to fluctuations differed little from those in cells from an oxygen-unlimited or an oxygen-limited culture. The respiration and fermentation capacities of cells exposed to fluctuations can be larger than the capacities of cells grown under oxygen-unlimited conditions.     

Competition between two microbial populations in a sequencing fed-batch reactor: theory, experimental verification, and implications for waste treatment applications

Competition between two microbial populations for a single pollutant (phenol) was studied in a sequencing fed-batch reactor (SFBR). A mathematical model describing this system was developed and tested experimentally. It is based on specific growth rate expressions revealed from pure culture batch experiments. The species employed were Pseudomonas putida (ATCC 17514) and Pseudomonas resinovorans (ATCC 14235). It was found that both species biodegrade phenol following inhibitory kinetics which can be described by Andrews' expression. The model predicts that the dynamics of a SFBR, and the kinetics of biodegradation, result in a complex set of operating regimes in which neither species, only one species, or both species can survive at steady cycle. The model also predicts the existence of multiple outcomes, achievable from different start-up conditions, in some domains of the operating parameter space. Experimental results confirmed the model predictions. There was excellent agreement between predicted and measured concentrations of phenol, total biomass, and the biomass of each individual species. This study shows how serious discrepancies can arise in scale-up of biodegradation data if population dynamics are not taken into account. It also further confirms experimentally the theory of microbial competition in periodically forced bioreactors. (c) 1993 John Wiley & Sons, Inc.     

Quantitative studies of bacterial chemotaxis and microbial population dynamics

Although there is a long history of conjecture regarding the role and significance of bacterial chemotaxis in microbial ecology, only recently has a significant body of work appeared attempting to address this issue. The purpose of this paper is to provide a concise overview of this work, which combined mathematical modeling of bacterial population migration and experimental measurement of the model parameters with modeling of competitive microbial population dynamics in a nonmixed environment. Predictions from the population dynamics models, based on experimental estimates of the various motility and growth parameter values, are related to the small number of experimental observations available to date dealing with the effects of bacterial motility on competition in a nonmixed environment. Current results indicate that cell motility and chemotaxis properties can be as important to population dynamics as cell growth kinetic properties, so that greater attention to this aspect of microbial behavior is warranted in future studies of microbial ecology.     

Modeling microbial dynamics in heterogeneous environments: growth on soil carbon sources

We have developed a new kinetic model to study how microbial dynamics are affected by the heterogeneity in the physical structure of the environment and by different strategies for hydrolysis of polymeric carbon. The hybrid model represented the dynamics of substrates and enzymes using a continuum representation and the dynamics of the cells were modeled individually. Individual-based biological model allowed us to explicitly simulate microbial diversity, and to model cell physiology as regulated via optimal allocation of cellular resources to enzyme synthesis, control of growth rate by protein synthesis capacity, and shifts to dormancy. This model was developed to study how microbial community functioning is influenced by local environmental conditions in heterogeneous media such as soil and by the functional attributes of individual microbes. Microbial community dynamics were simulated at two spatial scales: micro-pores that resemble 6-20-μm size portions of the soil physical structure and in 111-μm size soil aggregates with a random pore structure. Different strategies for acquisition of carbon from polymeric cellulose were investigated. Bacteria that express membrane-associated hydrolase had different growth and survival dynamics in soil pores than bacteria that release extracellular hydrolases. The kinetic differences suggested different functional niches for these two microbe types in cellulose utilization. Our model predicted an emergent behavior in which co-existence of membrane-associated hydrolase and extracellular hydrolases releasing organisms led to higher cellulose utilization efficiency and reduced stochasticity. Our analysis indicated that their co-existence mutually benefits these organisms, where basal cellulose degradation activity by membrane-associated hydrolase-expressing cells shortened the soluble hydrolase buildup time and, when enzyme buildup allowed for cellulose degradation to be fast enough to sustain exponential growth, all the organisms in the community shared the soluble carbon product and grew together. Although pore geometry affected the kinetics of cellulose degradation, the patterns observed for the bacterial community dynamics in the 6-20 μm-sized micro-pores were relevant to the dynamics in the more complex 111-μm-sized porous soil aggregates, implying that micro-scale studies can be useful approximations to aggregate scale studies when local effects on microbial dynamics are studied. As shown with examples in this study, various functional niches of the bacterial communities can be investigated using complex predictive mathematical models where the role of key environmental aspects such as the heterogeneous three-dimensional structure, functional niches of the community members, and environmental biochemical processes are directly connected to microbial metabolism and maintenance in an integrated model.     

Fluctuations in continuous mammalian cell bioreactors with retention.

Continuous flow bioreactors with cell retention have been increasingly used for the cultivation of mammalian cells. The potential advantages of such bioreactors are high cell concentrations and volumetric productivities. In many reported cases, these systems have shown fluctuations in cell concentrations of various frequency and magnitude. To analyze the dynamics of the fluctuations, a model-based approach is followed. Simulations showed that large fluctuations in biomass resulted in response to fluctuations in the retention ratio when the system is operated at high dilution rate and high cell retention. The dependence of cell concentration fluctuations on variations in dilution rate and retention ratio was established by a cross-correlation statistical analysis on available experimental data. The slower dynamics and the fluctuation propensity of retention systems suggest that continuous culture without retention is more convenient for kinetic studies. In all likelihood, continuous culture with retention can be stabilized by controlling both the retention ratio and the dilution rate.     

The effect of dilution rate variation on the performance of continuous fermentation

The effect of dilution rate variation on the performance of bioreactors used for continuous biomass producton is discussed. Calculations based on Powell's model of microbial dynamics show that such a mode of operation does not improve the performance of the process. Remarkable improvement of the process performance reported in literature is caused by incorrectness of the dynamic model of microbial growth which has been used in the calculations.     

Cell cycle model to describe animal cell size variation and lag between cell number and biomass dynamics

The use of cell numbers rather than mass to quantify the size of the biotic phase in animal cell cultures causes several problems. First, the cell size varies with growth conditions, thus yields expressed in terms of cell numbers cannot be used in the normal mass balance sense. Second, experience from microbial systems shows that cell number dynamics lag behind biomass dynamics. This work demonstrates that this lag phenomenon also occurs in animal cell culture. Both the lag phenomenon and the variation in cell size are explained using a simple model of the cell cycle. The basis for the model is that onset of DNA synthesis requires accumulation of G1 cyclins to a prescribed level. This requirement is translated into a requirement for a cell to reach a critical size before commencement of DNA synthesis. A slower growing cell will spend more time in G1 before reaching the critical mass. In contrast, the period between onset of DNA synthesis and mitosis, tau(B), is fixed. The two parameters in the model, the critical size and tau(B), were determined from eight steady-state measurements of mean cell size in a continuous hybridoma culture. Using these parameters, it was possible to predict with reasonable accuracy the transient behavior in a separate shift-up culture, i.e., a culture where cells were transferred from a lean environment to a rich environment. The implications for analyzing experimental data for animal cell culture are discussed. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 372-379, 1997.     

Engineering characterisation of a single well from 24-well and 96-well microtitre plates

The detailed engineering characterisation of shaken microtitre-plate bioreactors will enhance our understanding of microbial and mammalian cell culture in these geometries and will provide guidance on the scale-up of microwell results to laboratory and pilot scale stirred bioreactors. In this work computational fluid dynamics (CFD) is employed to provide a detailed characterisation of fluid mixing, energy dissipation rate and mass transfer in single well bioreactors from deep square 24-well and 96-well microtitre plates. The numerical predictions are generally found to be in good agreement with experimental observation of the fluid motion and measured values of the key engineering parameters. The CFD simulations have shown that liquid mixing is more intensive in 96-well than in 24-well bioreactors due to a significant axial component to the fluid velocity. Liquid motion is strongly dependent on the orbital shaking amplitude which generally has a greater impact than the shaking frequency. Average power consumptions of 70–100 W m⁻³ and 500–1000 W m⁻³, and overall mass transfer coefficient, k_La, values of 0.005–0.028 s⁻¹ and 0.056–0.10 s⁻¹ were obtained for 24-well and 96-well bioreactors respectively at an orbital shaking amplitude of 3 mm and shaking frequencies ranging from 500 rpm to 1500 rpm. The distribution of energy dissipation rates within each bioreactor showed these to be greatest at the walls of the well for both geometries. Batch culture kinetics of E. coli DH5 showed similar maximum specific growth rates and final biomass yields in shaken 24-well and shake flask bioreactors and in stirred miniature and 20 L bioreactors at matched k_La values. The CFD simulations thus give new insights into the local and overall engineering properties of microwell bioreactor geometries and further support their use as high throughput tools for the study and optimisation of microbial and mammalian cell culture kinetics at this scale.     

Organic tissues in rotating bioreactors: fluid-mechanical aspects, dynamic growth models, and morphological evolution

This analysis deals with advances in tissue-engineering models and computational methods as well as with novel results on the relative importance of "controlling forces" in the growth of organic constructs. Specifically, attention is focused on the rotary culture system, because this technique has proven to be the most practical solution for providing a suitable culture environment supporting three-dimensional tissue assemblies. From a numerical point of view, the growing biological specimen gives rise to a moving boundary problem. A "volume-of-fraction" method is specifically and carefully developed according to the complex properties and mechanisms of organic tissue growth and, in particular, taking into account the sensitivity of the construct/liquid interface to the effect of the fluid-dynamic shear stress (it induces changes in tissue metabolism and function that elicit a physiological response from the biological cells). The present study uses available data to introduce a set of growth models. The surface conditions are coupled to the transfer of mass and momentum at the specimen/culture-medium interface and lead to the introduction of a group of differential equations for the nutrient concentration around the sample and for the evolution of tissue mass displacement. The models are then used to show how the proposed surface kinetic laws can predict (through sophisticated numerical simulations) many of the known characteristics of biological tissues grown using rotating-wall perfused vessel bioreactors. This procedure provides a validation of the models and associated numerical method and also gives insight into the mechanisms of the phenomena. The interplay between the increasing size of the tissue and the structure of the convective field is investigated. It is shown that this interaction is essential in determining the time evolution of the tissue shape. The size of the growing specimen plays a critical role with regard to the intensity of convection and the related shear stresses. Convective effects, in turn, are found to impact growth rates, tissue size, and morphology, as well as the mechanisms driving growth. The method exhibits novel capabilities to predict and elucidate experimental observations and to identify cause-and-effect relationships.     

Classification of static behavior of a class of unstructured models of continuous bioprocesses

The stability characteristics of a class of unstructured models of continuous bioreactors are analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which the non-biomass product formation rate is linearly proportional to the utilization rate of limiting substrate. The kinetics expressions of cell growth and product synthesis are allowed to assume general forms of substrate and product. Global analytical conditions are derived that allow the construction of a practical picture in the multidimensional parameter space delineating the different static behavior these models can predict, including unique steady states, coexistence of non-trivial steady states with wash-out conditions, and multistability resulting from hysteresis. These general results are applied to specific examples of bioprocesses and allow the study of the effect of kinetic and operating parameters on the stability characteristics of these models.     

On maintenance models in severely and long-term limited membrane bioreactor cultivations

Membrane bioreactors (MBRs) are combinations of common bioreactors and membrane separation units for biomass retention. Through increased biomass concentration, they allow increased productivity (or smaller reactor volume, respectively). Besides high biomass concentrations, operation at very low growth rates is typical for MBRs. In this regime, maintenance metabolism where substrate uptake only yields energy for cell survival becomes of higher importance than in processes run at higher growth rates. While thermodynamically based correlations for the prediction of maintenance coefficients are available for chemostat or other medium growth rate processes, some authors have mentioned a change in energy demand in MBRs and a dependence of maintenance parameters on operating conditions. Due to the fact that often mixed cultures are used and resulting from the different evaluation methods used by different authors, views on the possible influences on maintenance parameters differ. However, it is accepted that common models describing microbial growth and production of metabolites or degradation of pollutants do not consider the effects caused by severe limitations and therefore cannot sufficiently be applied to MBRs. In this study, maintenance parameters were determined for a model organism (Ustilago maydis) and results from different evaluation methods were compared. A continuous fit of respiration data gave more consistent results than the traditional method of plotting specific uptake versus growth rate. They suggest that below micro = 10% micro(max) the maintenance coefficient drops to a third of the value in short-term limited cultures.     

In Silico Geobacter sulfurreducens Metabolism and Its Representation in Reactive Transport Models

Microbial activity governs elemental cycling and the transformation of many anthropogenic substances in aqueous environments. Through the development of a dynamic cell model of the well-characterized, versatile, and abundant Geobacter sulfurreducens, we showed that a kinetic representation of key components of cell metabolism matched microbial growth dynamics observed in chemostat experiments under various environmental conditions and led to results similar to those from a comprehensive flux balance model. Coupling the kinetic cell model to its environment by expressing substrate uptake rates depending on intra- and extracellular substrate concentrations, two-dimensional reactive transport simulations of an aquifer were performed. They illustrated that a proper representation of growth efficiency as a function of substrate availability is a determining factor for the spatial distribution of microbial populations in a porous medium. It was shown that simplified model representations of microbial dynamics in the subsurface that only depended on extracellular conditions could be derived by properly parameterizing emerging properties of the kinetic cell model.     

Nitrogen limitation of decomposition and decay: How can it occur?

The availability of nitrogen (N) is a critical control on the cycling and storage of soil carbon (C). Yet, there are conflicting conceptual models to explain how N availability influences the decomposition of organic matter by soil microbial communities. Several lines of evidence suggest that N availability limits decomposition; the earliest stages of leaf litter decay are associated with a net import of N from the soil environment, and both observations and models show that high N organic matter decomposes more rapidly. In direct contrast to these findings, experimental additions of inorganic N to soils broadly show a suppression of microbial activity, which is inconsistent with N limitation of decomposition. Resolving this apparent contradiction is critical to representing nutrient dynamics in predictive ecosystem models under a multitude of global change factors that alter soil N availability. Here, we propose a new conceptual framework, the Carbon, Acidity, and Mineral Protection hypothesis, to understand the effects of N availability on soil C cycling and storage and explore the predictions of this framework with a mathematical model. Our model simulations demonstrate that N addition can have opposing effects on separate soil C pools (particulate and mineral‐protected carbon) because they are differentially affected by microbial biomass growth. Moreover, changes in N availability are frequently linked to shifts in soil pH or osmotic stress, which can independently affect microbial biomass dynamics and mask N stimulation of microbial activity. Thus, the net effect of N addition on soil C is dependent upon interactions among microbial physiology, soil mineralogy, and soil acidity. We believe that our synthesis provides a broadly applicable conceptual framework to understand and predict the effect of changes in soil N availability on ecosystem C cycling under global change.     

A review of recent developments in modeling of microbial growth kinetics and intraparticle phenomena in solid-state fermentation

Mathematical models are important tools for optimizing the design and operation of solid-state fermentation (SSF) bioreactors. Such models must describe the kinetics of microbial growth, how this is affected by the environmental conditions and how this growth affects the environmental conditions. This is done at two levels of sophistication. In many bioreactor models the kinetics are described by simple empirical equations. However, other models that address the interaction of growth with intraparticle diffusion of enzymes, hydrolysis products and O₂ with the use of mechanistic equations have also been proposed, and give insights into how these microscale processes can potentially limit the overall performance of a bioreactor. The current article reviews the advances that have been made in both the empirical- and mechanistic-type kinetic models and discusses the insights that have been achieved through the modeling work and the improvements to models that will be necessary in the future.     

The effect of hydroxylamine on the activity and aggregate structure of autotrophic nitrifying bioreactor cultures

Addition of hydroxylamine (NH2OH) to autotrophic biomass in nitrifying bioreactors affected the activity, physical structure, and microbial ecology of nitrifying aggregates. When NH2OH is added to nitrifying cultures in 6-h batch experiments, the initial NH3-N uptake rates were physiologically accelerated by a factor of 1.4-13. NH2OH addition caused a 20-40% decrease in the median aggregate size, broadened the shape of the aggregate size distribution by up to 230%, and caused some of the microcolonies to appear slightly more dispersed. Longer term NH2OH addition in fed batch bioreactors decreased the median aggregate size, broadened the aggregate size distribution, and decreased NH3-N removal from >90% to values ranging between 75% and 17%. This altered performance is explained by quantitative fluorescence in situ hybridization (FISH) results that show inhibition of nitrifying populations, and by qPCR results showing that the copy numbers of amoA and nxrA genes gradually decreased by up to an order-of-magnitude. Longer term NH2OH addition damaged the active biomass. This research clarifies the effect of NH2OH on nitrification and demonstrates the need to incorporate NH2OH-related dynamics of the nitrifying biomass into mathematical models, accounting for both ecophysiological and structural responses.