Showing papers on "Chemostat published in 2017"

The Chemostat: Mathematical Theory of Microorganism Cultures

Abstract: Invented by J. Monod, and independently by A. Novick and L. Szilard, in 1950, the chemostat is both a micro-organism culturing device and an abstracted ecosystem managed by a controlled nutrient flow. This book studies mathematical models of single species growth as well as competition models of multiple species by integrating recent work in theoretical ecology and population dynamics. Through a modeling approach, the hypotheses and conclusions drawn from the main mathematical results are analyzed and interpreted from a critical perspective. A large emphasis is placed on numerical simulations of which prudent use is advocated. The Chemostat is aimed at readers possessing degree-level mathematical knowledge and includes a detailed appendix of differential equations relating to specific notions and results used throughout this book.

N-Species Competition in a Periodic Chemostat

Abstract: As we see from the previous chapter, the models of exploitative competition in a well-stirred chemostat operated under constant input and dilution, with competition for a nonreproducing substrate, predict that at most one competitor population avoids extinction. However, the coexistence of competing populations is obvious in nature, and so in order to explain this, it seems necessary to relax at least one of the assumptions in these models. One natural approach is to introduce periodic coefficients to represent, for example, daily or seasonal variations in the environment. The aim of this chapter is to present a general framework to study models of n-species competition in a periodically operated chemostat. Nutrient input, dilution, and species-specific removal rates are all permitted to be periodic (but of commensurate period). Furthermore, each species-specific nutrient uptake function is assumed to be a monotone increasing function of the substrate concentration, but can be periodic as a function of time (but again of commensurate period). Differential species-specific removal rates are also permitted.

A CRISPR/Cas9-based exploration into the elusive mechanism for lactate export in Saccharomyces cerevisiae.

Abstract: CRISPR/Cas9-based genome editing allows rapid, simultaneous modification of multiple genetic loci in Saccharomyces cerevisiae. Here, this technique was used in a functional analysis study aimed at identifying the hitherto unknown mechanism of lactate export in this yeast. First, an S. cerevisiae strain was constructed with deletions in 25 genes encoding transport proteins, including the complete aqua(glycero)porin family and all known carboxylic acid transporters. The 25-deletion strain was then transformed with an expression cassette for Lactobacillus casei lactate dehydrogenase (LcLDH). In anaerobic, glucose-grown batch cultures this strain exhibited a lower specific growth rate (0.15 vs. 0.25 h-1) and biomass-specific lactate production rate (0.7 vs. 2.4 mmol g biomass-1 h-1) than an LcLDH-expressing reference strain. However, a comparison of the two strains in anaerobic glucose-limited chemostat cultures (dilution rate 0.10 h-1) showed identical lactate production rates. These results indicate that, although deletion of the 25 transporter genes affected the maximum specific growth rate, it did not impact lactate export rates when analysed at a fixed specific growth rate. The 25-deletion strain provides a first step towards a 'minimal transportome' yeast platform, which can be applied for functional analysis of specific (heterologous) transport proteins as well as for evaluation of metabolic engineering strategies.

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures.

Abstract: In the continuous mode of cell culture, a constant flow carrying fresh media replaces culture fluid, cells, nutrients and secreted metabolites Here we present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations We derive a number of consequences from the model that are independent of parameter values The ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties This conclusion is robust even in the presence of multi-stability, which is explained in our model by a negative feedback loop due to toxic byproduct accumulation A complex landscape of steady states emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion On the other hand, we predict invariance laws between continuous cell cultures with different parameters A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced

Dynamics of some stochastic chemostat models with multiplicative noise

Abstract: In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, we analyze the existence and uniqueness of solutions for these models, as well as the existence of the random attractor associated to the random dynamical system generated by the solution. The analysis will be carried out by means of the well-known Ornstein-Uhlenbeck process, that allows us to transform our stochastic chemostat models into random ones.

Dynamics of the stochastic chemostat with Monod-Haldane response function.

Abstract: The stochastic chemostat model with Monod-Haldane response function is perturbed by environmental white noise. This model has a global positive solution. We demonstrate that there is a stationary distribution of the stochastic model and the system is ergodic under appropriate conditions, on the basis of Khasminskii’s theory on ergodicity. Sufficient criteria for extinction of the microbial population in the stochastic system are established. These conditions depend strongly on the Brownian motion. We find that even small scale white noise can promote the survival of microorganism populations, while large scale noise can lead to extinction. Numerical simulations are carried out to illustrate our theoretical results.

Single-cell microfluidics to study the effects of genome deletion on bacterial growth behavior

Abstract: By directly monitoring single cell growth in a microfluidic platform, we interrogated genome-deletion effects in Escherichia coli strains. We compared the growth dynamics of a wild type strain with a clean genome strain, and their derived mutants at the single-cell level. A decreased average growth rate and extended average lag time were found for the clean genome strain, compared to those of the wild type strain. Direct correlation between the growth rate and lag time of individual cells showed that the clean genome population was more heterogeneous. Cell culturability (the ratio of growing cells to the sum of growing and nongrowing cells) of the clean genome population was also lower. Interestingly, after the random mutations induced by a glucose starvation treatment, for the clean genome population mutants that had survived the competition of chemostat culture, each parameter markedly improved (i.e., the average growth rate and cell culturability increased, and the lag time and heterogeneity decreased). However, this effect was not seen in the wild type strain; the wild type mutants cultured in a chemostat retained a high diversity of growth phenotypes. These results suggest that quasi-essential genes that were deleted in the clean genome might be required to retain a diversity of growth characteristics at the individual cell level under environmental stress. These observations highlight that single-cell microfluidics can reveal subtle individual cellular responses, enabling in-depth understanding of the population.

Influence of oxygen availability on the metabolism and morphology of Yarrowia lipolytica : insights into the impact of glucose levels on dimorphism

Abstract: Dynamic behavior of Yarrowia lipolytica W29 strain under conditions of fluctuating, low, and limited oxygen supply was characterized in batch and glucose-limited chemostat cultures. In batch cultures, transient oscillations between oxygen-rich and -deprived environments induced a slight citric acid accumulation (lower than 29 mg L−1). By contrast, no citric acid was detected in continuous fermentations for all stress conditions: full anoxia (zero pO2 value, 100% N2), limited (zero pO2 value, 75% of cell needs), and low (pO2 close to 2%) dissolved oxygen (DO) levels. The macroscopic behavior (kinetic parameters, yields, viability) of Y. lipolytica was not significantly affected by the exposure to DO fluctuations under both modes of culture. Nevertheless, conditions of oxygen limitation resulted in the destabilization of the glucose-limited growth during the continuous cultivations. Morphological responses of Y. lipolytica to DO oscillations were different between batch and chemostat runs. Indeed, a yeast-to-mycelium transition was induced and progressively intensified during the batch fermentations (filamentous subpopulation reaching 74% (v/v)). While, in chemostat bioreactors, the culture consisted mainly of yeast-like cells (mean diameter not exceeding 5.7 μm) with a normal size distribution. During the continuous cultures, growth at low DO concentration did not induce any changes in Y. lipolytica morphology. Dimorphism (up to 80.5% (v/v) of filaments) was only detected under conditions of oxygen limitation in the presence of a residual glucose excess (more than 0.75 g L−1). These data suggest an impact of glucose levels on the signaling pathways regulating dimorphic responses in Y. lipolytica.

Microbial growth kinetics

Abstract: This chapter explains the basic principles of the growth kinetics of microbial and animal cell cultures in the context of large-scale processes. In discussing batch culture, the reader is introduced to the concept of exponential growth and the mathematical models that describe it in terms of specific growth rate (μ), the saturation constant (Ks), the yield factor (Y), maintenance energy, and the reaction of organisms to nutrient limitation. The behavior of both unicellular and mycelial microorganisms is considered as well as animal cell cultures. The kinetics of continuous culture in its various forms is investigated in detail and the relevance of these processes to large-scale cultivation of both microbial and animal cells discussed. The dominance of fed-batch culture in industrial processes is emphasized and its kinetics considered in the context of the control of a fermentation process.

An evolutionary optimization of a rhodopsin-based phototrophic metabolism in Escherichia coli.

Abstract: The expression of the Gloeobacter rhodopsin (GR) in a chemotrophic Escherichia coli enables the light-driven phototrophic energy generation. Adaptive laboratory evolution has been used for acquiring desired phenotype of microbial cells and for the elucidation of basic mechanism of molecular evolution. To develop an optimized strain for the artificially acquired phototrophic metabolism, an ancestral E. coli expressing GR was adaptively evolved in a chemostat reactor with constant illumination and limited glucose conditions. This study was emphasized at an unexpected genomic mutation contributed to the improvement of microbial performance. During the chemostat culture, increase of cell size was observed, which were distinguished from that of the typical rod-shaped ancestral cells. A descendant ET5 strain was randomly isolated from the chemostat culture at 88-days. The phototrophic growth and the light-induced proton pumping of the ET5 strain were twofold and eightfold greater, respectively, than those of the ancestral E. coli strain. Single point mutation of C1082A at dgcQ gene (encoding diguanylate cyclase, also known as the yedQ gene) in the chromosome of ET5 strain was identified from whole genome sequencing analysis. An ancestral E. coli complemented with the same dgcQ mutation from the ET5 was repeated the subsequently enhancements of light-driven phototrophic growth and proton pumping. Intracellular c-di-GMP, the product of the diguanylate cyclase (dgcQ), of the descendant ET5 strain was suddenly increased while that of the ancestral strain was negligible. Newly acquired phototrophic metabolism of E. coli was further improved via adaptive laboratory evolution by the rise of a point mutation on a transmembrane cell signaling protein followed by increase of signal molecule that eventually led an increase proton pumping and phototrophic growth.

Extracting phytoplankton physiological traits from batch and chemostat culture data

Abstract: As the role of phytoplankton diversity in ocean biogeochemistry becomes widely recognized, the description of plankton in ocean ecological models is becoming more sophisticated. This means that a growing number of plankton physiological traits need to be determined for various species and under various growth conditions. We investigate how these traits can be estimated efficiently from common batch culture and chemostat experiments. We use the Metropolis algorithm, a random-walk Monte Carlo method, to estimate phytoplankton parameter values, along with the uncertainties in these values. First, we fit plankton physiological models to high-resolution batch culture and chemostat data sets to obtain parameter sets that are as accurate as possible. Then, we subsample these data sets and assess to which extent the accuracy is sacrificed when fewer measurements are taken. Two measurement points within the exponential growth stage of the batch culture data set are sufficient to constrain the maximum protein synthesis rate, the maximum photosynthesis rate, and the chlorophyll-to-nitrogen ratio. Two measurements during the stationary phase of the batch culture experiment are then enough to constrain the parameters related to carbon excretion and the photoacclimation time. From the chemostat experiment, only four measured points are needed to constrain the parameters connected with the internal reserve dynamics of phytoplankton. Thus, we demonstrate that traits related to key biogeochemical and physiological processes can be determined with only a few batch culture and chemostat measurements, as long as the measurement points are selected appropriately.

Dynamics of a plankton-nutrient chemostat model with hibernation and it described by impulsive switched systems

Abstract: In this paper, we consider a hibernation plankton-nutrient chemostat model with impulsive switched systems describing. Employing the discrete dynamical system determined by the stroboscopic map, we obtain a plankton-extinction periodic solution. Further, it is globally asymptotically stable. The permanent condition of the system (2.1) is also obtained by the theory on impulsive differential equation. Our results reveal that the impulsive diffusion amount plays an important role on the chemostat system.

Periodic solution for the stochastic chemostat with general response function

Abstract: This paper addresses a stochastic chemostat model with periodic dilution rate and general class of response functions. The general functional response is assumed to satisfy two classifications of conditions, and these assumptions on the functional response are relative weak that are valid for many forms of growth response. For the chemostat with periodic dilution rate, we derive the sufficient criteria for the existence of the stochastic nontrivial positive periodic solution, by utilizing Khasminskii’s theory on periodic Markov process.

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

Abstract: A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.

Developing a low-cost milliliter-scale chemostat array for precise control of cellular growth

Abstract: Multiplexed milliliter-scale chemostats are useful for measuring cell physiology under various degrees of nutrient limitation and for experimental evolution. In each chemostat, fresh medium containing a growth rate-limiting metabolite is pumped into the culturing chamber at a constant rate, while culture effluent exits at an equal rate. Although such devices have been developed by various labs, key parameters - the accuracy and precision of flow rate and the operational range - are not explicitly characterized. Here we report the development of multiplexed milliliter-scale chemostats where flow rates for eight chambers can be independently controlled to vary within a wide range, corresponding to population doubling times of 3~ 13 hours. Importantly, flow rates are precise and accurate without the use of expensive feedback systems. Among the eight chambers, the maximal coefficient of variation in flow rate is less than 3%, and average flow rates are only slightly below targets, i.e., 3-6% for 13-hour and 0.6-1.0% for 3-hour doubling times. This deficit is largely due to evaporation and should be correctable. We experimentally demonstrate that our device allows accurate and precise quantification of population phenotypes.

A multiplex culture system for the long-term growth of fission yeast cells.

Abstract: Maintenance of long-term cultures of yeast cells is central to a broad range of investigations, from metabolic studies to laboratory evolution assays. However, repeated dilutions of batch cultures lead to variations in medium composition, with implications for cell physiology. In Saccharomyces cerevisiae, powerful miniaturized chemostat setups, or ministat arrays, have been shown to allow for constant dilution of multiple independent cultures. Here we set out to adapt these arrays for continuous culture of a morphologically and physiologically distinct yeast, the fission yeast Schizosaccharomyces pombe, with the goal of maintaining constant population density over time. First, we demonstrated that the original ministats are incompatible with growing fission yeast for more than a few generations, prompting us to modify different aspects of the system design. Next, we identified critical parameters for sustaining unbiased vegetative growth in these conditions. This requires deletion of the gsf2 flocculin-encoding gene, along with addition of galactose to the medium and lowering of the culture temperature. Importantly, we improved the flexibility of the ministats by developing a piezo-pump module for the independent regulation of the dilution rate of each culture. This made it possible to easily grow strains that have different generation times in the same assay. Our system therefore allows for maintaining multiple fission yeast cultures in exponential growth, adapting the dilution of each culture over time to keep constant population density for hundreds of generations. These multiplex culture systems open the door to a new range of long-term experiments using this model organism. © 2017 The Authors. Yeast published by John Wiley & Sons, Ltd.

Substrate-Limited and -Unlimited Coastal Microbial Communities Show Different Metabolic Responses with Regard to Temperature.

Abstract: Bacteria are the principal consumers of dissolved organic carbon (DOC) in the ocean and predation of bacteria makes organic carbon available to higher trophic levels. The efficiency with which bacteria convert the consumed carbon (C) into biomass (i.e., carbon growth efficiency, Y) determines their ecological as well as biogeochemical role in marine ecosystems. Yet, it is still unclear how changes in temperature will affect Y and, hence, the transfer of consumed C to higher trophic levels. Here, we experimentally investigated the effect of temperature on metabolic functions of coastal microbial communities inoculated in both nutrient-limited chemostats and nutrient-unlimited turbidostats. We inoculated chemostats and turbidostats with coastal microbial communities into seawater culture medium augmented with 20 and 100 μmol L-1 of glucose respectively and measured CO2 production, carbon biomass and cell abundance. Chemostats were cultured between 14 and 26°C and specific growth rates (μ) between 0.05 and 6.0 day-1, turbidostats were cultured between 10 and 26°C with specific growth rates ranging from 28 to 62 day-1. In chemostats under substrate limitation, which is common in the ocean, the specific respiration rate (r, day-1) showed no trend with temperature and was roughly proportional to μ, implying that carbon growth efficiency (Y) displayed no tendency with temperature. The response was very different in turbidostats under temperature-limited, nutrient-repleted growth, here μ increased with temperature but r decreased resulting in an increase of Y with temperature (Q10: 2.6). Comparison of our results with data from the literature on the respiration rate and cell weight of monospecific bacteria indicates that in general the literature data behaved similar to chemostat data, showing no trend in specific respiration with temperature. We conclude that respiration rates of nutrient-limited bacteria measured at a certain temperature cannot be adjusted to different temperatures with a temperature response function similar to Q10 or Arrhenius. However, the cellular respiration rate and carbon demand rate (both: mol C cell-1 day-1) show statistically significant relations with cellular carbon content (mol C cell-1) in chemostats, turbidostats, and the literature data.

About the chemostat model with a lateral diffusive compartment

Abstract: We consider the classical chemostat model with an additional compartment connected by pure diffusion, and analyze its asymptotic properties. We investigate conditions under which this spatial structure is beneficial for species survival and yield conversion, compared to single chemostat. Moreover we look for the best structure (volume repartition and diffusion rate) which minimizes the volume required to attain a desired yield conversion. The analysis reveals that configurations with a single tank connected by diffusion to the input stream can be the most efficient.

EvoBot: Towards a Robot-Chemostat for Culturing and Maintaining Microbial Fuel Cells (MFCs)

Abstract: In this paper we present EvoBot, a RepRap open-source 3D-printer modified to operate like a robot for culturing and maintaining Microbial Fuel Cells (MFCs). EvoBot is a modular liquid handling robot that has been adapted to host MFCs in its experimental layer, gather data from the MFCs and react on the set thresholds based on a feedback loop. This type of robot-MFC interaction, based on the feedback loop mechanism, will enable us to study further the adaptability and stability of these systems. To date, EvoBot has automated the nurturing process of MFCs with the aim of controlling liquid delivery, which is akin to a chemostat. The chemostat is a well-known microbiology method for culturing bacterial cells under controlled conditions with continuous nutrient supply. EvoBot is perhaps the first pioneering attempt at functionalizing the 3D printing technology by combining it with the chemostat methods. In this paper, we will explore the experiments that EvoBot has carried out so far and how the platform has been optimised over the past two years.

Determination of experimental and mathematical oscillatory conditions for Zymomonas mobilis with different death rates for viable and VBNC cells

Abstract: A chemostat inoculated with Zymomonas mobilis shows an oscillatory behavior when the ethanol concentration surpasses a critical value, as a consequence of the ethanol inhibitory effect. This phenomenon has been modeled with the Levenspiel law μmax(1 − P/kp)n, with n = 1. However, it has not been analytically determined whether for n ≠ 1, a super-critical Hopf bifurcation with respect to the dilution rate is responsible of the observed oscillations. In this contribution, it were determined that there is a unique Hopf point and a stability change of the non-trivial steady state, from unstable to stable as the dilution rate increases. Constraints were formulated for the product critical concentrations, the dilution rate and the parameter n. A Z. mobilis culture within a chemostat, under oscillatory conditions, was monitored to collect experimental data, that were compared with the analytical results. To improve the mathematical model, different death rates were proposed for the viable and the viable but not culturable cells. The local analytical results held for the modified model.

Competition in the Chemostat with Time-Dependent Differential Removal Rates

Abstract: For a chemostat with time-dependent removal rates that may differ between species, it is shown that a microbial species dies out if there is another species that has both a lower break-even concentration and a “less concave” functional response. Conditions are also derived for microbial concentrations to remain bounded and the overall microbial population to persist.

Chapter 12 – Cell Cultivation

Abstract: How does a cell become a “machine” or workhorse? There are two basic methods of cell cultivation: batch and continuous. Batch cultivations are commonly applied in pharmaceutical and food productions. Strict quality control up to the detailed process flow sheet by FDA, and the commonly low production rate are the main reasons for batch operations, among others. The primary form of continuous culture is a steady state continuous-flow stirred-tank reactor (CSTR) or chemostat. A chemostat ensures a time-invariant chemical environment for the cell cultivation. The growth rate can be directly manipulated and substrate concentration in the reactor is low, which can promote a desired product formation. The productivity of chemostat increases with increasing dilution rate to a maximum before sharply decreasing near the washout limit, which is affected by the endogenous needs and/or death rate. The growth and/or product formation patterns can be different between batch and continuous cultivations; for example, a lag-phase in batch and metabolic overflow (or Crabtree) effect in a continuous system. The use of cell recycle with a CSTR increases volumetric productivity and has found use in large-volume, consistent production demand and low-product-value processes (eg, waste treatment and fuel-grade ethanol production), as well as increased use in high-product-value processes (eg, pharmaceutical applications using perfusion systems with mammalian cells). Both analytical and graphical methods of solutions have been demonstrated in examples. To mimic the continuous culturing for high productivity and control while maintaining the certainty of a batch, one can employ fed-batch operations. Continuous culturing and mimicked continuous culturing can avoid the overflow metabolism (formation of side metabolites, such as acetate for Escherichia coli, lactic acid in cell cultures, ethanol in Saccharomyces cerevisiae), and oxygen limitation (anaerobiosis), which is often associated with batch culturing.