Structured model for Saccharomyces cerevisiae

Mechanistic Modelling of Biomass Growth, Glucose Consumption and Ethanol Production by Kluyveromyces marxianus in Batch Fermentation

This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by Kluyveromyces marxianus (K. marxianus). The mathematical model was formulated based on the biological assumptions underlying each variable and is given by a set of three coupled nonlinear first-order Ordinary Differential Equations. The model has ten parameters, and their values were fitted from the experimental data of 17 K. marxianus strains by means of a computational algorithm design in Matlab. The latter allowed us to determine that seven of these parameters share the same value among all the strains, while three parameters concerning biomass maximum growth rate, and ethanol production due to biomass and glucose had specific values for each strain. These values are presented with their corresponding standard error and 95% confidence interval. The goodness of fit of our system was evaluated both qualitatively by in silico experimentation and quantitative by means of the coefficient of determination and the Akaike Information Criterion. Results regarding the fitting capabilities were compared with the classic model given by the logistic, Pirt, and Luedeking-Piret Equations. Further, nonlinear theories were applied to investigate local and global dynamics of the system, the Localization of Compact Invariant Sets Method was applied to determine the so-called localizing domain, i.e., lower and upper bounds for each variable; whilst Lyapunov's stability theories allowed to establish sufficient conditions to ensure asymptotic stability in the nonnegative octant, i.e., R+,03. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation.

The Evolution of Cell Free Biomanufacturing

Cell-free systems are a widely used research tool in systems and synthetic biology and a promising platform for manufacturing of proteins and chemicals. In the past, cell-free biology was primarily used to better understand fundamental biochemical processes. Notably, E. coli cell-free extracts were used in the 1960s to decipher the sequencing of the genetic code. Since then, the transcription and translation capabilities of cell-free systems have been repeatedly optimized to improve energy efficiency and product yield. Today, cell-free systems, in combination with the rise of synthetic biology, have taken on a new role as a promising technology for just-in-time manufacturing of therapeutically important biologics and high-value small molecules. They have also been implemented at an industrial scale for the production of antibodies and cytokines. In this review, we discuss the evolution of cell-free technologies, in particular advancements in extract preparation, cell-free protein synthesis, and cell-free metabolic engineering applications. We then conclude with a discussion of the mathematical modeling of cell-free systems. Mathematical modeling of cell-free processes could be critical to addressing performance bottlenecks and estimating the costs of cell-free manufactured products.

Toward a genome scale sequence specific dynamic model of cell-free protein synthesis in Escherichia coli

In this study, we developed a dynamic mathematical model of E. coli cell-free protein synthesis (CFPS). Model parameters were estimated from a dataset consisting of glucose, organic acids, energy species, amino acids, and protein product, chloramphenicol acetyltransferase (CAT) measurements. The model was successfully trained to simulate these measurements, especially those of the central carbon metabolism. We then used the trained model to evaluate the performance, e.g., the yield and rates of protein production. CAT was produced with an energy efficiency of 12%, suggesting that the process could be further optimized. Reaction group knockouts showed that protein productivity was most sensitive to the oxidative phosphorylation and glycolysis/gluconeogenesis pathways. Amino acid biosynthesis was also important for productivity, while overflow metabolism and TCA cycle affected the overall system state. In addition, translation was more important to productivity than transcription. Finally, CAT production was robust to allosteric control, as were most of the predicted metabolite concentrations; the exceptions to this were the concentrations of succinate and malate, and to a lesser extent pyruvate and acetate, which varied from the measured values when allosteric control was removed. This study is the first to use kinetic modeling to predict dynamic protein production in a cell-free E. coli system, and could provide a foundation for genome scale, dynamic modeling of cell-free E. coli protein synthesis.

•

Protein production is biphasic, powered initially by glucose and later by pyruvate.

•

Protein is produced with an energy efficiency of only 12%.

•

Protein productivity is most sensitive to oxidative phosphorylation and glycolysis.

•

Protein production is robust to allosteric control.

Derivation of an Upscaled Model for Mass Transfer and Reaction for Non-Food Starch Conversion to Bioethanol

In this paper, we derive mathematical models for mass transfer and reaction taking place in first-generation bioreactors to convert non-food starch into bioethanol. Given the hierarchical nature of the system, we identified three scale levels ranging from inside bagasse fibers (the pore scale) where the reaction occurs, up to the bioreactor itself (macroscopic scale) where the various products obtained from this reaction are monitored. We derive a macroscopic model at the reactor scale by systematically upscaling the relevant information from the pore scale using the method of volume averaging. A salient feature of the model is that the effective medium coefficients involved are predicted by solving ancillary closure problems in representative unit cells of the different levels of scale. The predictions of the model in terms of CO2 production as well as cellular growth were validated with a close agreement with available experimental data. This work enhances our understanding of the relevance of transport phenomena taking place at the different scales in a bioreactor and may become an aid in design and operation applications of bioethanol production systems.

Dynamic flux balance analysis for synthetic microbial communities

Dynamic flux balance analysis (DFBA) is an extension of classical flux balance analysis that allows the dynamic effects of the extracellular environment on microbial metabolism to be predicted and optimised. Recently this computational framework has been extended to microbial communities for which the individual species are known and genome-scale metabolic reconstructions are available. In this review, the authors provide an overview of the emerging DFBA approach with a focus on two case studies involving the conversion of mixed hexose/pentose sugar mixtures by synthetic microbial co-culture systems. These case studies illustrate the key requirements of the DFBA approach, including the incorporation of individual species metabolic reconstructions, formulation of extracellular mass balances, identification of substrate uptake kinetics, numerical solution of the coupled linear program/differential equations and model adaptation for common, suboptimal growth conditions and identified species interactions. The review concludes with a summary of progress to date and possible directions for future research.

Development of a kinetic model for the alcoholic fermentation of must

We Propose a kinetic expression which accounts for the temperature dependence of ethanol yield losses in batch alcoholic fermentation. Moreover, the characteristic parameters of the microbial growth equation have been calculated for Saccharomyces cerevisiae under typical wine industry conditions. A substrate consumption equation is established which minimizes possible model deviations in the latter process stages. Experimental data were obtained in the laboratory and the proposed equations were then applied at an industrial level (2.5 x 10(4) L) where they described the data well.

In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae : I. Experimental observations

The goal of this work was to obtain rapid sampling technique to measure transient metabolites in vivo. First, a pulse of glucose was added to a culture of the yeast Saccharomyces cerevisiae growing aerobically under glucose limitation. Next, samples were removed at 2 to 5 s intervals and quenched using methods that depend on the metabolite measured. Extracellular glucose, excreted products, as well as glycolytic intermediates (G6P, F6P, FBP, GAP, 3-PG, PEP, Pyr) and cometabolites (ATP, ADP, AMP, NAD(+), NADH) were measured using enzymatic or HPLC methods. Significant differences between the adenine nucleotide concentrations in the cytoplasm and mitochondria indicated the importance of compartmentation for the regulation of the glycolysis. Changes in the intra- and extracellular levels of metabolites confirmed that glycolysis is regulated on a time scale of seconds. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 305-316, 1997.

Genome-scale analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture

A dynamic flux balance model based on a genome-scale metabolic network reconstruction is developed for in silico analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture. Metabolic engineering strategies previously identified for their enhanced steady-state biomass and/or ethanol yields are evaluated for fed-batch performance in glucose and glucose/xylose media. Dynamic analysis is shown to provide a single quantitative measure of fed-batch ethanol productivity that explicitly handles the possible tradeoff between the biomass and ethanol yields. Productivity optimization conducted to rank achievable fed-batch performance demonstrates that the genetic manipulation strategy and the fed-batch operating policy should be considered simultaneously. A library of candidate gene insertions is assembled and directly screened for their achievable ethanol productivity in fed-batch culture. A number of novel gene insertions with ethanol productivities identical to the best metabolic engineering strategies reported in previous studies are identified, thereby providing additional targets for experimental evaluation. The top performing gene insertions were substrate dependent, with the highest ranked insertions for glucose media yielding suboptimal performance in glucose/xylose media. The analysis results suggest that enhancements in biomass yield are most beneficial for the enhancement of fed-batch ethanol productivity by recombinant xylose utilizing yeast strains. We conclude that steady-state flux balance analysis is not sufficient to predict fed-batch performance and that the media, genetic manipulations, and fed-batch operating policy should be considered simultaneously to achieve optimal metabolite productivity.

Modeling of enzyme production kinetics

Models of single cells, cell populations, and cultures can be most useful in organizing information in a comprehensive system description, as well as in optimizing and controlling actual production operations. Models discussed in this article are of various degrees of biological structure and mathematical complexity. The models are developed based on the biomass formation, substrate consumption, and product formation. the potentials asn the limitations of all the models have been reported. The parameter estimation by different methods has been discussed in this communication. These parameters will be helpful to explore the areas where future-modeling studies may be especially valuable.

Modelling the growth of filamentous fungi

Despite the considerable industrial importance of filamentous fungi there have been very few attempts to model the complex growth process of these microorganisms. With a new generation of high performance, computerized bioreactors and new analytical techniques it is possible to obtain the necessary experimental data for setting up reliable structured models describing the growth process of filamentous fungi. It is therefore interesting to review the mathematical models described previously in the literature and the experimental data on which these models are built. Only structured models are considered due to the complex metabolism of filamentous fungi and to the natural cellular structuring of the biomass, i.e. the biomass can be divided into different cell types. In order to set up good structured models it is strictly necessary to have a detailed knowledge of the mechanisms underlying the growth process. This involves both biochemical insight and understanding of the interactions between different macromolecules and cytological organelles.

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.

Cellular growth in biofilms

In this paper we develop a macroscopic evolutionary equation for the growth of the cellular phase starting from a microscopic description of mass transport and a simple structured model for product formation. The methods of continuum mechanics and volume averaging are used to develop the macroscopic representation by carefully considering the fluxes of chemical species that pertain to cell growth. The concept of structured models is extended to include the transport of reacting chemical species at the microscopic scale. The resulting macroscopic growth model is similar in form to previously published models for the transport of a single substrate and electron donor and for the production of cellular mass and exopolymer. The method of volume averaging indicates under what conditions the developed growth model is valid and provides an explicit connection between the relevant microscopic model parameters and their corresponding macroscopic counterparts.

Single-cell models: promise and limitations

This article describes the development of single-cell models, their uses and accomplishments, the barriers to the greater adoption, and a perspective on challenges to the biochemical engineering community where the single-cell model approach may be used advantageously. In particular, it may become an important tool in relating genomic information to cellular regulation and dynamics.

Modeling of the aerobic growth of Saccharomyces cerevisiae on mixtures of glucose and ethanol in continuous culture

A structured model dedicated to fed-batch growth of baker's yeast is detailed in steady-state conditions. The simulated results for aerobic growth on mixtures of glucose and ethanol are provided. The model differentiates and identifies glucose utilisation (either oxido-reductive or by oxidation), state 1 and ethanol oxidation, state 2. Ethanol can be oxidised when glucose concentration is below a certain value, s(crit), only; ethanol is excreted when glucose concentration exceeds s(crit). The amount of ethanol co-consumed with glucose is controlled by s(crit) through the transition rate from X1 to X2. Two major novelties are introduced for modeling glucose metabolism. (1) The specific growth rate on glucose is constant, equal to D(crit), at low glucose concentrations, but follows Monod kinetics at high glucose concentrations. (2) Non-constant yields (i.e., Yx/s and Ye/s) are determined by means of dimensionless groups when the specific growth rate on glucose exceeds D(crit). The model is developed on experimentally easily accessible parameters found in the literature for Saccharomyces cerevisiae H1022. A remarkable prediction of the experimental data obtained by Rieger et al. (1983) (J. Gen. Microbiol. 129, 653-661) is highlighted. The simulations suggest that the specific growth rate on ethanol may be underestimated in limited respiratory capacity based models.

A structured model for vegetative growth and sporulation in Bacillus thuringiensis

A mathematical model has been developed for the delta-endotoxin producing Bacillus thuringiensis. The structure of the model involves the processes taking place during vegetative growth, those leading to the initiation of sporulation under conditions of carbon and/or nitrogen limitation, and the sporulation events. The key features in the model are the pools of compounds, such as PRPP, IMP, ADP/ATP, GDP/GTP, pyrimidine nucleotides, NAD/NADH2, amino acids, nucleic acids, cell wall, and vegetative and sporulation proteins. These, along with sigma-factors that control the nature of RNA-polymerase during the different phases, effectively stimulate the vegetative growth and sporulation. The initiation of sporulation is controlled by the intracellular concentration of GTP. Results of simulation of vegetative growth, initiation of sporulation, spore protein formation, and production of delta-endotoxin under C- or N-limitation are presented.