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.     

Literature mining supports a next-generation modeling approach to predict cellular byproduct secretion

The metabolic byproducts secreted by growing cells can be easily measured and provide a window into the state of a cell; they have been essential to the development of microbiology, cancer biology, and biotechnology. Progress in computational modeling of cells has made it possible to predict metabolic byproduct secretion with bottom-up reconstructions of metabolic networks. However, owing to a lack of data, it has not been possible to validate these predictions across a wide range of strains and conditions. Through literature mining, we were able to generate a database of Escherichia coli strains and their experimentally measured byproduct secretions. We simulated these strains in six historical genome-scale models of E. coli, and we report that the predictive power of the models has increased as they have expanded in size and scope. The latest genome-scale model of metabolism correctly predicts byproduct secretion for 35/89 (39%) of designs. The next-generation genome-scale model of metabolism and gene expression (ME-model) correctly predicts byproduct secretion for 40/89 (45%) of designs, and we show that ME-model predictions could be further improved through kinetic parameterization. We analyze the failure modes of these simulations and discuss opportunities to improve prediction of byproduct secretion.     

What CHO is made of: Variations in the biomass composition of Chinese hamster ovary cell lines

BackgroundCell line-specific, genome-scale metabolic models enable rigorous and systematic in silico investigation of cellular metabolism. Such models have recently become available for Chinese hamster ovary (CHO) cells. However, a key ingredient, namely an experimentally validated biomass function that summarizes the cellular composition, was so far missing. Here, we close this gap by providing extensive experimental data on the biomass composition of 13 parental and producer CHO cell lines under various conditions.ResultsWe report total protein, lipid, DNA, RNA and carbohydrate content, cell dry mass, and detailed protein and lipid composition. Furthermore, we present meticulous data on exchange rates between cells and environment and provide detailed experimental protocols on how to determine all of the above. The biomass composition is converted into cell line- and condition-specific biomass functions for use in cell line-specific, genome-scale metabolic models of CHO. Finally, flux balance analysis (FBA) is used to demonstrate consistency between in silico predictions and experimental analysis.ConclusionsOur study reveals a strong variability of the total protein content and cell dry mass across cell lines. However, the relative amino acid composition is independent of the cell line and condition and thus needs not be explicitly measured for each new cell line. In contrast, the lipid composition is strongly influenced by the growth media and thus will have to be determined in each case. These cell line-specific variations in biomass composition have a small impact on growth rate predictions with FBA, as inaccuracies in the predictions are rather dominated by inaccuracies in the exchange rate spectra. Cell-specific biomass variations only become important if the experimental errors in the exchange rate spectra drop below twenty percent.     

Predictive macroscopic modeling of cell growth,metabolism and monoclonal antibody production: Case study of a CHO fed-batch production

We describe a systematic approach to establish predictive models of CHO cell growth, cell metabolism and monoclonal antibody (mAb) formation during biopharmaceutical production. The prediction is based on a combination of an empirical metabolic model connecting extracellular metabolic fluxes with cellular growth and product formation with mixed Monod-inhibition type kinetics that we generalized to every possible external metabolite. We describe the maximum specific growth rate as a function of the integral viable cell density (IVCD). Moreover, we also take into account the accumulation of metabolites in intracellular pools that can influence cell growth. This is possible even without identification and quantification of these metabolites as illustrated with fed-batch cultures of Chinese Hamster Ovary (CHO) cells producing a mAb. The impact of cysteine and tryptophan on cell growth and cell productivity was assessed, and the resulting macroscopic model was successfully used to predict the impact of new, untested feeding strategies on cell growth and mAb production. This model combining piecewise linear relationships between metabolic rates, growth rate and production rate together with Monod-inhibition type models for cell growth did well in predicting cell culture performance in fed-batch cultures even outside the range of experimental data used for establishing the model. It could therefore also successfully be applied for in silico prediction of optimal operating conditions.     

Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110.

Flux balance models of metabolism use stoichiometry of metabolic pathways, metabolic demands of growth, and optimality principles to predict metabolic flux distribution and cellular growth under specified environmental conditions. These models have provided a mechanistic interpretation of systemic metabolic physiology, and they are also useful as a quantitative tool for metabolic pathway design. Quantitative predictions of cell growth and metabolic by-product secretion that are experimentally testable can be obtained from these models. In the present report, we used independent measurements to determine the model parameters for the wild-type Escherichia coli strain W3110. We experimentally determined the maximum oxygen utilization rate (15 mmol of O2 per g [dry weight] per h), the maximum aerobic glucose utilization rate (10.5 mmol of Glc per g [dry weight] per h), the maximum anaerobic glucose utilization rate (18.5 mmol of Glc per g [dry weight] per h), the non-growth-associated maintenance requirements (7.6 mmol of ATP per g [dry weight] per h), and the growth-associated maintenance requirements (13 mmol of ATP per g of biomass). The flux balance model specified by these parameters was found to quantitatively predict glucose and oxygen uptake rates as well as acetate secretion rates observed in chemostat experiments. We have formulated a predictive algorithm in order to apply the flux balance model to describe unsteady-state growth and by-product secretion in aerobic batch, fed-batch, and anaerobic batch cultures. In aerobic experiments we observed acetate secretion, accumulation in the culture medium, and reutilization from the culture medium. In fed-batch cultures acetate is cometabolized with glucose during the later part of the culture period.(ABSTRACT TRUNCATED AT 250 WORDS)     

Development of a mathematical model for evaluating the dynamics of normal and apoptotic Chinese hamster ovary cells

A metabolic flux based methodology was developed for modeling the metabolism of a Chinese hamster ovary cell line. The elimination of insignificant fluxes resulted in a simplified metabolic network which was the basis for modeling the significant metabolites. Employing kinetic rate expressions for growing and non-growing subpopulations, a logistic model was developed for cell growth and dynamic models were formulated to describe culture composition and monoclonal antibody (MAb) secretion. The model was validated for a range of nutrient concentrations. Good agreement was obtained between model predictions and experimental data. The ultimate goal of this study is to establish a comprehensive dynamic model which may be used for model-based optimization of the cell culture for MAb production in both batch and fed-batch systems.     

Segregated mathematical model for growth of anchorage-dependent MDCK cells in microcarrier culture

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.     

Combined in silico modeling and metabolomics analysis to characterize fed-batch CHO cell culture

The increasing demand for recombinant therapeutic proteins highlights the need to constantly improve the efficiency and yield of these biopharmaceutical products from mammalian cells, which is fully achievable only through proper understanding of cellular functioning. Towards this end, the current study exploited a combined metabolomics and in silico modeling approach to gain a deeper insight into the cellular mechanisms of Chinese hamster ovary (CHO) fed-batch cultures. Initially, extracellular and intracellular metabolite profiling analysis shortlisted key metabolites associated with cell growth limitation within the energy, glutathione, and glycerophospholipid pathways that have distinct changes at the exponential-stationary transition phase of the cultures. In addition, biomass compositional analysis newly revealed different amino acid content in the CHO cells from other mammalian cells, indicating the significance of accurate protein composition data in metabolite balancing across required nutrient assimilation, metabolic utilization, and cell growth. Subsequent in silico modeling of CHO cells characterized internal metabolic behaviors attaining physiological changes during growth and non-growth phases, thereby allowing us to explore relevant pathways to growth limitation and identify major growth-limiting factors including the oxidative stress and depletion of lipid metabolites. Such key information on growth-related mechanisms derived from the current approach can potentially guide the development of new strategies to enhance CHO culture performance.     

Dynamic model of CHO cell metabolism

Fed-batch cultures are extensively used for the production of therapeutic proteins. However, process optimization is hampered by lack of quantitative models of mammalian cellular metabolism in these cultures. This paper presents a new kinetic model of CHO cell metabolism and a novel framework for simulating the dynamics of metabolic and biosynthetic pathways of these cells grown in fed-batch culture. The model defines a subset of the intracellular reactions with kinetic rate expressions based on extracellular metabolite concentrations and temperature- and redox-dependent regulatory variables. The simulation uses the rate expressions to calculate pseudo-steady state flux distributions and extracellular metabolite concentrations at discrete time points. Experimental data collected in this study for several different CHO cell fed-batch cultures are used to derive the rate expressions, fit the parameters, and validate the model. The simulations accurately predicted the effects of process variables, including temperature shift, seed density, specific productivity, and nutrient concentrations.     

Staying alive

Quiescence is a state of reversible cell cycle arrest that can grant protection against many environmental insults. In some systems, cellular quiescence is associated with a low metabolic state characterized by a decrease in glucose uptake and glycolysis, reduced translation rates and activation of autophagy as a means to provide nutrients for survival. For cells in multiple different quiescence model systems, including Saccharomyces cerevisiae, mammalian lymphocytes and hematopoietic stem cells, the PI3Kinase/TOR signaling pathway helps to integrate information about nutrient availability with cell growth rates. Quiescence signals often inactivate the TOR kinase, resulting in reduced cell growth and biosynthesis. However, quiescence is not always associated with reduced metabolism; it is also possible to achieve a state of cellular quiescence in which glucose uptake, glycolysis and flux through central carbon metabolism are not reduced. In this review, we compare and contrast the metabolic changes that occur with quiescence in different model systems.     

Staying alive: Metabolic adaptations to quiescence

Quiescence is a state of reversible cell cycle arrest that can grant protection against many environmental insults. In some systems, cellular quiescence is associated with a low metabolic state characterized by a decrease in glucose uptake and glycolysis, reduced translation rates and activation of autophagy as a means to provide nutrients for survival. For cells in multiple different quiescence model systems, including Saccharomyces cerevisiae, mammalian lymphocytes and hematopoietic stem cells, the PI3Kinase/TOR signaling pathway helps to integrate information about nutrient availability with cell growth rates. Quiescence signals often inactivate the TOR kinase, resulting in reduced cell growth and biosynthesis. However, quiescence is not always associated with reduced metabolism; it is also possible to achieve a state of cellular quiescence in which glucose uptake, glycolysis and flux through central carbon metabolism are not reduced. In this review, we compare and contrast the metabolic changes that occur with quiescence in different model systems.     

Biofuel production improvement with genome-scale models: The role of cell composition

Genome-scale models have developed into a vital tool for rational metabolic engineering. These models balance cofactors and energetic requirements and determine biosynthetic precursor availability in response to environmental and genetic perturbations. In particular, allocation of additional reducing power is an important strategy for engineering potential biofuel production from microbes. Many potential biofuel solvents induce biomolecular changes on the host organism that are not yet captured by genome-scale models. Here, methods of construction for several biomass constituting equations are reviewed along with potential changes to cellular composition with potential biofuels exposure. The biomass constituting equations of potential host organisms with existing genome-scale models are compared side-by-side to explore their evolution over the years and to explore differences that arise when these equations are compiled by different research groups. Genome-scale model simulation results attempt to address and provide guidance for further research into: (i) whether inconsistencies in the biomass constituting equations are relevant to predictions of solvent production, (ii) what level of detail is necessary to accurately describe cellular composition, and (iii) future developments that may enable more accurate characterizations of biomolecular composition.     

A dynamic model linking cell growth to intracellular metabolism and extracellular by-product accumulation

Mathematical modeling of animal cell growth and metabolism is essential for the understanding and improvement of the production of biopharmaceuticals. Models can explain the dynamic behavior of cell growth and product formation, support the identification of the most relevant parameters for process design, and significantly reduce the number of experiments to be performed for process optimization. Few dynamic models have been established that describe both extracellular and intracellular dynamics of growth and metabolism of animal cells. In this study, a model was developed, which comprises a set of 33 ordinary differential equations to describe batch cultivations of suspension AGE1.HN.AAT cells considered for the production of α1-antitrypsin. This model combines a segregated cell growth model with a structured model of intracellular metabolism. Overall, it considers the viable cell concentration, mean cell diameter, viable cell volume, concentration of extracellular substrates, and intracellular concentrations of key metabolites from the central carbon metabolism. Furthermore, the release of metabolic by-products such as lactate and ammonium was estimated directly from the intracellular reactions. Based on the same set of parameters, this model simulates well the dynamics of four independent batch cultivations. Analysis of the simulated intracellular rates revealed at least two distinct cellular physiological states. The first physiological state was characterized by a high glycolytic rate and high lactate production. Whereas the second state was characterized by efficient adenosine triphosphate production, a low glycolytic rate, and reactions of the TCA cycle running in the reverse direction from α-ketoglutarate to citrate. Finally, we show possible applications of the model for cell line engineering and media optimization with two case studies.     

Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia

Background

It is a daunting task to identify all the metabolic pathways of brain energy metabolism and develop a dynamic simulation environment that will cover a time scale ranging from seconds to hours. To simplify this task and make it more practicable, we undertook stoichiometric modeling of brain energy metabolism with the major aim of including the main interacting pathways in and between astrocytes and neurons.

Model

The constructed model includes central metabolism (glycolysis, pentose phosphate pathway, TCA cycle), lipid metabolism, reactive oxygen species (ROS) detoxification, amino acid metabolism (synthesis and catabolism), the well-known glutamate-glutamine cycle, other coupling reactions between astrocytes and neurons, and neurotransmitter metabolism. This is, to our knowledge, the most comprehensive attempt at stoichiometric modeling of brain metabolism to date in terms of its coverage of a wide range of metabolic pathways. We then attempted to model the basal physiological behaviour and hypoxic behaviour of the brain cells where astrocytes and neurons are tightly coupled.

Results

The reconstructed stoichiometric reaction model included 217 reactions (184 internal, 33 exchange) and 216 metabolites (183 internal, 33 external) distributed in and between astrocytes and neurons. Flux balance analysis (FBA) techniques were applied to the reconstructed model to elucidate the underlying cellular principles of neuron-astrocyte coupling. Simulation of resting conditions under the constraints of maximization of glutamate/glutamine/GABA cycle fluxes between the two cell types with subsequent minimization of Euclidean norm of fluxes resulted in a flux distribution in accordance with literature-based findings. As a further validation of our model, the effect of oxygen deprivation (hypoxia) on fluxes was simulated using an FBA-derivative approach, known as minimization of metabolic adjustment (MOMA). The results show the power of the constructed model to simulate disease behaviour on the flux level, and its potential to analyze cellular metabolic behaviour in silico.

Conclusion

The predictive power of the constructed model for the key flux distributions, especially central carbon metabolism and glutamate-glutamine cycle fluxes, and its application to hypoxia is promising. The resultant acceptable predictions strengthen the power of such stoichiometric models in the analysis of mammalian cell metabolism.     

Towards a metabolic and isotopic steady state in CHO batch cultures for reliable isotope-based metabolic profiling

Attaining metabolic and isotopic balanced growth is one critical condition for physiological studies using isotope-labeled tracers, but is very difficult to obtain in batch culture due to the extensive metabolite exchange with the surrounding medium and related physiological changes. In the present study, we investigated metabolic and isotopic behavior of CHO cells in differently designed media. We observed that the assumption of balanced cell growth cannot be justified in batch culture of CHO cells directly using conventional, commercially available media. By systematically redesigning media composition and characterizing metabolic steady state based on mass balances and measurement of labeling dynamics, we achieved balanced cell growth for the main cellular substrates in CHO cells. This was done in a step-by-step analysis of growth and primary metabolism of CHO cells with the use of [U-¹³C]glucose feeding and adjusting concentrations of amino acids in the growth medium. The optimized media obtained at the end of the study provide balanced growth and isotopic steady state or at least asymptotic steady state. As a result, we established a platform to conduct isotope-based physiological studies of mammalian systems more reliably and therefore well suited for later use in metabolic profiling of mammalian systems such as ¹³C-labeled metabolic flux analysis.     

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.     

Application of dynamic flux balance analysis to an industrial Escherichia coli fermentation

We have developed a reactor-scale model of Escherichia coli metabolism and growth in a 1000L process for the production of a recombinant therapeutic protein. The model consists of two distinct parts: (1) a dynamic, process specific portion that describes the time evolution of 37 process variables of relevance and (2) a flux balance based, 123-reaction metabolic model of E. coli metabolism. This model combines several previously reported modeling approaches including a growth rate-dependent biomass composition, maximum growth rate objective function, and dynamic flux balancing. In addition, we introduce concentration-dependent boundary conditions of transport fluxes, dynamic maintenance demands, and a state-dependent cellular objective. This formulation was able to describe specific runs with high-fidelity over process conditions including rich media, simultaneous acetate and glucose consumption, glucose minimal media, and phosphate depleted media. Furthermore, the model accurately describes the effect of process perturbations—such as glucose overbatching and insufficient aeration—on growth, metabolism, and titer.