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.     

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.     

A hybrid mechanistic-empirical model for in silico mammalian cell bioprocess simulation

In cell culture processes cell growth and metabolism drive changes in the chemical environment of the culture. These environmental changes elicit reactor control actions, cell growth response, and are sensed by cell signaling pathways that influence metabolism. The interplay of these forces shapes the culture dynamics through different stages of cell cultivation and the outcome greatly affects process productivity, product quality, and robustness. Developing a systems model that describes the interactions of those major players in the cell culture system can lead to better process understanding and enhance process robustness. Here we report the construction of a hybrid mechanistic-empirical bioprocess model which integrates a mechanistic metabolic model with subcomponent models for cell growth, signaling regulation, and the bioreactor environment for in silico exploration of process scenarios. Model parameters were optimized by fitting to a dataset of cell culture manufacturing process which exhibits variability in metabolism and productivity. The model fitting process was broken into multiple steps to mitigate the substantial numerical challenges related to the first-principles model components. The optimized model captured the dynamics of metabolism and the variability of the process runs with different kinetic profiles and productivity. The variability of the process was attributed in part to the metabolic state of cell inoculum. The model was then used to identify potential mitigation strategies to reduce process variability by altering the initial process conditions as well as to explore the effect of changing CO₂ removal capacity in different bioreactor scales on process performance. By incorporating a mechanistic model of cell metabolism and appropriately fitting it to a large dataset, the hybrid model can describe the different metabolic phases in culture and the variability in manufacturing runs. This approach of employing a hybrid model has the potential to greatly facilitate process development and reactor scaling.     

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.     

The influence of high substrate concentrations on microbial kinetics

High substrate concentrations inhibit growth and may distort the metabolism of microorganisms. Mechanisms causing substrate inhibition are discussed and used to derive several mathematical models representative of the entire concentration range, including stimulation of growth by low substrate concentrations. These kinetic models are tested with a variety of batch culture measurements of specific growth rate and respiration rate at widely-ranging substrate concentrations. Using one of the kinetic models, equations are developed for batch, continuous, and exponential-feed reactors. Comparison of results obtained in continuous culture with results from exponential-feed culture systems is shown to offer a novel experimental method for evaluating the effect of the cell age distribution on the properties and metabolic activity of a culture.     

A comparison of mathematical model predictions to experimental measurements for growth and recombinant protein production in induced cultures of Escherichia coli

Recombinant cell growth and protein synthesis by a recombinant Escherichia coli under various inducing conditions are compared to the predictions of a mathematical model. The mathematical model used was a combination of two literature models: (1) an empirical kinetic model for recombinant growth and product formation and (2) a genetically structured model of the lac promoter-operator on a multicopy plasmid. The experimental system utilized was recombinant E. coli CSH22 bearing the temperature-sensitive plasmid pVH106/172, which codes for the synthesis of beta-galactosidase and the other lac operon genes under the control of a lac promoter. Mathematical model predictions for recombinant beta-galactosidase yield and specific growth rate were compared with fermentation measurements of these same quantities for conditions of chemical induction with cyclic AMP and IPTG, copy number amplification (by shifting culture temperature), and combined chemical induction and copy number amplification. The model successfully predicted experimental product yields for most cases of chemical induction even though the product yields varied from 0.34 x 10(3) to 1500 x 10(3) units/g cell mass. The kinetic model also correctly predicted a decline in the specific growth rate with increasing levels of plasmid and recombinant protein. The model was less successful at predicting product amplification at high copy numbers. A comparison of model predictions and experimental results was also used to investigate some of the assumptions used in constructing the mathematical models.     

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.     

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.     

From Enzyme Kinetics to Metabolic Network Modeling – Visualization Tool for Enhanced Kinetic Analysis of Biochemical Network Models

Model‐based analysis of enzyme kinetics allows the determination of optimal conditions for their use in biocatalysis. For biotransformations or fermentative approaches the modeling of metabolic pathways or complex metabolic networks is necessary to obtain model‐based predictions of steps which limit product formation within the network. To set up adequate kinetic models, relevant mechanistic information about enzyme properties is required and can be taken from in vitro studies with isolated enzymes or from in vivo investigations using stimulus‐response experiments which provide a lot of kinetic information about the metabolic network. But with increasing number of reaction steps and regulatory interdependencies in the network structure the amount of simulation data dramatically increases and the simulation results from the dynamic models become difficult to analyze and interpret. Demonstrated for an Escherichia coli model of the central carbon metabolism, methods for visualization and animation of simulation data were applied and extended to facilitate model analysis and biological interpretation. The dynamic metabolite pool and metabolic flux changes were visualized simultaneously by a software tool. In addition, a new quantification method for enzyme activation/inhibition was proposed, and this information was implemented in the metabolic visualization.     

Kinetic modeling of light limitation and sulfur deprivation effects in the induction of hydrogen production with Chlamydomonas reinhardtii: Part I. Model development and parameter identification

Chlamydomonas reinhardtii is a green microalga capable of turning its metabolism towards H2 production under specific conditions. However this H2 production, narrowly linked to the photosynthetic process, results from complex metabolic reactions highly dependent on the environmental conditions of the cells. A kinetic model has been developed to relate culture evolution from standard photosynthetic growth to H2 producing cells. It represents transition in sulfur-deprived conditions, known to lead to H2 production in Chlamydomonas reinhardtii, and the two main processes then induced which are an over-accumulation of intracellular starch and a progressive reduction of PSII activity for anoxia achievement. Because these phenomena are directly linked to the photosynthetic growth, two kinetic models were associated, the first (one) introducing light dependency (Haldane type model associated to a radiative light transfer model), the second (one) making growth a function of available sulfur amount under extracellular and intracellular forms (Droop formulation). The model parameters identification was realized from experimental data obtained with especially designed experiments and a sensitivity analysis of the model to its parameters was also conducted. Model behavior was finally studied showing interdependency between light transfer conditions, photosynthetic growth, sulfate uptake, photosynthetic activity and O2 release, during transition from oxygenic growth to anoxic H2 production conditions.     

Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three most common models, which are based on quite different biological assumptions, actually predict mathematically identical labeling curves with one parameter for the exponential up and down slope, and one parameter defining the maximum labeling level. By extending these previous models, we here propose a novel approach for the analysis of data from deuterium labeling experiments. We construct a model of “kinetic heterogeneity” in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a novel way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length.     

Stoichiometric model and flux balance analysis for a mixed culture of Leptospirillum ferriphilum and Ferroplasma acidiphilum

The oxidation process of sulfide minerals in natural environments is achieved by microbial communities from the Archaea and Bacteria domains. A metabolic reconstruction of two dominant species, Leptospirillum ferriphilum and Ferroplasma acidiphilum, which are always found together as a mixed culture in this natural environments, was made. The metabolic model, composed of 152 internal reactions and 29 transport reactions, describes the main interactions between these species, assuming that both use ferrous iron as energy source, and F. acidiphilum takes advantage of the organic compounds secreted by L. ferriphilum for chemomixotrophic growth. A first metabolic model for a mixed culture used in bacterial leaching is proposed in this article, which pretends to represent the characteristics of the mixed culture in a simplified manner. It was evaluated with experimental data through flux balance analysis (FBA) using as objective function the maximization of biomass. The growth yields on ferrous iron obtained for each microorganism are consistent with experimental data, and the flux distribution obtained allows understanding of the metabolic capabilities of both microorganisms growing together in a bioleaching process. The model was used to simulate the growth of F. acidiphilum on different substrates, to determine in silico which compounds maximize cell growth, and which are essential. Knockout simulations were carried out for L. ferriphilum and F. acidiphilum metabolic models, predicting key enzymes of central metabolism. The results of this analysis are consistent with experimental data from literature, showing a robust behavior of the metabolic model. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:307–315, 2015     

A systems approach to plant bioprocess optimization

A dynamic model for plant cell metabolism was used as a basis for a rational analysis of plant production potential in in vitro cultures. The model was calibrated with data from 3-L bioreactor cultures. A dynamic sensitivity analysis framework was developed to analyse the response curves of secondary metabolite production to metabolic and medium perturbations. Simulation results suggest that a straightforward engineering of cell metabolism or medium composition might only have a limited effect on productivity. To circumvent the problem of the dynamic allocation of resources between growth and production pathways, the sensitivity analysis framework was used to assess the effect of stabilizing intracellular nutrient concentrations. Simulations showed that a stabilization of intracellular glucose and nitrogen reserves could lead to a 116% increase in the specific production of secondary metabolites compared with standard culture protocol. This culture strategy was implemented experimentally using a perfusion bioreactor. To stabilize intracellular concentrations, adaptive medium feeding was performed using model mass balances and estimations. This allowed for a completely automated culture, with controlled conditions and pre-defined decision making algorithm. The proposed culture strategy leads to a 73% increase in specific production and a 129% increase in total production, as compared with a standard batch culture protocol. The sensitivity analysis on a mathematical model of plant metabolism thus allowed producing new insights on the links between intracellular nutritional management and cell productivity. The experimental implementation was also a significant improvement on current plant bioprocess strategies.     

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.     

k-Cone analysis: determining all candidate values for kinetic parameters on a network scale

The absence of comprehensive measured kinetic values and the observed inconsistency in the available in vitro kinetic data has hindered the formulation of network-scale kinetic models of biochemical reaction networks. To meet this challenge we present an approach to construct a convex space, termed the k-cone, which contains all the allowable numerical values of the kinetic constants in large-scale biochemical networks. The definition of the k-cone relies on the incorporation of in vivo concentration data and a simplified approach to represent enzyme kinetics within an established constraint-based modeling approach. The k-cone approach was implemented to define the allowable combination of numerical values for a full kinetic model of human red blood cell metabolism and to study its correlated kinetic parameters. The k-cone approach can be used to determine consistency between in vitro measured kinetic values and in vivo concentration and flux measurements when used in a network-scale kinetic model. k-Cone analysis was successful in determining whether in vitro measured kinetic values used in the reconstruction of a kinetic-based model of Saccharomyces cerevisiae central metabolism could reproduce in vivo measurements. Further, the k-cone can be used to determine which numerical values of in vitro measured parameters are required to be changed in a kinetic model if in vivo measured values are not reproduced. k-Cone analysis could identify what minimum number of in vitro determined kinetic parameters needed to be adjusted in the S. cerevisiae model to be consistent with the in vivo data. Applying the k-cone analysis a priori to kinetic model development may reduce the time and effort involved in model building and parameter adjustment. With the recent developments in high-throughput profiling of metabolite concentrations at a whole-cell scale and advances in metabolomics technologies, the k-cone approach presented here may hold the promise for kinetic characterization of metabolic networks as well as other biological functions at a whole-cell level.     

In Silico Models for Dynamic Connected Cell Cultures Mimicking Hepatocyte-Endothelial Cell-Adipocyte Interaction Circle

The biochemistry of a system made up of three kinds of cell is virtually impossible to work out without the use of in silico models. Here, we deal with homeostatic balance phenomena from a metabolic point of view and we present a new computational model merging three single-cell models, already available from our research group: the first model reproduced the metabolic behaviour of a hepatocyte, the second one represented an endothelial cell, and the third one described an adipocyte. Multiple interconnections were created among these three models in order to mimic the main physiological interactions that are known for the examined cell phenotypes. The ultimate aim was to recreate the accomplishment of the homeostatic balance as it was observed for an in vitro connected three-culture system concerning glucose and lipid metabolism in the presence of the medium flow. The whole model was based on a modular approach and on a set of nonlinear differential equations implemented in Simulink, applying Michaelis-Menten kinetic laws and some energy balance considerations to the studied metabolic pathways. Our in silico model was then validated against experimental datasets coming from literature about the cited in vitro model. The agreement between simulated and experimental results was good and the behaviour of the connected culture system was reproduced through an adequate parameter evaluation. The developed model may help other researchers to investigate further about integrated metabolism and the regulation mechanisms underlying the physiological homeostasis.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.