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.     

Tendency modeling: a new approach to obtain simplified kinetic models of metabolism applied to Saccharomyces cerevisiae

A novel approach to construct kinetic models of metabolic pathways, to be used in metabolic engineering, is presented: the tendency modeling approach. This approach greatly facilitates the construction of these models and can easily be applied to complex metabolic networks. The resulting models contain a minimal number of parameters; identification of their values is straightforward. Use of in vitro obtained information in the identification of the kinetic equations is minimized. The tendency modeling approach has been used to derive a dynamic model of primary metabolism for aerobic growth of Saccharomyces cerevisiae on glucose, in which compartmentation is included. Simulation results obtained with the derived model are satisfying for most of the carbon metabolites that have been measured. Compared to a more detailed model, the simulations of our model are less accurate, but taking into account the much smaller number of kinetic parameters (35 instead of 84), the tendency the modeling approach is considered promising.     

Examples of Mathematical Modeling: Tales from the Crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis.We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt.We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters.     

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.     

Segmented linear modeling of CHO fed‐batch culture and its application to large scale production

We describe a systematic approach to model CHO metabolism during biopharmaceutical production across a wide range of cell culture conditions. To this end, we applied the metabolic steady state concept. We analyzed and modeled the production rates of metabolites as a function of the specific growth rate. First, the total number of metabolic steady state phases and the location of the breakpoints were determined by recursive partitioning. For this, the smoothed derivative of the metabolic rates with respect to the growth rate were used followed by hierarchical clustering of the obtained partition. We then applied a piecewise regression to the metabolic rates with the previously determined number of phases. This allowed identifying the growth rates at which the cells underwent a metabolic shift. The resulting model with piecewise linear relationships between metabolic rates and the growth rate did well describe cellular metabolism in the fed‐batch cultures. Using the model structure and parameter values from a small‐scale cell culture (2 L) training dataset, it was possible to predict metabolic rates of new fed‐batch cultures just using the experimental specific growth rates. Such prediction was successful both at the laboratory scale with 2 L bioreactors but also at the production scale of 2000 L. This type of modeling provides a flexible framework to set a solid foundation for metabolic flux analysis and mechanistic type of modeling. Biotechnol. Bioeng. 2017;114: 785–797. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.     

A novel structured kinetic modeling approach for the analysis of plasmid instability in recombinant bacterial cultures

The instantaneous specific growth rate of a recombinant bacterial culture is directly calculated using a simple structured kinetic modeling approach. Foreign plasmid replication and foreign protein expression represent metabolic burdens to the host cell. The individual effects of these plasmid-mediated activities on the growth rate of plasmid-bearing cells are estimated separately. The dynamic and steady state simulations of the model equations show remarkable agreement with widely observed experimental trends in plasmid copy number and foreign protein content. The model provides an important tool for understanding and controlling plasmid instability in recombinant bacterial fermentations. The modeling framework employed here is suitable for studying the metabolism and growth of a variety of microbial cultures.     

Enhanced antibody production at slowed growth rates: experimental demonstration and a simple structured model.

A simple structured model for monoclonal antibody (MAb) production kinetics was formulated by combining the cell cycle theory with the estimated number of MAb-coded messenger RNA (mRNA) molecules per cell: it is assumed that the rate-controlling step is first order in this mRNA and that the growth rate variation does not alter the MAb synthesis rate within any cycle phase but only changes the relative time length of the individual phases. The model predicted "negatively growth associated" MAb production kinetics and thus an enhanced MAb production rate to be achieved by slowing the cell growth. Experiments consistent with these assumptions provided support for the model. Hybridoma cultures where growth was slowed by either a DNA synthesis inhibitor (thymidine or hydroxyurea) or by a selective inhibitor of initiation of nonantibody protein (potassium acetate) exhibited 50-130% MAb production rate enhancement for growth slowed up to 50%; however, further decreases in the growth rate also decreased the MAb production rate. Experiments inconsistent with these assumptions showed other behavior: general inhibition of protein chain elongation (by cycloheximide) or inhibition of ribosomal RNA (rRNA) synthesis (by actinomycin D) each slowed both growth and the specific MAb production rate, leading to net "positive" growth associated MAb production rates. Thus, a need for models with greater structure is also demonstrated.     

Optimization-driven identification of genetic perturbations accelerates the convergence of model parameters in ensemble modeling of metabolic networks

The ensemble modeling (EM) approach has shown promise in capturing kinetic and regulatory effects in the modeling of metabolic networks. Efficacy of the EM procedure relies on the identification of model parameterizations that adequately describe all observed metabolic phenotypes upon perturbation. In this study, we propose an optimization-based algorithm for the systematic identification of genetic/enzyme perturbations to maximally reduce the number of models retained in the ensemble after each round of model screening. The key premise here is to design perturbations that will maximally scatter the predicted steady-state fluxes over the ensemble parameterizations. We demonstrate the applicability of this procedure for an Escherichia coli metabolic model of central metabolism by successively identifying single, double, and triple enzyme perturbations that cause the maximum degree of flux separation between models in the ensemble. Results revealed that optimal perturbations are not always located close to reaction(s) whose fluxes are measured, especially when multiple perturbations are considered. In addition, there appears to be a maximum number of simultaneous perturbations beyond which no appreciable increase in the divergence of flux predictions is achieved. Overall, this study provides a systematic way of optimally designing genetic perturbations for populating the ensemble of models with relevant model parameterizations.     

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.     

The production of monoclonal antibody in growth-arrested hybridomas cultivated in suspension and immobilized modes.

The effects of the microenvironment and the nature of the limiting nutrient on culture viability and overall MAb productivity were explored using a hybridoma cell line which characteristically produces MAb in the stationary phase. A direct comparison was made of the changes in the metabolic profiles of suspension and PEG-alginate immobilized (0.8 mm beads) batch cultures upon entry into the stationary phase. The shifts in glucose, glutamine, and amino acid metabolism upon entry into the stationary phase were similar for both microenvironments. While the utilization of most nutrients in the stationary phase decreased to below 20% of that in the growth phase, antibody production was not dramatically affected. The immobilized culture did exhibit a 1.5-fold increase in the specific antibody rate over the suspension culture in both the growth and stationary phases. The role of limiting nutrient on MAb production and cell viability was assessed by artificially depleting a specific nutrient to 1% of its control concentration. An exponentially growing population of HB121 cells exposed to these various depletions responded with dramatically different viability profiles and MAb production kinetics. All depletions resulted in growth-arrested cultures and nongrowth-associated MAb production. Depletions in energy sources (glucose, glutamine) or essential amino acids (isoleucine) resulted in either poor viability or low antibody productivity. A phosphate or serum depletion maintained antibody production over at least a six day period with each resulting in a 3-fold higher antibody production rate than in growing batch cultures. These results were translated to a high-density perfusion culture of immobilized cells in the growth-arrested state with continued MAb expression for 20 days at a specific rate equal to that observed in the phosphate- and serum-depleted batch cultures.     

Prediction of microbial growth rate versus biomass yield by a metabolic network with kinetic parameters

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.     

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.     

Maximal Sum of Metabolic Exchange Fluxes Outperforms Biomass Yield as a Predictor of Growth Rate of Microorganisms

Growth rate has long been considered one of the most valuable phenotypes that can be measured in cells. Aside from being highly accessible and informative in laboratory cultures, maximal growth rate is often a prime determinant of cellular fitness, and predicting phenotypes that underlie fitness is key to both understanding and manipulating life. Despite this, current methods for predicting microbial fitness typically focus on yields [e.g., predictions of biomass yield using GEnome-scale metabolic Models (GEMs)] or notably require many empirical kinetic constants or substrate uptake rates, which render these methods ineffective in cases where fitness derives most directly from growth rate. Here we present a new method for predicting cellular growth rate, termed SUMEX, which does not require any empirical variables apart from a metabolic network (i.e., a GEM) and the growth medium. SUMEX is calculated by maximizing the SUM of molar EXchange fluxes (hence SUMEX) in a genome-scale metabolic model. SUMEX successfully predicts relative microbial growth rates across species, environments, and genetic conditions, outperforming traditional cellular objectives (most notably, the convention assuming biomass maximization). The success of SUMEX suggests that the ability of a cell to catabolize substrates and produce a strong proton gradient enables fast cell growth. Easily applicable heuristics for predicting growth rate, such as what we demonstrate with SUMEX, may contribute to numerous medical and biotechnological goals, ranging from the engineering of faster-growing industrial strains, modeling of mixed ecological communities, and the inhibition of cancer growth.     

Prospects for Biotechnology in Oil Palm (Elaeis guineensis) and Coconut (Cocos nucifera) Improvement

Abstract

Research into human metabolism is expanding rapidly due to the emergence of metabolism as a key factor in common diseases. Mathematical modeling of human cellular metabolism has traditionally been performed via kinetic approaches whose applicability for large-scale systems is limited by lack of kinetic constants data. An alternative computational approach bypassing this hurdle called constraint-based modeling (CBM) serves to analyze the function of large-scale metabolic networks by solely relying on simple physical-chemical constraints. However, while extensive research has been performed on constraint-based modeling of microbial metabolism, large-scale modeling of human metabolism is still in its infancy. Utilizing constraint-based modeling to model human cellular metabolism is significantly more complicated than modeling microbial metabolism as in multi-cellular organisms the metabolic behavior varies across cell-types and tissues. It is further complicated due to lack of data on cell type- and tissue-specific metabolite uptake from the surrounding microenvironments and tissue-specific metabolic objective functions. To overcome these problems, several studies suggested CBM methods that integrate metabolic networks with gene expression data that is easily measurable under various conditions. This specific objective functions are expected to improve the prediction accuracy of the presented methods. Such objective functions may be derived based on computational learning that would give optimal correspondence between predicted and measured metabolic phenotypes (Burgard, 2003).

The CBM methods presented here open the way for future computational investigations of metabolic disorders given the relevant expression data. A first attempt to visualize and interpret changes in gene expression data measured following gastric bypass surgery via a genome-scale metabolic network was done by Duarte et al (Duarte, 2007). Another potential application would be the prediction of diagnostic biomarkers for metabolic diseases that could be identified via biofluid metabolomics (Kell, 2007). Towards this goal, we have recently developed a CBM method for predicting metabolic biomarkers for in-born errors of metabolism by searching for changes in metabolite uptake and secretion rate due to genetic alterations (Shlomi, 2009). Incorporating cell type- and tissue-specific gene expression data within this framework can potentially improve the identification of diagnostic biomarkers. Overall, the methods presented here lay the foundation for studying normal and abnormal human cellular metabolism in tissue-specific manner based on commonly measured gene expression data.     

Descriptive parameter evaluation in mammalian cell culture

Several methods exist for assessing population growth and protein productivity in mammalian cell culture. These methods were critically examined here, based on experiments with two hybridoma cell lines. It is shown that mammalian cell culture parameters must be evaluated on the same basis. In batch culture mode most data is obtained on a cumulative basis (protein product titre, substrate concentration, metabolic byproduct concentration). A simple numerical integration technique can be employed to convert cell concentration data to a cumulative basis (cell-hours). The hybridoma lines used in this study included a nutritionally non-fastidious line producing low levels of MAb and a nutritionally fastidious hybridoma with high productivity. In both cases the cell-hour approach was the most appropriate means of expressing the relationship between protein productivity and cell population dynamics. The cell-hour approach could be used as the basis for all metabolic population parameter evaluations. This method has the potential to be used successfully for both prediction and optimization purposes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evaluation of exogenous siRNA addition as a metabolic engineering tool for modifying biopharmaceuticals

Traditional metabolic engineering approaches, including homologous recombination, zinc‐finger nucleases, and short hairpin RNA, have previously been used to generate biologics with specific characteristics that improve efficacy, potency, and safety. An alternative approach is to exogenously add soluble small interfering RNA (siRNA) duplexes, formulated with a cationic lipid, directly to cells grown in shake flasks or bioreactors. This approach has the following potential advantages: no cell line development required, ability to tailor mRNA silencing by adjusting siRNA concentration, simultaneous silencing of multiple target genes, and potential temporal control of down regulation of target gene expression. In this study, we demonstrate proof of concept of the siRNA feeding approach as a metabolic engineering tool in the context of increasing monoclonal antibody (MAb) afucosylation. First, potent siRNA duplexes targeting fut8 and gmds were dosed into shake flasks with cells that express an anti‐CD20 MAb. Dose response studies demonstrated the ability to titrate the silencing effect. Furthermore, siRNA addition resulted in no deleterious effects on cell growth, final protein titer, or specific productivity. In bioreactors, antibodies produced by cells following siRNA treatment exhibited improved functional characteristics compared to antibodies from untreated cells, including increased levels of afucosylation (63%), a 17‐fold improvement in FCgRIIIa binding, and an increase in specific cell lysis by up to 30%, as determined in an Antibody‐Dependent Cellular Cytoxicity (ADCC) assay. In addition, standard purification procedures effectively cleared the exogenously added siRNA and transfection agent. Moreover, no differences were observed when other key product quality structural attributes were compared to untreated controls. These results establish that exogenous addition of siRNA represents a potentially novel metabolic engineering tool to improve biopharmaceutical function and quality that can complement existing metabolic engineering methods. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 415–424, 2013     

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.     

Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics

This paper presents a new mathematical framework for modeling of in vivo dynamics and for metabolic re-design: the linlog approach. This approach is an extension of metabolic control analysis (MCA), valid for large changes of enzyme and metabolite levels. Furthermore, the presented framework combines MCA with kinetic modeling, thereby also combining the merits of both approaches. The linlog framework includes general expressions giving the steady-state fluxes and metabolite concentrations as a function of enzyme levels and extracellular concentrations, and a metabolic design equation that allows direct calculation of required enzyme levels for a desired steady state when control and response coefficients are available. Expressions giving control coefficients as a function of the enzyme levels are also derived. The validity of the linlog approximation in metabolic modeling is demonstrated by application of linlog kinetics to a branched pathway with moiety conservation, reversible reactions and allosteric interactions. Results show that the linlog approximation is able to describe the non-linear dynamics of this pathway very well for concentration changes up to a factor 20. Also the metabolic design equation was tested successfully.     

On-line metabolic pathway analysis based on metabolic signal flow diagram

In this work, an integrated modeling approach based on a metabolic signal flow diagram and cellular energetics was used to model the metabolic pathway analysis for the cultivation of yeast on glucose. This approach enables us to make a clear analysis of the flow direction of the carbon fluxes in the metabolic pathways as well as of the degree of activation of a particular pathway for the synthesis of biomaterials for cell growth. The analyses demonstrate that the main metabolic pathways of Saccharomyces cerevisiae change significantly during batch culture. Carbon flow direction is toward glycolysis to satisfy the increase of requirement for precursors and energy. The enzymatic activation of TCA cycle seems to always be at normal level, which may result in the overflow of ethanol due to its limited capacity. The advantage of this approach is that it adopts both virtues of the metabolic signal flow diagram and the simple network analysis method, focusing on the investigation of the flow directions of carbon fluxes and the degree of activation of a particular pathway or reaction loop. All of the variables used in the model equations were determined on-line; the information obtained from the calculated metabolic coefficients may result in a better understanding of cell physiology and help to evaluate the state of the cell culture process.