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.     

Theoretical analysis of insulin-dependent glucose uptake heterogeneity in 3D bioreactor cell culture

Three-dimensional (3D) cell cultures in bioreactors are becoming relevant as models for biological and physiological in vitro studies. In such systems, mathematical models can assist the experiment design that links the macroscopic properties to single-cell responses. We investigated the relationship between biochemical stimuli and cell response within a 3D cell culture in scaffold with heterogeneous porosity. Specifically, we studied the effect of insulin on the local glucose metabolism as a function of 3D pore size distribution. The multiscale mathematical model combines the mass transport within a 3D scaffold and a signaling pathways model. It considers the scaffold heterogeneity, and it describes spatiotemporal concentration of metabolites, biochemical stimuli, and cell density. The signaling model was integrated into this model, linking the local insulin concentration at cell membrane to the glucose uptake rate through glucose transporter type 4 (GLUT4) translocation from the cytosol to the cell membrane. The integrated model determines the cell response heterogeneities in a single channel, hence the biological response distribution in a 3D system. It also provides macroscopic outcomes to evaluate the feasibility of an experimental measurement of the system response. From our analysis, it became apparent that the flow rate is the most important operative variable, and that an optimum value ensures a fast and detectable cell response. This model on insulin-dependent glucose consumption rate offers insight into the cell metabolism physiology, which is a fundamental requirement for the study metabolic disorder such as Type 2 diabetes mellitus, in which the physiological insulin-dependent glucose metabolism is impaired.     

Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways.

It is now widely accepted that mathematical models are needed to predict the behaviour of complex metabolic networks in the cell, in order to have a rational basis for planning metabolic engineering with biotechnological or therapeutical purposes. The great complexity of metabolic networks makes it crucial to simplify them for analysis, but without violating key principles of stoichiometry or thermodynamics. We show here, however, that models for branched complex systems are sometimes obtained that violate the stoichiometry of fluxes at branch points and as a result give unrealistic metabolite concentrations at the steady state. This problem is especially important when models are constructed with the S-system form of biochemical systems theory. However, the same violation of stoichiometry can occur in metabolic control analysis if control coefficients are assumed to be constant when trying to predict the effects of large changes. We derive the appropriate matrix equations to analyse this type of problem systematically and to assess its extent in any given model.     

Macroscopic modelling of overflow metabolism and model based optimization of hybridoma cell fed-batch cultures

A macroscopic model that takes into account phenomena of overflow metabolism within glycolysis and glutaminolysis is proposed to simulate hybridoma HB-58 cell cultures. The model of central carbon metabolism is reduced to a set of macroscopic reactions. The macroscopic model describes three metabolism states: respiratory metabolism, overflow metabolism and critical metabolism. The model parameters and confidence intervals are obtained via a non linear least squares identification. It is validated with experimental data of fed-batch hybridoma cultures and successfully predicts the dynamics of cell growth and death, substrate consumption (glutamine and glucose) and metabolites production (lactate and ammonia). Based on a sensitivity analysis of the model outputs with respect to the parameters, a model reduction is proposed. Finally, the maximization of biomass productivity of hybridoma cell fed-batch cultures is analyzed. This model allows, on the one hand, quantitatively describing overflow metabolism in mammalian cell cultures and, on the other hand, will be valuable for monitoring and control of fed-batch cultures in order to optimize the process. This is illustrated in this contribution with the determination of optimal feeding profiles aiming at maximizing biomass productivity.     

Analysis of oscillations in yeast continuous cultures by a new simplified model

The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod’s classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model’s usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.     

Dynamic modeling of complex biological systems: a link between metabolic and macroscopic description

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples.     

DRUM: A New Framework for Metabolic Modeling under Non-Balanced Growth. Application to the Carbon Metabolism of Unicellular Microalgae

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.     

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 new generation of predictive models: The added value of hybrid models for manufacturing processes of therapeutic proteins

Due to the lack of complete understanding of metabolic networks and reaction pathways, establishing a universal mechanistic model for mammalian cell culture processes remains a challenge. Contrarily, data-driven approaches for modeling these processes lack extrapolation capabilities. Hybrid modeling is a technique that exploits the synergy between the two modeling methods. Although mammalian cell cultures are among the most relevant processes in biotechnology and indeed looks ideal for hybrid modeling, their application has only been proposed but never developed in the literature. This study provides a quantitative assessment of the improvement brought by hybrid models with respect to the state-of-the-art statistical predictive models in the context of therapeutic protein production. This is illustrated using a dataset obtained from a 3.5 L fed-batch experiment. With the goal to robustly define the process design space, hybrid models reveal a superior capability to predict the time evolution of different process variables using only the initial and process conditions in comparison to the statistical models. Hybrid models not only feature more accurate prediction results but also demonstrate better robustness and extrapolation capabilities. For the future application, this study highlights the added value of hybrid modeling for model-based process optimization and design of experiments.     

M5 mesoscopic and macroscopic models for mesenchymal motion

In this paper mesoscopic (individual based) and macroscopic (population based) models for mesenchymal motion of cells in fibre networks are developed. Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fibre networks, for example the invasion of tumor metastases through collagen networks. The movement of cells is guided by the directionality of the network and in addition, the network is degraded by proteases. The main results of this paper are derivations of mesoscopic and macroscopic models for mesenchymal motion in a timely varying network tissue. The mesoscopic model is based on a transport equation for correlated random walk and the macroscopic model has the form of a drift-diffusion equation where the mean drift velocity is given by the mean orientation of the tissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. The transport equation as well as the drift-diffusion limit are coupled to a differential equation that describes the tissue changes explicitly, where we distinguish the cases of directed and undirected tissues. As a result the drift velocity and the diffusion tensor are timely varying. We discuss relations to existing models and possible applications.Dedicated to K.P. Hadeler, a great scientist, teacher, and friend.     

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

MOTIVATION: Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. RESULTS: In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.     

Dynamic co‐culture metabolic models reveal the fermentation dynamics,metabolic capacities and interplays of cheese starter cultures

In this study, we have investigated the cheese starter culture as a microbial community through a question: can the metabolic behaviour of a co‐culture be explained by the characterized individual organism that constituted the co‐culture? To address this question, the dairy‐origin lactic acid bacteria Lactococcus lactis subsp. cremoris, Lactococcus lactis subsp. lactis, Streptococcus thermophilus and Leuconostoc mesenteroides, commonly used in cheese starter cultures, were grown in pure and four different co‐cultures. We used a dynamic metabolic modelling approach based on the integration of the genome‐scale metabolic networks of the involved organisms to simulate the co‐cultures. The strain‐specific kinetic parameters of dynamic models were estimated using the pure culture experiments and they were subsequently applied to co‐culture models. Biomass, carbon source, lactic acid and most of the amino acid concentration profiles simulated by the co‐culture models fit closely to the experimental results and the co‐culture models explained the mechanisms behind the dynamic microbial abundance. We then applied the co‐culture models to estimate further information on the co‐cultures that could not be obtained by the experimental method used. This includes estimation of the profile of various metabolites in the co‐culture medium such as flavour compounds produced and the individual organism level metabolic exchange flux profiles, which revealed the potential metabolic interactions between organisms in the co‐cultures.     

A multiscale model for red blood cell mechanics

The objective of this article is the derivation of a continuum model for mechanics of red blood cells via multiscale analysis. On the microscopic level, we consider realistic discrete models in terms of energy functionals defined on networks/lattices. Using concepts of Γ-convergence, convergence results as well as explicit homogenisation formulae are derived. Based on a characterisation via energy functionals, appropriate macroscopic stress–strain relationships (constitutive equations) can be determined. Further, mechanical moduli of the derived macroscopic continuum model are directly related to microscopic moduli. As a test case we consider optical tweezers experiments, one of the most common experiments to study mechanical properties of cells. Our simulations of the derived continuum model are based on finite element methods and account explicitly for membrane mechanics and its coupling with bulk mechanics. Since the discretisation of the continuum model can be chosen freely, rather than it is given by the topology of the microscopic cytoskeletal network, the approach allows a significant reduction of computational efforts. Our approach is highly flexible and can be generalised to many other cell models, also including biochemical control.     

NMR-based metabolic profiling of human hepatoma cells in relation to cell growth by culture media analysis

Metabolic profiling is a metabolomic approach that allows the characterization of metabolic phenotypes under specific set of conditions. In the present paper we investigated the metabolism of sparse and high density cultures in relation to different cell growth phases. Changes in the metabolome were evaluated by using 1H-NMR spectroscopy, correlation map and Multivariate Data Analysis on the net balances of metabolites in the medium. This approach allowed us to identify two different metabolic profiles in relation to the cell growth phases in subconfluence and confluence cultures. The results have been interpreted on the basis of patterns of correlations obtained in the two physiological cell states. Cells almost arrested in G0/G1 phase by contact dependent growth inhibition underwent changes in the channeling of amino acids utilization from synthetic to energetic purpose and in anaplerosis/cataplerosis regulation of the TCA cycle.     

Dynamics of microbial propagation: Models considering inhibitors and variable cell composition

Mathematical models for microbial growth in batch and continuous cultures are formulated. The models have been referred to as distributed models since the microbial population in a culture is looked upon as protoplasmic mass distributed uniformly throughout the culture. Growth is regarded as the increase in this mass by conversion of medium components into biological mass and metabolic products. Two sets of models have been presented. The first arise from introducing additional considerations into the model proposed by Monod to account for the stationary phase and the phase of decline in a batch culture. These have been referred to as unstructured, distributed models since they do not recognize any form of structure in the protoplasmic mass. The models in the second set are referred to as structured, distributed models. Structure is introduced by considering the protoplasmic mass to be composed of two groups of substances which interact with each other and with substances in the environment to produce growth. The structured models account for the dependence of growth on the past, history of the cells; thus they predict all growth phases observed in batch cultures, whereas the unstructured models do not predict a lag phase. The full implications of the models for continuous propagation, as determined by the method of stability analysis and transient calculations, are discussed. The models prediet a number of new results and should be confronted with experiments.     

Inferring Metabolic States in Uncharacterized Environments Using Gene-Expression Measurements

The large size of metabolic networks entails an overwhelming multiplicity in the possible steady-state flux distributions that are compatible with stoichiometric constraints. This space of possibilities is largest in the frequent situation where the nutrients available to the cells are unknown. These two factors: network size and lack of knowledge of nutrient availability, challenge the identification of the actual metabolic state of living cells among the myriad possibilities. Here we address this challenge by developing a method that integrates gene-expression measurements with genome-scale models of metabolism as a means of inferring metabolic states. Our method explores the space of alternative flux distributions that maximize the agreement between gene expression and metabolic fluxes, and thereby identifies reactions that are likely to be active in the culture from which the gene-expression measurements were taken. These active reactions are used to build environment-specific metabolic models and to predict actual metabolic states. We applied our method to model the metabolic states of Saccharomyces cerevisiae growing in rich media supplemented with either glucose or ethanol as the main energy source. The resulting models comprise about 50% of the reactions in the original model, and predict environment-specific essential genes with high sensitivity. By minimizing the sum of fluxes while forcing our predicted active reactions to carry flux, we predicted the metabolic states of these yeast cultures that are in large agreement with what is known about yeast physiology. Most notably, our method predicts the Crabtree effect in yeast cells growing in excess glucose, a long-known phenomenon that could not have been predicted by traditional constraint-based modeling approaches. Our method is of immediate practical relevance for medical and industrial applications, such as the identification of novel drug targets, and the development of biotechnological processes that use complex, largely uncharacterized media, such as biofuel production.     

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization,confidence bounds,and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.     

A SIMPLE COMPUTER SIMULATION MODEL FOR GROWING CELL POPULATIONS: ANALYSIS OF SYNCHRONIZED HELA CELL CULTURES

A simple simulation model is presented for growing cell populations. It consists of various ‘classes’of cells (usually thirty) with different cell cycle durations. The cells of each class are distributed in ‘compartments’(thirty to fifty) with different ages. A ‘typical cell’of each compartment is chosen at random and its behaviour weighed according to the number of cells of the compartment. When the parameters for cycle phase durations (G₂, S, G₁ and M) obtained from Quastler-Sherman curves on HeLa cell cultures are fed into the model and the initial distribution of cells is randomized according to the law of exponential growth, the model behaves as an exponentially growing culture with near stable values for the percentage of cells in the various phases of the cell cycle. The level of noise due to random sampling is not objectionable. The behaviour of the model is compared to that of HeLa cultures synchronized by two successive treatments with 2 mM thymidine. While a complete block of S gives very inadequate results, a slowing down of this phase to 25 or 30% of its original speed is enough to simulate all the modifications produced by the thymidine treatment on the cultures. It is not necessary to postulate any other effect. These biological conclusions are reached in spite of the simplicity of the system. The behaviour of the model stresses the fact that for simulating the actual behaviour of cell populations, some parameters of the cell cycle have to be known with considerable accuracy, others are less critical. The model is compared with other mathematical models of cell populations recently proposed and ways to improve it are discussed.     

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.