Analysis of Chinese hamster ovary cell metabolism through a combined computational and experimental approach

Optimization of cell culture processes can benefit from the systematic analysis of experimental data and their organization in mathematical models, which can be used to decipher the effect of individual process variables on multiple outputs of interest. Towards this goal, a kinetic model of cytosolic glucose metabolism coupled with a population-level model of Chinese hamster ovary cells was used to analyse metabolic behavior under batch and fed-batch cell culture conditions. The model was parameterized using experimental data for cell growth dynamics, extracellular and intracellular metabolite profiles. The results highlight significant differences between the two culture conditions in terms of metabolic efficiency and motivate the exploration of lactate as a secondary carbon source. Finally, the application of global sensitivity analysis to the model parameters highlights the need for additional experimental information on cell cycle distribution to complement metabolomic analyses with a view to parameterize kinetic models.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Kinetic models in industrial biotechnology – Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.     

Metabolic modeling of spatial heterogeneity of biofilms in microbial fuel cells reveals substrate limitations in electrical current generation

Microbial fuel cells (MFCs) have been proposed as an alternative energy resource for the conversion of organic compounds to electricity. In an MFC, microorganisms such as Geobacter sulfurreducens form an anode‐associated biofilm that can completely oxidize organic matter (electron donor) to carbon dioxide with direct electron transfer to the anode (electron acceptor). Mathematical models are useful in analyzing biofilm processes; however, existing models rely on Nernst–Monod type expressions, and evaluate extracellular processes separated from the intracellular metabolism of the microorganism. Thus, models that combine both extracellular and intracellular components, while addressing spatial heterogeneity, are essential for improved representation of biofilm processes. The goal of this work is to develop a model that integrates genome‐scale metabolic models with the model of biofilm environment. This integrated model shows the variations of electrical current production and biofilm thickness under the presence/absence of NH₄ in the bulk solution, and under varying maintenance energy demands. Further, sensitivity analysis suggested that conductivity is not limiting electrical current generation and that increasing cell density can lead to enhanced current generation. In addition, the modeling results also highlight instances such as the transformation into respiring cells, where the mechanism of electrical current generation during biofilm development is not yet clearly understood.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

Kinetics of pure cultures of hydrogen-oxidizing denitrifying bacteria and modeling of the interactions among them in mixed cultures

In this study we report the isolation of four denitrifying bacteria from a batch reactor, where the progress of hydrogenotrophic denitrification was examined. Only three of the strains had the ability to use hydrogen as electron donor. In the present work, kinetic batch experiments were carried out in order to study the dynamic characteristics of pure and defined mixed cultures of hydrogen-oxidizing denitrifying bacteria, under anoxic conditions, in a defined synthetic medium, in the presence of nitrates. Kinetic models were developed and the kinetic parameters were determined from the batch experiments for each bacterium separately. The behavior of mixed cultures and the interactions between the bacteria were described using kinetic models based on the kinetic models developed for each bacterium separately and their predictions were compared with the results from mixed culture experiments. The mathematical models that were developed and validated in the present work are capable of describing the behavior of the bacteria in pure and mixed cultures, and in particular, the kinetics of nitrate and nitrite reduction and cell growth.     

Exploring patterns of interspecific variation in quantitative traits using sequential phylogenetic eigenvector regressions

A number of metrics have been developed for estimating phylogenetic signal in data and to evaluate correlated evolution, inferring broad-scale evolutionary and ecological processes. Here, we proposed an approach called phylogenetic signal-representation (PSR) curve, built upon phylogenetic eigenvector regression (PVR). In PVR, selected eigenvectors extracted from a phylogenetic distance matrix are used to model interspecific variation. In the PSR curve, sequential PVR models are fitted after successively increasing the number of eigenvectors and plotting their R(2) against the accumulated eigenvalues. We used simulations to show that a linear PSR curve is expected under Brownian motion and that its shape changes under alternative evolutionary models. The PSR area, expressing deviations from Brownian motion, is strongly correlated (r= 0.873; P < 0.01) with Blomberg's K-statistics, so nonlinear PSR curves reveal if traits are evolving at a slower or higher rate than expected by Brownian motion. The PSR area is also correlated with phylogenetic half-life under an Ornstein-Uhlenbeck process, suggesting how both methods describe the shape of the relationship between interspecific variation and time since divergence among species. The PSR curve provides an elegant exploratory method to understand deviations from Brownian motion, in terms of acceleration or deceleration of evolutionary rates occurring at large or small phylogenetic distances.     

Structure-based kinetic modeling of excited-state transfer and trapping in histidine-tagged photosystem II core complexes from synechocystis

Chlorophyll fluorescence decay kinetics in photosynthesis are dependent on processes of excitation energy transfer, charge separation, and electron transfer in photosystem II (PSII). The interpretation of fluorescence decay kinetics and their accurate simulation by an appropriate kinetic model is highly dependent upon assumptions made concerning the homogeneity and activity of PSII preparations. While relatively simple kinetic models assuming sample heterogeneity have been used to model fluorescence decay in oxygen-evolving PSII core complexes, more complex models have been applied to the electron transport impaired but more highly purified D1-D2-cyt b(559) preparations. To gain more insight into the excited-state dynamics of PSII and to characterize the origins of multicomponent fluorescence decay, we modeled the emission kinetics of purified highly active His-tagged PSII core complexes with structure-based kinetic models. The fluorescence decay kinetics of PSII complexes contained a minimum of three exponential decay components at F(0) and four components at F(m). These kinetics were not described well with the single radical pair energy level model, and the introduction of either static disorder or a dynamic relaxation of the radical pair energy level was required to simulate the fluorescence decay adequately. An unreasonably low yield of charge stabilization and wide distribution of energy levels was required for the static disorder model, and we found the assumption of dynamic relaxation of the primary radical pair to be more suitable. Comparison modeling of the fluorescence decay kinetics from PSII core complexes and D1-D2-cyt b(559) reaction centers indicated that the rates of charge separation and relaxation of the radical pair are likely altered in isolated reaction centers.     

Optimal re-design of primary metabolism in Escherichia coli using linlog kinetics

This paper examines the validity of the linlog approach, which was recently developed in our laboratory, by comparison of two different kinetic models for the metabolic network of Escherichia coli. The first model is a complete mechanistic model; the second is an approximative model in which linlog kinetics are applied. The parameters of the linlog model (elasticities) are derived from the mechanistic model. Three different optimization cases are examined. In all cases, the objective is to calculate the enzyme levels that maximize a certain flux while keeping the total amount of enzyme constant and preventing large changes of metabolite concentrations. For an average variation of metabolite levels of 10% and individual changes of a factor 2, the predicted enzyme levels, metabolite concentrations and fluxes of both models are highly similar. This similarity holds for changes in enzyme level of a factor 4-6 and for changes in fluxes up to a factor 6. In all three cases, the predicted optimal enzyme levels could neither have been found by intuition-based approaches, nor on basis of flux control coefficients. This demonstrates that kinetic models are essential tools in Metabolic Engineering. In this respect, the linlog approach is a valuable extension of MCA, since it allows construction of kinetic models, based on MCA parameters, that can be used for constrained optimization problems and are valid for large changes of metabolite and enzyme levels.     

Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic

Modeling of metabolic pathway dynamics requires detailed kinetic equations at the enzyme level. In particular, the kinetic equations must account for metabolite effectors that contribute significantly to the pathway regulation in vivo. Unfortunately, most kinetic rate laws available in the literature do not consider all the effectors simultaneously, and much kinetic information exists in a qualitative or semiquantitative form. In this article, we present a strategy to incorporate such information into the kinetic equation. This strategy uses fuzzy logic‐based factors to modify algebraic rate laws that account for partial kinetic characteristics. The parameters introduced by the fuzzy factors are then optimized by use of a hybrid of simplex and genetic algorithms. The resulting model provides a flexible form that can simulate various kinetic behaviors. Such kinetic models are suitable for pathway modeling without complete enzyme mechanisms. Three enzymes in Escherichia coli central metabolism are used as examples: phosphoenolpyruvate carboxylase; phosphoenolpyruvate carboxykinase; and pyruvate kinase I. Results show that, with fuzzy logic‐augmented models, the kinetic data can be much better described. In particular, complex behavior, such as allosteric inhibition, can be captured using fuzzy rules. The resulting models, even though they do not provide additional physical meaning in enzyme mechanisms, allow the model to incorporate semiquantitative information in metabolic pathway models. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 62: 722–729, 1999.     

Modeling changes in biomass composition during microwave‐based alkali pretreatment of switchgrass

This study used two different approaches to model changes in biomass composition during microwave‐based pretreatment of switchgrass: kinetic modeling using a time‐dependent rate coefficient, and a Mamdani‐type fuzzy inference system. In both modeling approaches, the dielectric loss tangent of the alkali reagent and pretreatment time were used as predictors for changes in amounts of lignin, cellulose, and xylan during the pretreatment. Training and testing data sets for development and validation of the models were obtained from pretreatment experiments conducted using 1–3% w/v NaOH (sodium hydroxide) and pretreatment times ranging from 5 to 20 min. The kinetic modeling approach for lignin and xylan gave comparable results for training and testing data sets, and the differences between the predictions and experimental values were within 2%. The kinetic modeling approach for cellulose was not as effective, and the differences were within 5–7%. The time‐dependent rate coefficients of the kinetic models estimated from experimental data were consistent with the heterogeneity of individual biomass components. The Mamdani‐type fuzzy inference was shown to be an effective approach to model the pretreatment process and yielded predictions with less than 2% deviation from the experimental values for lignin and with less than 3% deviation from the experimental values for cellulose and xylan. The entropies of the fuzzy outputs from the Mamdani‐type fuzzy inference system were calculated to quantify the uncertainty associated with the predictions. Results indicate that there is no significant difference between the entropies associated with the predictions for lignin, cellulose, and xylan. It is anticipated that these models could be used in process simulations of bioethanol production from lignocellulosic materials. Biotechnol. Bioeng. 2010;105: 88–97. © 2009 Wiley Periodicals, Inc.     

An integrated metabolic model for the aerobic and denitrifying biological phosphorus removal

In this work, an integrated metabolic model for biological phosphorus removal is presented. Using a previously proposed mathematical model it was shown to be possible to describe the two known biological phosphorus removal processes, under aerobic and denitrifying conditions, with the same biochemical reactions, where only the difference in electron acceptor (oxygen and nitrate) is taken into account. Though, apart from the ATP/NADH ratio, the stoichiometry in those models is identical, different kinetic parameters were found. Therefore, a new kinetic structure is proposed that adequately describes phosphorus removal under denitrifying and aerobic conditions with the same kinetic equations and parameters. The ATP/NADH ratio (delta) is the only model parameter that is different for aerobic and denitrifying growth. With the new model, simulations of anaerobic/aerobic and anaerobic/denitrifying sequencing batch reactors (A(2) SBR and A/O SBR) were made for verification of the model. Not only short-term behavior, but also steady state, was simulated. The results showed very good agreement between model predictions and experimental results for a wide range of dynamic conditions and sludge retention times. Sensitivity analysis shows the influence of the model parameters and the feed substrate concentrations on both systems. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 434-450, 1997.     

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.     

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 reinforcement learning-based hybrid modeling framework for bioprocess kinetics identification

Constructing predictive models to simulate complex bioprocess dynamics, particularly time-varying (i.e., parameters varying over time) and history-dependent (i.e., current kinetics dependent on historical culture conditions) behavior, has been a longstanding research challenge. Current advances in hybrid modeling offer a solution to this by integrating kinetic models with data-driven techniques. This article proposes a novel two-step framework: first (i) speculate and combine several possible kinetic model structures sourced from process and phenomenological knowledge, then (ii) identify the most likely kinetic model structure and its parameter values using model-free Reinforcement Learning (RL). Specifically, Step 1 collates feasible history-dependent model structures, then Step 2 uses RL to simultaneously identify the correct model structure and the time-varying parameter trajectories. To demonstrate the performance of this framework, a range of in-silico case studies were carried out. The results show that the proposed framework can efficiently construct high-fidelity models to quantify both time-varying and history-dependent kinetic behaviors while minimizing the risks of over-parametrization and over-fitting. Finally, the primary advantages of the proposed framework and its limitation were thoroughly discussed in comparison to other existing hybrid modeling and model structure identification techniques, highlighting the potential of this framework for general bioprocess modeling.     

Analysis of cell locomotion on ligand gradient substrates

Directional cell motility plays a key role in many biological processes like morphogenesis, inflammation, wound repair, angiogenesis, immune response, and tumor metastasis. Cells respond to the gradient in surface ligand density by directed locomotion towards the direction of higher ligand density. Theoretical models which address the physical basis underlying the regulatory effect of ligand gradient on cell motility are highly desirable. Predictive models not only contribute to a better understanding of biological processes, but they also provide a quantitative interconnection between cell motility and biophysical properties of the extracellular matrix (ECM) for rational design of biomaterials as scaffolds in tissue engineering. In this work, we consider a one‐dimensional (1D) continuum viscoelastic model to predict the cell velocity in response to linearly increasing density of surface ligands on a substrate. The cell is considered as a 1D linear viscoelastic object with position dependent elasticity due to the variation in actin network density. The cell–substrate interaction is characterized by a frictional force, controlled by the density of ligand–receptor pairs. The generation of contractile stresses is described in terms of kinetic equations for the reactions between actins, myosins, and guanine nucleotide regulatory proteins. The model predictions show a reasonable agreement with experimentally measured cell speeds, considering biologically relevant values for the model parameters. The model predicts a biphasic relationship between cell speed and slope of gradient as well as a maximum limiting speed after a finite migration time. For a given slope of ligand gradient, the onset of the limiting speed appears at longer times for substrates with lower ligand gradients. The model can be applied to the design of biomaterials as scaffolds for guided tissue regeneration as it predicts an optimum range for the slope of ligand gradient. Biotechnol. Bioeng. 2009;103: 424–429. © 2009 Wiley Periodicals, Inc.     

Dynamics of asynchronous random Boolean networks with asynchrony generated by stochastic processes

An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897-923] for a varying number of parents. In both these papers the authors consider an asynchronous updating of all nodes, with asynchrony generated by various random distributions. We supplement those results by using various stochastic processes as generators for the number of nodes to be updated at each time point. In this paper we use the following stochastic processes: Poisson process, random walk, birth and death process, Brownian motion, and fractional Brownian motion. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed-point analysis. The dynamics of the system show that the number of nodes to be updated at each time point is of great importance, especially for the random walk, the birth and death, and the Brownian motion processes. Small or moderate values for the number of updated nodes generate order, while large values may generate chaos depending on the underlying parameters. The Poisson process generates order. With fractional Brownian motion, as the values of the Hurst parameter increase, the system exhibits order for a wider range of combinations of the underlying parameters.     

Critical review of activated sludge modeling: State of process knowledge,modeling concepts,and limitations

This work critically reviews modeling concepts for standard activated sludge wastewater treatment processes (e.g., hydrolysis, growth and decay of organisms, etc.) for some of the most commonly used models. Based on a short overview on the theoretical biochemistry knowledge this review should help model users to better understand (i) the model concepts used; (ii) the differences between models, and (iii) the limits of the models. The seven analyzed models are: (1) ASM1; (2) ASM2d; (3) ASM3; (4) ASM3 + BioP; (5) ASM2d + TUD; (6) Barker & Dold model; and (7) UCTPHO+. Nine standard processes are distinguished and discussed in the present work: hydrolysis; fermentation; ordinary heterotrophic organisms (OHO) growth; autotrophic nitrifying organisms (ANO) growth; OHO & ANO decay; poly‐hydroxyalkanoates (PHA) storage; polyphosphate (polyP) storage; phosphorus accumulating organisms PAO) growth; and PAO decay. For a structured comparison, a new schematic representation of these processes is proposed. Each process is represented as a reaction with consumed components on the left of the figure and produced components on the right. Standardized icons, based on shapes and color codes, enable the representation of the stoichiometric modeling concepts and kinetics. This representation allows highlighting the conceptual differences of the models, and the level of simplification between the concepts and the theoretical knowledge. The model selection depending on their theoretical limitations and the main research needs to increase the model quality are finally discussed. Biotechnol. Bioeng. 2013; 110: 24–46. © 2012 Wiley Periodicals, Inc.