Modelling cell metabolism : a review on constraint-based steady-state and kinetic approaches

ABSTRACT: Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed

A Dynamic Constraint-Based Modelling Approach of Cell Metabolism

RÉSUMÉ: La modélisation métabolique mathématique est une approche systématique pour déterminer les principales causes d'un changement métabolique observé dans un biosystème, et estimer les implications d'une perturbation métabolique induite. En fournissant des informations mécanistiquement pertinentes au niveau des systèmes sur un réseau de bioréactions, la modélisation dynamique basée sur les contraintes (DCBM) s'est révélée prometteuse en ingénierie métabolique et pour la conception de bioprocédés. Aussi, nous avons d'abord dressé l'état de l'art en approches de modélisation du métabolisme de cellules eucaryotes, sous la forme d'une revue. Nous avons, par la suite, développé une approche DCBM qui utilise une boîte à outils mathématique d'optimisation convexe et de régression non linéaire pour estimer les distributions dynamiques des flux métaboliques intracellulaires dans deux biosystèmes : dans un premier temps les globules rouges stockés comme élément critique pour la médecine transfusionnelle, et dans un deuxième temps, des cellules de l'ovaire de hamster chinois (CHO), lignée cellulaire en tant que principal organisme hôte pour produire des produits biopharmaceutiques recombinant par culture cellulaire. Nous avons créé un réseau métabolique ad hoc comportant 77 réactions et 74 métabolites pour les globules rouges. Nous avons acquis une dynamique de flux à grain fin des processus intracellulaires. Ensuite, pour une analyse dynamique de l'équilibre des flux (DFBA), nous avons créé quatre fonctions objectives liées à l'accumulation de stress oxydatif dans les globules rouges stockés. Des prédictions de flux résolues dans le temps ont été obtenues dans les quatre situations tout en respectant les exigences d'égalité et d'inégalité requises. Enfin, pour calculer la distance euclidienne entre les vecteurs de flux optimaux dynamiques, nous avons utilisé une approche de programmation quadratique (QP). L'approche DCBM que nous avons créée ici, couplée au réseau métabolique que nous avons développé, s'est avérée adaptée à l'analyse informatique du comportement métabolique des globules rouges, et on s'attend à ce qu'elle soit bénéfique pour d'autres biosystèmes. De plus, en raison de la complexité inhérente des cellules eucaryotes, l'optimisation de la dynamique de croissance cellulaire et de la bio-production à partir de cultures de cellules de mammifères est une tâche complexe au niveau cellulaire. En conséquence, les approches expérimentales heuristiques en l'ingénierie métabolique des organismes hôtes sont fréquemment complétées par des modèles mathématiques de culture cellulaire afin d'améliorer l'efficacité des bioprocédés et d'identifier les causes des améliorations connues. En utilisant la stoechiométrie des bilans de masse du réseau, les modèles métaboliques structurés sont capables de représenter avec précision la complexité d'un réseau métabolique. Les modèles métaboliques basés sur les contraintes ont progressé au cours des vi deux dernières décennies, passant de leur utilisation pour fournir une description linéaire des systèmes métaboliques à l'état d'équilibre, à la modélisation de la dynamique des systèmes non linéaires dans une formulation de problème d'optimisation résolue dans le temps ou dynamique. Cependant, bon nombre de ces approches échouent lorsqu'elles sont testées dans un contexte autre que celui pour lequel elles ont été développées, en raison d'un grand nombre d'hypothèses formulées au cours du processus de développement du modèle, ainsi que de diverses normes de modélisation utilisées par différents groupes de recherche, tous visant à révéler la complexité inhérente des réseaux métaboliques. Nous avons suivi les normes établies par la communauté telles que dans la reconstruction de réseaux et leur analyse basées sur les contraintes (COBRA). La plateforme COBRA in silico a été utilisée pour proposer une technique de modélisation dynamique basée sur les contraintes (gDCBM) à l'échelle du génome, et a permis de fournir la dynamique résolue dans le temps d'un réseau métabolique structuré pour le métabolisme des cellules CHO. Nous avons amélioré le réseau métabolique à l'aide d'un modèle métabolique de référence à l'échelle du génome (GSMM) de CHO, à savoir iCHO DG44 v1, puis imposé des contraintes dynamiques sur ses flux de transport à l'aide de données métabolomiques générées en interne. Pour anticiper les changements physiologiques dans les variants clonaux de CHO, nous avons utilisé cette technique gDCBM. Le modèle peut prédire les flux intracellulaires de manière continue et résolue dans le temps (par heure de temps de culture) pendant la croissance et vers le changement métabolique de non-croissance, a été confirmé en prédisant les concentrations en métabolites extracellulaires, y compris les acides aminés, ainsi que leur dynamique dans le temps. En conséquence, nous pouvons générer des hypothèses d'intervention et étudier les effets d'altération in silico avant ou en plus des expériences de culture cellulaire, qui sont chronophages et coûteuses. Le modèle est également utilisé pour décrire les altérations métaboliques globales entre les lignées cellulaires parentales et productrices élevées dans une autre application. Nous avons démontré que l'approche de modélisation établie peut être utilisée pour étendre ou réduire le réseau métabolique de manière systématique. ABSTRACT: Mathematical metabolic modelling is a systematic approach to determining the major causes of a metabolic change seen in a biosystem and estimating the implications of an induced metabolic perturbation. By providing mechanistically relevant systems-level information about a network of bioreactions, dynamic constraint-based modelling (DCBM) has shown promise in metabolic engineering and bioprocess design. Also, we first drew up the state of the art in approaches to modelling the metabolism of eukaryotic cells, in the form of a review article. Thus, we have developed a DCBM approach that uses a mathematical toolkit of convex optimization and nonlinear regression to estimate dynamic intracellular metabolic flux distributions in two biosystems: Firstly, stored red blood cells (RBCs) as a critical element for transfusion medicine, and secondly, Chinese hamster ovary (CHO) cell line as the main host organism producing recombinant biopharmaceuticals in cell culture technology. We created an ad hoc metabolic network including 77 reactions and 74 metabolites for RBCs. We acquired fine-grained flow dynamics of intracellular processes. Then, for a dynamic Flux Balance Analysis (DFBA), we created four objective functions related to the accumulation of oxidative stress in stored RBCs. Time-resolved flux predictions were obtained in all four situations while adhering to the required equality and inequality requirements. Finally, to calculate the Euclidean distance between the dynamic optimum flux vectors, we used a quadratic programming (QP) approach. The DCBM approach we created here, coupled with the metabolic network we developed, proved to be suitable for the computational analysis of RBC metabolic behaviour, and it is expected to be beneficial for other biosystems. In addition, because of the inherent complexity of eukaryote cells, optimising cell growth dynamics and bioproduction from mammalian cell cultures is a complex task at the cellular level. As a result, heuristic experimental approaches in metabolic engineering of host organisms are frequently complemented with mathematical models of cell culture in order to improve the odds of enhancing bioprocess efficiency and identifying causes for known improvements. By utilising the network's mass balances' stoichiometry, structured metabolic models are able to accurately represent the complexity of a metabolic network. Constraint-based metabolic models have advanced over the last two decades from being utilised to provide a linear description of metabolic systems at steady states to modelling nonlinear system dynamics in a time-resolved or dynamic optimization problem formulation. Many of these approaches, however, fail when tested in a setting other than the one for which they were developed, owing to a large number of assumptions made during the model development process, as well as diverse modelling standards used by different research groups, all aimed at revealing the viii inherent complexity of metabolic networks. We have followed the community's established standards as in Constraint-based reconstruction and analysis (COBRA). The COBRA in silico platform has been used to propose a genome-scale dynamic constraint-based modelling (gDCBM) technique that allows delivering time-resolved dynamics of a structured metabolic network for CHO cell metabolism. We improved the metabolic network using a reference genome-scale metabolic model (GSMM) of CHO, i.e., iCHO DG44 v1, and then imposed dynamic constraints on its transport fluxes using metabolomics data generated in-house. To anticipate physiological changes in CHO clonal variants, we used this gDCBM technique. The model can predict intracellular fluxes in a continuous time-resolved (per hour of culture time) manner during the growth to non-growth metabolic switch, and it has been confirmed by predicting concentrations of extracellular metabolites, including amino acids, dynamics of change in time. As a result, we may generate intervention hypotheses and study the alteration effects in silico before or in addition to the time-consuming and expensive cell culture experiments. The model is also used to describe global metabolic alterations between parental and high producer cell lines in another application. We demonstrated that the established modelling approach may be used to extend or reduce the metabolic network in a systematic way

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed

The ERK signaling pathway.

<p>Different subsystems and feedback loops are hierarchically organized to process the extracellular signal introduced by Growth Factor (GF). Red arrows indicate internal positive feedback loops. Green arrows represent the external feedback loops. Blue dashed lines and black dashed lines indicate the subsystems and the nucleus, respectively.</p

Generation of a desired ERK response profile by the external feedback loops.

<p>(A) ERK^PP response. (B) GF pulse. (C) External feedback loops EFBL1 and EBFL2. k_EFBL = 1 indicates that the loop is on and k_EFBL = 0 indicates it is off. kcat3 = 1.75, gpT = 10, knfb = 0.0. grA = 1.</p

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

<div><p>Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.</p></div

Steady-state response curves without the external feedback loops.

<p>GF (growth factor) is the bifurcation parameter that is being changed. Red and blue curves are the stable and unstable branches, respectively. LP: Limit Point bifurcation also called the turning point at which the switch between the low and high stable branches occurs. (A) Since bistability curve is so flat for the <b><i>SOS</i></b>_{<b><i>complex</i></b>}, the unstable blue branch is squeezed between the two red stable branches and is not visible. (B) <i>RasGTP</i> response. The switch between the low and high stable branches occurs at the turning points, and it is shown by the arrows. (C) Ultrasensitive <b><i>MEK</i></b>^{<b><i>PP</i></b>} response. (D) Bistability is sustained in <b><i>ERK</i></b>^{<b><i>PP</i></b>} response.</p

Limit cycles.

<p>(A) The limit cycles in phase-plane. (B) The response starting from a lower value of RasGTP converges to the limit cycle indicated by the spiral trajectory. (C) The response starting from a high RasGTP value converges to the stable non-oscillatory high state.</p