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.

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.

Optimizing mammalian cell growth and bioproduction is a tedious task. However, due to the inherent complexity of eukaryotic cells, heuristic experimental approaches such as, metabolic engineering and bioprocess design, are frequently integrated with mathematical models of cell culture to improve biological process efficiency and find paths for improvement. Constraint-based metabolic models have evolved over the last two decades to be used for dynamic modelling in addition to providing a linear description of steady-state metabolic systems. Formulation and implementation of the underlying optimization problems require special attention to the model's performance and feasibility, lack of defects in the definition of system components, and consideration of optimal alternate solutions, in addition to processing power limitations. Here, the time-resolved dynamics of a genome-scale metabolic network of Chinese hamster ovary (CHO) cell metabolism are shown using a genome-scale dynamic constraint-based modelling framework (gDCBM). The metabolic network was adapted from a reference model of CHO genome-scale metabolic model (GSMM), iCHO_DG44_v1, and dynamic restrictions were imposed to its exchange fluxes based on experimental results. We used this framework for predicting physiological changes in CHO clonal variants. Because of the methodical creation of the components for the flux balance analysis optimization problem and the integration of a switch time, this model can generate sequential predictions of intracellular fluxes during growth and non-growth phases (per hour of culture time) and transparently reveal the shortcomings in such practice. As a result of the differences exploited by various clones, we can understand the relevance of changes in intracellular flux distribution and exometabolomics. The integration of various omics data into the given gDCBM framework, as well as the reductionist analysis of the model, can further help bioprocess optimization.