A comparative analysis of kinetic models of erythrocyte glycolysis

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

This study aims to demonstrate the benefits of augmenting commercially available, real-time, in vitro glycolysis assays with phenomenological rate equation-based kinetic models, describing the contributions of the underpinning metabolic pathways. To this end, a commercially available glycolysis assay, sensitive to changes in extracellular acidification (extracellular pH), was used to derive the glycolysis pathway kinetics. The pathway was numerically modelled using a series of ordinary differential rate equations, to simulate the obtained experimental results. The sensitivity of the model to the key equation parameters was also explored. The cellular glycolysis pathway kinetics were determined for three different cell-lines, under nonmodulated and modulated conditions. Over the timescale studied, the assay demonstrated a two-phase metabolic response, representing the differential kinetics of glycolysis pathway rate as a function of time, and this behaviour was faithfully reproduced by the model simulations. The model enabled quantitative comparison of the pathway kinetics of three cell lines, and also the modulating effect of two known drugs. Moreover, the modelling tool allows the subtle differences between different cell lines to be better elucidated and also allows augmentation of the assay sensitivity. A simplistic numerical model can faithfully reproduce the differential pathway kinetics for three different cell lines, with and without pathway-modulating drugs, and furthermore provides insights into the cellular metabolism by elucidating the underlying mechanisms leading to the pathway end-product. This study demonstrates that augmenting a relatively simple, real-time, in vitro assay with a model of the underpinning metabolic pathway provides considerable insights into the observed differences in cellular systems.

Erythrocyte metabolism

Our aim is to present an updated overview of the erythrocyte metabolism highlighting its richness and complexity. We have manually collected and connected the available biochemical pathways and integrated them into a functional metabolic map. The focus of this map is on the main biochemical pathways consisting of glycolysis, the pentose phosphate pathway, redox metabolism, oxygen metabolism, purine/nucleoside metabolism, and membrane transport. Other recently emerging pathways are also curated, like the methionine salvage pathway, the glyoxalase system, carnitine metabolism, and the lands cycle, as well as remnants of the carboxylic acid metabolism. An additional goal of this review is to present the dynamics of erythrocyte metabolism, providing key numbers used to perform basic quantitative analyses. By synthesizing experimental and computational data, we conclude that glycolysis, pentose phosphate pathway, and redox metabolism are the foundations of erythrocyte metabolism. Additionally, the erythrocyte can sense oxygen levels and oxidative stress adjusting its mechanics, metabolism, and function. In conclusion, fine-tuning of erythrocyte metabolism controls one of the most important biological processes, that is, oxygen loading, transport, and delivery.

Is distance from equilibrium a good indicator for a reaction's flux control?

By analysing a large set of models obtained from the JWS Online and Biomodels databases, we tested to what extent the disequilibrium ratio can be used as an estimator for the flux control of a reaction, a discussion point that was already raised by Kacser and Burns, and Heinrich and Rapoport in their seminal MCA manuscripts. Whereas no functional relation was observed, the disequilibrium ratio can be used as an estimator for the maximal flux control of a reaction step. We extended the original analysis of the relationship by incorporating the overall pathway disequilibrium ratio in the expression, which made it possible to make explicit expressions for flux control coefficients.

Determining enzyme kinetics for systems biology with nuclear magnetic resonance spectroscopy

Enzyme kinetics for systems biology should ideally yield information about the enzyme’s activity under in vivo conditions, including such reaction features as substrate cooperativity, reversibility and allostery, and be applicable to enzymatic reactions with multiple substrates. A large body of enzyme-kinetic data in the literature is based on the uni-substrate Michaelis-Menten equation, which makes unnatural assumptions about enzymatic reactions (e.g., irreversibility), and its application in systems biology models is therefore limited. To overcome this limitation, we have utilised NMR time-course data in a combined theoretical and experimental approach to parameterize the generic reversible Hill equation, which is capable of describing enzymatic reactions in terms of all the properties mentioned above and has fewer parameters than detailed mechanistic kinetic equations; these parameters are moreover defined operationally. Traditionally, enzyme kinetic data have been obtained from initial-rate studies, often using assays coupled to NAD(P)H-producing or NAD(P)H-consuming reactions. However, these assays are very labour-intensive, especially for detailed characterisation of multi-substrate reactions. We here present a cost-effective and relatively rapid method for obtaining enzyme-kinetic parameters from metabolite time-course data generated using NMR spectroscopy. The method requires fewer runs than traditional initial-rate studies and yields more information per experiment, as whole time-courses are analyzed and used for parameter fitting. Additionally, this approach allows real-time simultaneous quantification of all metabolites present in the assay system (including products and allosteric modifiers), which demonstrates the superiority of NMR over traditional spectrophotometric coupled enzyme assays. The methodology presented is applied to the elucidation of kinetic parameters for two coupled glycolytic enzymes from Escherichia coli (phosphoglucose isomerase and phosphofructokinase). ³¹P-NMR time-course data were collected by incubating cell extracts with substrates, products and modifiers at different initial concentrations. NMR kinetic data were subsequently processed using a custom software module written in the Python programming language, and globally fitted to appropriately modified Hill equations.

The logic of kinetic regulation in the thioredoxin system

BACKGROUND

The thioredoxin system consisting of NADP(H), thioredoxin reductase and thioredoxin provides reducing equivalents to a large and diverse array of cellular processes. Despite a great deal of information on the kinetics of individual thioredoxin-dependent reactions, the kinetic regulation of this system as an integrated whole is not known. We address this by using kinetic modeling to identify and describe kinetic behavioral motifs found within the system.

RESULTS

Analysis of a realistic computational model of the Escherichia coli thioredoxin system revealed several modes of kinetic regulation in the system. In keeping with published findings, the model showed that thioredoxin-dependent reactions were adaptable (i.e. changes to the thioredoxin system affected the kinetic profiles of these reactions). Further and in contrast to other systems-level descriptions, analysis of the model showed that apparently unrelated thioredoxin oxidation reactions can affect each other via their combined effects on the thioredoxin redox cycle. However, the scale of these effects depended on the kinetics of the individual thioredoxin oxidation reactions with some reactions more sensitive to changes in the thioredoxin cycle and others, such as the Tpx-dependent reduction of hydrogen peroxide, less sensitive to these changes. The coupling of the thioredoxin and Tpx redox cycles also allowed for ultrasensitive changes in the thioredoxin concentration in response to changes in the thioredoxin reductase concentration. We were able to describe the kinetic mechanisms underlying these behaviors precisely with analytical solutions and core models.

CONCLUSIONS

Using kinetic modeling we have revealed the logic that underlies the functional organization and kinetic behavior of the thioredoxin system. The thioredoxin redox cycle and associated reactions allows for a system that is adaptable, interconnected and able to display differential sensitivities to changes in this redox cycle. This work provides a theoretical, systems-biological basis for an experimental analysis of the thioredoxin system and its associated reactions.

Complex coordination of multi-scale cellular responses to environmental stress

Cells and organisms are regularly exposed to a variety of stresses, and effective responses are a matter of survival. The article describes a multi-scale experimental and dynamical modeling analysis that clearly indicates concerted stress control in different temporal and organizational domains, and a strong synergy between the dynamics of genes, proteins and metabolites. Specifically, we show with in vivo NMR measurements of metabolic profiles that baker's yeast responds to a paradigmatic stress, heat, at three organizational levels and in two time regimes. At the metabolic level, an almost immediate response is mounted. However, this response is a "quick fix" in comparison to a much more effective response that had been pre-organized in earlier periods of heat stress and is an order of magnitude stronger. Equipped with the metabolic profile data, our modeling efforts resulted in a crisp, quantitative separation of response actions at the levels of metabolic control and gene regulation. They also led to predictions of necessary changes in protein levels and clearly demonstrated that formerly observed temperature profiles of key enzyme activities are not sufficient to explain the accumulation of trehalose as an immediate response to sudden heat stress.

A metabolic model of human erythrocytes: practical application of the E-Cell Simulation Environment

The human red blood cell (RBC) has long been used for modeling of complex biological networks, for elucidation of a wide variety of dynamic phenomena, and for understanding the fundamental topology of metabolic pathways. Here, we introduce our recent work on an RBC metabolic model using the E-Cell Simulation Environment. The model is sufficiently detailed to predict the temporal hypoxic response of each metabolite and, at the same time, successfully integrates modulation of metabolism and of the oxygen transporting capacity of hemoglobin. The model includes the mechanisms of RBC maintenance as a single cell system and the functioning of RBCs as components of a higher order system. Modeling of RBC metabolism is now approaching a fully mature stage of realistic predictions at the molecular level and will be useful for predicting conditions in biotechnological applications such as long-term cold storage of RBCs.

Uncovering metabolic objectives pursued by changes of enzyme levels

Expression profiling and proteomic techniques reveal significant variations in the levels of thousands of mRNAs and proteins in response to environmental changes such as substrate depletion, oxidative stress, and hormonal stimulation. However, in most cases the functional implications of these variations remain elusive. One crucial problem complicating the functional interpretation of high-throughput data is that changes of protein levels do not simply translate into equivalent changes in the rate of the associated chemical processes due to various modes of enzyme regulation and the instantaneous effect of changed metabolite concentrations on adjacent flux rates. Here, we outline a theoretical concept to exploit information on (relative) changes in the level of metabolic enzymes for the prediction of (relative) flux changes in the underlying metabolic network. Our approach rests on the assumption that size and direction of fluxes (flux distribution) in the network are determined by an optimization principle in that the production of the physiologically relevant output metabolites is accomplished with minimal total flux. The prediction method comprises two main steps. First, we approximate (unknown) flux changes by a linear combination of so-called minimal flux modes, each representing a specific flux distribution minimally required to accomplish the production of only one of the numerous functionally relevant output metabolites. Second, the unknown coefficients of this decomposition are chosen such that a maximal correlation with observed differential expression data is obtained. Based on simulated enzyme expression scenarios in a metabolic model of the human red blood cell, we demonstrate the predictive capacity of our method.

Kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws--a promising method for speeding up the kinetic modelling of complex metabolic networks

Kinetic modelling of complex metabolic networks - a central goal of computational systems biology - is currently hampered by the lack of reliable rate equations for the majority of the underlying biochemical reactions and membrane transporters. On the basis of biochemically substantiated evidence that metabolic control is exerted by a narrow set of key regulatory enzymes, we propose here a hybrid modelling approach in which only the central regulatory enzymes are described by detailed mechanistic rate equations, and the majority of enzymes are approximated by simplified(non mechanistic) rate equations (e.g. mass action, LinLog, Michaelis-Menten and power law) capturing only a few basic kinetic features and hence containing only a small number of parameters to be experimentally determined. To check the reliability of this approach, we have applied it to two different metabolic networks, the energy and redox metabolism of red blood cells, and the purine metabolism of hepatocytes, using in both cases available comprehensive mechanistic models as reference standards. Identification of the central regulatory enzymes was performed by employing only information on network topology and the metabolic data for a single reference state of the network [Grimbs S, Selbig J, Bulik S, Holzhutter HG & Steuer R (2007) Mol Syst Biol 3, 146, doi:10.1038/msb4100186].Calculations of stationary and temporary states under various physiological challenges demonstrate the good performance of the hybrid models. We propose the hybrid modelling approach as a means to speed up the development of reliable kinetic models for complex metabolic networks.