Current status and challenges in connecting models of erythrocyte metabolism to experimental reality

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.

Membrane flickering of the human erythrocyte: constrained random walk used with Bayesian analysis

The involvement of adenosine triphosphate (ATP) in erythrocyte (red blood cell; RBC) membrane flickering is of particular interest, because ATP turnover in the cell as a whole is not yet fully accounted for. We sought the origins of flickering by deriving a mathematical model of it, on the basis of the idea of thermally driven collisions of small molecules with the membrane, which responds like an over-damped spring. The model gave simulated responses that were similar to a constrained random walk and had the same frequency-spectral characteristics of membrane displacement as those recorded from RBCs by use of differential interference contrast light microscopy. Bayesian analysis was used as the basis for determination, from experimental results, of the values of the parameters in the model. The analysis was used in the accompanying article in which we investigated the response of membrane flickering to different effector molecules and physicochemical conditions. The results implied ATP was involved only indirectly in membrane flickering.

Membrane flickering of the human erythrocyte: physical and chemical effectors

Recent studies suggest a link between adenosine triphosphate (ATP) concentration and the amplitude of cell membrane flickering (CMF) in the human erythrocyte (red blood cell; RBC). Potentially, the origin of this phenomenon and the unique discocyte shape could be active processes that account for some of the ATP turnover in the RBC. Active flickering could depend on several factors, including pH, osmolality, enzymatic rates and metabolic fluxes. In the present work, we applied the data analysis described in the previous article to study time courses of flickering RBCs acquired using differential interference contrast light microscopy in the presence of selected effectors. We also recorded images of air bubbles in aqueous detergent solutions and oil droplets in water, both of which showed rapid fluctuations in image intensity, the former showing the same type of spectral envelope (relative frequency composition) to RBCs. We conclude that CMF is not directly an active process, but that ATP affects the elastic properties of the membrane that flickers in response to molecular bombardment in a manner that is described mathematically by a constrained random walk.

Stoichiometric relationship between Na(+) ions transported and glucose consumed in human erythrocytes: Bayesian analysis of (23)Na and (13)C NMR time course data

We examined the response of Na(+),K(+)-ATPase (NKA) to monensin, a Na(+) ionophore, with and without ouabain, an NKA inhibitor, in suspensions of human erythrocytes (red blood cells). A combination of (13)C and (23)Na NMR methods allowed the recording of intra- and extracellular Na(+), and (13)C-labeled glucose time courses. The net influx of Na(+) and the consumption of glucose were measured with and without NKA inhibited by ouabain. A Bayesian analysis was used to determine probability distributions of the parameter values of a minimalist mathematical model of the kinetics involved, and then used to infer the rates of Na(+) transported and glucose consumed. It was estimated that the numerical relationship between the number of Na(+) ions transported by NKA per molecule of glucose consumed by a red blood cell was close to the ratio 6.0:1.0, agreeing with theoretical prediction.

Stability of open pathways

We consider the steady state of an open biochemical pathway, with controlled flow. Previously we have shown that the steady state of open enzyme catalysed reactions may be unstable, which discourages the application of the quasi-steady-state approximation (QSSA) [IEE Proc.-Syst. Biol. 153 (2006) 187]. Here we examine basic open biochemical pathway structures, to see the stability of their steady states. Following De Leenheer et al. [J. Math. Chem. 41 (2007) 295], we employ the Gershgorin circle theorem, which elegantly assesses stability. This is the key tool for our analysis. Once we have the linear stability matrix laid out in a suitable form, the application of the method is straightforward. We find that in open biochemical pathways, simple chains, branches and loops always have stable steady states. We conclude that simple open pathways are stable.

A comparative analysis of kinetic models of erythrocyte glycolysis

Since the 1970s, with Heinrich as a pioneer in the field, numerous kinetic models of erythrocyte glycolysis have been constructed. A functional comparison of eight of these models indicates that the production of ATP and GSH in the red blood cell is largely controlled by the demand reactions. The rate characteristics for the supply and demand blocks indicate a good homeostatic control of ATP and GSH concentrations at different work loads for the pathway, while the production rates of ATP and GSH can be adjusted as needed by the demand reactions.

Isotopomer subspaces as indicators of metabolic-pathway structure

The relative abundances and rates of formation of particular isotopic isomers (isotopomers) of metabolic intermediates from (13)C-labelled substrates in living cells provide information on the routes taken by the initial (13)C-atoms. When a primary substrate such as [U,(13)C] d-glucose is added to human erythrocytes, the pattern of labels in terminal metabolites is determined by a set of carbon-group exchange reactions in both glycolysis and the pentose phosphate pathway (PPP). Of a given terminal metabolite, not all possible isotopomers will be produced from each possible primary substrate isotopomer. There are only 8 different (13)C-isotopomers of lactate but not all of these are produced when one of the 64 possible (13)C-isotopomers of glucose is used as the input substrate; thus a subset of all 63 glucose isotopomers x 8 lactate isotopomers+1 unlabelled glucose x 1 unlabelled lactate=505 pattern associations, would be produced if a complete experimental analysis were performed with all the glucose variants. The pattern of labelling in this isotopomer subspace reflects the nature of the re-ordering reactions that 'direct' the metabolism. Predicting the combinatorial rearrangements for particular sets of reactions and comparing these with real data should enable conclusions to be drawn about which enzymes are involved in the real metabolic system. An example of the glycolysis-PPP system is discussed in the context of a debate that occurred around the F- and L-type PPPs and which one actually operates in the human RBC. As part of this discussion we introduce the term 'combinatorial deficit' of all possible isotopomers and we show that this deficit is less for the F- than the L-type pathway.

Simulation study of methemoglobin reduction in erythrocytes. Differential contributions of two pathways to tolerance to oxidative stress

Methemoglobin (metHb), an oxidized form of hemoglobin, is unable to bind and carry oxygen. Erythrocytes are continuously subjected to oxidative stress and nitrite exposure, which results in the spontaneous formation of metHb. To avoid the accumulation of metHb, reductive pathways mediated by cytochrome b5 or flavin, coupled with NADH-dependent or NADPH-dependent metHb reductases, respectively, keep the level of metHb in erythrocytes at less than 1% of the total hemoglobin under normal conditions. In this work, a mathematical model has been developed to quantitatively assess the relative contributions of the two major metHb-reducing pathways, taking into consideration the supply of NADH and NADPH from central energy metabolism. The results of the simulation experiments suggest that these pathways have different roles in the reduction of metHb; one has a high response rate to hemoglobin oxidation with a limited reducing flux, and the other has a low response rate with a high capacity flux. On the basis of the results of our model, under normal oxidative conditions, the NADPH-dependent system, the physiological role of which to date has been unclear, is predicted to be responsible for most of the reduction of metHb. In contrast, the cytochrome b5-NADH pathway becomes dominant under conditions of excess metHb accumulation, only after the capacity of the flavin-NADPH pathway has reached its limit. We discuss the potential implications of a system designed with two metHb-reducing pathways in human erythrocytes.

ModellingStaphylococcus aureus–induced septicemia using NMR

We present a novel NMR-based study of the molecular aspects of the "attack" on human red blood cells (RBCs) by growing bacteria. Staphylococcus aureus expresses virulence factors, including alpha-hemolysin, which contribute to the clinical condition known as septic shock. alpha-Hemolysin is a pore-forming toxin and its secretion increases the permeability of a range of mammalian cell types infected with S. aureus. (31)P NMR spectra of the probe molecules dimethyl methylphosphonate (DMMP) and hypophosphite (HPA) in RBC suspensions show separate intra- and extracellular resonances. These resonances coalesced over time in RBC suspensions inoculated with S. aureus or pure alpha-hemolysin, due to increasing permeability of the RBC membrane. Increased RBC permeability resulted in leakage of intracellular proteins, plus an increase in the exchange rate of the solutes between the intra- and extracellular compartments, both effects contributing to the coalescence of the split peaks. The addition of antibiotics prevented peak coalescence and enabled the minimal inhibitory concentration (MIC) for eight strains of S. aureus to be determined for oxacillin and erythromycin. The MIC values obtained by using (31)P NMR spectroscopy were within one dilution of the MICs obtained using the standard National Committee for Clinical Laboratory Standards (NCCLS) method. The results are encouraging for the use of NMR spectroscopy in clinical microbiology.

The IUPS Physiome Project: a framework for computational physiology

The IUPS Physiome Project is an internationally collaborative open-source project to provide a public domain framework for computational physiology, including the development of modelling standards, computational tools and web-accessible databases of models of structure and function at all spatial scales. A number of papers in this volume deal with the development of specific mathematical models of physiological processes. This paper stands back from the detail of individual models and reviews the current state of the IUPS Physiome Project including organ and organ system continuum models, the interpretation of constitutive law parameters in terms of micro-structural models, and markup languages for standardizing cellular processes. Some current practical applications of the physiome models are given and some of the challenges for the next 5 years of the Physiome Project at the level of organs, cells and proteins are proposed.