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Glutamate plays diverse roles in neuronal cells, affecting cell energetics and reactive oxygen species (ROS) generation. These roles are especially vital for neuronal cells, which deal with high amounts of glutamate as a neurotransmitter. Our analysis explored neuronal glutamate implication in cellular energy metabolism and ROS generation, using a kinetic model that simulates electron transport details in respiratory complexes, linked ROS generation and metabolic reactions. The analysis focused on the fact that glutamate attenuates complex II inhibition by oxaloacetate, stimulating the latter's transformation into aspartate. Such a mechanism of complex II activation by glutamate could cause almost complete reduction of ubiquinone and deficiency of oxidized form (Q), which closes the main stream of electron transport and opens a way to massive ROS generating transfer in complex III from semiquinone radicals to molecular oxygen. In this way, under low workload, glutamate triggers the respiratory chain (RC) into a different steady state characterized by high ROS generation rate. The observed stepwise dependence of ROS generation on glutamate concentration experimentally validated this prediction. However, glutamate's attenuation of oxaloacetate's inhibition accelerates electron transport under high workload. Glutamate-oxaloacetate interaction in complex II regulation underlies the observed effects of uncouplers and inhibitors and acceleration of Ca2+ uptake. Thus, this theoretical analysis uncovered the previously unknown roles of oxaloacetate as a regulator of ROS generation and glutamate as a modifier of this regulation. The model predicted that this mechanism of complex II activation by glutamate might be operative in situ and responsible for excitotoxicity. Spatial-time gradients of synthesized hydrogen peroxide concentration, calculated in the reaction-diffusion model with convection under a non-uniform local approximation of nervous tissue, have shown that overproduction of H2O2 in a cell causes excess of its level in neighbor cells., Competing Interests: The authors have declared that no competing interests exist.

The liver performs many essential metabolic functions, which can be studied using computational models of hepatocytes. Here we present HepatoDyn, a highly detailed dynamic model of hepatocyte metabolism. HepatoDyn includes a large metabolic network, highly detailed kinetic laws, and is capable of dynamically simulating the redox and energy metabolism of hepatocytes. Furthermore, the model was coupled to the module for isotopic label propagation of the software package IsoDyn, allowing HepatoDyn to integrate data derived from 13C based experiments. As an example of dynamical simulations applied to hepatocytes, we studied the effects of high fructose concentrations on hepatocyte metabolism by integrating data from experiments in which rat hepatocytes were incubated with 20 mM glucose supplemented with either 3 mM or 20 mM fructose. These experiments showed that glycogen accumulation was significantly lower in hepatocytes incubated with medium supplemented with 20 mM fructose than in hepatocytes incubated with medium supplemented with 3 mM fructose. Through the integration of extracellular fluxes and 13C enrichment measurements, HepatoDyn predicted that this phenomenon can be attributed to a depletion of cytosolic ATP and phosphate induced by high fructose concentrations in the medium.

Background: Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution., Results: The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated 13C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells., Conclusions: The analysis of compartmentation of metabolic networks based on the measured 13C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured 13C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.

Increased production of reactive oxygen species (ROS) in mitochondria underlies major systemic diseases, and this clinical problem stimulates a great scientific interest in the mechanism of ROS generation. However, the mechanism of hypoxia-induced change in ROS production is not fully understood. To mathematically analyze this mechanism in details, taking into consideration all the possible redox states formed in the process of electron transport, even for respiratory complex III, a system of hundreds of differential equations must be constructed. Aimed to facilitate such tasks, we developed a new methodology of modeling, which resides in the automated construction of large sets of differential equations. The detailed modeling of electron transport in mitochondria allowed for the identification of two steady state modes of operation (bistability) of respiratory complex III at the same microenvironmental conditions. Various perturbations could induce the transition of respiratory chain from one steady state to another. While normally complex III is in a low ROS producing mode, temporal anoxia could switch it to a high ROS producing state, which persists after the return to normal oxygen supply. This prediction, which we qualitatively validated experimentally, explains the mechanism of anoxia-induced cell damage. Recognition of bistability of complex III operation may enable novel therapeutic strategies for oxidative stress and our method of modeling could be widely used in systems biology studies.

The biochemical effects of training programmes have been studied with a kinetic model of central metabolism, using enzyme activities and metabolite concentrations measured at rest and after 30 s maximum-intensity exercise, collected before and after long and short periods of training, which differed only by the duration of the rest intervals. After short periods of training the glycolytic flux at rest was three times higher than it had been before training, whereas during exercise the flux and energy consumption remained the same as before training. Long periods of training had less effect on the glycolytic flux at rest, but increased it in response to exercise, increasing the contribution of oxidative phosphorylation.

A current trend in neuroscience research is the use of stable isotope tracers in order to address metabolic processes in vivo. The tracers produce a huge number of metabolite forms that differ according to the number and position of labeled isotopes in the carbon skeleton (isotopomers) and such a large variety makes the analysis of isotopomer data highly complex. On the other hand, this multiplicity of forms does provide sufficient information to address cell operation in vivo. By the end of last millennium, a number of tools have been developed for estimation of metabolic flux profile from any possible isotopomer distribution data. However, although well elaborated, these tools were limited to steady state analysis, and the obtained set of fluxes remained disconnected from their biochemical context. In this review we focus on a new numerical analytical approach that integrates kinetic and metabolic flux analysis. The related computational algorithm estimates the dynamic flux based on the time-dependent distribution of all possible isotopomers of metabolic pathway intermediates that are generated from a labeled substrate. The new algorithm connects specific tracer data with enzyme kinetic characteristics, thereby extending the amount of data available for analysis: it uses enzyme kinetic data to estimate the flux profile, and vice versa, for the kinetic analysis it uses in vivo tracer data to reveal the biochemical basis of the estimated metabolic fluxes.

Motivation: Addition of labeled substrates and the measurement of the subsequent distribution of the labels in isotopomers in reaction networks provide a unique method for assessing metabolic fluxes in whole cells. However, owing to insufficiency of information, attempts to quantify the fluxes often yield multiple possible sets of solutions that are consistent with a given experimental pattern of isotopomers. In the study of the pentose phosphate pathways, the need to consider isotope exchange reactions of transketolase (TK) and transaldolase (TA) (which in past analyses have often been ignored) magnifies this problem; but accounting for the interrelation between the fluxes known from biochemical studies and kinetic modeling solves it. The mathematical relationships between kinetic and equilibrium constants restrict the domain of estimated fluxes to the ones compatible not only with a given set of experimental data, but also with other biochemical information., Method: We present software that integrates kinetic modeling with isotopomer distribution analysis. It solves the ordinary differential equations for total concentrations (accounting for the kinetic mechanisms) as well as for all isotopomers in glycolysis and the pentose phosphate pathway (PPP). In the PPP the fluxes created in the TK and TA reactions are expressed through unitary rate constants. The algorithms that account for all the kinetic and equilbrium constant constraints are integrated with the previously developed algorithms, which have been further optimized. The most time-consuming calculations were programmed directly in assembly language; this gave an order of magnitude decrease in the computation time, thus allowing analysis of more complex systems. The software was developed as C-code linked to a program written in Mathematica (Wolfram Research, Champaign, IL), and also as a C++ program independent from Mathematica., Results: Implementing constraints imposed by kinetic and equilibrium constants in the isotopomer distribution analysis in the data from the cancer cells eliminated estimates of fluxes that were inconsistent with the kinetic mechanisms of TK and TA. Fluxes measured experimentally in cells can be used to estimate better the kinetics of TK and TA as they operate in situ. Thus, our approach of integrating various methods for in situ flux analysis opens up the possibility of designing new types of experiments to probe metabolic interrelationships, including the incorporation of additional biochemical information., Availability: Software is available freely at: http://www.bq.ub.es/bioqint/selivanov.htm, Contact: martacascante@ub.edu

Motivation: Analysis of the conversion of (13)C glucose within the metabolic network allows the evaluation of the biochemical fluxes in interconnecting metabolic pathways. Such analyses require solving hundreds of equations with respect to individual isotopomer concentrations, and this assumes applying special software even for constructing the equations. The algorithm, proposed by others could be improved., Method: A C-code linked to the program written in Mathematica (Wolfram Research Inc.), constructs and solves differential equations for all isotopomer concentrations, using the general enzyme characteristics (K(m), equilibrium constant, etc.). This code uses innovative algorithm of determination for the isotopomers-products, thus essentially decreasing the computation time. Feasible metabolic fluxes are provided by the parameters of enzyme kinetics found from the data fitting., Results: The software effectively evaluates metabolic fluxes based on the measured isotopomer distribution, as was illustrated by the analysis of glycolysis and pentose phosphate cycle. The mechanism of transketolase and transaldolase catalysis was shown to induce a specific kind of isotopomer re-distribution, which, despite the significance of its effect, usually is not taken into account., Availability: The software could be freely downloaded from the site: http://bq.ub.es/bioqint/label_distribution/.

Recent evidence underlines a key role of mitochondrial Ca2+ fluxes in cell Ca2+ signalling. We present here a kinetic model simulating the Ca2+ fluxes generated by mitochondria during mitochondrial Ca(2+)-induced Ca2+ release (mCICR) resulting from the operation of the permeability transition pore (PTP). Our model connects the Ca2+ fluxes through the ruthenium redsensitive Ca2+ uniporter, the respiration-dependent and passive H+ fluxes, the rate of oxygen consumption, the movements of weak acids across the mitochondrial membrane, the electrical transmembrane potential (delta psi), and operation of the PTP. We find that two factors are crucial to account for the various mCICR profiles that can be observed experimentally: (i) the dependence of PTP opening and closure on matrix pH (pHi), and (ii) the relative inhibition of the respiratory rate consecutive to PTP opening. The resulting model can simulate irreversible Ca2+ efflux from mitochondria, as well as the genesis of damped or sustained Ca2+ oscillations, and of single Ca2+ spikes. The model also simulates the main features of mCICR, i.e. the threshold-dependence of mCICR triggering, and the all-or-nothing nature of mCICR operation. Our model should appear useful to further mathematically address the consequences of mCICR on the spatiotemporal organisation of Ca2+ signals, as a 'plug-in' module for the existing models of cell Ca2+ signalling.

A kinetic model of ionophore-induced oscillation of ion fluxes in mammalian erythrocytes is proposed. The model is based on the regulation by Ca2(+)-ions and calmodulin of (Ca2(+) + Mg2+)-dependent ATPase of erythrocytes. The results obtained are in a good agreement with the experimental data available.

A graph-theoretic approach is shown to be applicable within the framework of the metabolic control analysis. Kinetic differential equations linearized near a steady state are presented as kinetic graphs (schemes), their structure being correlated with kinetic properties of corresponding metabolic networks. The global properties may be expressed in terms of the local properties for steady states of metabolic systems. Instability, bistability, and concentrational oscillations are shown to be induced by specific graph fragments. The approach is illustrated by an example of systems showing the oscillatory kinetic behaviour.

Analysis of the earlier obtained data on the effect of hydroxyurea on megakaryocytopoiesis by a simulation model has shown that differentiation of proliferating precursors of the megakaryocytes depends on their amount in bone marrow; the time of their involvement in the proliferating pool increases if the number of proliferating cells decreases. Within 24 h after the treatment with hydroxyurea (900 mg/kg), the transit time for the mouse megakaryocytes is reduced by about 14 h due to acceleration of the latest developmental stages. A hypothesis is put forward which accounts for correlation between the duration of proliferative period and the volume and maturation time of megakaryocytes.

The role of cells capable of formation of megakaryocytic colonies (CFUm) in regulation of thrombocytopoiesis was studied using a simulation model of megakaryocytopoiesis. The CFUm were shown to be the least differentiated cells involved in regulation of megakaryocytopoiesis in mice upon immune thrombocytopenia and after intravenous injection of hydroxyurea. A correlation was found between the CFUm population productivity and the number of cells in a transit population of the megakaryocytic line which makes it possible to reproduce experimental kinetics in the model. The duration of cell development from CFUm to megakaryocytes is about 3 days.

A method of simulation has been proposed for studying megakaryocytopoiesis. A model has been developed which takes into account the age structure of cell population, the stochasticity of their maturation, and the principles of megakaryocytopoiesis regulation (known from the experiments). The mean number of divisions in a proliferating pool has been determined, as well as the duration of development of the cells with a positive acetylcholine esterase reaction.

Simulation experiments have shown that just after antiplatelet serum of rabbit blood is introduced into mice the transit time of early proliferating precursors of the megakaryocytes is reduced by about 17 h, the transit time for megakaryoblasts increases, and within 24 h after the treatment the transit time for mature megakaryocytes is reduced b about 17 h. The data obtained confirmed our earlier hypothesis on correlation between the duration of proliferative period and the mean size of megakaryocytes.

Mathematical modelling used in analysing the postirradiation changes in megakaryocytopoiesis permitted to determine the level of radiation-induced injury in each experiment conducted and to show that megakaryocytopoiesis regulation followed the same mechanism after irradiation as it does normally and after the effect of hydroxyurea and anti-thrombocyte serum. The analysis has demonstrated that after the stem cell death induced by ionizing radiation, the regeneration can be provided by the committed cells, and the level of regeneration is determined by the maturity of precursors.

A mathematical model of thrombocytopoiesis is proposed which accounts for the recent data on its regulation. It is shown that the compensatory response of the system to a decrease in the level of thrombocytes in the blood is controlled by the total amount of thrombocytes and megakaryocytes. The proliferation intensity of megakaryocytes and the total number of thrombocytes reveal, respectively, a lineary and a logarithmical dependence on the total number of thrombocytes and megakaryocytes. The limits of the post-transfusion level of thrombocytes are defined, within which the thrombocytopoiesis is controlled only by the number of thrombocytes. The values of parameters characterizing the behaviour of the thrombocytopoiesis system are calculated.