Statistical analysis of metabolic pathways of brain metabolism at steady state

Exploring the role of the Kölliker-Fuse nucleus in breathing variability by mathematical modelling

The Kölliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnoea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apnoeas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupnoeic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing. KEY POINTS: The Kölliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modelling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analysing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide testable hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.

Robustness analysis and identification for an enzyme-catalytic complex metabolic network in batch culture

Bioconversion of glycerol to 1,3-propanediol is a promising way to mitigate the shortage of energy. To maximize the production of 1,3-propanediol, it needs to control precisely microbial fermentation process. However, it might consume lots of human and material resources when conducting experimental tests many times. In this study, a nonlinear enzyme-catalytic dynamical system is developed to describe the bioconversion process of glycerol to 1,3-propanediol, especially continuous piecewise linear functions are used as identification parameters. The existence, uniqueness and continuity of solutions are also discussed. Then, considering the fact that the concentration of intracellular substances is difficult to measure in experiments, a new quantitative definition of biological robustness is introduced as a performance index to determine the identification parameters related to intracellular substances. Meanwhile, a two-phase optimization algorithm is constructed to solve the identification model. By comparison with the experimental data, it can be found that the present nonlinear dynamical system can describe the fermentation process very well. Finally, the present nonlinear dynamical system and the corresponding optimal identification parameters might be useful in future studies on the batch culture of glycerol to 1,3-propanediol.

Computational singular perturbation analysis of brain lactate metabolism

Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al. (J Cereb. Blood Flow Metab., 27:1766, 2007) and Mangia et al. (J of Neurochemistry, 109:55, 2009). As most mathematical models governing brain metabolism processes, this model is multi-scale in character due to the wide range of time scales characterizing its dynamics. Therefore, we utilize the Computational Singular Perturbation (CSP) algorithm, which has been used extensively in multi-scale systems of reactive flows and biological systems, to identify components of the system that (i) generate the characteristic time scale and the fast/slow dynamics, (ii) participate to the expressions that approximate the surfaces of equilibria that develop in phase space and (iii) control the evolution of the process within the established surfaces of equilibria. It is shown that a decisive factor on whether the ANLS or NALS configuration will develop during neuronal activation is whether the lactate transport between astrocytes and interstitium contributes to the fast dynamics or not. When it does, lactate is mainly generated in astrocytes and the ANLS hypothesis is realised, while when it doesn't, lactate is mainly generated in neurons and the NALS hypothesis is realised. This scenario was tested in exercise conditions.

Effects of cyclic AMP on the differentiation and bioenergetics of rat C6 glioma cells

INTRODUCTION

Elevation in the level of intracellular cAMP is known to induce astrocytic differentiation of C6 glioma cells by unknown mechanisms.

METHODS

Therefore, cytoskeletal protein genes (phalloidin) fluorescents to investigate morphological changes, cell proliferation assay, MTT assay, flow cytometry, western blotting, in-cell western, immune-cytochemical (protein expression and localization), and oxygen electrodes (oxygen consumption rate) after a treatment with 0.25 mM dbcAMP were conducted.

RESULTS

Undifferentiated cells (media without dbcAMP) showed a flat polygonal appearance, whereas those cultured in the presence of 0.25 mM dbcAMP exhibited a more differentiated astrocytic morphology. They had more numerous neurite-like thin processes. The cell proliferation of differentiated c6 glioma reduced at day 2 and then started to increase at day 3 till day 5 compared to undifferentiated c6 glioma cells. In terms of flow-cytometry data, dbcAMP had no apoptotic effect on the C6 glioma cells. There was an increase in the protein expression GFAP (specific marker for astrocytes). There was no significant effect between undifferentiated and 5-day differentiation regarding their response to glucose 10 mM. In addition, there were no significant effects of glucose on the basal of 5-day differentiation of C6 glioma cells. However, there was a significant correlation between the concentration of glucose and inhibition of the basal oxygen consumption. Finally, glucose 10 mM did not stimulate NAD (P)H levels of C6 glioma cells.

CONCLUSION

The above results showed that cAMP induce C6 glioma cells differentiation without affecting its bioenergetics. Therefore cAMP is considered to be the best differentiating agent.

Genome-Scale Brain Metabolic Networks as Scaffolds for the Systems Biology of Neurodegenerative Diseases: Mapping Metabolic Alterations

Systems-based investigation of diseases requires integrated analysis of cellular networks and high-throughput data of gene products. The use of genome-scale metabolic networks for such integration has led to the elucidation of cellular mechanisms for several cell types from microorganisms to plants. It has become easier and cheaper to generate high-throughput data over years in the form of transcriptome, proteome and metabolome. This has tremendously improved the quality and quantity of information extracted from such data enabling the documentation of active pathways and reactions in cell metabolism. A number of omics-based datasets for several neurodegenerative diseases are now available in public repositories. This increases the potential of using genome-scale brain metabolic networks as a scaffold for this type of data to map metabolic alterations for the purpose of elucidating disease mechanisms and for the diagnosis and treatment of such disorders. This chapter first reviews omics data collected for neurodegenerative diseases to map their effect on metabolism. Later, the potential for genome-scale metabolic modeling of such data is reviewed and discussed in light of recently reconstructed brain metabolic networks at genome-scale.

In silico profiling of cell growth and succinate production in Escherichia coli NZN111

Background

Succinic acid is a valuable product due to its wide-ranging utilities. To improve succinate production and reduce by-products formation, Escherichia coli NZN111 was constructed by insertional inactivation of lactate dehydrogenase (LDH) and pyruvate formate lyase (PFL) encoded by the genes ldhA and pflB, respectively. However, this double-deletion mutant is incapable of anaerobically growing on glucose in rich or minimal medium even with acetate supplementation. A widespread hold view is that the inactivation of NADH-dependent LDH limits the regeneration of NAD⁺ and consequently disables proper growth under anaerobic conditions.

Results

In this study, genome-scale metabolic core model of E. coli was reconstructed and employed to perform all simulations in silico according to the reconstruction of engineered strain E. coli NZN111. Non-optimized artificial centering hit-and-run (ACHR) method and metabolite flux-sum analysis were utilized to evaluate metabolic characteristics of strains. Thus, metabolic characteristics of the strains wild-type E. coli, ldhA mutant, pflB mutant, and NZN111 under anaerobic conditions were successfully unraveled.

Conclusions

We found a viewpoint contrary to the widespread realization that an NADH/NAD⁺ in NZN111 mainly resulted from the inactivation of PFL rather than the inactivation of LDH. In addition, the two alternative anaerobic fermentation pathways, lactate and ethanol production pathways, were blocked owing to the disruption of ldhA and pflB, resulting in insufficient NAD⁺ regeneration to oxidize or metabolize glucose for cell growth. Furthermore, we speculated reaction NADH16, the conversion of ubiquinone-8 (q8) to ubiquinol-8 (q8h2), as a potential amplification target for anaerobically improving cell growth and succinate production in NZN111.

Electronic supplementary material

The online version of this article (doi:10.1186/s40643-016-0125-5) contains supplementary material, which is available to authorized users.

A New Computational Model for Neuro-Glio-Vascular Coupling: Astrocyte Activation Can Explain Cerebral Blood Flow Nonlinear Response to Interictal Events

Developing a clear understanding of the relationship between cerebral blood flow (CBF) response and neuronal activity is of significant importance because CBF increase is essential to the health of neurons, for instance through oxygen supply. This relationship can be investigated by analyzing multimodal (fMRI, PET, laser Doppler…) recordings. However, the important number of intermediate (non-observable) variables involved in the underlying neurovascular coupling makes the discovery of mechanisms all the more difficult from the sole multimodal data. We present a new computational model developed at the population scale (voxel) with physiologically relevant but simple equations to facilitate the interpretation of regional multimodal recordings. This model links neuronal activity to regional CBF dynamics through neuro-glio-vascular coupling. This coupling involves a population of glial cells called astrocytes via their role in neurotransmitter (glutamate and GABA) recycling and their impact on neighboring vessels. In epilepsy, neuronal networks generate epileptiform discharges, leading to variations in astrocytic and CBF dynamics. In this study, we took advantage of these large variations in neuronal activity magnitude to test the capacity of our model to reproduce experimental data. We compared simulations from our model with isolated epileptiform events, which were obtained in vivo by simultaneous local field potential and laser Doppler recordings in rats after local bicuculline injection. We showed a predominant neuronal contribution for low level discharges and a significant astrocytic contribution for higher level discharges. Besides, neuronal contribution to CBF was linear while astrocytic contribution was nonlinear. Results thus indicate that the relationship between neuronal activity and CBF magnitudes can be nonlinear for isolated events and that this nonlinearity is due to astrocytic activity, highlighting the importance of astrocytes in the interpretation of regional recordings.

Systematic analysis of transcription-level effects of neurodegenerative diseases on human brain metabolism by a newly reconstructed brain-specific metabolic network

Network-oriented analysis is essential to identify those parts of a cell affected by a given perturbation. The effect of neurodegenerative perturbations in the form of diseases of brain metabolism was investigated by using a newly reconstructed brain-specific metabolic network. The developed stoichiometric model correctly represents healthy brain metabolism, and includes 630 metabolic reactions in and between astrocytes and neurons, which are controlled by 570 genes. The integration of transcriptome data of six neurodegenerative diseases (Alzheimer's disease, Parkinson's disease, Huntington's disease, amyotrophic lateral sclerosis, multiple sclerosis, schizophrenia) with the model was performed to identify reporter features specific and common for these diseases, which revealed metabolites and pathways around which the most significant changes occur. The identified metabolites are potential biomarkers for the pathology of the related diseases. Our model indicated perturbations in oxidative stress, energy metabolism including TCA cycle and lipid metabolism as well as several amino acid related pathways, in agreement with the role of these pathways in the studied diseases. The computational prediction of transcription factors that commonly regulate the reporter metabolites was achieved through binding-site analysis. Literature support for the identified transcription factors such as USF1, SP1 and those from FOX families are known from the literature to have regulatory roles in the identified reporter metabolic pathways as well as in the neurodegenerative diseases. In essence, the reconstructed brain model enables the elucidation of effects of a perturbation on brain metabolism and the illumination of possible machineries in which a specific metabolite or pathway acts as a regulatory spot for cellular reorganization.

Unraveling the complex metabolic nature of astrocytes

Since the initial description of astrocytes by neuroanatomists of the nineteenth century, a critical metabolic role for these cells has been suggested in the central nervous system. Nonetheless, it took several technological and conceptual advances over many years before we could start to understand how they fulfill such a role. One of the important and early recognized metabolic function of astrocytes concerns the reuptake and recycling of the neurotransmitter glutamate. But the description of this initial property will be followed by several others including an implication in the supply of energetic substrates to neurons. Indeed, despite the fact that like most eukaryotic non-proliferative cells, astrocytes rely on oxidative metabolism for energy production, they exhibit a prominent aerobic glycolysis capacity. Moreover, this unusual metabolic feature was found to be modulated by glutamatergic activity constituting the initial step of the neurometabolic coupling mechanism. Several approaches, including biochemical measurements in cultured cells, genetic screening, dynamic cell imaging, nuclear magnetic resonance spectroscopy and mathematical modeling, have provided further insights into the intrinsic characteristics giving rise to these key features of astrocytes. This review will provide an account of the different results obtained over several decades that contributed to unravel the complex metabolic nature of astrocytes that make this cell type unique.

The metabolism of neurons and astrocytes through mathematical models

Mathematical modeling of the energy metabolism of brain cells plays a central role in understanding data collected with different imaging modalities, and in making predictions based on them. During the last decade, several sophisticated brain metabolism models have appeared. Unfortunately, the picture of the metabolic details that emerges from them is far from coherent: while each model has its justification and is in agreement with some experimental data, some of the predictions of different models can diverge from each other significantly. In this article, we review some of the recent published models, emphasizing similarities and differences between them to understand where the differences in predictions stem from. In that context we present a probabilistic approach, which rather than assigning fixed values to the model parameters, regard them as random variables whose distributions are inferred on in the light of stoichiometric information and different observations. The probabilistic approach reveals how much intrinsic variability a metabolic system may contain, which in turn may be a valid explanation of the different findings.

Large-scale in silico modeling of metabolic interactions between cell types in the human brain

Metabolic interactions between multiple cell types are difficult to model using existing approaches. Here we present a workflow that integrates gene expression data, proteomics data and literature-based manual curation to model human metabolism within and between different types of cells. Transport reactions are used to account for the transfer of metabolites between models of different cell types via the interstitial fluid. We apply the method to create models of brain energy metabolism that recapitulate metabolic interactions between astrocytes and various neuron types relevant to Alzheimer's disease. Analysis of the models identifies genes and pathways that may explain observed experimental phenomena, including the differential effects of the disease on cell types and regions of the brain. Constraint-based modeling can thus contribute to the study and analysis of multicellular metabolic processes in the human tissue microenvironment and provide detailed mechanistic insight into high-throughput data analysis.

Energetics of inhibition: insights with a computational model of the human GABAergic neuron-astrocyte cellular complex

We investigate metabolic interactions between astrocytes and GABAergic neurons at steady states corresponding to different activity levels using a six-compartment model and a new methodology based on Bayesian statistics. Many questions about the energetics of inhibition are still waiting for definite answers, including the role of glutamine and lactate effluxed by astrocytes as precursors for γ-aminobutyric acid (GABA), and whether metabolic coupling applies to the inhibitory neurotransmitter GABA. Our identification and quantification of metabolic pathways describing the interaction between GABAergic neurons and astrocytes in connection with the release of GABA makes a contribution to this important problem. Lactate released by astrocytes and its neuronal uptake is found to be coupled with neuronal activity, unlike glucose consumption, suggesting that in astrocytes, the metabolism of GABA does not require increased glycolytic activity. Negligible glutamine trafficking between the two cell types at steady state questions glutamine as a precursor of GABA, not excluding glutamine cycling as a transient dynamic phenomenon, or a prominent role of GABA reuptake. Redox balance is proposed as an explanation for elevated oxidative phosphorylation and adenosine triphosphate hydrolysis in astrocytes, decoupled from energy requirements.

Metabolica: a statistical research tool for analyzing metabolic networks

Steady state flux balance analysis (FBA) for cellular metabolism is used, e.g., to seek information on the activity of the different pathways under equilibrium conditions, or as a basis for kinetic models. In metabolic models, the stoichiometry of the system, commonly completed with bounds on some of the variables, is used as the constraint in the search of a meaningful solution. As model complexity and number of constraints increase, deterministic approach to FBA is no longer viable: a multitude of very different solutions may exist, or the constraints may be in conflict, implying that no precise solution can be found. Moreover, the solution may become overly sensitive to parameter values defining the constraints. Bayesian FBA treats the unknowns as random variables and provides estimates of their probability density functions. This stochastic setting naturally represents the variability which can be expected to occur over a population and helps to circumvent the drawbacks of the classical approach, but its implementation can be quite tedious for users without background in statistical computations. This article presents a software package called Metabolica for performing Bayesian FBA for complex multi-compartment models and visualization of the results.

Use of randomized sampling for analysis of metabolic networks

Genome-scale metabolic network reconstructions in microorganisms have been formulated and studied for about 8 years. The constraint-based approach has shown great promise in analyzing the systemic properties of these network reconstructions. Notably, constraint-based models have been used successfully to predict the phenotypic effects of knock-outs and for metabolic engineering. The inherent uncertainty in both parameters and variables of large-scale models is significant and is well suited to study by Monte Carlo sampling of the solution space. These techniques have been applied extensively to the reaction rate (flux) space of networks, with more recent work focusing on dynamic/kinetic properties. Monte Carlo sampling as an analysis tool has many advantages, including the ability to work with missing data, the ability to apply post-processing techniques, and the ability to quantify uncertainty and to optimize experiments to reduce uncertainty. We present an overview of this emerging area of research in systems biology.

Astrocytes as the glucose shunt for glutamatergic neurons at high activity: an in silico study

The question of the preferred substrate of glutamatergic neurons at high neural activity has been vibrantly debated for over a decade since the classical hypothesis (CH) of the primacy of glucose has been challenged by the astrocyte-neuron lactate shuttle hypothesis (ANLSH), which replaces the primacy of glucose with astrocyte produced lactate. We perform Bayesian Flux Balance Analysis (BFBA) with a new mathematical model of cellular brain energetics, comprising detailed biochemical pathways in and between astrocytes and glutamatergic neurons and partitioning of each cell type into cytosol and mitochondria. Supported by the results of our in silico studies, which are in remarkable agreement with previously published results, we posit the Glucose Shunt Hypothesis (GSH) that during high activity, the inhibition of the phosphofructokinase (PFK) enzyme in neuron impairs neuronal glycolysis, enabling the process by which lactate effluxed by astrocytes is taken up by glutamatergic neurons, whereas at low activity, glucose remains the preferred substrate for neurons. We postulate that the ANLS is a shunt utilized by glutamatergic neurons to bypass their glycolysis impaired by the inhibition of PFK in connection with increased oxidative phosphorylation at high neuronal activity.

Kinetics of hydrogen peroxide elimination by astrocytes and C6 glioma cells analysis based on a mathematical model

Oxidative stress is implicated in a variety of disorders including neurodegenerative diseases, and H(2)O(2) is important in the generation of reactive oxygen and oxidative stress. In this study, we have examined the rate of extracellular H(2)O(2) elimination and relevant enzyme activities in cultured astrocytes and C6 glioma cells and have analyzed the results based on a mathematical model. As compared with other types of cultured cells, astrocytes showed higher activity of glutathione peroxidase (GPx) but lower activities for GSH recycling. C6 cells showed relatively low GPx activity, and treatment of C6 cells with dibutyryl-cAMP, which induces astrocytic differentiation, increased catalase activity and H(2)O(2) permeation rate but exerted little effect on other enzyme activities. A mathematical model [N. Makino, K. Sasaki, N. Hashida, Y. Sakakura, A metabolic model describing the H(2)O(2) elimination by mammalian cells including H(2)O(2) permeation through cytoplasmic and peroxisomal membranes: comparison with experimental data, Biochim. Biophys. Acta 1673 (2004) 149-159.], which includes relevant enzymes and H(2)O(2) permeation through membranes, was found to be fitted well to the H(2)O(2) concentration dependences of removal reaction with the permeation rate constants as variable parameters. As compared with PC12 cells as a culture model for neuron, H(2)O(2) removal activity of astrocytes was considerably higher at physiological H(2)O(2) concentrations. The details of the mathematical model are presented in Appendix.