Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism

Case for supporting astrocyte energetics in glucose transporter 1 deficiency syndrome

In glucose transporter 1 deficiency syndrome (Glut1DS), glucose transport into brain is reduced due to impaired Glut1 function in endothelial cells at the blood-brain barrier. This can lead to shortages of glucose in brain and is thought to contribute to seizures. Ketogenic diets are the first-line treatment and, among many beneficial effects, provide auxiliary fuel in the form of ketone bodies that are largely metabolized by neurons. However, Glut1 is also the main glucose transporter in astrocytes. Here, we review data indicating that glucose shortage may also impact astrocytes in addition to neurons and discuss the expected negative biochemical consequences of compromised astrocytic glucose transport for neurons. Based on these effects, auxiliary fuels are needed for both cell types and adding medium chain triglycerides (MCTs) to ketogenic diets is a biochemically superior treatment for Glut1DS compared to classical ketogenic diets. MCTs provide medium chain fatty acids (MCFAs), which are largely metabolized by astrocytes and not neurons. MCFAs supply energy and contribute carbons for glutamine and γ-aminobutyric acid synthesis, and decanoic acid can also block α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid glutamate receptors. MCTs do not compete with metabolism of ketone bodies mostly occurring in neurons. Triheptanoin, an anaplerotic but also gluconeogenic uneven MCT, may be another potential addition to ketogenic diets, although maintenance of "ketosis" can be difficult. Gene therapy has also targeted both endothelial cells and astrocytes. Other approaches to increase fuel delivery to the brain currently investigated include exchange of Glut1DS erythrocytes with healthy cells, infusion of lactate, and pharmacological improvement of glucose transport. In conclusion, although it remains difficult to assess impaired astrocytic energy metabolism in vivo, astrocytic energy needs are most likely not met by ketogenic diets in Glut1DS. Thus, we propose prospective studies including monitoring of blood MCFA levels to find optimal doses for add-on MCT to ketogenic diets and assessing of short- and long-term outcomes.

Lactate's behavioral switch in the brain: An in-silico model

Emerging evidence emphasizes lactate's involvement in both physiological processes (energy metabolism, memory, etc.) and disease (traumatic brain injury, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize and analyze the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.

Mathematical modelling with Bayesian inference to quantitatively characterize therapeutic cell behaviour in nerve tissue engineering

Cellular engineered neural tissues have significant potential to improve peripheral nerve repair strategies. Traditional approaches depend on quantifying tissue behaviours using experiments in isolation, presenting a challenge for an overarching framework for tissue design. By comparison, mathematical cell-solute models benchmarked against experimental data enable computational experiments to be performed to test the role of biological/biophysical mechanisms, as well as to explore the impact of different design scenarios and thus accelerate the development of new treatment strategies. Such models generally consist of a set of continuous, coupled, partial differential equations relying on a number of parameters and functional forms. They necessitate dedicated in vitro experiments to be informed, which are seldom available and often involve small datasets with limited spatio-temporal resolution, generating uncertainties. We address this issue and propose a pipeline based on Bayesian inference enabling the derivation of experimentally informed cell-solute models describing therapeutic cell behaviour in nerve tissue engineering. We apply our pipeline to three relevant cell types and obtain models that can readily be used to simulate nerve repair scenarios and quantitatively compare therapeutic cells. Beyond parameter estimation, the proposed pipeline enables model selection as well as experiment utility quantification, aimed at improving both model formulation and experimental design.

Mechanistic multiscale modelling of energy metabolism in human astrocytes reveals the impact of morphology changes in Alzheimer's Disease

Astrocytes with their specialised morphology are essential for brain homeostasis as metabolic mediators between blood vessels and neurons. In neurodegenerative diseases such as Alzheimer's disease (AD), astrocytes adopt reactive profiles with molecular and morphological changes that could lead to the impairment of their metabolic support and impact disease progression. However, the underlying mechanisms of how the metabolic function of human astrocytes is impaired by their morphological changes in AD are still elusive. To address this challenge, we developed and applied a metabolic multiscale modelling approach integrating the dynamics of metabolic energy pathways and physiological astrocyte morphologies acquired in human AD and age-matched control brain samples. The results demonstrate that the complex cell shape and intracellular organisation of energetic pathways determine the metabolic profile and support capacity of astrocytes in health and AD conditions. Thus, our mechanistic approach indicates the importance of spatial orchestration in metabolism and allows for the identification of protective mechanisms against disease-associated metabolic impairments.

Application of a multicomponent model of convectional reaction-diffusion to description of glucose gradients in a neurovascular unit

A supply of glucose to a nervous tissue is fulfilled by a cerebrovascular network, and further diffusion is known to occur at both an arteriolar and a microvascular level. Despite a direct relation, a blood flow dynamic and reaction-diffusion of metabolites are usually considered separately in the mathematical models. In the present study they are coupled in a multiphysical approach which allows to evaluate the effects of capillary blood flow changes on near-vessels nutrient concentration gradients evidently. Cerebral blood flow (CBF) was described by the non-steady-state Navier-Stokes equations for a non-Newtonian fluid whose constitutive law is given by the Carreau model. A three-level organization of blood-brain barrier (BBB) is modelled by the flux dysconnectivity functions including densities and kinetic properties of glucose transporters. The velocity of a fluid flow in brain extracellular space (ECS) was estimated using Darcy's law. The equations of reaction-diffusion with convection based on a generated flow field for continues and porous media were used to describe spatial-time gradients of glucose in the capillary lumen and brain parenchyma of a neurovascular unit (NVU), respectively. Changes in CBF were directly simulated using smoothing step-like functions altering the difference of intracapillary pressure in time. The changes of CBF cover both the decrease (on 70%) and the increase (on 50%) in a capillary flow velocity. Analyzing the dynamics of glucose gradients, it was shown that a rapid decrease of a capillary blood flow yields an enhanced level of glucose in a near-capillary nervous tissue if the contacts between astrocytes end-feet are not tight. Under the increased CBF velocities the amplitude of glucose concentration gradients is always enhanced. The introduced approach can be used for estimation of blood flow changes influence not only on glucose but also on other nutrients concentration gradients and for the modelling of distributions of their concentrations near blood vessels in other tissues as well.

A combined experimental and computational framework to evaluate the behavior of therapeutic cells for peripheral nerve regeneration

Recent studies have explored the potential of tissue‐mimetic scaffolds in encouraging nerve regeneration. One of the major determinants of the regenerative success of cellular nerve repair constructs (NRCs) is the local microenvironment, particularly native low oxygen conditions which can affect implanted cell survival and functional performance. In vivo, cells reside in a range of environmental conditions due to the spatial gradients of nutrient concentrations that are established. Here we evaluate in vitro the differences in cellular behavior that such conditions induce, including key biological features such as oxygen metabolism, glucose consumption, cell death, and vascular endothelial growth factor secretion. Experimental measurements are used to devise and parameterize a mathematical model that describes the behavior of the cells. The proposed model effectively describes the interactions between cells and their microenvironment and could in the future be extended, allowing researchers to compare the behavior of different therapeutic cells. Such a combinatorial approach could be used to accelerate the clinical translation of NRCs by identifying which critical design features should be optimized when fabricating engineered nerve repair conduits.

A Standardized Brain Molecular Atlas: A Resource for Systems Modeling and Simulation

Accurate molecular concentrations are essential for reliable analyses of biochemical networks and the creation of predictive models for molecular and systems biology, yet protein and metabolite concentrations used in such models are often poorly constrained or irreproducible. Challenges of using data from different sources include conflicts in nomenclature and units, as well as discrepancies in experimental procedures, data processing and implementation of the model. To obtain a consistent estimate of protein and metabolite levels, we integrated and normalized data from a large variety of sources to calculate Adjusted Molecular Concentrations. We found a high degree of reproducibility and consistency of many molecular species across brain regions and cell types, consistent with tight homeostatic regulation. We demonstrated the value of this normalization with differential protein expression analyses related to neurodegenerative diseases, brain regions and cell types. We also used the results in proof-of-concept simulations of brain energy metabolism. The standardized Brain Molecular Atlas overcomes the obstacles of missing or inconsistent data to support systems biology research and is provided as a resource for biomolecular modeling.

Modelling the effects of cerebral microthrombi on tissue oxygenation and cell death

Thrombectomy, the mechanical removal of a clot, is the most common way to treat ischaemic stroke with large vessel occlusions. However, perfusion cannot always be restored after such an intervention. It has been hypothesised that the absence of reperfusion is at least partially due to the clot fragments that block the downstream vessels. In this paper, we present a new way of quantifying the effects of cerebral microthrombi on oxygen transport to tissue in terms of hypoxia and ischaemia. The oxygen transport was simulated with the Green's function method on physiologically representative microvascular cubes, which was found independent of both microvascular geometry and length scale. The microthrombi occlusions were then simulated in the microvasculature, which were extravasated over time with a new thrombus extravasation model. The tissue hypoxic fraction was fitted as a sigmoidal function of vessel blockage fraction, which was then taken to be a function of time after the formation of microthrombi occlusions. A novel hypoxia-based 3-state cell death model was finally proposed to simulate the hypoxic tissue damage over time. Using the cell death model, the impact of a certain degree of microthrombi occlusions on tissue viability and microinfarct volume can be predicted over time. Quantifying the impact of microthrombi on oxygen transport and tissue death will play an important role in full brain models of ischaemic stroke and thrombectomy.

Brain energetics, mitochondria, and traumatic brain injury

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.

Partial differential model of lactate neuro-energetics: analytic results and numerical simulations

Interfaces play a key role on diseases development because they dictate the energy inflow of nutrients from the surrounding tissues. What is underestimated by existing mathematical models is the biological fact that cells are able to use different resources through nonlinear mechanisms. Among all nutrients, lactate appears to be a sensitive metabolic when talking about brain tumours or neurodegenerative diseases. Here we present a partial differential model to investigate the lactate exchanges between cells and the vascular network in the brain. By extending an existing kinetic model for lactate neuro-energetics, we first provide analytical proofs of the uniqueness and the derivation of precise bounds on the solutions of the problem including diffusion of lactate in a representative volume element comprising the interface between a capillary and cells. We further perform finite element simulations of the model in two test cases, discussing the relevant physical parameters governing the lactate dynamics.

Persistent changes in extracellular lactate dynamics following synaptic potentiation

A diverse array of neurometabolic coupling mechanisms exist within the brain to ensure that sufficient metabolite availability is present to meet both acute and chronic energetic demands. Excitatory synaptic activity, which produces the majority of the brain's energetic demands, triggers a rapid metabolic response including a characteristic shift towards aerobic glycolysis. Herein, astrocytically derived lactate appears to serve as an important metabolite to meet the extensive metabolic needs of activated neurons. Despite a wealth of literature characterizing lactate's role in mediating these acute metabolic needs, the extent to which lactate supports chronic energetic demands of neurons remains unclear. We hypothesized that synaptic potentiation, a ubiquitous brain phenomenon that can produce chronic alterations in synaptic activity, could necessitate persistent alterations in brain energetics. In freely-behaving rats, we induced long-term potentiation (LTP) of synapses within the dentate gyrus through high-frequency electrical stimulation (HFS) of the medial perforant pathway. Before, during, and after LTP induction, we continuously recorded extracellular lactate concentrations within the dentate gyrus to assess how changes in synaptic strength alter local glycolytic activity. Synaptic potentiation 1) altered the acute response of extracellular lactate to transient neuronal activation as evident by a larger initial dip and subsequent overshoot and 2) chronically increased local lactate availability. Although synapses were potentiated immediately following HFS, observed changes in lactate dynamics were only evident beginning ~24 h later. Once observed, however, both synaptic potentiation and altered lactate dynamics persisted for the duration of the experiment (~72 h). Persistent alterations in synaptic strength, therefore, appear to be associated with metabolic plasticity in the form of persistent augmentation of glycolytic activity.

Bioenergetic adaptations to HIV infection. Could modulation of energy substrate utilization improve brain health in people living with HIV-1?

The human brain consumes more energy than any other organ in the body and it relies on an uninterrupted supply of energy in the form of adenosine triphosphate (ATP) to maintain normal cognitive function. This constant supply of energy is made available through an interdependent system of metabolic pathways in neurons, glia and endothelial cells that each have specialized roles in the delivery and metabolism of multiple energetic substrates. Perturbations in brain energy metabolism is associated with a number of different neurodegenerative conditions including impairments in cognition associated with infection by the Human Immunodeficiency Type 1 Virus (HIV-1). Adaptive changes in brain energy metabolism are apparent early following infection, do not fully normalize with the initiation of antiretroviral therapy (ART), and often worsen with length of infection and duration of anti-retroviral therapeutic use. There is now a considerable amount of cumulative evidence that suggests mild forms of cognitive impairments in people living with HIV-1 (PLWH) may be reversible and are associated with specific modifications in brain energy metabolism. In this review we discuss brain energy metabolism with an emphasis on adaptations that occur in response to HIV-1 infection. The potential for interventions that target brain energy metabolism to preserve or restore cognition in PLWH are also discussed.

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.

Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

A Process for Digitizing and Simulating Biologically Realistic Oligocellular Networks Demonstrated for the Neuro-Glio-Vascular Ensemble

One will not understand the brain without an integrated exploration of structure and function, these attributes being two sides of the same coin: together they form the currency of biological computation. Accordingly, biologically realistic models require the re-creation of the architecture of the cellular components in which biochemical reactions are contained. We describe here a process of reconstructing a functional oligocellular assembly that is responsible for energy supply management in the brain and creating a computational model of the associated biochemical and biophysical processes. The reactions that underwrite thought are both constrained by and take advantage of brain morphologies pertaining to neurons, astrocytes and the blood vessels that deliver oxygen, glucose and other nutrients. Each component of this neuro-glio-vasculature ensemble (NGV) carries-out delegated tasks, as the dynamics of this system provide for each cell-type its own energy requirements while including mechanisms that allow cooperative energy transfers. Our process for recreating the ultrastructure of cellular components and modeling the reactions that describe energy flow uses an amalgam of state-of the-art techniques, including digital reconstructions of electron micrographs, advanced data analysis tools, computational simulations and in silico visualization software. While we demonstrate this process with the NGV, it is equally well adapted to any cellular system for integrating multimodal cellular data in a coherent framework.

A computational model integrating brain electrophysiology and metabolism highlights the key role of extracellular potassium and oxygen

The human brain is a small organ which uses a disproportionate amount of the total metabolic energy production in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing patterns, e.g., seizures, thus emphasizing the importance of the glial K⁺ buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a four compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen-glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature.

Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer's disease

Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer's disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia-driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients.

Combination Therapy for Multi-Target Manipulation of Secondary Brain Injury Mechanisms

Traumatic brain injury (TBI) is a major healthcare problem that affects millions of people worldwide. Despite advances in understanding and developing preventative and treatment strategies using preclinical animal models, clinical trials to date have failed, and a 'magic bullet' for effectively treating TBI-induced damage does not exist. Thus, novel pharmacological strategies to effectively manipulate the complex and heterogeneous pathophysiology of secondary injury mechanisms are needed. Given that goal, this paper discusses the relevance and advantages of combination therapies (COMTs) for 'multi-target manipulation' of the secondary injury cascade by administering multiple drugs to achieve an optimal therapeutic window of opportunity (e.g., temporally broad window) and compares these regimens to monotherapies that manipulate a single target with a single drug at a given time. Furthermore, we posit that integrated mechanistic multiscale models that combine primary injury biomechanics, secondary injury mechanobiology/neurobiology, physiology, pharmacology and mathematical programming techniques could account for vast differences in the biological space and time scales and help to accelerate drug development, to optimize pharmacological COMT protocols and to improve treatment outcomes.

Brain activity-induced neuronal glucose uptake/glycolysis: Is the lactate shuttle not required?

The astrocyte-neuron lactate shuttle (ANLS) hypothesis posits that during neuronal activation, astrocytic glycolysis consumes glucose and generates lactate, with the latter then imported by neurons as a preferred fuel. The hypothesis has been controversial, with multiple theoretical postulates for and against, and with empirical evidence that were either supportive or otherwise. Recent findings using direct in vivo imaging of lactate and glucose uptake as well as associated metabolic changes in neurons have now placed important constraints on the hypothesis. Here, I review these recent findings and discuss their implications on neuronal energetics.

Metabolite transport across the mammalian and insect brain diffusion barriers

The nervous system in higher vertebrates is separated from the circulation by a layer of specialized endothelial cells. It protects the sensitive neurons from harmful blood-derived substances, high and fluctuating ion concentrations, xenobiotics or even pathogens. To this end, the brain endothelial cells and their interlinking tight junctions build an efficient diffusion barrier. A structurally analogous diffusion barrier exists in insects, where glial cell layers separate the hemolymph from the neural cells. Both types of diffusion barriers, of course, also prevent influx of metabolites from the circulation. Because neuronal function consumes vast amounts of energy and necessitates influx of diverse substrates and metabolites, tightly regulated transport systems must ensure a constant metabolite supply. Here, we review the current knowledge about transport systems that carry key metabolites, amino acids, lipids and carbohydrates into the vertebrate and Drosophila brain and how this transport is regulated. Blood-brain and hemolymph-brain transport functions are conserved and we can thus use a simple, genetically accessible model system to learn more about features and dynamics of metabolite transport into the brain.

From in silico astrocyte cell models to neuron-astrocyte network models: A review

The idea that astrocytes may be active partners in synaptic information processing has recently emerged from abundant experimental reports. Because of their spatial proximity to neurons and their bidirectional communication with them, astrocytes are now considered as an important third element of the synapse. Astrocytes integrate and process synaptic information and by doing so generate cytosolic calcium signals that are believed to reflect neuronal transmitter release. Moreover, they regulate neuronal information transmission by releasing gliotransmitters into the synaptic cleft affecting both pre- and postsynaptic receptors. Concurrent with the first experimental reports of the astrocytic impact on neural network dynamics, computational models describing astrocytic functions have been developed. In this review, we give an overview over the published computational models of astrocytic functions, from single-cell dynamics to the tripartite synapse level and network models of astrocytes and neurons.

Lactate Shuttles in Neuroenergetics-Homeostasis, Allostasis and Beyond

Understanding brain energy metabolism—neuroenergetics—is becoming increasingly important as it can be identified repeatedly as the source of neurological perturbations. Within the scientific community we are seeing a shift in paradigms from the traditional neurocentric view to that of a more dynamic, integrated one where astrocytes are no longer considered as being just supportive, and activated microglia have a profound influence. Lactate is emerging as the “good guy,” contrasting its classical “bad guy” position in the now superseded medical literature. This review begins with the evolution of the concept of “lactate shuttles”; goes on to the recent shift in ideas regarding normal neuroenergetics (homeostasis)—specifically, the astrocyte–neuron lactate shuttle; and progresses to covering the metabolic implications whereby homeostasis is lost—a state of allostasis, and the function of microglia. The role of lactate, as a substrate and shuttle, is reviewed in light of allostatic stress, and beyond—in an acute state of allostatic stress in terms of physical brain trauma, and reflected upon with respect to persistent stress as allostatic overload—neurodegenerative diseases. Finally, the recently proposed astrocyte–microglia lactate shuttle is discussed in terms of chronic neuroinflammatory infectious diseases, using tuberculous meningitis as an example. The novelty extended by this review is that the directionality of lactate, as shuttles in the brain, in neuropathophysiological states is emerging as crucial in neuroenergetics.

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

A Theoretical Study on the Role of Astrocytic Activity in Neuronal Hyperexcitability by a Novel Neuron-Glia Mass Model

Recent experimental evidence on the clustering of glutamate and GABA transporters on astrocytic processes surrounding synaptic terminals pose the question of the functional relevance of the astrocytes in the regulation of neural activity. In this perspective, we introduce a new computational model that embeds recent findings on neuron-astrocyte coupling at the mesoscopic scale intra- and inter-layer local neural circuits. The model consists of a mass model for the neural compartment and an astrocyte compartment which controls dynamics of extracellular glutamate and GABA concentrations. By arguments based on bifurcation theory, we use the model to study the impact of deficiency of astrocytic glutamate and GABA uptakes on neural activity. While deficient astrocytic GABA uptake naturally results in increased neuronal inhibition, which in turn results in a decreased neuronal firing, deficient glutamate uptake by astrocytes may either decrease or increase neuronal firing either transiently or permanently. Given the relevance of neuronal hyperexcitability (or lack thereof) in the brain pathophysiology, we provide biophysical conditions for the onset identifying different physiologically relevant regimes of operation for astrocytic uptake transporters.

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.

Physiology-based kinetic modeling of neuronal energy metabolism unravels the molecular basis of NAD(P)H fluorescence transients

Imaging of the cellular fluorescence of the reduced form of nicotinamide adenine dinucleotide (phosphate) (NAD(P)H) is one of the few metabolic readouts that enable noninvasive and time-resolved monitoring of the functional status of mitochondria in neuronal tissues. Stimulation-induced transient changes in NAD(P)H fluorescence intensity frequently display a biphasic characteristic that is influenced by various molecular processes, e.g., intracellular calcium dynamics, tricarboxylic acid cycle activity, the malate-aspartate shuttle, the glycerol-3-phosphate shuttle, oxygen supply or adenosine triphosphate (ATP) demand. To evaluate the relative impact of these processes, we developed and validated a detailed physiologic mathematical model of the energy metabolism of neuronal cells and used the model to simulate metabolic changes of single cells and tissue slices under different settings of stimulus-induced activity and varying nutritional supply of glucose, pyruvate or lactate. Notably, all experimentally determined NAD(P)H responses could be reproduced with one and the same generic cellular model. Our computations reveal that (1) cells with quite different metabolic status may generate almost identical NAD(P)H responses and (2) cells of the same type may quite differently contribute to aggregate NAD(P)H responses recorded in brain slices, depending on the spatial location within the tissue. Our computational approach reconciles different and sometimes even controversial experimental findings and improves our mechanistic understanding of the metabolic changes underlying live-cell NAD(P)H fluorescence transients.

Multi-timescale modeling of activity-dependent metabolic coupling in the neuron-glia-vasculature ensemble

Glucose is the main energy substrate in the adult brain under normal conditions. Accumulating evidence, however, indicates that lactate produced in astrocytes (a type of glial cell) can also fuel neuronal activity. The quantitative aspects of this so-called astrocyte-neuron lactate shuttle (ANLS) are still debated. To address this question, we developed a detailed biophysical model of the brain’s metabolic interactions. Our model integrates three modeling approaches, the Buxton-Wang model of vascular dynamics, the Hodgkin-Huxley formulation of neuronal membrane excitability and a biophysical model of metabolic pathways. This approach provides a template for large-scale simulations of the neuron-glia-vasculature (NGV) ensemble, and for the first time integrates the respective timescales at which energy metabolism and neuronal excitability occur. The model is constrained by relative neuronal and astrocytic oxygen and glucose utilization, by the concentration of metabolites at rest and by the temporal dynamics of NADH upon activation. These constraints produced four observations. First, a transfer of lactate from astrocytes to neurons emerged in response to activity. Second, constrained by activity-dependent NADH transients, neuronal oxidative metabolism increased first upon activation with a subsequent delayed astrocytic glycolysis increase. Third, the model correctly predicted the dynamics of extracellular lactate and oxygen as observed in vivo in rats. Fourth, the model correctly predicted the temporal dynamics of tissue lactate, of tissue glucose and oxygen consumption, and of the BOLD signal as reported in human studies. These findings not only support the ANLS hypothesis but also provide a quantitative mathematical description of the metabolic activation in neurons and glial cells, as well as of the macroscopic measurements obtained during brain imaging.

The brain has remarkable information processing capacity, yet is also very energy efficient. How this metabolic efficiency is achieved given the spatial and metabolic constraints inherent to the designs and energy requirements of brain cells is a fundamental question in neurobiology. The major cell classes in mammalian nervous systems include neurons, glia and the microvasculature that supplies the molecular substrates of energy and metabolism. Together, this neuron-glia-vasculature (NGV) ensemble constitutes the functional unit that underlies the cost infrastructure of computation. In spite of its importance, a comprehensive understanding of this dynamic system remains elusive. While it is well established that glucose feeds the brain, few of the details regarding the destiny of glucose intermediates in metabolic pathways are known. Controversy remains regarding the degree of cooperativity between glia and neurons in sharing lactate, the product of aerobic glycolysis (Warburg effect) and one of the substrates for further energy extraction by oxidative processes. Specifically, while experimental data support the occurrence of a flow of lactate from glia to neurons, the astrocyte-neuron lactate shuttle (ANLS), some theoretical considerations have been proposed to support the occurrence of lactate transport in the other direction (NALS). Our computational model is the first to integrate multiple timescales of the NGV unit. It provides a quantitative mathematical description of metabolic activation in neurons and astrocytes, and of the macroscopic measurements obtained during brain imaging that uses metabolism as a proxy for neuronal activity.

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

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.

Energy metabolism and glutamate-glutamine cycle in the brain: a stoichiometric modeling perspective

Background

The energetics of cerebral activity critically relies on the functional and metabolic interactions between neurons and astrocytes. Important open questions include the relation between neuronal versus astrocytic energy demand, glucose uptake and intercellular lactate transfer, as well as their dependence on the level of activity.

Results

We have developed a large-scale, constraint-based network model of the metabolic partnership between astrocytes and glutamatergic neurons that allows for a quantitative appraisal of the extent to which stoichiometry alone drives the energetics of the system. We find that the velocity of the glutamate-glutamine cycle (V_cyc) explains part of the uncoupling between glucose and oxygen utilization at increasing V_cyc levels. Thus, we are able to characterize different activation states in terms of the tissue oxygen-glucose index (OGI). Calculations show that glucose is taken up and metabolized according to cellular energy requirements, and that partitioning of the sugar between different cell types is not significantly affected by V_cyc. Furthermore, both the direction and magnitude of the lactate shuttle between neurons and astrocytes turn out to depend on the relative cell glucose uptake while being roughly independent of V_cyc.

Conclusions

These findings suggest that, in absence of ad hoc activity-related constraints on neuronal and astrocytic metabolism, the glutamate-glutamine cycle does not control the relative energy demand of neurons and astrocytes, and hence their glucose uptake and lactate exchange.

On a minimal model for hemodynamics and metabolism of lactate: application to low grade glioma and therapeutic strategies

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy (1)H/(31)P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas.

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.

Ménage à trois: the role of neurotransmitters in the energy metabolism of astrocytes, glutamatergic, and GABAergic neurons

This work is a computational study based on a new detailed metabolic network model comprising well-mixed compartments representing separate cytosol and mitochondria of astrocytes, glutamatergic and gamma aminobutyric acid (GABA)ergic neurons, communicating through an extracellular space compartment and fed by arterial blood flow. Our steady-state analysis assumes statistical mass balance of both carbons and amino groups. The study is based on Bayesian flux balance analysis, which uses Markov chain Monte Carlo sampling techniques and provides a quantitative description of steady states when the two exchangers aspartate-glutamate carrier (AGC1) and oxoglutarate carrier (OGC) in the malate-aspartate shuttle in astrocyte are not in equilibrium, as recent studies suggest. It also highlights the importance of anaplerotic reactions, pyruvate carboxylase in astrocyte and malic enzyme in neurons, for neurotransmitter synthesis and recycling. The model is unbiased with respect to the glucose partitioning between cell types, and shows that determining the partitioning cannot be done by stoichiometric constraints alone. Furthermore, the intercellular lactate trafficking is found to depend directly on glucose partitioning, suggesting that a steady state may support different scenarios. At inhibitory steady state, characterized by high rate of GABA release, there is elevated oxidative activity in astrocyte, not in response to specific energetic needs.

Mathematical modeling of metabolism and hemodynamics

We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma. This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.

Computational modelling of the piglet brain to simulate near-infrared spectroscopy and magnetic resonance spectroscopy data collected during oxygen deprivation

We describe a computational model to simulate measurements from near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS) in the piglet brain. Piglets are often subjected to anoxic, hypoxic and ischaemic insults, as experimental models for human neonates. The model aims to help interpret measurements and increase understanding of physiological processes occurring during such insults. It is an extension of a previous model of circulation and mitochondrial metabolism. This was developed to predict NIRS measurements in the brains of healthy adults i.e. concentration changes of oxyhaemoglobin and deoxyhaemoglobin and redox state changes of cytochrome c oxidase (CCO). We altered and enhanced the model to apply to the anaesthetized piglet brain. It now includes metabolites measured by ³¹P-MRS, namely phosphocreatine, inorganic phosphate and adenosine triphosphate (ATP). It also includes simple descriptions of glycolysis, lactate dynamics and the tricarboxylic acid (TCA) cycle. The model is described, and its simulations compared with existing measurements from piglets during anoxia. The NIRS and MRS measurements are predicted well, although this requires a reduction in blood pressure autoregulation. Predictions of the cerebral metabolic rate of oxygen consumption (CMRO₂) and lactate concentration, which were not measured, are given. Finally, the model is used to investigate hypotheses regarding changes in CCO redox state during anoxia.

Astrocyte-neuron lactate shuttle may boost more ATP supply to the neuron under hypoxic conditions--in silico study supported by in vitro expression data

Background

Neuro-glial interactions are important for normal functioning of the brain as well as brain energy metabolism. There are two major working models - in the classical view, both neurons and astrocytes can utilize glucose as the energy source through oxidative metabolism, whereas in the astrocyte-neuron lactate shuttle hypothesis (ANLSH) it is the astrocyte which can consume glucose through anaerobic glycolysis to pyruvate and then to lactate, and this lactate is secreted to the extracellular space to be taken up by the neuron for further oxidative degradation.

Results

In this computational study, we have included hypoxia-induced genetic regulation of these enzymes and transporters, and analyzed whether the ANLSH model can provide an advantage to either cell type in terms of supplying the energy demand. We have based this module on our own experimental analysis of hypoxia-dependent regulation of transcription of key metabolic enzymes. Using this experimentation-supported in silico modeling, we show that under both normoxic and hypoxic conditions in a given time period ANLSH model does indeed provide the neuron with more ATP than in the classical view.

Conclusions

Although the ANLSH is energetically more favorable for the neuron, it is not the case for the astrocyte in the long term. Considering the fact that astrocytes are more resilient to hypoxia, we would propose that there is likely a switch between the two models, based on the energy demand of the neuron, so as to maintain the survival of the neuron under hypoxic or glucose-and-oxygen-deprived conditions.

Modeling the contribution of neuron-astrocyte cross talk to slow blood oxygenation level-dependent signal oscillations

A consistent and prominent feature of brain functional magnetic resonance imaging (fMRI) data is the presence of low-frequency (<0.1 Hz) fluctuations of the blood oxygenation level-dependent (BOLD) signal that are thought to reflect spontaneous neuronal activity. In this report we provide modeling evidence that cyclic physiological activation of astroglial cells produces similar BOLD oscillations through a mechanism mediated by intracellular Ca(2+) signaling. Specifically, neurotransmission induces pulses of Ca(2+) concentration in astrocytes, resulting in increased cerebral perfusion and neuroactive transmitter release by these cells (i.e., gliotransmission), which in turn stimulates neuronal activity. Noticeably, the level of neuron-astrocyte cross talk regulates the periodic behavior of the Ca(2+) wave-induced BOLD fluctuations. Our results suggest that the spontaneous ongoing activity of neuroglial networks is a potential source of the observed slow fMRI signal oscillations.

Bayesian comparison of neurovascular coupling models using EEG-fMRI

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, it is an indirect measure of underlying neuronal activity and the processes that link this activity to BOLD signals are still a topic of much debate. In order to relate findings from fMRI research to other measures of neuronal activity it is vital to understand the underlying neurovascular coupling mechanism. Currently, there is no consensus on the relative roles of synaptic and spiking activity in the generation of the BOLD response. Here we designed a modelling framework to investigate different neurovascular coupling mechanisms. We use Electroencephalographic (EEG) and fMRI data from a visual stimulation task together with biophysically informed mathematical models describing how neuronal activity generates the BOLD signals. These models allow us to non-invasively infer the degree of local synaptic and spiking activity in the healthy human brain. In addition, we use Bayesian model comparison to decide between neurovascular coupling mechanisms. We show that the BOLD signal is dependent upon both the synaptic and spiking activity but that the relative contributions of these two inputs are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then the BOLD response is best explained by synaptic activity. However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal.

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, the relationship between neuronal activity and blood flow, the basis of fMRI, is still under much debate. A growing body of evidence from animal studies suggests that fMRI signals are more closely coupled to synaptic input activity than to the spiking output of a neuronal population. However, data from neurosurgical patients does not seem to support this view and this hypothesis hasn't yet been tested in the healthy human brain. Here we design a powerful and efficient modelling framework that can be used to non-invasively compare different biologically plausible hypotheses of neurovascular coupling. We use this framework to explore the contribution of these two aspects of neuronal activity (synaptic and spiking) to the generation of hemodynamic signals in human visual cortex, with Electroencephalographic (EEG)-fMRI data. Our results provide preliminary evidence that depending on the frequency of the visual stimulus and underlying firing rate, fMRI relates closer to synaptic activity (low-frequencies) or to both synaptic and spiking activities (high-frequencies).

Response to 'comment on recent modeling studies of astrocyte-neuron metabolic interactions': much ado about nothing

For many years, a tenet of cerebral metabolism held that glucose was the obligate energy substrate of the mammalian brain and that neuronal oxidative metabolism represented the majority of this glucose utilization. In 1994, Pellerin and Magistretti formulated the astrocyte-neuron lactate shuttle (ANLS) hypothesis, in which astrocytes, not neurons, metabolized glucose, with subsequent transport of the glycolytically derived lactate to fuel the energy needs of the neuron during neurotransmission. By considering the concentrations and kinetic characteristics of the nutrient transporter proteins, Simpson et al later supported the opposite view, in which lactate flows from neurons to astrocytes, thus leading to the neuron-astrocyte lactate shuttle (NALS). Most recently, a commentary was published in this journal attempting to discredit the NALS. This challenge has stimulated the present response in which we detail the inaccuracies of the commentary and further model several different possibilities. Although our simulations continue to support the predominance of neuronal glucose utilization during activation and neuronal to astrocytic lactate flow, the most important result is that, regardless of the direction of the flow, the overall contribution of lactate to cerebral glucose metabolism is found to be so small as to make this ongoing debate 'much ado about nothing'.

Astrocytes and energy metabolism

Astrocytes are glial cells, which play a significant role in a number of processes, including the brain energy metabolism. Their anatomical position between blood vessels and neurons make them an interface for effective glucose uptake from blood. After entering astrocytes, glucose can be involved in different metabolic pathways, e.g. in glycogen production. Glycogen in the brain is localized mainly in astrocytes and is an important energy source in hypoxic conditions and normal brain functioning. The portion of glucose metabolized into glycogen molecules in astrocytes is as high as 40%. It is thought that the release of gliotransmitters (such as glutamate, neuroactive peptides and ATP) into the extracellular space by regulated exocytosis supports a significant part of communication between astrocytes and neurons. On the other hand, neurotransmitter action on astrocytes has a significant role in brain energy metabolism. Therefore, understanding the astrocytes energy metabolism may help understanding neuron-astrocyte interactions.

An energy systems approach to Parkinson's disease

The cause of Parkinson's disease (PD) remains unknown despite it being the second most prevalent neurodegenerative condition. Indeed, there is a growing consensus that there is no single cause, and that PD is a multifactorial systemic condition, in which a number of factors may determine its etiopathogenesis. We describe a systems approach that addresses the multifactorial aspects of PD and overcomes constraints on conventional experimentation imposed by PD's causal complexity, its long temporal duration, and its uniqueness to human brains. Specifically, a mathematical model of brain energy metabolism is used as a core module to which other modules describing cellular processes thought to be associated with PD can be attached and studied in an integrative environment. Employing brain energy usage as the core of a systems approach also enables the potential role that compromised energy metabolism may have in the etiology of PD. Although developed for PD, it has not escaped our attention that the energy systems approach outlined here could also be applied to other neurodegenerative disorders-most notably Alzheimer's disease.

Dynamic activation model for a glutamatergic neurovascular unit

This article considers a dynamic spatially lumped model for brain energy metabolism and proposes to use the results of a Markov chain Monte Carlo (MCMC) based flux balance analysis to estimate the kinetic model parameters. By treating steady state reaction fluxes and transport rates as random variables we are able to propagate the uncertainty in the steady state configurations to the predictions of the dynamic model, whose responses are no longer individual but ensembles of time courses. The kinetic model consists of five compartments and is governed by kinetic mass balance equations with Michaelis-Menten type expressions for reaction rates and transports between the compartments. The neuronal activation is implemented in terms of the effect of neuronal activity on parameters controlling the blood flow and neurotransmitter transport, and a feedback mechanism coupling the glutamate concentration in the synaptic cleft and the ATP hydrolysis, thus accounting for the energetic cost of the membrane potential restoration in the postsynaptic neurons. The changes in capillary volume follow the balloon model developed for BOLD MRI. The model follows the time course of the saturation levels of the blood hemoglobin, which link metabolism and BOLD FMRI signal. Analysis of the model predictions suggest that stoichiometry alone is not enough to determine glucose partitioning between neuron and astrocyte. Lactate exchange between neuron and astrocyte is supported by the model predictions, but the uncertainty on the direction and rate is rather elevated. By and large, the model suggests that astrocyte produces and effluxes lactate, while neuron may switch from using to producing lactate. The level of ATP hydrolysis in astrocyte is substantially higher than strictly required for neurotransmitter cycling, in agreement with the literature.

Glycogenolysis in astrocytes supports blood-borne glucose channeling not glycogen-derived lactate shuttling to neurons: evidence from mathematical modeling

In this article, we examined theoretically the role of human cerebral glycogen in buffering the metabolic requirement of a 360-second brain stimulation, expanding our previous modeling study of neurometabolic coupling. We found that glycogen synthesis and degradation affects the relative amount of glucose taken up by neurons versus astrocytes. Under conditions of 175:115 mmol/L (∼1.5:1) neuronal versus astrocytic activation-induced Na(+) influx ratio, ∼12% of astrocytic glycogen is mobilized. This results in the rapid increase of intracellular glucose-6-phosphate level on stimulation and nearly 40% mean decrease of glucose flow through hexokinase (HK) in astrocytes via product inhibition. The suppression of astrocytic glucose phosphorylation, in turn, favors the channeling of glucose from interstitium to nearby activated neurons, without a critical effect on the concurrent intercellular lactate trafficking. Under conditions of increased neuronal versus astrocytic activation-induced Na(+) influx ratio to 190:65 mmol/L (∼3:1), glycogen is not significantly degraded and blood glucose is primarily taken up by neurons. These results support a role for astrocytic glycogen in preserving extracellular glucose for neuronal utilization, rather than providing lactate to neurons as is commonly accepted by the current 'thinking paradigm'. This might be critical in subcellular domains during functional conditions associated with fast energetic demands.

Changes in glucose uptake rather than lactate shuttle take center stage in subserving neuroenergetics: evidence from mathematical modeling

In this paper, we combined several mathematical models of cerebral metabolism and nutrient transport to investigate the energetic significance of metabolite trafficking within the brain parenchyma during a 360-secs activation. Glycolytic and oxidative cellular metabolism were homogeneously modeled between neurons and astrocytes, and the stimulation-induced neuronal versus astrocytic Na(+) inflow was set to 3:1. These assumptions resemble physiologic conditions and are supported by current literature. Simulations showed that glucose diffusion to the interstitium through basal lamina dominates the provision of the sugar to both neurons and astrocytes, whereas astrocytic endfeet transfer less than 4% of the total glucose supplied to the tissue. Neuronal access to paracellularly diffused glucose prevails even after halving (doubling) the ratio of neuronal versus astrocytic glycolytic (oxidative) metabolism, as well as after reducing the neuronal versus astrocytic Na(+) inflow to a nonphysiologic value of 1:1. Noticeably, displaced glucose equivalents as intercellularly shuttled lactate account for approximately 6% to 7% of total brain glucose uptake, an amount comparable with the concomitant drainage of the monocarboxylate by the bloodstream. Overall, our results suggest that the control of carbon recruitment for neurons and astrocytes is exerted at the level of glucose uptake rather than that of lactate shuttle.

Activated astrocytes: a therapeutic target in Alzheimer's disease?

Astrocytes become activated in Alzheimer's disease, contributing to and reinforcing an inflammatory cascade. A large body of evidence suggests that by transforming from a basal to a reactive state, astrocytes neglect their neurosupportive functions, thus rendering neurons vulnerable to neurotoxins, including proinflammatory cytokines and reactive oxygen species. This review highlights three important astrocytic functions that may be impaired in neurodegenerative diseases such as Alzheimer's disease. These are: the uptake of glucose and release of lactate; the uptake of glutamate and release of glutamine; and the uptake of glutathione precursors and release of glutathione. Astrocytes could become promising targets of therapeutic intervention for Alzheimer's disease, if these compromised functions can be normalized with pharmacological agents that are specifically designed to return astrocytes to a quiescent phenotype or to supplement any factors that activated astrocytes fail to produce.

The Possible Role of CO(2) in Producing A Post-Stimulus CBF and BOLD Undershoot

Comprehending the underlying mechanisms of neurovascular coupling is important for understanding the pathogenesis of neurodegenerative diseases related to uncoupling. Moreover, it elucidates the casual relation between the neural signaling and the hemodynamic responses measured with various imaging modalities such as functional magnetic resonance imaging (fMRI). There are mainly two hypotheses concerning this mechanism: a metabolic hypothesis and a neurogenic hypothesis. We have modified recent models of neurovascular coupling adding the effects of both NO (nitric oxide) kinetics, which is a well-known neurogenic vasodilator, and CO₂ kinetics as a metabolic vasodilator. We have also added the Hodgkin–Huxley equations relating the membrane potentials to sodium influx through the membrane. Our results show that the dominant factor in the hemodynamic response is NO, however CO₂ is important in producing a brief post-stimulus undershoot in the blood flow response that in turn modifies the fMRI blood oxygenation level-dependent post-stimulus undershoot. Our results suggest that increased cerebral blood flow during stimulation causes CO₂ washout which then results in a post-stimulus hypocapnia induced vasoconstrictive effect.