Modelling of calcium dynamics in brain energy metabolism and Alzheimer's disease

Advances in Astrocyte Computational Models: From Metabolic Reconstructions to Multi-omic Approaches

The growing importance of astrocytes in the field of neuroscience has led to a greater number of computational models devoted to the study of astrocytic functions and their metabolic interactions with neurons. The modeling of these interactions demands a combined understanding of brain physiology and the development of computational frameworks based on genomic-scale reconstructions, system biology, and dynamic models. These computational approaches have helped to highlight the neuroprotective mechanisms triggered by astrocytes and other glial cells, both under normal conditions and during neurodegenerative processes. In the present review, we evaluate some of the most relevant models of astrocyte metabolism, including genome-scale reconstructions and astrocyte-neuron interactions developed in the last few years. Additionally, we discuss novel strategies from the multi-omics perspective and computational models of other glial cell types that will increase our knowledge in brain metabolism and its association with neurodegenerative diseases.

Mathematical Models to Shed Light on Amyloid-Beta and Tau Protein Dependent Pathologies in Alzheimer's Disease

The number of patients suffering from dementia due to Alzheimer's disease (AD) is constantly rising worldwide. This has accordingly resulted in huge burdens on the health systems and involved families. Lack of profound understanding of neural networking in normal brain and their interruption in AD makes the treatment of this neurodegenerative multifaceted disease a challenging issue. In recent years, mathematical and computational methods have paved the way towards a better understanding of the brain functional connectivity. Thus, much attention has been paid to this matter from both basic science researchers and clinicians with an interdisciplinary approach to determine what is not functioning properly in AD patients and how this malfunctioning can be addressed. In this review, a number of AD-related articles and well-studied pathophysiologic topics (e.g., amyloid-beta, neurofibrillary tangles, Ca²⁺ dysregulation, and synaptic plasticity alterations) has been literally surveyed from a computational and systems biology point of view. The neural networks were discussed from biological and mathematical point of views and their alterations in recent findings were further highlighted. Application of the graph theoretical analysis in the brain imaging was reviewed, depicting the relations between brain structure and function, without diving into mathematical details. Moreover, differential rate equations were briefly articulated, emphasizing the potential use of these equations in simplifying complex processes in relevance to pathologies of AD. Comprehensive insights were given into the AD progression from neural networks perspective, which may lead us towards potential strategies for early diagnosis and effective treatment of AD.

What can computational modeling offer for studying the Ca2+ dysregulation in Alzheimer's disease: current research and future directions

Ca²⁺ dysregulation is an early event observed in Alzheimer’s disease (AD) patients preceding the presence of its clinical symptoms. Dysregulation of neuronal Ca²⁺ will cause synaptic loss and neuronal death, eventually leading to memory impairments and cognitive decline. Treatments targeting Ca²⁺ signaling pathways are potential therapeutic strategies against AD. The complicated interactions make it challenging and expensive to study the underlying mechanisms as to how Ca²⁺ signaling contributes to the pathogenesis of AD. Computational modeling offers new opportunities to study the signaling pathway and test proposed mechanisms. In this mini-review, we present some computational approaches that have been used to study Ca²⁺ dysregulation of AD by simulating Ca²⁺ signaling at various levels. We also pointed out the future directions that computational modeling can be done in studying the Ca²⁺ dysregulation in AD.

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.

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.

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.

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.

Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling

Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.

Mitochondrial Ca2+ uniporter blockers influence activation-induced CBF response in the rat somatosensory cortex

Effects of mitochondrial calcium signaling blockade on neural activation-induced CBF response were studied in urethane-anesthetized rats. Ruthenium red (RuR), a nonspecific inhibitor of the mitochondrial calcium uniporter (MCU), and Ru360, a highly specific inhibitor of the MCU, were delivered intravenously (i.v.) or intracerebroventricularly (i.c.v.). Baseline cerebral blood flow (CBF) and cerebral hyperemic response to whisker stimulation were measured through a thinned skull over the somatosensory cortex using laser Doppler imaging (LDI). Ruthenium red or Ru360 did not alter the baseline CBF at all doses used. However, the hyperemic response, defined as the activation area and amplitude of CBF increase in response to mechanical whisker stimulation, was significantly reduced in the presence of either RuR or Ru360 delivered i.c.v. The hyperemic response reduced significantly with a dose of 14.5 nmol RuR (i.c.v.), showing a further decrease with 29 nmol RuR (i.c.v.). A comparable decrease in the hyperemic response was observed during treatment with a relatively lower dose of 4.5 and 9 nmol Ru360 (i.c.v.). Delivered intravenously, Ru360 significantly diminished the cerebral hyperemic response at doses greater than 80 microg/kg i.v., up to a dose of 320 microg/kg i.v. However, RuR (i.v.) had an opposite effect with an enhancement in the cerebral hyperemic response at all doses studied. Ruthenium red or Ru360 had no significant effect on the cerebral reactivity to hypercapnia, indicating that altered cerebral hyperemic response to whisker stimulation was predominantly neural. We conclude that mitochondrial calcium signaling through the MCU mediates neural activation-induced CBF response in vivo.

Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia

BACKGROUND

It is a daunting task to identify all the metabolic pathways of brain energy metabolism and develop a dynamic simulation environment that will cover a time scale ranging from seconds to hours. To simplify this task and make it more practicable, we undertook stoichiometric modeling of brain energy metabolism with the major aim of including the main interacting pathways in and between astrocytes and neurons.

MODEL

The constructed model includes central metabolism (glycolysis, pentose phosphate pathway, TCA cycle), lipid metabolism, reactive oxygen species (ROS) detoxification, amino acid metabolism (synthesis and catabolism), the well-known glutamate-glutamine cycle, other coupling reactions between astrocytes and neurons, and neurotransmitter metabolism. This is, to our knowledge, the most comprehensive attempt at stoichiometric modeling of brain metabolism to date in terms of its coverage of a wide range of metabolic pathways. We then attempted to model the basal physiological behaviour and hypoxic behaviour of the brain cells where astrocytes and neurons are tightly coupled.

RESULTS

The reconstructed stoichiometric reaction model included 217 reactions (184 internal, 33 exchange) and 216 metabolites (183 internal, 33 external) distributed in and between astrocytes and neurons. Flux balance analysis (FBA) techniques were applied to the reconstructed model to elucidate the underlying cellular principles of neuron-astrocyte coupling. Simulation of resting conditions under the constraints of maximization of glutamate/glutamine/GABA cycle fluxes between the two cell types with subsequent minimization of Euclidean norm of fluxes resulted in a flux distribution in accordance with literature-based findings. As a further validation of our model, the effect of oxygen deprivation (hypoxia) on fluxes was simulated using an FBA-derivative approach, known as minimization of metabolic adjustment (MOMA). The results show the power of the constructed model to simulate disease behaviour on the flux level, and its potential to analyze cellular metabolic behaviour in silico.

CONCLUSION

The predictive power of the constructed model for the key flux distributions, especially central carbon metabolism and glutamate-glutamine cycle fluxes, and its application to hypoxia is promising. The resultant acceptable predictions strengthen the power of such stoichiometric models in the analysis of mammalian cell metabolism.

ON THE INTEGRATION OF PHYSIOLOGICAL MECHANISMS IN THE NERVOUS TISSUE USING THE MTIP: SYNAPTIC PLASTICITY DEPENDING ON NEURONS-ASTROCYTES-CAPILLARIES INTERACTIONS

The objective in this work is twofold: (i) to illustrate the use of the Mathematical Theory of Integrative Physiology (MTIP) [13], that is a general theory and practical method for the systematic and progressive mathematical integration of physiological mechanisms; (ii) to study a complex neurobiological system taken as an example, i.e., the synaptic plasticity depending on brain activity, on astrocytic and neuronal metabolism, and on brain hemodynamics. The functional organization of the nervous tissue is presented in the framework of the MTIP, the ultimate objective being the study of learning and memory by coupling the three networks of neurons, astrocytes and capillaries. Specifically in this paper, we study the influence of the variation of capillaries arterial oxygen on the induction of LTP/LTD by coupling validated mathematical models of AMPA, NMDA, VDCC channels, calcium current in the dendritic spine, vesicular glutamate dynamics in the presynaptic bouton derived from glycolysis and neuronal glucose, mitochondrial respiration, Ca/Na pumps, glycolysis, and calcium dynamics in the astrocytes, hemodynamics of the capillaries. The integration of all these models is discussed by claiming the advantages of using a common framework and a specific dedicated computing system, PhysioMatica.