Mathematical Modelling of Cerebral Metabolism : From Ion Channels to Metabolic Fluxes

• The brain is the most metabolically active organ in the human body and therefore rely on a continuous supply of oxygen and glucose. Neuronal stimulation in specific regions of the leads to the firing of action potentials, a process facilitated by voltage-gated ion channels in the neurons’ cell membranes. This activation of the ion channels significantly elevates the brain’s metabolic energy demand, compelling neurons to ramp up their metabolic activity in response. Concurrently, this neuronal activation also initiates a signalling cascade that induces vasodilation and increases blood flow, thereby ensuring that regions with elevated neural activity are adequately supplied with oxygen and nutrients. This dynamic interplay between neuronal activity and cerebral blood flow (CBF) regulation constitutes the neurovascular coupling (NVC). The NVC is a cornerstone in interpreting functional Magnetic Resonance Imaging (fMRI) Blood Oxygen Level-Dependent (BOLD) responses. The BOLD response is an indirect, non-invasive, and highly sensitive indicator of neuronal activity, reflecting changes in blood oxygenation and flow associated with the neuronal and metabolic activity in the brain. By examining these responses, we can gain insights into the complex interactions between neuronal activity, energy metabolism, and CBF.Additionally, techniques such as 13C Metabolic Flux Analysis (13C MFA) makes it possible to gain further insight into the cerebral metabolism. This method enables a detailed examination of metabolic pathways and fluxes by tracking the incorporation of 13C-labelled substrates into various metabolites. By using 13C MFA, researchers can quantify the flow of substrates through metabolic networks, offering a deeper understanding of how cell such as neurons adapt their metabolism during different functional states and conditions.Central to exploring these multifaceted aspects of cerebral metabolism is the use of mathematical modelling and systems biology. These disciplines provide a framework for integrating diverse biological data, allowing for the simulation and prediction of complex neurovascular interactions under various physiological and pathological conditions. Mathematical models can encapsulate the dynamics of ion channel kinetics, metabolic pathways, and neurovascular coupling, offering a comprehensive view of the interplay between neuronal activity, metabolism, and cerebral blood flow. This approach is instrumental in bridging the gap between molecular-scale events and observable physiological phenomena, enhancing our understanding of cerebral metabolism and its critical role in the brain’s function.Paper I sets the foundation by developing a mechanistic model that integrates the mechanisms of the NVC with the metabolism. This model connects cerebral regulation of blood flow and metabolism, using small mechanistic model to represent the central metabolism. By integrating experimental data based on nuclear magnetic resonance spectroscopy (NMRS), the model successfully captures the dynamics of metabolites in response to neuronal stimuli, providing a crucial link between metabolic changes and NVC.Paper II extends the investigation to the realm of ion channel kinetics. By developing a generic model structure for voltage-gated ion channels, this paper explores how ion channel activity, a fundamental aspect of neuronal function, influences cerebral metabolism. The model, validated against experimental data and existing kinetic models, accurately predicts various channel behaviours and action potential characteristics. It includes mechanisms like voltage sensor movements and rate constants dependent on membrane voltage, offering a universal approach for studying all types of voltage-gated ion channels in neural networks and other applications.Paper III further explores the neurovascular relationship by examining the influence of inhibitory neurons on CBF and metabolism. This study introduces an expanded mathematical model that integrates the effects of γ-aminobutyric acid(GABA)ergic inhibitory neurons on vascular responses, aligning with new experimental evidence and enhancing understanding of neurovascular coupling (NVC). The model, validated with data from various studies, not only captures vascular changes triggered by inhibitory neuron activation but also reveals how these neurovascular responses vary with stimulation frequency, underscoring the important role of inhibitory neuron in the NVC.Paper IV tackles the critical aspect of accurately measuring metabolic fluxes in cells, focusing on 13C MFA. This study introduces a novel approach for model selection in MFA, ensuring that the chosen models accurately represent the underlying metabolic processes. This method enhances our ability to identify and understand key metabolic pathways and reactions, providing deeper insights into various metabolic conditions. Connecting back to the cerebral metabolism, application of 13C MFA to neuronal systems offers a powerful tool for studying metabolically linked neuropathology such as the development of Alzheimer’s disease.In Conclusion, this thesis establishes key components for understanding the mechanisms of the cerebral metabolism. The integration of mathematical modelling across different scales, from ion channels to cerebral blood flow, is used to provide a comprehensive perspective on how cerebral metabolism is regulated and how it interacts with other physiological processes. This work not only advances our basic scientific knowledge but also holds significant potential for improving our understanding of neurological disorders where metabolism and neurovascular function are impaired.

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NATURVETENSKAP  -- Data- och informationsvetenskap -- Bioinformatik (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Bioinformatics (hsv//eng)

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