Uncertainty quantification in flux balance analysis of spatially lumped and distributed models of neuron–astrocyte metabolism

MITODYN: An Open Source Software for Quantitative Modeling of Mitochondrial and Cellular Energy Metabolic Flux Dynamics in Health and Disease

Mitochondrial respiratory chain (RC) transforms the reductive power of NADH or FADH2 oxidation into a proton gradient between the matrix and cytosolic sides of the inner mitochondrial membrane, that ATP synthase uses to generate ATP. This process constitutes a bridge between carbohydrates' central metabolism and ATP-consuming cellular functions. Moreover, the RC is responsible for a large part of reactive oxygen species (ROS) generation that play signaling and oxidizing roles in cells. Mathematical methods and computational analysis are required to understand and predict the possible behavior of this metabolic system. Here we propose a software tool that helps to analyze individual steps of respiratory electron transport in their dynamics, thus deepening understanding of the mechanism of energy transformation and ROS generation in the RC. This software's core is a kinetic model of the RC represented by a system of ordinary differential equations (ODEs). This model enables the analysis of complex dynamic behavior of the RC, including multistationarity and oscillations. The proposed RC modeling method can be applied to study respiration and ROS generation in various organisms and naturally extended to explore carbohydrates' metabolism and linked metabolic processes.

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.

Mathematical Biology Models of Parkinson's Disease

Parkinsons disease (PD) is a progressive neurodegenerative disease with substantial and growing socio-economic burden. In this multifactorial disease, aging, environmental, and genetic factors contribute to neurodegeneration and dopamine (DA) deficiency in the brain. Treatments aimed at DA restoration provide symptomatic relief, however, no disease modifying treatments are available, and PD remains incurable to date. Mathematical modeling can help understand such complex multifactorial neurological diseases. We review mathematical modeling efforts in PD with a focus on mechanistic models of pathogenic processes. We consider models of α-synuclein (Asyn) aggregation, feedbacks among Asyn, DA, and mitochondria and proteolytic systems, as well as pathology propagation through the brain. We hope that critical understanding of existing literature will pave the way to the development of quantitative systems pharmacology models to aid PD drug discovery and development.

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.