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With the advent of advanced MRI techniques it has become possible to study axonal white matter non-invasively and in great detail. Measuring the various parameters of the long-range connections of the brain opens up the possibility to build and refine detailed models of large-scale neuronal activity. One particular challenge is to find a mathematical description of action potential propagation that is sufficiently simple, yet still biologically plausible to model signal transmission across entire axonal fibre bundles. We develop a mathematical framework in which we replace the Hodgkin-Huxley dynamics by a spike-diffuse-spike model with passive sub-threshold dynamics and explicit, threshold-activated ion channel currents. This allows us to study in detail the influence of the various model parameters on the action potential velocity and on the entrainment of action potentials between ephaptically coupled fibres without having to recur to numerical simulations. Specifically, we recover known results regarding the influence of axon diameter, node of Ranvier length and internode length on the velocity of action potentials. Additionally, we find that the velocity depends more strongly on the thickness of the myelin sheath than was suggested by previous theoretical studies. We further explain the slowing down and synchronisation of action potentials in ephaptically coupled fibres by their dynamic interaction. In summary, this study presents a solution to incorporate detailed axonal parameters into a whole-brain modelling framework., Author summary With more and more data becoming available on white-matter tracts, the need arises to develop modelling frameworks that incorporate these data at the whole-brain level. This requires the development of efficient mathematical schemes to study parameter dependencies that can then be matched with data, in particular the speed of action potentials that cause delays between brain regions. Here, we develop a method that describes the formation of action potentials by threshold activated currents, often referred to as spike-diffuse-spike modelling. A particular focus of our study is the dependence of the speed of action potentials on structural parameters. We find that the diameter of axons and the thickness of the myelin sheath have a strong influence on the speed, whereas the length of myelinated segments and node of Ranvier length have a lesser effect. In addition to examining single axons, we demonstrate that action potentials between nearby axons can synchronise and slow down their propagation speed.

Mitochondrial toxicity is a primary source of pre-clinical drug attrition. Methods that detect mitochondrial toxicity as early as possible during the drug development process are required. Here we introduce a new method for detecting mitochondrial toxicity based on MDA-MB-231 cells stably expressing the genetically-encoded FRET lactate indicator, Laconic. The method takes advantage of the high cytosolic lactate accumulation observed during mitochondrial stress, regardless of the specific toxicity mechanism, explained by compensatory glycolytic activation. IC50 determination using a standard multi-well plate reader, shown that the methodology allowed to detect metabolic toxicity induced by azide, antimycin, oligomycin, rotenone and myxothiazol with high sensitivity. Suitability for high-throughput screening applications was evaluated resulting in a Z’-factor > 0.5 and CV% < 20. A pilot screening allowed sensitive detection of commercial drugs that were previously withdrawn from the market due to liver/cardiac toxicity issues, such as camptothecin, ciglitazone, troglitazone, rosiglitazone, and terfenadine, in ten minutes. We envisage that the availability of this technology, based on a fluorescent genetically-encoded indicator will allow direct assessment of mitochondrial metabolism, and will make the early detection of mitochondrial toxicity in the drug development process possible, saving time and resources.

Optogenetic targeting of astrocytes provides a robust experimental model to differentially induce Ca2+ signals in astrocytes in vivo. However, a systematic study quantifying the response of optogenetically modified astrocytes to light is yet to be performed. Here, we propose a novel stochastic model of Ca2+ dynamics in astrocytes that incorporates a light sensitive component—channelrhodopsin 2 (ChR2). Utilizing this model, we investigated the effect of different light stimulation paradigms on cells expressing select variants of ChR2 (wild type, ChETA, and ChRET/TC). Results predict that depending on paradigm specification, astrocytes might undergo drastic changes in their basal Ca2+ level and spiking probability. Furthermore, we performed a global sensitivity analysis to assess the effect of variation in parameters pertinent to the shape of the ChR2 photocurrent on astrocytic Ca2+ dynamics. Results suggest that directing variants towards the first open state of the ChR2 photocycle (o1) enhances spiking activity in astrocytes during optical stimulation. Evaluation of the effect of Ca2+ buffering and coupling coefficient in a network of ChR2-expressing astrocytes demonstrated basal level elevations in the stimulated region and propagation of calcium activity to unstimulated cells. Buffering reduced the diffusion range of Ca2+ within the network, thereby limiting propagation and influencing the activity of astrocytes. Collectively, the framework presented in this study provides valuable information for the selection of light stimulation paradigms that elicit desired astrocytic activity using existing ChR2 constructs, as well as aids in the engineering of future application-oriented optogenetic variants., Author summary Optogenetics is a novel technique involving the targeted delivery of light-sensitive ion channels like Channelrhodopsin-2 (ChR2) to cells. Recently, this technique has been expanded to non-neuronal cell types, e.g., astrocytes. Optogenetic control of astrocytes in vivo can aid in further understanding the intricacies of their debated roles in the brain. Here, using a mathematical model, we evaluate the effect of short and long-term light stimulation of ChR2-expressing astrocytes on their Ca2+ spiking activity and basal level. We further investigate how ChR2 gating dynamics, buffering, and coupling coefficient of Ca2+ influence astrocytic activity in a single cell and a network. Results of our study can serve as a tool for experimental design and engineering of new application-oriented optogenetic constructs targeting astrocytes.

Neural networks are required to meet significant metabolic demands associated with performing sophisticated computational tasks in the brain. The necessity for efficient transmission of information imposes stringent constraints on the metabolic pathways that can be used for energy generation at the synapse, and thus low availability of energetic substrates can reduce the efficacy of synaptic function. Here we study the effects of energetic substrate availability on global neural network behavior and find that glucose alone can sustain excitatory neurotransmission required to generate high-frequency synchronous bursting that emerges in culture. In contrast, obligatory oxidative energetic substrates such as lactate and pyruvate are unable to substitute for glucose, indicating that processes involving glucose metabolism form the primary energy-generating pathways supporting coordinated network activity. Our experimental results are discussed in the context of the role that metabolism plays in supporting the performance of individual synapses, including the relative contributions from postsynaptic responses, astrocytes, and presynaptic vesicle cycling. We propose a simple computational model for our excitatory cultures that accurately captures the inability of metabolically compromised synapses to sustain synchronous bursting when extracellular glucose is depleted.