Models that contain the Model Concept : Potassium buffering

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    Models   Description
1.  A mathematical model of a neurovascular unit (Dormanns et al 2015, 2016) (Farrs & David 2011)
Here a lumped parameter numerical model of a neurovascular unit is presented, representing an intercellular communication system based on ion exchange through pumps and channels between neurons, astrocytes, smooth muscle cells, endothelial cells, and the spaces between these cells: the synaptic cleft between the neuron and astrocyte, the perivascular space between the astrocyte and SMC, and the extracellular space surrounding the cells. The model contains various cellular and chemical pathways such as potassium, astrocytic calcium, and nitric oxide. The model is able to simulate neurovascular coupling, the process characterised by an increase in neuronal activity followed by a rapid dilation of local blood vessels and hence increased blood supply providing oxygen and glucose to cells in need.
2.  A model for recurrent spreading depolarizations (Conte et al. 2017)
A detailed biophysical model for a neuron/astrocyte network is developed in order to explore mechanisms responsible for cortical spreading depolarizations. This includes a model for the Na+-glutamate transporter, which allows for a detailed description of reverse glutamate uptake. In particular, we consider the specific roles of elevated extracellular glutamate and K+ in the initiation, propagation and recurrence of spreading depolarizations.
3.  A model of neurovascular coupling and the BOLD response (Mathias et al 2017, Kenny et al 2018)
Here a lumped parameter numerical model of a neurovascular unit is presented, representing an intercellular communication system based on ion exchange through pumps and channels between neurons, astrocytes, smooth muscle cells, endothelial cells, and the spaces between these cells: the synaptic cleft between the neuron and astrocyte, the perivascular space between the astrocyte and SMC, and the extracellular space surrounding the cells. The model contains various cellular and chemical pathways such as potassium, astrocytic calcium, and nitric oxide. The model is able to simulate neurovascular coupling, the process characterised by an increase in neuronal activity followed by a rapid dilation of local blood vessels and hence increased blood supply providing oxygen and glucose to cells in need. The model also incorporates the BOLD response.
4.  Anoxic depolarization, recovery: effect of brain regions and extracellular space (Hubel et al. 2016)
The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region-specific neuronal damage. Neurons in higher brain regions have stronger ADs and are more easily injured than neurons in lower brain region. The mechanism leading to such differences is not clear. We use a computational model based on a Hodgkin-Huxley framework which includes neural spiking dynamics, processes of ion accumulation, and homeostatic mechanisms like vascular coupling and Na/K-exchange pumps. We show that a large extracellular space (ECS) explains the recovery failure in high brain regions. A phase-space analysis shows that with a large ECS recovery from AD through potassium regulation is impossible. The code 'time_series.ode' can be used to simulate AD for a large and a small ECS and show the different behaviors. The code ‘continuations.ode’ can be used to show the fixed point structure. Depending on our choice of large or small ECS the fixed point curve implies the presence/absence of a recovery threshold that defines the potassium clearance demand.
5.  Disentangling astroglial physiology with a realistic cell model in silico (Savtchenko et al 2018)
"Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. ..."
6.  Electrodiffusive astrocytic and extracellular ion concentration dynamics model (Halnes et al. 2013)
An electrodiffusive formalism was developed for computing the dynamics of the membrane potential and ion concentrations in the intra- and extracellular space in a one-dimensional geometry (cable). This (general) formalism was implemented in a model of astrocytes exchanging K+, Na+ and Cl- ions with the extracellular space (ECS). A limited region (0< x<l/10 where l is the astrocyte length) of the ECS was exposed to an increase in the local K+ concentration. The model is used to explore how astrocytes contribute in transporting K+ out from high-concentration regions via a mechanism known as spatial buffering, which involves local uptake from high concentration regions, intracellular transport, and release of K+ in regions with lower ECS concentrations.
7.  Inhibition and glial-K+ interaction leads to diverse seizure transition modes (Ho & Truccolo 2016)
"How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K+]o) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled ..."
8.  Subiculum network model with dynamic chloride/potassium homeostasis (Buchin et al 2016)
This is the code implementing the single neuron and spiking neural network dynamics. The network has the dynamic ion concentrations of extracellular potassium and intracellular chloride. The code contains multiple parameter variations to study various mechanisms of the neural excitability in the context of chloride homeostasis.

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