Electrodiffusive model for astrocytic and neuronal ion concentration dynamics

Electrical neural signalling typically takes place at the time-scale of milliseconds, and is typically modeled using the cable equation. This is a good approximation for processes when ionic concentrations vary little during the time course of a simulation. During periods of intense neural signalling, however, the local extracellular K+ concentration may increase by several millimolars. Clearance of excess K+ likely depends partly on diffusion in the extracellular space, partly on local uptake by- and intracellular transport within astrocytes. This process takes place at the time scale of seconds, and can not be modeled accurately without accounting for the spatiotemporal variations in ion concentrations. The work presented here consists of two main parts: First, we developed a general electrodiffusive formalism for modeling ion concentration dynamics in a one-dimensional geometry, including both an intra- and extracellular domain. The formalism was based on the Nernst-Planck equations. It ensures (i) consistency between the membrane potential and ion concentrations, (ii) global particle/charge conservation, and (iii) accounts for diffusion and concentration dependent variations in resistivities. Second, we applied the formalism to model how astrocytes exchange ions with the ECS, and identified the key astrocytic mechanisms involved in K+ removal from high concentration regions. We found that a local increase in extracellular K\textsuperscript{+} evoked a local depolarization of the astrocyte membrane, which at the same time (i) increased the local astrocytic uptake of K\textsuperscript{+}, (ii) suppressed extracellular transport of K+, (iii) increased transport of K+ within astrocytes, and (iv) facilitated astrocytic relase of K+ in extracellular low concentration regions. In summary, these mechanisms seem optimal for shielding the extracellular space from excess K+.Comment: 19 pages, 5 figures, 1 table (Equations 37 & 38 and the two first equations in Figure 2 were corrected May 30th 2013

Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow

We review modeling of astrocyte ion dynamics with a specific focus on the implications of so-called spatial potassium buffering, where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. We thus include the key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure

An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain

Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.publishedVersio

A Computational Study of Astrocytic GABA Release at the Glutamatergic Synapse: EAAT-2 and GAT-3 Coupled Dynamics

Neurotransmitter dynamics within neuronal synapses can be controlled by astrocytes and reflect key contributors to neuronal activity. In particular, Glutamate (Glu) released by activated neurons is predominantly removed from the synaptic space by perisynaptic astrocytic transporters EAAT-2 (GLT-1). In previous work, we showed that the time course of Glu transport is affected by ionic concentration gradients either side of the astrocytic membrane and has the propensity for influencing postsynaptic neuronal excitability. Experimental findings co-localize GABA transporters GAT-3 with EAAT-2 on the perisynaptic astrocytic membrane. While these transporters are unlikely to facilitate the uptake of synaptic GABA, this paper presents simulation results which demonstrate the coupling of EAAT-2 and GAT-3, giving rise to the ionic-dependent reversed transport of GAT-3. The resulting efflux of GABA from the astrocyte to the synaptic space reflects an important astrocytic mechanism for modulation of hyperexcitability. Key results also illustrate an astrocytic-mediated modulation of synaptic neuronal excitation by released GABA at the glutamatergic synapse

A computational study of astrocytic glutamate influence on post-synaptic neuronal excitability

<p><b>Postsynaptic activity due to synaptic and intrinsic currents</b>, triggered by (a) synaptic glutamate [Glu]_syn (b-d) simulation with [Glu]_ast,eq = 1.5mM, 5mM, and 10mM respectively, synaptic currents (I_syn) combined AMPA- and NMDA-mediated currents in response to synaptic glutamate, membrane potential (V_m) of postsynaptic neuron resulting from combination of I_syn and voltage-gated currents (Na⁺, K⁺ and leak). Prolonged time course of synaptic glutamate leads to enhanced synaptic currents (I_syn) and higher frequency postsynaptic firing response (V_m depolarisations) as [Glu]_ast,eq increases.</p