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#### Small fluctations of the Nernst membrane potentials caused by astrocytic spatial buffering in the rodent hippocampus

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https://www.frontiersin.org/10.3389/conf.fncom.2011.53.00225/event_abstract

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##### Citation

Noori, H. (2011). *Small fluctations of the Nernst membrane
potentials caused by astrocytic spatial buffering in the rodent hippocampus*. Poster presented at Computational
Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany.

Cite as: http://hdl.handle.net/21.11116/0000-0002-1CB9-F

##### Abstract

Introduction: Removal of potassium by glial cells implies the net uptake of potassium at sites of elevated potassium, i.e. where neurons are firing action potentials, and release of potassium at sites where no or little neuronal activity is going on, resulting in a redistribution of extracellular potassium (Figure 1). While there is evidence that glial uptake of potassium is partly mediated by Na+/K+ ATPase, many studies indicate that influx of potassium through inward rectifier ion channels plays a predominant role (Kofuji and Newman, 2009). It is firmly established that glial cells remove excess potassium from the extracellular space by mechanisms like spatial buffering as proposed for astrocytes, or potassium siphoning, proposed in the retina (Kofuji and Newman, 2009; Newman and Reichenbach, 1996). The resting membrane potentials of both neurons and glial cells are largely defined by a high plasma membrane conductance for potassium ions, and thus attain negative values close to the Nernstian equilibrium potential for potassium ions (Hodgkin and Katz, 1949; Somjen, 2002). Accordingly, small variations of the potassium concentration in extracellular space [K+]ex lead to changes in the membrane potential of neurons and to alterations in neuronal firing thresholds and neurotransmitter release (Newman, 1985; Somjen, 2002). Impaired extracellular potassium buffering has also been proposed as a significant mechanism underlying various neurological deficits related to abnormal neuronal depolarization, hyperexcitability, and seizures (Somjen, 2002). Despite the worthwhile computational studies on the influence of glial dynamics on the neuronal membrane potentials (Clay, 2005; Cressman et al., 2009; David et al., 2009; Park and Durand, 2006; Somjen et al., 2008; Ullah et al., 2009), there exists a need for fundamental investigation of glial influences on synaptic systems at equilibrium states. Potassium and other ionic resting potentials, which are obtained by Nernst equation, are substantial parameters of major electrophysiological equations such as the Hodgkin-Huxley equations.
Materials and Methods: In order to investigate the effects of glial spatial buffering on the Nernst potentials, we modified the Poisson-Nernst-Planck equation by adding a functional of potassium concentration F(c)(x,t), which depends on the gradient of the extracellular potassium concentration as well as on the glial ionic exchange rate with the extracellular space. The Nernst equation is then derived as a phase space relationship of the steady state solutions of the modified Nernst-
Planck equation. The restriction of the modified equation into one-dimension is a valid first approximation to the higher dimensions, which even provides analytic solutions. Thus, we will focus only on the one-dimensional equation. The analytic solution of the modified Nernst-Planck equation suggests that the modifications by the spatial buffering functional induce an additive correction term for the Nernst equation.
Results: By estimating the equation parameters from the experimental data, we can identifiy the magnitude of the correction term. It appears that the range of the glial impact on the neuronal Nernst potential is approximately between -0.9 and 2.9mV. This means an average glial influence of about +1mV resp. a current of 100pA. Although, there are no experimental studies validating these estimations, the calculated electrophysiological values appears to be plausible in the framework
of glial research. While these fluctuations of about 5% of the potassium Nernst potential are comparatively small (as expected), they provide parameter corrections for especially the Hodgkin-Huxley equations, which are of interest for further computational investigations of neuron-glia interactions.
Discussion: Although the achieved results are feasible from the experimental point of view, the present mathematical model leaves place for improvements. For instance, potassium uptake by glial cells is not only done through channels. There is also evidence that glial cells take up potassium by Na+/K+ ATPase or other transporters such as Na+/K+/2Cl- co-transport. Because these processes are mainly governed by the gradient of ion concentrations, the subsequent modifications of the Nernst-Planck equation by these processes appear to be of the same form as the introduced functional F(c). Therefore, it is expected that the extension of our model with further gradient-dependent uptake mechanisms reveal a similar analytical behavior with a potentially different range for the values of the glial impact. Nevertheless, the consideration of different types of ions in the modeling of glial homeostatic processes will increase the complexity of the mathematical analysis and requires further investigations.