Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations.
ABSTRACT Sustained inward currents in neuronal membranes underlie tonic-clonic seizure discharges and spreading depression (SD). It is not known whether these currents flow through abnormally operating physiological ion channels or through pathological pathways that are not normally present. We have now used the NEURON simulating environment of Hines, Moore, and Carnevale to model seizure discharges and SD. The geometry and electrotonic properties of the model neuron conformed to a hippocampal pyramidal cell. Voltage-controlled transient and persistent sodium currents (I(Na,T) and I(Na,P)), potassium currents (I(K,DR) and I(K,A)), and N-methyl-D-aspartate (NMDA) receptor-controlled currents (I(NMDA)), were inserted in the appropriate regions of the model cell. The neuron was surrounded by an interstitial space where extracellular potassium and sodium concentration ([K(+)](o) and [Na(+)](o)) could rise or fall. Changes in intra- and extracellular ion concentrations and the resulting shifts in the driving force for ionic currents were continuously computed based on the amount of current flowing through the membrane. A Na-K exchange pump operated to restore ion balances. In addition, extracellular potassium concentration, [K(+)](o), was also controlled by a "glial" uptake function. Parameters were chosen to resemble experimental data. As long as [K(+)](o) was kept within limits by the activity of the Na-K pump and the "glial" uptake, a depolarizing current pulse applied to the cell soma evoked repetitive firing that ceased when the stimulating current stopped. If, however, [K(+)](o) was allowed to rise, then a brief pulse provoked firing that outlasted the stimulus. At the termination of such a burst, the cell hyperpolarized and then slowly depolarized and another burst erupted without outside intervention. Such "clonic" bursting could continue indefinitely maintained by an interplay of the rise and fall of potassium and sodium concentrations with membrane currents and threshold levels. SD-like depolarization could be produced in two ways, 1) by a dendritic NMDA-controlled current. Glutamate was assumed to be released in response to rising [K(+)](o). And 2) by the persistent (i.e., slowly inactivating) Na-current, I(Na,P). When both I(NMDA) and I(Na,P) were present, the two acted synergistically. We conclude that epileptiform neuronal behavior and SD-like depolarization can be generated by the feedback of ion currents that change ion concentrations, which, in turn, influence ion currents and membrane potentials. The normal stability of brain function must depend on the efficient control of ion activities, especially that of [K(+)](o).
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ABSTRACT: We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.Journal of Biological Physics 06/2011; 37(3):361-73. · 1.86 Impact Factor
Article: Spontaneous Excitation Patterns Computed for Axons with Injury-like Impairments of Sodium Channels and Na/K Pumps.[show abstract] [hide abstract]
ABSTRACT: In injured neurons, "leaky" voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na(+)-loading and "Nav-CLS", i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted I(Na-window). A recent computation study revealed that CLS-based I(Na-window) left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic "smeared" injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For "mild CLS injury", a prominent feature is slow pump/leak-mediated E(Ion) oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist "device" could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.PLoS Computational Biology 09/2012; 8(9):e1002664. · 5.22 Impact Factor
Article: Extracellular potassium dynamics in the hyperexcitable state of the neuronal ictal activityCommunications in Nonlinear Science and Numerical Simulation 01/2011; · 2.81 Impact Factor