Seizure-like afterdischarges simulated in a model neuron

The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.

The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states. II. Network and glial dynamics

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin-Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.

Calcium sensitive non-selective cation current promotes seizure-like discharges and spreading depression in a model neuron

As described by others, an extracellular calcium-sensitive non-selective cation channel ([Ca(2+)](o)-sensitive NSCC) of central neurons opens when extracellular calcium level decreases. An other non-selective current is activated by rising intracellular calcium ([Ca(2+)]( i )). The [Ca(2+)](o)-sensitive NSCC is not dependent on voltage and while it is permeable by monovalent cations, it is blocked by divalent cations. We tested the hypothesis that activation of this channel can promote seizures and spreading depression (SD). We used a computer model of a neuron surrounded by interstitial space and enveloped in a glia-endothelial "buffer" system. Na(+), K(+), Ca(2+) and Cl(-) concentrations, ion fluxes and osmotically driven volume changes were computed. Conventional ion channels and the NSCC were incorporated in the neuron membrane. Activation of NSCC conductance caused the appearance of paroxysmal afterdischarges (ADs) at parameter settings that did not produce AD in the absence of NSCC. The duration of the AD depended on the amplitude of the NSCC. Similarly, NSCC also enabled the generation of SD. We conclude that NSCC can contribute to the generation of epileptiform events and to spreading depression.

Computer simulations of neuron-glia interactions mediated by ion flux

Extracellular potassium concentration, [K(+)](o), and intracellular calcium, [Ca(2+)](i), rise during neuron excitation, seizures and spreading depression. Astrocytes probably restrain the rise of K(+) in a way that is only partly understood. To examine the effect of glial K(+) uptake, we used a model neuron equipped with Na(+), K(+), Ca(2+) and Cl(-) conductances, ion pumps and ion exchangers, surrounded by interstitial space and glia. The glial membrane was either "passive", incorporating only leak channels and an ion exchange pump, or it had rectifying K(+) channels. We computed ion fluxes, concentration changes and osmotic volume changes. Increase of [K(+)](o) stimulated the glial uptake by the glial 3Na/2K ion pump. The [K(+)](o) flux through glial leak and rectifier channels was outward as long as the driving potential was outwardly directed, but it turned inward when rising [K(+)](o)/[K(+)](i) ratio reversed the driving potential. Adjustments of glial membrane parameters influenced the neuronal firing patterns, the length of paroxysmal afterdischarge and the ignition point of spreading depression. We conclude that voltage gated K(+) currents can boost the effectiveness of the glial "potassium buffer" and that this buffer function is important even at moderate or low levels of excitation, but especially so in pathological states.