Identifying essential conditions for refractoriness of Leão's spreading depression-computational modeling

A mathematical description of the restoring ionic mechanisms in a compartmentalized electrochemical model of neuronal tissues was developed aiming at studying the essential conditions for refractoriness of Leão's spreading depression (SD). The model comprehends the representation of a plexiform layer, composed by synaptic terminals and glial process immersed in an extracellular space where the space-temporal variations of the ionic concentrations were described by electrodiffusion equations. The synaptic transmission was described by differential equations representing the corresponding chemical reactions associated with the neurotransmitter release, diffusion, binding to its receptor in the postsynaptic membrane and the uptake by the presynaptic terminals. The effect of the neurotransmitter binding to the receptor induces changes in the permeability of the postsynaptic membrane and the corresponding transmembrane fluxes were calculated. The fluxes promote changes in the external ionic concentrations, changing the ionic electrodiffusion through the extracellular space. The description of these mechanisms provides the reaction-diffusion structure of the model and allows simulating the wave propagation. The simulations of experimental maneuvers of application of two consecutive stimuli for inducing SD suggest: (i) the extracellular space acts coupling the postsynaptic terminals and glial cells recovery mechanisms in such a way that the extracellular ionic concentrations change only during the wave front; (ii) the potassium removed from the extracellular by the glial cells, originated from the depolarization of the synaptic terminals returns slowly limited by the glial release, contributing for the refractoriness of the tissue; (iii) critical points for sodium and potassium transmembrane fluxes could be identified, allowing proposing specific conditions for the interplay between channels and pumps fluxes for determining the absolute and relative refractory periods.