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A Steady-State Model of Spreading Depression Predicts the Importance of an Unknown Conductance in Specific Dendritic Domains

Julia Makarova ^* , José M. Ibarz , Santiago Canals  and Oscar Herreras ^*

^* Cajal Institute of Neurobiology, Consejo Superior de Investigaciones Cientificas, Madrid, Spain; Department of Applied Mathematics, School of Optics, University Complutense of Madrid, Madrid, Spain; Department of Research, Hospital Ramón y Cajal, Madrid, Spain; and Max Planck Institute for Biological Cybernetics, Tuebingen, Germany

Correspondence: Address reprint requests to Julia Makarova, Cajal Institute for Neurobiology, C.S.I.C. Av. Dr. Arce 37, Madrid 28002, Spain. Tel.: 34-915854744; Fax: 34-915854754; E-mail: makarovaj{at}cajal.csic.es.

Spreading depression (SD) is a pathological wave of transient neuronal inactivation. We recently reported that the characteristic sustained complete depolarization is restricted to specific cell domains where the input resistance (R_in) first becomes negligible before achieving partial recovery, whereas in adjacent, more polarized membranes it drops by much less. The experimental study of the participating membrane channels is hindered by their mixed contribution and heterogeneous distribution. Therefore, we derived a biophysical model to analyze the conductances that replicate the subcellular profile of R_in during SD. Systematic variation of conductance densities far beyond the ranges reported failed to fit the experimental values. Besides standard potassium, sodium, and Glu-mediated conductances, the initial opening and gradual closing of an as yet undetermined large conductance is required to account for the evolution of R_in. Potassium conductances follow in the relative contribution and their closing during the late phase is also predicted. Large intracellular potential gradients from zero to rest are readily sustained between shunted and adjacent SD-spared membranes, which remain electroregenerative. The gradients are achieved by a combination of high-conductance subcellular domains and transmembrane ion redistribution in extended but discrete dendritic domains. We conclude that the heterogeneous subcellular behavior is due to local membrane properties, some of which may be specifically activated under extreme SD conditions.