Dependence of spontaneous neuronal firing and depolarization block on astroglial membrane processes
Catherine
Lloyd
Auckland Bioengineering Institute
Model Status
This CellML model is a tranlsation based on the orignal paper and Matlab code. The model runs in both COR and OpenCell to recreate the published results. This particular version of the model recreates Figure 2A, with a stimulus duration of 0.6s.
Model Structure
ABSTRACT: The chain of events where a neural activity-induced elevation of the extracellular space (ECS) potassium concentration ([K+]o) is followed by a decreased neuronal firing threshold which in turn causes increased neural activity, represents a positive feedback loop. Here we combine a relatively detailed model of glial membrane transport of water and ions and a Hodgkin-Huxley type neuron model to examine the effectof perturbing the magnitudes of transport rates in the glial membrane that may influence this feedback. The perturbations reflect pathological conditions and/or heterogeneity in glial membrane transporter density. When exposed to elevated [K+]o, the combined model responds either (i) by a brief period of neuronal firing followed by a rapid drop in [K+]o or (ii) by a much longer period where the neuron experiences depolarization block during which [K+]o first increases and later slowly returns to baseline levels. By solving the model equations repeatedly for a large number of empirically valid parameter sets, we find that both the high [K+]o-induced duration of neuronal firing and the prevalence of depolarization block show high sensitivities to variation in the time scale of the glial membrane dynamics and to the magnitudes of the sodium-potassium pump rate and the potassium ion channel conductance. In contrast, firing duration is much less sensitive to perturbations of the magnitude of Na+/K+/2Cl- (NKCC1) cotransporter permeability and Na+/2HCO-3 (NBC) cotransporter conductance. An analysis focusing on the model's ability to fire spontaneously discloses the feedback mechanism and allows us to predict which combinations of ion concentrations that give rise to spontaneous firing of action potentials. The results suggest that when [K+]o becomes elevated, spatiotemporal heterogenity of ion and water transport across the astroglialmembrane in the brainmay cause very different potassium clearance profiles that are possibly of biomedical importance. The above insights point to the importance of combining neuronal and astroglial models of some sophistication in order to disclose phenomena associated with the astroglia-neuron interaction.
Schematic diagram of the model displaying the channels, pumps and exchangers allowing ion transfer between the neuron, the extracellular matrix and the glia.
Vm_n
neuron membrane potential
i_NaT
transient sodium current
i_NaP
persistent sodium current
i_KDR
delayed rectifier potassium current
i_KA
transient potassium current
i_NaKATPase_n
neuron sodium-potassium pump
i_leakNa
sodium leak current
i_leakK
potassium leak current
i_leakf
unspecified ion leak current
Vm_g
glial membrane potential
J_Na
glial transmembrane sodium ion flux
J_K
glial transmembrane potassium ion flux
J_NaKATPase_g
glial transmembrane sodium-potassium ion flux via the NaK pump
J_NBC
glial transmembrane sodium and bicarbonate ion flux via the NBC cotransporter
J_NKCC1
glial transmembrane sodium potassium and chloride ion flux via the NKCC1 cotransporter
N_Nag
number of sodium ions per unit glial area
N_Kg
number of potassium ions per unit glial area
wg
ratio of glial volume to glial area
wo
extracellular space volume to area ratio
N_Nao
number of sodium ions in the extracellular space
N_Ko
number of potassium ions in the extracellular space
N_HCO3o
number of bicarbonate ions in the extracellular space
electric_potentials
electric potentials
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OleOttersen10001000000.01electrophysiologyneurobiologyastrogliaAuckland Bioengineering InstituteIvarOstbyStigOmholtAuckland Bioengineering InstituteCellML TeamCatherineLloydMayLievOyehaugDependence of spontaneous neuronal firing and depolarization block on astroglial membrane processes2009-08-20T00:00:00+00:002009-00-00 00:00CatherineLloydkeywordc.lloyd@auckland.ac.nzGauteEinevoll