An Active membrane model of the cerebellar Purkinje cellII: Simulation of synaptic responses. Schutter, E. D. and Bower, J. M. J. Neurophysiology, 71(1):401-419, 1994.
abstract   bibtex   
1. A detailed compartmental model of a cerebellar Purkinje cell with active dendritic membrane was constructed. The model was based on anatomic reconstructions of single Purkinje cells and included 10 different types of voltage-dependent channels described by Hodgkin-Huxley equations, derived from Purkinje cell-specific voltage-clamp data where available. These channels included a fast and persistent Na+ channel, three voltage-dependent K+ channels, T-type and P-type Ca2+ channels, and two types of Ca2+-activated K+ channels. 2. The ionic channels were distributed differentially over three zones of the model, with Na+ channels in the soma, fast K+ channels in the soma and main dendrite, and Ca2+ channels and Ca2+-activated K+ channels in the entire dendrite. Channel densities in the model were varied until it could reproduce Purkinje cell responses to current injections in the soma or dendrite, as observed in slice recordings. 3. As in real Purkinje cells, the model generated two types of spiking behavior. In response to small current injections the model fired exclusively fast somatic spikes. These somatic spikes were caused by Na+ channels and repolarized by the delayed rectifier. When higher-amplitude current injections were given, sodium spiking increased in frequency until the model generated large dendritic Ca2+ spikes. Analysis of membrane currents underlying this behavior showed that these Ca2+ spikes were caused by the P-type Ca2+ channel and repolarized by the BK-type Ca2+-activated K+ channel. As in pharmacological blocking experiments, removal of Na+ channels abolished the fast spikes and removal of Ca2+ channels removed Ca2+ spiking. 4. In addition to spiking behavior, the model also produced slow plateau potentials in both the dendrite and soma. These longer-duration potentials occurred in response to both short and prolonged current steps. Analysis of the model demonstrated that the plateau potentials in the soma were caused by the window current component of the fast Na+ current, which was much larger than the current through the persistent Na+ channels. Plateau potentials in the dendrite were carried by the same P-type Ca2+ channel that was also responsible for Ca2+ spike generation. The P channel could participate in both model functions because of the low-threshold K2-type Ca2+-activated K+ channel, which dynamically changed the threshold for dendritic spike generation through a negative feedback loop with the activation kinetics of the P-type Ca2+ channel. 5. These model responses were robust to changes in the densities of all of the ionic channels. For most of the channels, modifying their densities by factors of greater than or equal to 2 resulted only in left or right shifts of the frequency-current curve. However, changes of >20% to the amount of P-type Ca2+ channels or of one of the Ca2+-activated K+ channels in the model either suppressed dendritic spikes or caused the model to always fire Ca2+ spikes. Modeling results were also robust to variations in Purkinje cell morphology. We simulated models of two other anatomically reconstructed Purkinje cells with the same channel distributions and got similar responses to current injections. 6. The model was used to compare the electrotonic length of the Purkinje cell in the presence and absence of active dendritic conductances. The electrotonic distance from soma to the tip of the most distal dendrite increased from 0 57 lambda in a passive model to 0.95 lambda in a quiet model with active membrane. During a dendritic spike generated by current injection the distance increased even more, to 1.57 lambda. 7. Finally, the model was used to study the probable accuracy of experimental voltage-clamp data. Whole-cell patch-clamp conditions were simulated by blocking most of the K+ currents in the model. The increased electrotonic length due to the active dendritic membrane caused space clamp to fail, resulting in membrane potentials in proximal and distal dendrites that differed critically from the holding potential in the soma.
@article{ DeSchutter_Bower94b,
  author = {De Schutter, E. and Bower, J. M.},
  title = {An Active membrane model of the cerebellar {P}urkinje cell{II: S}imulation
	of synaptic responses},
  journal = {J. Neurophysiology},
  year = {1994},
  volume = {71},
  pages = {401-419},
  number = {1},
  abstract = { 1. A detailed compartmental model of a cerebellar Purkinje cell with
	active dendritic membrane was constructed. The model was based on
	anatomic reconstructions of single Purkinje cells and included 10
	different types of voltage-dependent channels described by Hodgkin-Huxley
	equations, derived from Purkinje cell-specific voltage-clamp data
	where available. These channels included a fast and persistent Na+
	channel, three voltage-dependent K+ channels, T-type and P-type Ca2+
	channels, and two types of Ca2+-activated K+ channels. 2. The ionic
	channels were distributed differentially over three zones of the
	model, with Na+ channels in the soma, fast K+ channels in the soma
	and main dendrite, and Ca2+ channels and Ca2+-activated K+ channels
	in the entire dendrite. Channel densities in the model were varied
	until it could reproduce Purkinje cell responses to current injections
	in the soma or dendrite, as observed in slice recordings. 3. As in
	real Purkinje cells, the model generated two types of spiking behavior.
	In response to small current injections the model fired exclusively
	fast somatic spikes. These somatic spikes were caused by Na+ channels
	and repolarized by the delayed rectifier. When higher-amplitude current
	injections were given, sodium spiking increased in frequency until
	the model generated large dendritic Ca2+ spikes. Analysis of membrane
	currents underlying this behavior showed that these Ca2+ spikes were
	caused by the P-type Ca2+ channel and repolarized by the BK-type
	Ca2+-activated K+ channel. As in pharmacological blocking experiments,
	removal of Na+ channels abolished the fast spikes and removal of
	Ca2+ channels removed Ca2+ spiking. 4. In addition to spiking behavior,
	the model also produced slow plateau potentials in both the dendrite
	and soma. These longer-duration potentials occurred in response to
	both short and prolonged current steps. Analysis of the model demonstrated
	that the plateau potentials in the soma were caused by the window
	current component of the fast Na+ current, which was much larger
	than the current through the persistent Na+ channels. Plateau potentials
	in the dendrite were carried by the same P-type Ca2+ channel that
	was also responsible for Ca2+ spike generation. The P channel could
	participate in both model functions because of the low-threshold
	K2-type Ca2+-activated K+ channel, which dynamically changed the
	threshold for dendritic spike generation through a negative feedback
	loop with the activation kinetics of the P-type Ca2+ channel. 5.
	These model responses were robust to changes in the densities of
	all of the ionic channels. For most of the channels, modifying their
	densities by factors of greater than or equal to 2 resulted only
	in left or right shifts of the frequency-current curve. However,
	changes of >20% to the amount of P-type Ca2+ channels or of one of
	the Ca2+-activated K+ channels in the model either suppressed dendritic
	spikes or caused the model to always fire Ca2+ spikes. Modeling results
	were also robust to variations in Purkinje cell morphology. We simulated
	models of two other anatomically reconstructed Purkinje cells with
	the same channel distributions and got similar responses to current
	injections. 6. The model was used to compare the electrotonic length
	of the Purkinje cell in the presence and absence of active dendritic
	conductances. The electrotonic distance from soma to the tip of the
	most distal dendrite increased from 0 57 lambda in a passive model
	to 0.95 lambda in a quiet model with active membrane. During a dendritic
	spike generated by current injection the distance increased even
	more, to 1.57 lambda. 7. Finally, the model was used to study the
	probable accuracy of experimental voltage-clamp data. Whole-cell
	patch-clamp conditions were simulated by blocking most of the K+
	currents in the model. The increased electrotonic length due to the
	active dendritic membrane caused space clamp to fail, resulting in
	membrane potentials in proximal and distal dendrites that differed
	critically from the holding potential in the soma.},
  en_number = {5.4:18}
}
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