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. 2012;7(12):e51169.
doi: 10.1371/journal.pone.0051169. Epub 2012 Dec 20.

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

Michael D Forrest  1 , Mark J Wall, Daniel A Press, Jianfeng Feng
Affiliations

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

Michael D Forrest et al. PLoS One. 2012.

Abstract

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na(+)/K(+) pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na(+)/K(+) pump. The model can replicate these recordings. We propose that Na(+)/K(+) pump activity controls the intrinsic firing mode of cerbellar Purkinje cells.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. In the absence of synaptic input, the Purkinje cell model fires spontaneously in a repeating trimodal pattern.
A, The model cell's default morphology with somatic and dendritic recording points labeled. B, An alternative morphology used for the model. C, A single trimodal repeat, recorded at the soma, with the constituent tonic (t), burst (b) and silent (s) modes labeled. D, The same trimodal repeat as (C) but recorded from a point within the dendritic tree. E, With no high-threshold spikes in the dendrites (i), firing is tonic at the soma (ii). With high-threshold dendritic spikes (iii), somatic firing has a stereotypical burst waveform (iv). A single dendritic spike is co-incidental with each somatic burst. The peak of the dendritic spike (* in sub-panel iii) causes the sudden and rapid depolarization that ends the somatic burst (iv). F, Single trimodal repeat recorded from the soma of a model variant that lacks the Kv1.2 channel. It has a markedly shorter tonic mode [t] than the standard model (C). G, The same trimodal repeat as (D) but recorded from a point within the model's dendritic tree. H, Without Kv1.2 channels, the dendritic spike frequency is higher (i) which results in a smaller number of spikes per somatic burst (ii). Panels C, D, F and G are scaled by the first scale bar (40 mV, 5 s) and panels E and H by the second scale bar (40 mV, 50 ms).
Figure 2
Figure 2. Changing ion concentrations drive the transition of modes in the Purkinje cell model's trimodal pattern of firing.
All panels plot over the same period of time. A, Somatic membrane potential. The three different modes of a single trimodal repeat – tonic, burst, quiescent - are labelled. B, Membrane potential at a point in the dendrites. The burst mode at the soma corresponds with high threshold Ca2+ spiking in the dendrites. C, Extracellular K+ concentration ([K+]o) to the dendritic compartments. [K+]o increases during firing as a function of voltage-gated K+ efflux. [K+]o recedes (resets) during quiescence as voltage-gated K+ efflux stops whilst the Na+/K+ pump maintains K+ influx into the cell. [K+]o cannot exceed 3.03 mM. This is our setting for the “ceiling” to [K+]o accumulation (refer Methods) and is set for real Purkinje cells by the glial buffer system. As [K+]o accumulation passes a critical point, firing is switched from the tonic to the burst mode. As described in the Results , this is because [K+]o accumulation reduces the driving force, and current flow, for the Kv1.2 K+ current and this ultimately permits the dendrites to fire high threshold Ca2+ spikes which invade the soma and cause bursting. D, Somatic intracellular Na+ concentration, in a “fuzzy space” underneath Na+/K+ pumps ([Na+]i). [Na+]i increases during firing, as a function of voltage-gated Na+ entry. However, changes in [Na+]i are lagged by τ = 5 s to account for the duration of sodium's diffusion from channels to pumps (refer Methods and Discussion ). As [Na+]i increases past a critical point, the hyperpolarising force of Na+/K+ pumping achieves sufficient strength to drive the model cell to quiescence. [Na+]i decreases during quiescence, as voltage-gated Na+ influx stops whilst the Na+/K+ pump maintains Na+ efflux. This decrease in [Na+]i is lagged by τ = 5 s after the onset of quiescence.
Figure 3
Figure 3. The KNa, KK and τ model parameters set the model's trimodal repeat length.
We present durations of the tonic mode, bursting mode, firing mode (tonic+bursting), quiescent mode and trimodal repeat length (tonic+bursting+quiescent) for different model settings. A, With default settings [KNa = 40 mM; KK = 2.245 mM; τ = 5 s] the trimodal repeat length is ∼20 s. B, Reducing KNa (40 mM to 20 mM) shortens the firing (tonic+burst) duration. C, Increasing KK (2.245 mM to 20 mM) shortens the tonic duration. D, Reducing τ (5 s to 1 s) shortens the quiescent mode. E, With KNa, KK and τ all modified [KNa = 10.5 mM; KK = 50 mM; τ = 1 s] the trimodal repeat length is ∼3 s. F, When the model was run with a different reconstructed Purkinje cell morphology, but with the same parameters as (E), the trimodal repeat length was not majorly changed.
Figure 4
Figure 4. Removal of Na+ channels (simulated TTX block of Na+ channels) abolishes the model's Na+ spiking, at the soma, but not it's Ca2+ spiking in the dendrites.
A, The model's somatic membrane potential (vs. Time), when Na+ channels are absent. There are no Na+ spikes but periods of small deflections in the membrane potential, which alternate with quiescent periods (bimodal behaviour). B, The model's dendritic membrane potential (vs. Time), when Na+ channels are absent. Ca2+ spikes persist in the dendrites and travel to the soma to produce the aforementioned small somatic deflections in membrane potential. This figure shows that the model's dendritic spiking is generated de novo and is not reliant upon an excitatory drive from the soma.
Figure 5
Figure 5. The Purkinje cell model can replicate experimentally observed bimodal patterns of Purkinje cell firing.
Left panels are somatic membrane potential and right panels are dendritic membrane potential (vs. Time). By referring to the dendritic membrane potential one can distinguish bursting from tonic firing at the soma. Because bursting (unlike tonic firing) is co-incidental with dendritic spiking. A, The standard Purkinje cell model fires in a repeating trimodal pattern. B, Addition of inhibitory input switches the standard model out of the trimodal pattern and into a repeating bimodal pattern of tonic spiking and quiescence. C, Modifying the KK parameter (50 to 0.8) makes the model intrinsically bimodal - firing bimodally (tonic spiking and quiescence) in the absence of inhibitory input. D, With the bimodal model of panel (C), removal of Kv1.2 channels switches it to fire in a trimodal pattern. E, With the trimodal model of panel (A), removal of P-type Ca2+ channels switches it to fire in a bimodal pattern.
Figure 6
Figure 6. Ouabain block of the Na+/K+ pump switches Purkinje cell activity out of the trimodal firing pattern and into a continuous burst mode.
Panel A shows a whole cell patch clamp recording from a Purkinje cell (with 10 µM bicuculline already present to block GABAergic inputs) following the application of 2.5 µM ouabain. The arrow denotes the time at which we feel that ouabain starts to modify Purkinje cell firing. Panels B, C, D, and E correspond to the labelled parts of panel A. Panels F, G, H and I show individual bursts from B, D, D and E respectively. The initial firing mode, before any Na+/K+ pump block, is trimodal (panel B). With time, as Na+/K+ pumps become blocked, the trimodal pattern's quiescent periods get shorter until they are eventually abolished and the cell fires continuously (panel A). Over this same period the length of the trimodal pattern's tonic mode also decreases, ceding to an increasing propensity to burst (compare panels B and C). Indeed, by the time of continuous firing (panel D) there is only bursting and no tonic fraction at all. After a period, this continuous bursting acquires a gradient of depolarization (Panel A). As it depolarizes, the number of spikes per burst steadily decreases (F, G, H) until the soma enters depolarization block and there are none. In this case, the only deflections observed are those of the Ca2+ spikes that have travelled into the soma from the dendritic arborisation (E, I). Panel A scaling is encoded in the first scale bar (50 mV, 50 s). The scaling of panels B, C, D and E is encoded in the second scale bar (50 mV, 3 s). The scaling of panels F, G, H and I is encoded in the third scale bar (50 mV, 100 ms).
Figure 7
Figure 7. The model can recapitulate the response of Purkinje cells (firing in the trimodal pattern) to Na+/K+ pump block by ouabain.
A, Somatic membrane potential (vs. Time) with the arrow denoting the onset of Na+/K+ pump block. Panels B, C, D, E and F correspond to the labelled parts of Panel A. Panels G, H, I and J show individual bursts from B, D, F and F respectively. The firing pattern in control, before any Na+/K+ pump block, is trimodal (panel B). Following the onset of Na+/K+ pump block, the trimodal pattern's quiescent periods get shorter until eventually they are abolished and the cell fires continuously (panel A). Over this same period the duration of the trimodal pattern's tonic mode also decreases, leading to an increased proportion of burst firing (compare panels B, C and D). Indeed, by the time cells are continuously active the firing only consists of bursts, with no tonic mode remaining (panel E). After a period, this continuous bursting acquires a gradient of depolarization (Panel A). As it depolarizes, the number of spikes per burst steadily decreases (G, H, I) until the soma enters depolarization block and there are none. In this case, the only deflections observed are those produced by Ca2+ spikes that have travelled to the soma from the dendritic arborisation (F, J). Panel A scaling is encoded in the first scale bar (80 mV, 1 s). The scaling of panels B, C, D, E and F is encoded in the second scale bar (80 mV, 100 ms). The scaling of panels G, H, I and J is encoded in the third scale bar (80 mV, 30 ms).
Figure 8
Figure 8. With inhibitory synaptic inputs unblocked, some Purkinje cells fire in a repeating bimodal pattern; ouabain block of Na+/K+ pumps switches these cells into the trimodal firing pattern and then a continuous burst mode.
A, Whole cell patch clamp recording from a Purkinje cell (with GABA synaptic inputs intact/unblocked) in control and following the application of 2.5 µM ouabain. The red arrow denotes the time at which we feel that ouabain starts to modify Purkinje cell firing. Panels B, C, D, and E correspond to the labelled parts of panel A. In control, the Purkinje cell activity is in the repeating bimodal pattern (B). Following the addition of ouabain, the firing pattern is switched from bimodal to trimodal (C) and then transitions into continuous bursting (D). After a period, this bursting acquires a gradient of depolarization and ultimately converges upon a somatic depolarization block, in which the only deflections observed are those of Ca2+ spikes that have travelled into the soma from the dendritic arborisation (E). Panel A scaling is encoded in the first scale bar (20 mV, 100 s). Panel B scaling is encoded in the second scale bar (20 mV, 5 s). The scaling of panels C, D and E is encoded in the third scale bar (20 mV, 5 s).
Figure 9
Figure 9. With inhibitory synaptic inputs unblocked, some Purkinje cells fire in a repeating bimodal pattern (tonic spiking/quiescence) and the model can replicate their response to Na+/K+ pump block by ouabain.
Panels B, C, D, and E correspond to the labelled parts of panel A. A, With simulated GABAergic synaptic inputs innervating the model, it fires in a bimodal pattern of tonic spiking and quiescence (B). The red arrow denotes the onset of simulated ouabain application. Following this onset, the firing pattern is switched from bimodal to trimodal (C) and then transitions into continuous bursting (D). After a period, this bursting acquires a gradient of depolarization and ultimately converges upon a somatic depolarization block, in which the only deflections observed are those of Ca2+ spikes that have travelled into the soma from the dendritic arborisation (E). Panel A scaling is encoded in the first scale bar (20 mV, 1 s). The scaling of panels B, C, D and E is encoded in the second scale bar (20 mV, 0.2 s).
Figure 10
Figure 10. Upon Na+ channel block, real and model Purkinje cells express a repeating bimodal pattern (Ca2+ spike activity/quiescence) and Na+/K+ pump block eradicates its quiescent component.
A, Whole cell patch clamp recording from a Purkinje cell in the presence of 1 µM TTX (to block Na+ channels), which sets a repeating bimodal pattern of Ca2+ spike activity and quiescence, before the introduction of 2 µM ouabain (to block the Na+/K+ pump) eradicates quiescence and renders continuous activity. B, The model's somatic membrane potential (vs. Time), with arrows denoting the onset of TTX simulation (Na+ channel density = 0) and ouabain simulation (Na+/K+ pump densities reduced as a function of time). The model replicates the principal features of the experimental recording. However, the model's transition into a continuous activity mode, without any quiescent periods, occurs faster than in experiment. Ouabain blocks a greater and greater fraction of Na+/K+ pump molecules over time, until all Na+/K+ pump molecules are blocked. Upon experimental ouabain application (panel A), one further quiescent period is observed before the rising ouabain block compromises a sufficient fraction, such that no further quiescent periods are observed. Upon simulated ouabain application (panel B), no further quiescent periods are observed. Ouabain application was simulated in the Purkinje cell model by decreasing the Na+/K+ pump densities by arbitrary functions of time (Methods). A slower transition, to the ouabain rendered behaviour, could be achieved in the model by using slower functions of decline for the model's Na+/K+ pump densities. However, the model does not employ such slower functions; it abstracts on the time course.
Figure 11
Figure 11. The 1089, 41 and 5 compartment models of the cerebellar Purkinje cell can all spontaneously fire in the trimodal pattern of activity.
Figure 12
Figure 12. The 1089, 41 and 5 compartment models of the cerbellar Purkinje cell can all respond equivalently (qualitatively) to a simulated ouabain block of the Na+/K+ pump.
See this image and copyright information in PMC

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