Burst initiation and termination in phasic vasopressin cells of the rat supraoptic nucleus: a combined mathematical, electrical, and calcium fluorescence study

Abstract

Vasopressin secreting neurons of the rat hypothalamus discharge lengthy, repeating bursts of action potentials in response to physiological stress. Although many electrical currents and calcium-dependent processes have been isolated and analyzed in these cells, their interactions are less well fathomed. In particular, the mechanism of how each burst is triggered, sustained, and terminated is poorly understood. We present a mathematical model for the bursting mechanism, and we support our model with new simultaneous electrical recording and calcium imaging data. We show that bursts can be initiated by spike-dependent calcium influx, and we propose that the resulting elevation of bulk calcium inhibits a persistent potassium current. This inhibition depolarizes the cell above threshold and so triggers regenerative spiking and further calcium influx. We present imaging data to show that bulk calcium reaches a plateau within the first few seconds of the burst, and our model indicates that this plateau occurs when calcium influx is balanced by efflux and uptake into stores. We conjecture that the burst is terminated by a slow, progressive desensitization to calcium of the potassium leak current. Finally, we propose that the opioid dynorphin, which is known to be secreted from the somatodendritic region and has been shown previously to regulate burst length and phasic activity in these cells, is the autocrine messenger for this desensitization.

Figure 1.

Experimental (a) and model (b) DAPs and their associated calcium transients. Data taken from a whole-cell recording from the SON of a hypothalamic slice; spikes were evoked with a 5 msec depolarizing pulse and have been truncated for clarity. Left panels, Single spike followed by a DAP that is subthreshold for firing. The decay of the DAP tracks that of intracellular calcium, returning to rest with a time constant of τ = ∼1.85 sec (Roper et al., 2003). Right panels, DAP summation and the initiation of phasic activity: the stimulation protocol elicits two spikes, and the resulting summed DAP crosses spike threshold. The consequent action potentials further raise intracellular calcium, which in turn maintains the suppression of I_K,leak and so supports a regenerative plateau potential.

Figure 2.

Putative steady-state voltage- and calcium-dependent modulation of the potassium leak current, I_K,leak. Note that f_∞ is zero when bulk calcium is at its resting level ([Ca²⁺]_rest = 113 nm), increases with [Ca²⁺]_i, but can go negative if [Ca²⁺]_i is brought below rest (Eq. 10 and Fig 6).

Figure 3.

Simultaneous whole-cell recording and calcium imaging of evoked bursts in vivo (a), and model of evoked burst with corresponding calcium concentration (b). Note that calcium initially rises rapidly until it approaches a steady state and then decays once electrical activity has ceased. The top trace in each experimental figure plots the calcium concentration at three different locations in each cell, and these locations are shown in the photographs to the right of each figure. The trace that corresponds to each position is as follows: dashed line (1), black line (2), and gray line (3).

Figure 4.

Instantaneous firing rate (quantified by the reciprocal of the interspike interval) versus time for experimental recording (a) and model (b) (compare with Poulain et al., 1988, their Fig. 11). Note that the rate first rises rapidly to a peak and then slowly adapts to ∼10 Hz. Firing then remains steady until the burst abruptly terminates. c shows that blocking the AHP in the model, by setting I_AHP = 0, both prevents spike frequency adaptation and also shortens the burst. This should be compared with block of the AHP in vitro with apamin [Kirkpatrick and Bourque (1996), their Fig. 7]. Parameters of the model are otherwise the same for b and c.

Figure 11.

Phasic activity occurs in MNCs during sustained depolarization: experimental recordings (a) and model (b). Note that the silent phase is characterized first by postburst DAP and then by slow depolarization. Both active and silent phases of the burst have a mean length of ∼20 sec (see Results) but display a wide variability both in vitro and in vivo. Model parameters are I_app = 1.28, λ = 0.6, and Γ = 0.4. Phasic activity only occurs when the model is depolarized above spike threshold, and the oscillation is driven by an upregulation of I_K,leak, which transiently depresses V below threshold and interrupts firing. c, Model with same parameters as b, but the DAP has been “blocked” by setting f = 0, and the model fires continuously (cf. Ghamari-Langroudi and Bourque, 1998).

Figure 5.

Burst termination and the interburst period: model (a) and whole-cell electrode recording from the SON of a hypothalamic slice (b). Note that the firing frequency remains steady until the end of the burst. The final spikes are succeeded first by a postburst DAP, which in turn is followed by a lengthy slow depolarization. The experimental trace has been low-pass filtered to remove membrane noise and to make the general trend more evident. Spikes have been trimmed for clarity.

Figure 6.

Proposed action of dynorphin on the activation of the DAP. We infer that the activation of the κ-opioid receptor by dynorphin desensitizes I_K,leak to calcium and so shifts the activation curve rightward along the calcium axis. Note that the axis in the bottom panel has been lengthened.

Figure 7.

Secretion, binding, and clearance of dynorphin and κ-receptors. (1) DCG fuses to cell membrane and spills dynorphin into the extracellular space. The DCG membrane also carries κ-receptors (Shuster et al., 1999), and so fusion of the granule also upregulates the receptor. (2) Extracellular dynorphin binds to the κ-receptor, and the bound complex begins to signal. (3) The bound complex is internalized, dephosphorylated, and ceases signaling.

Figure 8.

Comparison of time periods for active and silent phases for the simple model of increase and clearance of D (Eq. 17). D both rises and falls exponentially with the same time constant, but, note that for this model, the silent phase is significantly longer than the active phase, although both in vivo and in vitro they are found to be almost equal. Thus, the simple model does not adequately describe the dynamics of D.

Figure 9.

Proposed time course of D (the transduction of κ-receptor activation by dynorphin) during a burst; compare this with the profile of [Ca²⁺]_i shown in Figure 3. D evolves according to Equations 13 and 18 and decays to rest exponentially when the cell is silent.

Figure 10.

The evolution of [Ca²⁺]_i and D throughout and between bursts and the corresponding upmodulation and downmodulation of I_K,leak (shown schematically). The cycle starts from top left and moves clockwise, and the activation of the DAP, or plateau, at any time is denoted by the circle. Threshold denotes the calcium threshold for triggering the plateau potential and not spike threshold, and depends on spike frequency. Note that the function f denotes the modulation, and not the activation, of I_K,leak. f therefore starts at zero but can go negative if [Ca²⁺]_i decays while it is still right-shifted. This negative modulation corresponds to an upmodulation of I_K,leak and leads to a hyperpolarization of the membrane potential. The sequence of events is as follows: (1) spike-driven Ca²⁺ influx depolarizes the cell by depressing I_K,leak. The depolarization triggers more spikes, further increasing [Ca²⁺]_i and so sustaining a plateau and initiating a burst; (2) subsequent spikes cause further influx and so saturate the inhibition of I_K,leak; (3) D starts to increase, desensitizing I_K,leak to Ca²⁺ and raising the plateau threshold until it is no longer self-sustaining. The plateau then collapses, and the burst terminates; (4) D decays more slowly than Ca²⁺ and so remains elevated while Ca²⁺ decays. Thus I_K,leak remains transiently desensitized, causing f to go negative and temporarily hyperpolarizing the membrane. Hyperpolarization decays as D is cleared, and becomes manifest as a slow depolarization. As both [Ca²⁺]_i and D decay, the cell returns to its initial state.

Figure 12.

MNCs show a transient response during an aggressively applied stimulus and briefly discharge a fast-continuous pattern before the onset of phasic activity. We propose that this transient fast-continuous pattern occurs because the dynorphin–κ-receptor desensitization mechanism initially develops slowly, and so there is a short time for which the inhibition caused by the upregulation of I_K,leak does not interrupt firing (compare with Fig. 11c). We further propose that this slow onset is caused by the slow filling of a releasable pool of dense-core granules from a docked pool of granules.