Accumulation of cytoplasmic calcium, but not apamin‐sensitive afterhyperpolarization current, during high frequency firing in rat subthalamic nucleus cells

Abstract

The autonomous firing pattern of neurons in the rat subthalamic nucleus (STN) is shaped by action potential afterhyperpolarization currents. One of these is an apamin-sensitive calcium-dependent potassium current (SK). The duration of SK current is usually considered to be limited by the clearance of calcium from the vicinity of the channel. When the cell is driven to fire faster, calcium is expected to accumulate, and this is expected to result in accumulation of calcium-dependent AHP current. We measured the time course of calcium transients in the soma and proximal dendrites of STN neurons during spontaneous firing and their accumulation during driven firing. We compared these to the time course and accumulation of AHP currents using whole-cell and perforated patch recordings. During spontaneous firing, a rise in free cytoplasmic calcium was seen after each action potential, and decayed with a time constant of about 200 ms in the soma, and 80 ms in the dendrites. At rates higher than 10 Hz, calcium transients accumulated as predicted. In addition, there was a slow calcium transient not predicted by summation of action potentials that became more pronounced at high firing frequency. Spike AHP currents were measured in voltage clamp as tail currents after 2 ms voltage pulses that triggered action currents. Apamin-sensitive AHP (SK) current was measured by subtraction of tail currents obtained before and after treatment with apamin. SK current peaked between 10 and 15 ms after an action potential, had a decay time constant of about 30 ms, and showed no accumulation. At frequencies between 5 and 200 spikes s −1 , the maximal SK current remained the same as that evoked by a single action potential. AHP current did not have time to decay between action potentials, so at frequencies above 50 spikes s −1 the apamin-sensitive current was effectively constant. These results are inconsistent with the view that the decay of SK current is governed by calcium dynamics. They suggest that the calcium is present at the SK channel for a very short time after each action potential, and the current decays at a rate set by the deactivation kinetics of the SK channel. At high rates, repetitive firing was governed by a fast apamin-insensitive AHP current that did not accumulate, but rather showed depression with increases in activation frequency. A slowly accumulating AHP current, also insensitive to apamin, was extremely small at low rates but became significant with higher firing rates.

Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types

“…The SK conductance does decay slowly, raising the possibility that it could accumulate across ISIs if the cell was firing fast enough; that would mean that it could not be treated as a simple function of time since the immediately preceding spike. However, SK currents show very little accumulation in STN cells even at firing rates far higher than those used here (Teagarden et al 2008), and we built that feature into our model (Fig. 1B).…”

“…If SK currents in STN cells tracked intracellular Ca 2ϩ as measured, for example, by fluorescence of a Ca 2ϩ indicator such as fura 2, it would be straightforward to design a simple model whose Ca 2ϩ dynamics reproduced the behavior of the SK current in STN cells. However, STN SK currents do not behave in this way: although dependent on internal [Ca 2ϩ ], SK currents decay faster than measured Ca 2ϩ transients, and SK currents do not accumulate with high rates of repetitive firing, whereas measured Ca 2ϩ does accumulate (Teagarden et al 2008). Indeed, SK channels in subthalamic neurons behave as if the Ca 2ϩ driving their activation disappears very quickly so that SK currents cannot accumulate even at very high firing rates, and their decay is governed by the channel's own deactivation kinetics rather than by the decay of available Ca 2ϩ (Teagarden et al 2008).…”

“…However, STN SK currents do not behave in this way: although dependent on internal [Ca 2ϩ ], SK currents decay faster than measured Ca 2ϩ transients, and SK currents do not accumulate with high rates of repetitive firing, whereas measured Ca 2ϩ does accumulate (Teagarden et al 2008). Indeed, SK channels in subthalamic neurons behave as if the Ca 2ϩ driving their activation disappears very quickly so that SK currents cannot accumulate even at very high firing rates, and their decay is governed by the channel's own deactivation kinetics rather than by the decay of available Ca 2ϩ (Teagarden et al 2008). Such a situation can arise if Ca 2ϩ entering the cell during an action potential cascades through a g is the maximal conductance, V H is the half-activation (or -inactivation) voltage for steady-state activation (inactivation), and V S is the slope factor specifying the steepness of the voltage dependence for Na ϩ , K ϩ delayed rectifier (KDR), persistent Na ϩ (NaP), Ca 2ϩ , small-conductance Ca 2ϩ -dependent K ϩ (SK), and leak conductances (see MATERIALS AND METHODS).…”

“…We omit HCN and T-type Ca 2ϩ currents from our model, as they are largely deactivated or inactivated, respectively, over the voltage range encountered during autonomous oscillations or during excitatory synaptic input (Atherton et al 2010;Bevan et al 2002a). This model differs from our past subthalamic model (Terman et al 2002) in several ways, incorporating several new experimental findings on the nature of the subthalamic AHP (Hallworth et al 2003;Teagarden et al 2008), the overall current-voltage (I-V) curve (Farries et al 2010), and the limited role of HCN and T currents in ongoing spontaneous activity (Atherton et al 2010;Bevan et al 2002a).…”

“…This suggests that a model that correctly accounts for Ca 2ϩ dynamics and SK activation in STN cells would be quite complicated. Rather than attempt to construct such a model, which would be very underdetermined by the data anyway, we have devised a simpler model linking Ca 2ϩ currents to SK activation that reproduces three basic properties of SK currents in STN cells: 1) they peak 10 -15 ms after the spike; 2) they decay with a time constant of about 30 ms irrespective of any Ca 2ϩ dynamics; and 3) they do not accumulate at high firing rates (Hallworth et al 2003;Teagarden et al 2008). …”