Phase-resetting curve determines how BK currents affect neuronal firing

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Journal of Computational Neuroscience (Impact Factor: 1.74). 04/2011; 30(2):211-23. DOI: 10.1007/s10827-010-0246-3
Source: PubMed


BK channels are large conductance potassium channels gated by calcium and voltage. Paradoxically, blocking these channels has been shown experimentally to increase or decrease the firing rate of neurons, depending on the neural subtype and brain region. The mechanism for how this current can alter the firing rates of different neurons remains poorly understood. Using phase-resetting curve (PRC) theory, we determine when BK channels increase or decrease the firing rates in neural models. The addition of BK currents always decreases the firing rate when the PRC has only a positive region. When the PRC has a negative region (type II), BK currents can increase the firing rate. The influence of BK channels on firing rate in the presence of other conductances, such as I
and I
, as well as with different amplitudes of depolarizing input, were also investigated. These results provide a formal explanation for the apparently contradictory effects of BK channel antagonists on firing rates.

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    • "Activation of BK currents limit firing rates in some neurons (Nelson et al., 2003; Mathews et al., 2009), while in others they can enhance excitability, presumably through secondary mechanisms such as the reactivation of voltage-gated Na + conductances (McKay and Turner, 2004; Gittis et al., 2005). A recent modeling study by Ly et al. (2010) demonstrated how BK currents interacting with M-or H-currents can differentially control spiking output, and would therefore likely be influenced by β4 accessory subunits (Ly et al. 2010). Dentate granule cells lack significant H-current expression (Santoro et al., 2000) and the impact of M-currents on dentate granule cell excitability remains to be determined. "
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    ABSTRACT: The BK channel is a Ca(2+) and voltage-gated conductance responsible for shaping action potential waveforms in many types of neurons. Type II BK channels are differentiated from type I channels by their pharmacology and slow gating kinetics. The β4 accessory subunit confers type II properties on BK α subunits. Empirically derived properties of BK channels, with and without the β4 accessory subunit, were obtained using a heterologous expression system under physiological ionic conditions. These data were then used to study how BK channels alone (type I) and with the accessory β4 subunit (type II) modulate action potential properties in biophysical neuron models. Overall, the models support the hypothesis that it is the slower kinetics provided by the β4 subunit that endows the BK channel with type II properties, which leads to broadening of action potentials and, secondarily, to greater recruitment of SK channels reducing neuronal excitability. Two regions of parameter space distinguished type II and type I effects; one where the range of BK-activating Ca(2+) was high (>20 μM) and the other where BK-activating Ca(2+) was low (∼0.4-1.2 μM). The latter required an elevated BK channel density, possibly beyond a likely physiological range. BK-mediated sharpening of the spike waveform associated with the lack of the β4 subunit was sensitive to the properties of voltage-gated Ca(2+) channels due to electrogenic effects on spike duration. We also found that depending on Ca(2+) dynamics, type II BK channels may have the ability to contribute to the medium AHP, a property not generally ascribed to BK channels, influencing the frequency-current relationship. Finally, we show how the broadening of action potentials conferred by type II BK channels can also indirectly increase the recruitment of SK-type channels decreasing the excitability of the neuron.
    Preview · Article · Jun 2011 · Neuroscience
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    ABSTRACT: There are several different biophysical mechanisms for spike frequency adaptation observed in recordings from cortical neurons. The two most commonly used in modeling studies are a calcium-dependent potassium current I ahp and a slow voltage-dependent potassium current, I m . We show that both of these have strong effects on the synchronization properties of excitatorily coupled neurons. Furthermore, we show that the reasons for these effects are different. We show through an analysis of some standard models, that the M-current adaptation alters the mechanism for repetitive firing, while the afterhyperpolarization adaptation works via shunting the incoming synapses. This latter mechanism applies with a network that has recurrent inhibition. The shunting behavior is captured in a simple two-variable reduced model that arises near certain types of bifurcations. A one-dimensional map is derived from the simplified model.
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