Phase-resetting curve determines how BK currents affect neuronal firing
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 Im and Ih, 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.
KeywordsBK channel Phase-resetting curve (PRC) Outward current h-current m-current
- Borg-Graham, L. (1987). Master’s thesis: Modelling the somatic electrical behavior of hippocampal pyramidal neurons. PhD thesis, Massachusetts Institute of Technology.Google Scholar
- Borg-Graham, L. (1998). The surf-hippo neuron simulation system. http://www.cnrs-gif.fr/iaf/iaf9/surf-hippo.html, v2.8.
- Borg-Graham, L. (1999), Interpretations of data and mechanisms for hippocampal pyramidal cell models. In E. Jones, P. Ulinski, & A. Peters (Eds.), Cerebral cortex (Vol. 13, pp. 19–138). Plenum Publishing Corporation.Google Scholar
- Borg-Graham, L., & Schramm, A. (2009). In vivo dynamic clamp: The functional impact of synaptic and intrinsic conductances in visual cortex. In A. Destexhe, & T. Bal (Eds.), In dynamic clamp: From principles to applications (Vol. 13, pp. 19–138). Springer.Google Scholar
- Ermentrout, G. B. (2002). Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. Society for Industrial and Applied Mathematics (SIAM).Google Scholar
- Kuramoto, Y. (1984). Chemical oscillations, waves and turbulence. New York: Springer.Google Scholar
- Rinzel, J., & Ermentrout, G. B. (1989). Analysis of neural excitability and oscillations. In I. Segev (Ed.), Methods in neuronal modeling: From synapses to networks (pp. 135–169). MIT Press.Google Scholar
- Stiefel, K., Gutkin, B., & Sejnowski, T. (2008). Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons. PLoS One 3.Google Scholar
- Storm, J. (1985). Calcium-dependent spike repolarization, and three kinds of after-hyperpolarization (AHP) in hippocampal pyramidal cells. Society for Neuroscience, 11, 1183.Google Scholar
- Storm, J. (1986a). A-current and ca-dependent transient outward current control the initial repetitive ring in hippocampal neurons. Biophysical Journal, 49, 369a.Google Scholar
- Storm, J. (1986b). Evidence that C-current and A-current contribute to repolarization of the action potential in CA1 hippocampal pyramidal cells of rat hippocampus. Society for Neuroscience, 12, 764.Google Scholar