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
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(m) and I(h), 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.
Available from: ncbi.nlm.nih.gov
- "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.
Neuroscience 06/2011; 192:205-18. DOI:10.1016/j.neuroscience.2011.06.028 · 3.36 Impact Factor
Available from: Boris Gutkin
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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.
Neural Computation 09/2001; 13(6). DOI:10.1162/08997660152002861 · 2.21 Impact Factor
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ABSTRACT: Laboratory joint wear simulator testing has become the standard means for preclinical evaluation of wear resistance of artificial knee joints. Recent simulator designs have been advanced and become successful at reproducing the wear patterns observed in clinical retrievals. However, a single simulator test can be very expensive and take a long time to run. On the other hand computational wear modelling is an alternative attractive solution to these limitations. Computational models have been used extensively for wear prediction and optimisation of artificial knee designs. However, all these models have adopted the classical Archard's wear law, which was developed for metallic materials, and have selected wear factors arbitrarily. It is known that such an approach is not generally true for polymeric bearing materials and is difficult to implement due to the high dependence of the wear factor on the contact pressure. Therefore, these studies are generally not independent and lack general predictability. The objective of the present study was to develop a new computational wear model for the knee implants, based on the contact area and an independent experimentally determined non-dimensional wear coefficient. The effects of cross-shear and creep on wear predictions were also considered. The predicted wear volume was compared with the laboratory simulation measurements. The model was run under two different kinematic inputs and two different insert designs with curved and custom designed flat bearing surfaces. The new wear model was shown to be capable of predicting the difference of the wear volume and wear pattern between the two kinematic inputs and the two tibial insert designs. Conversely, the wear factor based approach did not predict such differences. The good agreement found between the computational and experimental results, on both the wear scar areas and volumetric wear rates, suggests that the computational wear modelling based on the new wear law and the experimentally calculated non-dimensional wear coefficient should be more reliable and therefore provide a more robust virtual modelling platform.
Journal of Biomechanics 02/2011; 44(6):1108-16. DOI:10.1016/j.jbiomech.2011.01.027 · 2.75 Impact Factor
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