High-Threshold K⁺ Current Increases Gain by Offsetting a Frequency-Dependent Increase in Low-Threshold K⁺ Current

Block of high-threshold K⁺ currents has a frequency-dependent effect on the F-I relationship and spike waveform shape of ELL pyramidal cells. A, Bath-applied 500 μm TEA selectively reduces the gain response of the F-I relationship in the high-frequency region while having little effect at low frequencies. The difference in firing frequency between control and TEA conditions is subtracted and plotted as a function of the control frequency (middle panel). The average difference between the low-frequency (80-120 Hz) and high-frequency (200-240 Hz) firing rates is significantly different (right) between TEA and control conditions (^*p < 0.01; n = 4). B, Bath-applied 500 μm TEA has a larger effect on general waveform shape at high frequencies while having little impact when the neuron is firing at low frequencies. The 10th spike in the spike trains is shown enlarged and superimposed (right panel).

Block of high-threshold K⁺ current has a frequency-dependent effect on spike parameters. A-D, Four spike parameters are measured: AHP (A), rate of spike decay (B), spike half-width (C), and spike height (D). The left panels show a representative case of the specific spike parameter plotted as a function of firing frequency in control (▪) and TEA condition (○). The right panels show the effects of TEA on spike parameters normalized to control under two conditions: low frequency (80-120 Hz) and high frequency (200-240 Hz). For all four parameters, TEA has a statistically significant effect at high frequencies while having a small effect at low frequencies compared with control (^*p < 0.05, ^**p ≤ 0.001 between low and high frequency; n = 4). In the first three conditions (A-C), spike parameters in TEA are binned into low- or high-frequency ranges and normalized to control values averaged through the entire frequency range. In the case of spike height (D), the populations were inhomogeneous within these frequency ranges. Therefore, values in TEA are normalized to the corresponding frequency range in control.

Block of high-threshold K⁺ current has a frequency-dependent effect on the rate of spike rise. A, The rate of spike rise is used to infer the available Na⁺ current. Bath-applied 500 μm TEA significantly decreases the rate of spike rise at high frequencies (200-240 Hz) but has no effect at low frequencies (80-120 Hz) compared with control (^*p < 0.001; n = 4). Rate of spike rise with TEA is normalized to control value averaged through the entire frequency range. B, Representative cases showing that the spike height and size of the AHP are strongly correlated with the rate of spike rise (left panel). Under normal conditions (▪), spike height and AHP size are relatively stable at different frequencies (see Fig. 2 B for representative spike traces). The application of TEA (○) spreads the distribution of spike height and AHP size, which correlates with a decrease in the rate of spike rise.

Incorporation of K⁺ currents in a firing model reproduces experimental observations. A, The F-I relationship generated by the model with IK_HT (▪) and without IK_HT (○). Like the experimental results, the removal of IK_HT preferentially affects the F-I relationship at high frequencies. B, Spike waveforms from the model with IK_HT (black line) and without IK_HT (gray lines) are shown superimposed. Note that spike waveforms are similar at low frequencies but diverge at high frequencies. The right inset indicates the similarity of spike responses at low and high frequencies when IK_HT is intact. C, Preventing Na⁺ current inactivation by artificially resetting the h variable after each spike (h = 0.09) (▵) in the absence of IK_HT does not fully restore the F-I relationship compared with control. A subsequent increase of IK_LT density shifts the F-I relationship further to the right, indicating that IK_LT is unable to substitute for IK_HT in preventing Na⁺ inactivation. D, Reducing Na⁺ current inactivation does not fully recover the spike waveform. Superimposed spike waveforms with h reset in the presence of IK_HT (black line) or absence of IK_HT (gray lines) are shown. Using the h reset fully restored the rate of spike rise and spike amplitude but only partially restored the rate of spike repolarization, spike half-width, and AHP size (right). In the low and high frequency with IK_HT (B, right), spike waveforms are identical, whereas with the h reset and no IK_HT (D, right) spike waveforms in the two frequency ranges differ in terms of rate of spike repolarization, spike half-width, and AHP size. All spikes shown are the fifth spike of each train.

Low-threshold K⁺ current shows a frequency-dependent accumulation during the interspike interval. A, Spike waveforms from the firing model taken at low and high firing frequencies in the presence or absence of IK_HT. Like the experimental results, the AHP size in the model is reduced in a frequency-dependent manner in the absence of IK_HT. Without IK_HT, the peak negative voltage during low-frequency firing reaches -65 mV (bottom, left), whereas at high frequencies this value rises well above -60 mV (bottom, right). B,IK_LT produced from the spikes shown in A. The change in AHP size and general increase in interspike voltage at high frequencies without IK_HT (A, bottom right) leads to an increase in IK_LT during the interspike interval at high frequencies. C, Whole-cell K⁺ currents recorded from pyramidal cells (isolated after TEA application) evoked using spike waveforms. All traces are corrected for leak and capacitive current. Spike waveforms consisted of spikes with interspike interval voltages of -60 mV, a half-width of 1 ms, and a spike height of 70 mV (-70 to 0 mV). Spike waveforms were applied at 100 Hz (top) and 200 Hz (bottom). With 100 Hz spike trains, both IK_HT and IK_LT show little or no current during the interspike interval (top). With 200 Hz, IK_HT continues to show no current during the interspike interval, but now IK_LT shows a significant increase (bottom) similar to the model (B, bottom right).

High-threshold K⁺ current prevents the increased activation of IK_LT, contributing to an increase in the gain of the F-I relationship, and stability of high-frequency firing can by analyzed in the firing model. A, To prevent the accumulation of IK_LT in the absence of IK_HT, the n variable (conductance variable for IK_LT) was reset to a value of 0.56 at the beginning of the AHP after each spike. IK_LT in the model is shown during spiking at high frequencies with (black line) or without (gray line) the n reset. B, Comparison of the F-I relationship generated from the model using the n reset (▵) and F-I relationships generated with (▪) or without (○) IK_HT and no n reset. Incorporating the n reset into the model partially recovered the F-I relationship compared with control (▪). C, Comparison of the F-I relationship generated from the model using both the n and h reset (•) and F-I relationships generated with (▪) or without (○) IK_HT and no resets. Combining both resets generated an F-I relationship nearly identical to that with IK_HT. D, Comparison of n and h open probabilities during the interspike interval with or without IK_HT as a function of firing frequency. The presence of IK_HT slows the onset of the n variable accumulation and h variable inactivation in a frequency-dependent manner. E, Time course of the n and h gating variables during the interspike interval in response to a current ramp (cell firing frequency, 120-200 Hz). The time course n and h open probabilities during the interspike interval are affected in a similar manner by the presence of IK_HT as in the frequency domain (D).