Figure 2. Modulated subthreshold membrane potentials account for the rate adaptation of PRCs.

(A and B) Experimental and simulated voltage trajectories in PCs at different rates. All voltage trajectories are shown from trough to peak within normalized ISIs. The model used (Zang et al., 2018) was not fitted to this specific experimental data. Spike thresholds at different rates are labeled in plots. The Na⁺ activation threshold is defined as −55 mV (stippled line). Right plots show phase dependence of Na⁺-activation threshold on firing rates. (C) Stimulus-triggered variations of inward ionic currents (solid) and outward ionic currents (dashed) at different phases and rates. Ionic currents are shifted to 0 (grey line) at the onset of stimulus to compare their relative changes. At phase = 0.2, the outward current is still decreasing due to the inactivation of the large conductance Ca²⁺-activated K⁺ current at 162 Hz. (D) Larger slopes of the Na⁺ activation curve at high membrane potentials.

Figure 2—figure supplement 1 . Effect of Subthreshold Membrane Potentials on Shaping PRCs.

We examined whether the critical role of subthreshold membrane potentials in shaping PRC profiles (Figure 2) also applies to other neuron types. A frequently used pyramidal neuron model, the Traub model (Ermentrout et al., 2001) was tested. It shows an opposite rate adaptation of PRCs compared to PCs (A). In the Traub model, responses become smaller and relatively phase-independent at high firing rates. This demonstrates that the normalization used in Equation 1 does not always lead to increasing PRC peak amplitudes for smaller ISIs. These PRC shapes can be explained by significantly lower subthreshold membrane potentials at high rates, compared to PCs, (B). This is due to the accumulation of delayed rectifier K⁺ current (kdr, C), which has a low activation threshold and large conductance. The lower subthreshold membrane potentials are far below the Na⁺-activation threshold, making responses to weak stimuli passive at high firing rates. Accordingly, PRCs in the model become smaller and relatively phase-independent at high rates. We minimally modified the Traub model by reducing the conductance of the kdr current, raising its activation threshold and increasing the AHP current (details in Materials and methods) (D-F). With these modifications, subthreshold membrane potentials are significantly elevated at high firing rates lower than 110 Hz. Accordingly, onset-phases of phase-dependent responses shift left and peaks increase at high rates. These simulation results show that spike rate-dependent subthreshold membrane potentials and their effect on nonlinear activation of Na⁺ currents can be crucial in shaping neuronal PRC profiles in many types of neurons. Surprisingly, when firing rates are higher than 110 Hz, PRCs decrease again, suggesting other undetermined biological mechanisms may be involved in determining the phase responses. (A) Rate adaptation of PRCs in the original Traub model. (B) Lowered ISI membrane potential at high rates. (C) Comparison of ionic currents at low (solid, 7 Hz) and high (dashed, 227 Hz) rates. (D) Rate adaptation of PRCs in the modified Traub model. (E) Elevated ISI membrane potential at high rates. (F) Comparison of ionic currents at low (solid, 9 Hz) and high (dashed, 49 Hz) rates. In (C) and (F), current peaks are truncated to show currents during ISIs. In (E), spike peaks are truncated to show the elevated ISI membrane potential at high rates.