Spike phase locking in CA1 pyramidal neurons depends on background conductance and firing rate

Abstract

Oscillatory activity in neuronal networks correlates with different behavioral states throughout the nervous system, and the frequency-response characteristics of individual neurons are believed to be critical for network oscillations. Recent in vivo studies suggest that neurons experience periods of high membrane conductance, and that action potentials are often driven by membrane potential fluctuations in the living animal. To investigate the frequency-response characteristics of CA1 pyramidal neurons in the presence of high conductance and voltage fluctuations, we performed dynamic-clamp experiments in rat hippocampal brain slices. We drove neurons with noisy stimuli that included a sinusoidal component ranging, in different trials, from 0.1 to 500 Hz. In subsequent data analysis, we determined action potential phase-locking profiles with respect to background conductance, average firing rate, and frequency of the sinusoidal component. We found that background conductance and firing rate qualitatively change the phase-locking profiles of CA1 pyramidal neurons versus frequency. In particular, higher average spiking rates promoted bandpass profiles, and the high-conductance state promoted phase-locking at frequencies well above what would be predicted from changes in the membrane time constant. Mechanistically, spike rate adaptation and frequency resonance in the spike-generating mechanism are implicated in shaping the different phase-locking profiles. Our results demonstrate that CA1 pyramidal cells can actively change their synchronization properties in response to global changes in activity associated with different behavioral states.

Figure 1.

Action potential phase locking in response to current-based cosines. A, Response to current-based cosines at average firing rates of 2 spikes/s under low (i) and high (ii) conductance. Sinusoidal modulation at 8 Hz is indicated below the voltage traces. iii, Average spike–phase histogram in response to 8 Hz modulation at average spike rates of 2 spikes/s. Low conductance is shown in black, high conductance is shown in red. B, Response to current-based cosines at average firing rates of 8 spikes/s under low (i) and high (ii) conductance. Sinusoidal modulation at 8 Hz is indicated below the voltage traces. iii, Average spike–phase histogram in response to 8 Hz modulation at average spike rates of 8 spikes/s. Low conductance is shown in black; high conductance is shown in red. C, Vector strength versus modulation frequency plots for low (black) and high (red) conductance at average firing rates of 2 (solid squares) and 8 (open squares) spikes/s. Tested modulation frequencies were as follows: 0.1, 0.5, 1, 4, 8, 12, 20, 50, 100, and 500 Hz.

Figure 2.

Prediction of vector strength for a modulation frequency of 0.1 Hz through gain measured using step responses. Neurons received step depolarizations and hyperpolarizations while held at baseline firing rates of 2 and 8 spikes/s. A, Example voltage traces showing responses to depolarizing (right traces in each panel) and hyperpolarizing (left traces in each panel) current steps from baseline firing rates of 2 (i, iii) and 8 (ii, iv) spikes/s. A recording under low conductance is shown in i and ii; a recording under high conductance is shown in iii and iv. B, Example plots of firing rate versus step size, at base firing rates of 2 (i) and 8 (ii) spikes/s. A step size of zero indicates the DC value used to keep the neuron at the respective firing rate. Recording under low conductance is shown in black; high conductance is shown in red. The solid lines indicate linear fits used to calculate the gain (slope of the linear fit). Ci, Average gain values for recordings at baseline firing rates of 2 (solid squares) and 8 (open squares) spikes/s. Low conductance is shown in black; high conductance is shown in red. ii, Comparison of measured and predicted vector strength. Predictions were derived using Equation 4 for a modulation frequency of 0.1 Hz and are denoted by triangles. Measured vector strengths are given for the same modulation frequency and are shown as squares. The closed symbols refer to 2 spikes/s average firing rate; open symbols refer to mean rates of 8 spikes/s. Low conductance is shown in black; high conductance is shown in red.

Figure 3.

Prediction of vector strength for higher modulation frequencies through gain measured using step responses at baseline firing rates of 8 spikes/s. Analysis was done on the same dataset shown in Figure 2. A, Gain for different step lengths associated with modulation frequencies of 0.1, 0.5, 1, 4, and 10 Hz. Step length was one-half the period of the respective frequency (5000, 1000, 500, 125, and 50 ms, respectively). B, Comparison of measured and predicted vector strength for different modulation frequencies under low conductance. Predictions are shown as triangles and were derived using Equation 4 and the frequency-specific gain shown in A. Measured vector strengths are shown as squares. C, Comparison of measured and predicted vector strength for different modulation frequencies under high conductance. Predictions are shown as triangles and were derived using Equation 4 and the frequency-specific gain shown in A. Measured vector strengths are shown as squares.

Figure 4.

Introduction of an adaptation current selectively reduces action potential phase locking to lower modulation frequencies. A, Response to current-based cosines at average firing rates of 4 spikes/s under low conductance. Sinusoidal modulation at 10 Hz is indicated below the voltage traces. B, Response to current-based cosines at average firing rates of 4 spikes/s under low conductance with addition of an artificial adaptation current. Sinusoidal modulation at 10 Hz is indicated below the voltage traces. C, Average spike–phase histogram in response to 10 Hz modulation at average spike rates of 4 spikes/s. Low conductance is shown in black; low conductance with an additional adaptation current is shown in gray. D, Vector strength versus modulation frequency under low conductance (black) and low conductance with added adaptation current (gray); at average firing rates of 4 spikes/s. Tested modulation frequencies were as follows: 0.1, 1, 4, and 10 Hz. Note the decreased locking to 0.1 and 1 Hz with added adaptation current.

Figure 5.

Action potential phase-locking peaks are sensitive to changes in firing rate. A, Phase locking at average firing rates of 1 spike/s under high conductance with a modulation amplitude of 15 pA. i, Example voltage trace. Sinusoidal modulation at 8 Hz is indicated below the voltage trace. ii, Average spike–phase histogram in response to 8 Hz modulation at an average spike rate of 1 spike/s. iii, Vector strength versus modulation frequency. Tested modulation frequencies were as follows: 0.1, 1, 4, and 8 Hz. iv, Comparison between vector strength at average firing rates of 1 (upward triangles) and 2 (squares) spikes/s. The vector strength normalized to 0.1 Hz modulation is plotted versus the modulation frequency. Note the change from low pass at 1 spike/s average rate to bandpass at 2 spikes/s mean rate. B, Phase locking at average firing rates of 3 spikes/s under low conductance with a modulation amplitude of 5 pA. i, Example voltage trace. Frequency modulation of 8 Hz is indicated by the sinusoid below the voltage trace. ii, Average spike–phase histogram in response to 8 Hz modulation at an average spike rate of 3 spikes/s. iii, Vector strength versus modulation frequency. Tested modulation frequencies were as follows: 0.1, 1, 4, and 8 Hz. iv, Comparison between vector strength at average firing rates of 3 (downward triangles) and 2 (squares) spikes/s. Vector strength normalized to 0.1 Hz modulation is plotted versus the modulation frequency. Modulation amplitude for 2 spikes/s mean rates was 7.5 pA; amplitude for 3 spikes/s mean rate was 5 pA. Note the change from low pass at 2 spikes/s average rate to bandpass at 3 spikes/s mean rate.

Figure 6.

Application of 5 nm TTX reduces phase locking to low frequencies. Ai, Response to current-based cosines at average firing rates of 2 spikes/s under low conductance. Modulation amplitude was 7.5 pA. ii, Response to current-based cosines at average firing rates of 1.5 spikes/s under high conductance. Modulation amplitude was 15 pA. Sinusoidal modulation at 8 Hz is indicated below the voltage traces in i and ii. iii, Average spike–phase histograms in response to 8 Hz modulation under low (black) and high (gray) conductance. iv, Vector strength versus modulation frequency under low (black) and high (gray) conductance. Tested modulation frequencies were as follows: 0.1, 1, 4, 8, 12, and 20 Hz. B, Comparison between vector strength in the presence (large triangles) and absence (small squares) of 5 nm TTX under low (black) and high (gray) conductance. Locking to low modulation frequencies is selectively reduced by TTX.

Figure 7.

Evidence for an intrinsic frequency preference. A, Subthreshold impedance profile under low (black) and high (gray) conductance. The gray lines show sliding window averages. Note the reduced peak under high conductance. B, Mean operating voltages at average firing rates of 2 (solid squares) and 8 (open squares) spikes/s under low (black) and high (gray) conductance (values for 8 Hz modulation frequency are presented; we observed no significant differences between modulation frequencies; one-way ANOVA). C, Principal-component analysis of spike-triggering events at average firing rates of 2 spikes/s. i, Spike-triggered averages of the input current for mean firing rates of 2 spikes/s under low (black) and high (gray) conductance. Input currents used to measure spike-triggering events in neurons did not include any frequency modulation. ii, Average first principal components of the spike-triggering events under low (black) and high (gray) conductance at mean firing rates of 2 spikes/s. iii, Average normalized activity versus phase for a modulation frequency of 8 Hz. Activity for low conductance is shown in black; high conductance is shown in red. iv, Frequency preference index of the first principal components under low (black) and high (gray) conductance. Tested modulation frequencies were as follows: 0.1, 0.5, 1, 2, 4, 8, 10, 20, 50, 100, and 500 Hz.

Figure 8.

Principal-component analysis of spike-triggering events at 8 spikes/s mean rate under control conditions, and at 2 (low g) and 1.5 (high g) spikes/s mean rate in the presence of 5 nm TTX. Ai, Spike-triggered averages of the input current for mean firing rates of 8 spikes/s under low (black) and high (gray) conductance. Input currents used to measure spike-triggering events in neurons did not include any frequency modulation. ii, Average first principal components of the spike-triggering events under low (black) and high (gray) conductance at mean firing rates of 8 spikes/s. iii, Frequency preference index of the first principal components under low (black) and high (gray) conductance. Tested modulation frequencies were as follows: 0.1, 0.5, 1, 2, 4, 8, 10, 20, 50, 100, and 500 Hz. Bi, Spike-triggered averages of the input current for mean firing rates of 2 (low g; black) and 1.5 (high g; gray) spikes/s, in the presence of 5 nm TTX. Input currents used to measure spike-triggering events in neurons did not include any frequency modulation. ii, Average first principal components of the spike-triggering events under low (black) and high (gray) conductance in the presence of 5 nm TTX. iii, Frequency preference index of the first principal components under low (black) and high (gray) conductance. Tested modulation frequencies were as follows: 0.1, 0.5, 1, 2, 4, 8, 10, 20, 50, 100, and 500 Hz.

Figure 9.

Phase-locking profiles of CA1 pyramidal neurons can be qualitatively reproduced in a simple model incorporating spike frequency adaptation and a resonant current. A, Example of simulated voltage traces under low (top trace) and high (bottom trace) conductance, at mean rates of 1.5 spikes/s. B, Average spike–phase histogram in response to 8 Hz modulation at average spike rates of 1.5 spikes/s. Low conductance is shown in black; high conductance is shown in gray. C, Vector strength versus modulation frequency at a mean rate of 1.5 spikes/s under low (black) and high (gray) conductance. Model parameters were as follows: low g, g_L = 0.03 mS/cm², I_DC = −0.098 μA/cm², I_A = 0.018 μA/cm², g_n = 0.04 μA/cm ²; high g, g_L = 0.18 mS/cm², I_DC = 0.43 μA/cm², I_A = 0.098 μA/cm², g_n = 0.2 μA/cm². Tested modulation frequencies were as follows: 0.1, 0.5, 1, 2, 4, 8, 10, 20, and 100 Hz. D, Vector strength versus modulation frequency at a mean rate of 4 spikes/s under low (black) and high (gray) conductance. Model parameters were as follows: low g, g_L = 0.03 mS/cm², I_DC = −0.058 μA/cm², I_A = 0.018 μA/cm², g_n = 0.04 μA/cm²; high g, g_L = 0.18 mS/cm², I_DC = 0.68 μA/cm², I_A = 0.098 μA/cm², g_n = 0.2 μA/cm². Tested modulation frequencies were as follows: 0.1, 0.5, 1, 2, 4, 8, 10, 20, and 100 Hz.

Figure 10.

Phase-locking of CA1 pyramidal neurons in response to rate-modulated Poisson processes driving artificial synaptic-current waveforms at 2 spikes/s average firing rate. A, Normalized vector strength versus modulation frequency for modulated excitation (red; 2 ms decay time constant), modulated inhibition (blue; 8 ms decay time constant), and modulation through current cosines (black; same dataset shown in Fig. 1) under low (i) and high (ii) conductance. B, Dependence of the modulation amplitude on the modulation frequency and the decay time constant of the artificial synaptic-current waveforms. i, Comparison of modulation amplitudes derived from the same Poisson processes used in the experiments with amplitudes derived analytically. For amplitudes derived numerically, the process driving the inhibitory artificial synaptic current waveforms was rate modulated with an amplitude of 5% and the decay time constant was varied. Results for decay time constants of 8 (open blue squares) and 2 ms (open red squares) are shown. Superposition of the analytical solution (black lines) shows a good agreement with the numerical results. Note the steeper drop in amplitude with the larger decay time constant. ii, Normalized analytical amplitudes for a range of decay time constants. Modulation amplitudes decreased with increasing modulation frequency. Attenuation for decay time constants ranging from 1 to 10 ms are shown. Note the stronger decrease with higher decay time constants.