Signals relayed through electrical synapses are amplified by I_NaP. (A) Gap junction-relayed responses in cell 2 at different baseline membrane potentials (top) and response to hyperpolarizing current injection in cell 1 (bottom, V_m = −67 mV for all trials). Scale bar is 0.2 s, 15 mV (bottom), 5 mV (top). (B) At a baseline of V_m = −50 mV (left), both hyperpolarizing and depolarizing responses in cell 2 are amplified by I_NaP (blue traces); blockade of I_NaP by TTX eliminates the amplification (red traces). At V_m = −77 mV (right), I_NaP is inactive and does not amplify hyperpolarizing or depolarizing gap junctional responses. Scale bar is 0.1 s, 0.5 mV. (C) Coupling coefficients measured from cell 1 to cell 2 (cc₁₂ = ΔV_{cell 2}/ΔV_{cell 1}) plotted against the baseline voltage of cell 2, for a single pair. Blue data were recorded in control ACSF; red data in 100 nM TTX. (D) Coupling coefficients (filled circles) and conductance (open squares) measured from cell 2 to cell 1 (cc₂₁ = ΔV_{cell 1}/ΔV_{cell 2}) as cell 2 is depolarized, plotted against the baseline voltage of cell 2. (E) The persistent sodium current, I_NaP, is mediated by voltage-sensitive channels that flicker between open and closed states once activated. At depolarized potentials, more channels are persistently active (blue) and available to amplify responses by opening in response to depolarizing inputs or by closing in response to hyperpolarizing inputs. At hyperpolarized baseline potentials (bottom) most channels are inactive (red) and do not amplify responses. (F) I_NaP was measured by subtraction of currents from slow (10 mV/s) voltage-clamp ramps in TRN neurons. Blue trace is membrane current measured in control ACSF, red trace in 100 nM TTX, and black trace is the point-by-point subtraction, for a single TRN cell. (G) Summary plot of cc₁₂ against baseline voltage from N = 14 pairs before and after TTX. Data are normalized to most-hyperpolarized values. Dotted line is I_NaP/max(I_NaP), measured from ramps as in (C) in N = 6 neurons.

Bursts, spikes, and amplification. (A) From hyperpolarized baseline voltages, TRN cells emit bursts (bottom; V_m = −77 mV). At depolarized potentials, TRN cells spike regularly in tonic mode (top; V_m = −53 mV). Scale bar is 25 ms, 25 mV. (B) The corresponding postsynaptic signals at electrical synapses: spikelets (top), and burstlets (bottom), for these different spiking modes are also amplified by membrane voltage; colored traces are at depolarized potentials (spikelet V_m = −50 mV, burstlet V_m = −61 mV) and black traces are at hyperpolarized potentials (spikelet V_m = −71 mV burstlet V_m = −76 mV. Scale bar is 5 ms, 1 mV (spikelets); 4 mV, 50 ms (burstlets). (C) Summary of scaling for steplets, spikelets, and burstlets measured in N = 12 pairs of neurons, plotted against baseline voltage in the receiving cell. Data are normalized to the most-hyperpolarized voltages.

Tonic-spike synchrony in coupled neurons is enhanced synergistically by I_NaP and spontaneous synaptic input. (A) A pair of gap junction-coupled neurons driven to spike at similar frequencies. Scale bar 100 ms. (B) Time-course cross-correlograms for a pair of electrically coupled neurons in control (ACSF) and following 100 nM TTX application. In both conditions, spikes fired at ∼50 Hz; color bar represents 0 (navy) to 7 (dark red) correlated spikes within a given 50 ms window (y-axis); bin width = 2 ms. (C) Example cross-correlogram for paired spiking before (blue) and after (red) TTX application. Inset: spikes in a TRN cell in ACSF (blue) and in 100 nM TTX (red). Scale bar is 10 mV, 2 ms. (D) Peak correlation coefficients before and after TTX. In TTX, correlation coefficients were 34.4 ± 5.9% lower than in ACSF (mean ± SEM, N = 7 pairs, p < 0.01, one-tailed t-test). (E) Peak correlation coefficients before and after TTX application in the presence of DNQX + APV to block excitatory chemical synaptic activity. In TTX, correlation coefficients were 15.8 ± 3.2% lower than in ACSF (N = 9 pairs, p < 0.01). (F) Correlation coefficients before and after application of DNQX + APV. Here, correlation coefficients were 10.0 ± 3.3% lower than in ACSF (N = 10 pairs, p < 0.01).Thick gray lines in (D–F) represent population averages. (G) Representative spikelets (gray) and sEPSPs (blue or red) were numerically amplified and summed to demonstrate the corresponding experimental conditions of (D–F) (note the number of events crossing threshold in each case). In ACSF, spikelets and burstlets were numerically amplified by the experimentally determined factors. Scale bar is 2 mV, 50 ms.

Spontaneous excitatory postsynaptic events (sEPSPs) in coupled neurons. (A) Sample data from a TRN cell with average V_m = −55 mV (top, light blue) and −77 (bottom, dark blue) in ACSF. Scale bar is 0.1 s, 1 mV. (B) Sample data with average V_m = −55 mV (top, light red) and −77 (bottom, dark red) in 100 nM TTX. (C) Average sEPSP amplitude (mean ± SEM) plotted against V_m for recordings in ACSF (blue, circles) and recordings in TTX (red, squares). Both data sets are normalized to their respective values at V_m = −77 mV for comparison (normalized values at V_m = −55 mV are 1.08 ± 0.01 in ACSF; 0.93 ± 0.01 in TTX). (D) Percentages of sEPSPs arriving in both cells of a coupled pair within a 1 ms window in ACSF (4.6 ± 0.93 for V_m = −77 mV, dark blue; 4.9 ± 1.1 for V_m = −55 mV, light blue) and in TTX (3.6 ± 0.54 for V_m = −77 mV, dark red; 3.6 ± 0.54 for V_m = −55 mV, light red). There were no significant effects of voltage or TTX on the data (ANOVA). (E) In a strongly coupled pair (mean cc = 0.4), average sEPSP in cell 2 (a, black trace) and corresponding trigger-averaged electrical PSP (ePSP) simultaneously recorded in cell 1 (a, gray trace); average sEPSP in cell 1 (b, gray grace) with corresponding average ePSP simultaneously recorded in cell 2 (b, black trace). Randomly selected data from the same number of samples are shown in light gray. All traces in (E) represent the average of 554 events. Scale bar is 0.1 mV, 10 ms.

Bursts are unsynchronized events. (A) Demonstration of the stimulation paradigm for paired burst firing. First, current thresholds for bursts were determined independently for each cell (trial 1). Next, bursts were elicited in coupled neurons by delivering peri-threshold current injections to both neurons simultaneously (trial 2). Traces are offset for clarity. Scale bar: 25 mV, 50 ms. Burst synchrony is taken as the absolute value of the difference in burst onset times between cell 1 and cell 2. (B) Finer time-scale of 15 burst trials in a pair of coupled neurons. Bursts rarely synchronized, and individual burst onsets also varied by tens of ms. Scale bars: 25 mV, 50 ms. (C) With spontaneous synaptic activity intact, burst synchrony did not show a significant change after blocking I_NaP with 100 nM TTX. Mean difference in burst onsets in ACSF: 27.6 ± 6.0 ms (mean ± SEM, N = 6 pairs); mean difference in burst onsets in TTX: 28.6 ± 8.5 ms (p = 0.94, paired, two-tailed t-test). (D) In the presence of synaptic blockers (DNQX and APV), burst synchrony between coupled cells also showed no significant change after TTX application. Mean difference in burst onset in ACSF: 33.7 ± 4.5 ms (N = 7 pairs); mean difference in burst onset in TTX: 33.6 ± 8.7 ms (p = 0.99, paired, two-tailed t-test). Differences between values with and without blockers were insignificant (p > 0.4 for all comparisons, ANOVA). Data points in (C–F) represent average values for 20–30 trials at burst thresholds for each pair. (E) Gap junction-driven spikes in a strongly coupled pair (mean cc = 0.4) demonstrate the difference between burst and tonic spike synchrony. The burst onset difference (i) was 23 ms; the closest two spikes within the bursts were 7.4 ms apart. The tonic spikes (ii) were 1.9 ms apart. V_rest = −70 mV for both cells. Scale bar 15 mV, 50 ms. (F) Fine resolution of the paired bursts (i) and the paired tonic spikes (ii), offset for clarity. Scale bar 20 mV, 20 ms.

Simulation results. (A) Three representative voltage traces (black) from a single-compartment Hodgkin–Huxley model of a TRN cell driven to spike tonically with applied DC current (I_app) and provided with spikelet inputs of increasing amplitude (from bottom to top) preceding spikes during the regular spiking period. Spikelet shown is a response in an unstimulated TRN cell, for a spikelet arriving 10 ms before spikes in traces above. Gray trace: I_T during the first (bottom) simulation. Scale bar: 25 ms, 100 mV (V_m), 2 mV (spikelet) 15 μA/cm² (I_T). Inset: example postsynaptic spikelet. Scale bar 10 ms, 1 mV. (B) Shift in arrival time of the next spike, expressed as a percent of the interspike interval (ISI) between the input and an unperturbed spike, plotted against spikelet amplitude. Results from three sets of simulations are plotted for a spikelet applied 10 (solid), 15 (dashed), or 20 (dots) ms before the unperturbed spike. (C) Voltage traces (black) of the model driven at its burst threshold by applied DC current and provided with burstlets of increasing amplitudes (bottom to top) preceding the native burst. Burstlet shown is a response in an unstimulated TRN cell, starting 20 ms before the bursts in the traces above. I_T during the first (bottom) simulation is shown in gray. Scale bar: 25 ms, 100 mV (V_m), 2 mV (burstlet), 15 μA/cm² (I_T). Inset: example postsynaptic burstlet. Scale bar 10 ms, 1 mV. (D) Shift in subsequent spike times following burstlet inputs, plotted against postsynaptic burstlet amplitude. Results from three sets of simulations are plotted for a burstlet applied 20 (solid), 35 (dashed), or 50 (dots) ms before the first spike of the unperturbed burst.

sEPSPs. (A) Visual description of the algorithm used to find spontaneous excitatory postsynaptic potentials (sEPSPs) in voltage traces. Raw data were smoothed lightly (dark and light blue traces, respectively) and convolved (green trace) with a template. Peaks in the convolution correspond to where the data best match the template; thus, to find candidate sEPSPs, the convolution was subjected to a threshold (black line). For each event, if the amplitude exceeded a size threshold, which was taken as a fraction of the SD of the smoothed data, it was identified as an sEPSP (red asterisk; the template, scaled to each sEPSPs individual amplitude, is superimposed on the data in red). Locations of events too small to be confirmed as sEPSPs are noted by black triangles. Convolution and amplitude thresholds were adjusted for each cell by hand. (B) Distribution of sEPSP amplitudes for V_m = −55 mV in ACSF (0.43 ± 0.004 mV, N = 5855 sEPSPs from 19 cells). (C) Distribution of sEPSP amplitudes for V_m = −77 mV in ACSF (0.40 ± 0.004 mV, N = 8145 sEPSPs from 19 cells). (D) Distribution of sEPSP amplitudes for V_m = −55 mV, in 100 nM TTX (0.43 ± 0.005 mV, N = 5598 sEPSPs from 17 cells). (E) Distribution of sEPSP amplitudes for V_m = −77 mV, in 100 nM TTX (0.46 ± 0.005 mV, N = 6592 sEPSPs from 17 cells).

Burst jitter. (A) Example of 16 overlaid trials of aligned bursts from a pair of electrically coupled neurons. Note that even though their slow depolarizations (calcium spikes) are aligned, their spikes are rarely aligned. Average coupling coefficient at V_rest, was 0.14. (B) Spike cross-correlogram for data shown in (A). Spikes were represented by Hanning windows, 2 ms-wide. Cross correlation was done at the same temporal resolution as the data, 0.05 ms. (C) Burst synchrony (Δ burst start times, y-axis) is uncorrelated with electrical synaptic coupling strength (x-axis; R² = 0.06) in both ACSF (blue symbols) and in TTX (R² = 0.01, red symbols, N = 14 pairs). (D) A reduction in the jitter of burst synchrony (SD of the absolute difference in onset times) is loosely correlated with greater coupling strength (slope −83 per ms, R² = 0.29) in both ACSF (blue symbols) and in TTX (slope −78 per ms, R² = 0.48, red symbols; N = 14 pairs). Each data point in (C,D) represents the average value per pair for 20–30 trials at the two burst thresholds. (E) Changes in jitter and difference in burst arrival times. All data, except solo jitter are derived from paired burst stimulation at threshold for both neurons. Population responses of all pairs tested in normal ACSF (without blockers). Each black dash represents the average for one pair, and the green circles represent the population average derived from the individual averages. N = 7. (F) The same results as in (E) but in the presence of fast synaptic blockers. N = 7.