Relationships between spike-free local field potentials and spike timing in human temporal cortex

Abstract

Intracortical recordings comprise both fast events, action potentials (APs), and slower events, known as local field potentials (LFPs). Although it is believed that LFPs mostly reflect local synaptic activity, it is unclear which of their signal components are most closely related to synaptic potentials and would therefore be causally related to the occurrence of individual APs. This issue is complicated by the significant contribution from AP waveforms, especially at higher LFP frequencies. In recordings of single-cell activity and LFPs from the human temporal cortex, we computed quantitative, nonlinear, causal dynamic models for the prediction of AP timing from LFPs, at millisecond resolution, before and after removing AP contributions to the LFP. In many cases, the timing of a significant number of single APs could be predicted from spike-free LFPs at different frequencies. Not surprisingly, model performance was superior when spikes were not removed. Cells whose activity was predicted by the spike-free LFP models generally fell into one of two groups: in the first group, neuronal spike activity was associated with specific phases of low LFP frequencies, lower spike activity at high LFP frequencies, and a stronger linear component in the spike-LFP model; in the second group, neuronal spike activity was associated with larger amplitude of high LFP frequencies, less frequent phase locking, and a stronger nonlinear model component. Spike timing in the first group was better predicted by the sign and level of the LFP preceding the spike, whereas spike timing in the second group was better predicted by LFP power during a certain time window before the spike.

Fig. 1.

Example of removal of spike waveforms from local field potentials (LFPs). A: spike-triggered average of LFP before (blue trace) and after (red trace) the removal of spike waveforms. B: spike-triggered average spectral contents of LFP before (left) and after (right) the removal of spike waveforms. Notice that power of low-frequency components (e.g., <20 Hz) has not been affected by the spike removal process.

Fig. 2.

Preference of spiking activity for particular LFP phases and amplitudes at various LFP frequencies, before and after the removal of spike waveforms from the LFP recordings, in a total of 69 single-neuron/LFP recordings. A: probability of spiking, relative to that expected by chance, as a function of LFP phase at a particular frequency (abscissa) at different LFP frequencies (ordinate). By convention, a phase value of 0 corresponds to the trough of the cycle (electrode potential more negative), and a value of 180 corresponds to the positive peak (electrode potential more positive). Top: before the removal of spike waveforms from LFPs. Bottom: after the removal of spike waveforms from LFPs. Tip of arrow points to the peak of the distribution at ∼220 deg at 70 Hz. B: probability of spiking, relative to that expected by chance, as a function of LFP amplitude, expressed as a percentage of maximum LFP amplitude at a particular frequency (abscissa), at different LFP frequencies (ordinate). Top: before the removal of spike waveforms. Bottom: after the removal of spike waveforms. Tip of arrow points to the peak of the distribution at ∼30% of maximum LFP amplitude at 40 Hz. The apparent discontinuities in some of the images at around 60 Hz is due to the omission from the plots of frequencies between 55 and 65 Hz.

Fig. 3.

Change in the performance of the spike-LFP models between single-electrode cases (unit activity and LFPs recorded on the same electrode) and the corresponding dual-electrode cases (same units, LFPs recorded on a neighboring electrode) for models computed from various LFP frequencies (4–8, 8–14, 14–30, 30–80, and 80–100 Hz) and for 3 different cell groups [all cells, low-frequency-responsive (LF) cells, and high-frequency-responsive (HF) cells]. Performance is expressed as true positive fraction (TPF; the percentage of spikes whose timing is correctly predicted by the model). Change in performance is expressed as the TPF in a dual-electrode case minus the TPF in the corresponding single-electrode case. Histogram bars indicate average TPF changes; error bars indicate standard mean errors.

Fig. 4.

Representative example of the performance of the model on a portion of a recording where high-frequency LFP (80–150 Hz) was predictive of spike timing. This recording was performed during a paired-associate learning task, 5 min after the beginning of the task. The TPF for this case was 27.8% (mean TPF for high-frequency LFP was 24.6%), the second-order contribution was 67% (mean second-order contribution was 76.7%), and the cell was not phase-locked at either low or high frequencies (only 9 of 60 cells were phase-locked to high-frequency LFPs). A: raw LFP signal, including several action potentials. B: superimposed waveforms of the isolated single-unit spikes from the recording portion shown. Vertical dotted lines denote the peaks of the spikes. C: LFP signal after removal of spikes. D: filtered version of signal shown in C, used as input to the model. E: continuous model output, calculated by the convolution of the input signal in D and the computed kernels. Horizontal dotted line represents the model trigger threshold. F: predicted spike train. G: actual spike train.

Fig. 5.

Representative example of the performance of the model on a portion of a recording where low-frequency LFP (8–14 Hz) was predictive of spike timing. This recording was performed during an identification task, 7 min after the beginning of the task. The TPF for this case was 14% (mean TPF for low-frequency LFP was 19.2%), the second-order contribution was 44% (mean second-order contribution was 29.4%), and the cell was phase-locked to the ascending phase of the 8–14 Hz LFP oscillation, after the trough (22 of 55 cells were phase-locked to low-frequency LFPs). A–G follow the same conventions as described in Fig. 4. Note that the continuous model output (E) peaks at the trough of the 8–14 Hz LFP oscillation, where spikes tend to occur.

Fig. 6.

A: TPF rates (predicted spikes as a percentage of actual spikes) at high (80–150 Hz)- vs. low (8–14 Hz)-frequency spike-free LFPs in cases where the model performance was significantly better than a random predictor. Each case is represented by a point; for points lying below the line of identity, the model performance at low frequencies is higher than that at high frequencies (14 cases in total), and vice versa for points above the line of identity (10 cases in total). B: average second-order contribution to the computed models across all recordings (solid line) and percentage of phase-locked cells among all cells entered in the analyses (dashed line) at different LFP frequency ranges.

Fig. 7.

Distributions of spike-free LFP phases (A) and amplitudes (B) associated with spiking activity in those cases where low-frequency LFPs were predictive of spike timing (top panels, total of 14 cases) and in those cases where high-frequency LFPs were predictive of spike timing (bottom panels, total of 10 cases). Figure conventions are the same as described in Fig. 2. As with Fig. 2, discontinuities in some of the images are due to omission from the plots of frequencies around 60 Hz.

Fig. 8.

Spike-field coherence values at 2 different frequency ranges (4–10 and 80–100 Hz) for cells responding to low-frequency LFP (LF cases) and for cells responding to high-frequency LFP (HF cases). Each dot represents 1 recording of unit activity and LFP on the same electrode.

Fig. 9.

Mean firing rates (MFR; ± standard mean errors) of the 2 groups of cells (LF and HF) for the 2 different behavioral events: paired associate (PA) and object identification (ID).

Fig. 10.

First- (top panels) and second-order (bottom panels) kernels for 2 cases where LFP at different frequencies was predictive of spike timing. A: a case where LFP at the range of 80–200 Hz was predictive. B: a case where LFP at 4–8 Hz was predictive. In both cases, time 0 corresponds to the occurrence of the spike, and after that the time axis extends in the past (e.g., time 10 ms corresponds to 10 ms before the occurrence of the spike). Note that both first- and second-order kernels include positive and negative values.