Figure 1.
Example single-unit recording and spike waveforms. A
: Single-unit activity recorded in the anterior pretectal nucleus of an unanaesthetised, unrestrained rat in during iontophoretic application of glutamate (between arrows). B: Individual spikes recorded from three different cells in the anterior pretectal nucleus (left, same recording as A), the substantia nigra pars reticulata (middle) and a triphasic spike from the substantia nigra pars compacta (right). C: Spikes from single-wire, single-unit recordings are similar to spikes from multi-unit recordings. Left: The mean spikes from 20 randomly selected hippocampal CA1 neurons (blue) and the mean of all those means (black). Right: The mean spike shape for each of the 23 biphasic cells (blue) recorded and analysed using the single-unit protocol, and the mean of all the mean shapes (black). CA1 data are courtesy of the Buzsaki group from the Collaborative Research in Computational Neuroscience data-sharing website (crcns.org).
Figure 2.
Action potential amplitude and shape vary with firing rate for the majority of neurons. A
: Action potential spike-timing stability can vary with increased firing rate in certain neurons, as shown by two neurons (A1 and A3, stable and variable respectively) recorded from the substantia nigra pars reticulata in awake animals. Spikes were binned into five equally sized groups based on the firing rate of the neuron at the time each spike was emitted (see Methods for firing rate calculation method). The shapes of spikes in each bin were averaged, after which the spike start point (circles, left), first zero crossing (stars, left, corresponding approximately to the peak of the intracellular spike) and second zero crossing (crosses, left, corresponding to the approximate trough of the intracellular spike) were determined (see text for calculation methods). These points were then used to calculate spike rise time, fall time and half width (respectively blue, green and red lines on the graphs A2 and A4) for each spike bin. A1 and A2: No significant spike-timing change. A3 and A4: Significant spike-timing change. Significance was tested using an ANOVA of the five bins of each set of rise, fall and half-width times for each neuron. B: Rise-time, fall-time and half-width changes for all neurons. Mean changes were respectively +4.6±9.0% (p<0.007), +0.8±9.3% (p>0.64) and +5.2±7.9% (p<0.0008). Significance was tested with a standard one sample t-test. C: Spike amplitude decreased with increased firing rate. Spike amplitude at the lowest firing rate for each neuron was normalised to 1, after which the relative amplitude at the highest firing rate was plotted. 84% of cells displayed a significant amplitude decrease (C1). The distribution of maximum spike-amplitude variations (when a cell showed a transition from its lowest to its highest firing rate) across all cells reveals the majority of cells showed a clear spike-amplitude reduction (C2). The average amplitude change was –12.9±11.2% (p<10−7).
Table 1.
Rise-time, fall-time, half-width and amplitude changes and significance levels for all cells, for awake vs. anaesthetised rats, and for control vs. pharmacologically manipulated conditions.
Figure 3.
Spike variability increases dramatically at low SNRs and causes large misclassification errors. A
: Spike-to-spike variability plotted against the SNR of the recording shows a rapid increase in variability at low SNR (A). Each data point indicates the average variability of each spike to the mean spike from that cell (see text for details). Error bars indicate one standard deviation. There was a slight general trend towards larger standard deviation in the variability at lower SNRs, although this was in addition to the effect of spike-timing changes which, for some cells, substantially increased the spike deviation even at higher SNRs. The fit curve shown is the fit line 1–√(1–1/SNR2) (see text and Material S1). B: Percentage of spikes for each neuron that would be classified as coming from a different neuron if the two neurons were recorded simultaneously (and were recorded with similar SNR – that is, have similar amplitudes, so that amplitude could not be used to discriminate between the spikes). Cells 1 to 9 are cells with triphasic spikes (9 cells) whereas all others (23 cells) have biphasic spikes. Triphasic spikes are unlikely to be confused with biphasic spikes (the large, mostly dark regions at the top and left of the figure represent low misclassification rates for cells 1 to 9 when paired with all other cells). Cells 10 to 15 are anterior pretectal nucleus cells in awake (4 cells) and asleep (2 cells) animals, 16 to 27 are substantia nigra pars reticulata cells in awake (8 cells) and anaesthetised (4 cells) animals, 28 is a substantia nigra pars compacta cell in an awake animal, 29 is a zona incerta cell in an awake animal, and 30 to 32 are deep mesencephalic nucleus cells in awake animals.
Figure 4.
Most neurons will be recorded with an SNR of 2.5 or less; at these SNRs, the probability of misclassifying each spike approaches 1 (i.e. 100%) in some cases.
A: The SNR follows the inverse square of distance. Left: Prediction of SNR vs. distance based on an assumed inverse square law of peak amplitude, average biphasic spike shape, and least squares-fitted to (assumed) peak amplitude vs. distance relationship (see text). Open circles show the SNRs of the recordings made for this study, fitted to the curve to estimate the distance to the recording electrode for each. Right: Marginal frequency distribution of spikes at lowest cell density, assuming 100% firing. For any randomly placed electrode, SNRs below 2.5 are most likely, and SNRs of 3 or more are unlikely to be recorded. Higher SNRs can potentially be obtained by strategic electrode placement (e.g. advancing the electrode towards a nearby cell to increase the SNR). B: Schematic illustration of estimation of spike misclassification probability, and minimisation of error using Z-score boundary (or cluster cut-off). The frequency distribution of spikes in amplitude–shape space for a hypothesised neuron (neuron B) is shown as the centre-most Gaussian curve. For a particular set of bounds around the mean of this distribution (in this case a Z-score of 2 or μ±2σ), a number of spikes from neuron B are incorrectly excluded from the cluster (false negatives in grey) whereas other spikes from surrounding neurons are included incorrectly (false positives in red). A Z-score limit for minimising the misclassification rate can be found for each distribution of neurons in amplitude–shape space, which varies according to the recording SNR and neural density in the particular brain region. C: Spike misclassification rates for single-wire recordings show that the probability of misclassifying any given spike approaches 1 at low SNRs. Top: Spike misclassification for lowest (left, 1.73×104 neurons/mm3) and highest (right, 17.7×104 neurons/mm3) cell densities (see text for details), assuming that 100% (top trace), 10% (middle trace) and 1% (bottom trace) of neurons fire. Bottom: Corresponding Z-score boundary which minimised the misclassification at each SNR. Note that the order of the traces is reversed (1%, 10% and 100% respectively from top to bottom).
Figure 5.
Spike sorting examples show common difficulties of separating spikes from different neurons at all but very high SNRs.
A: Hybrid trace 1 was easily separated into two clusters corresponding to spikes from the two cells (the axes for all hybrid traces in this figure are the first and second principal components of spike shape). 5A1 Left: Initial unsorted clusters. Middle: Spike classification using K-means scan clustering with default parameters, which detected the two clusters but failed to correctly allocate all spike waveforms. Right: Spike classification using valley-seeking clustering, which correctly allocated almost all spike waveforms. 5A2: Sorted waveforms. B: Hybrid trace 2 was more difficult to separate into the two clusters corresponding to spikes from the two cells. 5B1 Left: Initial unsorted clusters showing large spread of one cluster and significant noise. Middle: Spike classification using K-means scan clustering with default parameters, which detected the two major clusters but failed to correctly allocate all spike waveforms. Right: Spike classification using valley-seeking clustering, which incorrectly detected three spike clusters. 5B2: Ideally sorted waveforms (not achieved by the sorting). C: Hybrid trace 3 was difficult to separate into the two clusters corresponding to spikes from the two cells. 5C1 Left: Initial unsorted clusters; spikes around and to the left of the midline are noise whereas spikes to the right of the midline are the spikes from the two cells. Middle: Spike classification using K-means scan clustering with default parameters, which detected a noise cluster and a cluster combining the two cells. Right: Spike classification using valley-seeking clustering, which detected the two spike clusters as well as two noise clusters. 5C2: Ideally sorted waveforms. D: Systematic classification errors can cause false interpretations of data that are very difficult to detect. 5D1: Auto-correlograms and the cross-correlogram for hybrid trace 2 with two correctly identified units (auto-correlograms are on the main diagonal). 5D2: Auto- and cross-correlograms for hybrid trace 2 with three falsely identified units, showing that the extraneous third unit appears to have different firing characteristics (the auto-correlogram at bottom right) and different interactions with the other identified spike sources (cross-correlograms off the main diagonal). Based on this result, the erroneous identification of three distinct neurons in this recording would appear to be well justified.