Discovering spike patterns in neuronal responses

Abstract

When a cortical neuron is repeatedly injected with the same fluctuating current stimulus (frozen noise) the timing of the spikes is highly precise from trial to trial and the spike pattern appears to be unique. We show here that the same repeated stimulus can produce more than one reliable temporal pattern of spikes. A new method is introduced to find these patterns in raw multitrial data and is tested on surrogate data sets. Using it, multiple coexisting spike patterns were discovered in pyramidal cells recorded from rat prefrontal cortex in vitro, in data obtained in vivo from the middle temporal area of the monkey (Buracas et al., 1998) and from the cat lateral geniculate nucleus (Reinagel and Reid, 2002). The spike patterns lasted from a few tens of milliseconds in vitro to several seconds in vivo. We conclude that the prestimulus history of a neuron may influence the precise timing of the spikes in response to a stimulus over a wide range of time scales.

Figure 1.

Clustering method. A, Example of a surrogate cluster of 50 trials generated around four randomly timed events (arrow heads below the time axis) with a controlled amount of jitter (5 msec), six extra spikes per trial, and 20% missing event spikes. B, Two other clusters (C1 and C3) were similarly generated around different events (top), and the three clusters were randomly shuffled (middle) to yield the input to the clustering algorithm. The original and shuffled rastergrams had the same spike time histogram (bottom). C, Clustering method. The similarity matrix was first computed on the basis of the shuffled set of trials (a); the distribution of similarity values was determined (b) and passed through a sigmoid function centered on the peak of the distribution yielding the flattest possible histogram (c; slope = 0.14). The sigmoid was then applied to the similarity matrix (d), which was used as inputs to the clustering algorithm. The result of the clustering was a reordering of the columns of the matrix such that similarities within clusters were maximized and similarities between clusters were minimized (e; dark pixels indicate low similarity values). The same reordering was applied to the input trials (f; performance was 97% correct; fuzziness factor, 2).

Figure 2.

Creation of spike patterns in vitro. A, A prefrontal pyramidal neuron was somatically injected with a sine wave current waveform (bottom trace). The frequency was twice the preferred frequency of the cell for this sine wave amplitude and DC level (Fellous et al., 2001). After a transient, the cell spiked once every two cycles, either on the even (top) or odd (middle) cycles. The overall reliability of the cell was 0.49. B, Rastergram showing 100 trials for the same cell as in A. C, Same rastergram as in A, with trials reordered according to whether the cell settled on the even or odd cycles. Two separate reliable sets of trials are apparent for the even (reliability, 0.89) and odd (reliability, 0.92) cycles. The dashed line separates the two sets. Dots indicate spike times that are common to the two sets.

Figure 3.

Sample clustering results on surrogate data sets containing two clusters (A, 4 events per clusters; 10 msec jitter; three extra spikes/trial; 15% missing spikes; 35 trials per cluster) and five clusters (B, 4–5 events per clusters; 10 msec jitter; three extra spikes/trial; 15% missing spikes; 35 trials per cluster). For each panel: a, the input to the clustering algorithm; b, the corresponding distance matrix; c, the result of the clustering on the distance matrix; and d, the corresponding reordering of the rastergram are shown.

Figure 4.

Overall performance of the fuzzy K-means algorithm. The fuzzy clustering algorithm was used to recover two, three, and five clusters (A–C, respectively) in the surrogate data sets. The results are plotted as a function of jitter for different numbers of extra spikes (left), and replotted as a function of the number of extra spikes for different amounts of jitter (right). Chance levels of performance are shown on the left (arrowheads), and on the right (dashed curves) for different numbers of extra spikes. Each point is the average across 20 random rastergrams.

Figure 5.

Evidence for spike patterns in vitro. A, A layer 5 prefrontal pyramidal cell was repeatedly injected with the same current waveform; 150 trials are shown. The histogram is shown below the rastergram. Labels 1–4 indicate the sample times when histogram peaks are clearly detected (arrows). B, The stimulus was a linear superposition of two broadband stimuli. C, E, Expanded view of two sample sections depicted by the left and right boxes in A, respectively. D, F, show the reordering of the trials in C and E, using the fuzzy K-mean clustering algorithm. The algorithm was run separately on C and E. The clustering algorithm reveals the presence of temporal structure within trials. In the two cases, the trials can be separated in two groups that show distinct firing patterns (a–d, arrows). These patterns were not apparent from the raw rastergrams (C, E). The stimulus is reproduced under each rastergram.

Figure 6.

Evidence for spike patterns in monkey area MT in vivo (Buracas et al., 1998). A, Rastergram response of MT cells during passive viewing of an alternating sequence of moving Gabor patches in the preferred and anti-preferred directions. Arrows mark spike times when a reliable event was detected. Two sections of this rastergram are indicated by dashed boxes and are reproduced in B (left box) and D (right box). C, E, Corresponding reorderings of these two sections according to the fuzzy clustering algorithm (see Materials and Methods) that was run for K = 2, f = 2 (C; average D = 3.5) and K = 5, f = 2 (E; average D = 3.0). Horizontal dashed lines in C and E separate the different clusters.

Figure 7.

Evidence for spike patterns in cat LGN in vivo. A, Rastergram of an LGN ON X cell recorded in vivo in the anesthetized cat. The receptive field of the cell was presented with 128 repetitions of the same 8 sec long visual stimulus (for clarity, only 80 of 128 trials for the first 2 sec are shown). The clustering algorithm was applied to this data, assuming the presence of two clusters on the first five events. B, Reordered rastergram showing two strong clusters. Arrows point to events that were present in one cluster but not the other. C, Plot of the reliable events in each cluster (vertical bars). The dashed boxes indicate the region that yielded maximal cluster strength, and the horizontal lines show the regions where the two patterns overlap (within a 5 msec window).

Figure 8.

Choice of the parameters of the clustering algorithms. A, Sensitivity to initial conditions. a–c show the performance results for the K-means, extended K-means, and fuzzy K-means algorithms, respectively, on three surrogate rastergrams (diamonds, triangles, and circles). The small symbols show the performance (percentage correct) of 150 individual runs and are plotted against average cluster strength D (see Materials and Methods). The larger symbols in b and c are the runs that were chosen by the extended algorithms (region of densest D). The insets in b and c show this choice for 10 surrogate rastergrams based on the same statistics and include the three examples shown in the expanded graphs. d shows the average performance error for the three algorithms. The difference between extended K-means (EK) and K-means (K) was statistically significant (p < 0.01). The fuzzy K-means (FK) algorithm was the least sensitive to the choice of initial conditions. B, Choice of initial fuzziness factor. a (circles) shows the average performance of the fuzzy K-means algorithms for different values of the initial fuzziness factor f, computed on the data set used in A. Triangle and star symbols show the average performance for the K-means and extended K-means algorithms, respectively. b (circles) shows the mean difference in performance relative to f = 2. C, Actual fuzziness factor used as a function of the amount of jitter (a) and extra spikes (b) present in the surrogate data set (initial fuzziness factor was three in all cases). c shows the distribution of all actual fuzziness factors (bins = 0.05). For clarity, the peak at 3 was truncated.

Figure 9.

Determination of the optimal σ for the fuzzy K-means clustering algorithm. A, Clustering was performed on the three cluster surrogate data set processed with different values of σ. The performance of the clustering is plotted as a function of σ for two values of the jitter. Each curve represents a different number of extra spikes per trials. All curves show the maximum performance for a preferred σ. B, Preferred σ as a function of the amount of jitter in the rastergram. Each point is an average of 20 rastergrams. The distribution was fitted by a line of slope 1.0.