Introduction
How sensory systems encode behaviorally meaningful stimuli during active, natural sensation is a central problem in neuroscience that can be effectively studied in the tactile system1, 2, 3. Rat whiskers are highly sensitive tactile detectors3, 4, 5, similar to primate fingertips6, that are actively moved through the environment to extract information about object position7, 8, shape4 and surface features such as texture9, 10. Whisker movement across objects creates dynamic input streams, but which features of these input streams are encoded by the nervous system and are relevant for perception are largely unknown3, 11. For the case of surfaces, whisker motion generates complex micro-motion, including discrete, transient slip-stick events driven by frictional interactions with the surface. Slip-stick events have been observed in a variety of behavioral conditions and carry information about surface properties12, 13, 14. However, whether and how natural slip-stick events are encoded in the brain are unknown.
Passively applied whisker deflections and active whisker contact events evoke low-probability responses in primary somatosensory (S1) cortex15, 16, 17, 18, 19. Sensory coding in S1 has therefore been proposed to be sparse4 and sparse activation of small numbers of S1 neurons to be behaviorally detectable20, 21. This type of sparse coding, which results from low response probability, is distinct from the predominant sparse coding strategy proposed for V1 and A1, which is based on strong and reliable single-unit responses to a narrow range of preferred stimuli22, 23, 24. Whether complex, temporally dense whisker input streams during active whisking on surfaces are also sparsely encoded is not known.
To address these issues, we simultaneously measured whisker micro-motion and neural activity in S1 in actively behaving rats trained to whisk on textured surfaces. We found that discrete slip-stick events (which we refer to as slips) were encoded by S1 neurons with sparse, low-probability, precisely timed spikes during continuous whisking on surfaces. Temporally precise slip-evoked responses drove transient correlation between S1 neurons. These transient correlations encoded slips very efficiently, provided higher signal-to-noise detection of surfaces than slower modulation of firing rate and were an important cue for surface texture. Thus, whisker slips are fundamental encoded features of natural whisker input streams and are encoded by a sparse coding strategy, which is based on probabilistic responses in neural ensembles, rather than on narrow stimulus selectivity.
Results
Slips are prominent during active whisking on surfaces
We trained freely behaving rats with one intact whisker to position their nose in an aperture (nose poke) and whisk across sandpaper surfaces or in air while we simultaneously recorded whisker motion and spiking in contralateral S1 (Fig. 1a,b and Supplementary Video 1 online). Whisker motion was measured with a high-resolution CCD (charge-coupled device) imaging array (
5-
m and 0.25-ms resolution)12.
Figure 1: High-acceleration, high-velocity whisker slips are prominent during active whisking on surfaces.
(a) Behavior and recording apparatus to simultaneously measure whisker motion and spiking of S1 neurons during active surface palpation. (b) Sequence of events in a single behavior trial. A noise cue was delivered on completion of a criterion number of whisks, signaling reward availability. t, variable-length intervals. (c) Example of whisker motion on P150 sandpaper (boxes are first slips detected by acceleration threshold crossings). Gray time period is expanded on the right. (d) Peak acceleration and velocity of all slip events in one behavior session for interleaved trials in air and on P150 surface. Red and green lines indicate 95th percentile values for whisking in air. Blue line represent 0.32 mm ms-2 acceleration threshold for detecting slips.
Full size image (96 KB)Superimposed on slow, continuous, 5–12-Hz whisking motion3, 4, 5 on surfaces were dense sequences of discrete slips, which are known to be induced by whisker interaction with surfaces12 (Fig. 1c,d and Supplementary Fig. 1 online). Slips have been hypothesized to be elementary features of active whisker input and to convey information about surface properties12, 13. Slips consisted of transient (2 ms), high-velocity, high-acceleration movements that were often followed by brief oscillatory ringing of the whisker (Fig. 1c) and occurred during both forward (protraction) and backward (retraction) motion (Fig. 1c and Supplementary Fig. 1). Acceleration and velocity of slips were highly correlated (r = 0.83 
0.01, mean s.e.m., range = 0.72–0.92, n = 22 recording sites, P < 0.01 for all recording sites, t statistic), as reported previously12. Whisker motion in air was smoother, with fewer high-acceleration peaks (Fig. 1d and Supplementary Fig. 1).
Slips were detected as acceleration transients that surpassed defined acceleration thresholds (
). Thresholds were determined from the measured distribution of acceleration on surfaces (see Online Methods) with = 0.32 mm ms-2, corresponding to four standard deviations above mean acceleration, used unless otherwise noted (Fig. 1d). Analysis was confined to initial slips in slip-ring sequences (first slips, defined as slips with no prior acceleration threshold crossing in 20 ms). First slips occurred frequently (median interslip interval = 62 ms, 25th–75th percentile = 40–99 ms) and had high peak velocity (0.2–1.2 mm ms-1, corresponding to 300–1,900 s-1) and acceleration (0.2–1 mm ms-2), suggesting that they drive spikes in vivo15, 16, 25.
Slips drive sparse, precisely timed spikes in S1 neurons
To determine whether slips are encoded in S1, we made neurophysiological recordings using a chronic, moveable tetrode implanted in the S1 column corresponding to the intact, imaged whisker4, 5, 15, 16 (Fig. 2a). The whisker corresponding to the recorded column (the principal whisker) was determined from spiking responses to whisker deflection under anesthesia, and all but that whisker (D1, D2 or E1) were trimmed. Single-neuron spike trains were isolated by spike sorting (see Online Methods26; Fig. 2b–d and an additional example is shown in Supplementary Fig. 2 online). In all, 90 single units were isolated from 22 recording sites in four cortical columns of three rats (2–6 units per site, mean of 4.1). Recording sites were located in cortical layers (L) 4 and 5, as determined by recording depth27, and later confirmed by histology relative to cytochrome oxidase staining.
Figure 2: Recording configuration and single-unit sorting using tetrodes.
(a) Spiking activity was recorded using chronically implanted, moveable tetrodes in an ultra-miniature microdrive. Left, schematic of the implanted microdrive. Right, cytochrome oxidase–stained across-row section (see Online Methods) showing a marking lesion and reconstructed recording track (red crosses). Barrels are visible in L4. (b) Example tetrode recording (850 m, layer 4) showing raw signal on all four tetrode channels (Ch1, Ch2, Ch3 and Ch4). Spikes of three isolated single neurons are denoted by circles at bottom. (c) Amplitude plots for the three isolated units from b. Amplitudes were stable throughout the recording session. (d) Density plots of spike waveforms for these three units (E1–4 are waveforms on the four tetrode channels). Bottom, ISI histograms showing refractory periods. Red lines indicate 1 ms.
First slips evoked sparse, but precisely timed, spikes in most S1 neurons, as revealed by rasters and peristimulus time histograms (PSTHs) aligned to first slips across multiple whisking trials (Fig. 3a,b). PSTHs aligned to all slips (including both first and subsequent slips and rings) showed weaker, more temporally dispersed responses (Fig. 3c). For each neuron, we fit the first slip-aligned PSTH with a Bayesian adaptive regression splines (BARS) algorithm28 (Fig. 3b). We found statistically significant slip-evoked response peaks in 62 out of 90 (70%) neurons (P < 0.05, as determined by confidence intervals from the fit). Response magnitude was quantified using a slip response index (SRI) representing the percent increase above the pre-slip baseline firing rate of the response peak. Slip-responsive neurons (n = 62) had a mean SRI of 141.8 13.3%, short latency to peak response (8.3 0.6 ms) and low jitter (13.0 1.2 ms, full width at half maximum of the response peak) (Fig. 3d). Thus, slip timing is encoded in S1 with 20-ms resolution. A separate, multiple regression analysis29 revealed that whisker acceleration and velocity in 20-ms temporal windows (that is, the kinetic parameters that define slips) were significant predictors of instantaneous spiking probability in slip-responsive neurons, whereas whisker position was not (P < 0.05; data not shown). Thus, slips are a basic encoded element in natural whisker input streams.
Figure 3: Slips drive sparse, precisely timed spikes in S1 neurons.
(a) Spike rasters for two slip-responsive neurons aligned to first slip events. (b,c) PSTHs (2-ms bins) aligned to first slips (b) and all slips (c) for the neurons shown in a. Blue curve indicates BARS fit with confidence intervals. Orange line denotes the mean firing rate of the neuron averaged over the entire recording session. (d) SRI versus depth for all neurons. Red indicates slip-responsive neurons. Right, response latency and jitter for all slip-responsive neurons.
Full size image (96 KB)Some first slips are rapidly followed by one or more oscillations (rings) at the whisker's resonance frequency12. Rings have been suggested to amplify sensory responses30. We found that rings modestly, but significantly, increased responses to slips, consistent with this hypothesis (P = 0.01, t test; Supplementary Note and Supplementary Fig. 3 online).
Slips contribute to surface-driven spikes
S1 neurons show sparse background firing in awake rodents18, 19, 31 and modest firing-rate elevations during surface palpation32, 33 and other active sensory tasks34. We found average firing rates, calculated over entire recording sessions (30 min to 2 h, dominated by nonwhisking epochs), of 0.3–48 Hz (mean, 7.5 0.8 Hz (s.e.m); median, 5.7 Hz; n = 90 neurons; Supplementary Fig. 4 online). During whisking on surfaces, 69% of neurons (62 of 90 neurons) significantly increased firing rate (measured over the entire whisking epoch) relative to pre-whisk baseline (t test, P < 0.05 criterion, 65–365 trials per neuron, median = 160; Fig. 4a,b). These were termed surface-excited neurons. We found that 11% of the neurons (10 of 90) were significantly surface inhibited (P < 0.05 criterion) and 20% (18 of 90) were surface nonresponsive (this latter class included some cells with onset responses followed by inhibition; Fig. 4b and Supplementary Fig. 4). On average, surface-excited neurons increased their firing rate by a factor of 2.21 0.13 during whisking epochs. In a subset of surface-excited neurons tested with interleaved trials on surface and air (n = 15 neurons, three recording sites), the firing rate increased during whisking on surfaces, but not during whisking in air (Fig. 4c). Thus, surface interactions, not motor commands or sensory reafference from whisker self-motion, drive increased firing during surface whisking.
Figure 4: Slips drive a substantial fraction of spikes during surface whisking.
(a) PSTH (20-ms bins) of firing of one surface-excited neuron, aligned to whisking onset. Lick onset indicates the onset of licking for water reward in the lick port. The orange line indicates the baseline (average) firing rate. NP, nose poke. (b) Mean PSTHs (25-ms bins, normalized to pre-whisk firing rate) for the three response classes during surface whisking. The colored regions represent 95% confidence intervals. **P < 0.01. (c) Mean PSTHs (50-ms bins) for 15 neurons during interleaved trials of surface whisking and whisking in air. (d) Correlation between SRI and increase in firing rate during surface whisking (t statistic, P < 0.001). (e) Example neurons illustrating correlation between number of spikes (mean s.e.m.) and number of all slips in 40-ms windows (t statistic, P < 0.01 for all three neurons). Regression lines are overlaid. The colored bars on the left denote the average firing rate of neurons. (f) Mean spike counts in slip and nonslip epochs per trial, compared with total spike count per trial, for slip-responsive neurons (n = 56).
We assessed whether slip-evoked responses contribute to surface-induced changes in firing rate. Across neurons, SRI correlated with the magnitude of firing rate increase on surfaces (r = 0.43, P < 0.001; Fig. 4d). Moreover, the firing rate in 40-ms periods during surface whisking was significantly correlated with the number of slips in those periods for 75% of slip-responsive neurons (n = 42 of 56 neurons with sufficient trial length, P < 0.05 criterion, all slips exceeding 0.16 mm ms-2 acceleration threshold, corresponding to 2 s.d. above the mean, were used in this analysis; see Online Methods and Fig. 4e). To estimate the fraction of surface-driven spikes that were attributable to slips, we calculated for each slip-responsive neuron the number of spikes in 20-ms response windows following all first slips, and compared it with the total number of spikes in the same trials (only the first 250 ms of each trial was considered). On average, 3.4 0.05 slips occurred per 250-ms trial (n = 56 neurons, 40–235 trials per neuron). Slip-response windows contained 1.02 0.18 spikes per trial, which constituted 34.8 1.4% of the 3.07 0.6 total spikes per trial. This was significantly higher than the 0.52 0.07 spikes, or 19.0 1.3% of total spikes, that occurred in an equivalent number of non-slip epochs that were randomly chosen from the same trials (t test, P = 0.012; Fig. 4f and Supplementary Fig. 5 online). Thus, first slips drove 16% of the total spikes that occurred during surface whisking. Because only about half of the total spikes are driven by surface interactions (whisking on surfaces increases firing rate 2.2-fold over pre-whisk baseline), first slips account for 30% of the surface-driven increase in firing rate. Although this is not the majority of spikes, these slip-driven spikes may encode important information about whisker slips and related stimuli.
Slip responses are sparse and probabilistic
Responses to passive whisker deflection in anesthetized and awake rats evoke low-probability spiking responses15, 16, 17, 19. Similarly, we found that slip responses during active whisking on surfaces were sparse and probabilistic, occurring only in response to a small fraction of slips, even for highly slip-responsive neurons (for example, SRI = 296 and 449, and 164 for Figs. 3a and 5a, respectively). Across all slip-responsive neurons, only 24.0 2.1% of first slips (defined as exceeding = 0.32 mm ms-2) were associated with spikes in the subsequent 20 ms, as compared with 15.4 1.9% of pre-slip (background) epochs (although modest, this was a highly significant increase, P < 0.001, t test). When slip responses did occur, they were nearly always single spikes, and occasionally doublets, similar to spontaneous firing during pre-whisk epochs (Fig. 5b,c). On the ensemble level, net spike probability (mean response probability in the 20 ms after each slip – that before the slip) measured across all 90 recorded neurons was 0.09 0.01 for = 0.32 mm ms-2 and increased to 0.13 0.01 for the largest slips (Fig. 5d). Thus, slips generate sparse, low-probability, one- or two-spike responses in single S1 neurons and modest, transient elevations in firing rate on the ensemble level. We could not detect any difference in response probability between initial and subsequent slip events occurring in single trials, indicating that sparse responses are not the results of adaptation accruing during slip trains (data not shown).
Figure 5: Slip responses are sparse and probabilistic.
(a) First slip ( = 0.32 mm ms-2) aligned raster for a representative neuron (average firing rate, 5.2 Hz; SRI, 164), illustrating sparse responses to a small fraction of slips. (b) Percentage of pre-slip (background) and post-slip (response) epochs (20-ms duration) containing 0, 1, 2 or >2 spikes for all 62 slip-responsive neurons (overlaid: median inter-quartile range). (c) Spike raster and instantaneous firing rate (Gaussian-filtered raster, 
= 50 ms) for a neuron (firing rate, 4 Hz) across 5 trials in one behavioral session. Gray areas: 1,500-ms behavior period, starting at nose-poke onset. (d) Net spike probability (spikes per 20-ms window) above background probability for the population of 90 neurons, as a function of slip acceleration threshold. Inset: Mean net spike probability in the population for each threshold (mean s.e.m.). *P < 0.05, **P < 0.01.
Low response probability could reflect either probabilistic responsiveness or tuning for whisker kinetic properties that vary from slip to slip. S1 and thalamic neurons are sensitive to whisker-deflection velocity15, 16, 25, 35 and acceleration36 and are weakly tuned for direction of deflection25, 37. In awake animals, neurons are also modulated by position in the whisking cycle (phase)38. To test whether slip acceleration (or velocity, which is highly correlated with acceleration) is encoded, we calculated slip-evoked PSTHs from slips that were identified with increasing acceleration thresholds12. The net spiking probability increased with increasing acceleration threshold, indicating that high-acceleration (and high-velocity) slips were most strongly encoded by single neurons (Fig. 6a). However, even the highest acceleration slips ( = 0.80 mm ms-2, 10 s.d. above the mean) evoked responses on only a fraction (0.13) of trials (Fig. 5d). Across all neurons, the lowest acceleration threshold that elicited a significant slip-evoked response (P < 0.05 criterion, termed the response threshold) was 0.17 0.01 mm ms-2 (n = 62, mean s.e.m.; Fig. 6b), which closely matched the acceleration of the weakest slips evoked on surfaces relative to air (Fig. 1 and Supplementary Fig. 1). Thus, S1 neurons encode even the weakest surface-relevant slips. Neurons varied widely in gain, defined as the fold-change in peak firing probability per two standard deviations (0.16 mm ms-2) of acceleration (mean gain = 1.5 0.1, n = 62; Fig. 6b).
Figure 6: Encoding of slip properties.
(a) Slip-acceleration response plot for an example neuron. Each row of the matrix is the normalized first slip-locked PSTH at one acceleration threshold. The horizontal black line denotes the response threshold of the neuron. (b) Distribution of response threshold and gain in the population. (c) Example neurons with selective responses for direction of motion, protraction (left) and retraction (right). The mean acceleration of protraction slips was 0.239 0.004 mm ms-2 (n = 450 slips), and the mean acceleration of retraction slips was 0.240 0.003 mm ms-2 (n = 832 slips). (d) Distribution of direction-selective neurons (retraction selective, green; protraction selective, magenta) in the population. Inset, distribution of modulation indexes. Neurons with significant direction-selective responses (P < 0.05 criterion, nonparametric one-way ANOVA for each neuron) are indicated by colored bars. (e) Distribution of slip responses in the population on the basis of absolute position. Significance for each neuron was assessed by nonparametric one-way ANOVA, P < 0.05 criterion.
To determine whether S1 neurons were tuned for slip direction or whisking phase (which covary during natural whisking), we compared responses to forward slips, which occur during protraction, and backward slips, which occur during retraction. Comparisons were restricted to slips of matched acceleration (see Online Methods and Supplementary Fig. 6 online). For low-acceleration slips, relatively few neurons (13 of 62) showed a significant preference for direction/phase (nonparametric one-way ANOVA for each neuron, P < 0.05 criterion) and the magnitude of selectivity was weak (modulation index = [protraction response minus retraction response]/average response, mean |modulation index| = 0.57 0.10, n = 62), similar to a previous study in L2/3 of anesthetized rats17 (Fig. 6c,d). Identical results were observed for higher acceleration slips (Supplementary Fig. 6). Thus, selectivity for slip direction and whisking phase was weak, as has been predicted previously39. Finally, we tested whether S1 neurons were tuned for slips occurring at a particular absolute whisker position. Slips were divided into four interquartile ranges of absolute position (calculated from all trials at a recording site, Supplementary Fig. 6). We found no significant modulation of slip response amplitude by whisker position (measured at slip onset, nonparametric one-way ANOVA for each neuron, P < 0.05 criterion; Fig. 6e).
Thus, neither tuning for acceleration/velocity, slip direction/phase or absolute position can account for the observed low-probability slip responses. We therefore conclude that slips elicit probabilistic, infrequent responses in single neurons. Because these responses are indistinguishable in single trials from background firing, slips are probably encoded in ensemble activity of S1 neurons.
Population representation of slips
To determine whether slips are detectable from sparse population activity in single trials, we simulated single-trial ensemble responses to slips using neural response profiles drawn from all 90 recorded neurons. In each iteration (one slip), we constructed the ensemble response by assigning 0 or 1 spikes to a pre-slip (background) or post-slip response window (20-ms window size) for each neuron on the basis of the neuron's empirically measured spike probabilities for slips exceeding a specific acceleration threshold and by summing the total spikes of the population in each time window (Fig. 7a). This gives the instantaneous population response to a slip in the time window. This model assumes independence between neurons, which is consistent with low firing correlations seen between L2/3 neurons in awake S1 (ref. 31) and with the joint spiking probability of neuron pairs in L4 and L5 measured in our experiments (see below). The accuracy of detecting a slip from the single-trial response was quantified using receiver operating characteristic (ROC) analysis40 from distributions of ensemble spike counts (100 iterations) for background and post-slip windows (Supplementary Fig. 7 online).
Figure 7: Slips are efficiently represented by transient synchronous activity in small neuronal ensembles.
(a) Schematic of simulation design, with simulated ensemble response for a single slip. Spikes were assigned to 2-ms time bins for display only. The simulation was run on total spike counts in the entire 20-ms background and response windows. (b) Probability of correct detection of a slip as a function of population size on the basis of ROC analysis. Inset shows the distributions of spike counts in background and response windows for the 100-neuron population size. (c) Probability of correct detection as a function of time window used in the simulation and population size. (d) Population neurometric curves for varying slip amplitudes and population sizes, using 20-ms windows. Each curve shows the probability of correct detection from ROC analysis. (e) Accurate detection of small slips in a 400-neuron population. Distributions correspond to the gray bar in d. Each curve shows the distribution of total spike number in the population (20-ms time window) for 100 iterations for the background epoch (black trace) and for slip-response epochs for corresponding acceleration threshold. Mean values of distributions are denoted by dotted lines. All distributions were well-separated from background.
Full size image (96 KB)Varying the simulated population size to generate a population neurometric curve revealed that a 100 neuron population can detect a large slip ( = 0.8 mm ms-2) with >95% accuracy (Fig. 7b). The optimal window size for detecting a slip was 20 ms, independent of population size (Fig. 7c). Large slips were more robustly encoded at all population sizes and 400 neurons were sufficient to detect even the smallest of slips ( = 0.16 mm ms-2) with >95% accuracy (Fig. 7d,e). Thus, sparse activation in a population of a few hundred S1 neurons in a brief, 20-ms time window efficiently encodes the occurrence of slips. This constitutes a temporal code for slips on the basis of transient, stimulus-induced elevation in population firing rate, leading to increased firing correlations between neurons.
Coding of slips and surface texture by synchronous firing
This finding predicts that slips are encoded by transient increase in firing synchrony over background spiking, which is known to be sparse and relatively poorly correlated in S1 (at least in L2/3)17, 31, 41. Here, synchrony denotes raw firing correlations, not adjusted for correlations resulting from independent firing. In fact, joint spiking probability (total correlated firing) for neuron pairs after slips was equal to the product of the individual spiking probabilities in the population (Supplementary Fig. 8 online), indicating that L4 and L5 neurons fire largely independently during active whisking, as reported for L2/3 neurons31 (that is, internal correlations are low). Consistent with the predictions of the model, synchronous firing of simultaneously recorded neuron pairs in vivo was significantly greater in the 20-ms window after slips than before (ratio = 2.34 0.17, P = 0.029; Fig. 8a and Supplementary Fig. 9 online) and higher-acceleration slips drove a greater increase in response synchrony than lower-acceleration slips (Fig. 8a). To determine whether this measurement of firing synchrony was biased by the inability to detect exactly simultaneous spikes (<1-ms interspike interval, ISI) on single tetrodes, we estimated the number of undetected simultaneous spikes (0-ms delay) from spikes at 1-ms delay in cross-correlation histograms42. Inclusion of these undetected spikes had no effect on our measures of increased firing synchrony following slips or independence between units (Supplementary Fig. 8).
Figure 8: Coding of slips and surfaces by synchronous firing.
(a) Synchronous spiking in simultaneously recorded neuron pairs in vivo in 20-ms windows before and after slips (n = 63 pairs, mean s.e.m. overlaid). Right, synchrony ratio (after slip:before slip) as a function of slip acceleration threshold (mean s.e.m.). (b) Firing rate and synchronous firing probability (20-ms bins) before and during surface whisking for a pair of simultaneously recorded neurons. The blue trace denotes expected synchrony for independent firing of neurons. Inset, signal to noise for firing rate and synchrony during surface whisking, relative to pre-whisk baseline (mean s.e.m., n = 56 neurons, n = 63 pairs). The blue bar indicates the expected synchrony for independent neurons. (c–e) Distribution of frequency of slips of different magnitudes (c), mean firing rates of neurons (mean s.e.m., n = 9 neurons, two recording sites, d) and number of synchronous spikes per s in pairs of neurons (mean s.e.m., n = 16 pairs, two recording sites, e) during whisking on P150 surface, smooth surface and whisking in air. (f–h) Distribution of frequency of slips of different magnitudes (f), mean firing rates of neurons (mean s.e.m., n = 17 neurons, four recording sites, g) and the number of synchronous spikes per s in pairs of neurons (mean s.e.m., n = 28 pairs, four recording sites, h) during whisking on P150, P400, P800 and P1200 surfaces.
Because slips occur on surfaces, firing synchrony should be elevated on surfaces. Indeed, firing synchrony for neuron pairs (measured in cascading 20-ms bins, without knowledge of whether or when slips occurred) provided a higher signal-to-noise measure of whisking on surfaces, relative to pre-whisk baseline, than individual neuron firing rates (t test, P < 0.001; Fig. 8b). The increase in synchrony during surface whisking matched that expected from the product of individual neuron firing rates, confirming that firing rate increased independently between neurons (t test, P = 0.653; Fig. 8b). Thus, synchronous activation of S1 neurons provides a robust code for detecting surfaces.
Because the statistics of slips vary with texture12, 13, 14, slip-evoked firing rate and synchrony may be cues for texture. At two recording sites, we confirmed that a rough surface (P150 sandpaper, 228 trials) elicited a greater rate of high-acceleration slips than a smooth surface (polished aluminum, 165 trials) or whisking in air (171 trials) (P < 0.01, two-way ANOVA; Fig. 8c). The mean firing rate (n = 9 neurons) was significantly higher on the rough surface (9.4 0.8 Hz) than on the smooth surface (7.3 0.7 Hz, P = 0.03, Kolmogorov-Smirnoff test) and was higher on the smooth surface than in air (4.6 0.9 Hz, P < 0.01, Kolmogorov-Smirnoff test), as was seen in rats discriminating textured surfaces33 (Fig. 8d). Synchronous firing in pairs of neurons (n = 16 pairs, measured in cascading 20-ms bins) showed an even greater difference with texture (rough, 4.0 0.5 synchronous spikes per s; smooth, 2.3 0.3; air, 1.0 0.2; all P < 0.01, Kolmogorov-Smirnoff test; Fig. 8e). The utility of a firing synchrony code for texture was especially apparent during whisking on four similar textures in interleaved trials (P150, P400, P800 and P1200 sandpapers, n = 195, 151, 173, 160 trials, respectively). High-acceleration slips were more common on P150–800 than on P1200 surfaces, as reported previously12 (Fig. 8f). Although the mean firing rate (n = 17 neurons, four recording sites) was not different between these surfaces (7.1 1.3 Hz, 7.0 1.3 Hz, 6.5 1.2 Hz and 6.0 1.2 Hz for P150, P400, P800 and P1200 sandpapers, respectively; P 
0.19 for all comparisons, Kolmogorov-Smirnoff test), firing synchrony in neuron pairs (n = 28 pairs) was systematically stronger on the rougher surfaces (3.3 0.5, 3.1 0.5, 2.8 0.6 and 2.1 0.5 synchronous spikes per s, respectively; P < 0.01 for P150 versus P1200 and P = 0.04 for P400 versus P1200, Kolmogorov-Smirnoff test; Fig. 8g,h). This difference in firing synchrony between textures was not seen on the 100-ms time scale (8.3 1.7, 7.7 1.6, 8.6 1.8 and 6.7 1.4 synchronous spikes per s for P150, P400, P800 and P1200 sandpapers, respectively; P 0.17 for all comparisons, Kolmogorov-Smirnoff test; Supplementary Fig. 10 online).
Discussion
Our results indicate that slips are fundamental encoded elements of whisker input streams during active, natural whisking on surfaces. Slip responses accounted for a substantial fraction of surface-driven spikes (30%). Slips were encoded with high temporal precision by synchronous, but low-probability, spikes on a background of sparse, poorly correlated firing. Thus, natural whisking transforms spatially continuous tactile stimuli (surfaces) into a stream of discrete, high-acceleration/high-velocity elements (slips) and represents these elements by temporally precise population activity in the corresponding cortical column in S1. Precise spike timing, which is relevant for coding of sensory events with an explicit temporal structure, such as contact with an object18, 43, may therefore be crucial for encoding of surface properties.
Temporally precise slip responses drive transient synchronous firing of S1 neurons, resulting in a synchrony code for slips. This type of synchrony coding does not involve any increase in synchrony beyond that expected from independent firing probability, unlike synchrony coding models in V1 (ref. 44), and is instead a straightforward consequence of rapid firing-rate modulation that should be readily detectable, in principle, by downstream cells or networks that spatially integrate across multiple S1 neurons in narrow time windows. Detection of synchronous responses to slips may be facilitated by decorrelation of background synaptic activity during whisking31. Increased raw firing correlations after slips (on the 20-ms time scale) provide a higher signal-to-noise measure of slips and surfaces than mean firing rate alone or than firing correlation on the 100-ms time scale. Thus, population coding of slips occurs on a shorter time scale than coding by firing-rate modulation during tactile flutter sensation in primate S1 (ref. 1).
One goal of this study was to test whether low-probability sensory responses, as have been observed many times in anesthetized S1 (refs. 15,16,17,25) and in response to passive stimulation in awake animals19, also occur during active whisker sensation of complex, natural stimuli. We found that whisker slips evoked low-probability responses during active whisking (0.10), leading to a small, varying set of active neurons for each slip. Although such low-probability responses could be generated deterministically by hidden stimulus selectivity for kinetic properties that vary across slips, we failed to detect neuronal selectivity for acceleration, direction, phase or position that could account for the sparse responses. Instead, we hypothesize that responses to individual slips were determined probabilistically by low intrinsic firing probabilities of S1 neurons, resulting in a small number of total S1 spikes per slip. This 'probabilistic sparse coding' is distinct from sparse coding that has been proposed in awake visual and auditory cortex or hippocampus, in which neurons respond highly selectively to small subsets of stimuli, but with large increases in firing rate23, 24, 45. True firing probability is probably even lower than our data indicate, as a result of the many S1 neurons that spike too infrequently to be detected by extracellular recording4, 17, 18. High signal-to-noise encoding of slips and surfaces was possible despite low spike numbers by detection of stimulus-induced firing synchrony.
In S1, assuming 4,200 neurons per column in L4 and L5 (ref. 46), a moderate whisker slip will elicit a single spike from 420 neurons, which is sufficient for robust behavioral detection20, 21. Probabilistic sparse coding may represent a means of achieving the metabolic and computational advantages of sparse coding22 in systems with low stimulus selectivity and may minimize synaptic and spiking adaptation during temporally dense sensory streams, similar to the volley principle in the auditory nerve47.
Because the rate and magnitude of slips vary with surface texture12, 13, 14, slip-evoked firing synchrony may code for surface texture. Consistent with this hypothesis, rougher surfaces evoked greater firing synchrony in neuron pairs than did smoother surfaces or whisking in air, and the signal-to-noise ratio for synchronous firing was greater than for mean firing rate. Our results confirm that firing rate varies between highly distinct textures33 but indicate that for closely related textures firing correlations on the 20-ms time scale provide a more robust code than mean firing rate12, 14. This synchrony-based coding of texture may complement firing rate–based codes for large texture differences33, and additional codes may also be available3, 14.
Note: Supplementary information is available on the Nature Neuroscience website.
Author Contributions
S.P.J., J.W. and D.E.F. designed the experiments. S.P.J. and J.W. performed the experiments. S.P.J. and D.E.F. analyzed the data and wrote the paper. All of the authors discussed the results and commented on the manuscript.
6-cm pieces of sandpaper glued to an aluminum plate and positioned parallel to the face at a distance of 5 mm from the tip of the intact whisker
impedance). Signals were amplified (20 
