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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Nat Neurosci. Author manuscript; available in PMC 2010 May 4.
Published in final edited form as:
PMCID: PMC2863011
NIHMSID: NIHMS192025

Phase-to-rate transformations encode touch in cortical neurons of a scanning sensorimotor system

Abstract

Sensory perception involves the dual challenge of encoding external stimuli and managing the influence of changes in body position that alter the sensory field. To examine mechanisms used to integrate sensory signals elicited by both external stimuli and motor activity, we recorded from rats trained to rhythmically sweep their vibrissa in search of a target. We found a select population of neurons in primary somatosensory cortex that are transiently excited by the confluence of touch by a single vibrissa and the phase of vibrissa motion in the whisk cycle; different units have different preferred phases. This conditional response enables the rodent to estimate object position in a coordinate frame that is normalized to the trajectory of the motor output, as defined by phase in the whisk cycle, rather than angle of the vibrissa relative to the face. The underlying computation is consistent with gating by an inhibitory shunt.

The perception of object location relative to the body depends on tracking sensor position—eyes for seeing or fingers for touching—as much as on the activation of those sensors by features of an object. Over a half century ago, von Holst1 emphasized that one cannot hope to understand sensation without consideration of the effects “produced on the sensory-receptors by the motor impulses which initiate a muscular movement.” von Holst factored the signals required for sensation into three components. One is an afferent signal that originates from environmental influences—for example, light for the case of looking and pressure for the case of touching—and is denoted ex-afference. A second component is an afferent signal that results from activation of sensory receptors by self-motion and is called reafference. The motor-driven sensory input can involve the same receptors that encode external stimuli, as in the case of peripheral reafference, or a separate group of receptors, as in the case of proprioception. A final sensory component may be provided by an efference copy of the motor command; this corresponds to the intended rather than actual motor activation of sensory receptors. The ex-afferent component can interact with one or both motor signals (that is, reafference or efference copy) to produce a perceptually stable representation of the identity and location of external stimuli relative to a changing body configuration.

The coexistence and possible interaction of ex-afference, reafference and efference copy signals has been demonstrated from peripheral to thalamocortical levels2. In gaze control, reafferent signals of actual eye position and efference copy of the intended position of gaze3 gate the input to vestibular nuclei as part of the vestibular ocular response4. In the visual system, neurons in cat thalamus5 and primary visual cortex6 respond to visual stimuli (the ex-afferent signal) and to the stimulation of extra-ocular muscle proprioceptors (a reafferent signal). Further, interactions between ex-afference visual signals and a presumed reafference of eye position have been observed at multiple levels of cortical processing in primates7. Responses to combinations of ex-afference, reafference and efference copy signals lie at the heart of transformations to place sensory input in body-centered coordinates. Yet mechanistic and conceptual understandings of how ex-afference and reafference interact to generate such transformations are lacking.

Rats sweep their vibrissae through space with stereotypical rhythmic motions as they locomote and search for objects in their immediate environment. Multiple features of the rat vibrissa system make it an ideal nervous system for studying the interaction of ex-afference and reafference. First, behavioral work has shown that rats can determine the position of an object relative to that of its head through the use of a single moving vibrissa8. This implies that the underlying computation of touch in a head-centered coordinate system depends on the interaction of an ex-afference signal (that is, vibrissa contact) with either a reafference or an efference copy that reports vibrissa position. A substrate for such interactions is provided by anatomical connections among sensory and motor areas, at the levels of brainstem through cortex9,10, that form nested feedback loops11,12. Efferent signals give rise to rhythmic motor activity that results in stereotypical whisking behavior13. This motion in turn generates a robust peripheral reafference that is locked to the phase of the vibrissae in the whisk cycle14 and strongly modulates the output of neurons in vibrissa primary sensory (S1) cortex1517, with different neurons having different preferred phases15. Recent evidence suggests that reafference and ex-afference signals are communicated along parallel pathways from the brainstem to cortex18,19. Thus ex-afferent and reafferent signals associated with vibrissa-based touch are likely to remain separate until they are allowed to interact in vibrissa S1 cortex.

Here, we test the hypothesis that ex-afference touch signals are modulated by reafference signals associated with sensor motion to form a representation of object location relative to the animal’s body plan. We ask the following questions: first, what is the nature of ex-afferent vibrissa touch signals encoded by single units in vibrissa S1 cortex? Past results consider only responses that are induced by passive rather than active vibrissa movement. Second, is touch represented in a coordinate system that is matched to the region currently scanned, defined by the phase of the vibrissa in the whisk cycle, or one that spans the full range of vibrissa position? Past results1517 imply that the reafferent signal encodes phase, which suggests but does not establish that touch is also encoded in terms of phase. Finally, how can known cortical circuits give rise to the observed interaction of ex-afferent and reafferent signals?

RESULTS

Rats were trained to palpate a sensor with their vibrissae in either a free-ranging (Fig. 1a) or a body-constrained (Fig. 1b) behavioral configuration. In both paradigms, whisking was accompanied by large movements of the head, so that contact of a vibrissa with the sensor spanned all possible phases of the whisk cycle (Supplementary Fig. 1 online); there was a small but significant (P < 0.01) excess of touch events at protraction over retraction. Animals that succeeded in this task underwent surgery to implant a microwire head stage20 above vibrissa S1 cortex to record broadband electrical activity. These signals were subsequently sorted into single units21, as verified by the consistency of spike waveforms across instances and autocorrelation functions that decay toward zero at equal time (Fig. 1c). We established the principal vibrissa22 for each of two to four electrodes in S1 cortex and trimmed all but these vibrissae; no systematic differences in whisking or touch were observed that were related to different numbers of intact vibrissae. Further, microwires were implanted into the mystacial pad to record the differential electromyogram ([nabla]EMG) of the muscles that drive the vibrissa motion.

Figure 1
Experimental setups and data acquisition. (a) Free ranging apparatus. The rat cranes from a perch to contact a piezoelectric touch sensor that is held in position by a pneumatic piston and imaged with a high-speed camera. Five seconds after the initial ...

The rectified [nabla]EMG was used to deduce the phase of the vibrissae, denoted ϕ(t), during contact events and during periods of time when rats were coaxed to whisk freely in the air16. These epochs of free-whisking13 allowed the reafferent response to whisking to be assessed (Fig. 1d and Supplementary Fig. 2 online). Videographic imaging was used to deduce the phase and angular position, θ(t), of the vibrissae surrounding contact events, and to confirm that only a single vibrissa touched the sensor (Fig. 1c). The resulting spike, [nabla]VEMG data, videographic data and touch sensor signals were sufficient to calculate the spiking as a function of phase in the whisk cycle during free whisking as well as spiking as a function of both phase and absolute angle during epochs of vibrissa contact (Fig. 1d and Supplementary Fig. 2).

The instantaneous phase in the whisk cycle is denoted ϕ(t); this can be expressed as ϕ(t) = [2πfwhiskt – ϕwhisk]modulo 2π during rhythmic whisking, where fwhisk is the whisking frequency and ϕwhisk is the preferred phase. A preferred phase of ϕwhisk = 0 corresponds to the protracted position, ϕwhisk = ± π is the retracted position, and negative (positive) angles indicate protraction (retraction). The instantaneous angular position and phase are related by θ(t) = θmidpoint(t) + Δθ(t) · cos[ϕ(t)], when the midpoint, θmidpoint(t), and amplitude, Δθ(t), vary only slowly on the timescale of the period of whisking, that is, 1/fwhisk.

Single units respond during free whisking as well as touch

We recorded 152 single units in the vibrissa S1 cortex of nine rats, a majority of which responded to whisking in free air. No differences were seen between free-ranging (Fig. 1a) versus body-constrained (Fig. 1b) paradigms. Cross-correlations between spiking activity and the rectified [nabla]EMG show that individual units tend to spike at specific phases of the whisk cycle (Fig. 2a–d, left column). The presence of units whose spike rate remains phasically modulated in time follows from the narrow distribution of whisking frequencies13 (fwhisk = 8.7 ± 1.3 Hz; mean ± s.d.). In an extension of past work, we found that the spike rate during free whisking epochs appears unchanged from that during periods of negligible mystacial [nabla]EMG activity, such as when an animal walks without whisking (Fig. 2e). Thus whisking tends to reorganize the timing of spikes rather than add new spikes, which is reminiscent of the effect of finger taps on the response of neurons in the primary somatosensory area of monkeys23.

Figure 2
Free whisking and exemplar touch responses of all single units. (a–d) Spike rates for rapidly excited (a), slowly inhibited (b), slowly excited (c) and no (d) response. The left column is a histogram of the average spike rate centered on the peaks ...

Most single units responded to active touch (Fig. 2a–d, middle column). Three broad classes of responses emerged based on trial-averaged responses: rapid excitation (Fig. 2a), slow net inhibition (Fig. 2b) similar to that seen under nonwhisking conditions24 and slow net excitation (Fig. 2c). The temporal delineation between rapidly and slowly responding cells was sharp (Supplementary Fig. 3 online), and all classes of neurons contained both narrow and broad spike waveforms25 (Supplementary Fig. 4 online). Rapidly excited units responded to touch with phasic spiking that had a latency to onset of 5 to 9 ms and ranged from 12 to 44 ms in duration. These units had the greatest maximum spike rate (Fig. 2f) and fired about 2% of their action potentials in bursts (Supplementary Fig. 5 online). They were largely confined to the granular and deep infragranular layers (Fig. 2g and Supplementary Fig. 6 online), which is consistent with data gathered from anesthetized animals in which whisking was driven by electrical stimulation of the vibrissa motor nerve18,26. Both categories of slowly responding neurons encode the behavioral task per se (as well as touch) in that their spike rates change as the rat cranes and whisks vigorously as it attempts to touch the sensor (Fig. 2c, middle row). Neurons that exhibited slow excitation upon touch dominated the supragranular and infragranular layers, whereas those with slow inhibitory responses were uniformly distributed among all layers (Supplementary Fig. 6).

Phase in the whisk cycle gates the rapid touch response

We observed that 20% of the single units were both rapidly excited by touch and modulated by whisking. These units, designated as RE touch/whisking neurons, form the locus of our analysis on the confluence of ex-afferent touch and reafferent whisking signals. Our goal was to test whether the touch responses were modulated by the phase of the vibrissa in the whisk cycle at the time of contact. We illustrate the analysis process in terms of the data for three example units whose preferred phases span the full range of whisking (Fig. 3a–d). First, we fit sinusoids to the rectified [nabla]EMG signal surrounding each contact event as a means to model rhythmic whisking and determine the phase in the whisk cycle at the time of contact (Fig. 3a). Second, a smooth rate function was fit to the event-averaged touch response for each unit (Fig. 3b). Third, individual touch responses were sorted into one of eight phase intervals within the whisk cycle. The average touch response within each phase interval was fit as a scaled version of the previously derived smooth rate function for that neuron (Fig. 3c); we note that the shape of the touch response appeared invariant to amplitude. Finally, the peak amplitude of the eight fitted functions defined a tuning curve of touch response versus phase in the whisk cycle (Fig. 3d).

Figure 3
Examples of the interaction between phase in the whisk cycle, as determined from the [nabla]EMG signal, and the response of rapidly excited touch-sensitive single units. (a) Histograms of the spike responses to free whisking in air. The spike rates ...

We observed that the touch response for each unit is strongly modulated by vibrissa position, such that the response is maximal at or near the preferred phase during free whisking (compare panels in Fig. 3a with those in Fig. 3d); this is highlighted when the spike response is visualized on a logarithmic scale (Fig. 3e). There is no systematic change in the amplitude of whisking as a function of where contact occurs in the whisk cycle (Supplementary Fig. 7 online). The maximum spike rate for the response to touch is about tenfold higher, on average, than the approximately 9-Hz average spike rate during whisking. The strong modulation of the touch response is suggestive of a nonlinear interaction between reafference and ex-afference.

In general, RE touch/whisking units showed responses to touch that were tuned to the phase of the whisk cycle (28 of 35 units) (all responses in Supplementary Figs. 8 and 9 online). A summary shows that the phase at the maximal touch response for each unit, denoted as ϕtouch (Fig. 3d), is statistically equal to the unit’s preferred phase during free whisking; that is, ϕtouch ≈ ϕwhisk (Fig. 4a). All values of preferred phase are represented, with a distribution that is biased toward retraction (Fig. 4a, side bars). All tuning curves are relatively broad, with an average half width at half maximum of 0.32π ± 0.05π radians (mean ± s.d.) (Fig. 4b, thick line); this coincides with the π/3 radian width for cosine-shaped tuning curves.

Figure 4
Summary of the phase sensitivity and spike rate modulation of rapidly excited touch-sensitive single units. (a) Scatter plot of the preferred phase for free whisking versus the preferred phase for touch. Shown are mean values plus 95% confidence intervals ...

We next determined whether the spike rate during free whisking is predictive of the peak rate upon touch. In contrast to naïve expectations, the maximum rate upon touch was nearly independent of the average spike rate during free whisking (P = 0.05) (Fig. 4c). A related analysis considers the modulation depth of the spike rates (Fig. 4d, inset)

Modulation depthMaximum spike rateMinimum spike rateMean spike rate
(1)

The modulation depth of the tuning curve for the touch response was, on average, four times greater than that for the free whisking response. Neither the spike rate nor the modulation depth showed a systematic dependence on preferred phase in the whisk cycle (Supplementary Fig. 10 online). Critically, the modulation depth for touch at different phases in the whisk cycle was statistically independent (P = 0.8) of the modulation of the rate during free whisking (Fig. 4d).

Vibrissa angle is a poor modulator of the touch response

We revisited the possibility that the spike response upon contact may be a function of angular position, which depends on the midpoint angle and amplitude of the whisk, in addition to phase in the whisk cycle (Fig. 4a,b). Position data were derived from videographic images during contact events (Fig. 1c). As a control, we compared the phase of the vibrissae in the whisk cycle at the time of contact derived from the videographic data (Fig. 5a,b and Supplementary Fig. 8) with the phases derived from the [nabla]EMG data. The two sets of data closely match (Supplementary Fig. 11 online). We next considered modulation in the spike rate upon contact as a function of position (Fig. 5c,d) and observed a relatively small and insignificant modulation.

Figure 5
Comparison of the phase dependence versus angular position dependence of the touch response, derived from videographic analysis of vibrissa position, for rapidly excited touch-sensitive single units. (a) Histograms of the touch response parsed according ...

The modulation of the touch response by phase in the whisk cycle was relatively high: an average of 1.2 across the 2π radian range of phase (Fig. 5e). In contrast, the modulation of the touch response by position averaged only 0.4 across the full range of whisking angles and was statistically significant (P < 0.05) in only 14% of the cases (Fig. 5f). As an average over all RE touch/whisking units, the amplitude of whisking varied by 12° between trials, or 70% of the average value of Δ θ, whereas the midpoint of the region of whisking varied by 6° between trials, or 35% of the average amplitude (Fig. 5g). In summary, RE touch/whisking units encode touch in terms of phase, which is normalized to the particular amplitude and midpoint, as opposed to angular position, on a given trial.

We consider the possibility that the broad tuning curve for the touch response as a function of phase in the whisk cycle (Fig. 4b) results from a preferred phase, ϕtouch, that is modulated by the amplitude or the frequency of whisking. Under these contingencies, the observed broad curve could be the sum of multiple narrow curves, each with a slightly different value of ϕtouch. For the example of unit three (Figs. 3 and and5),5), we observe no difference in either the preferred phase ϕwhisk or the width of the tuning curve when the dataset is equally divided based on trials with large-amplitude versus small-amplitude whisks (Fig. 6a–c). A similar invariance occurs when the dataset is equally divided based on trials with lower versus higher whisking frequencies (Fig. 6a,d,e), for which time delay could in principle lead to a frequency-dependent phase. Signal-to-noise constraints allowed us to perform this analysis for only 6 of the 28 RE touch/whisking units, yet all showed statistically significant invariance (P < 0.02) with regard to preferred phase and broad tuning (Supplementary Fig. 12 online).

Figure 6
Example of the phase dependence as a function of whisking parameters for a rapidly excited touch-sensitive single unit. (a) The response for unit 3 (Figs. 3 and and5)5) averaged over all trials, for which ϕwhisk = 0.45 π. (b,c ...

DISCUSSION

Active sensing by the rat vibrissa system involves two sensory signals: a reafferent signal of motor activity that encodes the phase of the vibrissa in the whisk cycle and an ex-afferent signal that encodes touch (Fig. 2). We have shown that these two signals are merged in a highly nonlinear manner (Figs. 3 and and4)4) in vibrissa S1 cortex and that contact is coded with respect to vibrissa phase rather than angular position (Fig. 5). The coding is robust and invariant with respect to changes in whisking parameters (Fig. 6).

The representation of contact in a normalized, relative coordinate system that is dynamically generated by the motor trajectory is somewhat similar to the coding of visual stimuli in dynamic, objected-centered coordinates, as occurs in parietal and premotor cortices in primates7,27. This is in contrast to the static, retinotopic coordinates instantiated by primary visual areas. Coding in phase coordinates implies that there is a common pathway for the reafferent and ex-afferent signals, or that these signals follow separate pathways with similar adaptation. To the extent that separate pathways are used, as has been suggested18, we propose a neuronal circuit that computes the location of objects within a sensory field (Fig. 7a).

Figure 7
Shunting-inhibition model for the phase sensitivity of active touch. (a) Circuit diagram for the three-compartment neuron that captures the essence of shunting inhibition. The whisking signal is ‘inverted’ by a local inhibitory neuron ...

Origin of the reafferent signal

A reafference signal that encodes the phase in the whisking cycle is present at the level of primary sensory neurons in the trigeminal ganglion14,28. In animals that whisk (for example, mice, rats and gerbils), vibrissa follicles are innervated with both deep and superficial nerve endings29. Both innervations are distinct and highly structured, and they terminate in different regions of the trigeminal complex. Notably, animals that do not whisk (for example, cats, guinea pigs and rabbits) either completely lack superficial follicle receptors or the innervation is sparse and largely unstructured. This led to the hypothesis that superficial nerve innervation serves as proprioceptive reafference for vibrissa motion29. The mechanism by which compression of the follicle during movement is transformed into a phase code is unknown, but it could involve adaptation to the range of whisking30.

A second issue involves the possibility that the reafference and ex-afference form separate thalamocortical tracks19. There are four pathways—one that involves posterior medial thalamus and three that involve subdivisions of ventral posterior medial thalamus—that originate from different populations of secondary sensory cells in the trigeminal nuclei31. Recent reports provide evidence (albeit controversial) that the posterior medial thalamic pathway encodes predominantly vibrissa motion18,32, whereas at least one of the ventral posterior medial thalamic pathways encodes predominantly touch18.

Model for the interaction of contact and whisking signals

A biophysical model for gating of the active touch response must account for four phenomena. First, the ex-afferent touch signals and the reafferent free whisking responses are enhanced at the same phase in the whisk cycle (Fig. 4a). Second, the spike rate amplitudes and modulation depths of the spike rates for touch and free whisking responses are independent (Fig. 4c,d). Third, the modulation of the touch response is much greater than the relatively small modulation of the spike rate by free whisking (Figs. 2d and 4c,d). Fourth, the whisking reafference essentially does not change the background spike rate (Fig. 2e).

Summation of the ex-afferent and reafferent inputs, followed by a spike-generating mechanism whose firing rate is a steeply increasing function of input current, is a potential mechanism for the observed phenomena. However, a substantial increase in the slope of spike rate versus input current is unprecedented for cortical neurons33. A related scheme makes use of the summation of signals near threshold33. However, both whisking and touch events ride on a substantial background rate for all of our units (Figs. 24). Multiplication of the ex-afferent touch signal with the reafferent whisking signal is a potential nonlinearity that can strongly modulate the touch response by the phase in the whisk cycle. One expectation for this scheme that is implicit from studies on the multiplication of signals by neurons3437 is that the amplitude of the touch response should track that of the whisking response. However, in contrast to this expectation, the modulation depth for touch at different phases in the whisk cycle was independent of the modulation of the rate during free whisking (Fig. 4d).

We propose that shunting inhibition of a putative touch pathway by a whisking pathway provides a likely circuit to gate the touch response by the phase in the whisk cycle. Shunting inhibition38 also provides a means for one input to modulate the synaptic gain of a second input. A minimal model consists of a neuron with three compartments, each with a leak battery with resistance R and potential EL, arranged so that (i) an active zone has a bias battery, with conductance GB and potential EB, and generates spikes; (ii) a soma receives shunting—that is, GABAA-mediated synaptic input with a battery with conductance GS and inhibitory potential ES, where ES ~ EL; and (iii) a dendritic compartment receives excitatory synaptic input with a battery with conductance GE and excitatory potential EE (Fig. 7a). The sequential arrangement of the compartments, taken for simplicity to be one electrotonic length apart, allows the inhibitory whisking input to both modulate the background spike rate and gate an excitatory touch input (Figs. 2a and and3).3). Putative inhibitory neurons that are strongly modulated by whisking but not touch in close proximity to rapidly excited touch cells is consistent with our laminar analysis of different classes of single units (Fig. 2g and Supplementary Fig. 6).

Insight into the mechanism of shunting inhibition can be gleaned from a linear analysis of the circuit because the spike rate tracks the membrane potential in the presence of high background activity39. For simplicity, we ignore the bias current and assume that the maximal synaptic conductances are large (Fig. 7a). Contact at the preferred phase in the whisk cycle, that is, ϕ = ϕwhisk so that RGS = 0, leads to a membrane potential of Vm ~ (4EL + EE)/5 at the active zone, which exceeds the rest level Vm ~ EL. In contrast, when contact occurs at ϕ = ϕwhisk ± π, so that RGS [dbl greater-than sign] 1, the excitatory touch input is shunted by the inhibitory whisking input, and the membrane potential falls to Vm ~ (EL + ES)/2 + EE/(2RGS), which is close to the rest level. The independence of touch and whisking is seen by estimating their modulation depths (equation (1)), with Vm as a surrogate for spike rates

Modulation depth|Whisking14|ELESEL|EL~ES0
(2)

which approaches zero when the shunt and leak potentials are equal, and

Modulation depth|Touch25{3(ELES)+EE+|2ES||3ELES|}EL~ES15
(3)

which approaches a constant in the same limit. Thus the modulation depth for touch can be both independent of that for whisking and larger, which is consistent with our observations (Fig. 4d).

Numerical analysis of the model (Fig. 7a) with a Hindmarsh-Rose– type mechanism for spike generation and parameters appropriate for cortical neurons40 clearly shows that the response to touch is enhanced at the preferred phase in the whisk cycle (Fig. 7b,c). Simulations with different bias conductances show that whisking has only a marginal effect on the spike rate (Fig. 7d). Simulations with different shunt conductances show that the amplitude of the touch response is independent of the amplitude of the free whisking spike rate (Fig. 7e), and that modulation in the spike rate by changes in vibrissa position is both much greater than and independent of the modulation during free whisking (Fig. 7f). The proposed circuit can, in principle, be confirmed or refuted by recording the intracellular potential from layer 4 spiny stellate or star pyramidal cells in rats that are trained to whisk17,41. A combination of ion blockers and voltage clamping should reveal whether the whisking response is mediated by inhibitory input.

Spike rates and angular resolution

The average ongoing rate of spiking hovers around 9 Hz (Fig. 2e), and the average modulation of the spike rate by whisking per se is ± 2 spikes per second. This corresponds to ~0.4 spikes per whisk, on top of a fluctuating background of ~1 spike per whisk. We estimate that the output from ~200 neurons must thus be summed to achieve a resolution of π/3 radians, as set by the tuning curve (Fig. 4b), to specify the phase in the whisk cycle on a single trial basis. Decoding schemes that make use of the absence of a response at nonpreferred phases may lower this estimate. On the other hand, the consensus view of the spike rate of neurons in vibrissa S1 cortex is evolving, with evidence from intracellular studies that the ongoing rates for many neurons may lie closer to 1Hz than 10Hz42,43. A lower average rate would increase the variability and increase the estimate.

With regard to contact-induced spikes, active touch leads to an average, integrated response of 2 spikes per contact within a window of ~20 ms (Fig. 3b); this further coincides with the time spent in each resolvable phase interval of π/3 radians (Fig. 4b). The additional spikes generated by active touch substantially exceed the ~0.4 spikes generated by whisking alone and should be sensed with high fidelity. Resolution at a scale much finer than π/3 radians may be achieved by averaging the responses from multiple neurons. Finally, for the average whisking range of ±17° (Fig. 5g), the corresponding angular resolution is ~5°, which approximates the typical threshold for bilateral perceptual acuity with a vibrissa44.

Relation to directional tuning

Directional tuning is a common metric used to quantify neuronal response of vibrissa units in the anesthetized animal45. It measures the bias in the activity of neurons as a vibrissa is deflected in different directions. Notably, directional tuning forms a fine-scale map within a cortical column46.

Directional tuning may be derived from an asymmetry in the phase preference of a neuron. With phase tuning for contact defined as T(ϕ–ϕtouch) (Figs. 3d, ,4b4b and Fig. 6), the directional tuning along the anterior-posterior axis is

D(ϕtouch)=2π0dϕ{T(ϕϕtouch)}oddπ0dϕ{T(ϕϕtouch)}even

where odd and even refer to the odd and even parts of the function. The directional tuning is double-valued over the whisk cycle, so that the phase preference of a neuron cannot be uniquely determined from its directional preference. Nonetheless, to the extent that active and passive touch lead to neuronal responses with similar directional preference, neurons with different preferred phases in the whisk cycle are expected to conform to the map for directional tuning.

METHODS

Training and behavior

We successfully trained nine female Long-Evans rats (Charles River), 270 to 300 g initial weight, to whisk against a piezoelectric sensor (DT1–028K; Measurement Specialties Inc.) in return for a liquid food reward (0.2 ml per trial; LD–100; PMI Feeds). We used two behavioral paradigms. In the ‘free ranging’ paradigm (Fig. 1a), we trained unconstrained animals to perch on the edge of a platform and crane their necks to gain access to the sensor. Each trial was initiated when the rat first contacted the sensor. We collected video images at a frame rate of ~100 frames per second while the rat palpated the sensor to confirm that the longest vibrissa touched the sensor. After an approximately 3-s period of palpation, the trial was terminated by removal of the sensor and concomitant pumping of the liquid reward to a nearby well on the platform. The sensor remained retracted for 5s, then was restored to its previous position so that a new trial could begin. In the ‘body constrained’ paradigm (Fig. 1b), we placed the animals in a sack and held them in a tube within proximity of a sensor. A trial began when an animal craned and initially touched the sensor and, as above, was terminated after a 3-s period of touch events.

Successful learning of either of the above behaviors took about two weeks. Once training was completed, a small chamber that contained an array of 2 to 4 stereotrodes was fit over the vibrissa area of parietal cortex and secured to the skull with screws and dental acrylic20. We individually advanced the stereotrodes through the dura into cortex with a vacuum insertion technique that prevented damage to the upper layers20. We threaded fine wires into the left and right mystacial pads to record the EMG13. The care and experimental manipulation of our animals were in strict accord with guidelines from the US National Institutes of Health and have been reviewed and approved by the Institutional Animal Care and Use Committee of the University of California, San Diego.

After several days of post-operative recovery, we briefly anesthetized the animals and individually stimulated each contralateral vibrissa with a brief air puff47 in order to determine the principal vibrissa response for each stereotrode. The designation of the principal vibrissa was based on the amplitude and latency of the stimulus-locked spikes48. Once we determined the principal vibrissae across the full complement of stereotrodes, we trimmed all other vibrissae at ~1 mm from the surface of the skin. The rats were returned to their behavioral setup and invariably performed the task with the single, longest vibrissa. We then acquired spiking data with the electrode that had this vibrissa as its principal vibrissa; the electrode was lowered at the start of each recording session by 80 µm, or until single unit spikes were detected. Once this electrode had been lowered through the full depth of cortex, we trimmed the longest vibrissa and proceeded to take data from the next longest vibrissa, and so forth.

Estimation of electrode depth

We exploited the stereotypic form of the radial current source density to identify the lamina of each recording. After all electrodes were lowered through the cortex and data collection was completed, the rat was anesthetized with 5% (w/v) halothane. All electrodes were fully retracted, then lowered in increments of 80 mm while air puffs were delivered at 1.3 puffs per second to passively stimulate all of the vibrissae. We recorded the local field potential at each depth as an average over 100 air puffs16. The second spatial derivative was then calculated across all of the averaged local field potential responses to produce an estimate of the one-dimensional current source density profile for each electrode. Current sinks corresponded to the afferent inputs in layers 4 and 6A; these calibration data allowed us to specify the lamella and depth of every record (Fig. 2g and Supplementary Fig. 6).

Data acquisition

Continuous time series from the cortical and EMG microwires were band-pass filtered from 0.35Hz (1 pole) to 10kHz (6 poles), and the piezoelectric sensor was band-pass filtered from 4 kHz (2 poles) to 8 kHz (2 poles). We sampled all data at 32 kHz and stored blocks of approximately 3 s in duration that incorporated each epoch of touch on computer disk, together with the time-locked video images. We obtained additional spike-train records, 10 s in length, as animals were coaxed to whisk in air without contact by placing their home cage just out of reach16. We digitally high-pass filtered the broadband cortical and EMG signals at 300 Hz (4 poles). Pairs of EMG signals that spanned the mystacial pad were subtracted to form the [nabla]EMG13.

We collected high-speed videography (ES310 charge coupled device camera; Kodak, Inc.) acquired at 100 frames per second during trials where rats contacted the touch sensor with their vibrissae. Synchronization between video and electrophysiological data acquisition was accomplished through a hardware trigger on the Real-Time System Integration Bus (National Instruments). We calculated the angular position of the principal vibrissa on a frame-by-frame basis as the angle between one straight line that followed the midline of the snout and another straight line that followed the first 6 to 10 mm of the vibrissa shaft (Fig. 1c). The lines were drawn manually, for each frame, with the aid of a Matlab (The Mathworks)-based graphical user interface.

Data analysis

An offline non-Gaussian cluster analysis algorithm21 was used to isolate spikes from an apparent common source in each cortical signal. We characterized modulation of the spike rate of single units during epochs of rhythmic whisking in air, which occurred before and after contact trials, by cross-correlating [nabla]EMG peak times with spike times. This method allowed us to normalize the correlation in terms of spike rate. We first band-pass filtered the rectified [nabla]EMG from 3 to 22 Hz and set an appropriate threshold for the signal as a means to isolate the interval that surrounded the peak of the waveform, then calculated the center of mass in these intervals to obtain a point process that represents the peaks of the [nabla]EMG. We then shifted this time series by 20 ms to account for the measured time delay between the onset of muscle activity, as measured by the [nabla]EMG, and movement of the vibrissae13. The resultant cross-correlation corresponds to the [nabla]EMG-triggered average spiking rate (Fig. 2a–d, gray histograms in left column, and Fig. 4a). The sinusoidal nature of the cross-correlation was characterized by Poisson-distributed maximum likelihood estimates (MLE) of the mean spike counts49 for a series of complex exponential functions that spanned the frequency range of 5 to 20 Hz, plus a constant term (function glmfit in Matlab with the log-link function). The frequency of the modulation was defined as the estimate with the highest likelihood among all of the complex exponential estimates in the series. We calculated the phase and amplitude of each response from the real and imaginary parts of the estimate. Finally, we normalized the cross-correlations in terms of spike rates by multiplying the spike counts in each bin by the width of the bin (2 ms) and dividing by the number of [nabla]EMG peaks in the average (Fig. 2a–d, gray histograms in left column, and Fig. 3a). We used sampling distributions of maximum likelihood estimators to construct 95% confidence intervals of the mean spike rate and parameter estimates.

We estimated touch responses from contact-triggered averages, either across all trials (Fig. 2a – d, gray histograms in middle column, and Fig. 3b) or first parsed according to the phase of whisking at the time of contact (Fig. 3b, gray histograms). Smoothed values for all estimates made use of the Poisson-distributed Bayesian adaptive regression splines nonparametric smoothing algorithm50 (http://lib.stat.cmu.edu/~kass/bars).

We determined the phases of touch events within the whisk cycle by fitting a series of complex exponentials to the band-pass filtered [nabla]EMG or to spline-interpolated videographic traces, centered in a 200-ms window that surrounded the time of vibrissa touch. The procedure was as described above for spike events, except that we now used a Gaussian- rather than Poisson-distributed MLE, as the [nabla]EMG data are a continuous function rather than a point process. We quantified goodness of fit by calculating the ratio of the amplitude of the fit relative to the r.m.s. residual of the fit; we discarded contact events with ratios less than two.

To assess the touch responses as a function of phase in the whisk cycle, cycles in which touch occurred were first divided into eight intervals of π/4 radians. We then binned touch responses according to the interval in which the touch events occurred to produce a set of eight histograms for each single unit (Figs. 3c and 5a,e). To ensure that our results were statistically reliable across the full range of phase intervals, we excluded sessions with less than eight touch events in any phase interval. We then modeled touch responses for each whisk cycle phase interval with a Poisson-distributed MLE as scaled versions of the overall touch response, computed as described above (Fig. 3c–e, red and black curves). We used the peak amplitudes for each of the best fits to construct the tuning curve for the single unit (Figs. 3d and and5b).5b). We calculated confidence intervals (95%) for mean spike rates from sampling distributions of maximum likelihood estimators. A similar procedure was followed to assess the touch responses as a function of angle in the whisk cycle, for which videographic data were used to determine vibrissa position relative to the midline (Fig. 1c).

Model

The circuit model (Fig. 7a) consists of three compartments with equal membrane capacitances, C, and resistances, R, that are joined by a resistance of R so that the compartments are one electrotonic length apart in the absence of synaptic input. We define EL, EB, ES and EE as the reversal potentials for the leak, excitatory bias, inhibitory synaptic shunt and excitatory synaptic currents, respectively, GL as the fixed leak conductance, GB as the conductance of a slowly varying bias current, and GS and GE as the conductances for the vibrissa-driven inhibitory shunt and touch-driven excitation, respectively. For constant values of the conductances, the steady state subthreshold voltage of the active zone, denoted Vm, is given by:

Vm=(8+2RGS+4RGE+RGSRGE)EL+RGB(5+2RGS+3RGE+RGSRGE)+EB+RGS(2+RGE)ES+RGEEE8+5RGB+2(2+RGB)RGS+(5+3RGB)+RGE+(2+RGB)RGSRGE
(4)

The full dynamics are found by solving five equations, which include a third-order Hindmarsh-Rose system to generate spikes in a cortical cell with adaptation, and additive band-limited Gaussian noise to approximate the variability in synaptic arrival time. We have

dVmdt=1τm{(a+bVm+cVm2)(ENaVm)+RGR(EKVm)U+RGA(EKVm)W+RGB(EBVm)+(VsVm)+Inoise}
(5)

dUdt=1τU{U+eVm+f+g(EKAVm)2}
(6)

dWdt=1τW{W+h(E1Vm)(E2Vm)}
(7)

dVSdt=1τm{(ESVS)RGS+(ELVS)RGL+(VmVS)+(VEVS)}
(8)

dVEdt=1τm{(EEVE)RGE+(ELVE)RGL+(VSVE)}
(9)

where the leak term RGL(EL –Vm) in the dynamics for Vm is subsumed in the active currents, and τm = 1 ms, τU = 1 ms, τW = 99 ms, ENa = 48 mV, EK = –95 mV, EKA = −38 mV, ES = EL = −74 mV, EB = EE = +10 mV, E1 = −75.4 mV, E2 = −69 mV, RGR = 26, RGA = 13, RGB = 0.2 (ranges 0.05 to 0.8), RGL = 1, a = 17.8, b = 0.476 mV−1, c = 3.38 × 10−3 mV−2, e = 1.3 × 10−2, f = 0.8, g = 3.3 × 10−4 and h = 1.1 × 10−3 in our simulations. The noise current has an r.m.s. value of 2.0 mV; the shunting inhibitory conductance was of the form

RGS=RGSO2{1+cos(2πfwhisktϕwhisk)}
(10)

where RGSO = 10 (ranges 0 to 20) and fwhisk = 9Hz; and the excitatory touch conductance was of the form

RGE=RGEOe(ttEO)2/2τEO2
(11)

where RGEO = 40, τEO = 20 ms and tEO is a random variable with a mean of 0.25 s that marks touch events.

Supplementary Material

Supplementary

ACKNOWLEDGMENTS

We thank S.B. Mehta for assistance with spike sorting, E.N. Brown and R.E. Kass for instruction on spike-train analysis, G.A. White for electronics support, E. Ahissar, W. Denk, M. Deschenes, M.E. Diamond, A.L. Fairhall, D.N. Hill and T.J. Sejnowski for relevant discussions, D. Matthews for reading of the manuscript, and the US National Institutes of Health (NS051177), the US National Science Foundation (IGERT) and the US/Israel Binational Foundation (2003222) for financial support.

Footnotes

Supplementary information is available on the Nature Neuroscience website.

Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions/

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