# Whisking kinematics

Post-publication activity

Curator: Per M Knutsen

Figure 1: a. Example of typical whisking behavior. Solid black line is the time-varying azimuth angle of the C2 vibrissa relative to the head. The angle envelope (gray area) is indicated by the retraction (blue) and protraction (green) set-points (dotted lines) showing that the vibrissa position fluctuates on a slower timescale than the protraction (up) and retraction (down) whisk cycles. Data was obtained from a head restrained rat, and is adapted from (Pietr et al., 2010)⁠ with permission. b. Representation of the vibrissa azimuth angle ($$\theta$$), as seen from a top-down perspective. Blue and green lines display the vibrissa at retraction and protraction set-points respectively. Dotted lines indicate the vibrissa azimuth, estimated as the tangent at the base of the shaft. c. Conventions for representing vibrissa position, translation and rotation in head-centered Cartesian coordinates. $$X$$ indicate direction of nose (anterior), $$Y$$ points lateral and $$Z$$ upwards (dorsal). The origin is arbitrarily set to the retraction set-point of the follicle in the previous whisk cycle (blue dot). After a protraction, the follicle is displaced a distance $$x$$ anterior and $$z$$ dorsal with respect to the skull (green dot). The shape and position of the vibrissa at the protraction set-point (green lines) is projected down and back onto the transverse (light red) and coronal (light orange) planes, respectively. The azimuth ($$\theta$$), elevation ($$\phi$$) and torsion ($$\zeta$$) angles are measured with respect to the skull. d. Single whisk cycle from a. Top: Vibrissa angle (azimuth, $$\theta$$). Middle: Vibrissa angular velocity ($$\theta'$$). Bottom: Phase of the whisk cycle. All traces plotted versus time. Conventions as in b.

Whisking refers to a behavioral process, whereby motile facial vibrissae are repeatedly and rhythmically moved back and forth in order to sample the proximal environment (Fig. 1a). The primary functions of whisking are spatial search and tactile exploration of objects and surfaces (see Vibrissal Behavior and Function). Non-rhythmic vibrissae movements also serve many behavioral processes, such as social interactions (Wolfe et al., 2011)⁠ and discrimination of lateral gaps (Krupa et al., 2001)⁠. Whisking is coordinated with head and body movements, which enables rapid sampling of the proximal environment during spatial exploration. Following contact, motor control of the vibrissae is modulated on several time scales as the animal approaches an object with head, nose and micro-vibrissae. Whisking has been studied primarily in rats, mice and shrews.

## Descriptions of vibrissae motion

Vibrissae movements are produced by contractions of facial musculature, head movements and locomotion. Vibrissae positions relative to the head are typically measured by high-speed videography (Knutsen et al., 2005)⁠, in conjunction with head and body movements (Mitchinson et al., 2007)⁠ or while an animal has been partially immobilized (Bermejo et al., 1998)⁠.

Vibrissae movements relative to the head are described by three angles of rotation (azimuth, $$\theta$$; elevation, $$\phi$$; and torsion, $$\zeta$$) and translation of the vibrissa base (horizontal and vertical; Fig. 1b,c). The largest spatial displacement of the vibrissae tips is due to azimuthal rotation, which moves the vibrissae back and forth along the longitudinal axis. This movement co-varies with small changes in elevation. Torsion, or roll, refers to a rotation of a vibrissa about its own axis. The torsional angle is linearly correlated with the azimuth and the ratio $$\delta\zeta / \delta\theta$$ changes as a function of the vertical location of the vibrissa follicle on the mystacial pad. Torsion alters the forward facing surface of the vibrissae shaft that contacts the opposing surface and, because the vibrissae are curved, displaces the whisker tips relative to the head (Knutsen et al., 2008a; Huet and Hartmann, 2014)⁠.

The time-varying three-dimensional position of a vibrissa is described by (1) its shape $$W$$, approximated as a quadratic function $$W = a + bu + cu^2$$ with the intrinsic curvature $$\kappa_{(u = 0)} = \frac{2b}{(1 + c^2)^{1.5}}$$, (2) its base position $$U(x,y,z)$$ which is a single 3D coordinate, and (3) by the angles $$\theta$$, $$\phi$$ and $$\zeta$$ at which the vibrissa protrudes from the mystacial pad, measured with respect to a head-centered coordinate system (Fig. 1c). The angles $$\theta$$ and $$\zeta$$ are dependent variables, such that $$\zeta \approx \alpha\theta + \beta$$ for vibrissae rows A, D and E and $$\zeta \approx \gamma\theta^2 + \alpha\theta + \beta$$ for rows B and C. Since $$\phi$$ is typically small and $$\kappa$$ is constant, it is therefore in most cases sufficient to describe the kinematics of the vibrissae in terms of $$\theta$$ and translations of the base position $$U$$ (Knutsen et al., 2008a)⁠.

### Kinematic profile of the whisk cycle

Whisking is a repetition of discrete whisk cycles that is executed and interrupted in discrete epochs (Fig. 1a). Vibrissa protraction is initiated by the extrinsic m. nasalis muscle which pulls the mystacial pad forward. This phase is followed by contraction of the intrinsic sling muscles associated with individual follicles that rotate the vibrissae further forward. Vibrissa retraction involves the relaxation of protractor muscles and activation of the m. nasolabialis and m. maxillolabialis muscles that together pull the pad backward (Hill et al., 2008) (see Whisking musculature)⁠. This coordinated tri-phasic activation of the mystacial muscles generates stereotyped protraction and retraction trajectories. By definition, the whisk cycle is initiated from the retraction set-point of the previous cycle $$\theta_{rs}$$ and protracts each vibrissa to a new protraction set-point $$\theta_{ps}$$. Upon reaching $$\theta_{ps}$$, the vibrissae retracts back to $$\theta_{rs}$$ and the whisk cycle starts over (Fig. 1d). The protraction phase is typically slower and lasts longer than the retraction phase. A typical whisk cycle has a single velocity maximum during protraction and retraction. The coordination between the protractor muscles, however, can vary during free-air whisking or contact due to neuromuscular feedback such that two or three velocity maxima can occur during protraction (Towal and Hartmann, 2008; Deutsch et al., 2012)⁠.

The frequency of whisking is typically described by the peak frequency of vibrissa angle (azimuth). The zeroth harmonic of vibrissa angle typically correspond to the slow fluctuations of the whisking envelope (Fig. 1a), and the first harmonic to the coupling of vibrissa movements to basal respiration. Thus, the first harmonic is at a lower frequency in rats (1 – 2 Hz) compared to mice (1.5 – 4 Hz) due to the slower respiratory rate of rats. The second harmonic of angle corresponds to the faster whisking, which is also synchronized with respiration (Mitchinson et al., 2011; Moore et al., 2013; Sofroniew et al., 2014). Because velocity is highest during whisking, however, it is more common the estimate the whisking frequency from the angular velocity ($$\theta'$$) which contains a single harmonic typically denoted $$f_0$$ (Berg and Kleinfeld, 2003). The whisking frequency is both species and context dependent. Rats whisk at rates between 6 – 12 Hz during locomotion, 4 – 8 Hz during head-restraint and between 15 – 25 Hz during palpation of objects and object localization (Berg and Kleinfeld, 2003; Knutsen et al., 2006)⁠. Mice whisk at rates between 9 – 16 Hz during locomotion and above 20 Hz during episodes of intense whisking (Jin et al., 2004; Mitchinson et al., 2011; Sofroniew et al., 2014)⁠. Etruscan shrews (smallest known mammals by mass) whisk at even higher average rates (12 – 17 Hz) consistent with their very high basal respiratory rate (10 – 14 Hz) (Munz et al., 2010). During exploration the whisking frequency can be maintained remarkably stable during each whisking epoch, with frequency changes occurring between whisking epochs (Berg and Kleinfeld, 2003)⁠.

Whisking can be decomposed into rapidly and slowly varying parameters (Hill et al., 2011)⁠. The rapid parameter is the phase which places the whisk position on a normalized time axis from -π (protraction onset) to π (retraction set-point; Fig. 1d). Slowly varying protraction and retraction set-points result in fluctuating protraction and retraction amplitudes, sometimes referred to as the whisking envelope (Fig. 1a). These slowly varying whisk amplitudes suggest that the control of whisking amplitude is uncoupled from the patterning of whisking frequency. Indeed, direct tests demonstrate that amplitude can be modulated independently of frequency via the cannabinoid type 1 receptor (CB1R). Activation of CB1R, which reduce cortical synchronization in the theta and gamma frequency bands, reduce amplitudes without any effects on whisk timing (Pietr et al., 2010)⁠.

### Modes of whisking

Figure 2: Average azimuth angle ($$\theta$$) and velocity ($$\theta'$$) during whisking, as a function of whisk period. Time has been normalized so that the abscissa represents the duration of one whisk cycle. The average position of the protraction set-point is indicated by solid, black lines. During foveal whisking (periods below 100 ms), both retraction and protraction set-points are on average higher. Data obtained from head-fixed rat, in absence of contact (Knutsen et al., 2008a)⁠.
Figure 3: Peak velocities during whisk protraction as a function of whisk amplitude and period (or, instantaneous frequency). Velocity ($$\theta'$$) is represented by color. Dots are individual whisk cycles. Same data as in Fig. 2.

It has been proposed that whisking in rats has at least two discrete modes, foveal and exploratory. During exploratory whisking, the vibrissae are spread further apart, whisks have larger amplitudes and whisking frequencies are in the lower ranges. During foveal whisking, the vibrissae tips are concentrated in a smaller volume while being thrust forward, whisks have small amplitudes and whisking frequencies are in the upper ranges (Berg and Kleinfeld, 2003)⁠. Thus, different whisking modes result in different instantaneous spatial resolutions of the vibrissae array and varying rates of scanned volumes. While exploratory whisking is well suited for scanning large volumes at low instantaneous resolution, foveal whisking scans a smaller volume but at a higher resolution due to compression of the vibrissae array. Discrete whisking modes have not been described, but are thought to be present, in other species than rat.

Whisking modes can also be described on the basis of kinematic features. During exploratory whisking, retraction set-points are lower, protraction set-points occur later in the whisk cycle and amplitudes ($$\theta_{ps} - \theta_{rs}$$) are larger (Figs. 2a, 3). During foveal whisking, retraction and protraction set-points are higher, amplitudes smaller and angular velocities larger (Figs. 2a-b, 3). In the head-fixed rat, the transition between exploratory and foveal whisking is sharply delineated such that practically all foveal whisking occurs above 12 Hz with amplitudes smaller than 20 deg (Fig. 3). High-frequency, foveal whisking is driven almost entirely by the intrinsic sling muscles (Berg and Kleinfeld, 2003)⁠, which are composed primarily of type 2B muscle fibers thought to provide for the high maximum contraction velocities (Jin et al., 2004)⁠.

### Comparisons with saccadic eye movements

Vibrissae movements have been compared to saccadic eye-movements. Saccades are ballistic movements, with stereotyped trajectories. Whisks are not ballistic and differ from saccades both in terms of motor generation and sensory processing. The trajectories of saccades are smooth with peak velocities that correlate strongly with amplitudes, a correlation known as the saccadic 'main sequence'. Similarly, peak angular velocities during whisking can exhibit strong linear correlations with whisk amplitudes during limited sample windows (Bermejo et al., 1998)⁠. Across modes of whisking, however, there is no consistent linear correlation between velocity and amplitude (Fig. 3), and the movements of individual whisk cycles can be complex with variable velocity trajectories (Towal and Hartmann, 2008; Mitchinson et al., 2011)⁠. During saccadic eye movements, visual sensory processing is selectively blocked. During whisking, tactile information can be processed throughout the whisk cycle (O'Connor et al., 2013)⁠. Additionally, whisking trajectories are modulated by fast neuromuscular feedback during contact (Nguyen and Kleinfeld, 2005; Deutsch et al., 2012)⁠.

## Coordination with other behaviors

Whisking is coordinated with head, nose and body movements as well as respiration (Welker, 1964)⁠, These correlations occur both on cycle-by-cycle basis and on slower time scales. Whisking derives its rhythm from the brainstem respiratory central pattern generator (see Whisking Pattern Generation). Thus, vibrissae movements are coordinated with respiratory events, both during basal respiration and accelerated sniffing. During accelerated sniffing, above 5 Hz in rat, each inspiratory event is coordinated with individual whisk cycles. During basal respiration, below 3 – 4 Hz in rat, each inspiration is precisely synchronized to vibrissae protraction followed by multiple intervening whisks with decreasing amplitudes until the next breath occurs (Moore et al., 2013)⁠.

During development, the emergence of exploratory whisking occurs alongside improved locomotor abilities. Thus, vibrissae movements early in development are limited to unilateral retractions during head and body turns (Grant et al., 2012a)⁠. This behavior is also reflected in adult behavior. In both adult mice and rats, the difference in set-point between left and right side is modulated by running direction, such that right-side vibrissae are relatively retracted compared to left-side vibrissae during turning towards the right (Towal and Hartmann, 2006). Additionally, vibrissae are more protracted during faster running and individual strides phase-lock with whisking. Thus, during locomotion the vibrissae are oriented and scan along and ahead of the running trajectory (Mitchinson et al., 2011; Arkley et al., 2014; Sofroniew et al., 2014)⁠. This behavior is consistent with the observation that active vibrissae movements are required for localization along the longitudinal (forward direction), but not the transverse (lateral direction), axis (Krupa et al., 2001; Knutsen et al., 2006)⁠.

Vibrissae movements are also coordinated with finer head movements during tactile scanning of objects. Following contact and detection of an object with the vibrissae, rats approach objects while making small (~5 mm) vertical head movements that repeatedly press the microvibrissae against the object at rates up to 8 Hz (Grant et al., 2012b)⁠.

## Whisking in spatial exploration

Figure 4: The vibrissal array is displaced by translational shifts in position of the mystacial follicle array. In this example, the array of follicles was tracked by high-speed video. Each colored patch represents the extent of translation by a single follicle across a 30-minute session. The two black outlines inside each patch represent the extent of follicle translation during two different whisking epochs (5 – 10 s). It can be seen that across the two whisking epochs, a large static vertical translation of the entire follicle array occurred (unpublished results).

The vibrissae diverge from a small grid of sinus hair follicles arranged in rows (A through E) and columns (1 through 6 for the largest vibrissae; Fig. 4). When the vibrissae do not move, the spatial sampling is discrete and resolution low since the space between vibrissae is not sampled. During exploratory whisking, the entire vibrissae array is swept back and forth and thus samples the covered space continuously along the horizontal plane. The vertical space between vibrissae is sampled by two mechanisms. First, individual vibrissae elevate and lower by a small angle during protraction and retraction, thus tracing the contours of an approximately curved, elliptical cone in each whisk cycle (Bermejo et al., 2002; Knutsen et al., 2008b)⁠. Second, the entire vibrissae array can be vertically shifted by the transversus muscle which pulls the pad upwards when contracted and lowers it when relaxed (Hill et al., 2008)⁠ (Fig. 4). Thus, over time, the total volumes scanned by individual vibrissae during exploratory whisking overlap and comprise a complete coverage of the spatial, proximal volume out to the vibrissae tips. The total volume explored per unit time is a function of whisking frequency and the size of the search space. The search space is determined by vibrissae lengths, whisking amplitudes and the angular spread of the rostral and caudal most vibrissae (Huet and Hartmann, 2014)⁠. The positional envelope of the vibrissa during exploratory whisking is continuously modulated by running speed (Arkley et al., 2014; Sofroniew et al., 2014)⁠ and environmental contacts (Mitchinson et al., 2007; Munz et al., 2010)⁠.

## Kinematics during contact

Upon contact with objects and surfaces, whisking rodents rapidly modify their behaviors on multiple time scales. Environmental contact activates a fast within-cycle, disynaptic excitatory brainstem loop which results in increased protraction of all vibrissae on the contacting side. This fast neuromuscular modulation occurs without a change in vibrissae movement synchrony or whisk cycle duration (Sachdev et al., 2003; Nguyen and Kleinfeld, 2005; Deutsch et al., 2012; Matthews et al., 2014)⁠. Contact also results in orienting responses of the head and body which subsequently results in asymmetric modulation of vibrissae set-points on either side of the head (Mitchinson et al., 2007; Sofroniew et al., 2014)⁠ (see Coordination with other behaviors).

The vibrissae contact objects with their tips or shafts, resulting in bending and distortions of the intrinsic shape. These distortions result in axial forces that activate mechanoreceptors in the follicles. The range of forces and moments at the base of a vibrissa vary as a function of intrinsic curvature, radial contact location as well as the torsional orientation of the shaft (Quist and Hartmann, 2012)⁠. Simulations suggest that the magnitude of angular velocity has little effect on these contact signals, although the degree of continued protraction after contact does (Quist et al., 2014)⁠. Thus, whisking kinematics is a major determinant of contact related signals (see also Vibrissa Mechanical Properties).

There is evidence to suggest that both rats and mice adjust their whisking kinematics during, or in expectation of, contact. During exploration, rats rapidly modify the protraction set-point in response to contact (Mitchinson et al., 2007)⁠. In tasks where animals are trained to localize targets along the horizontal (rostro-caudal) axis, mice maximize contact with targets (O’Connor et al., 2010)⁠ and rats shift the angular position of their vibrissae to that of targets (Knutsen et al., 2003)⁠. Features of whisking kinematics also correlate with object position. The curvature of the vibrissa shaft correlate with the radial distance of a wall during locomotion (Sofroniew et al., 2014)⁠ and with the angular position of an object during object localization (Bagdasarian et al., 2013)⁠. Performance in an object localization task can additionally be predicted on the basis of whisking spectral power (Knutsen et al., 2003)⁠.

## Neural representations of whisking kinematics

Whisking is represented in the neural activity of multiple brain regions receiving vibrissal sensory inputs. A subset of neurons in the trigeminal (Gasserian) ganglion and in the posterior medial nucleus (POm) of the thalamus exhibit position dependence during artificial vibrissae movements in anesthetized rats (Szwed et al., 2003; Yu et al., 2006)⁠. In awake, freely-moving rats neurons have been found in the primary vibrissa somatosensory cortex (vS1) that exhibit phase dependence during whisking but do not report slowly varying whisking parameters such as amplitude (Fee et al., 1997; Curtis and Kleinfeld, 2009)⁠. The envelope of whisking is instead reported by efferent signaling in both primary vibrissa motor cortex (vMC) and vS1 (inherited from vMC; see Whisking control by motor cortex), suggesting that both afferent and efferent signals are required for cortical circuits to compute the absolute position, or angle, of the vibrissae and contacted objects (Ahrens and Kleinfeld, 2004; Hill et al., 2011)⁠.

## Evolution of whisking

Although species in several mammalian orders exhibit motile facial vibrissae, only a few members of the Muridae family of the Rodentia order (such as rats, mice and shrews), as well as some members of the marsupial Didelphimorphia order (opossums), whisk their vibrissae. Thus, the ancestral whisking species is likely to predate the earliest known placental mammal ancestor at about 65 Ma (O’Leary et al., 2013)⁠. Whisking species are often prolific climbers and nocturnal. Thus, whisking may have evolved as a strategy to navigate uneven, elevated surfaces in reduced lighting conditions. The evolution of the facial musculature that controls vibrissae movements have been traced to homologies in the gill-arch musculature involved in respiration in teleostome fishes (Huber, 1930)⁠. Thus, the coordination between whisking and respiration seen in rodents likely represents an early evolutionary re-purposing of facial musculature used for respiration into an active sensing organ. Interestingly, similarly specialized facial active sensory organs have evolved within other classes and orders of animals, such as the fleshy appendages of the star-nosed mole (Soricomorpha: Condylura cristata) and catfishes (Siluriformes). Whether movements of these organs are similarly coordinated with respiration is unknown.

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