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- Search: Mechanical[Title] AND Variables[Title] AND Underlying[Title] AND Object[Title] AND Localization[Title] AND along[Title] AND Axis[Title] AND Whisker[Title]
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# The mechanical variables underlying object localization along the axis of the whisker.

### Author information

- 1
- Janelia Farm Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia 20147, USA.

### Abstract

Rodents move their whiskers to locate objects in space. Here we used psychophysical methods to show that head-fixed mice can localize objects along the axis of a single whisker, the radial dimension, with one-millimeter precision. High-speed videography allowed us to estimate the forces and bending moments at the base of the whisker, which underlie radial distance measurement. Mice judged radial object location based on multiple touches. Both the number of touches (1-17) and the forces exerted by the pole on the whisker (up to 573 μN; typical peak amplitude, 100 μN) varied greatly across trials. We manipulated the bending moment and lateral force pressing the whisker against the sides of the follicle and the axial force pushing the whisker into the follicle by varying the compliance of the object during behavior. The behavioral responses suggest that mice use multiple variables (bending moment, axial force, lateral force) to extract radial object localization. Characterization of whisker mechanics revealed that whisker bending stiffness decreases gradually with distance from the face over five orders of magnitude. As a result, the relative amplitudes of different stress variables change dramatically with radial object distance. Our data suggest that mice use distance-dependent whisker mechanics to estimate radial object location using an algorithm that does not rely on precise control of whisking, is robust to variability in whisker forces, and is independent of object compliance and object movement. More generally, our data imply that mice can measure the amplitudes of forces in the sensory follicles for tactile sensation.

- PMID:
- 23595731
- PMCID:
- PMC3733083
- DOI:
- 10.1523/JNEUROSCI.4316-12.2013

- [Indexed for MEDLINE]

**, Schematic of the experimental situation treated in this study. A mouse protracts a single whisker (whisker C2) against a pole (highlighted in red) to determine its position. The pole exerts a force**

*A**F*on the whisker.

**, Mice could estimate radial distance from time-dependent or protraction-dependent stresses in the follicles (force-dependent radial distance measurement). These are produced by**

*B**M*

_{0},

*F*

_{ax}, and

*F*

_{lat}.

**, Triangulation with multiple whiskers. In this example, mice touch the object (red) with two whiskers (**

*C**w*

_{1},

*w*

_{2}), separated by

*d*. The radial distance

*D*can be extracted using θ

_{touch}of both whiskers as

*d*/tan(θ

_{touch}(

*w*

_{1}) − θ

_{touch}(

*w*

_{2})).

**, Triangulation with one whisker over multiple touches. In this example, mice touch the object two or more times (at times**

*D**t*

_{1}and

*t*

_{2}). The whisker follicle moves a distance

*d*from time

*t*

_{1}to

*t*

_{2}. The radial distance

*D*can be extracted as

*d*/tan(θ

_{touch}(

*t*

_{1}) − θ

_{touch}(t

_{2})).

**, Schematic of the task. Left, The pole is out of reach. Right, The pole is within reach of the spared (C2) whisker. Mice judge the radial distance to the pole and respond according to the pole's location (Go stimulus, lick, blue; No Go stimulus, no-lick, red).**

*A***, Top view of the pole positions. Trial types are defined by the location of the pole along the radial dimension (i.e., along the whisker).**

*B***, Temporal structure of behavioral trials (top, correct No Go, “correct rejection”; bottom, correct Go, “hit”). During the sampling period (typically 0.7–1 s), mice explored the object with their whiskers and licking was not scored. During the answer period, licking was scored as a response (circles, answer licks from three typical trials; mean reaction time of three mice, five sessions, 635 ms). After the response, animals were allowed to drink (2 s). If the animal failed to respond, as in the No Go trial, the pole ascended 2 s after the beginning of the trial.**

*C***, Performance during three typical behavioral sessions for three mice (fraction of trials correct, running average over 100 trials).**

*D***, Radial distance discrimination as a function of offset between Go and No Go stimuli for one mouse (16 sessions). Circles indicate mean performance averaged over one session (colors indicate the sequence of behavioral sessions across time); black line, average.**

*E***, Average performance (mean ± SD;**

*F**n*= 5 mice; 16–18 sessions per mouse). For some pole offsets, the error bars are smaller than the symbol.

**, Raw video frame (same as in**

*A**A*) showing a C2 whisker bent during contact with a pole (bottom view). The shadow of the mouse face is in the top left. All subsequent panels use the same video frame.

**, The tracker extracts a sub-pixel resolution series of points (**

*B**x*

_{i},

*y*

_{i}), representing the medial axis of the whisker.

**, The (**

*C**x*

_{i},

*y*

_{i}) points were fitted by a parametric curve (magenta) comprising fifth-order polynomials fitted to both

*x*- and

*y*-coordinates as a function of arc length along the whisker. Derivatives used in subsequent steps for computing angle at different points along the whisker were based on this fitted curve.

**, To avoid noise in whisker angle and length near the face induced by fur on the whisker pad, we effectively truncated the whisker at an intersection with a “mask' (cyan). Angle at the base of the whisker (θ**

*D*_{base}) was estimated from the angle at the intersection between mask and whisker; this is warranted because the whisker is very stiff and straight close to the face. Similarly, the arc length origin was set to occur at this intersection, rather than at the first tracked point, which could vary depending on how far “into the fur” a whisker was tracked (see for more details). A second-order polynomial was fitted to

*x*- and

*y*-coordinates in a small region of interest defined by arc length (

**) along the whisker. This region of interest was chosen to maximize the signal-to-noise ratio in curvature estimates (green region in**

*s***). Derivatives used in subsequent steps to measure whisker curvature were based on this “secondary” parametric curve.**

*F***, The location of the whisker follicle (indicated by the red X) must be known to compute moment at the follicle. The follicle location was estimated by linearly extrapolating for a fixed distance past the mask based on the angle at the base of the whisker (left magnified box). The location of whisker-object contact was computed by linearly extrapolating beyond the last tracked point along the whisker and defining the contact point as the closest point along this line to the center of the pole (right magnified box).**

*E***–**

*F***, Illustration of calculations. In these panels, the raw image from**

*I***–**

*A***is omitted, but all fitted quantities are shown: raw whisker (**

*E**x*

_{i},

*y*

_{i}) points (blue, but obscured because of successful fitting by the magenta curve), primary fitted curve (magenta), secondary fitted curve (green), mask (cyan), and follicle location (red X). The pole is illustrated schematically by the red circle at bottom. Images are slightly enlarged from those in (

**–**

*A***) for clarity.**

*E***, We defined azimuthal angles (θ) for the whisker and for vectors with respect to the axis perpendicular to the midline of the mouse (i.e., the medial-lateral axis; shown by gray dashed line). An angle of 0 implies parallelism with the medial-lateral axis. Protraction corresponded to increasing angle. The first step was to calculate the magnitude of moment at a point,**

*F**p*, along the whisker (

*M*

_{p}). This requires a measurement of change in curvature (from the undeflected case; Δκ

_{p}) and the bending stiffness (

*EI*

_{p}) at

*p*. In principle, we could have used any

*p*, but we chose

*p*for a high signal-to-noise ratio for curvature measurement. Because the whisker is linearly tapered, the larger curvatures occur farther from the whisker base, leading to more reliable measures of curvature. However,

*p*should not be too close to the pole because the lever arm inducing curvature eventually vanishes and tracking errors near the intersection of whisker and pole can interfere with curvature measurement. Bending stiffness of individual whiskers was estimated using measurements on isolated whiskers (see Materials and Methods; ).

**, The magnitude of the contact force (**

*G**F*), can be calculated from

*M*

_{p}, together with the length of the vector (

*r⃗*

_{p}) connecting

*p*to the site of whisker-object contact, and the angle (Θ

_{1}) between

*r*

_{p}and the contact force vector (

*F⃗*). Because contact force is perpendicular to the whisker at contact (with negligible friction), Θ

_{1}can be obtained using only the angle of

*r⃗*

_{p}(denoted θ

_{p}) and the angle of the whisker at contact (Θ

_{contact}).

**, Having measured**

*H**F*, the moment at the follicle (

*M*

_{0}) can be obtained after measuring the length of the vector (

*r⃗*

_{0}) connecting the point of contact to the follicle, and the angle (Θ

_{2}) between

*r⃗*

_{0}and contact force vector

*F⃗*.

**, Magnitudes of the axial (**

*I**F*

_{ax}) and lateral (

*F*

_{lat}) components of force can be calculated as the length of the projection of

*F⃗*onto the long and short axes of the whisker at the follicle, respectively. Inset shows how the angles between vectors are computed using the angle of the whisker at base (θ

_{base}) and the angle at contact (θ

_{contact}).

**, Illustration of the steps involved in measuring whisker angle and curvature from raw tracked video. Each image shows a projection through time across one trial. Raw**

*A**x-y*pairs representing the medial axis of the whisker (black) are first fitted with a parametric curve (magenta, shown overlaid on black). A secondary parametric curve (green) is then fitted over an arc-length region of interest (ROI). A “mask” (blue) truncates the whisker at its noisy edge near the fur on the face and defines the arc-length origin. Magnified panel at right shows the pixilation of the raw

*x-y*pairs (in black) and the smooth fitted curves (magenta and green).

**–**

*B***, Illustration of contamination of whisker tracing by fur on the face. Small hairs on the whisker pad can cause spurious measurements of shape and angle at the base of the whisker.**

*E***, Example time-projection through a trial showing how contamination by fur and lickport occlusion can interfere with measurement of shape and angle at base, as well as interfere with defining a constant region of arc-length (note how the green arc-length ROI is staggered from frame to frame).**

*B***, Schematic of problem shown in**

*C***for a single pair of frames.**

*B***, Example from**

*D***improved by the addition of a mask (blue), which effectively truncates the whisker at its intersection with the mask. The mask allows only the faithfully traced portion to be used for further analysis, and prevents the arc-length ROI (green) from being staggered from frame to frame.**

*B***, Schematic of the improvements shown in**

*E***for a single pair of frames.**

*D***–**

*F***, Illustration of the purpose of the secondary fitted curve (green), fitted over an arc-length ROI. A parametric curve will in general have a slightly different shape when fitted over different regions of even the same whisker in the same frame.**

*H***, Example of how the extent of the traced whisker in our videos could vary from frame to frame, for example due to the shadow of the pole entering the image.**

*F***, Because of frame-to-frame variability in the extent of the traced whisker, the curvature of the primary fitted curve (magenta) at a point reflected not only the true whisker curvature but also fitting artifacts. Magenta shading at top indicates region of whisker fitted. Curvature is measured at the point (**

*G**p*) indicated by the arrow, and the local region around this point is magnified at the bottom. Magenta curves at bottom show the fitted curve over the local, magnified region. Left and right columns indicate a frame in which the full whisker is traced (left) and a frame in which the whisker is traced only as far as the pole (right; pole indicated by gray circle).

**, To minimize artifacts due to fitting variable lengths of whisker, we fitted a secondary parametric curve over a constant arc-length region of interest. Curvature measured from this secondary fitted curve was much more reliable. Green box at top indicates the arc-length region of interest over which the secondary curve was fitted. Green curves at bottom show the fitted secondary curve over the local, magnified region.**

*H***, Scanning electron microscopy images of one C2 whisker toward the middle of the whisker (top: scale bar, 20 μm) and the tip of the whisker (bottom: scale bar, 10 μm).**

*A***, Radii of three C2 whiskers (**

*B**x*and *, light microscopy; o, electron microscopy).

**, Results of Young's Modulus estimation for one C2 whisker. Comparison of measured values and model predictions for deflections of a C2 whisker by force application at 1 mm increments along the whisker (different curves, indicated by legend). Model prediction error (**

*C**y*-axis) was calculated for a range of Young's Modulus values (

*x*-axis). Values of Young's Modulus that minimized the error between model and measurement clustered around 5 GPa. See Materials and Methods for details.

**, Schematic of the simulation (**

*D***,**

*E***). A conical whisker presses against a stiff pole. Forces act both normal to the whisker and tangential to the whisker (if the friction coefficient is not zero). The axial force pushes the whisker into the follicle, whereas the lateral force pushes the whisker laterally within the follicle. Friction results in a force pulling the whisker out of the follicle (**

*F**F*). Lateral stresses in the follicle are dominated by the bending moment on the whisker. Here, θ

_{t}_{total}= θ

_{base}− θ

_{touch}because protractions were not associated with follicle translation (compare with

*A*).

**, Simulated forces and bending moments for friction coefficient μ = 0, so that the pole exerts a force normal to the whisker (**

*E**F*= 0). Target, 5 mm; distracter, 8 mm.

_{t}**, Simulated forces and bending moments for friction coefficient μ = 0.3, so that**

*F**F*= 0.3

_{t}*F*. In the presence of friction, forces are not normal to the whisker. Furthermore, the axial force changes sign as a function of protraction. For small protractions, the whisker is pulled out of the follicle, whereas for larger protractions, the axial force pushes the whisker into the follicle. Target, 5 mm; distracter, 8 mm.

**, Time-lapse sequence showing one contact. The black line is the medial axis of the tracked whisker. The small circle indicates the cross section of the object (a thin pole). Distance from the pole to the follicle, 5 mm.**

*A***, θ**

*B*_{base},

*M*

_{0},

*F*

_{ax}, and

*F*

_{lat}for one correct Go trial. Green indicates manually scored contact periods. The initial time point in a contact period is defined as the first touch (first video frame showing contact between whisker and object). Blue circles indicate licks. The first answer lick defines the reaction time. Gray patch is after reaction time.

**,**

*C***, Same as**

*D***and**

*A***but for a correct No Go trial. Distance from the pole to the follicle, 8 mm.**

*B***, The distribution of the number of contacts for Go (blue) and No Go (red) trials before the reaction time (3 mice, 5 sessions).**

*E***, The fraction of trials correct as a function of the number of contacts for Go (blue) and No Go (red) trials (three mice, five sessions). Bars indicate performance (left**

*F**y*-axis); lines, number of trials with a given number of contacts (right

*y*-axis).

**–**

*G***, Moments and forces across trial types. Performance as a function of the maximum value of a mechanical parameter across trials for Go (blue) and No Go (red) trials (one mouse, one session). Bars indicate performance (left**

*I**y*-axis); lines, number of trials with a particular maximum moment or force (right

*y*-axis). Note that this mouse performed perfectly for the 100 consecutive trials shown.

**, Maximum bending moment.**

*G***, Maximum axial force.**

*H***, Maximum lateral force.**

*I***, Spread of the azimuthal angle at first touch (θ**

*A*_{touch}) across contacts of one session. Later (earlier) contacts within trials are coded by warmer (colder) colors. Distance from the pole to the follicle: Left, 5 mm, Go; right, 8 mm, No Go. Note that the spread of θ

_{touch}is larger for proximal objects (left) compared with distal objects (right), producing a possible azimuthal cue for object localization.

**, The larger spread of θ**

*B*_{touch}with changing

*d*

_{f}for more proximal object locations is a consequence of geometry.

**, Azimuthal angle at first touch (θ**

*C*_{touch}) as a function of whisker pad movement,

*d*

_{f}, for one session. Difference in the slope of Go (blue) versus No Go (red) data points represents greater impact of

*d*

_{f}on θ

_{touch}for more proximal objects (corresponding to Go). Target, 5 mm; distracter, 8 mm. Same session as in

**. Striped pattern reflects finite resolution of whisker tracking due to fixed pattern noise in video images.**

*B***, Correct and incorrect trials as a function of the spread of θ**

*D*_{touch}across contacts (three mice, five sessions). Each point corresponds to a trial. Points are randomly displaced in the

*y*-axis for clarity. Values of zero correspond to trials with single contacts.

**, Schematic showing the introduction of 3° of azimuthal jitter. See Materials and Methods for details.**

*E***, θ**

*F*_{touch}as a function of

*d*

_{f}with azimuthal jitter (±3°). Target, 5 mm; distracter, 8 mm (one mouse, one session). The slopes of Go (blue) versus No Go (red) points are indistinguishable.

**, Performance on sessions without (first 50 trials) and with (rest of the session, >100 trials) random azimuthal jitter (two mice shown by black and gray data points, five sessions). Azimuthal jitter consisted of azimuthal angle offsets (range ± 3°) added to pole positions across trials.**

*G***, Schematic illustrating computation of the protraction parameter θ**

*A*_{total}. θ

_{total}accounts for protraction due to changes in both θ

_{base}and

*d*

_{f}. The same whisker is shown early (gray) and late (black) during a protraction. Gray “

*x*” marks the intersection point of a line defined by θ

_{touch}with a line running along the anterior–posterior axis at the approximate lateral distance of the contact point for the Go position (5 mm from the follicle).

**–**

*B***, Bending moment (**

*D***), axial force (**

*B***), or lateral force (**

*C***), acting on the follicle as a function of the protraction parameter for Go (blue) and No Go (red) trials. All time points corresponding to contact periods in one session are overlaid with partial transparency.**

*D***, Schematic of the “illusion” experiment. Mice discriminated a proximal Go position (5 mm) and a range of distal No Go positions (7–13 mm). In a subset of unrewarded illusion trials, a compliant pole replaced the stiff pole in the Go position.**

*A***, Behavior for trials with stiff and compliant poles (five mice, 36 sessions). The fraction of trials with licks during the answer period is plotted for different conditions.**

*B***–**

*C***, Parameters producing stresses in the follicle for Go trials with the stiff pole (blue), No Go trials with the stiff pole (red), and unrewarded Go trials with the compliant pole (gray; one session).**

*E***,**

*C**M*

_{0}as a function of θ

_{total}.

**,**

*D**F*

_{ax}as a function of protraction.

**,**

*E**F*

_{lat}as a function of protraction.

**, Forces and moments at the follicle that could be read out for force-dependent radial object localization. Left,**

*A**F*

_{lat}. Right, Mice could use a combination of at least two of the three force/moment variables, with

*M*

_{0}and

*F*

_{ax}being the most likely.

**, Schematic illustrating how forces and the bending moment might couple to different directional stresses in the follicle. The whisker (thick black line) is embedded in the follicle (pink). It is coupled to the whisker pad through springs and rotates around the fulcrum (F). A indicates anterior; P, posterior; M, medial; and L, lateral. The bending moment and lateral force mainly cause compression or rarefaction in springs along the A-P axis, whereas the axial force affects the spring along the M-L axis. Note that little is known about stresses in the follicle that are actually sensed by mechanosensitive cells.**

*B***, Forces and bending moment in Go trials with the stiff pole (blue), No Go trials with the stiff pole (red), and Go trials with the compliant pole (gray; same session as**

*C**D–F*). Data from Go trials with the compliant pole (gray) is masked by the data from Go trials with the stiff pole (blue). Inset: The axial force as a function of bending moment for Go trials with the stiff pole, No Go trials with the stiff pole, and unrewarded Go trials with the compliant pole (same session as

*D–F*).

**, Simulated forces and bending moment in Go trials with the stiff pole (blue), with the compliant pole (gray) and No Go trials with the stiff pole (red). The dashed black line midway between Go and No Go indicates a putative decision boundary. Arrowheads indicate direction along the trajectories when protracting against an object. Inset: Projection in the**

*D**F*

_{ax}–

*M*

_{0}plane. The decision boundary separates distal objects and proximal objects in our binary choice task.

**–**

*E***, Whisker-stiffening experiment.**

*J***, Time-lapse images of whisker-object contacts for each trial category in the whisker stiffening experiment. Note the small curvature changes of the whisker upon contacting the object. Target, 5 mm; distracter, 8 mm.**

*E***, Model underlying the stiffened whisker experiment. The solid lines show simulated**

*F**F*

_{ax}as a function of

*M*

_{0}for Go (blue) and No Go (red) positions. Mice could measure

*F*

_{ax}and

*M*

_{0}and judge all points above a decision boundary (dotted black line) as corresponding to a distal object, and below the boundary as corresponding to a proximal object. Stiffening the whisker reduces axial force for a given bending moment (black arrows and dashed lines), dropping the red curve below the decision boundary. The model predicts that mice with stiff whiskers will misinterpret distal objects as a proximal object.

**, Behavior for trials with stiff and control whiskers (two mice, four consecutive sessions per mouse). Before every session (distance from the follicle, Go 5 mm, No Go 8 mm) three cut whiskers from the contralateral side were glued to the principal whisker with hairspray, with two of them antiparallel and the third parallel (see “Whisker trimming and manipulation” section). This stiffened the whisker and abolished its taper.**

*G**F*

_{ax}was therefore small compared with all values of

*M*

_{0}. Distal objects now produced combinations of

*M*

_{0}and

*F*

_{ax}that were usually only seen for proximal objects. The fraction of trials with licks during the answer period is plotted for different conditions. Mice now interpreted distal objects as proximal objects (unpaired

*t*test,

*p*= 0.8). The behavioral responses are consistent with the mice perceiving distal objects as proximal objects. Alternatively, the mice might have been generally confused, confounding the interpretation of the whisker stiffening experiment. Several lines of evidence argue against this. Stiffening whiskers on the contralateral side did not impair the mice in performing the task (unpaired

*t*test,

*p*< 0.05), ruling out nonspecific effects of the whisker manipulation. Additional evidence arguing that the mice continued to perform the object location task with stiffened whiskers is presented in the next panels.

**,**

*H***, We tested other metrics of mouse behavior for evidence of confusion. Reaction times in hit trials for two mice with stiffened whiskers (gray) and with the stiffened C2 whisker on the contralateral side (black). We scored touches in 100 trials of one session of one mouse with a stiffened whisker (mean reaction time, 0.4 s). In 79% of trials, the mouse touched the pole at least once before making its decision. If mice stopped trying to solve the task and rather were impulsively licking to get water rewards, we would expect the mice to start licking as soon as the pole drop was audible (0 s).**

*I***, Mean reaction time in hit trials in sessions with stiffened whiskers (gray) and sessions without whisker stiffening or stiffening of the contralateral C2 whisker (black).**

*J*### Publication type, MeSH terms, Grant support

#### Publication type

#### MeSH terms

- Algorithms
- Animals
- Computer Simulation
- Corneal Topography
- Cues
- Decision Making/physiology
- Exploratory Behavior/physiology*
- Functional Laterality
- Male
- Mice
- Mice, Inbred C57BL
- Microscopy, Electron, Scanning
- Models, Biological
- Physical Stimulation/methods
- Psychophysics
- Time Factors
- Touch/physiology*
- Vibrissae/anatomy & histology*
- Vibrissae/physiology*
- Vibrissae/ultrastructure