Beyond cones: an improved model of whisker bending based on measured mechanics and tapering

Comparative morphology of the whiskers and faces of mice (Mus musculus) and rats (Rattus norvegicus)

Understanding neural function requires quantification of the sensory signals that an animal's brain evolved to interpret. These signals in turn depend on the morphology and mechanics of the animal's sensory structures. Although the house mouse (Mus musculus) is one of the most common model species used in neuroscience, the spatial arrangement of its facial sensors has not yet been quantified. To address this gap, the present study quantifies the facial morphology of the mouse, with a particular focus on the geometry of its vibrissae (whiskers). The study develops equations that establish relationships between the three-dimensional (3D) locations of whisker basepoints, whisker geometry (arclength, curvature) and the 3D angles at which the whiskers emerge from the face. Additionally, the positions of facial sensory organs are quantified relative to bregma-lambda. Comparisons with the Norway rat (Rattus norvegicus) indicate that when normalized for head size, the whiskers of these two species have similar spacing density. The rostral-caudal distances between facial landmarks of the rat are a factor of ∼2.0 greater than the mouse, while the scale of bilateral distances is larger and more variable. We interpret these data to suggest that the larger size of rats compared with mice is a derived (apomorphic) trait. As rodents are increasingly important models in behavioral neuroscience, the morphological model developed here will help researchers generate naturalistic, multimodal patterns of stimulation for neurophysiological experiments and allow the generation of synthetic datasets and simulations to close the loop between brain, body and environment.

Pre-neuronal processing of haptic sensory cues via dispersive high-frequency vibrational modes

Sense of touch is one of the major perception channels. Neural coding of object textures conveyed by rodents' whiskers has been a model to study early stages of haptic information uptake. While high-precision spike timing has been observed during whisker sweeping across textured surfaces, the exact nature of whisker micromotions that spikes encode remains elusive. Here, we discovered that a single micro-collision of a whisker with surface features generates vibrational eigenmodes spanning frequencies up to 10 kHz. While propagating along the whisker, these high-frequency modes can carry up to 80% of shockwave energy, exhibit 100× smaller damping ratio, and arrive at the follicle 10× faster than low frequency components. The mechano-transduction of these energy bursts into time-sequenced population spike trains may generate temporally unique "bar code" with ultra-high information capacity. This hypothesis of pre-neuronal processing of haptic signals based on dispersive temporal separation of the vibrational modal frequencies can shed light on neural coding of haptic signals in many whisker-like sensory organs across the animal world as well as in texture perception in primate's glabrous skin.

On the intrinsic curvature of animal whiskers

Facial vibrissae (whiskers) are thin, tapered, flexible, hair-like structures that are an important source of tactile sensory information for many species of mammals. In contrast to insect antennae, whiskers have no sensors along their lengths. Instead, when a whisker touches an object, the resulting deformation is transmitted to mechanoreceptors in a follicle at the whisker base. Previous work has shown that the mechanical signals transmitted along the whisker will depend strongly on the whisker's geometric parameters, specifically on its taper (how diameter varies with arc length) and on the way in which the whisker curves, often called "intrinsic curvature." Although previous studies have largely agreed on how to define taper, multiple methods have been used to quantify intrinsic curvature. The present work compares and contrasts different mathematical approaches towards quantifying this important parameter. We begin by reviewing and clarifying the definition of "intrinsic curvature," and then show results of fitting whisker shapes with several different functions, including polynomial, fractional exponent, elliptical, and Cesàro. Comparisons are performed across ten species of whiskered animals, ranging from rodents to pinnipeds. We conclude with a discussion of the advantages and disadvantages of using the various models for different modeling situations. The fractional exponent model offers an approach towards developing a species-specific parameter to characterize whisker shapes within a species. Constructing models of how the whisker curves is important for the creation of mechanical models of tactile sensory acquisition behaviors, for studies of comparative evolution, morphology, and anatomy, and for designing artificial systems that can begin to emulate the whisker-based tactile sensing of animals.

Demonstration of three-dimensional contact point determination and contour reconstruction during active whisking behavior of an awake rat

The rodent vibrissal (whisker) system has been studied for decades as a model of active touch sensing. There are no sensors along the length of a whisker; all sensing occurs at the whisker base. Therefore, a large open question in many neuroscience studies is how an animal could estimate the three-dimensional (3D) location at which a whisker makes contact with an object. In the present work we simulated the shape of a real rat whisker to demonstrate the existence of several unique mappings from triplets of mechanical signals at the whisker base to the three-dimensional whisker-object contact point. We then used high speed video to record whisker deflections as an awake rat whisked against a peg, and used the mechanics resulting from those deflections to extract the contact points along the peg surface. These results demonstrate that measurement of specific mechanical triplets at the base of a biological whisker can enable 3D contact point determination during natural whisking behavior. The approach is viable even though the biological whisker has non-ideal, non-planar curvature, and even given the rat’s real-world choices of whisking parameters. Visual intuition for the quality of the approach is provided in a video that shows the contour of the peg gradually emerging during active whisking behavior.

A novel stimulator to investigate the tuning of multi-whisker responsive neurons for speed and the direction of global motion: Contact-sensitive moving stimulator for multi-whisker stimulation

BACKGROUND

The rodent vibrissal (whisker) systcnsorimotor integration and active tactile sensing. Experiments on the vibrissal system often require highly repeatable stimulation of multiple whiskers and the ability to vary stimulation parameters across a wide range. The stimulator must also be easy to position and adjust. Developing a multi-whisker stimulation system that meets these criteria remains challenging.

NEW METHOD

We describe a novel multi-whisker stimulator to assess neural selectivity for the direction of global motion. The device can generate repeatable, linear sweeps of tactile stimulation across the whisker array in any direction and with a range of speeds. A fiber optic beam break detects the interval of whisker contact as the stimulator passes through the array.

RESULTS

We demonstrate the device's function and utility by recording from a small number of multi-whisker-responsive neurons in the trigeminal brainstem. Neurons had higher firing rates in response to faster stimulation speeds; some also exhibited strong direction-of-motion tuning.

COMPARISON WITH EXISTING METHODS

The stimulator complements more standard piezo-electric stimulators, which offer precise control but typically stimulate only single whiskers, require whisker trimming, and travel through small angles. It also complements non-contact methods of stimulation such as air-puffs and electromagnetic-induced stimulation. Tradeoffs include stimulation speed and frequency, and the inability to stimulate whiskers individually.

CONCLUSIONS

The stimulator could be used - in either anesthetized or awake, head-fixed preparations - as an approach to studying global motion selectivity of multi-whisker sensitive neurons at multiple levels of the vibrissal-trigeminal system.

Independent representations of self-motion and object location in barrel cortex output

During active tactile exploration, the dynamic patterns of touch are transduced to electrical signals and transformed by the brain into a mental representation of the object under investigation. This transformation from sensation to perception is thought to be a major function of the mammalian cortex. In primary somatosensory cortex (S1) of mice, layer 5 (L5) pyramidal neurons are major outputs to downstream areas that influence perception, decision-making, and motor control. We investigated self-motion and touch representations in L5 of S1 with juxtacellular loose-seal patch recordings of optogenetically identified excitatory neurons. We found that during rhythmic whisker movement, 54 of 115 active neurons (47%) represented self-motion. This population was significantly more modulated by whisker angle than by phase. Upon active touch, a distinct pattern of activity was evoked across L5, which represented the whisker angle at the time of touch. Object location was decodable with submillimeter precision from the touch-evoked spike counts of a randomly sampled handful of these neurons. These representations of whisker angle during self-motion and touch were independent, both in the selection of which neurons were active and in the angle-tuning preference of coactive neurons. Thus, the output of S1 transiently shifts from a representation of self-motion to an independent representation of explored object location during active touch.

Tapered Polymer Whiskers to Enable Three-Dimensional Tactile Feature Extraction

Many mammals use their vibrissae (whiskers) to tactually explore their surrounding environment. Vibrissae are thin tapered structures that transmit mechanical signals to a wealth of mechanical receptors (sensors) located in a follicle at each vibrissal base. A recent study has shown that-provided that the whisker is tapered-three mechanical signals at the base are sufficient to determine the three-dimensional location at which a whisker made contact with an object. However, creating biomimetic tapered whiskers has proved challenging from both materials and manufacturing standpoints. This study develops and characterizes an artificial whisker for use as part of a sensory input device that is a biomimic of the biological rat whisker neurosensory system. A novel manufacturing process termed surface conforming fiber drawing (SCFD) is developed to produce artificial whiskers that meet the requirements to be a successful mechanical and geometric mimic of the biological rat vibrissae. Testing the sensory capabilities of the artificial whisker shows improved performance over previous nontapered filaments. SCFD-manufactured tapered whiskers demonstrate the ability to predict contact point locations with a median distance error of 0.47 cm.

The Euler spiral of rat whiskers

This paper reports on an analytical study of the intrinsic shapes of 523 whiskers from 15 rats. We show that the variety of whiskers on a rat's cheek, each of which has different lengths and shapes, can be described by a simple mathematical equation such that each whisker is represented as an interval on the Euler spiral. When all the representative curves of mystacial vibrissae for a single rat are assembled together, they span an interval extending from one coiled domain of the Euler spiral to the other. We additionally find that each whisker makes nearly the same angle of 47^∘ with the normal to the spherical virtual surface formed by the tips of whiskers, which constitutes the rat's tactile sensory shroud or "search space." The implications of the linear curvature model for gaining insight into relationships between growth, form, and function are discussed.

The Sensorimotor Basis of Whisker-Guided Anteroposterior Object Localization in Head-Fixed Mice

Active tactile perception combines directed motion with sensory signals to generate mental representations of objects in space. Competing models exist for how mice use these signals to determine the precise location of objects along their face. We tested six of these models using behavioral manipulations and statistical learning in head-fixed mice. Trained mice used a whisker to locate a pole in a continuous range of locations along the anteroposterior axis. Mice discriminated locations to ≤0.5 mm (<2°) resolution. Their motor program was noisy, adaptive to touch, and directed to the rewarded range. This exploration produced several sets of sensorimotor features that could discriminate location. Integration of two features, touch count and whisking midpoint at touch, was the simplest model that explained behavior best. These results show how mice locate objects at hyperacute resolution using a learned motor strategy and minimal set of mentally accessible sensorimotor features.

Quantification of vibrissal mechanical properties across the rat mystacial pad

Recent work has quantified the geometric parameters of individual rat vibrissae (whiskers) and developed equations that describe how these parameters vary as a function of row and column position across the array. This characterization included a detailed quantification of whisker base diameter and arc length as well as the geometry of the whisker medulla. The present study now uses these equations for whisker geometry to quantify several properties of the whisker that govern its mechanical behavior. We first show that the average density of a whisker is lower in its proximal region than in its distal region. This density variation appears to be largely attributable to the presence of the whisker cuticle rather than the medulla. The density variation has very little effect on the center of mass of the whisker. We next show that the presence of the medulla decreases the deflection of the whisker under its own weight and also decreases its mass moment of inertia while sacrificing <1% stiffness at the whisker base compared with a solid whisker. Finally, we quantify two dimensionless parameters across the array. First, the deflection-to-length ratio decreases from caudal to rostral: caudal whiskers are longer but deflect more under their own weight. Second, the nondimensionalized radius of gyration is approximately constant across the array, which may simplify control of whisking by the intrinsic muscles. We anticipate that future work will exploit the mechanical properties computed in the present study to improve simulations of the mechanosensory signals associated with vibrissotactile exploratory behavior. NEW & NOTEWORTHY The mechanical signals transmitted by a whisker depend critically on its geometry. We used measurements of whisker geometry and mass to quantify the center of mass, mass moment of inertia, radius of gyration, and deflection under gravity of the whisker. We describe how variations in these quantities across the array could enhance sensing behaviors while reducing energy costs and simplifying whisking control. Most importantly, we provide derivations for these quantities for use in future simulation work.

Design principles of hair-like structures as biological machines

Hair-like structures are prevalent throughout biology and frequently act to sense or alter interactions with an organism's environment. The overall shape of a hair is simple: a long, filamentous object that protrudes from the surface of an organism. This basic design, however, can confer a wide range of functions, owing largely to the flexibility and large surface area that it usually possesses. From this simple structural basis, small changes in geometry, such as diameter, curvature and inter-hair spacing, can have considerable effects on mechanical properties, allowing functions such as mechanosensing, attachment, movement and protection. Here, we explore how passive features of hair-like structures, both individually and within arrays, enable diverse functions across biology. Understanding the relationships between form and function can provide biologists with an appreciation for the constraints and possibilities on hair-like structures. Additionally, such structures have already been used in biomimetic engineering with applications in sensing, water capture and adhesion. By examining hairs as a functional mechanical unit, geometry and arrangement can be rationally designed to generate new engineering devices and ideas.

Dynamic cues for whisker-based object localization: An analytical solution to vibration during active whisker touch

Vibrations are important cues for tactile perception across species. Whisker-based sensation in mice is a powerful model system for investigating mechanisms of tactile perception. However, the role vibration plays in whisker-based sensation remains unsettled, in part due to difficulties in modeling the vibration of whiskers. Here, we develop an analytical approach to calculate the vibrations of whiskers striking objects. We use this approach to quantify vibration forces during active whisker touch at a range of locations along the whisker. The frequency and amplitude of vibrations evoked by contact are strongly dependent on the position of contact along the whisker. The magnitude of vibrational shear force and bending moment is comparable to quasi-static forces. The fundamental vibration frequencies are in a detectable range for mechanoreceptor properties and below the maximum spike rates of primary sensory afferents. These results suggest two dynamic cues exist that rodents can use for object localization: vibration frequency and comparison of vibrational to quasi-static force magnitude. These complement the use of quasi-static force angle as a distance cue, particularly for touches close to the follicle, where whiskers are stiff and force angles hardly change during touch. Our approach also provides a general solution to calculation of whisker vibrations in other sensing tasks.

Vibrations play an important role in the sense of touch in many species, but exactly how they influence touch perception remains mysterious. An important reason for this mystery is the difficulty in measuring vibrations during touch. Mice are a powerful model system for investigating touch perception because they actively sweep their whiskers into objects and the resulting bending from touch can be video recorded. However, vibrations of the whiskers during touch are usually too small and fast to be seen. To overcome this limitation, we develop a new mathematical approach to calculating whisker vibrations from the speed at impact, maximum whisker bending during touch, and location of contact along a whisker, which is more easily observed. We find that vibration frequency and amplitude is strongly dependent on the location of contact along the whisker, which mice may use to deduce the distance between their face and touched objects. We confirm our calculations with high-speed imaging of whisker vibration during touch.

What the whiskers tell the brain

A fundamental question in the investigation of any sensory system is what physical signals drive its sensory neurons during natural behavior. Surprisingly, in the whisker system, it is only recently that answers to this question have emerged. Here, we review the key developments, focussing mainly on the first stage of the ascending pathway - the primary whisker afferents (PWAs). We first consider a biomechanical framework, which describes the fundamental mechanical forces acting on the whiskers during active sensation. We then discuss technical progress that has allowed such mechanical variables to be estimated in awake, behaving animals. We discuss past electrophysiological evidence concerning how PWAs function and reinterpret it within the biomechanical framework. Finally, we consider recent studies of PWAs in awake, behaving animals and compare the results to related studies of the cortex. We argue that understanding 'what the whiskers tell the brain' sheds valuable light on the computational functions of downstream neural circuits, in particular, the barrel cortex.

Active Touch and Self-Motion Encoding by Merkel Cell-Associated Afferents

Touch perception depends on integrating signals from multiple types of peripheral mechanoreceptors. Merkel-cell associated afferents are thought to play a major role in form perception by encoding surface features of touched objects. However, activity of Merkel afferents during active touch has not been directly measured. Here, we show that Merkel and unidentified slowly adapting afferents in the whisker system of behaving mice respond to both self-motion and active touch. Touch responses were dominated by sensitivity to bending moment (torque) at the base of the whisker and its rate of change and largely explained by a simple mechanical model. Self-motion responses encoded whisker position within a whisk cycle (phase), not absolute whisker angle, and arose from stresses reflecting whisker inertia and activity of specific muscles. Thus, Merkel afferents send to the brain multiplexed information about whisker position and surface features, suggesting that proprioception and touch converge at the earliest neural level.

Variations in vibrissal geometry across the rat mystacial pad: base diameter, medulla, and taper

Many rodents tactually sense the world through active motions of their vibrissae (whiskers), which are regularly arranged in rows and columns (arcs) on the face. The present study quantifies several geometric parameters of rat whiskers that determine the tactile information acquired. Findings include the following. 1) A meta-analysis of seven studies shows that whisker base diameter varies with arc length with a surprisingly strong dependence on the whisker's row position within the array. 2) The length of the whisker medulla varies linearly with whisker length, and the medulla's base diameter varies linearly with whisker base diameter. 3) Two parameters are required to characterize whisker "taper": radius ratio (base radius divided by tip radius) and radius slope (the difference between base and tip radius, divided by arc length). A meta-analysis of five studies shows that radius ratio exhibits large variability due to variations in tip radius, while radius slope varies systematically across the array. 4) Within the resolution of the present study, radius slope does not differ between the proximal and distal segments of the whisker, where "proximal" is defined by the presence of the medulla. 5) Radius slope of the medulla is offset by a constant value from radius slope of the proximal portion of the whisker. We conclude with equations for all geometric parameters as functions of row and column position.NEW & NOTEWORTHY Rats tactually explore their world by brushing and tapping their whiskers against objects. Each whisker's geometry will have a large influence on its mechanics and thus on the tactile signals the rat obtains. We performed a meta-analysis of seven studies to generate equations that describe systematic variations in whisker geometry across the rat's face. We also quantified the geometry of the whisker medulla. A database provides access to geometric parameters of over 500 rat whiskers.