Cochlear tonotopy from proteins to perception

A ubiquitous feature of the auditory organ in amniotes is the longitudinal mapping of neuronal characteristic frequencies (CFs), which increase exponentially with distance along the organ. The exponential tonotopic map reflects variation in hair cell properties according to cochlear location and is thought to stem from concentration gradients in diffusible morphogenic proteins during embryonic development. While in all amniotes the spatial gradient is initiated by sonic hedgehog (SHH), released from the notochord and floorplate, subsequent molecular pathways are not fully understood. In chickens, BMP7 is one such morphogen, secreted from the distal end of the cochlea. In mammals, the developmental mechanism differs from birds and may depend on cochlear location. A consequence of exponential maps is that each octave occupies an equal distance on the cochlea, a spacing preserved in the tonotopic maps in higher auditory brain regions. This may facilitate frequency analysis and recognition of acoustic sequences.


INTRODUCTION
Sensory receptors, aside from detecting the presence of the appropriate physical stimulus, also convey broader information about its details. While the main function of auditory hair cells is to convert sound vibrations into electrical signals, these cells are also specialized for distinguishing between different acoustic frequencies. Such frequency discrimination is crucial for animal communication with relatives and survival from predators, though the underlying mechanisms and frequency range differ among vertebrate animals ( Figure 1). The auditory organ is homologous in all amniotes (reptiles, birds, and mammals, but not amphibians) and consists of a long tube, the cochlear duct, it operates only up to about 1 kHz, being limited by the activation speed of the K + channels. [3] Electrical tuning is the sole mechanism in turtles, but in other amniotes, additional mechanisms are recruited to broaden the hearing range above 1 kHz. For instance, mechanical resonances of the hair bundles in lizards may extend frequency tuning up to 5 kHz. [4,5] Mammals lack electrical tuning, and frequency selectivity is achieved primarily by a mechanical resonance due to the mass and stiffness of the basilar membrane. However, such frequency selectivity achieved by passive resonance is greatly amplified by outer hair cells, contracting and elongating in synchrony with the cycles of the receptor potential. [6] Enhancement of sensitivity is underpinned by the voltage-dependent motor protein prestin [7,8] to expand the upper frequency limit to over 100 kHz. Avian basilar papillae possess two kinds of hair cells like mammals, with "tall" inner hair cells synapsing on afferent nerve terminals and "short" outer hair cells with a possible amplificatory role. There is evidence that prestin may also be employed in birds over the upper frequency range, 1 to 5 kHz, [9] but hair cells tuned below 1 kHz are served by an electrical resonance. [10,11] In all amniotes, the hair-cell epithelium comprises a bank of resonant (electrical or mechanical) filters, each tuned to a different characteristic frequency (CF). The CFs are laid out along the cochlea as a tonotopic map, in which the resonant frequency varies systematically from one end to the other. The CF is thus set by cochlear location. With one or two exceptions, low frequencies are encoded at the apex of the cochlea and high frequencies at its base.
The aim of this review is to relate the tonotopic map to gradients in cellular properties, particularly those of the hair cells, and consider how positional information is specified. Do all maps have the same polarity, and reflect similar cellular features? The variation in cellular properties underlying such maps represents one of the most precise patterns of cellular organization in the body and is the first step in pitch discrimination, which is replicated at each stage of the auditory pathway.
I shall also assess the current evidence on the mechanism for establishing the map during development. In its simplest form, this process is thought to involve a diffusional gradient in a secreted morphogen protein determining the properties of the cellular and extracellular elements along the cochlea. But there is still incomplete knowledge of the identity of the morphogens or their generality among species.

Tonotopic maps in birds and mammals
The tonotopic organization of the cochlea was first seen in isolated temporal bones of human cadavers and other animals by Georg von Békésy, [15] and the conclusion was subsequently confirmed by recording electrical responses near auditory threshold in a variety of other animals. The most detailed results are from the cat, where characteristic frequencies (CFs) of auditory nerve fibers were first determined from threshold tuning curves and the fibers were then labeled by ionophoresis of horseradish peroxidase to define their cochlear origin. [16] The mean relationship between CF and normalized distance along the basilar membrane, d, is exponential over 80% of the cochlea, though it is compressed at the apex, where a smaller distance encodes a larger frequency range. Thus, the logarithm of the CF is proportional to the distance, d, of the cell from the apex (Figure 2A). A similar exponential representation has been found in other mammals including the rat, [17] gerbil, [18] mouse, [19] and chinchilla. [20] The tonotopic relation between CF and d is can be described by the equation [21] : where A, α, and k F are constants; for fits to measurements, k F lies between 0 and 1 and accounts for the small apical compression; when k F = 0, this generates an exponential function over the entire cochlea.
An exponential frequency map is also evident in the basilar papilla of the chicken [22,23] ( Figure 2C) and the pigeon. [24] Frequency tuning in the turtle basilar papilla, deduced from electrical resonance of the hair cells, also increases exponentially, albeit over a narrower frequency range. [25][26][27] This exponential increase in the CF of the sensory neurons with position is present in all amniotes despite the differences in tuning mechanisms among species. It is remarkable that the exponential maps are superimposable despite the substantial differences in cochlear dimensions; for example, the gerbil has a 12 mm long cochlea and the cat is on average 25 mm, but their maps are identical when scaled for cochlear length ( Figure 2A). As will be seen later, the mathematical form of the map may have significance for the developmental process underlying its formation: it could reflect diffusion and exponential decay of a morphogen secreted from one or other end of the organ. [28] Anomalous tonotopic maps For those animals considered so far, the exponential relation spans 80% or more of the frequency range. However, some mammals are anomalous and deviate from this quantitative picture by harboring an acoustic fovea that encompasses a smaller range of frequencies with finer res-olution; in such mammals, the fovea may occupy at least half of the cochlea. This cochlear region is referred to as an acoustic fovea because of its increased frequency resolution, by analogy with the retinal fovea which possesses a greater spatial resolution than the extra-fovea. The most striking examples are the echolocating bats ( Figure 2B), where the narrow range is for resolving the Doppler shifted echoes from their single frequency call. In this frequency span, a call emitted from the bat is reflected by objects in the environment, including moths.
The frequency modulation and delay of the echo provide the bat with information about the direction and motion of its source, necessitating finer frequency resolution over this limited range. For example, in the mustache bat, Pteronotus parnelli, the frequencies from 54 to 70 kHz, around the call frequency of 60 kHz, cover 50% of the cochlear length [29] ( Figure 2B). At the other extreme of the acoustic spectrum is the African mole rat, Cryptomys hottentotus, with an acoustic fovea between 0.6 and 1 kHz. By analogy with echolocating bats, about half of the cochlea in the mole rat is devoted to analysis of this narrow frequency band; other frequencies up to 12.6 kHz are encoded over the non-foveal region toward the base. [30] It has been speculated that the low frequencies are utilized for communication with other members of the species in subterranean tunnels. In both echo-locating bats and mole rats, the cochlea's tonotopic map is discontinuous and includes zones of abrupt slope change.
Another type of abnormality is present in Gekkonid lizards, such as the Tokay gecko (Gekko gecko) [31] the crested gecko (Correlophus ciliatus) and the mourning gecko (Lepidodactylus lugubris). [4] Even though there exists a continuous tonotopic map, the orientation of the map in geckos is of opposite polarity to that of mammals and birds, with neurons tuned to high-CFs located toward the apex of the basilar papilla and low-CFs toward the base ( Figure 2D). The Gekkonid basilar papilla also has an unusual structure. It partitions into a conventional low CF region with hair bundles covered by a continuous tectorial membrane, and a high CF region where hair cells have elongated hair bundles enclosed in discrete clumps of tectorial material known as sallets. [5,32] In the lizard salletal region, hair bundles heights decrease from 16 μm at a CF of 0.4 kHz to 5 μm at 5 kHz and compared to other amniotes are unusually tall, but display the same gradient in height with CF: tall bundles at low CF and short bundles at high CF. The tectorial sallets mass load the bundles, and together with the hair bundle stiffness confer a mechanical resonance at the appropriate CF. [4,33] Recall that for a mechanical resonance produced by a mass M and a stiffness K (as with displacement of a metal ball suspended from the end of a spring, causing it to oscillate up and down) the resonant frequency F R can be calculated from: The resonant frequency is raised by an increase in stiffness, so a systematic change in hair bundle height generates a gradient in CF. [4] A homologous anatomical arrangement, with division of the basilar papilla into a salletal region encoding high CFs and a non-salletal region coding for low CFs, is seen in the bobtail skink (Tiliqua rugosa), but the orientation of the tonotopic map, high CFs at base, is conventional, [5] F I G U R E 2 Conventional and anomalous tonotopic maps determined from tuning curves of auditory nerve fibers and hair cells. (A) Cat, filled circles [16] ; gerbil (open circles [18] fit with the exponential map, Equation (1), with A = 0.456, α = 0.048, k F = 0.8; from. [21] (B) Mustached bat, filled circles. [29] (C) Chicken, auditory nerve fibers (filled squares, [22] ) and tall hair cells (filled circles. [10] ) (D) Gekkonid lizard, auditory nerve fibers, blue circles [31] ; hair cells, black circles. [4] All position measurements normalized to mean length of cochlea: cat, 25 mm; gerbil (Meriones unguiculatus), 12 mm; bat (Pteronotus parnelli); 14 mm; chicken 4 mm; geckos, 1.5 mm (hair cell, crested gecko Correlophus ciliatus), 2.0 mm (nerve fibers, Tokay gecko, Gekko gecko).
and thus opposite to the Gekkonidae. This observation provides the important conclusion that the mechanism for determining the map is independent of its orientation. However, the significance of the reversed map for Gekkonid hearing is unclear.

Gradients in properties underlying frequency maps
In all cochleae, the tonotopic frequency map is associated with longitudinal gradients in the physiological and morphological properties of the hair cells and of the cochlear duct. [12] As might be expected, the variable features differ according to the tuning mechanism, some being directly related, others more peripheral. For electrical tuning, there is a primary gradient in the density and kinetics of the hair-cell large-conductance Ca 2+ -activated K + channel (Kcnma1, here abbreviated BK Ca ) underlying the resonance ( Figure 3A-D) [3,[34][35][36][37] ; variation in the BK Ca channel is accompanied by concomitant changes in the number of voltage-dependent (Ca1.3) Ca V channels [34,38] and in the intracellular calcium buffer, calbindinD28k. [39,40] For both turtle and chicken hair cells, the BK Ca and Ca V channel densities increase from apex to base, resulting in larger and faster electrical feedback to produce hair cells tuned to higher frequencies. Such feedback arises because, on depolarizing the hair cell membrane, opening of the BK Ca channel draws the membrane potential negative, but with F I G U R E 3 Tonotopic organization in the basilar papilla of the turtle. (A) Three hair cells with CFs increasing two-fold, depicting the tonotopic changes in BK Ca potassium channels and Ca V calcium channels with CF. For the BK Ca channel there is an increase in number and decrease in activation time constant produced by binding fewer beta subunits. Note the occupancy of the beta subunit goes from 1.0 to 0.5 to 0.25 with an increase in resonant frequency. (B) Resonant frequency of hair cell electrical tuning [25,26] papilla length = 0.8 mm. (C) Variation in number of BK Ca channels per cell. [34] (D) Decrease in BK Ca channel linear time constant. [35] a delay dictated by the speed of channel activation, so generating resonance. The BK Ca channel beta subunits (Kcnm1b and Kcnm4b) are a major factor controlling the BK Ca channel variation, and are expressed as gradients along the papilla, from their highest concentration at the low-frequency apex. [41] The presence of the BK Ca channel beta subunit slows the kinetics of the BK Ca channel alpha subunit. [41,42] The activation time constant is thought to be continuously adjusted by the fractional occupancy of the channel by between one and four beta subunits, [43] the greater the occupancy, the slower the channel. Apart from slowing the kinetics, the beta subunit may also decrease BK Ca channel expression. [44] A declining concentration of the beta subunit toward the base of the cochlea could in theory control both the increasing BK Ca channel density and the faster kinetics. [45] In contrast to birds and reptiles, mammals possess a cochlear frequency selectivity stemming from a mechanical resonance of the cochlear cross-section. The hair cells are housed in an organized conglomerate of specialized supporting cells and capped by a gelatinous tectorial membrane, together referred to as the organ of Corti ( Figure 4A). The mechanical resonance is partially attributable to the local stiffness of the basilar and tectorial membranes along with the dimensions of the cochlear cross-section [15,[46][47][48][49] (Figure 4A,B). Both the width and thickness of the basilar membrane vary from apex to base to generate a several hundred-fold change in stiffness along the cochlea. The large range stems from stiffness being a third-power function of dimensions: a fourfold increase in thickness and a halving of width, as observed, cause a 256-fold stiffness variation. [50] The stiffness of the tectorial membrane is also location specific and is in  [53,57] stiffness of three outer hair cell hair bundles (red circles), calculated from hair bundle heights and stereociliary number and calibrated from [111] have comparable stiffness to the tectorial membrane. Note stiffness axes in (C) and (D) are identical allowing stiffness of the tectorial membrane and hair bundles to be compared. Stiffness of the basilar membrane [47] and tectorial membranes [48] reproduced with permission of the authors.  (2), is thought to originate in the mass of the organ of Corti and the mass of moving fluids. [50] The tuning is mechanical, depending on the structure of the cochlear cross-section. Thus, a dichotomy exists between mammalian and non-mammalian amniotes, reflecting differences in tuning mechanisms. The changed features of the auditory system in mammals probably evolved to extend the frequency range above 5 kHz.

Positional markers
A positional marker for tonotopy common to all amniotes is the organization of the hair bundle, the length and number of the stereocilia.
This is best exemplified in the chicken basilar papilla, [51] where hair bundle height, H, decreases five-fold from apex to base and the number of stereocilia, (Ns) increases by a similar amount, from 50 at the apex to 300 at the base. Since bundle stiffness K B is given approximately by K B = N S /H 2 , these two factors will increase stiffness by at least 150 times. Gradients of comparable range have been documented in mammals [52][53][54] and reptiles. [4,55,56] Despite changes in bundle morphology being a generic feature of all auditory organs, the role in frequency tuning is not usually obvious; more importantly, variation in stereociliary complement is indicative of the numbers of mechanotransducer (MET) channels and produces an increase in sensitivity from apex to base. [57,58] Thus, given a fixed number of MET channels per tip link, the amplitude of the MET current is two to three-fold larger in basal high-CF hair cells than in apical low-CF ones. [10, [59][60][61] Only in lizards are the gradients in height and number of stereocilia directly relevant to frequency tuning as they underscore the changes in hair bundle stiffness that contribute to the mechanical resonance of each hair cell. [4,33] Shorter hair bundles are stiffer and will possess higher resonant frequency. By contrast, the stereociliary heights in non-lizards are too short, and the bundles too stiff to endow a mechanical resonance at the CF appropriate for the location. [55] The gradients in bundle morphology, as well as those for calbindinD28k, appear early in embryonic development and can be used as a positional marker in experiments to study the origins of tonotopy. [62,63]

Exponential morphogens gradients
The factors responsible for organizing tonotopy have been studied in both chicken and mouse on the assumption that graded levels of a diffusible morphogen provides instructive clues to position along the cochlea, as originally proposed for limb development. [64,65] Diffusion of a morphogen from one end of the cochlea would be the simplest explanation for the exponential tonotopic map seen in most amniotes, as steady state diffusion of a substance from a point source can under some conditions yield an exponential decline in concentration from the source. How the morphogen concentration is read out at each position along the axis into a discrete cellular state is unknown. An exponential morphogen gradient is unlikely to be generated by free diffusion of the morphogen, and must require a restricted diffusion, due to loss by uptake and destruction at points along the epithelium. This process can be modeled as analogous to heat conduction along a semi-infinite rod, heated at one end, with heat loss from the surface of the rod. [66] The rod, like a poker, is hot at one end and cool at the other. For restricted diffusion, the governing equation is where the morphogen concentration, C, depends on distance x along the cylinder, D is a diffusion coefficient and λ is a constant representing the rate of substance absorption or metabolism. The "d" prefixes in Equation (3) denote differentiation with respect to distance x or time t. This analysis assumes that the transverse concentration of the morphogen is uniform. The solution in the steady state (dC/dT = 0) is This exponential gradient could account for the exponential frequency map provided the space constant (D/λ) 1/2 is less than the length of the organ.

Morphogen specification of tonotopy in non-mammals
The ubiquitous morphogen sonic hedgehog (SHH), secreted early in development by the notochord and floorplate, is required for formation of the chicken basilar papilla and mouse cochlea. [63,67] Establishment of the cochlear apex requires a higher SHH protein concentration than does the base, indicated by expression of its receptor "patched." The differential concentration has been exploited to modulate the map by bathing developing cochleae in beads soaked in SHH [63] ; the SHH can leave the beads and diffuse some multicellular distance. This manipulation causes the base of the chicken basilar papilla to become more apical-like as assessed by hair bundle structure and calbindin expression in embryonic day (E)16 birds. [63] SHH soaked beads also caused apical genes to be upregulated in the base of the developing mouse cochlea.
In the chicken, the pathway downstream of SHH is thought to involve bone morphogenetic protein (BMP7) which is expressed at a several fold higher level in the apex [62] (Figure 5). BMP is an important morphogen. Dorsoventral patterning of the early vertebrate embryo depends on a concentration gradient in BMP, the highest concentration specifying the ventral region. [68] Culturing early embryonic basilar papillae has shown that determination of the tonotopic map is complete after E6.5. Bathing cultures, isolated at this age and cultured for a further 6 days, in BMP7 in the bulk medium, or in beads soaked in BMP7, induces an apical phenotype in the basal region as judged by hair bundle structure or calbindin expression. [62] This effect is reproduced in ovo by electroporation of the E2.5 otocyst with a vector containing a BMP7-cDNA construct. Expression of the BMP7 construct produces changes in basal hair cells that are comparable with the effects of BMP7 protein treatment in vitro. The action of the BMP7 morphogen can normally be assessed by monitoring phosphorylation of its intracellular signal transducer Smad, but in the chicken basilar papilla BMP7 seems to operate via a non-canonical Tak1/Map kinase pathway [62] .
There is no guarantee that the spatial gradient in the effect of BMP7 mimics its concentration gradient, as interactions with antagonists and intracellular signaling may distort the exponential map. [68,69] BMP7 is assumed to be secreted by supporting cells at the distal (apical) end of the basilar papilla and that it diffuses extracellularly to activate cells along the length of the papilla. The cell type from which BMP7 is secreted has not been identified, nor is it known whether it diffuses alone or bound to another protein that will slow diffusion. [69] Some evidence suggests that the positional information may be retained in the supporting cells along the chicken basilar papilla.
Destruction of the hair cells in adult chickens over a limited frequency range, either by injection of ototoxic drugs such as gentamicin or delivery of loud sounds, initiates, after several weeks, regeneration of the hair cells from the supporting cells. [70] While it has been suggested that the map is duplicated in the new hair cells, [71] detailed characterization of the phenotype of the new hair cells (e.g., from hair bundle structure) has not been performed. Studies of functional recovery in the pigeon basilar papilla following exposure to the ototoxic agent gentamicin have shown that the response properties of auditory nerve fibers innervating areas of hair cell damage are abnormal. It was concluded that functional recovery was incomplete especially in cells tuned to higher frequencies. [72] As is discussed below, the mammalian cochlea differs in several ways from non-mammals such as birds, and hair cell regeneration after ototoxic or noise trauma does not occur in the mammalian cochlea. [73] Activation at a given location is normally considered to depend on the concentration of the morphogen. However, it seems likely that signaling along an epithelium several hundred microns in length (at E6.5) will become increasingly noisy with distance from the source.
One way around this problem is to have a simultaneous opposing gradient in a second morphogen ( Figure 5C). Differences in expression between apex and base were demonstrated by RNA-seq and showed  [62] reproduced with the permission of the authors.
A counter gradient in CHRDL-1, [62] which acts as a BMP7 antagonist, could accentuate formation of the map. Retinoic acid, produced from dietary vitamin A, is also involved. For retinoic acid, there is a basalapical gradient in the retinoic acid synthesizing enzyme RALDH3, and an opposite gradient in the metabolizing enzyme CYPC1. [74] While gradients in all morphogens are present at E6.5, they can alter or reverse with development. [62] For instance, BMP7 shows an apical-basal gradient at both E6.5 and E14, but the basal-apical gradient in CHRDL1, present at E6.5 disappears by E14. Similarly, the mRNA for RALDH3 was 16-fold higher at the base (proximal end) than apex (distal end) at E6.5 but this basal-apical gradient had reversed by E14. [74] If the tonotopic map is fully established at E6.5, it must be held in stasis for several days before its effects are manifested in the organ. The tonotopic variation in hair bundle structure is not fully developed until after E11. [75]

Morphogen specification of tonotopy in mammals
Several lines of evidence argue that the BMP7 pathway does not regulate tonotopy in the mammalian cochlea. BMP7 is not graded along the tonotopic axis nor is it positively regulated by SHH signaling in the developing mouse cochlea. [63] Moreover, both BMP7 and BMP4 are down regulated by constitutively activated SHH signaling in the mouse cochlea, implying that SHH regulates BMPs differently between the avian and mouse cochleae. The structure of the mammalian cochlea differs substantially from the basilar papilla of non-mammals, particularly in the variety of specialized supporting cells, such as pillar cells and Deiters cells, that partition the organ of Corti. [1] There is also a difference in the time course of its development relative to non-mammals. The terminal mitosis of the hair cell sensory progenitors occurs at around E12.5, beginning at the apex and proceeding toward the base over the next 2 days. [67] Differentiation of the hair cells then progresses in the opposite direction, from base to apex.
The factors governing differentiation are unknown, but Activin A (a member of the TGF-β superfamily of cytokines) and its antagonist Follistatin have been proposed to be important for its timing. [76] Activin and Follistatin are known to have major roles in cellular proliferation and differentiation. [77] Other genes that might be involved in tonotopy were identified from RNA-seq by their displaying an apex-base expression gradient, beginning at the time of cochlear specification and maintained throughout embryonic development. [78] As in the developing chicken, multiple genes are expressed differentially between apex and base of the mouse cochlea. [79] In E15.5 cochleae, these genes include Fst (Follistatin), Msx1 (a Homeobox gene) and Efnb2 (EPHRINB2, a ligand for EPH receptors involved with cell-cell interactions), all with greater expression at the apex than the base; and Inhba, (encoding a subunit of Activin A), which is expressed more at the base. [79] It has been shown, using a conditional Fst knockout, that Follistatin is required for maintenance of the apical cochlea, but, unlike SHH, it is not needed for its induction. In the Fst knockout, a shorter cochlea, lacking its apical region, is produced. [79] Fst knockout leads to down-regulation of Msx1 and Efnb2 at the apex, and results in lowfrequency hearing loss (3 to 8 kHz), reflecting absence of the cochlear apex.
These results suggest the apical portion of the mammalian cochlea is special and differs from the middle and base in its development.
Several observations indicate functional differences between apex and base. The apical portion of the tonotopic map exhibits a curved deviation from the logarithmic plot, with a slope change at low frequencies encoded in the apical 20% of cochlea (Figure 2A). [16,18,53] In addition, the auditory nerve tuning curves display shape changes with position along the cochlea ( Figure 1A). Cells tuned to frequencies above 2 kHz have a narrow sharply tuned peak and a lower frequency tail, whereas cells tuned to frequencies below 1 kHz have a broad selectivity curve often with a small tail above the CF for cats and gerbils. [1,80,81] This frequency division has been correlated with abrupt changes in the phase behavior of chinchilla auditory nerve firing, [82] occurring at about 2 kHz. Since the mouse does not hear below 3 kHz, [83] its auditory nerve tuning curves lack substantial shape changes, [83] and so functional divisions of the cochlea into apical and basal segments may not be relevant. Nevertheless, the mouse apex is known to be unusual in exhibiting stem cell-like behavior into adults, manifest at 1 year of age as expression of nestin in the Deiters cells, one of the types of supporting cell connected to outer hair cells. [84] It is possible that other unknown morphogens downstream of SHH specify the tonotopic organization over the entire mammalian cochlea.
A variety of morphogens may be required to reflect the more diverse cellular structure of the mammalian cochlea. The organ of Corti comprises not only two types of hair cell but also at least five different types of supporting cells compared to one or two types in the chicken. [14] These differences in supporting cell identity may account for the lack of hair cell regeneration following trauma in the mammalian cochlea relative to the chicken basilar papilla, where new hair cells originate from the supporting cells. [71] The different categories of mammalian supporting cells run the length of the cochlea, and in any segment are divisible into a medial cellular stripe that includes inner hair cells, and a lateral band encompassing outer hair cells. The two types of hair cell, with distinct morphological and functional properties, have distinct longitudinal maps. For example, outer hair cells display an apical-basal decrease in cell length and bundle height [1,53] absent in inner hair cells; also, the number of mechano-electrical transducer channels increase toward the base in outer hair cells but not in inners. [85] These bands may have their own longitudinal organizers and be influenced by transcription factors that set up radial organization of the cochlear duct [86] and the functional divergence of inner and outer hair cells. [87,88] CENTRAL TONOTOPY

Central tonotopic maps
The auditory signals originating from the two ears are processed and combined over multiple subcortical nuclei as they head toward the auditory cortex ( Figure 6A). The exponential tonotopic map, once established in the cochlea, is preserved in the higher auditory circuits ( Figures 6B,C), in the brainstem, [89] central nucleus of the inferior colliculus (ICC) [90,91] and the ventral division of the medial geniculate, MGV, [92] which projects to the primary auditory cortex (AI) ( Figure 6E).
Although early electrophysiological recordings demonstrated a rough tonotopic organization in AI, the precise arrangement had been less clear. [93,94] One problem that has confounded tonotopic mapping in the auditory cortex is that a fraction of the neurons has more than one peak in their frequency tuning curves. A range of techniques have been applied, but the most successful has been Ca 2+ imaging, using the genetically encoded sensor, GCaMP, targeted with a neuron-selective promoter such as Syn1 or Thy1. [95,96] Ca 2+ imaging provides a measure of the neuronal activity from which frequency-tuning curves can be ascertained and is preferable to single electrode recordings as it affords a better spatial sampling and overall picture in a single preparation. Using two-photon Ca 2+ measurements, tonotopy has been described in the primary auditory cortex of unanesthetized and behaving mice ( Figure 6E). However, differing degrees of frequency tuning among neighboring neurons, and between cortical layers, have been reported, ranging from well-ordered local maps [95] to moderately heterogeneous tuning. [96,97] Furthermore, an ultrasonic area (UF) with CFs from 49 to 70 kHz exists in the mouse next to the high-CF pole of AI and may not show strong tonotopic organization. [98] Apart from tonotopy, cortical neurons exhibit more complex selectivity for sound features than do subcortical neurons. These additional features include the time varying aspects of the acoustic stimulus, [99] which may lead to extraction of the pitch of the sound. Pitch is a perceived attribute of sounds that for simple tones is equivalent to the frequency. However, for more complex sounds, it is related to the fundamental (lowest) frequency component and may be derived from a combination of spectral clues (tonotopy) and the temporal envelope or periodicity of neuronal discharge, often referred to as phase locking. [100] For example, a pure tone at middle "C" has a frequency of 260 Hz; however, a middle "C" played on a violin or clarinet will contain multiple harmonics due to resonances of the musical instrument but will still retain the pitch heard as "C." In the marmoset, an exponential tonotopic map exists in AI [101] and a pitch center is thought to occur in a neighboring cortical area abutting the low-CF region of AI. [100,102] A similar separation of tonotopy and pitch discrimination has been inferred from fMRI signals in the human auditory cortex. [103] Every auditory area exhibits an exponential frequency-to-place mapping with the consequence that each doubling in frequency (octave) occupies approximately equal spacing on the brain nucleus.
Why should the topographical representation of sound frequency in the central nuclei remain exponential? Is it the most economical arrangement for representing spectral information as it allows interactions between cells tuned to similar frequencies? The tonotopic map of the cat ICC shows a stepwise progression in CF, [90] a feature also observed in the rat [91] ; each step has been referred to as "frequencyband lamina," and is about 0.3 octaves in width. [104] If it is assumed that there are iso-frequency laminae, then synaptic interactions between neurons tuned to different frequencies will take place between layers, and neighboring layers will possess constant ratios of frequency. [90] For example, recordings in the MGV showed an exponential tonotopic organization as the electrode penetrated the nucleus from dorsal (low-CF) to ventral (high CF) ( Figure 6C). This was associated with a neuronal laminar architecture correlated with the width of the dendritic fields, [92] the major axis of which is oriented orthogonal to the tonotopic axis. [105] The laminar arrangement evident in the ICC and medial genicu- (B) Tonotopic map in the ventral division of the medial geniculate nucleus in rabbit; the two sets of symbols are for different electrode penetrations into the nucleus. [92] (C) Tonotopic map for the central nucleus of the inferior colliculus in the cat. [90] This map was derived from sequential recordings during advancement of electrode into nucleus. (D) Schematic of the mouse auditory cortex showing primary AI and AFF (anterior auditory field) areas, an ultrasonic UF area, and a secondary AII area. [95] The tonotopic gradient in AI and AFF are indicated by arrows from low frequency (LF) to high frequency (HF). Neurons with CFs from 47 to 70 kHz are contained in the UF area and do not show strong tonotopic arrangement. [98] (E) CFs of neurons in AI from Ca 2+ signal amplitudes. (D) and (E) from. [95] The maps in (B), (C), and (E) are reproduced with the permission of the authors.
in humans or other mammals. For instance, in listening to speech or music, the precise pattern of tonal intervals must be identified and remembered. However, if the same sequence is heard later after transposition to a different key, the melody is still recognizable, so the absolute frequencies are not crucial, only their relative values. The pitch intervals are the categorical element of perception. [106] If the sequence of intervals is regarded as a pattern of activity on a brain nucleus, the exponential tonotopic map allows the entire pattern to be spatially represented across the nucleus and then shifted with transposition of the key. The same process must occur on listening to male speakers whose voices are lower compared to women or children, but speech in either direction is intelligible. This gender difference may be expressed in terms of the formant frequencies, usually two or three frequency bands, produced by resonances of the vocal tract, that define each vowel. For example, the first two formants in males for "bet" are 526 and 1850 Hz, whereas first two for "boy" are 550 and 850 Hz. [107] The formant frequencies in most men are 60%-80% lower than those in women or children, whether in English [108] or non-English languages. [109] CONCLUSIONS Physiological studies in numerous vertebrates have documented the topographical variation in the CFs of neurons along the cochlea, underpinned by gradients in electrical or mechanical properties of the hair cells and tissue components. In all amniotes, there is a precise exponential map in CFs, probably generated by an exponential concentration gradient in one or more morphogens downstream of SHH. While information is available in the chicken for transcription factors acting on the DNA, those for specifying the tonotopic gradient in the mammalian cochlea are less well understood. Even with the chick, the cellular source of the morphogen BMP7 is not known, nor how its interactions with other antagonistic factors such as CHRDL-1 and retinoic acid affect the gradient. And is the gradient stored in avian supporting cells so that it may be recalled after hair cell death? More detailed characterization of the morphogenetic pathway may stem from spatial transcriptomics and the recent advances in the ability to assay gene expression at a single-cell level. One future goal would be to examine the development of the reversed tonotopic map in the geckos, such as the crested gecko or the mourning gecko [4,110] for which the embryonic development and the transcriptome for the late-stage embryo have already been determined. [110]