Tuning of Ranvier node and internode properties in myelinated axons to adjust action potential timing

Action potential timing is fundamental to information processing; however, its determinants are not fully understood. Here we report unexpected structural specializations in the Ranvier nodes and internodes of auditory brainstem axons involved in sound localization. Myelination properties deviated significantly from the traditionally assumed structure. Axons responding best to low-frequency sounds had a larger diameter than high-frequency axons but, surprisingly, shorter internodes. Simulations predicted that this geometry helps to adjust the conduction velocity and timing of action potentials within the circuit. Electrophysiological recordings in vitro and in vivo confirmed higher conduction velocities in low-frequency axons. Moreover, internode length decreased and Ranvier node diameter increased progressively along the distal axon segments, which simulations show was essential to ensure precisely timed depolarization of the giant calyx of Held presynaptic terminal. Thus, individual anatomical parameters of myelinated axons can be tuned to optimize pathways involved in temporal processing.

I n the grey matter of the brain, neuronal dendrites and synapses have highly varying morphologies, which are adapted to particular information-processing tasks 1 . In contrast, the white matter is generally assumed to be comprised of axons with a canonical structure defined by a ratio of internode length (L) to myelin outer diameter (D) of B100 (refs 2,3) and a 'g-ratio' (the ratio of internodal axon diameter, d, to myelin diameter, D) of B0.75 (ref. 4). These concepts came from a theoretical analysis (tested against experimental data) 2 , which assumed that the physical size of all parts of myelinated axons should scale together, so that L/D should be constant (empirically measured as B100 for the peripheral nervous system), as should g ¼ d/D; furthermore, a g-ratio of B0.6 was suggested to maximize the spread of signals between nodes (but the experimental value is 0.7-0.8, both in the peripheral nervous system and central nervous system (CNS)).
However, it would be surprising if myelinated CNS axons were as structurally invariant as is commonly assumed because the shape and timing of action potentials (APs) play a crucial role in synaptic transmission, information processing, rhythm generation and plasticity [5][6][7][8][9] , and variation of any of the geometrical parameters of myelinated axons could be used to tune their conduction speed and AP shape. For example, varying axon diameter at the node of Ranvier will alter the axial resistance and membrane capacitance (and possibly the number of voltage-gated Na þ channels) at the node, varying internodal axon diameter will change axial current flow along the axon, while altering internode length will change the fraction of the axon that benefits from the capacitance-reducing effect of myelination. Indeed, in the peripheral nervous system, the internode length is reduced near synaptic terminals (at the neuromuscular junction) to increase the effective Na þ current available to depolarize the terminals 10 , while in the CNS the myelination pattern can vary significantly along axons and between similar neurons, possibly to tune conduction time [11][12][13][14] . We demonstrate here how gradation of the node and internode properties along axons that are myelinated everywhere can tune conduction speed.
A model system for a detailed morphometric analysis of single myelinated axons in vertebrates is the sound localization circuitry that processes spatial information with exquisite precision. For instance, it has been shown that, in the bird pathway processing interaural time differences (ITD), variation in axon morphology is used for adjusting AP arrival times. There, thicker axons with longer internodes compensate for different axonal lengths 13,14 . The analogous mammalian auditory brainstem circuits that process ITDs and interaural level differences (ILDs) have similar exceptional needs for temporal precision in AP propagation, synaptic transmission and postsynaptic integration 15 . Both the ITD-and ILD-processing circuits contain a structure not present in birds, the medial nucleus of the trapezoid body (MNTB), which receives excitatory input from the contralateral cochlear nucleus globular bushy cells (GBCs) via the giant calyx of Held synapses. MNTB neurons are themselves glycinergic and provide inhibition to the binaural comparator neurons in the medial and lateral superior olive (MSO and LSO, respectively). While excitatory inputs from spherical bushy cells (SBCs) in the cochlear nucleus innervate MSO and LSO neurons directly (Fig. 1a), the inhibitory pathway includes the calyx of Held in the MNTB as an additional synapse. Despite the additional synaptic delay of several hundred microseconds, recent experimental and theoretical reports indicate an earlier arrival time for inhibitory than for excitatory input at the MSO 16,17 . Moreover, inhibitory and excitatory inputs arrive at about the same time at the LSO (reviewed in ref. 18), despite the additional synapse in the MNTB and the longer length of the inhibitory pathway. This suggests the involvement of structural adaptations for speeding up the conduction of inhibitory information in the binaural circuit. Indeed, it is reported that GBC axons represent the largest diameter fibres of the trapezoid body 18,19 . However, detailed knowledge of the geometrical parameters determining conduction velocity in GBC and SBC axons is lacking. Moreover, APs in the GBC-MNTB pathway are known to be particularly short 20,21 , can propagate along axons at extremely high frequencies (4600 Hz (refs 20,22)) and are transmitted via the calyx of Held securely with short synaptic delays 23 . The influence of axon morphology on these properties has not been studied so far.
Here we show that GBC-myelinated axons, and in particular those of cells tuned to low sound frequencies (for which ILDs are minimal, and processing ITDs of only microseconds is important), deviate significantly from the canonically assumed structure in a paradoxical way: low-frequency (GBClat) fibres are thicker but exhibit a shorter internodal length than highfrequency (GBCmed) fibres. Our simulations as well as our recordings in vitro and in vivo indicate that this makes AP conduction particularly fast and precise. Furthermore, while it has been proposed that a long (20-40 mm) heminode is necessary for depolarizing the giant calyx of Held presynaptic terminal in juvenile animals 24 , we found that the heminode at the adult calyx is 10-fold shorter than this. Resolving this discrepancy, we demonstrate a novel mechanism that promotes calyx depolarization: the internode length decreases and the node diameter increases progressively towards the presynaptic terminal, and our detailed simulations predict that these gradations are crucial for precisely timed depolarization of the calyx of Held.

Results
Structural differences between SBC and GBC fibres. We first measured the internodal axon diameter and internode length in SBC fibres innervating the MSO and in GBC fibres innervating the MNTB. A combination of dye filling of axons (Fig. 1b) and immunohistochemical labelling of nodal and juxtaparanodal proteins allowed us to measure axon diameter, to unambiguously identify the position of nodes of Ranvier along axons (Fig. 1c) and to follow single axons with an identified termination site for up to 2,200 mm. The internodal axon diameter of GBC axons was more than twice that of SBC axons (measured far from their synaptic terminals where internode length is constant (Fig. 1d): SBC 1.35±0.03 mm at 4500 mm from the medial somatodendritic region of the MSO, GBC 2.87 ± 0.05 mm at 4700 mm from the terminals; Po0.001; Mann-Whitney test; Fig. 1e). The mean internode length (far from the synaptic terminals) in the thicker GBC fibres was also larger than in the thinner SBC fibres (SBC 164.8 ± 12.4 mm, GBC 208.9 ± 7.0 mm, P ¼ 0.005, t-test; Fig. 1f). Simulations presented below assess how this difference of parameters affects the conduction speed in the pathways bringing excitatory and inhibitory inputs to the MSO.
GBC fibre parameters vary with tonotopic identity. The MNTB is a tonotopically organized nucleus, with GBC axons conveying high sound frequencies targeting the medial region and those conveying low sound frequencies targeting the lateral region 25 (Fig. 2a). Tracing individual GBC axons to their calyx of Held terminals enabled us to categorize them by their termination region in the MNTB, that is, providing input to the medial half of the nucleus (GBCmed or high-frequency) or to the lateral half (GBClat or low-frequency). In nine GBClat and eight GBCmed axons we determined internodal axon diameter, node of Ranvier diameter and internode length, three major structural determinants of the conduction speed of APs 26 , at different points ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9073 along the axon (Fig. 2b). Interestingly, we observed systematic differences in the two populations of GBC axons. GBClat axons had a significantly larger mean internodal axon diameter than GBCmed axons (GBClat 3.21 ± 0.05 mm averaged over all positions, GBCmed 2.40±0.05 mm, Po0.001, Mann-Whitney test; Fig. 2b-d). The diameter of nodes of Ranvier was also larger in GBClat axons than in GBCmed axons (GBClat 1.91±0.04 mm, GBCmed 1.60 ± 0.05 mm, Po0.001, t-test; Fig. 2e,f). However, despite the larger diameter of GBClat axons, the mean length of internodes located further than 700 mm away from the calyx (where internode length was constant, see below) was smaller in GBClat than in GBCmed axons (GBClat 195.7±8.5 mm, GBCmed 230.4 ± 11.1 mm, P ¼ 0.015, t-test; Fig. 2g,h). This surprising finding contradicts the long-assumed notions 2 that internode length is proportional to axon diameter, and that axons with similar function exhibit structural similarity.
This structural difference became even more apparent when the ratio of internode length to internodal axon diameter (L/d)   (a) Schematic of the tonotopically organized MNTB with GBC axons terminating in the lateral low-frequency region (GBClat; dark blue) and in the medial high-frequency region (GBCmed; light blue). (b) Schematic of a myelinated axon segment illustrating the structural parameters analysed. (c,e,g) Internodal axon diameter, node diameter and internode length plotted as functions of distance from the heminode. In GBCmed and GBClat axons, node diameter increases (e), whereas internode length decreases (g) closer to the synaptic terminals (see also Supplementary Fig. 1). The x-value of each data point represents the position of the centre of each internode or node along the axon. (d,f) Internodal axon diameter and node diameter are larger in GBClat than in GBCmed axons (averaged over all positions; Po0.001 for internodal axon diameter, Mann-Whitney test; Po0.001 for node of Ranvier diameters, t-test).
(h) For 4700 mm upstream of the heminode (dashed line in g) internode length is significantly larger in GBCmed than in GBClat axons (P ¼ 0.015, t-test). was compared (Fig. 2i). GBCmed axons had, far from the calyx, a mean L/d ratio of B100. In contrast, for GBClat axons the mean ratio was B35% smaller (GBClat 64.9±3.1; GBCmed 99.6±5.7; Po0.001, Mann-Whitney test; Fig. 2j). Both of these values are lower than the canonical value of 133, which is predicted (for a g-ratio of 0.75, see Fig. 3d below and ref. 4) from Rushton's 2 classical summary of the properties of peripheral nervous system fibres as having a ratio of internode length to myelin outer diameter of B100. These data suggest strongly that there are systematic differences in the structure of GBC axons that can be related to the tonotopic organization, and thus to the function of these axons in the sound localization circuits processing interaural time and level differences.
Myelin thickness in GBC fibres. Another major structural determinant of AP conduction velocity in myelinated axons is the thickness of the myelin sheath 26 . Increasing the number of myelin wraps lowers the capacitance along the internode, reducing the time required to charge the internodal membrane. This means that consecutive nodes of Ranvier reach threshold quicker and, therefore, the conduction velocity is increased. In addition, it increases the effective membrane resistance, thus reducing radial current leak between consecutive nodes of Ranvier. We determined myelin thickness from transmission electron micrographs of GBC fibres (Fig. 3a) in parasagittal ultrathin sections by measuring the axon perimeter and the fibre perimeter (Fig. 3b,c). The g-ratio was calculated by dividing the measured inner (axon) perimeter by the measured outer (myelin) perimeter 27 . As expected 28 , g-ratio increased slightly with axon diameter, that is, myelin thickness relative to axon diameter decreased at larger axon diameters (Fig. 3d). Estimated g-ratio values for the mean internodal axon diameter of GBCmed and GBClat axons were 0.748 and 0.764, respectively, which were used in our detailed computational axon model described below.
Spatial variation of axon structure towards the calyx. In addition to the variation of the mean geometrical parameters between fibres with different tonotopic identity, we found a systematic variation of structural parameters along the distal part of all GBC fibres (Fig. 2e,g). From B700 mm before reaching the heminode, the internode length decreased progressively from 195.7 ± 8.5 to 53.5 ± 0.2 mm at the last internode in GBClat fibres, and from 230.4±11.1 to 36.9±3.0 mm at the last internode in GBCmed fibres ( Fig. 2g and Supplementary Fig. 1A). The observed decrease in internode lengths was not a secondary effect necessary to allow fibre branching 29,30 , as only 5 of the 17 analysed GBC axons gave rise to a branch in their distal part. A gradation along the axon was also found for node diameters ( Fig. 2e and Supplementary Fig. 1B). On average, node diameter increased by 35%, approaching the synaptic terminal in the most distally located eight nodes of Ranvier of GBClat fibres, and by 40% in the most distally located four nodes of GBCmed fibres. This increase in node diameter will decrease the nodal axial resistance and (for a fixed channel density per membrane area) increase the number of voltage-gated Na þ channels per node which, together with the increased density of nodes associated with shorter internode lengths, could support an increased current flow down the axon to promote reliable AP invasion into the giant calyx of Held. We test this idea in simulations presented below.
Morphometry of the pre-terminal axon segment. The myelinated part of GBC fibres was followed by a short unmyelinated 24 pre-terminal axon segment that connected the last internode to the calyx of Held. Immunohistochemical staining revealed that it consisted of a sodium channel-containing heminode, directly adjacent to the last internode, and a sodium channel-free segment, which we refer to as the post-heminode ( Fig. 4a-c). The heminode had a similar length in medially and laterally terminating fibres (2.13 ± 0.13 mm in GBClat and 2.18 ± 0.19 mm in GBCmed; Fig. 4d). In accordance with the differences in internodal axon and node diameters in GBClat and GBCmed fibres ( Fig. 2c-f), the heminode diameter was significantly larger in GBClat fibres (GBClat 2.04 ± 0.09 mm, GBCmed 1.60±0.15 mm, P ¼ 0.022, Mann-Whitney test, Fig. 4e). The diameter of the post-heminode was significantly larger than the heminode diameter in both GBClat (2.70±0.19 mm, P ¼ 0.007, paired t-test) and GBCmed axons (2.26 ± 0.20 mm, P ¼ 0.002, paired t-test). The post-heminode ranged in length from 7 to 30 mm (mean 13.2 ± 2.1 mm) in GBClat, and from 4 to 14 mm (10.7±1.3 mm) in GBCmed fibres (Fig. 4d). Consequently, it constitutes a large capacitance and has potentially strong effects on AP invasion into the calyx of Held.
Dependence of simulated conduction velocity on L/d ratio.
To explore how the morphological differences between SBC, GBClat and GBCmed axons affect AP propagation, we carried out detailed computer simulations 31 informed by the measured anatomical parameters for each axon type, as described in the Methods section and Supplementary Tables. The conduction velocity of the computed AP far from the synaptic terminals was 4.4 m s À 1 in SBC axons, 8.5 m s À 1 in GBCmed axons and 11.3 m s À 1 (33% faster) in GBClat axons that have a lower ratio of internode length to axon diameter (arrowed values in Fig. 5a). The lower velocity in SBC axons than in GBC(lat) axons correlates well with inhibitory information arriving before excitatory information at the MSO 17 (Fig. 1a). To estimate how much of the 33% increase in conduction velocity in GBClat axons (compared with GBCmed axons) was due to their smaller internode length to axon diameter (L/d) ratio, we systematically explored the effect of varying the internode length (without changing the axon diameter, node diameter or g-ratio) in both populations of axon ( Fig. 5a). At low internode lengths the conduction velocity decreases because a smaller fraction of the axon is myelinated, while at long internode lengths it decreases because of inefficient transfer of depolarization between nodes, giving an optimum value of L/d to maximize conduction velocity 32 . Increasing the internode length to increase L/d in GBClat axons from 64.9 to 99.6, the ratio we found in GBCmed axons (dashed arrow in Fig. 5a), decreased the conduction speed from 11.3 to 9.8 m s À 1 . Thus, the smaller L/d ratio in GBClat fibres, which generates a conduction speed closer to the highest value that can be produced for these axons by varying L/d in our simulations (Fig. 5a), increases the conduction velocity by 15% (while 18% of the increase in speed of these axons is due to the larger internode and node diameters).
Both lateral and medial GBC axons have an internode length greater than the value that maximizes conduction velocity in our simulations (Fig. 5a), which has been suggested to decrease energy use with little decrease in conduction velocity 2 . We assessed this idea by calculating (from our simulations) the Na þ entering to generate an AP for internode length to axon diameter ratios in Fig. 5a chosen to be either as observed experimentally (solid arrows in Fig. 5a) or which would maximize the conduction speed (peaks of the curves in Fig. 5a). For SBC, GBCmed and GBClat axons, the observed values of L/d reduced the conduction speed by 28%, 22% and 15%, respectively (compared with the maximum velocities attainable in our simulations) but reduced the energy needed for Na þ pumping by a larger percentage (53%, 49% and 45% respectively).  Dependence of simulated AP shape on L/d ratio. The presynaptic AP waveform is a crucial determinant of the timing (synaptic delay) and strength of synaptic transmission 7,33 . In sound localization circuits, brief APs are not only crucial for keeping synaptic delays short and for preserving temporal information during synaptic transmission but also support precise and reliable propagation of high-frequency AP trains up to 500-800 Hz as observed in vivo 34,35 , a prerequisite for neurons tuned to low sound frequencies to respond in a cycle by cycle manner to a specific phase of the sound wave 36 . The simulated AP in GBClat fibres exhibited a more rapid rate of rise of the upstroke (1,202 V s À 1 ), a shorter half-width (0.41 ms) and larger amplitude (101 mV) than in GBCmed fibres (rate of rise 1,039 V s À 1 ; half-width 0.44 ms; amplitude 94.1 mV; Fig. 5b-d).
Notably, this effect depended on the smaller L/d ratio in GBClat fibres because increasing the ratio to 99.6 decreased the rate of rise by 29% to 859 V s À 1 , increased the AP half-width by 14% to 0.47 ms and decreased the amplitude by 13% to 87.8 mV. This effect of internode length probably occurs because, for larger L/d ratios, less efficient transfer of current from one node to an adjacent node results in less synchronous activation of Na þ channels (resulting in a less rapid rate of rise) and to a less rapid and synchronous activation of potassium channels, both of which may contribute to an increase in half-width. Briefer APs in GBClat fibres should allow for shorter intervals between APs and hence temporally more reliable responses to fast incoming signals (that is, allowing the phase locking that is exhibited by low-frequency GBC fibres) 36 , and a larger amplitude may increase the reliability (by increasing the safety factor) of AP propagation in these axons. Moreover, briefer APs have been shown to be associated with a smaller synaptic delay 7,33,37 , and increased fidelity of synaptic transmission 20 , which is fundamental to binaural processing of temporal information in sound localization circuits 15,38 .
Factors aiding AP invasion into the calyx. To test the effect of the internode length and node diameter gradations towards the end of GBClat axons on AP invasion into the calyx of Held, we simulated the end terminal as three cylinders corresponding to the heminode, post-heminode and calyx (Fig. 4a, details of the parameters chosen are in the Methods section and Supplementary Tables). The dimensions of the heminode and post-heminode were taken from the anatomical observations above. The calyx of Held was modelled as an equivalent cylinder that represented the complex processes that make up the calyx (see Methods section) and had a total surface area of 1,700 mm 2 (in the observed range 39 ). Without any spatial gradation of internode length, node diameter and internode diameter with distance from the synaptic terminal, for GBClat axons APs did not propagate successfully into the calyx (the maximum depolarization was 19.9 mV, measured at the distal end of the calyx, Fig. 6a dark blue trace). After introducing the observed spatial gradation of internode length (shorter nearer the calyx), AP propagation into the calyx was facilitated (the maximum depolarization was 31.4 mV, Fig. 6a light blue trace). A facilitation was achieved by introducing ARTICLE only the gradation of internode length, without introducing the gradation of internode and node diameters. However, additional introduction of the observed gradation of node diameter and internode diameter led to a more rapid entry of the AP into the calyx (a 34-ms speeding of the AP was observed with gradation of internode length only versus a 51-ms speeding for all gradations included; delays were measured from the time for the AP to pass À 60 mV). The gradation of node diameter and internode diameter, when introduced alone, had little effect on the AP waveforms (Fig. 6a, green and red traces). However, when the gradation of node diameter and internode diameter was introduced on top of that of the internode length, this led to a more rapid rate of rise of the AP upstroke (maximum rate of rise: 96.7 V s À 1 without any gradations, 126.0 V s À 1 with gradation of internode length only and 155.7 V s À 1 with gradations of node diameter, internode diameter and internode length) and a larger AP amplitude (52.3 mV, Fig. 6a magenta trace). The calyx shape varies considerably during development 40 . We varied systematically the diameter of the processes of the simplified calyx while keeping the total calyx surface area constant (by adjusting the process length) to examine how robustly the AP invaded calyces of different shapes, and the role of the gradation of axonal properties in ensuring this invasion. The simulations revealed that gradations of internode length, and of nodal and internodal diameters, are essential for successful propagation of the AP into the GBClat terminal over a wide range of calyx geometries (Fig. 6b), as observed experimentally 20 . Similar behaviour was observed in simulations of GBCmed axons (Fig. 6a,b), except that the surface area of the calyx had to be reduced to 1,250 mm 2 (also in the observed range 39 ) in order for APs to depolarize the calyx beyond À 40 mV. For both panels in Fig. 6b, the initial rise in the maximum voltage as the process diameters are increased from zero is due to the resulting decrease in axial resistance along the calyx. Since we are measuring the voltage at the distal end of the calyx, a lower axial resistance leads to less voltage drop along the calyx. However, for all the curves, except those in which all the parameters are graded with position, as the diameter of the processes increases further the calyx becomes more isopotential and the effective input resistance at the proximal end of the calyx decreases. This decrease in input resistance reduces the depolarization occurring in the heminode and post-heminode and therefore prevents activation of voltagegated Na þ channels in the heminode. Thus, a decrease in the maximum depolarization in the calyx occurs at the point when the threshold for activation of Na channels in the heminode is no longer reached.

Measurement of conduction speed in GBCmed and GBClat fibres.
To verify the simulated conduction velocities of GBC fibres we performed in vitro recordings in brain slices. The conduction velocity of single GBC fibres was measured far from the calyx of The membrane potential waveform in the calyx has a shorter delay, larger amplitude and faster rate of rise when gradations of node diameter, internode diameter and internode length are included. (b) Action potential propagation into the calyx of GBClat (left) and GBCmed (right) axons occurs over a wider range of calyx geometries when experimentally observed gradations of the axon anatomy are included. When the diameter of the calyx processes was varied, while retaining the same calyx membrane surface area (thus, altering the longitudinal resistance into the calyx processes, but retaining the same conductance and capacitance across the calyx membrane), it was found that graded properties of the axon towards the end of the presynaptic axon allowed propagation of the action potential into the synaptic terminal over a wider range of calyx dimensions. Dotted line indicates calyx process diameter for which the membrane potential waveforms are shown in a. Calyx surface area was 1,700 mm 2 for GBClat and 1,250 mm 2 for GBCmed.
Held by whole-cell patch clamp recording from MNTB neurons while electrically stimulating the trapezoid body fibres in two locations (Fig. 7a). One stimulating electrode was placed near the midline and the other one further on the contralateral side. To estimate the axonal conduction velocity, the distance between the two stimulating electrodes was divided by the difference in the latency of the postsynaptic response when stimulating with electrode S1 or S2 (Fig. 7b). These experiments gave a mean axonal conduction speed for GBC axons of 9.67 ± 1.25 m s À 1 (n ¼ 23; Fig. 7c), which is comparable to the simulated conduction speed values (8.5 m s À 1 in GBCmed and 11.3 m s À 1 in GBClat axons, see Fig. 5a). The estimated conduction velocity tended to increase with distance from the midline (P ¼ 0.0275), that is, laterally terminating GBC fibres tended to have a higher conduction velocity than medially terminating GBC fibres (Fig. 7d), as in Fig. 5a. Thus, these results indicate that the parameters chosen for the computer simulations result in realistic conduction velocities, and successfully predict a greater conduction speed for GBClat than for GBCmed fibres.
To further investigate differences in conduction speed between high-and low-frequency fibres, we performed in vivo recordings extracellularly at different positions in the MNTB. First, responses of single MNTB neurons were elicited by acoustic stimulation and the characteristic frequency (CF) of each neuron was determined. Consistent with previous reports 25,41 , the CF correlated with the neuron's position along the mediolateral axis of the MNTB (P ¼ 5.6 Â 10 À 8 ), with high-CF neurons being located in the medial part of the nucleus and low-CF neurons being located in the lateral part (Fig. 7e). After determining the neuron's CF, responses were evoked electrically in the cochlear nucleus, circumventing delays between the sensory periphery and the cochlear nucleus ( Fig. 7f; histological verification of the position was obtained by DiI labelling). Only neurons with characteristic complex waveforms consisting of a prepotential (reflecting the activity of the calyx of Held presynaptic terminal) followed by a postsynaptic spike were included in the analysis (Fig. 7g). The latency of axonal AP propagation was defined as the time between the peak of the stimulation artefact and the peak of the calyceal AP (the peak of the prepotential of the complex waveform recorded extracellularly; Fig. 7g). The latency of the prepotential decreased with increasing distance of the recording site from the midline (P ¼ 0.014; Fig. 7h). Accordingly, the latency correlated positively with the neuron's CF (P ¼ 0.002; Fig. 7i). Thus, as in the brain slices, these results strongly indicate that AP conduction velocity is higher in low-frequency GBClat axons than in high-frequency GBCmed axons, as predicted in Fig. 5a.

Discussion
We have identified several unusual morphological parameters of axons transmitting information to the MSO and LSO. First, the diameter and internode length of GBC axons, which transmit information that passes through an extra synapse in the MNTB and provide inhibition to the MSO and LSO (Fig. 1a), are larger than those of the SBC axons transmitting excitatory information. The resulting increase in transmission speed of the inhibitory information could explain why inhibitory information can arrive approximately simultaneously with the excitatory information in the LSO and even before excitatory information at the MSO 17,18 despite the additional synaptic delay in the MNTB. An analysis of the analogous ITD-processing circuit in birds suggests that a different anatomical tuning mechanism occurs: differences of axon diameter and internode length may tune different length branches of the same myelinated axons to provide the required AP arrival times 13,14 .
Second, the present study provides evidence that structural specializations in myelinated GBC axons that strongly deviate from the canonically assumed behaviour can additionally tune their conduction velocity, and thus the timing of APs. Specifically, we found systematic differences in the structure of GBC axons that correlate with their target region in the MNTB, and hence with their tonotopic identity. Lateral (low frequency) GBCs had a larger internodal axon diameter (d), but, paradoxically, a shorter internode length (L) than medial (high frequency) GBCs. This result contradicts the principle of structural similarity of myelinated axons 2 , which suggested that L/d should be the same for all myelinated axons. Our simulations predict that this difference in structure results in GBClat axons conducting APs 33% faster than GBCmed axons (Fig. 5a), which may serve to compensate for the longer path length of GBClat axons and allow simultaneous arrival at the MNTB of afferent signals tuned to different sound frequencies. About half of this increase in speed in GBClat compared with GCBmed axons is attributable to the lower L/d ratio in GBClat fibres. In addition, the lower L/d ratio increased the rate of rise and decreased the half-width of the AP in GBClat axons, which is a prerequisite for temporally precise synaptic transmission at the calyx of Held. A first indication of differences of axon structure potentially related to tonotopic identity came from an investigation of peripheral auditory axons 42 . In the light of our analysis of how individual structural parameters contribute to myelinated axon function in the CNS, it is likely that these peripheral nervous system adaptations are also crucial for increasing the reliability and temporal precision of AP propagation in axons conveying low-frequency sound information for binaural processing.
It has been questioned whether the auditory circuits involved in temporal processing, which exhibit energy-demanding highfrequency APs, are designed to use energy efficiently 43 . Far from their synaptic terminals, SBC axons had a ratio of internode length to internodal axon diameter of 122, which is similar to the canonical value of 133 derived from peripheral axons 2 by assuming a g-ratio of 0.75, while both GBC axon types had significantly lower values (GBCmed 99.6 and GBClat 64.9), which increases their conduction speed (Fig. 5a). It is noteworthy that the ratio of internode length to internodal axon diameter in GBC and SBC axons is significantly higher than the value that maximizes conduction speed (Fig. 5a)-a situation that our simulations show reduces energy consumption 2 on pumping out the Na þ that enters to generate the AP-and that the value that maximizes speed is much less than the value of 133 expected from peripheral nerve data. For SBC, GBCmed and GBClat axons, the observed values of L/d reduced the conduction speed compared with the maximum velocities attainable, but reduced the energy needed for Na þ pumping by a larger percentage.
Finally, we found unexpected gradations of geometrical parameters in CNS axons of the GBC-MNTB pathway, which seem to be structurally and functionally analogous to those of peripheral nervous system motorneurons close to the neuromuscular junction. In GBCs the internode length, internodal axon diameter and node diameter all change systematically with distance from the synaptic terminal in the calyx of Held (Fig. 2). This spatial variation is crucial for ensuring a rapid depolarization of the calyx of Held (Fig. 6a), which is reliable over a range of simulated calyx morphologies (Fig. 6b). Strikingly, in our simulations, for large calyces the shortening of internode length near the synaptic terminal (which has previously been suggested to promote synaptic depolarization in the peripheral nervous system 10 and has been speculated to also exist in GBC fibres to promote depolarization of the long unmyelinated pre-terminal axon segment 24 ) was not sufficient to ensure that a large and rapid depolarization occurred in the synaptic terminal, but additionally including the spatial variation of nodal and internodal axon diameters did ensure this. Interestingly, it has been proposed that 20-40-mm-long Na v -positive structures in the MNTB of young rats represent heminodes of GBC fibres, and that these putative heminodes might be necessary for depolarizing the giant calyx of Held presynaptic terminal 24 . However, our labelling with Na v , neurofilament heavy chain (NFH) and K v 1 antibodies showed that the heminode in pre-calyceal segments of GBC axons of adult gerbils is only B2 mm long. This indicates that the spatial variation of structural parameters, rather than a particularly long heminode, is the mechanism promoting precisely timed depolarization of the calyx. The variation of the morphological parameters of myelinated axons that we report here thus plays a crucial role in the processing of temporal information for sound localization (as does the presence of myelin itself 44,45 ), although we cannot rule out an additional influence of factors we have not investigated, such as differences in ion channel density. More generally, given that remodelling of the properties of myelinated axons can occur in adults 46 , our data highlight the fact that adjustment of parameters such as internode length, internodal axon diameter and node diameter can optimize information processing, and may contribute to the changes of white matter structure that contribute to learning 47 .

Methods
All animal procedures were performed in accordance with the German guidelines for the care and use of laboratory animals as approved by the Regierung of Oberbayern (AZ 55.2-1-54-2531-105-10, Bavaria, Germany). Mongolian gerbils (Meriones unguiculatus) were housed in a vivarium with a normal light-dark cycle (12 h light/12 h dark). Gerbils of both sexes, aged P25-30, were used for the anatomical experiments (in vitro axon tracing, immunohistochemistry and electron microscopy).
In vitro axon tracing. Gerbils were deeply anaesthetized with pentobarbital (2 mg per kg body weight) and intracardially perfused with ice-cold Ringer's solution containing heparin. After decapitation, the brainstem was quickly removed from the skull under ice-cold dissecting artificial cerebrospinal fluid (aCSF) comprising (in mM) 125 NaCl, 2.5 KCl, 1 MgCl 2 , 0.1 CaCl 2 , 25 glucose, 1.25 NaH 2 PO 4 , 25 NaHCO 3 , 0.4 ascorbic acid, 3 myoinositol and 2 pyruvic acid (all chemicals from Sigma-Aldrich). For anterograde tracing of GBC axons, borosilicate micropipettes with a tip diameter of 10-15 mm were filled with a 10% solution of tetramethylrhodamine dextran (3,000 molecular weight (MW); Invitrogen, La Jolla, CA) and visually guided to the anterior ventral cochlear nucleus (AVCN) in brainstem explants using a stereo microscope. Tracer was pressure-injected (15 pounds per square inch (PSI)) into the GBC area of the AVCN using a picospritzer (Picospritzer III, Parker, Cleveland, OH), followed by several electroporation pulse trains (modified from another study 40 ). Pulses (50 ms) had an amplitude of 50 V and were applied at 10 Hz using an isolated pulse stimulator (A-M Systems). For anterograde tracing of SBC axons the brainstem was sectioned along the posterior-anterior axis until the outlines of the LSO were clearly visible. Tracer was applied in the region of the medial limb of the LSO through pressure injections and electroporation as described above. SBC fibres (originating in the cochlear nucleus) pass through this region on their way to the contralateral MSO. This allowed us to label SBC axons without labelling GBC axons, and to reduce the time needed for the tracer to diffuse within the axons to the contralateral MSO. Subsequently, the explants were transferred to a chamber with oxygenated incubating aCSF (the same as the dissecting aCSF described above except with 2 mM instead of 0.1 mM CaCl 2 ), and incubated for 2 h at room temperature to allow for homogeneous distribution of the tracer in axons. Thereafter, the brainstems were immersion-fixed at room temperature overnight in 4% paraformaldehyde (PFA) solution.
Immunohistochemistry. Brainstems were sectioned coronally at 120 mm using a vibratome slicer. After rinsing in PBS, sections were transferred to a blocking solution containing 1% bovine serum albumin, 2% Triton X-100 and 0.1% saponin in PBS. Multiple-immunofluorescence labelling was performed with the following primary antibodies (incubation time 2 days): ankyrin G (Santa Cruz, USA; sc-28561; rabbit polyclonal IgG; 1:500); K v 1.2 (NeuroMab, USA; 75-008 clone K14/16; Mouse IgG2b; 1:500); NFH (AbCam, UK; ab4680; chicken polyclonal IgY; 1:400); Pan Na v (Sigma, Germany; S6936; rabbit polyclonal IgG; 1:300); MAP2 (Neuromics, USA; CH22103 chicken polyclonal, 1:1,000). After incubation with secondary antibodies overnight, sections were rinsed 3 Â 10 min in PBS and coverslipped with Vectashield mounting medium. For each optical section the images were collected sequentially for two to five fluorochromes. Stacks of 8-bit greyscale images were obtained with axial distances of 290 nm between optical sections and pixel sizes of 120-1,520 nm depending on the selected zoom factor and objective. To improve the signal-to-noise ratio, images were averaged from four successive scans. After stack acquisition, chromatic aberration-induced Z shift between colour channels was corrected for using a custom plugin written by Dr Boris Joffe. RGB stacks, montages of RGB optical sections and maximum-intensity projections were assembled using the ImageJ 1. Identification of GBC and SBC axons. GBC fibres were unambiguously identified as such from their prominent giant presynaptic endings (calyces of Held) that terminated in the contralateral MNTB. On the basis of their exact site of termination in the MNTB (in the medial or lateral half of the MNTB), GBC axons were classified as being either medially or laterally terminating. MNTB borders were determined using a counterstain (MAP2 or fluorescent Nissl stain). SBC fibres were identified as axons that could be followed to the medial somatodendritic region of the MSO (the MSO contralateral to where tracer was applied in the medial limb of the LSO; see also section on in vitro axon tracing above). Some fibres formed varicosities in this region. Other fibres became very thin in the medial dendritic region and could not be followed any further, indicating that they terminated there. Since they were located in the middle of the slice (not on the surface), we can rule out that they were cut during the slicing procedure.
Morphometry. Using the ImageJ 1.37k paint-brush tool, individual axons of GBCs and SBCs filled with tetrametylrhodamine dextran were manually labelled by following a single axon successively through each optical section of the confocal image stack. Subsequently, the neighbouring axons were digitally deleted. We refer to this method as digital extraction. The same axon was identified in the neighbouring overlapping confocal image stacks and digitally extracted. This allowed us to follow single axons for up to B2,200 mm. Nodes of Ranvier were identified on the basis of immunohistochemical labelling of nodal and juxtaparanodal marker proteins (Ankyrin G and K v 1.2). Distances between nodes of Ranvier (that is, internode lengths measured mid-node to mid-node) were measured in three dimensions in confocal image stacks using the ImageJ 1.37k Sync Measure three-dimensional tool. Internodal axon diameter and node diameter (a) Schematic of a coronal brain slice illustrating the measurements of conduction velocity in GBC fibres in vitro. (b) Averaged EPSCs of an MNTB neuron in response to electrical stimulation of the afferent fibres at two locations as shown in a. Response latency was measured at half-maximal amplitude of the postsynaptic response. Axonal conduction speed was calculated by dividing the distance between the two stimulating electrodes by the difference in the latency of the postsynaptic response when stimulating with electrode S1 or S2. (c) The mean conduction velocity measured in GBC fibres far from the calyx ( ± s.e.m.). (d) Estimated conduction velocity of GBC fibres plotted against the mediolateral position of their termination region in the MNTB (slope is significantly greater than zero, P ¼ 0.0275 from F test). (e) Characteristic frequency of MNTB neurons recorded in vivo plotted against their mediolateral position (distance from midline). The slope is significantly greater than zero (P ¼ 5.6 Â 10 À 8 from F test). (f) Schematic illustrating the latency measurements in vivo. (g) Example traces of MNTB principal cell responses to repeated electrical stimulation (10 mA). One trace is highlighted in red to illustrate how latency was measured in single traces. Electrical artefacts at the beginning of traces are truncated. (h) The mean latency of presynaptic responses to electrical stimulation (10-40 responses) from calyceal inputs plotted against the tonotopic location of the MNTB principal cells from which recordings were obtained (slope is significantly greater than zero, P ¼ 0.014 from F test). (i) The mean latency of presynaptic responses to electrical stimulation plotted against the postsynaptic MNTB neuron's characteristic frequency (slope is significantly greater than zero, P ¼ 0.002 from F test). Data in c are represented as mean ± s.e.m. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9073 ARTICLE measurements were made in two dimensions from maximum-intensity projections of confocal image stacks.
Electron microscopy. Gerbils were deeply anaesthetized with pentobarbital (2 mg per kg body weight) and intracardially perfused with Ringer's solution. This was followed by perfusion with 2.5% glutaraldehyde plus 2% PFA in cacodylate buffer (CB). Subsequently, the brainstem was removed from the skull and postfixed in the same fixative overnight at 4°C. After washing for 3 Â 10 min in CB, brainstems were sectioned parasagittally at 200 mm using a vibratome slicer. Thereafter, a 1 mm Â 1 mm block containing the trapezoid body fibres was extracted using a razor blade. Tissue was then washed four times in CB and postfixed in 1% OsO 4 in CB for 1-2 h. After washing and dehydrating in graded series of acetone, tissue was embedded in resin. Before ultrathin sectioning, several semithin sections were cut for light microscopic investigation.
Statistics. Data are represented as mean ± s.e.m. Tests for normal distribution and equal variance were performed using the Kolmogorov-Smirnov test and the Levene Median test, respectively. P values are from Student's two-tailed t-tests (for normally distributed data) or Mann-Whitney rank sum tests (for data that were not normally distributed). Tests were performed using the SigmaStat 3.5 software. For multiple comparisons, P values were corrected using a procedure equivalent to the Holm-Bonferroni method (for N comparisons, the most significant P value is multiplied by N, the second most significant by N À 1, the third most significant by N À 2 and so on; corrected P values are significant if they are less than 0.05). Data presented in Fig. 1d and Fig. 2c,e,g,i were fit with linear or exponential functions using the Igor Pro 5.02 (Wavemetrics).
Simulations. The myelinated axon model of Halter and Clark 48 was implemented in MATLAB, modified to remove the periaxonal space in that model by setting its conductivity to zero and adapted to the dimensions of GBClat, GBCmed and SBC axons. The values for the geometrical parameters are shown in Supplementary  Tables 1-3, and the values for the electrophysiological parameters are shown in  Supplementary Table 4. Keeping the electrophysiological parameters fixed for all the simulations allows us to demonstrate that the differences of anatomical parameters alone suffice to determine the relative conduction speed of the different axons and to determine whether or not APs propagate reliably into the calyx.
The trans-myelin capacitance was calculated according to the equation C my ¼ 2pLc my /(S(1/r i )), where the r i are the radii of the individual myelin membranes making up the sheath (assumed to occur at equally spaced radii between the axon radius and the outer radius of the sheath), L is the internode length and c my is the specific capacitance/m 2 of a single membrane in the myelin. The trans-myelin conductance was calculated in a similar way. The differential equations of the model were derived and solved according to the method used in ref. 48. For simulations examining the conduction velocity far from the calyx, 200 internodes were simulated with each internode being represented as 10 segments, an AP was initiated in the first node through brief current stimulation and the conduction speed was derived from the time needed for the AP to pass from the 71st to the 90th internode. The nodes of Ranvier contained inactivating Na þ and low-threshold K þ (K LT ) channels with Hodgkin-Huxley-like kinetics taken from refs 49,50, respectively, as well as a leak conductance. Explicitly, the equation governing current flow across the membrane in the node was: where C n is the capacitance of the node (C n ¼ pL n d n c n , where L n is the length of the node, d n is the diameter of the node and c n is the specific capacitance of the nodal membrane), G Lkn is the leak conductance in the node (G Lkn ¼ pL n d n g Lkn , where g Lkn is the specific leak conductance of the nodal membrane) and V is the (timevarying) membrane potential in the node. E Na , E K and E Lkn are the Na þ , K þ and nodal leak reversal potentials, respectively, and where G Na and G KLT are the peak conductances of the Na þ and K þ currents, respectively, in the node (derived from the specific conductances in a similar manner to G Lkn ). The variables m, h, w and z are functions of membrane potential and time, and satisfy: where, for all these equations, V is in mV and the rate constants are in ms À 1 . The Na þ current kinetics were adjusted for temperature, T (in°C), as written in the equations above. The low-threshold K þ current kinetics were defined at 22°C and similarly adjusted for temperature using a Q 10 value of 3.0. For simulations examining AP propagation into the calyx of Held, 50 internodes were simulated and APs were again initiated in the first node of Ranvier. The end terminal was simulated by extending the last node by three compartments corresponding to the heminode, post-heminode (represented as 10 segments) and calyx. The morphometric parameters for the heminode and post-heminode were taken from this paper (Supplementary Table 3). The heminode contained the inactivating Na þ , low-threshold K þ and leak channels as described above for the nodes of Ranvier. The post-heminode was taken to be a capacitor without conductance. The calyx was represented as a single cylinder (divided into 50 equal serial segments), equivalent to five smaller cylinders representing the main processes of the calyx structure, with a surface area of 1,700 or 1,250 mm 2 (see main text), consistent with published values 39 . Membrane potential was measured in the most distal segment of the calyx. When investigating the effect of altering calyx geometry, the radius of these smaller cylinders was varied, with corresponding alterations in their length to keep the surface area constant. A single cylinder of A mm diameter and L mm length can be shown to be equivalent to N parallel cylinder 'processes' each with diameter A/N 2/3 mm and length L/N 1/3 mm. Therefore, a simulated calyx equivalent cylinder of 10 mm diameter and 54.1 mm length (giving a surface area of 1,700 mm 2 ) represents five parallel cylinders of diameter 3.42 mm and length 31.6 mm. The calyx contained high-threshold K þ (K HT ) and hyperpolarization-activated cation (I h ) conductances with Hodgkin-Huxley-like kinetics taken from ref. 50. It also contained a calcium conductance taken from ref. 51. Explicitly, the equation governing current flow across the membrane in the calyx was: where C c is the capacitance of the calyx, G Lkc is the leak conductance in the calyx, E Ca and E h are the reversal potentials of the calcium and I h currents and, where G Ca , G KHT and G h are the peak conductances (conductance values were taken from ref. 52, but G h was reduced 10-fold to increase the input resistance of the calyx to make it more similar to published values (Forsythe measured a value of 388 ± 228 MO (ref. 53); in the model, GBClat and GBCmed calyces had input resistances of 240 and 325 MO, respectively), and s, n, p and r are functions of membrane potential and time that satisfy: ; where x ¼ s; n; p; or r