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1 Temporally Precise Coding: The Problem of Broadband Transients

Speed and temporal precision are at the heart of auditory processing. Auditory nerve fibers (ANFs) in mice can detect sound pressure fluctuations with periods as short as 12 μs (Taberner and Liberman 2005), and humans can detect differences of as little as 10 μs in the time of arrival of a sound between the ears (Mills 1958). By contrast, sensory systems that rely on G-protein-coupled receptors, such as vision and olfaction, process information ~10,000 times more slowly (Hille 1994). The phenomenal speed of mammalian auditory systems is made possible by the precise transduction of sound pressure waves in air into a traveling wave down the basilar membrane in the cochlea (Fig. 14.1a). This traveling wave performs a spectral decomposition into a spatial frequency map along a logarithmically spaced frequency axis (Dallos 1992). The cochlea can thus be thought of as a log-spaced parallel bank of band-pass filters (Yang et al. 1992) with exquisite temporal and frequency resolution that approaches the physical limits of sound (Weisburn and Parks 1992).

Fig. 14.1
figure 1

The cochlear traveling wave delay results in a somatopetal wave of activation down the dendrites of octopus cells. (a) A schematic representation of the traveling wave spreading down the basilar membrane of the cochlea of a mouse from base to apex (left) resulting in a delay line in the activation of auditory nerve fibers (middle). This delay profile results in a somatopetal wave of dendritic activity in the dendrites of octopus cells in responses to broadband transient sounds. The asterisk indicates the axon of the reconstructed octopus cell. (b) The traveling wave delay in mice is apparent in first-spike latencies in responses recorded in vivo to clicks. The black curve is the result of a least-squares regression fit of the Gabor uncertainty function (T c = 1.8 ± 0.1 ms and α = 0.36 ± 0.04). Parts of panels (a) and (b) are reproduced with permission from Fig. 14.1 of ref. McGinley et al. (2012)

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Temporal precision in the processing of broadband sounds presents a special problem to auditory systems. In the filter bank model of the cochlea, for each frequency channel (i.e., each hair cell or ANF) there is an inherent trade-off between its spectral and temporal resolution, encapsulated by the Gabor uncertainty principle (Gabor 1946): Δt × Δf ≥ 1/π; Δt is the uncertainty in time, and Δf is the uncertainty in frequency, originally inspired by the Heisenberg uncertainty principle (Heisenberg 1927). Simply put, it takes time to determine the frequency of an oscillation with precision. As a result of this trade-off, the uncertainty in, for example, the time of onset of each spectral component of a broadband sound is inversely related to the uncertainty in the frequency of that component. Since the uncertainty in frequency is related to the frequency itself (approximately proportional to the log of the frequency) (Taberner and Liberman 2005), the temporal uncertainty varies systematically with the frequency of the sound component.

The cochlear traveling wave can thus be viewed as a particular solution to the Gabor uncertainty problem. This idea can be tested by analyzing the timing of firing of the first action potential by an ANF in response to a click sound (Fig. 14.1b). The latency from tone onset to first action potential consists of a constant delay, T c, reflecting the acoustic system, axonal propagation, etc., and a group delay that varies with the sound frequency, T(f), corresponding to the traveling wave delay. The total delay is the sum of the two: T t = T c + T(f). From the Gabor uncertainty perspective, T(f), the frequency-dependent delay, is equal to the uncertainty in the time of the signal, Δt. Equating these terms makes the assertion that the group delay at each frequency reflects an accumulation of evidence overcoming the temporal uncertainty, after which time an action potential codes the occurrence of sound energy in that frequency channel. Next, we assume that the uncertainty in frequency, Δf, is proportional to the log of the frequency, reflecting the log-based spacing of the cochlear filter bank. Substituting the uncertainty relationship into the equation for total delay yields \( {T}_t={T}_{\mathrm{c}}+\frac{1}{\left(p\times a\times \ln (f)\right)} \), where α is the proportionality constant.

A fit to the first spike latency data with a delay function derived from the Gabor uncertainty relationship is in reasonably good agreement with the data (Fig. 14.1b). In particular, it captures the tendency of traveling wave delays to be proportionately larger at lower frequencies, corresponding to the slowing of the traveling wave as it approaches the apex of the cochlea. This slowing effect is prominent in animals with low-frequency hearing (Ruggero 1992). A better prediction would be generated by incorporating the experimentally measured frequency dependence of sharpness of tuning of ANFs (e.g., ref. Taberner and Liberman 2005, Fig. 14.3b) into the function for frequency uncertainty, rather than assuming a linear dependence on log frequency.

Whether viewed as a solution to the Gabor uncertainty problem or simply as a temporal dispersion, the cochlear traveling wave delay, which lasts 1.6 ms in mice (McGinley et al. 2012) and up to 8 ms in animals with low-frequency hearing, including humans (Ruggero and Rich 1987), results in asynchronous activity in the population of auditory nerve fibers in response to broadband transient sounds. This asynchrony must be dealt with by downstream neurons or circuits if broadband transient sounds are to be encoded precisely, for example to signal the snapping of a branch under the foot of a predator.

2 Biophysical Specializations of Octopus Cells: Built for Speed

From the cochlea, ANFs project their axons to the cochlear nucleus where they synapse on several classes of principal neurons that in turn carry acoustic information to the next stage of the auditory pathway (Fig. 14.1a). One of the principal classes, octopus cells, is in all respects built for speed. They have extraordinarily brief membrane time constants (~300 μs) and low input resistances (~5 MΩ) (Golding et al. 1995, 1999), making them perhaps the fastest neurons in the mammalian brain (Spruston et al. 2007). Their fast membranes result from a high density of low-voltage-activated potassium conductance (gKL) and hyperpolarization-activated, cyclic nucleotide-gated, channels in their soma and dendrites (Oertel et al. 2008), which oppose each other in a balance at the resting potential (Bal and Oertel 2000, 2001; Cao and Oertel 2011). Octopus cells also have brief synaptic currents, mediated through rapid calcium-permeable AMPA receptors (Gardner et al. 1999, 2001; Raman and Trussell 1992). Octopus cells express voltage-gated calcium channels (Golding et al. 1999; Bal and Oertel 2007), but their physiological role is not known. There is an atypical developmental profile of cholinergic receptors in octopus cells, which may influence their intracellular calcium dynamics (Morley and Happe 2000).

The high density of gKL channels in octopus cells results in an unusual action potential generation mechanism. If an octopus cell is depolarized slowly, gKL channels open, shunt the sodium current, and prevent the generation of an action potential (Fig. 14.2a). If instead an octopus cell is depolarized quickly, gKL channels do not have time to open, creating a window for sodium channel activation to cause an action potential (Fig. 14.2a). Thus, octopus cells have a threshold in rate of depolarization or dV/dt (Fig. 14.2b, left) (Ferragamo and Oertel 2002; Cai et al. 1997). This dV/dt threshold is a feature of other auditory neurons with high gKL, including bushy cells (McGinley and Oertel 2006) and neurons in the medial superior olive (Golding and Oertel 2012; Cai et al. 2000), which have intrinsic membrane properties that are very similar to octopus cells. The dV/dt threshold creates an integration window or time during which somatic depolarization must occur to result in an action potential (McGinley and Oertel 2006), which results in extremely stringent coincidence detection (Oertel et al. 2009; Golding and Oertel 2012; König et al. 1996). The integration window in octopus cells is ~1 ms (Fig. 14.2b, right) (McGinley and Oertel 2006).

Fig. 14.2
figure 2

The unique biophysics and morphology of octopus cells. (a) The membrane voltage of an octopus cell (top) during application of linear current ramps of varying durations (bottom). Black traces show the membrane voltage just below and above the rate-of-depolarization (dV/dt) threshold. Longer duration subthreshold ramps do not trigger an action potential (not shown; see refs. Morley and Happe 2000; Cai et al. 1997). The visually determined approximate voltage threshold for each action potential is indicated with an asterisk symbol. (b) The dV/dt threshold and integration window vary between several principal cell types of the VCN. Octopus cells have higher dV/dt thresholds and shorter integration windows than bushy cells. Stellate cells exhibit classical “integrator” characteristics. They do not have a dV/dt threshold, so their integration window is not limited by the action potential generation mechanism. (c) Photomicrograph of a biocytin-labeled octopus cell against a Nissel stain background (left) and 3D digital reconstruction of the same neuron (right). D dorsal; M medial. (d) A box representation of the dendritic morphology of octopus cells. Each box corresponds to a branch order. The x-axis is length, and the y-axis is total surface area. Each box is the average across cells of the average across branches within each order for each cell. The oval corresponds to the soma; the x-axis is the diameter, and the y-axis is the surface area of a sphere with equivalent surface area to a reconstruction of the soma. Panel (b) is reproduced with permission from Fig. 5 of ref. McGinley and Oertel 2006 and panels (c) and (d) from Fig. 8 of ref. McGinley et al. (2012)

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As a result of the dV/dt threshold, excitatory postsynaptic potentials (EPSPs) in octopus cells must rise quickly in order to elicit an action potential. EPSPs must also result in sufficient depolarization to activate sodium channels, and thus octopus cells also have a voltage threshold. The relationship between the rate-of-depolarization threshold and the voltage threshold for an action potential has not been explored. Determining the function describing this relationship, V thresh(dV/dt), would provide a more complete picture of the input–output relationship of neurons with a dV/dt threshold. Furthermore, knowing this relationship would motivate a natural definition of the efficacy of a composite EPSP waveform:

$$ {\varepsilon}_{syn}=\Big\{\begin{array}{ll}{A}_{syn}/({V}_{thresh}\left(\mathrm{d}{V}_{syn}\right)-{V}_{rest})\hfill & if\mathrm{d}{V}_{syn}\ge \mathrm{d}V/\mathrm{d}{t}_{thresh}\hfill \\ {}0\hfill & if\mathrm{d}{V}_{syn}<\mathrm{d}V/\mathrm{d}{t}_{thresh}\hfill \end{array} $$

where A syn is the EPSP amplitude and dV syn is the rate of depolarization during the rising phase of the EPSP. Visual inspection of the voltage response to current ramps suggests that the voltage threshold does not change dramatically with rate of depolarization (Fig. 14.2a). Therefore, the amplitude of an EPSP is a reasonable first approximation to its efficacy when the rate of rise is above dV/dt threshold. Steady depolarization—which may arise from ongoing synaptic activity or modulatory influences—does not affect the dV/dt threshold, at least in bushy cells (McGinley and Oertel 2006). However, it may affect the voltage threshold (Levy and Kipke 1998), also warranting further investigation.

Octopus cells put their extraordinary speed to use when processing sounds. They respond rapidly and with great temporal precision to onset transients in broadband sounds such as clicks or in loud narrowband sounds. In cats, they respond with sub-millisecond temporal precision to clicks (Godfrey et al. 1975), having a jitter that is less than 200 μs during a 500 Hz click train (Oertel et al. 2000), and can fire at every cycle of a loud 800 Hz tone (Rhode and Smith 1986). They encode rapid temporal components of vocalizations by strongly phase locking to the fundamental frequency in the presence of formants (Rhode 1998) and to the signal envelope of rapid amplitude modulations (Rhode 1994), which are prominent in speech and music. They may contribute to pitch representation, which occurs explicitly in primary auditory cortex by unexplained mechanisms (Rhode 1995; Bendor and Wang 2005). Thus, octopus cells respond with temporal precision to broadband transients in sounds in a variety of contexts, despite the cochlear traveling wave delay. The sound responses and cellular and synaptic biophysics of octopus cells have been reviewed in detail elsewhere (Oertel et al. 2000, 2009; Golding and Oertel 2012).

3 Morphology and Connectivity of Octopus Cells: Positioned to Integrate Broadband Sounds

Octopus cells were named on the basis of their striking morphology; they have several thick primary dendrites that emanate and branch from only one side of the cell body (Fig. 14.2c) (Osen 1969). Octopus cells also have thick daughter branches throughout their dendritic trees. This can be seen when comparing the diameter of parent and daughter branches to the so-called 3/2 power law of Rall: d 3/2p  = d 3/2d,1  + d 3/2d,2 , where d p is the diameter of the parent dendrite, and d d “1” and “2” are the diameters of the daughter dendrites at a branch point (Rall 1964). If a branch point obeys this power law, the impedance at the branch will be matched. Octopus dendritic branch points consistently violate the power law, with the right side of the equation being larger than the left for nearly all branches due to large daughter branches (see ref. McGinley et al. 2012, Fig. 8d). This could serve several functions for octopus cell dendritic integration, including increased distal dendritic surface area, rapid transmission of dendritic signals, or delays due to impedance mismatch.

The tendency of thick daughter dendrites to increase distal dendritic surface area can be seen in a simple box representation of octopus cell morphology; substantial surface area is distributed across many branch orders (Fig. 14.2d). Since the surface area of a cylinder is linearly proportional to its diameter, branches obeying the 3/2 power law would distribute less surface area into their daughter dendrites. Thick daughter dendrites could increase the speed of signal transmission by reducing the axial resistance, whereas the impedance mismatch at branch points would delay propagation from smaller to larger diameter dendrites (Agmon-Snir and Segev 1993; Lanzinger 1987). The original study demonstrating that octopus cells compensate traveling wave delays predicted a delay compensation of ~0.5 ms, matching in vivo delays measured in the same species (McGinley et al. 2005, 2012). A more recent study that did not incorporate detailed morphological information predicted compensation for about half of that delay (~0.28 ms) (Spencer et al. 2012), suggesting that the precise morphology is important.

The dominant source of synaptic input to octopus cells is excitation from the auditory nerve (Oertel et al. 2000). ANFs are tonotopically organized in the cochlear nucleus of all mammals studied, including mice (Osen 1970; Wickesberg and Oertel 1988). Octopus cells orient their dendrites across the tonotopic axis, so ANFs that encode higher frequencies synapse closer to the tips of the dendrites, and those that encode lower frequencies synapse closer to the soma (Fig. 14.1a, see also ref. Golding et al. 1995). Octopus cells show some diversity in morphology (Rhode et al. 1983) and, in mice but not cats, excite one another through axon collaterals (Golding et al. 1995), serving unknown functions in the processing of sounds (Godfrey et al. 1975; Rhode et al. 1983).

The role of inhibitory connections onto octopus cells is uncertain but may be minimal. Stimulation of the auditory nerve does not elicit GABAergic or glycinergic inhibition in octopus cells in mice (Golding et al. 1995). Consistent with this observation, there is a marked lack of glycinergic staining in the octopus cell area (Wenthold et al. 1987; Wickesberg et al. 1994), and tuberculoventral glycinergic interneurons exclude their projection from the octopus cell area (Wickesberg et al. 1991). However, GABAergic terminals exist on octopus cell dendrites (Marie et al. 1989), and glycine may be expressed in terminals in the octopus cell area of guinea pigs (Kolston et al. 1992), though glycine expression is sensitive to experimental conditions (Wickesberg et al. 1994).

4 Rapid Integration Across Tonotopy: A Marriage of Morphology and Connectivity with Biophysics

The relationship of tonotopy in the cochlear nucleus (Osen 1970) with the dendritic morphology of octopus cells (Osen 1969) led to early speculation about their role in sound processing. It was suggested that octopus cells’ dendritic orientation might determine the sensitivity to frequency-modulated (FM) sweeps of different rates or direction (Morest et al. 1973). This idea was later related to Rall’s developing view of spatiotemporal integration in dendrites (Szentagothai and Arbib 1974). The discovery in mice that octopus cells orient their dendrites in a consistent orientation and direction with respect to the tonotopic organization led to the hypothesis that octopus cells compensate the traveling wave delay in their dendrites (Golding et al. 1995; Wickesberg and Oertel 1988).

This hypothesis was directly tested in mice by combining in vivo measurements of the traveling wave delay, in vitro recordings from octopus cells, morphological reconstruction, and passive and active compartmental modeling (McGinley et al. 2012). The traveling wave delay was measured in mice and found to be ~1.6 ms across the full hearing range (see Fig. 14.1b). Because octopus cells’ dendrites span about 1/3 of the tonotopy in the VCN (Golding et al. 1995), during a broadband transient sound each neuron will be exposed to an ~0.5-ms sweep of dendritic activation spreading somatopetally (towards the soma) (see Fig. 14.1a). In separate experiments, whole-cell recordings in the current-clamp configuration were made from octopus cells in acute slices of the VCN from mice. Families of current steps were applied to determine the passive and active response of the membrane (Fig. 14.3a, b, black traces). After fixation, morphological reconstructions were made of recorded neurons (Fig. 14.2c, left) and imported into the software NEURON (Hines and Carnevale 1997) for computation modeling (Fig. 14.2c, right).

Fig. 14.3
figure 3

Sensitivity to somatopetal sweeps of synaptic activation in biophysically and morphologically realistic models of octopus cells. (a) An example recording corrected for I h (black curve) and the superimposed best-fit passive simulation (yellow curve). The series resistance drop, indicated by the break, was removed. The inset shows a diagram of the circuit used in passive simulations: I app applied current; V e electrode voltage; R s series resistance; V m membrane voltage. (b) Response of an octopus cell (top black traces) to a family of long current steps (bottom traces). Superimposed magenta traces show the responses to current steps of the same magnitude in an active compartmental model of the same octopus cell. (c) Somatic EPSP in response to a sweep of 0.6-ms duration from a typical passive model (yellow), active model (magenta), active model with spatially randomized inputs (blue), and a passive point model (green). (d) A comparison of the shape parameters between models for a sweep duration of 0.6 ms. Color scheme same as in panel (c). Statistical comparisons are in Table 3 of McGinley et al. (McGinley et al. 2012). Panels (a) and (b) are reproduced with permission from Fig. 14.2, panel (c) from Fig. 14.3, and panel (d) from Fig. 14.4 of ref. McGinley et al. (2012)

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Passive compartmental models of octopus cells were built from current-clamp recordings and morphological reconstructions, using simulated annealing (Kirkpatrick and Vecchi 1983) to optimize fits of the models to the data (Fig. 14.3a). Active models were constructed using a model of the low-voltage-activated potassium conductance (gKL) derived from medial superior olive neurons (Khurana et al. 2011), which have very similar gKL channels to octopus cell neurons (Golding and Oertel 2012; Bal and Oertel 2001; Scott et al. 2005; Mathews et al. 2010), and a model of hyperpolarization-activated, cyclic nucleotide-gated channels derived from octopus cells (Bal and Oertel 2000; McGinley et al. 2012). Model parameters were adjusted for each model to result in a close match to the current-clamp recordings from the modeled neuron (Fig. 14.3b). Because gKL- and hyperpolarization-activated channels are known to reside in the dendrites of octopus cells and medial superior olivary neurons (Scott et al. 2005; Mathews et al. 2010; Oertel et al. 2008), these channels were included in the dendrites in active models. The kinetics of excitatory synaptic conductances were set to match previous recordings from octopus cells (Gardner et al. 1999).

To test the sensitivity of octopus cells to somatopetal sweeps of synaptic activation arising from the traveling wave delay, the waveform of the somatic EPSP was determined in passive and active models in response to somatopetal sweeps of excitation with different durations. A single-compartment (point) model with identical input resistance and membrane time constant to each passive model was compared in order to evaluate the role of dendrites in shaping the somatic EPSP. Comparison was also made to a passive model with the location of arrival of each input randomized in order to evaluate the role of tonotopy and the resulting somatopetal wave of activation in EPSP shape. A final model was generated with the magnitude of the synaptic conductance at each dendritic location adjusted so that the somatic EPSP in response to individual synaptic activation was approximately constant. Such “input normalization” was discovered and thought to be important for reducing the location dependence of synaptic efficacy in hippocampal pyramidal neurons (Magee and Cook 2000). Surprisingly, input normalization had no effect on the dependence of somatic EPSP shape on somatopetal sweep duration (ref. McGinley et al. 2012, Fig. 14.3).

In active and passive models, somatopetal sweeps of activation lasting 0.6 ms—approximately equal to the duration expected in each octopus cell from the traveling wave delay—resulted in somatic EPSPs that were tall and sharp, and sharpest in active models (Fig. 14.3c, magenta and yellow curves). Responses in point models or passive models with randomized synaptic locations had smaller and more slowly rising EPSPs (Fig. 14.3c, blue and green curves). Active and passive models had short integration windows (the duration of the rising phase of the EPSP; ~0.2 and 0.3 ms, respectively), whereas randomized or point models had long integration windows (~0.5 ms; Fig. 14.3d, left). Thus, octopus cells are effective at compensating traveling wave delays in part due to their morphology and fast membranes.

5 The Role of Low-Voltage-Activated Potassium Channels

Although both active and passive models responded to sweeps matching the traveling wave delay with comparable rising rates and integration windows, half-widths were dramatically shorter in active than in passive models (0.5 vs. 1.2 ms; Fig. 14.3d, right). This reduction in half-width resulted from activation of gKL channels during the EPSP, consistent with experimental observations in octopus cells and medial superior olivary neurons (Golding et al. 1999; Ferragamo and Oertel 2002; Svirskis et al. 2002; Scott et al. 2007). The large effect of gKL channels on the falling phase of EPSPs is similar to the shortening of the falling phase of the action potential by potassium currents in classical and contemporary observations (Hodgkin et al. 1952; Bean 2007). The shortening of the falling phase of the EPSP by gKL channels rapidly repolarizes EPSPs, which is important when they occur at high rates in the face of ongoing activity (Svirskis et al. 2004; Scott et al. 2007).

Activation of gKL channels is also important in shaping the rising phase of the EPSP during somatopetal sweeps of activation in octopus cells. This can be seen in calculations of the sweep duration that results in the fastest rising and largest EPSP in passive versus active models. In active models, EPSPs were largest for sweeps lasting ~0.5 ms, with little variance between models (Fig. 14.4a, magenta symbol) in good agreement with the measured traveling wave delay of 0.53 ms per octopus cell (McGinley et al. 2012). Too slow of a sweep allows gKL to activate and thereby reduce the EPSP amplitude. In passive models, however, the sweep duration with maximum EPSP amplitude varied between models from 0.8 to 1.6 ms (Fig. 14.4a, black symbol). Similarly, the rate of rise (dV/dt) of the EPSP was significantly larger in active than in passive models for physiological sweep durations; active models had a dV/dt of 50–70 mV/ms compared to 40–48 mV/ms in passive models for sweep durations of 0.4–0.6 ms (see ref. McGinley et al. 2012, Fig. 14.3b). The half-widths of EPSPs in passive and active models were similar to amplitudes in their dependence on sweep duration (Fig. 14.4a), further evidence of the role of gKL in octopus cells’ precise responses in the face of the cochlear traveling wave.

Fig. 14.4
figure 4

Determinants of rapid signal transmission of octopus cells’ dendrites. (a) The sweep duration that produces EPSPs with the largest amplitude or the narrowest half-width—the optimal sweep duration—is plotted against the input resistance for best-fit passive models (black and grey squares) and best-fit active models (magenta triangles) or active models with scaled membrane conductance (other colored symbols). Black lines and filled symbols are for amplitude; grey lines and open symbols are for half-width. Conductance magnitudes for active models indicated below with colors matching the symbols. (b) The total synaptic conductance is plotted against the input resistance, for the same models as in panel A. To facilitate comparisons, the synaptic conductance for each cell in each model was adjusted so that the EPSP amplitude for zero sweep duration was 15 mV. (c) The transfer impedance in best-fit passive models (black) and passive models with 10-fold (light blue) or 100-fold (orange) reduced membrane conductance superimposed on the EPSC power spectrum plotted against frequency (red). Arrows indicate maximum frequency up to which each model has relatively constant transfer impedance. Grey bands indicate ±1 SD, calculated across models (n = 4). (d) Color maps of the spatial profile of the voltage for a sweep duration of 0.6 ms in an example simulated passive octopus cell. The time corresponding to each color map is indicated on the simulated EPSP traces (insets) with a green dot. Panels (a) and (b) are reproduced with permission from Fig. 5 and panel (d) from Fig. 8 of ref. McGinley et al. (2012)

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6 Compensating Longer Delays in Low-Frequency-Hearing Animals

Octopus cells in mice have specialized dendritic morphology, connectivity, and biophysics tailored to compensate cochlear traveling wave delays and encode broadband transient sounds. However, several important aspects of octopus cell physiology remain unexplored, particularly relating to species with lower frequency hearing and thus longer traveling wave delays (Ruggero 1992; Ruggero and Rich 1987). Current findings motivate several possible mechanisms for octopus cells to compensate longer delays, including larger size, lower overall membrane conductance, lower dendritic gKL conductance, or differences in the span of best frequencies in ANFs. Octopus cells in humans are large (Adams 1986). Octopus cells in cats and dogs have lower membrane conductance than in mice, but measurements have been made only in relatively immature animals (Bal and Baydas 2009; Bal et al. 2009).

The effect of overall membrane conductance on dendritic delay compensation was studied in active compartmental models of octopus cells (McGinley et al. 2012). Decreasing active and passive ion channel concentrations by 3-, 10-, 30-, or 100-fold changed the dendritic sweep duration that resulted in the largest and sharpest EPSPs over a range from 0.5 to 2.0 ms (Fig. 14.4a). Surprisingly, somatic input resistance changed only 25-fold, and the necessary synaptic conductance to elicit a large EPSP changed only 3-fold with the 100-fold change in ion channel concentration (Fig. 14.4b), demonstrating the importance of cytoplasmic resistance in dendritic integration. Bigger animals could use larger diameter dendrites to overcome cytoplasmic resistivity. Channels for gKL have an ~3-fold lower density in the dendrites of MSO neurons (Mathews et al. 2010). Octopus cells might use a similar conductance gradient to compensate longer delays. However, changing the dendritic-to-somatic leak conductance over a 10,000-fold range had little effect on dendritic delay compensation in passive octopus cell models (see Fig. 7 of ref. McGinley et al. 2012). The role of conductance gradients of active channels in dendritic delay compensation should be studied further.

There is a trade-off between rapid membrane responsiveness and slow dendritic integration that limits the length of delays that octopus cells can compensate in their dendrites and still fire rapidly. Bushy cells in mice and octopus cells in immature cats and dogs have lower gKL conductances resulting in lower dV/dt thresholds and thus less stringent coincident detection (McGinley and Oertel 2006; Bal and Baydas 2009; Bal et al. 2009). Octopus cells’ low membrane resistance allows them to transmit fast synaptic signals down their dendrites. This can be seen by calculating the frequency dependence of the transfer impedance between the tips of the dendrites and the soma, using the ztransfer tool in NEURON (Hines and Carnevale 1997). Normalized transfer impedance values can be calculated by dividing by the value at 0.1 kHz in that model. In best-fit passive models of octopus cells, the normalized transfer impedance is flat up to ~20 kHz (Fig. 14.4c, black curve and arrow).

Thus, octopus cells’ dendrites in mice transmit the frequency content in their excitatory postsynaptic currents (EPSCs) (Gardner et al. 1999). This can be seen in the power spectrum of a double-exponential fit to EPSC waveforms from the synaptic conductance, g syn measured in octopus cells, which can be derived, and is

$$ P(f)=\frac{g_{\max}^2\times {\left({w}_f-{w}_r\right)}^2}{\eta^2\times \left({w}_r^2+{f}^2\right)\times \left({w}_f^2+{f}^2\right)}, $$

where f is the frequency in kHz, w = 1/τ, “r” and “d” refer to the rising and falling time constants of the double exponential, and η is a normalization factor, following ref. McGinley et al. (2012). Defining normalized EPSG power as log(Ρ(f)/Ρ(0.1)), where Ρ(0.1) is the power at 0.1 kHz, illustrates that the EPSC power spectrum in octopus cells is significant out to very high frequencies as a result of the extremely fast rise of the EPSC (Fig. 14.4c, red curve) (Gardner et al. 1999). When the conductance values in active models are divided by 10 (Fig. 14.4c, blue curve) or 100 (Fig. 14.4c, orange curve) while keeping all other parameters the same, they no longer reliably transfer the high-frequency components of EPSCs. For 10-fold reduction, the transfer impedance was flat up to ~2 kHz (Fig. 14.4c, blue arrow), and with 100-fold it was flat up to ~0.2 kHz (Fig. 14.4c, orange arrow). As a result of octopus cells’ effective transfer of fast signals down their dendrites, a rapid somatopetal sweep of excitation results in progressive activation of the dendritic tree and rapidly rising EPSPs (Fig. 14.4d). The role of active conductances, particularly gKL, and conductance gradients in shaping the dendrite-to-soma transfer impedance warrants further exploration.

7 Downstream Processing and Comparison to Other Systems

Octopus cells are perhaps the fastest dendritic integrators in the brain (Golding and Oertel 2012; McGinley et al. 2012; McGinley and Oertel 2006; Oertel et al. 2000, 2009; Spruston et al. 2007) and encode sounds with extraordinary temporal precision (Godfrey et al. 1975; Oertel et al. 2000; Rhode 1994, 1998; Rhode and Smith 1986). Yet, our understanding of how this exquisite spectro-temporal processing is utilized by downstream circuits is based on indirect evidence and speculation. Octopus cells project predominantly to the contralateral ventral subdivision of the ventral nucleus of the lateral lemniscus (VNLLv) with exceptionally thick axons (Adams 1997; Smith et al. 2005; Schofield and Cant 1997) where they form large endbulb endings onto somas (Adams 1997; Vater and Feng 1990). This configuration results in rapid and powerful excitation of their targets (Schofield and Cant 1997; Vater and Feng 1990; Willard and Ryugo 1983), which are similar morphologically—and perhaps physiologically—to the temporally precise large spherical bushy cells in the VCN (Adams 1997; Wu 1999; McGinley and Oertel 2006; Oertel et al. 2009). VNLLv spherical bushy cells are inhibitory neurons (Saint Marie et al. 1997; Moore and Moore 1987; Winer et al. 1995) and project predominantly non-topographically to the ipsilateral inferior colliculus (IC) (Adams 1979; Brunso‐Bechtold et al. 1981; Roth et al. 1978; Whitley and Henkel 1984; Loftus et al. 2010).

Consistent with anatomical predictions, neurons in the VNLL synchronize to rapid sound modulations (Zhang and Kelly 2006). Some neurons in VNLL respond to clicks with large-amplitude, short-duration, onset inhibition, probably further sharpening the output to IC (Nayagam et al. 2005). There is substantial physiological evidence of rapid and broadly tuned inhibition in the IC. Short latency inhibition is seen in a large fraction of unit responses in the IC of cats and rabbits to a wide range of sounds, particularly when unanesthetized (Kuwada et al. 1989; Carney and Yin 1989; Fitzpatrick et al. 1995, 1999; Bock et al. 1972). Pharmacological evidence supports that short latency inhibition is a direct GABAergic or glycinergic input to the IC (Casseday et al. 2000). Rapid and/or side-band hyperpolarization of the membrane potential plays a key role in response area of many intracellularly recorded IC neurons (Kuwada et al. 1997). Much of this rapid and broadband input could be driven by the octopus cell-to-VNLL pathway. However, broadly tuned inputs to the central nucleus of IC, including from the DNLL and elsewhere in the VNLL, are also inhibitory, possibly because broadband excitation would degrade the tonotopic organization (Oertel and Wickesberg 2002).

The temporally precise disynaptic inhibitory pathway from octopus cells, through the VNLL, to the IC may be preserved from birds and reptiles, through rodents, bats, and cats, to humans (Adams 1979, 1997; Carr and Code 2000), and yet its function is unknown. It has been hypothesized that the function relates to pattern recognition in natural sounds (Oertel and Wickesberg 2002). Alternatively, the pathway could serve to sharpen tonotopy in the IC by providing lateral inhibition (Blakemore et al. 1970), though it is not clear why extraordinary speed would be necessary for this purpose (Amari 1977). Instead, the disynaptic inhibitory pathway could aid in sound source separation or stream segregation (Bregman 1994) by “wiping the slate” of activity in IC neurons at the initiation of sounds, providing a signal for “binding” immediately subsequent activity into a percept (Treisman 1996; Shadlen and Movshon 1999). This binding mechanism could contribute to the precedence effect (Langner 1992; Litovsky et al. 1999) and echo suppression (Yin 1994), because the first instance of the sound would usually contain the sharpest onsets and thus engage the binding mechanism most strongly. The disynaptic pathway likely contributes to transforming the rapid temporal code in the auditory periphery into a rate code or a slower temporal code in the IC suitable for processing by thalamocortical circuits (Eggermont 2001; Joris et al. 2004).

Octopus cells compensate the cochlear traveling wave delay using sensitivity to somatopetal sweeps of excitation, with passive cable properties playing a significant role. Thus, octopus cells may be the clearest example to date of a computation performed using Rall’s prediction in 1964 of dendritic sensitivity to sweeps (Rall 1964). Some amacrine and ganglion cells in the retina use sensitivity to dendritic sweeps to compute object motion (Euler et al. 2002; Vaney et al. 2012). However, motion occurs over a wide range of temporal and spatial scales, and thus multiple complex circuit, synaptic, and intrinsic mechanisms play a role in this computation (Briggman et al. 2011; Vaney et al. 2012; Chap. 13 in this book). It has been demonstrated that cortical neurons are sensitive to sweeps of excitation, possibly to aid in detection of temporal input sequences (Branco et al. 2010; Chap. 15 in this book). However, sweep sensitivity in cortical neurons occurs on a much slower time scale than in octopus cells, supported by impedance gradients and other nonlinearities in cortical dendrites (Branco et al. 2010). Given the primitive state of our understanding of the precise distribution of ion channels in dendrites and the in vivo patterns of dendritic activation in most brain areas (Briggman et al. 2011; Bock et al. 2011; Johnston and Narayanan 2008), dendritic sweep sensitivity—predicted by Rall and exploited elegantly by octopus cells—will be the subject of study for decades to come.