A basic concept in theoretical neuroscience is the idea of pooling across a population of noisy inputs to achieve a more reliable measure of the encoded variable. This appears to be the computation that ICcc neurons are performing. There are few other demonstrations of a neural processing stage devoted to noise reduction. Phase locking in the auditory system improves from the auditory nerve to the anteroventral cochlear nucleus of the cat (Joris et al., 1994a
), which has been modeled using both a summative mechanism (Kuhlmann et al., 2002
) and a coincidence detection mechanism (Carney, 1992
); a similar decrease in temporal jitter is seen from the electroreceptors to the midbrain torus of Eigenmannia
(Carr et al., 1986
). Retinal ganglion cells also improve on photoreceptor noise levels, using mechanisms such as temporal or spatial summation (Aho et al., 1993
; Warrant, 1999
), lateral inhibition (Srinivasan et al., 1982
; Balboa and Grzywacz, 2000
), and channel properties (Dhingra et al., 2005
; Ichinose et al., 2005
). All of these examples occur within two synapses of their respective sensory receptor. ICcc appears to be unusual for both its distance from the sensory receptors and its operation on a derived signal rather than unprocessed sensory information.
The information processing inequality (Cover and Thomas, 1991
) states that no operation can increase the amount of information present in the inputs; therefore, our results indicate that there is a convergence of NL afferents onto ICcc neurons. Even under the simplest mechanistic hypothesis of some linear combination of NL inputs, a prediction based on the difference in dynamic range as shown in would likely underestimate the degree of convergence. As – illustrate, there is a degree of rectification in the rate-ITD functions of ICcc that is not present in the NL functions. If we consider the theoretical dynamic range of the unrectified function, then it will exceed the actual dynamic range by a factor of nearly 2. A consequence of this rectification is the possibility of obfuscation of ITDs in the troughs. As can be seen in a few of the examples of , some ranges of unfavorable ITDs are all encoded with a firing rate of 0. The conclusion is that ICcc neurons combine a large number of inputs from NL to ensure that changes in ITD within the owl’s physiological range induce firing rate fluctuations that extend over the majority of the dynamic range of the neurons, even at the expense of rectification attributable to thresholding.
Current theoretical work has tended to emphasize that it is population coding, and not the information carried by single units, that is of primary salience in neural codes (Panzeri et al., 1999
; Dayan and Abbott, 2001
; Sahani and Dayan, 2003
; Johnson and Ray, 2004
; Latham and Nirenberg, 2005
). By this reasoning, it is not clear what benefit the system gains by doing this pooling for noise reduction explicitly within ICcc as opposed to performing it at the same time as the frequency convergence or the emergence of combination selectivity to ITD and ILD that takes place later in the pathway (Takahashi and Konishi, 1986
). One possible implication is that it is important to have an accurate estimate of the ITD alone within a narrow frequency band before integrating across frequency channels. It is known that ICcc projects not only to the lateral shell of the inferior colliculus but also directly to the thalamus (Proctor and Konishi, 1997
; Cohen et al., 1998
). Because the thalamus also receives projections from the lateral shell, there is no a priori reason based solely on considerations of sound localization to require a thalamic projection from ICcc. That such a projection does exist suggests a particular role for band-limited ITD information in the thalamic processing stream. Because interaural correlation, which is the basis of ITD detection, will be influenced not only by the location of the sound in space but by features of the acoustic environment, such as the presence of echoes, the existence of multiple sound sources, and distorting effects of the environment, it is plausible that it plays some role in nonlocalization perceptual tasks. Additionally, work in the lateral shell has suggested that frequency convergence is a gradual process, occurring in a cascade of neurons that terminates in the true space-specific neurons of the external nucleus of the inferior colliculus (ICx) rather than in a single step (Mazer, 1995
). There may be a biophysical constraint on the number of inputs that can be managed by a single lateral shell neuron that requires that noise reduction in the ITD domain occurs before any process of frequency convergence begins.
A similar relay is also seen in mammalian systems, from the homolog to NL, the medial superior olive (MSO), to the central nucleus of the inferior colliculus (ICc). Because mammals do not use ITDs as spatial cues for high frequencies, they do not need to integrate across frequency channels to address phase ambiguity, but it has been argued that pooling of ICc units does occur based on psychophysical evidence (Hancock and Delgutte, 2004
); this model would place ICc in a stage of processing analogous to the position of ICcc. Additionally, Fitzpatrick et al. (1997)
showed a sharpening of rate-ITD functions from neurons in the superior olivary complex to the inferior colliculus and auditory thalamus. The results of Fitzpatrick et al. are consistent with our reports of rectification, although they did not rule out the possibility that they could be explained by frequency convergence; they also make no prediction regarding the decrease in noise or the increase in dynamic range. Together, the work of Hancock and Delgutte (2004)
and that of Fitzpatrick et al. (1997)
suggest that the mammalian ICc may serve the same function as ICcc. At the same time, the frequencies relevant to ITD detection used by mammals are significantly lower than those examined in this study, and there is clear entrainment of MSO responses to a single cycle of a binaural beat stimulus (Yin and Chan, 1990
). Thus, it may be that additional noise reduction is not necessary.
The question also arises why this noise reduction must be done after NL or equivalently why the NL neurons are noisy. It seems likely that the neurons of NL are already performing near the neural limits for coincidence detection. The temporal jitter of the inputs is significant compared with the stimulus period at the frequencies involved (Köppl, 1997
), and the timescales of the coincidences require specialized neurons with fast time constants (Han and Colburn, 1993
; Gerstner et al., 1996
). Under these conditions, greater reliability may not be possible within the co-incidence detectors themselves, requiring that an additional stage of processing perform the necessary pooling. Models of both NL (Gerstner et al., 1996
; Agmon-Snir et al., 1998
) and MSO (Brand et al., 2002
; Zhou et al., 2005
) seem to demonstrate greater dynamic ranges and less overall noise than what we observe in NL; this is likely because the dearth of available NL and MSO data had led to some aspects of the models being based on data from ICcc and ICc. If this is the case, then the models are in effect trying to accomplish with a single neuron what the auditory system accomplishes with several.
One possible mechanism that could accomplish this noise reduction would be averaging. However, strictly speaking, averaging suggests that the dynamic range of the averaging unit should be on the same order as the dynamic range of its inputs, and the dynamic range is in fact larger in ICcc than in NL. This increase may serve to accelerate the process of frequency convergence that occurs in the next stage of the sound localization pathway (Mazer, 1998
). The premise of frequency convergence, confirmed in the nucleus ICx (Takahashi and Konishi, 1986
), includes summation in the ITD domain (Takahashi and Konishi, 1986
; Mori, 1997
; Mazer, 1998
) with thresholding to eliminate peaks that do not correspond to the true ITD (Peña and Konishi, 2000
). This process is influenced by the absolute magnitude of the component rate-ITD functions: the larger their initial amplitude, the larger the absolute difference between true and secondary peaks in the summed function will be, simplifying the task to be accomplished by threshold ().
Figure 8 A schematic to illustrate the effects of dynamic range on frequency convergence. In a, two cosines of different frequencies are plotted. In b, the same cosines are plotted, but the dynamic range has been increased by a factor of 2. In addition, the cosines (more ...)
It has been shown that the owl can localize sounds as short as 10 ms in duration (Konishi, 1973
). Our results indicate that there is a move toward reliable short timescale ITD encoding on a single neuron level within the sound localization pathway. The spiking response of neurons of the ICx, which feature low firing rates with little or no sustained response (Wagner, 1990
; Peña and Konishi, 2000
), represents the culmination of this trend, and it has been reported that single ICx neurons can in fact match the behavioral performance (Bala et al., 2003
). Experiments in ICx have indicated that summation and thresholding of inputs is a crucial component of the neuronal computation of space specificity (Peña and Konishi, 2000
). The computations in ICcc provide a necessary basis for this, with the amplification of dynamic range and the reduction of noise working together to ensure that only the desired portions of the ITD response will exceed threshold.