These results suggest that at the locus of computation of ITD in the barn owl the behavior of the coincidence detectors can be characterized as the cross-correlation between the stimuli presented to the two ears, up to a scaling factor and an offset. Consistent with the theory presented here, Yin et al. (1986)
showed a correspondence between the sync-rate curve (the FTC weighted by a synchronization coefficient, which is the vector strength weighted by the firing rate) and the Fourier transform of the ITD curve. A direct comparison is difficult because Yin et al. (1986)
did their work in the inferior colliculus, which receives inputs from and does not itself feature coincidence detector neurons (Shackleton et al., 2000
), and spectral tuning was measured differently. However, it appears that their results are a close match for the FTC data presented here. Given that their sync-rate curve shares many of the limitations in estimating the effective frequency tuning using the FTC, it is possible that the relationship between spectral and ITD tuning also holds for the neurons they examined.
We show that the responses of coincidence detector neurons in NL are consistent with a linear-quadratic model. The model assumes that the filtered monaural input signals are reconstructed in the membrane potential and combined additively without distinguishing between left and right input spikes. ITD sensitivity arises because of the quadratic input—output property of the neuron. The existence of a quadratic mapping between membrane potentials and spikes in laminaris neurons may be simply attributable to noise in the subthreshold response (Hansel and van Vreeswijk, 2002
; Miller and Troyer, 2002
). Whereas the nature of the input—output properties of laminaris neurons remains an open question, such a power-law relationship between membrane potentials and spikes is evident in the owl’s inferior colliculus (Peña and Konishi, 2002
). The presence of a quadratic nonlinearity in the model was derived from the NL data and produces a response that is equal to the sum of the ideal cross-correlation of the filtered input signals, monaural terms, and a constant term as seen in the time average of the instantaneous spiking probability:
As shown in the simulations, the relationship between the ITD-dependent and -independent contributions to the response is as seen in the data. This is consistent with the observation of Batra and Yin (2004)
that the neurons of MSO were more likely to be driven by coincidences because of synchronicity in the monaural afferents than predicted by an ideal cross-correlator. Although the model reproduces the observed ITD sensitivity of NL neurons for stimuli with zero ILD, the model fails to accurately describe the balance between monaural and binaural responses as the ILD deviates greatly from zero. The balancing of interaural intensity, thought to be accomplished via the superior olive (Viete et al., 1997
), addresses this concern and may be included in a more detailed model as a gain control mechanism.
For perfect cross-correlation to take place in coincidence detector neurons, a representation of the effective monaural input must emerge in the membrane potential of coincidence detector neurons. The large number of NM axons connecting to each NL cell (Carr and Boudreau, 1993
), coupled with the high spontaneous rate of NM neurons (Köppl, 1997
), is consistent with a mechanism of convergence able to recreate an unrectified copy of the sound in NL neurons using only excitatory phase-locked inputs. The shape of the instantaneous spiking probability estimated from the NL data suggests that an unrectified representation of the effective monaural stimulus is reconstructed in the membrane potential. For each neuron, the spiking probability when one input is fixed at a high positive value is reduced as the contralateral effective input signal is decreased (). The decrease in spiking probability continues as the input signal becomes negative, suggesting that the signal is not rectified. The reconstruction of the effective stimulus in the membrane potential has been predicted by models of the owl’s NL as a sound-analog synaptic input being formed by phase-locked spikes of NM axons (Ashida et al., 2007
Previous work has established that the coincidence detector neurons of the MSO (Yin and Chan, 1990
) show behavior consistent with cross-correlation. However, it has also been shown that inhibition plays a critical role in determining the tuning to ITD (Brand et al., 2002
). Although this inhibition seems to determine the location of the peak, it is not clear whether or not it distorts the overall shape of the rate-ITD function to an extent that would alter the linearity in the spectral domain between the input and the output of MSO neurons and therefore create deviations from the cross-correlation model. There is, at this point, no evidence that the barn owl uses inhibition to alter the shape of the rate-ITD functions of NL neurons; indeed, all evidence to date would seem to be consistent with the model of Jeffress (1948)
(Carr and Konishi, 1990
; Peña et al., 2001
). By confirming that the ITD response of NL neurons is consistent with the cross-correlation theorem, we not only validate one of the key tenets of the Jeffress model but have set forth a methodology for examining this issue in other models in which the question remains open.