As shown in , the NL neurons fire well when their ipsilateral and contralateral inputs are in phase. At low frequencies the dendritically extensive NL neurons fire poorly as the interaural phase difference (IPD) increases – the hallmark of a good ITD-sensitive coincidence detector. At high frequencies the dendritically compact NL neurons still fire at large IPDs, meaning that their ability to discriminate between ITDs worsens. There is also a significant enhancement of the vector strength of the output over the vector strength of the input, even at nonzero IPD, a potential flaw in the model.
As shown in , ITD discrimination is good until ~2 kHz. The sharp phase tuning at low frequencies, and specifically the firing rate dropping to zero, appears as ceiling effect on the ITD discrimination index at those low frequencies. The lower panel shows the same neurons, but receiving inputs from NM with vector strength enhanced to match that of barn owl. In this case, ITD discrimination is significantly stronger, up to ~4 kHz. By fine-tuning parameters of the model (particularly by adding more dendrites), this can be pushed up to ~6 kHz (not shown), but this is still not as effective as the barn owl, which can discriminate up to ~ 10 kHz (Carr and Konishi 1990
Synaptic sublinearity occurs due to finite synaptic reversal potential, as predicted by cable theory (Rall 1959
; Agmon-Snir et al. 1998
), and it also appears functionally as a drop in ITD discrimination when the excitatory reversal potential is depolarized (not shown). The most interesting effect of synaptic sublinearity can be seen when the dendritic length gradient is turned off or, equivalently, neurons are allowed to receive stimuli at frequencies (unphysiologically) far from their BF. As shown in , for every stimulus frequency there is a dendritic length longer than that at which performance no longer increases. The effect is most pronounced at lower frequencies. The optimal length of the dendrite increases with decreasing frequency. Thus, the dendritic length gradient is predicted under the assumption that dendritic length is minimized while optimizing for ITD discrimination. This is in agreement with Agmon-Snir et al. (1998)
The model also demonstrates a subtraction nonlinearity, due to the presence of KLVA
channels acting as a current sink, and it also appears functionally as a drop in ITD discrimination when the KLVA
conductance is reduced (not shown). This has an interesting additional manifestation: the out-of-phase rate is suppressed relative to monaural rate, even in the absence of spontaneous activity from the contralateral side (). This is because the high input activity from the out-of-phase case activates KLVA
and suppresses depolarization sufficiently to reach spike threshold. This result is in agreement with experimental findings (Goldberg and Brown 1968
; Yin and Chan 1990
) but without the spontaneous activity needed by more linear models (e.g., Colburn et al. 1990
). Note that for the monaural case the average current injected via excitatory synapses is roughly half that of the binaural out-of-phase case, even though the spike rate of the former is greater than that of the latter. Furthermore, by comparing the firing rates for monaural inputs among different neurons (with enhanced KLVA
or missing the opposite dendrite), it can be seen that KLVA
plays an important role in reducing the firing rate, and, in particular, the opposite dendrite can act as a current sink.
Fig. 4 a Firing rate as a function of stimulus frequency (and dendritic length) for three different stimuli. The top and bottom curves are firing rates for binaural stimuli that are, respectively, in-phase and out-of-phase (as in ). The center curve is (more ...)
A finely detailed, yet still highly functional, model of chick NL has been constructed. Typical parameters allow ITD discrimination up to 2 kHz, and enhancements for barn owl allow ITD discrimination up to 6 kHz. There are two nonlinearities that aid ITD discrimination: intradendritic inputs sum sublinearly, and interaction with KLVA subtractively suppresses outof-phase inputs. The response to monaural input does not require any spontaneous activity from the contralateral side. The dendritic length gradient of NL is predicted from optimization of ITD discrimination.