The model supports the adequacy of coincidence for onset responses, without the need for additional currents. This is particularly true of the OL class. It also reproduces the wide variety of RL functions for BF-tones and some for broad band noise. The models are also consistent with the data in that PSTH types (OL versus OC) and pure tone RL function types are not apparently related. By removing many of the complexities of other models we have been able to concentrate on functional significance of dendritic processing, and explore parameter space more thoroughly. This has revealed more clearly the scope and the limitations of dendritic processing for reproducing VCN onset responses.
The model, however, is unrealistic in some important aspects. It is effectively a model of stellate responses, as it lacks the specialized membrane properties of bushy and octopus cells. There are none of the non-linear effects associated with sub-threshold depolarisation in even a basic compartmental model, such as Kipke and Levy (1997)
. Intracellular measurements of OC cells show a sustained depolarisation which is insufficient for firing in chopper cells (Smith and Rhode 1989
), suggesting some threshold shift may be occurring. There is also evidence of inhibition shaping responses (Palombi and Caspary 1992
). The strength of the model is that, despite missing all these characteristics it still accounts for so much of the data. It suggests that AN innervation is sufficient for forming onset responses in the VCN and that differences in AN innervation can account for much of the variation.
The deficiencies of the model are also informative. Parameter exploration makes it clear where the omitted mechanisms might have a crucial role to play. The most dramatic failure of the model is for broad band noise (BBN) RL functions. In response to BBN all input fibers are stimulated equally, so the cell input resembles a very strong HSR fiber input. This cannot produce RL plateaus in a model that fires as a monotonic function of input. This might suggest a role for fibers of different thresholds, inhibition, some inactivation mechanism, or a combination of mechanisms. It might also suggest a role for inputs other than HSR auditory nerve fibers. The auditory nerve model used here also reproduces realistic RL functions for medium- and low-spontaneous rate auditory nerve fibers, which are quite different to HSR fibers. It was however beyond the scope of this study to explore this possibility.
Another consistent shortcoming is that the initial chopping interval of OC responses is too long. Lowering the integration time constant (τm
) reduces the interval, but it also increases the sustained discharge rate (not shown). A peri-stimulatory threshold shift of some kind would reduce this problem. Justification for this may lie in intracellular recordings. Under current injection, D-stellates frequently show a two-component recovery after an action potential (Oertel et al., 1990
In this model, OI responses require a narrow receptive field or AN inputs will cause the inputs to grow. Experimentally, many OI units respond across wide frequency ranges (Smith and Rhode 1989
). This suggests that a narrow band OI response is possible with a coincidence mechanism alone. Narrow tuning would be expected in bushy (Rouiller and Ruygo, 1984; Smith et al., 1991
) cells. However, this limitation of the model suggests that wide-band OI responses, such as those originating from octopus cells, would require additional mechanisms.
Kipke and Levy (1997)
and Kalluri and Delgutte (2003a)
found that an OL model can be created from an OC by using a smaller number of fibers with stronger input strengths. This was also evident in our models. However, the precision of the onset must also be affected. Kalluri and Delgutte (2003a,b
) have proposed that OI and OL responses required an additional stimulus dependant refractory time. This was to support entrainment, which requires very precise onsets. We did not test entrainment due to the lack of evidence at 5 kHz BF, to which the model was restricted. Strong entrainment has only been seen in low-BF neurons (Rhode and Smith 1986; Godfrey et al., 1975
). In our model low-pass filtered inputs contribute to sustained activity but not the onsets. They can therefore produce a precise- single-onset spike and sustained activity. Furthermore, the main evidence for entrainment is from the posterior VCN, so these units may have been octopus cells. Kalluri and Delgutte's proposed mechanism might be functionally equivalent to the membrane currents found in octopus cells.
Our simulations suggest low-pass filtering could be a factor in determining whether a response would be OC or OL. In the model, the response in the first few milliseconds depends on the strength of the inputs, and the degree of low-pass filtering. If the input at onset is weak, the neuron will reach threshold only once before the AN adapts. Dendritic filtering confers a delay, and changes the shape of the depolarisation, which renders input ineffective during the onset of the tone. Thus OLs are more likely to be produced by a model with severe dendritic filtering. There is good theoretical evidence that dendritic transmission affects the shape of post-synaptic potentials (PSPs) (Rall 1977, Major et al., 1994
). Palmer and Winter (1996)
examined the temporal integration of two-tone inputs, with different frequencies and different onset times, in VCN onset cells. They found temporal integration windows were typically in the range of 10-20 ms. They did not report any differences between OC and OL units. However, there are many factors that affect this in the model. The number of fibers is one determinate, as discussed already. Also, OC response could not be produced if the membrane time constant (τm
) was 2 ms or more (not shown here). Further, the range of frequencies of off-BF tones used by Palmer and Winter (1996)
was limited by the time for which a neuron could be held. One neuron (an OC) was held for five hours. It showed great variation in temporal integration at different frequencies. Given the difference in complexity between dendritic fields that can arise in nature and this simple model, predictions must be drawn very carefully.
This model cannot be taken as evidence against other mechanisms for onset production. Given that cytoarchitectonic details do shape the responses of cells in the way that this and other studies suggest, then the variation in the degree of branching, the extent and orientation of dendrites within a morphological class, suggest that many different patterns of innervation of a neuron should produce different responses. But it is also clear that membrane currents are often shaping responses. Our model is not meant as a model of the responses of bushy cells or octopus cells, and so comparison with these is not appropriate. Numerous previous models (Meyer, 1993; Kipke and Levy 1997, Levy and Kipke 1997
, Kalluri (2001) have been successful in reproducing both OL and OC responses. All these models have convergence of large numbers of inputs and differ widely in their tuning, and this confers on them the basic characteristics of broad tuning and a phasic response. The models differ mainly in their mechanism for producing OL responses. Our models demonstrate that neither intrinsic currents nor the degree of coincidence are crucial in determining responses. They also show more realistic rate-level functions for pure tones, ISIHs, first spike precision and even two-tone facilitation (although not shown here). None of these have been modeled accurately in previous studies. However, no models have shown to be successful in reproducing well the responses to BBN. This is logically therefore the next challenge, and may offer insights into the real constraints of different mechanisms.
The success of this simple model raises interesting general questions about cells in VCN. One issue is: which features of a neuron actually contribute to the responses? The coincidence detection mechanism relies on the adaptation of the auditory nerve input, so in a sense the essential mechanism for producing an onset occurs at the neurons' inputs. However, without convergence of many inputs, stochasticity would obscure the onset. The broad BF range of inputs is not necessary for the onset response (as seen in ), but produces pure tone RLFs with a wide dynamic range. Although we have not described the tuning properties of these models, most do show the broad tuning seen in onset cells. Thus the properties of the responses result from an interaction of cell processing and properties inherent in cells' inputs. A second issue is the extent to which cells in the VCN can be considered as coming from separate classes. There are some clear anatomical distinctions. For example, octopus cells occupy a restricted region of posterior-VCN and D-stellate cells project only within VCN and to the VCN on the opposite side. However, in terms of PSTH response type, RLFs and tuning, our models clearly vary along a continuum from onset to sustained choppers. This suggests that real cells in VCN might also be less distinct than is implied by classification schemes (Blackburn and Sachs 1989, Winter and Palmer 1995