Asymmetries in circuit architecture can have a significant effect on ITD processing. Specifically, the contralateral projections from ventral cochlear nucleus (VCN) to MSO are longer than those from the ipsilateral side (, difference in afferent lengths between ipsilateral VCN to MSO and contralateral VCN to MSO ≈2.45 mm; Paul Nakamura and Karina Cramer, personal communication). To measure this difference functionally we used a thick brain slice preparation from gerbils that preserves the afferent pathways to the superior olivary complex (; see Methods
). Whole cell recordings were obtained from MSO neurons while activating each pathway at the same anatomical position on each side; the pathway between the stimulation point and the cochlea, which is eliminated in this preparation, is assumed to be identical for each side (). We first found that the response latency did, in fact, differ between the two pathways. An analysis of evoked postsynaptic potentials (PSPs) and currents (PSCs) showed that the latencies to peak of contralateral responses were on average about 500 µs longer than those of ipsilateral responses on the same recorded neuron (; average differences in latency to peak for PSPs: 573±62 µs, n
54; for PSCs: 589±81 µs, n
37, see Methods
section). This difference was apparent on a cell-by-cell basis because the difference of latencies (contralateral - ipsilateral) was significantly different than zero (see gray bars in ).
Time difference processing in gerbil MSO in vitro.
In presenting the following experiments, we refer to the in vitro inter-stimulus time difference as ITD. Thus, if threshold were to depend solely on PSP amplitude, then the measured disparity in PSP latencies would predict that the peak ITD response would occur when the contralateral PSP leads by approximately 500 µs (; predicted, thin curve). This ITD value is sufficiently large that the response function would fall largely outside of the physiological range for gerbils, which is ±130 µs 
. In contrast, we found ITD response functions in which MSO firing rate was maximal when bilateral stimuli were delivered with smaller delays of ≈100 µs (; measured, thick curve). This finding suggests that an intrinsic integration mechanism must compensate for the longer contralateral path.
MSO neurons are exquisitely sensitive to the rate of depolarization. Therefore, in order to understand the integration of subthreshold bilateral inputs that lead to a spike, we examined the dynamics of synaptic inputs. Our starting assumption had been that synaptic properties are identical for each of the two excitatory inputs to MSO. We examined this assumption by measuring the rising PSP slopes because their time scale is within the same range as the coincidence detection window as manifested by the width of the ITD response function (i.e., 0–250 µs). Ipsilaterally evoked PSCs had significantly steeper rising slopes than contralateral PSCs () (ipsilateral: 1.04±0.15 nA/ms, contralateral: 0.62±0.06 nA/ms; p
35). This difference was apparent on a cell-by-cell basis because the difference of PSC slopes (contralateral - ipsilateral) was significantly different than zero (see gray bar in ). This result was independent of stimulus amplitude in all tested neurons (see Figure S1
). The differences in the slopes of the PSCs could compensate, in part, for the disparity in delay between the two pathways. Our computational model (below) showed that even a modest asymmetry in rising slopes could shift the ITD response function from its hypothetical position (based on latencies to peak) to the observed location in the in vitro experiment ().
To determine how this asymmetry in excitatory synapse kinetics might compensate for the differences in path length, it was first necessary to determine the contribution of synaptic inhibition. To address this issue, we obtained ITD response functions under current clamp (CC), before and after application of a glycine receptor antagonist, strychnine (SN). As shown in , when synaptic inhibition was present (control), the maximal firing occurred for contralateral leading stimulation, consistent with in vivo recordings 
. When synaptic inhibition was blocked (, SN) the maximal firing rate was close to zero ITD, also consistent with an in vivo study 
. We calculated the ITD at which peak firing probability occurred (“best ITD”) for the population of recorded neurons () and found that under control conditions the peak was at 105±35 µs (contra-leading), while under SN conditions it was at −62±38 µs (ipsi-leading). Therefore, the effect of synaptic inhibition was to shift ITD tuning towards contralateral leading stimuli. Since this shift is in the wrong direction to compensate for the longer contralateral path, we next considered the role of asymmetric excitatory responses.
Effect of asymmetric PSPs and EPSPs in setting best ITD position.
In the presence of inhibition (control), the ipsilaterally evoked normalized PSP slope was 2.71±0.12 ms−1
and the contralateral slope was 2.49±0.10 ms−1
(). When inhibition was blocked (SN), evoked EPSP slopes were significantly different between ipsi- and contralateral responses (ipsilateral: 2.61±0.11 ms−1
; contralateral: 2.21±0.14 ms−1
, see and also Figure S2
). Blockade of glycinergic inhibition increases the differences in the PSP slopes. More specifically, inhibition always increases the slope (, from squares to triangles), but more so for the contralateral responses (, right column). Such steepening occurs for either fast or slow inhibitory synaptic conductance transients (see Figure S3
for theoretical support). In the fast case (Figure S3
, left), the decaying brief IPSC coincides with rising EPSC and the summed current therefore rises faster than the EPSC alone. The effect is stronger on contralateral inputs because the IPSC will more fully decay during the EPSC rise. In the slow case, the IPSC transiently reduces the effective time constant, accelerating the rise although less dramatically than does a fast IPSC (Figure S3
, right). The effect is stronger for contralateral inputs partly because integration of slower inputs is affected more by time constant changes (leakage matters in addition to capacitive integration). Another major contributing factor related to active currents is explained below with our model. Thus, we confirmed that synaptic inhibition reduced the effect of shifting the ITD response function towards zero ITD, and leads us to suggest that the compensation arises from the excitatory asymmetry described above ().
How can such a small asymmetry in EPSP slope influence ITD sensitivity in MSO neurons? We addressed this question by using a computational MSO neuron model that was driven by bilateral trains of excitatory and inhibitory inputs temporally modulated with a periodic function representing VCN responses to pure tone stimuli. Each cycle's composite input was generated from many small excitatory postsynaptic conductances (EPSGs) with statistics that depended on VCN afferent activity that varied with sound frequency and amplitude (see Methods
). shows a simplified version of the simulated MSO inputs to illustrate the variability of the composite EPSGs and integrated EPSPs due only to the jitter on the mini-EPSGs time release. Here, we exclude firing rate modulation throughout the sinusoidal input's cycles, although it is employed in the detailed model used for the simulated ITD functions. Using only differences in vector strength of the simulated inputs from the VCN arriving to each dendrite of the MSO neuron model we modeled differences in rising slope of the bilateral EPSPs (Notice: without delaying the composite EPSP peak, see triangles in for EPSG peaks). These differences led to shifts in the ITD response function that are large enough to compensate for the longer contralateral input pathway. For a given EPSG input, the evoked EPSPs and spike threshold will be determined by the active currents. In MSO and other auditory processing centers, a low threshold potassium current
) exerts control on spike threshold 
. This fast IKLT
imposes a filtering effect on the synaptic inputs allowing only steep EPSG slopes to evoke an action potential 
. Therefore, steeper EPSGs are more likely to trigger spikes, even when shallower EPSGs may have greater amplitude, as is shown in our simulations.
Example of composite EPSGs for an input train (500 Hz) using an idealized auditory nerve fiber model (sinusoidally modulated Poisson rate for mini-EPSG times).
When bilateral subthreshold inputs arrive at an MSO neuron, there is a higher probability of eliciting a spike when the steeper EPSG arrives first. shows how a pair of EPSGs, one fast and one slow, can produce a very different outcome, depending on their order of arrival. When a faster input arrives first this will enable spike generation (, left side). When a slower input arrives earlier it leads to a slower rising EPSP that recruits more IKLT conductance, which hinders spike generation even though a faster EPSG arrives subsequently (, right side).
The differential dependence of spike probability on EPSP's slope disappears when IKLT is disabled.
To show the essence of the ITD response function shift due to the asymmetry in the kinetics of the excitatory inputs we delivered inputs to the model with different vector strength () and calculated their probability to evoke spikes for different input delays (ITD response function, ). If the contralateral composite EPSP was slower-rising, the bilateral combined EPSP had different rising dynamics when the ipsilateral inputs led than when the contralateral inputs led (, EPSPs schematics). Consistent with previous findings 
, the shallower-leading combined EPSP was associated with a lower probability of firing. Therefore, the ITD function shifted towards the ipsilateral leading side (). The asymmetry in firing rate probability caused by an asymmetry in inputs' rising slopes is due to the voltage-dependence of IKLT
conductance. We explain this () by showing that with the same set of bilateral asymmetric EPSPs that generate a shift of ~400 µs (, thick black curve), the shift of the ITD's response function disappears (, brown curve) if we fix the IKLT
conductance at its resting value, in order to maintain the neuron model's time constant and input resistance intact.
We next asked whether the asymmetry in the excitatory inputs could compensate for an intrinsic input delay of ≈500 µs as measured in our in vitro preparation. The simulations showed that the integration of hypothetical symmetric EPSPs led to an ITD response function that was shifted to the contralateral leading side due to the intrinsic contralateral axonal delay (, thin black curve). When asymmetric EPSGs were introduced in the model to generate EPSP slopes similar to those found in our experiments, the ITD function shifted towards the ipsilateral-leading direction due to the favorable response when a steep EPSP occurs first (, thick black curve).
Model prediction of ITD response function using experimental data.
Our experimental data were consistent with this theoretical explanation: most of the neurons displayed this asymmetry in excitatory inputs. Thus, when we subtracted contralateral slope from ipsilateral slope for each individual neuron, the average difference was 0.69±0.18 nA/ms for EPSCs and 0.40±0.12 ms−1
for normalized EPSPs. Inclusion of synaptic inhibition made the simulated EPSPs less asymmetric. The hyperpolarization from inhibition transiently reduced IKLT
. The reduction of this conductance would no longer favor spike generation when fast EPSPs are followed by slow EPSPs. The ITD response function was reduced on the ipsilateral-leading side, giving the appearance of a shift towards the contralateral-leading side (, orange and violet curves), as observed experimentally in vitro () and as reported previously in vivo