Fig 1.
Recorded responses of cat LSO neurons to AM sounds.
A: Monaural AM responses with varied modulation frequencies. Different lines are used for different LSO units. Several response types of AM-tuning were found and shown in different colors. Some units exhibited characteristics of multiple response types. B: Binaural AM responses with varied ITDs. Different line types correspond to different modulation frequencies. Adapted and redrawn from Figs 13B and 16B of Joris and Yin [36] with permission.
Fig 2.
LSO coincidence counting model.
A: Modeled AM-frequency dependence of the excitatory input rates. B: Modeled AM-frequency dependence of phase-locking of excitatory inputs. C: Modeled operation of coincidence detection. Each vertical bar corresponds to a spike. An input coincidence is counted when the number of inputs in the coincidence window W (vertical gray rectangle) reaches or exceeds the threshold θ. In this example, threshold θ is 3. The small arrow indicates an output spike rejected by the refractory period T. Effects of inhibitory inputs were modeled as threshold increase δ in the inhibition window Δ (dotted rectangle). D: Monaural AM-tuning curve with the default parameter set (θ = 8 inputs, W = 0.8 ms, T = 1.6 ms). Peak rate = 138.3 spikes/sec. Peak frequency = 265 Hz. Baseline = 9.7 spikes/sec. Half-peak frequency = 549 Hz. E: Binaural AM-phase coding with the default parameter set (fm = 300 Hz, δ = 2 inputs and Δ = 1.6 ms). Peak rate = 130.7 spikes/sec. Peak phase = −137 deg. Trough rate = 18.7 spikes/sec. Trough phase = +46 deg. Half-peak width = 191 deg. F: Modeled level-dependence of input spike rates. G: Modeled level-dependence of phase-locking. Both excitatory and inhibitory inputs were assumed to share the rate-level and VS-level functions. H: Effects of modulation frequency fm on coincidence detection. Depending on frequency, the length of one modulation cycle could be larger (at low fm) or smaller (at high fm) than width W of the coincidence window. Thick curves show the spike rates of the phase-locked inputs. Broken lines show the time-averaged (non-phase-locked) spike rates.
Table 1.
(#1) Sanes [51] reported that the number of excitatory subthreshold inputs was 9.6 ± 2.8 in gerbils, which serves as the lower bound of the total number of excitatory inputs. The MSO neuron, which has a similar anatomical structure to the LSO neuron, receives a few times more excitatory inputs than inhibitory inputs [53]. Assuming a similar ratio, 20 excitatory inputs (derived from 8 inhibitory inputs) would be reasonable. (#2) Measured membrane time constants of gerbil LSO cells were 1.1 ± 0.4 ms and minimum durations of excitatory synaptic inputs were 1.5 ± 0.8 ms [51]. We assumed that these values roughly limit the maximum width of the coincidence window. (#3) Based on the measured minimum durations of inhibitory synaptic inputs of 3.2 ± 1.7 ms in gerbils [51], we assumed the inhibition window to be twice as long as the coincidence window. (#4) As far as we know, there is no direct measurement available. See Discussion for more information on relevant experimental values.
Fig 3.
A: Effects of non-uniform input intensities. (Black curve: uniform intensity) The default input intensity of λ0 = 180 spikes/sec (at zero modulation frequency) was used for all input fibers. (Gray curves: varied intensity) The input intensity λ0 of each fiber was randomly chosen from a uniform distribution between 80 and 280 spikes/sec. Results for ten simulation trials are shown. B: Effects of input parameters on spike rates. In the 'constant rate' condition, the average input rate was fixed at 180 spikes/sec. In the 'constant VS' condition, VS was fixed to 0.65. Otherwise, these parameters were varied with the modulation frequency (see Materials and Methods). C: Effects of input parameters on the modulation gain. Line types in C correspond to those in B.
Fig 4.
Effects of coincidence threshold θ.
A: AM-tuning curves (rate-MTFs). B: Peak and baseline spike rates. C: Peak and corner frequencies of the rate-MTFs. D: Modulation gains (synch-MTFs). Line types in D correspond to those in A.
Fig 5.
Effects of coincidence window W.
A: AM-tuning curves (rate-MTFs). B: Peak and baseline spike rates. C: Peak and corner frequencies of the rate-MTF curves. D: Modulation gains (synch-MTFs). Line types in D correspond to those in A.
Fig 6.
Combined effects of coincidence threshold θ and coincidence window W with a fixed ratio of θ/W.
A: AM-tuning curves (rate-MTFs). B: Peak and baseline spike rates. C: Peak and corner frequencies of the rate-MTF curves. D: Modulation gains (synch-MTFs). Note that also for panels B and C, both the coincidence threshold and window were changed together as in panels A and D.
Fig 7.
Combined effects of coincidence threshold θ and coincidence window W with fixed maximum spike rates.
A: AM-tuning curves (rate-MTFs). B: Peak and baseline spike rates. C: Peak and corner frequencies of the rate-MTF curves. D: Modulation gains (synch-MTFs). Note that also for panels B and C, both the coincidence threshold and window were together changed as in panels A and D.
Fig 8.
Effects of refractory period T.
A: AM-tuning curves (rate-MTFs). B: Peak and baseline spike rates. C: Peak and corner frequencies of the rate-MTFs. D: Modulation gains (synch-MTFs). A jump in the peak frequency in C reflects transitions of AM-tuning between low-pass and band-pass. Line types in D correspond to those in A.
Fig 9.
Effects of spontaneous inhibitory inputs.
A: AM-tuning curves (rate-MTFs). B: Modulation gains (synch-MTFs). Curves for θ = 8 (default threshold: thick lines) and 7 (reduced threshold: thin line) are shown for comparison. Spontaneous rates λinh of inhibitory inputs were: 0 (no inhibition), 30 (default) and 60 (doubled inhibition).
Fig 10.
Effects of coincidence detection parameters on binaural phase coding.
A-C: Effects of the coincidence threshold θ. D-F: Effects of the coincidence window W. G-I: Effects of the refractory period T. A,D,G: Phase-tuning curves. B,E,H: Peak and trough rates of the phase tuning curves. C,F,I: Half-peak width and trough phase of the phase tuning curves.
Fig 11.
Effects of inhibition parameters on binaural phase coding.
A-C: Effects of the threshold increase δ. D-F: Effects of the inhibition window width Δ. A,D: Phase-tuning curves. B,E: Peak and trough rates of the phase tuning curves. C,F: Half-peak width and trough phase of the phase tuning curves.
Fig 12.
Effects of window parameters on binaural temporal coding.
A: Combined effects of coincidence window W and inhibition window Δ. Phase-tuning curves for simulated AM inputs at 150, 300, 450 and 600 Hz are shown. Input phase differences (abscissa) are converted into milliseconds to facilitate comparison across frequencies. Different rows and columns correspond to different widths of the coincidence window W (0.4, 0.8, and 1.2 ms) and inhibition window Δ (0.8, 1.6, and 2.4 ms), respectively. B: Dependence of trough positions on covaried coincidence window W and inhibition window Δ. These window parameters were varied while their difference Δ-W was fixed at 0.4, 0.8 or 1.2 ms. C: Dependence of trough positions PT on the window size difference Δ-W. Either of the window parameters was fixed at the default value (black: W = 0.8 ms; gray: Δ = 1.6 ms), while the other parameter was varied. The dotted diagonal line shows a slope of 0.5 (i.e., PT = (Δ-W)/2). In B and C, the input modulation frequency was fixed at 300 Hz. D: Schematic drawing of how the inhibition window interacts with the coincidence window.
Fig 13.
Effects of level difference on binaural temporal coding.
A. Simulated output spike rate of the model LSO neuron for non-modulating inputs (fm = 0 Hz). The ipsilateral sound pressure driving excitatory inputs was fixed at five different levels (25–45 dB) and the contralateral level was varied. B. Phase-tuning curves for different ILDs. C. ILD-dependence of the peak and trough spike rates of the phase-tuning curves. In B and C, the input modulation frequency and the average binaural level (defined as the arithmetic mean of the bilateral sound input levels) were fixed at 300 Hz and 20 dB, respectively, which corresponded to an input rate of 150 spikes/sec at ILD = 0.
Fig 14.
Response of pure integrator model.
A: Simulated monaural AM-tuning curves (rate-MTFs). B: Modulation gains (synch-MTFs). C: Binaural phase-tuning curves at different frequencies. The same input parameter set as for Fig 2D and 2E was used. The threshold was fixed to 8 inputs in C.