Fig 1.
A. Schematic drawing of the LSO circuit. Excitatory inputs are shown in blue and back, and inhibitory inputs in red. AN: auditory nerve; GBC: globular bushy cell; LSO: lateral superior olive; MNTB: medial nucleus of the trapezoid body; SBC: spherical bushy cell. B. Modeled level-dependence of spike rates of SBCs and MNTB neurons used for simulating ILD coding. C-D. Simulated excitatory (blue) and inhibitory (red) synaptic inputs driven by binaural non-modulated tones with two different ILDs, and the resulting membrane potentials (black). Spike shapes are created by spike-mimicking current (see Materials and methods). E. Simulated ILD-tuning curve. Bars indicate the standard deviation of the spiking rate for 500-ms stimulations repeated 4000 times. Triangles show the ILD values used for the examples in C and D. (Inset) Fano factor of ILD-tuning curve. F. Neuronal discriminability for the ILD tuning curve (see Materials and methods for the definition). Neighboring ILD values in E (2-dB step) was used for the calculations. G-H. Simulated excitatory (blue) and inhibitory (red) synaptic inputs driven by binaural AM tones with two different input phase differences, and the resulting membrane potentials (black). I. Simulated binaural envelope phase-tuning curve at 300 Hz. Bars indicate the standard deviation of the spiking rate for each 500-ms stimulation. Triangles show the input phase differences used for the examples in G and H. (Inset) Fano factor of phase-tuning curve. J. Neuronal discriminability for the envelope phase-tuning curve. Neighboring phase difference values in I (10-deg step) was used for the calculations.
Table 1.
Equations and parameters for the active IF model.
Units: t [ms], V [mV], Ispike [nA], αd [1/ms], and βd [1/ms]. Equations for the synaptic currents Iex and Iinh are given in Table 3. See [41] for the complete description of this LSO neuron model and justification of the parameters.
Table 2.
Equations and parameters for the passive IF model.
See [41] for the complete description of this LSO neuron model and justification of the parameters.
Table 3.
Equations and parameters for excitatory and inhibitory synaptic inputs.
Iexm and Iinhm are the number of spikes of the m-th excitatory and inhibitory fibers, respectively. tmi denotes the timing of the i-th spike of the m-th fiber. fm is the modulation frequency in Hz. SPL is the sound level in dB. The unit for the intensities λ is spikes/s. See [41] for the complete description of the synapse model and justification of the parameters.
Fig 2.
Simulated effects of inhibition loss on binaural tuning of LSO without amplitude compensation.
A. Schematic drawing of the LSO circuit with a loss of inhibitory synaptic inputs. Lost inputs are shown by dotted lines. B. Simulated ILD-tuning curves for different numbers of inhibitory inputs. C. (Thin lines) peak (max) and trough (min) rates of the ILD-tuning curves. (Thick line) Modulation depth defined as the difference between maximum and minimum rates. D. Neuronal discriminability of ILD tuning curves averaged over the range between -45 and +15 dB and normalized to the value for 8 inhibitory inputs. E. Simulated envelope phase-tuning curves at 300 Hz for different numbers of inhibitory inputs. F. (Thin lines) peak (max) and trough (min) rates of the envelope phase-tuning curves. (Thick line) Modulation depth defined as the difference between maximum and minimum rates. G. Neuronal discriminability of envelope phase-tuning curves averaged over the range between -180 and +180 degrees and normalized to the value for 8 inhibitory inputs. In panels C, D, F, and G, the filled circles show the response for the default number of inputs (Minh = 8).
Fig 3.
Simulated effects of inhibition loss on binaural tuning of LSO with amplitude compensation.
A. Schematic drawing of the LSO circuit with a loss of inhibitory synaptic inputs and potentiation of remaining inputs. Lost inputs are shown by dotted lines and potentiated inputs are indicated by thick lines. B. Simulated ILD-tuning curves for different numbers of inhibitory inputs. C. (Thin lines) peak (max) and trough (min) rates of the ILD-tuning curves. (Thick solid line) Modulation depth defined as the difference between maximum and minimum rates. D. Neuronal discriminability of ILD tuning curves averaged over the range between -45 and +15 dB and normalized to the value for 8 inhibitory inputs. E. Simulated envelope phase-tuning curves at 300 Hz for different numbers of inhibitory inputs. F. (Thin lines) peak (max) and trough (min) rates of the envelope phase-tuning curves. (Thick solid line) Modulation depth defined as the difference between maximum and minimum rates. G. Neuronal discriminability of envelope phase-tuning curves averaged over the range between -180 and +180 degrees and normalized to the value for 8 inhibitory inputs. In panels C, D, F, and G, simulated data for the uncompensated case (same curves as in the corresponding panels in Fig 2) are shown by gray dot-dashed lines for comparison; the filled circles show the response for the default number of inputs (Minh = 8).
Fig 4.
Simulated effects of inhibition loss on binaural tuning of LSO with amplitude overcompensation.
A. Total amount of inhibitory synaptic inputs normalized to the value for the default (Minh = 8 inputs). In the uncompensated case (gray dot-dashed line; data shown in Fig 2), the total inputs depended linearly on the number of inputs, while in the compensated case (thin gray line; data shown in Fig 3), the total inputs were kept constant. In the present overcompensation case (solid black line), the summed inhibitory conductance was a linear decreasing function of the number of inhibitory inputs. Namely, in comparison to the default condition, the LSO neuron model receives stronger inhibition in total, when the number of inhibitory inputs was reduced. B. Simulated ILD-tuning curves for different numbers of inhibitory inputs. C. (Thin lines) peak (max) and trough (min) rates of the ILD-tuning curves. (Thick solid line) Modulation depth defined as the difference between maximum and minimum rates. D. Neuronal discriminability of ILD tuning curves averaged over the range between -45 and +15 dB and normalized to the value for 8 inhibitory inputs. E. Simulated envelope phase-tuning curves at 300 Hz for different numbers of inhibitory inputs. F. (Thin lines) peak (max) and trough (min) rates of the envelope phase-tuning curves. (Thick solid line) Modulation depth defined as the difference between maximum and minimum rates. G. Neuronal discriminability of envelope phase-tuning curves averaged over the range between -180 and +180 degrees and normalized to the value for 8 inhibitory inputs. In panels C, D, F, and G, simulated results for the uncompensated case (gray dot-dashed lines; same data as in the corresponding panels in Fig 2) and for the perfectly compensated case (thin gray lines; same data as in the corresponding panels in Fig 3) are shown for comparison; the filled circles show the response for the default number of inputs (Minh = 8).
Fig 5.
Simulated effects of inhibition loss on binaural phase tuning of LSO.
A-D. Responses of the model LSO neuron to 150-Hz amplitude-modulated sounds. E-H. Responses of the model LSO neuron to 450-Hz amplitude-modulated sounds. Panels A, B, E and F present simulated envelope phase-tuning curves for different numbers of inhibitory inputs either without (A,E) or with (B,F) amplitude compensation. The color code used is the same as in Figs 2–4. Thin lines in C and G show peak (max) and trough (min) rates of the corresponding phase-tuning curves in B and F, respectively. Thick solid lines in C and G show the modulation depth defined as the difference between maximum and minimum rates for the compensated case, while gray dot-dashed lines show that for the uncompensated case. D and H present the neuronal discriminability of envelope phase-tuning curves averaged over the range between -180 and +180 degrees and normalized to the value for 8 inhibitory inputs either for the compensated case (solid black) or uncompensated case (dot-dashed gray).
Fig 6.
Simulated effects of inhibition loss on binaural tuning of LSO modeled with a passive IF model.
A-D. Simulated ILD-tuning. E-H. Simulated envelope phase-tuning at 300 Hz. Panels A, B, E and F present simulated binaural ILD- or phase-tuning curves for different numbers of inhibitory inputs either without (A,E) or with (B,F) amplitude compensation. The color code used is the same as in Figs 2–4. Thin lines in C and G show peak (max) and trough (min) rates of the corresponding binaural tuning curves in B and F, respectively. Thick solid lines in C and G show the modulation depth defined as the difference between maximum and minimum rates for the compensated case, while gray dot-dashed lines show that for the uncompensated case. Panel D presents neuronal discriminability of ILD tuning curves averaged over the range between -45 and +15 dB and normalized to the value for 8 inhibitory inputs. Panel H presents the neuronal discriminability of binaural tuning curves averaged over the range between -180 and +180 degrees and normalized to the value for 8 inhibitory inputs. In D and H, solid black lines indicate the compensated case, while gray dash-dotted lines indicate the uncompensated case.
Fig 7.
Simulated effect of inhibition loss on LSO population coding.
A1-A5. Simulated ILD-tuning curves with varied midpoint locations (black) and their mirrored images (gray). Bars indicate the standard deviation of the spiking rate for repeated 500-ms stimulations. B1-B5. Bilateral spike rate differences, defined as the rate difference of each LSO pair (i.e., original and mirrored). C1-C5. Neuronal discriminability functions calculated from the bilateral spike rate differences. D. Population average of the neuronal discriminability functions, plotted for different number of inhibitory inputs without amplitude compensation. E. Population average of the neuronal discriminability functions, plotted for different number of inhibitory inputs with amplitude compensation. F. Population-averaged discriminability that was further averaged over the ILD range between -35 and +35 dB and normalized to the value for 8 inhibitory inputs.