Signal-to-noise ratio in the membrane potential of the owl's auditory coincidence detectors

Abstract

Owls use interaural time differences (ITDs) to locate a sound source. They compute ITD in a specialized neural circuit that consists of axonal delay lines from the cochlear nucleus magnocellularis (NM) and coincidence detectors in the nucleus laminaris (NL). Recent physiological recordings have shown that tonal stimuli induce oscillatory membrane potentials in NL neurons (Funabiki K, Ashida G, Konishi M. J Neurosci 31: 15245-15256, 2011). The amplitude of these oscillations varies with ITD and is strongly correlated to the firing rate. The oscillation, termed the sound analog potential, has the same frequency as the stimulus tone and is presumed to originate from phase-locked synaptic inputs from NM fibers. To investigate how these oscillatory membrane potentials are generated, we applied recently developed signal-to-noise ratio (SNR) analysis techniques (Kuokkanen PT, Wagner H, Ashida G, Carr CE, Kempter R. J Neurophysiol 104: 2274-2290, 2010) to the intracellular waveforms obtained in vivo. Our theoretical prediction of the band-limited SNRs agreed with experimental data for mid- to high-frequency (>2 kHz) NL neurons. For low-frequency (≤2 kHz) NL neurons, however, measured SNRs were lower than theoretical predictions. These results suggest that the number of independent NM fibers converging onto each NL neuron and/or the population-averaged degree of phase-locking of the NM fibers could be significantly smaller in the low-frequency NL region than estimated for higher best-frequency NL.

Fig. 1.

Schematic drawings of the synaptic input and the signal-to-noise ratio (SNR) of the nucleus laminaris (NL) neuron. A: formation of the oscillatory synaptic input. A tonal stimulus induces periodic spike rate changes of cochlear nucleus magnocellularis (NM) neurons. Phase-locked spikes of NM fibers that converge onto an NL neuron create a periodically oscillating synaptic input. Note that troughs of the sound-driven input rate can be below the baseline because of the high spontaneous spike rate of NM fibers (see Funabiki et al. 2011 for related discussion). EPSC, excitatory postsynaptic current. B: summation of the synaptic input from ipsi- and contralateral NM fibers. The oscillation amplitude of the bilateral synaptic input to NL is maximal when the 2 inputs arrive perfectly in phase, whereas it is minimal when the 2 inputs are out of phase. Note that, for clarity, higher harmonics and noise components are not included in this schematic. δ, Phase difference. C: power spectral densities (PSDs) of the input and the membrane potential. Top, PSD of the phase-locked NM inputs. Phase-locking produces the fundamental frequency component and its harmonics in addition to the flat baseline noise. Middle, PSD of the total synaptic input. The low-pass property of the synaptic filtering leads to the PSD of the synaptic input decaying with frequency. Bottom, PSD of the membrane potential. Synaptic input is further filtered by the low-pass membrane processes. Because of the synaptic and membrane filtering, the second harmonic is, in general, smaller than the fundamental frequency component by a few orders of magnitude. Whereas the synaptic and membrane filters alter the overall shape of the PSDs, the band-limited SNR (indicated by gray arrows) remains unchanged throughout these processes.

Fig. 2.

In vivo intracellular recordings from barn owl NL. Two representative examples are shown [A–D: best frequency (BF) = 3,400 Hz; E–H: BF = 2,000 Hz]. A: membrane potential of an NL neuron. Unfiltered and bandpass-filtered (3,350–3,450 Hz) traces are shown. A binaural tonal stimulus at BF is delivered at a favorable interaural time difference (ITD; +2 μs). The membrane potential oscillates at the same fundamental frequency as the stimulus tone. B: membrane potential of the same NL neuron as in A, but for a binaural tonal stimulus at BF delivered at an unfavorable ITD (−109 μs). The oscillation amplitude of the membrane potential is much smaller than that with a favorable ITD. Arrowheads in A and B indicate spikes. C: ITD-dependent spike rate of the NL neuron. Error bars are SD. D: ITD-dependent oscillation amplitude (AC) of the membrane potential. The solid line shows the absolute cosine fit (see materials and methods). E: membrane potential of another NL neuron. Unfiltered and bandpass-filtered (1,950–2,050 Hz) traces are shown. The binaural tonal stimulus at BF is delivered at a favorable ITD (+193 μs). F: membrane potential of the same neuron as in E, but for a binaural tonal stimulus at BF delivered at an unfavorable ITD (−59 μs). G: ITD-dependent spike rate. Error bars are SD. H: ITD-dependent membrane AC component. The solid line shows the absolute cosine fit. To calculate the spike rates (C and G) and oscillation amplitudes (D and H), three 40-ms trials per ITD were used.

Fig. 3.

PSD and band-limited SNR of NL neurons. Data are from the same 2 neurons as in Fig. 2 (A–C: BF = 3,400 Hz; D–F: BF = 2,000 Hz). A: PSD of the membrane potential trace with a favorable ITD. The curve shows a sharp peak at the stimulus frequency (3,400 Hz; open arrowhead) and a smaller peak at the second harmonic (6,800 Hz; filled arrowhead). Dashed gray lines show the stimulus frequency component (“signal”) and the baseline “noise” at the surrounding frequencies. The height of the signal above the noise gives the band-limited SNR. B: PSD of the membrane potential trace with an unfavorable ITD. The peak at the stimulus frequency (open arrowhead) is much smaller than that in A. C: ITD dependence of band-limited SNR. Note the logarithmic scale in the ordinate. D: PSD of the trace with a favorable ITD. The stimulus frequency component (2,000 Hz) is indicated by an open arrowhead, and higher harmonics are indicated by filled arrowheads. E: PSD of the trace with an unfavorable ITD. F: band-limited SNR of the same neuron. The solid lines in C and F show absolute cosine fits (see materials and methods). Three 40-ms traces per ITD were used in C and F. To reduce jitter in the PSD curves (in A, B, D, and E), we averaged 3 PSDs at each ITD.

Fig. 4.

Maximum band-limited SNRs of 21 NL neurons. Each point shows the highest SNR value taken for each neuron (BF = 0.8–5.6 kHz). Solid gray lines show the theoretical upper and lower limits for the SNR. The dashed gray line shows the median of the theoretically estimated SNR (see materials and methods for the equation and Table 1 for the parameters used).

Fig. A1.

Effect of the choice of the bandwidth on band-limited SNR. A: band-limited SNRs calculated with different frequency bandwidths. Each line corresponds to 1 neuron. The vertical dashed gray line at 1 kHz indicates the default bandwidth used in our analysis. B: average effect of the selection of the bandwidth. Changes in SNR with a bandwidth varied from the default bandwidth (1 kHz) are plotted (error bars are SD, n = 21). The gray band shows ±1 dB.