Figure 1.
Complex Waveforms (CW) in AVCN and MNTB and overview of the general task.
(A) In the AVCN the CW usually has three components, P, A, and B [11]. Aside from this CW, also the combination of only P and A occurs, constituting candidates of failed transmission. Since A is usually larger than P, the height of A was used for triggering the P-A combinations. Hence, in the AVCN A is the trigger potential (TP). (B) In the MNTB the CW has two components, C1 and C2 [13]. Here, the height of the presynaptic C1 serves to detect failure candidates, i.e. constitutes the TP here. (C) To check the reliability of transmission, three cases need to be distinguished (here illustrated without noise for a mean CW from an MNTB unit): (top) If the CW has a strong C1 component, but no potentials of a similar height (iPs) occur in the remaining trace, then the recording is from a single unit and there is no indication for failures. (middle) If iPs occur, but some of them are located too close (less than the refractory period, RP) to their counterpart (C1) in the CW, then the recording is from multiple units and the iPs do not stem from failures. (bottom) If iPs occur and they all respect the RP, then they likely correspond to failures (assuming other correlation factors, e.g. phase locking, are ruled out). (D) Under realistic recording conditions, iPs could be due to failures (only C1), other cells, or just noise fluctuations. Classical spike-sorting cannot reliably distinguish between these cases. If an iP is detected close to a C1, failures cannot necessarily be excluded since this could have been a noise fluctuation. To decide whether these violations are due to noise, a statistical test is required that compares the distribution of iPs at different distances from C1. In the AVCN, a corresponding argument would replace C1 with the P-A waveform.
Figure 2.
Schematic of the Independence Analysis of Potentials (IAP).
We subjected three data sets to the IAP: voltage recordings from AVCN, MNTB, and simulations. I. First, candidate waveforms were collected by triggering at a visually chosen threshold (A, red) and then (B) aligned at their minimum. (C) Next, these waveforms were spike sorted using principal component and cluster analysis. (D) The cluster containing the complex waveforms (CWs, blue) was selected, thus excluding waveforms of different shape (black). II. The height and relative position of the trigger potential (TP = prepotential in MNTB; = A-component in AVCN) were detected in the average CW. (blue: mean; gray: ±1 SD) III. Isolated potentials (iPs, small vertical bars in upper graph) were triggered at the TPs height (red horizontal line) and collected into a histogram relative to the TP of the CW. Each box color corresponds to an iP preceding a given spike. Different colors indicate which CW they correspond to (compare to upper graph, box size does not indicate actual bin-size). IV. Whether the iPs derive from the CW's source or from a different source is assessed by comparing the density of triggered iPs in the period immediately preceding the CW (one refractory period, CritWin) with the period preceding CritWin (1–5 ms, RefWin). If the iP rate in CritWin was significantly smaller than in RefWin, the recording was classified as containing dependent iPs (Dep), otherwise to not contain dependent iPs (No Dep). This decision was based on the test statistic and the decision point
(for details see Methods).
Figure 3.
(A) is determined by the intersection of the β-error distributions for the two cases Dep (blue, corresponding to failures) and No Dep (orange, corresponding to two units) which were generated from simulated voltage recordings. (B) Average
assigned by IAP to simulations with matched parameters (colors as above). On average, IAP separates Dep and No Dep for all values of the total number of iPs in the RefWin and CritWin (
) and the signal-to-noise ratio of the TP (SNR
). (C) One-sided 5% β-error surfaces for Dep and No Dep. The curve of intersection between these surfaces marks the parameter combinations where the common β-error drops below 5%, the criterion for including recordings. If
of a given recording lies below the surface of equal β-errors (yellow), it is classified as Dep, otherwise as No Dep.
Figure 4.
Distribution of signal to noise ratios of the TP (SNR) and spontaneous firing rates.
(A) The distributions of SNR in the AVCN and MNTB are quite similar. SNR is defined as the size of a potential divided by the standard deviation of the noise (see Methods). (B) Spontaneous firing rates between the two nuclei differ in distribution with AVCN rates concentrated in the range 40–100 Hz. MNTB firing rates reach similarly high values but were concentrated below 40 Hz. 35% of MNTB firing rates exceed 30 Hz.
Figure 5.
Examples of IAP for simulated, AVCN, and MNTB recordings of spontaneous activity.
The left column shows voltage traces (black) and trigger levels for complex (red) and candidate waveforms (orange) for each unit. The corresponding average complex waveform (black) and its pointwise standard deviation (gray) is depicted in the middle column. The trigger potential (TP) (MNTB: presynaptic spike, AVCN: postsynaptic potential, probably the EPSC) is also indicated. The right column shows the histograms (orange) generated by triggering at the height of the TP (after aligned subtraction of the average complex waveform). Further the interspike interval histograms of the complex waveforms are shown, mainly for visual comparison. For the simulated data (A2, B2) the histograms reflect the failure containing condition by a decrease in CritWin (A2), and conversely the lack of decrease in the two unit condition (B2). Guided by the results from the known datasets, the AVCN data (C2, D2) can be interpreted: A substantial number of cells exhibited histograms similar to the cell in C2, suggesting failures of transmission, while the remaining cells showed histograms similar to the cell in D2. If a decrease occurred, its timing was predicted by the ISI histogram (blue). In the MNTB (E2, F2, G2) the most frequent finding was the absence of iP at the TPs height, leading to an empty histogram as in E2. Most of the units with iPs of sufficient height, exhibited no decrease of the histogram in CritWin, as in F2. In a small fraction of recordings a decrease was observed, yet, this could be accompanied by unusually high variability in timing from the presynaptic to the postsynaptic side as in G2 (see individual trace in middle column). IAP classified the recordings in A,B, and G as Dep and the remaining as no Dep.
Figure 6.
IAP results and proportion of iPs for AVCN and MNTB for each recording condition.
(A) For spontaneous activity the majority (56%) of the AVCN, but less than 5% of the MNTB recordings contained dependent iPs. (B) In the excitatory response condition the percentage of AVCN Dep recordings decreased to 50%. In the MNTB no Dep recordings were found. (C) In the inhibitory/suppressive response condition the percentage of AVCN Dep recordings increased to 80%, whereas again none of the MNTB recordings was classified as Dep. For AVCN Dep recordings the proportion of iPs with respect to the total number of (presynaptic) events estimates the insecurity of transmission (if iPs correspond to failures of transmission). (D) During spontaneous activity No Dep had a significantly smaller iP proportion than Dep, consistent with failures. (E) In the excitatory condition the iP proportion does not differ significantly between the No Dep and the Dep cases, although they both increase compared to the spontaneous condition. (F) In the inh./sup. condition the distribution of iP proportion for the Dep cases increases significantly compared to both previous conditions, whereas the corresponding distribution for the No Dep cases stays similar to the excitatory condition.
Figure 7.
Dep recordings are not correlated with CF.
(A) The distributions of CF for both nuclei differ: AVCN units (blue) are concentrated in the low frequency range reaching up to 3 kHz. The MNTB CFs (red) range over the whole spectrum, yet typically exceeding 3 kHz. The overlap of the MNTB with the AVCN range amounts to 16%. (B) Distribution of Dep and No Dep recordings in the AVCN with respect to CF for all recording conditions (see legend). If the classification as Dep was correlated with lower CFs (where stronger phase-locking occurs), the average CF of the Dep cases should be significantly lower than the average CF of the No Dep cases. The statistical comparison was not significant in any of the conditions (spontaneous, excitatory, single [black] and two-tone [gray] stimulations in the low- [LF] and high-frequency [HF] inhibitory/suppressive response regions) with all (Wilcoxon rank sum test for different medians of two groups).
Figure 8.
Statistics and correlations for the number of iPs and different iP rates.
(A1–3) #iPs in the two windows (RefWin,CritWin) for all recording conditions. In the AVCN iPs are generally more abundant, reflected in higher #iPs in the windows. In the MNTB the #iPs in the windows rises in the excited condition, probably due to activation of neighboring units. In the inh./sup. condition the #iPs in the windows is again reduced, probably due to correlated inh./sup. areas for neighboring units. (B1–3) The iP rate in RefWin equals or exceeds the overall iP rate, thus confirming that the IAP is not biased by considering only iPs close to the CWs. Especially for the MNTB, low iP rates in RefWin entail similarly low overall iP rates, hence correspond to very low #iPs rel. to #CWs. (C1–3) A comparison of SNR and the overall iP rate between the two nuclei shows that for the best SNR
, in the AVCN the overall iP rate often remains substantial, whereas it drops to vanishingly low values in the MNTB. This indicates that in the MNTB virtually no iPs remain under conditions where dependent iPs should be best detectable.