Overview of the datasetsWe demonstrate the method by utilizing simulated signals and subsequently test it on diverse amperometry datasets generated through different experiments under different stimulation conditions. Simulated signals or artificial spike trains were generated through spikes modeled with a linear rise and Gaussian decay. The three candidate datasets we chose to explore in the frequency domain are steps: 1 Hofmeister series dataset31, steps: 2 Dimethyl Sulfoxide (DMSO) dataset32, and steps: 3 Electrodes dataset (first presented in this study). The Hofmeister series dataset makes an excellent candidate to demonstrate that the spike-by-spike frequency analysis method preserves time-domain spike characteristics. The investigation of the relationship between inorganic anions and exocytosis was carried out by He et al.31 and it was shown that anions regulate pore geometry, opening duration, and pore closure in the exocytosis process.Specifically, when chromaffin cells were stimulated by counteranions along the Hofmeister series (from \(\textrm{Cl}^-\), \(\textrm{Br}^-\), \(\textrm{NO}_3^-\), \(\textrm{ClO}_4^-\), \(\textrm{SCN}^-\)) in \(\textrm{K}^+\) solution, the spike width (including \(t_\textrm{rise}\), \(t_\mathrm {\frac{1}{2}}\) and \(t_\textrm{fall}\)) increases and the PSF parameters (including \(N_\textrm{molecules}\), \(\frac{N_\textrm{foot}}{N_\textrm{events}}\) and \(I_\textrm{foot}\) where N is the number of molecules and I is the current) decreases in the Hofmeister order while the number of spike events appears to be similar across all stimulations. With the stimulation of chaotropic anions (such as \(\textrm{SCN}^-\)), the expansion and closing time of the fusion pore is longer when compared to that of kosmotropic ions (such as \(\textrm{Cl}^-\)). The Hofmeister series dataset has therefore been well-studied in the time domain.Another compound, DMSO has also been shown to affect the fusion pore opening rate and increase neurotransmitter content while leaving vesicular contents unchanged. Unlike for example, the Hofmeister series, DMSO affects only the rising phase, \(t_\textrm{rise}\). The DMSO dataset was generated through IVIEC experiments conducted on chromaffin cells using a nanotip electrode. Analysis of control and \(0.6\%\) DMSO datasets in the time domain has been established and hence makes an interesting dataset for frequency analysis. We also demonstrate frequency analysis methods on the electrode dataset which constitute VIEC experiments on chromaffin vesicles using three electrode materials: carbon, platinum, and gold. Sample amperometric traces of all the above datasets are shown in Fig. 18, 19 and 20 of the supplementary section.Hypothesis verification using simulated signalsTo verify the hypothesis of the relationship between spike shape and mean frequency, we generated simulated signals that mimic the behavior of the Hofmeister ions in the time domain. Simulated to mimic the amperometry spikes, the artificial spikes consist of a linear rising segment and a Gaussian decay. Note that Gaussian decay models an exponentially decaying amperometry spike which simulates the signal decay more accurately compared to Dirac delta spikes.The artificially generated set of spike trains mimics the behaviors of the Hofmeister series dataset observed in the time domain, e.g. kosmotropic anions in the Hofmeister series cause thin spikes (hence high-frequency oscillations) in comparison to the wide spikes (low-frequency oscillations) of the chaotropic ions. In other words, in the time domain, the median of the spike width, \(t_\mathrm {\frac{1}{2}}\), of the artificial spikes increases in average along the “Hofmeister” order (see Fig. 3).Thus we artificially assigned each anion type in the artificial data with a range of width that does not overlap with the others, as can be seen in Fig. 3A. Since the number of samples generated per artificial data category was sufficient and homogeneous across categories, we see that the width of standard error of mean bar is quite short and relatively consistent across all categories along with high standard error. In addition, for a detailed description of artificial data generation procedure refer to the supplementary section.We found that the averaged mean frequency of the artificially generated spike trains decreases along the Hofmeister order with no exception, which is consistent with the observations on real data. Since a thinner sine function oscillates with a higher frequency, a kosmotropic anion like \(\textrm{Cl}^-\) will behave similarly, as can be seen from Fig. 3B. Relationship between spike shape and frequency and their influences on spike morphology with explanations on spike detection, and comparison of corresponding sine wave frequency components and Gaussian decay model is discussed in detail in the supplementary section.Figure 3FFT on simulated signals: (A) Spike characteristics in the time domain shown by median of \(t_\mathrm {1/2}\). (B) Spike characteristics in the frequency domain shown by median of mean frequency, \(f_\textrm{mean}\). Hofmeister-like arrangement of mean frequency in the simulated spike trains (“art” stands for artificial). Standard error of mean of the median of \(t_\mathrm {1/2}\) and the median of mean frequency are shown by the error bars. Bars represent the mean of the medians of t-half across multiple simulated signals, with error bars representing the standard error of the mean of the medians…..Figure 4FFT on the Hofmeister dataset. Left: Spike characteristics due to different anion stimulation in the time domain shown by \(t_\mathrm {1/2}\). Right: Spike characteristics in the frequency domain shown by median of mean frequency, \(f_\textrm{mean}\). The averaged median of mean frequency (shown with solid bar) shows a clear dependency on the stimulating anion, i.e. it decreases along the Hofmeister-order (here from left to right) except for the anion \(\mathrm {ClO_4^{-}}\), which also showed its abnormality during the time-domain analysis. Additionally, the cross-cell standard error of mean of the median of \(t_\mathrm {1/2}\) and the median of mean frequency are denoted by the error bars. Bars represent the mean of the medians of t-half across multiple datasets, with error bars representing the standard error of the mean of the medians.Figure 5FFT on the DMSO dataset. Left: Spike characteristics for control and \(0.6\%\) DMSO in the time domain shown by \(t_\textrm{rise}\) (25–100%). Right: Spike characteristics in the frequency domain shown by median of mean frequency, \(f_\textrm{mean}\). Standard error of mean of the median of \(t_\mathrm {1/2}\) and the median of mean frequency are shown by the error bars. Bars represent the mean of the medians of t-half across multiple datasets, with error bars representing the standard error of the mean of the medians.Figure 6FFT on the electrodes dataset. Left: Spike characteristics due to different electrodes in the time domain shown by \(t_\mathrm {1/2}\). Right: Spike characteristics in the frequency domain shown by median of mean frequency, \(f_\textrm{mean}\). Standard error of mean of the median of \(t_\mathrm {1/2}\) and the median of mean frequency are shown by the error bars. Bars represent the mean of the medians of t-half across multiple datasets, with error bars representing the standard error of the mean of the medians.Comparison across datasetsThe mean frequency was selected as a representative metric for spike analysis as it captures the central tendency of the frequency components within each spike, weighted by their amplitudes. While the distribution of frequencies for an individual spike may not be normal, the mean frequency provides a consistent and interpretable summary of the overall oscillatory behavior of the spike. This choice allows for a robust comparison of spikes across different experimental conditions, without assuming normality in the underlying frequency distribution. The median of the mean frequency represents the overall frequency content of the spike and can be associated with different time-domain parameters, such as t-rise or t-half, depending on the experimental conditions. This relationship reflects the influence of exocytosis dynamics on the frequency components of the spike. In new data, this frequency indicator can be used to infer shifts in vesicle fusion dynamics or exocytosis duration based on how it correlates with known time-domain parameters.Given that the distribution of t-half (spike width) values is often non-normal, we use the median as a measure of central tendency. The median is more robust to outliers and skewed distributions compared to the mean, making it an appropriate choice for summarizing the spike width across different experimental conditions.To compare across different datasets or experimental conditions, we compute the mean of the medians of t-half. This allows us to provide an overall summary of the central tendency of spike widths across multiple experimental trials.The standard error of the mean of the medians is calculated to estimate the variability in the mean of the median t-half values across experimental repetitions. This measure helps assess the precision of the estimate and ensures that any observed differences between conditions are statistically meaningful.Although the individual t-half values are non-normally distributed, the Central Limit Theorem (CLT) justifies the use of the mean of the medians and the calculation of standard error. The CLT states that the distribution of the sample mean (in this case, the mean of medians) will approximate normality with a sufficiently large sample size, allowing us to calculate the standard error and make valid statistical inferences.Observations on the amperometry datasetsIn the time domain, the mean of medians of spike width of the Hofmeister dataset traces increases in the Hofmeister order, however with the exception of the nitrate ion (left panel of Fig. 4). In the frequency domain, the mean frequency decreases along with the Hofmeister order, or increases exactly in the opposite order due to the inverse relationship between spike shape and mean frequency. The atypical ordering between the chlorate ion and nitrate ion is captured in the frequency domain as well (right panel of Fig. 4). Our use of median-based statistics, along with the calculation of the standard error of the mean of the medians, ensures robust and reliable comparisons of spike characteristics across experimental conditions, accounting for the inherent variability in biological data.DMSO incubation influences only certain spike characteristics, specifically, it increases \(t_\textrm{rise}\). This is evident from the median of spike width in the time domain, where the control group shows a lower mean of the median value of \(t_\textrm{rise}\) compared to DMSO. In the frequency domain, DMSO shows lower mean frequency on average (Fig. 5). Similar observations can be made on our third and final candidate, i.e. the electrodes dataset (Fig. 6).The standard error of mean error bars per category, and the corresponding standard errors, reflect the effect of sample sizes (5–10 each category), as can been seen for example, in the electrodes dataset that has poor sample sizes. The datasets used here as candidates along with their respective sample sizes and other attributes are summarized in the supplementary section.This method is therefore amenable for statistical validation of any amperometry dataset in the frequency domain. However, it is important to note that (as can been seen from the electrodes dataset), the sample size and length of measurements play a key role as well. Too few samples or too short measurements per category may not be sufficient for statistical tests of frequency analysis, and may result in extremely low standard error of means.Although a workaround for this issue of large error bars might be removing outliers, this is highly discouraged since this would reduce the credibility of the observations made – in particular when the sample size is small. The procedure outlined herein is available as an open-source tool specifically dedicated to the analysis of amperometry signals in the frequency domain. The program implementation is also detailed in the supplementary section.In this work, we have outlined a method for spike-based frequency analysis of amperometry traces that also provides statistical validation of observations on spike characteristics in the time domain. To our knowledge, this is the first fully automated open-source tool available for analyzing amperometric spikes in the frequency domain. We have shown that the time-domain information could be retrieved from spike-based frequency analysis. The proposed method provides a more systematic way of analyzing amperometry data compared to IgorPro QuantaAnalysis which involves manual interventions with the GUI and on Excel.We have outlined quite a diverse set of amperometry datasets that illustrates the relationship between spike shape and mean frequency. Although a few steps of the frequency analysis method are user-dependent (such as data filtering and cut-off factor), the majority of our program is fully automated and has provided consistent results on different amperometric datasets. However, the frequency analysis implementation is a Python package that is not as mature as IgorPro QuantaAnalysis software which, for instance, has functionalities to handle the separation of overlapping spikes automatically. Further, the package does not have a GUI and interaction happens through a Command Line Interface. In addition, this method may not be suitable for datasets that have too few traces.Though with Fourier Transform methods it is possible to evaluate all the frequencies in a signal, the time at which they occur cannot be determined since the signal is represented only in the frequency domain. This bottleneck may be overcome by using methods such as wavelet analysis which can represent a signal in the time and frequency domain at the same time33,34. Using discrete wavelet analysis on the detected spikes will give the time localization of the key frequency levels as well.
