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Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval

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Abstract

Several studies of the behavior in the voltage and frequency fluctuations of the neural electrical activity have been performed. Here, we explored the particular association between behavior of the voltage fluctuations in the inter-spike segment (VFIS) and the inter-spike intervals (ISI) of F1 pacemaker neurons from H. aspersa, by disturbing the intracellular calcium handling with cadmium and caffeine. The scaling exponent α of the VFIS, as provided by detrended fluctuations analysis, in conjunction with the corresponding duration of ISI to estimate the determination coefficient R 2 (48–50 intervals per neuron, N = 5) were all evaluated. The time-varying scaling exponent α(t) of VFIS was also studied (20 segments per neuron, N = 11). The R 2 obtained in control conditions was 0.683 ([0.647 0.776] lower and upper quartiles), 0.405 [0.381 0.495] by using cadmium, and 0.151 [0.118 0.222] with caffeine (P < 0.05). A non-uniform scaling exponent α(t) showing a profile throughout the duration of the VFIS was further identified. A significant reduction of long-term correlations by cadmium was confirmed in the first part of this profile (P = 0.0001), but no significant reductions were detected by using caffeine. Our findings endorse that the behavior of the VFIS appears associated to the activation of different populations of ionic channels, which establish the neural membrane potential and are mediated by the intracellular calcium handling. Thus, we provide evidence to consider that the behavior of the VFIS, as determined by the scaling exponent α, conveys insights into mechanisms regulating the excitability of pacemaker neurons.

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Acknowledgements

The first author acknowledges the Universidad Autonoma Metropolitana Unidad Iztapalapa and the Mexican Council for Science and Technology (CONACyT) for supporting his studies (Grant 358414).

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  1. Universidad Autonoma Metropolitana Iztapalapa Division de Ciencias Basicas e Ingenieria, Mexico City, Mexico

    Alberto Seseña Rubfiaro, José Rafael Godínez & Juan Carlos Echeverría

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  1. Alberto Seseña Rubfiaro
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  2. José Rafael Godínez
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  3. Juan Carlos Echeverría
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Correspondence to Alberto Seseña Rubfiaro.

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Ethical standard

The H. aspersa experiments were performed according to the guidelines for the use of animals of the Universidad Autónoma Metropolitana Unidad Iztapalapa (Mexico City) and the “Norma Oficial Mexicana NOM-062-ZOO-1999.” These guidelines are in accordance with those approved by the National Institutes of Health Guidelines for the Care and Use of Laboratory Animals (revised 1996).

Appendices

Appendix: Inter-Spike Voltage Fluctuations and Noise

We estimated the signal-to-noise ratio (SNR) to characterize and compare the noise generated by our recording setup with the inter-spike voltage fluctuations before and after introducing the electrode in the F1 neuron. 20 time series containing an average of 22000 ± 3000 samples of one specimen were considered (Fig. 5). See Appendix Figs. 5 and 6.

Fig. 5
figure 5

The panel a shows a typical example of the inter-spike voltage fluctuations and the noise generated by our recording setup before and after introducing the electrode in the F1 neuron. Also depicted are the results obtained by the DFA analysis that provides the scaling exponent α. 20 time series containing an average of 22,000 ± 3000 samples of one specimen were considered. In addition, the panel b shows the result obtained by estimating the SNR. (The assessment of the SNR for the inter-spike voltage fluctuations was performed once removing the ISI baseline drift or increasing trend to avoid an overestimation by using a detrending procedure similar to that illustrated in Fig. 6)

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Fig. 6
figure 6

The panel a shows a typical example of the inter-spike voltage fluctuations. The panel b depicts the integration (see “Detrended Fluctuation Analysis (DFA)” section) of the raw inter-spike voltage fluctuations (Black line, Y(k)). The time series Y(k) were divided in non-overlapping segments or boxes of equal length n = 10 and for each box a least-square regression was used to obtain Y n (k) (White line). The local linear trends of Y(k) can be removed by subtracting from each segment Y n (k) as appreciated in the panel c

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The mean of the SNR before the electrode was introduced in the F1 neuron was 0.732 ± 0.182 dB ([0.647 0.817] lower and upper confidence interval to 95%), 24.08 ± 0.086 dB ([24.04 24.12]) once introduced in the F1 neuron, and 0.312 ± 0.245 dB ([0.197 0.426]) after the electrode was extracted. Significant SNR differences were confirmed by one-way ANOVA test (P = 0.0001).

Additionally, we analyzed the behavior of the same data series with DFA, obtaining a median for the scaling exponent α before the electrode was introduced in the F1 neuron of 0.500 ([0.494 0.516] lower and upper quartiles), 1.034 ([1.014 1.053]) indicating long-term correlations once recording inter-spike voltage fluctuations, and 0.570([0.567 0.582]) after the electrode was extracted. Significant differences were similarly confirmed by the Kruskal–Wallis test (P = 0.0001), see (Fig. 5, panel a, b).

Detrending of the Inter-Spike Voltage Fluctuations

The detrended fluctuations analysis (DFA) is a useful method that identifies the presence of long-term correlations in time series (Peng et al. 1995); this analysis has the advantage of avoiding the detection of spurious long-term correlations that are a non-stationary artifacts (Hu et al. 2001). We present an example of the detrended inter-spike voltage fluctuations of the segment presented at the panel A of Fig. 5. This trend elimination is necessary for a reliable estimation of the root-mean-squared fluctuation R(n) at the scale illustrated in Fig. 6.

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Rubfiaro, A.S., Godínez, J.R. & Echeverría, J.C. Relationship in Pacemaker Neurons Between the Long-Term Correlations of Membrane Voltage Fluctuations and the Corresponding Duration of the Inter-Spike Interval. J Membrane Biol 250, 249–257 (2017). https://doi.org/10.1007/s00232-017-9956-z

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