Kinetic Diversity of Single-Channel Burst Openings Underlying Persistent Na+ Current in Entorhinal Cortex Neurons  Jacopo Magistretti, David S. Ragsdale, Angel Alonso  Biophysical Journal  Volume 85, Issue 5, Pages 3019-3034 (November 2003) DOI: 10.1016/S0006-3495(03)74721-3 Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 1 Different “persistent” Na+-channel burst openings can display major differences in open- and closed-time duration. The figure shows exemplary burst openings chosen from those recorded in six different patches to illustrate the kinetic diversity typically observed in such events at the same membrane potential (Vm). Each trace is a detail of a single burst. Burst openings were elicited with 500-ms step depolarizations at three different Vm measurements (−40mV, −30mV, and −10mV). Bursts 1–3, 7, 10, 14–16, and 18 are from patch C8708; bursts 8, 9, and 17 from patch B8708; bursts 4 and 13 from patch F8711; bursts 5 and 11 from patch A8721; burst 6 from patch A8618; and burst 12 from patch D8708. Calibration bars are 1pA, 25ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 2 Prominent differences in burst gating properties can be observed in single patches. The figure shows six consecutive sweeps from a patch (A8721) displaying the activity of two channels characterized by prominent differences in intraburst open- and closed-time behaviors. The voltage protocol applied is illustrated in the upper panel. In traces 1 and 2, burst openings characterized by an intense “flickering” behavior are seen. The bursts observed in traces 5 and 6 show much more “stable” opening and closing events. In traces 3 and 4, burst openings characterized by the two different gating modalities occurred simultaneously and appear superimposed (arrows). Calibration bars are 1 pA, 50ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 3 Display and analysis of intraburst open- and closed-time data from single bursts. (A) Frequency-distribution diagrams of intraburst open times for a single, exemplary burst recorded at −40mV. (B) Frequency-distribution diagrams of intraburst closed times for the same burst. The burst from which the analysis here presented was derived is depicted in B1, inset (calibration bars are 1pA, 50ms). A1 and B1 show histograms constructed after linear binning of original data and displayed on a double-linear scale (bin width is 0.1ms in both cases). A2 and B2 are logarithmic histograms. Data were binned logarithmically (11.4 bins/decade), and the natural logarithm of the numbers of observations per ms, i.e., ln(n/ms), was plotted as a function of time in a logarithmic (insets) or linear (main panels) scale. In log-linear histograms, the x-value of each point is the logarithmic midpoint of the corresponding bin. Smooth, enhanced lines are first-order (A2) or second-order (B2) exponential functions obtained by applying the fitting function of Eq. 1 (Methods) to log-log histograms. Smooth, dotted lines in B2 are the single exponential components shown separately. Fitting parameters are W=336.5, τo(b)=795.2μs (A2); and W1=537.0, τc(b)1=133.0μs, W2=164.6, τc(b)2=567.3μs (B2). In log-linear histograms (main panels), single exponential fitting components appear as straight lines. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 4 Diversity of open times. (A) Frequency distribution of time constants describing intraburst open times (τo(b)s) at −40mV. The τo(b)-values used to construct the histogram were derived from individual bursts (n=67) recorded in nine different patches. Note the two different bin widths (0.1ms for τo(b)<1.1ms and 0.2ms for τo(b)≥1.1ms). The inset shows the same histogram constructed as a stack-column diagram, with each column pattern corresponding to data from a single patch. The histogram was best fitted with the sum of four Gaussian functions (smooth line), which returned the fitting parameters A1=26.33, μ1=0.343ms, σ1=0.181ms; A2=35.93, μ2=0.769ms, σ2=0.229ms; A3=4.11, μ3=1.74ms, σ3=0.167ms; and A4=10.15, μ4=2.982ms, σ4=0.635ms. The arrowheads indicate the previously-reported τo(b)-values obtained by pooling data from different patches (Magistretti and Alonso, 2002). (B) Frequency distribution of τo(b)s for randomly-generated open times. Seventeen groups of numeric values distributed exponentially according to a time constant of 0.343ms (a value which coincides with the μ1 returned by the Gaussian fitting illustrated above) were generated randomly. Each group consisted of 49–255 values (see the text), which were binned logarithmically, as explained in the legend for Fig. 3, to construct a “simulated” open-time frequency distribution. Each of the histograms thus obtained was best-fitted with a single exponential function, and the time-constant values returned by fittings (“simulated”τo(b)s) were in turn binned to construct a “simulated”-τo(b) histogram, shown here. The smooth line is the best fitting obtained applying a single Gaussian function; fitting parameters were A=16.04, μ=0.325ms, and σ=0.154ms. (C) Frequency distribution of τo(b) at −30mV. τo(b)-values were derived from individual bursts (n=87) recorded in 11 different patches. Note the two different bin widths (0.2ms for τo(b)<2ms and 0.4ms for τo(b)≥2ms). Arrowheads are as in A. (D) Plot of the average number of openings per burst as a function of Vm. Data were obtained by dividing the average burst duration (τ¯b) by the sum τ¯o(b)+τ¯c(b) (where τ¯o(b) is the mean open time and τ¯c(b) is the mean closed time) for each Vm. τ¯b-, τ¯o(b)-, and τ¯c(b)-values were derived from Magistretti and Alonso (2002). Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 5 Single channels can generate multiple τo(b)s and gating modes. (A, B) Open-time analysis of two long-lasting burst openings (patch C8708 in A, A8716 in B; Vm=−50mV in A, −10mV in B). A1 and B1 show the original bursts; note that, in both, a relatively “stable” gating modality (wide arrowheads) was preceded and/or followed by a more “flickering” one (thin arrowheads). Calibration bars are 1 pA, 50ms. A2 and B2 show the frequency distributions of open times within the same bursts. Data were binned logarithmically and in the main subpanels are shown in a log-linear plot. In the insets, the same data are shown as log-log histograms. Two exponential components are clearly recognizable in both cases. In all subpanels, the smooth, continuous line is the best second-order exponential fitting obtained applying Eq. 1 to the log-log plot. Dotted lines are the single exponential components of the fitting functions shown separately. Fitting parameters are W1=232.72, τo(b)1=0.765ms; W2=4.49, τo(b)2=19.283ms (A2); W1=76.45, τo(b)1=1.345ms; and W2=30.46, τo(b)2=10.093ms (B2). A3 and B3 show the distributions of the null statistic, S*, for the same bursts (see the text for details). The variability statistic, S, was calculated by dividing each burst into six subsections, each with an approximately equal number of openings. S-values (1.517 in A3 and 44.48 in B3) are indicated by the arrows. Each set of individual bars is a histogram of 1000 values of S*, obtained by repeatedly scrambling the order of the burst’s open times and recalculating the variability statistic. Note that S is >S* for 996 out of 1000 of the observed S*-values in A3, and for all S*-values in B3, indicating that the open-time variability along these bursts is greater than expected from a random occurrence of open times. (C) Another example of burst opening showing distinct gating modalities (patch F8711; Vm=−10mV). Both stable and flickering gating modalities (wide and thin arrowheads, respectively) were observed in bursts from the same patch, and occasionally occurred in sequence within a single burst (double arrow). Calibration bars are 1pA, 25ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 6 Statistical analysis of open-time variability within bursts. (A) The burst shown in A1 (from B8708; Vm=−30mV; calibration bars are 1pA, 50ms) showed a biexponential distribution of open times, as illustrated in A2. Open-time data were binned logarithmically and in the main subpanel are shown in a log-linear plot. In the inset, the same data are shown as a log-log histogram. Two exponential components are clearly recognizable. In both subpanels, the smooth, continuous line is the best second-order exponential fitting obtained applying Eq. 1 to the log-log plot. Dotted lines are the single exponential components of the fitting function shown separately. Fitting parameters are W1=75.33, τo(b)1=0.784ms; and W2=109.22, τo(b)2=2.552ms. A3 compares the distribution of the null statistic, S*, with the variability statistic, S, for the same burst (see the text and Fig. 5, legend, for details). The value of S (0.955) is indicated by the arrow. Note that S is well within the random S* distribution, indicating that the open-time variability along this burst is consistent with a random occurrence of open times. (B) The cumulative frequency distribution of %S*>S was determined for 37 bursts recorded at −40 or −30mV, values in all bins were normalized for the total number of observations, and the percentages thus obtained were subtracted from the “theoretical” percentages predicted on the basis of the null hypothesis. Note the prominent excess of positive values (indicative of a more frequent occurrence than expected on the basis of chance) in the leftmost portion of the plot, i.e., for low values of %S*>S. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 7 Diversity of closed times. (A) Frequency distribution of time constants describing intraburst open times (τc(b)s) at −40mV. The τc(b)-values used to construct the histogram were derived from individual bursts (n=67) recorded in nine different patches. Note the two different bin widths (0.1ms for τo(b)<1.0ms and 0.2ms for τo(b)≥1.0ms). The inset shows the same histogram constructed as a stack-column diagram, with each column pattern corresponding to data from a single patch. The histogram was best-fitted with the sum of four Gaussian functions (smooth line), which returned the following fitting parameters: A1=38.07, μ1=0.241ms, σ1=0.207ms; A2=37.61, μ2=0.543ms, σ2=0.419ms; A3=13.06, μ3=1.475ms, σ3=0.589ms; and A4=7.48, μ4=2.581ms, σ4=0.521ms. The arrowheads indicate the previously-reported τc(b)-values obtained by pooling data from different patches (Magistretti and Alonso, 2002). (B) Histograms of “fast”τc(b) (τc(b)1: B1) and “slow”τc(b) (τc(b)2: B2) for bursts in which closed times were distributed according to a double exponential function. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 8 Correlation between τo(b) and τc(b). (A) Scatter plot of τc(b) as a function of τo(b) for single bursts. In the cases of bursts in which open and/or closed times were distributed according to a double exponential component, the prevalent τo(b) and/or τc(b) (in terms of the corresponding weight coefficient) were considered. (B) Detail of the region of the τc(b)(τo(b)) plot delimited by the dotted-line box in A. Two clusters of points are evident (solid and open symbols). Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 9 Single channels preferentially operate according to a specific gating modality. (A) Consecutive sweeps recorded at the step potential of −30mV in a patch (A8721) in which a single channel continued to generate long-lasting burst openings for prolonged periods. The characteristic and homogeneous pattern of gating of these bursts, with relatively prolonged and stable openings and closings, clearly appears at a simple visual inspection. Calibration bars are 1pA, 50ms. (B) Frequency distribution of τo(b) for 22 bursts recorded at −30mV in the same patch of A. The histogram was best-fitted with a single Gaussian function (continuous line), which returned the fitting parameters of A=17.72, μ=3.227ms, and σ=1.562ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 10 Diversity of burst duration. (A) Exemplary traces recorded at −40mV or −10mV in three different patches that displayed prevalence of medium-duration (A1), long (A2), and very long (A3) bursts. The arrows point to exemplary bursts selected for burst-duration analysis. When superimposed bursts were recorded, only those ones the starting point and the end of which could be clearly identified (i.e., when the burst’s starting point coincided with the depolarizing pulse’s onset; see A2) were considered for burst-duration analysis. Note in A3, third trace from top, two very-long-lasting openings superimposed. Calibration bars are 2pA, 50ms. (B) Bar diagram of the percent of bursts that exceeded in duration the 500ms of the depolarizing pulses applied in the three above patches. (C) Frequency distribution of burst duration in the two patches illustrated in A1 and A2. Data were binned logarithmically as explained in Methods, and in the main subpanels are shown in a log-linear plot. In the insets, the same data are shown as a log-log histogram. In all subpanels, the smooth, continuous line is the best second-order (C1) or first-order (C2) exponential fitting obtained applying Eq. 1 to the log-log plot. Dotted lines in C1 are the single exponential components of the fitting function shown separately. Fitting parameters are W1=252.9, τb1=29.33ms; W2=17.25, τb2=239.9ms (C1); and W=254.1, τb=209.6ms (C2). Note that the two plots are shown on the same x- and y-scales. (D) Frequency distribution of time constants describing burst duration (τbs). The τb histogram was constructed after binning data according to a logarithmic scale that yielded 10.8 bin/decade, and is shown on a linear x-scale in the main panel, and a logarithmic x-scale in the inset. The smooth line in both subpanels is the fitting obtained applying a double Gaussian function. Fitting parameters are A1=8.637, μ1=20.75ms, σ1=7.73ms; and A2=8.174, μ2=191.26ms, σ2=168.48ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions

Figure 11 Correlation between intraburst mean open times and burst duration. The bursts recorded at −40mV in all patches were divided in three groups according to their duration, Δtb: group 1 (open bars), Δtb<100ms; group 2 (hatched bars), 100ms≤Δtb<500ms; group 3 (filled bars), Δtb≥500ms. (A) Bar diagram of the mean intraburst open time, τ¯o(b). The bars are average τ¯o(b)-values calculated for each burst group: n=26 (group 1), 24 (group 2), and 16 (group 3). Key: * is p<0.05 and *** is p <0.001 with respect to group 1; ## is p<0.01 with respect to group 2. (B) Bar diagram of the burst percentage, within each of the above burst groups, in which the predominant τo(b) was i) <0.45ms; ii) ≥0.45 and <1.1; and iii) ≥1.1ms. Biophysical Journal 2003 85, 3019-3034DOI: (10.1016/S0006-3495(03)74721-3) Copyright © 2003 The Biophysical Society Terms and Conditions