Mak DO , Foskett JK .

	Figure 2. Typical multiple-channel current record showing seven equally-spaced current levels at the beginning of the recording. Channel activity duration for this record is 70.2 s (from the beginning of the record to the final closing event as the last observed channel inactivated). Vapp was 20 mV. Data were digitized at 2 kHz and filtered digitally at 300 Hz.
	Figure 3. (A) Histogram analysis of current levels observed in 740 patches (unshaded histogram with thick outline). Also plotted (shaded histogram with thin outline) is the Poisson distribution with the same mean current level number per patch (0.44 current level/patch for 740 patches), calculated by assuming that each current level represents an individual IP3R that exhibited only the M state and that the channels were evenly distributed on the outer nuclear membrane. (B) Histogram analysis of number of channels in the 740 patches (unshaded histogram with thick outline) assuming that all IP3R channels observed exhibited the D state, such that every two current levels detected represents one channel. The theoretical Poisson distribution with the same mean channel number per patch (0.25 channel/patch for 740 patches) is also plotted (shaded histogram with thin outline). In both cases, the large number of observed multiple-channel patches compared with the number of observed single-channel patches suggests that the IP3R channels are not evenly distributed in the outer nuclear membrane of oocytes.
	Figure 4. (A) Current trace and open probability histogram of a typical current record with the IP3R channel in the main and closed states. Base-line current level fluctuated in the record because current recording was started before the gigaseal completely stabilized. The channel in the current record inactivated permanently by 9 s after seal formation. Bin width for the histograms is 0.25 s. (B) Open probability histogram for a single IP3R with longer duration of channel activity. Bin width is 1 s. For both records Vapp was 20 mV, data were digitized at 2 kHz and filtered at 300 Hz digitally.
	Figure 5. Dwell time histograms for the closed state C and open state M of the IP3R at Vapp = (A) 20 and (B) 40 mV, respectively. Only states C and M were observed in the single-channel current records used for this analysis. 6 records with total duration of 139.1 s were used for A, and 1 record with duration of 42.8 s was used for B. The smooth curves are theoretical probability density functions consisting of two exponentials fitted to the histograms by the maximum likelihood method (Sigworth and Sine, 1987). The time constants for the exponentials fitted are labeled in ms beside the corresponding peaks in the curves. (C) Duration histograms of inter-burst closed state and the activity bursts of an IP3R channel in the flicker mode at Vapp = 40 mV. The activity burst duration was defined as the interval between the departure of the channel from the closed state into either one of the flicker states (F1 or F2) and its subsequent return to the closed state for a period longer than 1 ms. Data were digitized at 2 kHz, filtered at 800 Hz and analyzed using MacTac software with channel dwell time corrected for the filtering (Colquhoun and Sigworth, 1995).
	Figure 6. The effect of applied potential on IP3R channel open probability. 〈Po〉 is the overall open probability of the channel averaged over the interval during which the applied potential Vapp was constant. Bin width of the Po histogram is 0.25 s. The intervals (2– 6 s) during which the applied potential was changed in the experiment were omitted in the graphs to avoid confusion. (A) A single-channel patch in which only states C and M were observed in the entire current record up to the failure of the gigaseal at t = 615 s. (B) A patch showing two equally-spaced channel current levels. The channel(s) observed inactivated at t = 262 s. 〈PD〉 is the probability of observing the channel current in the higher level D, averaged over the interval indicated by the width of the bin. Channel current level D was not observed after t = 117.5 s. Po is the probability of the channel being open, i.e., Po = PD + PM, where PM is the probability of observing the channel current in the main state level.
	Figure 7. Current traces showing rarely observed conductance states L (A) and S (B) for channels in normal kinetic mode from 2 separate experiments. Data were digitized at 2 kHz and filtered at 1 kHz. Vapp = 20 mV for (A) and 50 mV for (B).
	Figure 8. Open probability histograms for experiments in which two evenly spaced current levels (M and D) were detected. (A and B) Histogram bin width is 5 s. Unshaded histogram bars are the measured probability of the channel current in level D (PD); shaded bars with thin error bars are the measured probability (± SEM) of the channel in state M (PM). Assuming that current level D is caused by two independent and equivalent channels contained in the same membrane patch opening to state M simultaneously, the theoretical probability P1 of the channel current being at the level corresponding to a single channel in state M is given by the binomial distribution,\documentclass[10pt]{article} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \begin{equation*}P_{1}=2\sqrt{P_{2}}(1-\sqrt{P_{2}})\;.\end{equation*}\end{document} The solid lines represent the theoretical probability P1 evaluated using the measured probability PD as P2. The thick error bars represent the errors in P1 evaluated from the SEM of PD. In A, the measured PM agreed well with the theoretical P1 calculated from PD, indicating that the patch probably contained two independent and equivalent channels until one channel inactivated after t = 70 s. In B, which is typical of the majority of channel current records showing two evenly spaced current levels, PM and PD measured did not obey the binomial distribution expected for two independent and equivalent channels. (C) Open probability histogram of an experiment with current level D that exhibited long quiescent periods. Histogram bin width is 0.1 s. Unshaded histogram bars represent PD; shaded bars represent PM.
	Figure 9. Open probability (Po) and applied voltage (Vapp) graphs of an experiment showing the two different types of channel inactivation: the voltage-reverted inactivation occurring at t = 32.25 s that was reversed by the increase of Vapp from 20 to 60 mV at t = 60.0 s; and the irreversible inactivation occurring at t = 99.0 s. Bin width of the histogram is 0.25 s.
	Figure 10. Channel activity-duration histograms of the IP3R for (A) single-channel experiments in which only one channel current level (state M) was observed (n = 24, including six inactivations after reactivation by a voltage jump); (B) multiple-channel experiments in which three or more channel current levels were observed (n = 41, including six inactivations after reactivation by a voltage jump). Note the compressed time scale of (A) after t =180 s. The measured duration of channel activity was the duration between the formation of the gigaseal (when seal resistance exceeded 200 MΩ) and the last observed channel closing event. The smooth curve in A is a single exponential functions fitted to the activity duration histogram with time constant of 21.1 ± 0.6 s. The smooth curve in B represents the theoretical functions fitted to the activity duration histogram for k = 4 with time constant of 41 ± 3 s. The theoretical fits for k = 3, 5, and 6 are very similar in shape, with different values for the time constant. Experiments in which the gigaseal broke before the channel(s) inactivated (n = 3 and 18 for A and B, respectively) were excluded from the activity duration histograms. Their duration distributions (shaded histograms) showed that failure of the gigaseal probably does not cause any significant systematic bias in the activity-duration histograms.
	Figure 11. Typical current trace of an IP3R channel (A) in the normal kinetic mode (B) in the flicker kinetic mode with bursts of activities and (C) in a transition from flicker mode to the normal mode without closing. The dashed lines indicate the current levels of the various conductance states. Vapp was 50 mV. Data were digitized at 12.5 kHz and filtered at 5 kHz.
	Figure 12. (A) Current amplitude histogram of a channel in the flicker kinetic mode. Segments of current traces during which the channel showed bursts of activities were selected to generate the histogram with bin width of 0.1 pA. Vapp was 50 mV. Data were digitized at 12.5 kHz and filtered at 5 kHz. Theoretical fit to the histogram (smooth curve) is the sum of three Gaussian functions representing the closed state C (dashed curve), and the flicker states F1 and F2 (shaded areas). (B) Ratios of the channel current amplitude IF1/IM and IF2/IM under various applied potentials. The current amplitudes IF1, IF2, and IM used for each data point were obtained in the same patch clamp experiment. Solid circles represent IF1/IM and open circles IF2/IM. Dashed lines indicate the mean ratios assuming no voltage dependence (0.27 for IF1/IM and 0.78 for IF2/IM). Most of the error in the ratios came from the fitting of the channel current amplitude histogram with the Gaussian functions. (C) Voltage dependence of the relative occupation probability of the flicker channel states PF2/PF1. Each type of open symbol (squares, triangles, circles, and diamonds) represents a series of data points obtained from the same single-channel patch. Filled circles are data points each from an individual patch at only one voltage. The straight line is the theoretical fit assuming that the occupation probability follows a Boltzmann distribution. The larger error in the data points for 20 mV is due to difficulty in fitting the Gaussian function to the scarce F2 state.
	Figure 13. Effect of applied potential on the dwell time distributions of the flicker states F1 and F2. In A and B, Vapp = 30 mV for the unfilled histograms, and the solid curves are the theoretical probability density functions each with one exponential component fitted using the maximum likelihood method (Sigworth and Sine, 1987). Vapp = 60 mV for the shaded histograms and the dashed curves are their fitted single-exponential probability density functions. The transition counts were normalized so that the peaks of the fitted probability density functions have the same height. There are 784 and 209 transitions for 30 and 60 mV, respectively, in A; and 543 and 380 transitions for 30 and 60 mV, respectively, for B. Analysis was done on data digitized at 12.5 kHz and filtered at 2 kHz using pClamp 6.0.2. (C) is the graph of the time constants τ of the theoretical probability density functions fitted to the dwell time histograms of the flicker states under various applied potentials. Squares are time constants for F1 and circles are for F2. Open and filled symbols are from two different experiments. The lines are theoretical time constant values fitted according to the Arrhenius theory.
	Figure 14. Schematic diagram of the double-gate model, showing transitions, especially voltage-dependent ones, between various kinetic states for the two gates controlling the kinetic behavior of the IP3R channel.

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