Zei PC , Aldrich RW .

GM07365 NIGMS NIH HHS , T32 GM007365 NIGMS NIH HHS

	Figure 2. (A) Ensemble averages of single-channel patch currents expressed as open probabilities at several voltages. Open probability is calculated by dividing the ensemble average current by the number of channels in the patch (single channel patches were used in most of the ensemble averages shown) and the measured unitary current amplitude. The voltages are indicated in the panel. Recording conditions were as described in Fig. 1. (B) Voltage dependence of the steady state open probability. Peak probabilities recorded from the ensemble averages are plotted against voltage. Data from several patches are shown. The smooth curve represents a fit to a Boltzmann function expressed by the following equation: \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_{o}=P^{max}_{o} \left[ \frac{1}{1+e^{-(V-V_{1/2})zF/RT}} \right] ,\end{equation*}\end{document} where Pomax is the maximum open probability (0.7), V is membrane voltage, V1/2 is the voltage where the Boltzmann distribution is equal to 0.5 (−143 mV), z is the equivalent charge movement associated with the Boltzmann distribution (1.36 electronic charges), F is Faraday's constant, R is the universal gas constant, and T is the absolute temperature. The dotted line represents the Boltzmann fit to the macroscopic G(V) relationship (Zei, 1998). The macroscopic G(V) fit has been scaled to the maximum single channel open probability, Pomax.
	Figure 3. (A) Cumulative distributions of first latencies recorded at several voltages. The distributions show the probabilities that the channel first opened by the times indicated. The openings were elicited in response to 1,000-ms pulses from a prepulse potential of −40 mV. (Bottom) The cumulative first latency distributions have been scaled to a probability of 1 to compare their time courses. (B) Median first latencies measured from the distributions in A and several additional patches are plotted as a function of pulse potential. Several different patches are represented among the data points. (C) The cumulative first latency distributions are superimposed on the ensemble averages from the same patch at each voltage indicated. The thin, relatively noisy lines represent the ensemble averages, and the thick, smoother lines represent the first latency distributions. The curves are scaled so that the steady state levels coincide.
	Figure 4. (A) The number of openings per sweep over an entire experiment are plotted contiguously at −110 and −140 mV. The x-axis indicates consecutive sweep number. The data represent two different patches. (B) The test parameter (Z) for runs analysis (see text) is plotted at several voltages. Only those experiments with a significant number of blank sweeps are shown. The dotted line represents a Z value of 1.6. Z values greater than or equal to 1.6 indicate statistically significant clustering of blank sweeps.
	Figure. (scheme I)
	Figure. (scheme II)
	Figure 5. (A) Frequency histograms of open durations measured at several voltages from KAT1 channels. The data were fitted with single exponential functions, represented by the solid curves. The histograms are plotted using the log-binning transformation of Sigworth and Sine (1987) as described in methods. (B) Time constants derived from the exponential fits to the open time distributions are plotted as a function of voltage. The data points represent several patches. The exponential fits have been corrected for the left and right censor times, as described in methods.
	Figure 6. (A) Frequency histograms of closed-time durations measured at several voltages from KAT1 channels. The data were fitted with a sum of two exponential functions and displayed as described in methods. The solid curves represent the overall fits, and the dashed curves represent the individual exponential components. (B) The time constants and relative amplitudes for the brief and long components of the fits to closed time distributions are plotted as functions of voltage.
	Figure 7. (A) Frequency histograms of interburst closed durations measured at several voltages from KAT1 channels. The data have been fitted with single exponential functions, represented by the solid lines. (B) The interburst duration distribution time constants derived from the single exponential fits are plotted as a function of voltage.
	Figure 8. (A) Frequency histograms of within-burst closed durations measured at several voltages from KAT1 channels. A burst criterion of 20 ms was used. The solid lines represent single exponential fits to the data. (B) Time constants derived from the exponential fits to the within-burst closed time duration histograms are plotted as a function of voltage.
	Scheme III.
	Scheme IV.
	Scheme V.
	Figure 9. (A) Comparison of interburst closed durations (thin lines) and first latency (thick lines) distributions plotted as tail distributions at −140, −160, and −190 mV. The distributions represent the probabilities that the interburst and first latency durations are longer than the times indicated on the axis. (B) Mean interburst closed durations and mean first latencies are plotted together as functions of voltage.
	Scheme VI.
	Figure 10. (A) Frequency histograms of the number of openings per burst at several voltages, using a burst criterion of 20 ms. The data are fitted by a geometric distribution (Eq. 6), represented by the dots. The probability of terminating a burst (q) and the total number of openings are shown for each voltage. (B) The probability of terminating a burst (q), derived from the geometric fits, is plotted as a function of voltage.
	Figure 11. (A) The rate constants k23, k34, k32, and k43 from Scheme IV, calculated using Eqs. 3–6, are plotted as functions of voltage. The voltage dependences of the four rate constants are plotted on logarithmic scales. (B) Comparison of the mean burst durations measured directly using a burst criterion of 20 ms (○) and calculated using Eq. 7 and the rate constants derived from burst analysis (▵). The COC bursting scheme is shown at right for reference.
	Scheme VII.
	Scheme VIII.
	Figure 12. (A) Fits of Scheme SVIII to KAT1 ensemble averages at several voltages. Best fits were determined by eye. The rate constants k23, k34, k32, and k43 were determined by the burst analysis as shown in Fig. 19, and the reverse transitions k10 and k21 were set to zero over the voltage range examined in this figure. The thick, smooth lines represent the fits, while the thin, noisy lines represent the ensemble averages. Voltages are indicated. (B) Fits of Scheme SVIII to cumulative first latency distributions for KAT1 at several voltages. All rate constants except forward transitions before first opening, k01, k12, and k23, were set to zero over the entire voltage range examined. The solid lines represent the first latencies, and the dashed lines represent the fits.
	Figure 19. (A) Frequency histograms of open durations measured at several voltages from R177Q channels, with voltages as indicated. The data were fitted with single exponential functions, represented by the solid curves and displayed as described in methods. (B) Frequency histograms of open durations measured at several voltages from R176L channels, with voltages as indicated. The data were fitted with single exponential functions, represented by the solid curves and displayed as described in methods. (C) Voltage dependence of the time constants derived from exponential fits to open time distributions for R177Q currents (□). Open duration time constants for wild-type KAT1 currents are superimposed (○). The data points represent several patches. The open duration distribution time constants have been corrected for missed events as described in methods. (D) Voltage dependence of the time constants derived from the exponential fits to open time distributions for R176L currents (▵). Open duration time constants for wild-type KAT1 currents are superimposed (○). The data points represent several patches.
	Figure 13. (A) Fits of KAT1 macroscopic deactivation tail currents to Scheme VIII. The tails were elicited after a 500-ms activating pulse to −160 mV, followed by a 500-ms tail pulse over a voltage range of −100 to −10 mV in 10-mV steps. The tail currents have been reversed in polarity to facilitate fits using the model. The tail currents were scaled at their initial points to coincide with the steady state open probability predicted by the model for the activating potential used (−160 mV). The distributions of initial probabilities among the various states in Scheme SVIII were determined by fits of the model to the burst, ensemble average, and first latency data. (B) Fits of Scheme SVIII to the steady state open probability versus voltage relationship for wild-type KAT1 currents. The steady state open probability (○) was determined as described in Fig. 2. The open probabilities calculated from the model (▪) were determined by measuring the steady state open probability from the calculated waveforms.
	Figure 14. Rate constants for Scheme SVIII are plotted as functions of voltage. The rate constants k23, k34, k32, and k43 were determined by burst analysis as shown, while the rate constants k01 and k12, and the final value for k23 were determined by fits of the model to the first latency and ensemble averages, given the rate constants determined by burst analysis in the COC model. The rate constants k10 and k21 were set to zero over the activation voltage range between −110 and −190 mV, and fits of the model to macroscopic deactivation tail currents were used to determine these rate constants between −100 and −10 mV. Several patches are represented by the data points.
	Figure 15. Amino acid sequences of wild-type KAT1, R177Q, and R176L mutant channels. The charged amino acid residues at every third position are highlighted, and the mutated residues are shown below the wild-type KAT1 S4 sequence.
	Figure 16. Representative single channel currents from wild-type KAT1 (left), R177Q (middle), and R176L (right) channels recorded in the inside-out patch configuration in response to hyperpolarizing voltage pulses. The voltages are indicated. The data for wild-type KAT1 at all voltages shown were filtered at 0.6 kHz and sampled at 1.54 kHz, and are the same traces as shown in Fig. 1. The data for R177Q at −180, −160, −140, −120, −100, −80, and −60 mV were filtered at 0.6, 0.6, 0.7, 0.7, 0.7, 0.2, and 0.15 kHz, respectively, and sampled at 0.95 kHz. The data for R177Q at −180, −160, −140, −120, −100, −80 and −60 mV were filtered at 0.9, 0.9, 0.3, 0.5, 0.4, 0.4, and 0.15 kHz, respectively, and sampled at 0.95, 0.95, 0.95, 1.54, 1.54, 1.54, and 0.95 kHz, respectively. The voltage pulses were delivered every 2–6 s. The prepulse, tail, and holding potentials were −40 mV for wild-type currents and 0 mV for both R177Q and R176L currents.
	Figure 17. (A) Ensemble averages of R177Q single-channel currents expressed as open probabilities at several voltages. Open probability is calculated by dividing the ensemble average current by the number of channels in the patch (only single channel patches were used in the ensemble averages shown) and the measured unitary current amplitude. Voltages are indicated. Recording conditions were as described in Fig. 16. Fits of Scheme SVIII to the ensemble averages have been superimposed, represented by the solid lines. (B) Ensemble averages of R176L single-channel currents expressed as open probabilities at several voltages. Open probability was calculated as described in A, and fits to the ensemble averages using Scheme SVIII have been superimposed, represented by the solid lines. (C) Voltage dependence of the steady state open probability for R177Q single channel currents, with wild-type open probabilities superimposed. Data from several patches are shown. The smooth curves represent Boltzmann functions expressed by Eq. 1. (D) Voltage dependence of the steady state open probability for R176L single channel currents, with wild-type open probabilities superimposed. Data from several patches are shown. The smooth curves represent Boltzmann functions as described in C.
	Figure 18. (A) Cumulative distributions of first latencies recorded at several voltages for R177Q currents. The distributions show the probabilities that the channel first opened by the times indicated. The openings were elicited in response to 1,000–1,600-ms pulses from a prepulse potential of 0 mV. Fits of Scheme SVIII to cumulative first latency distributions are superimposed. All rate constants except forward transitions before first opening, k01, k12, and k23, were set to zero over the entire voltage range examined. The solid lines represent the first latency distributions and the dashed lines represent the fits. (B) Cumulative distributions of first latencies recorded at several voltages for R176L currents. The conditions are as described in A. Fits of Scheme SVIII to cumulative first latency distributions are superimposed. (C) Median first latencies for R177Q currents (□) are plotted as a function of pulse potential, with median first latencies for wild-type KAT1 superimposed (○). Several patches are represented by the data points. (D) Median first latencies for R176L currents (▵) are plotted as a function of pulse potential, with median first latencies for wild-type KAT1 superimposed (○). Several patches are represented by the data points.
	Figure 20. (A) Frequency histograms of closed durations measured at several voltages for R177Q currents. The data were fitted with a sum of two exponential functions. The solid curves represent the overall fits, and the dashed curves represent the individual exponential components. The data are displayed as described in methods. (B) Frequency histograms of closed durations measured at several voltages for R176L currents. The data were fitted with a sum of two exponential functions. The solid curves represent the overall fits, and the dashed curves represent the individual exponential components. The data are displayed as described in methods. (C) Voltage dependence of the time constants and relative amplitudes for the fast and slow exponential components of the fits to R177Q closed-time distributions (□). Corresponding data from wild-type KAT1 currents have been superimposed (○). (D) Voltage dependence of the time constants and relative amplitudes for the fast and slow exponential components of the fits to R176L closed-time distributions (▵). Corresponding data from wild-type KAT1 currents have been superimposed (○).
	Figure 21. (A and B) Time constants from single exponential fits to interburst closed time distributions for R177Q (□) and R176L (▵) currents are plotted as functions of voltage (□). Interburst duration distribution time constants from wild-type KAT1 currents are superimposed (○). (C and D) The time constants from single exponential fits to the within-burst closed time distributions for R177Q (□) and R176L (▵) currents are plotted as functions of voltage. Corresponding time constants from wild-type KAT1 currents are superimposed (○). (E and F) The probability of terminating a burst (q) derived from geometric fits to the distributions of the number of openings per burst is plotted as functions of voltage for R177Q (□) and R176L (▵) currents. Corresponding data for wild-type KAT1 currents are superimposed for comparison. A burst criterion of 20 ms was used in all analysis in this figure.
	Figure 22. Rate constants for Scheme SVIII are plotted as a function of voltage for R177Q currents (□). The rate constants k23, k34, k32, and k43 were determined by burst analysis as described in the text, while the rate constants k01 and k12 were determined by fits of the model to the first latency distributions and ensemble averages, given the rate constants determined by burst analysis. The rate constants k10 and k21 were set to zero over the activation voltage range between −100 and −180 mV. Several patches are represented by the data points. The rate constants k10 and k21 were determined by fits of Scheme SVIII to deactivation tails measured using the cut-open oocyte clamp technique. Tail currents were elicited using an activating pulse to −160 mV. Each rate constant has been fitted to the single exponential function \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*}k_{n}=n_{0}e^{-z_{n}FV/RT},\end{equation*}\end{document} represented by the solid lines, where n0 is the rate constant at 0 mV, zn is the equivalent charge, and F, R, and T have their usual meanings. Corresponding rate constants for wild-type KAT1 currents have been superimposed (○).
	Figure 23. Rate constants for Scheme SVIII are plotted as a function of voltage for R176L currents (▵). The rate constants k23, k34, k32, and k43 were determined by burst analysis as described in the text, while the rate constants k01 and k12 were determined by fits of the model to the first latency distributions and ensemble averages, given the rate constants determined by burst analysis. The rate constants k10 and k21 were set to zero over the activation voltage range between −100 and −180 mV. Several patches are represented by the data points. The rate constants k10 and k21 were determined by fits of Scheme SVIII to deactivation tails measured using the cut-open oocyte clamp technique. Deactivation tail currents used in these fits were elicited using an activating pulse to −160 mV. Each rate constant except k12 has been fitted to the single exponential function \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*}k_{n}=n_{0}e^{-z_{n}FV/RT},\end{equation*}\end{document} represented by the solid lines, where n0 is the rate constant at 0 mV, zn is the equivalent charge, and F, R, and T have their usual meanings. The rate constant was fitted to the equation \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*}k_{n}=a+n_{0}e^{-z_{n}FV/RT}.\end{equation*}\end{document} Corresponding rate constants for wild-type KAT1 currents have been superimposed (○).
	Figure 24. (A) Fits of Scheme SVIII to the single channel g(V) relationship for R177Q currents. □ represent measured steady state open probabilities, while ▪ represent fits from the model. The fits derived from the model were determined by measuring steady-state open probabilities from calculated open probability waveforms over the voltage range shown. (B) Fits of Scheme SVIII to the single channel G(V) relationship for R176L currents. ▵ represent measured steady state open probabilities, while ▴ represent fits from the model. The open probabilities derived from the model were determined by measuring steady state open probabilities from calculated open probability waveforms over the voltage range shown.

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