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Figure 14. Box plots of rate constants for the C0 ↔ O1 ↔ C2 scheme. Box plots of the k01, k10, k12, and k21 rate constants for the C0 ↔ O1 ↔ C2 from 14 different patches. Values for the rate constants were determined by HMM analysis. The horizontal line within each box indicates the median of the data, boxes show the 25th and 75th percentiles of the data, and whiskers show the 5th and 95th percentiles. Extreme data points are also indicated.
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Figure 13. Box plots of rate constants for the C0′ ↔ C1′ ↔ O2′ scheme. Box plots of the k01′, k10′, k12′, and k21′ rate constants for the C0′ ↔ C1′ ↔ O2′ scheme from 14 different patches. Values for the rate constants were determined by HMM analysis. The horizontal line within each box indicates the median of the data, boxes show the 25th and 75th percentiles of the data, and whiskers show the 5th and 95th percentiles. Extreme data points are also indicated.
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Figure 1. Bimodal single-channel activity. Shown are 23.33 s of a continuous current recording from a patch containing a single BROD CNG channel. The upper and lower dotted lines, separated by 2.1 pA, indicate the open and closed current levels, respectively. The currents were recorded at +80 mV in the inside-out configuration and in the continuous presence of 16 mM cGMP applied to the cytoplasmic face of the patch. The data were filtered at 5 kHz and sampled at 25 kHz.
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Figure 2. Structures of cyclic nucleotides.
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Figure 3. Macroscopic current– voltage families. Current families for an inside-out patch were elicited by 16 mM cGMP, 16 mM cIMP, or 16 mM cAMP in the presence (A) or absence (B) of 1 μM Ni2+. Voltage pulses were applied from 0 mV to potentials between −80 and +80 mV in 20-mV steps. Control currents in the absence of cyclic nucleotides were subtracted. The currents were normalized (using the +80-mV trace) to the maximum current in the presence of 16 mM cGMP and 1 μM Ni2+.
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Figure 4. Representative single-channel currents. Single-channel currents were recorded in the presence of 16 mM cGMP, cIMP, or cAMP with the membrane voltage clamped at +80 mV. Each sweep was 200 ms in duration. The upper and lower dotted lines indicate the open and closed levels, respectively, and are separated by 2.3 pA. The amplitude histograms were normalized to unit area and were fit by the sum of two Gaussians with variances σclosed2 and σopen2 for the closed and open distributions, respectively. Parameters for amplitude histograms were as follows: control solution: σclosed = 280 fA; 16 mM cGMP: σclosed = 300 fA, Pclosed = 0.05, μopen = 2.4 pA, σopen = 349 fA, Popen = 0.95; 16 mM cIMP: σclosed = 289 fA, Pclosed = 0.71, μopen = 2.3 pA, σopen = 431 fA, Popen = 0.29; 16 mM cAMP: σclosed = 287 fA, Pclosed = 0.997, μopen = 2.4 pA, σopen = 500 fA, Popen = 0.003.
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Figure 5. Representative single-channel currents in the presence of Ni2+. Single-channel currents were recorded in the presence of 16 mM cGMP, cIMP, or cAMP, and 1 μM Ni2+. Data are for the same patch as in Fig. 4. Each sweep was 200 ms in duration. The upper and lower dotted lines indicate the open and closed levels, respectively, and are separated by 2.3 pA. The amplitude histograms were normalized to unit area and were fit by the sum of two Gaussians. Parameters for amplitude histograms were as follows: control solution + 1 μM Ni2+: σclosed = 353 fA; 16 mM cGMP + 1 μM Ni2+: σclosed = 2 pA, Pclosed = 0.01, μopen = 2.5 pA, σopen = 374 fA, Popen = 0.99; 16 mM cIMP + 1 μM Ni2+: σclosed = 236 fA, Pclosed = 0.03, μopen = 2.5 pA, σopen = 311 fA, Popen = 0.97; 16 mM cAMP + 1 μM Ni2+: σclosed = 360 fA, Pclosed = 0.28, μopen = 2.3 pA, σopen = 457 fA, Popen = 0.72.
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Figure 16. Box plot comparison between the values for ΔG0 from macroscopic and single-channel experiments. For macroscopic experiments, the free energy change of the allosteric transition ΔG0 was calculated as ΔG0 = −RT ln L, where L is the equilibrium constant and was calculated using Ni2+ potentiation. For the single-channel experiments, ΔG0 was calculated as ΔG0 = −RT ln k01/k10, where k01 and k10 are maximum-likelihood rate constants from the HMM analysis for the C0 ↔ O1 ↔ C2 model.
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Figure 6. Effects of inverse filtering on cAMP openings. Representative cAMP current traces at +80 mV are shown before (A) and after (B) inverse filtering along with amplitude histograms shown on log-linear axes. The dotted lines on the traces are separated by 2.2 pA. The amplitude histograms were fit by the sum of two Gaussians, which appear as parabolas on log-linear axes. The fit parameters before inverse filtering were: μopen = 1.5 pA, σclosed = 0.29 pA, σopen = 0.65 pA, Popen = 0.006. The fit parameters after inverse filtering were μopen = 2.1 pA, σclosed = 0.49 pA, σopen = 0.61 pA, Popen = 0.004.
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Figure 7. Amplitude histograms on log–linear axes with inverse filtering. The amplitude histograms were fit by the sum of two Gaussians, which appear as parabolas on a log scale. Parameters for the histograms in the absence of Ni2+ were as follows: control solution: σclosed = 480 fA; 16 mM cGMP: σclosed = 580 fA, Pclosed = 0.045, μopen = 2.2 pA, σopen = 590 fA, Popen = 0.955; 16 mM cIMP: σclosed = 490 fA, Pclosed = 0.71, μopen = 2.2 pA, σopen = 640 fA, Popen = 0.286; 16 mM cAMP: σclosed = 500 fA, Pclosed = 0.989, μopen = 2.0 pA, σopen = 960 fA, Popen = 0.011. Parameters for the histograms in the presence of Ni2+ were as follows: control solution + 1 μM Ni2+: σclosed = 520 fA; 16 mM cGMP + 1 μM Ni2+: σclosed = 590 fA, Pclosed = 0.036, μopen = 2.4 pA, σopen = 600 fA, Popen = 0.964; 16 mM cIMP + 1 μM Ni2+: σclosed = 470 fA, Pclosed = 0.071, μopen = 2.4 pA, σopen = 500 fA, Popen = 0.929; 16 mM cAMP + 1 μM Ni2+: σclosed = 510 fA, Pclosed = 0.525, μopen = 2.2 pA, σopen = 620 fA, Popen = 0.475.
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Figure 8. Single-channel amplitude variation across experiments. Box plots of the values for the single-channel amplitude as determined by fitting the sum of two Gaussians to inverse-filtered data. The horizontal line within each box indicates the median of the data; boxes show the 25th and 75th percentiles of the data; whiskers show the 5th and 95th percentiles. Extreme data points are also indicated. The median single-channel conductance was 2.25 pA for cGMP, 2.27 pA for cIMP, 1.87 pA for cAMP, 2.15 pA for cGMP with Ni2+, 2.46 pA for cIMP with Ni2+, and 2.21 pA for cAMP with Ni2+.
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Figure 9. Half-amplitude threshold analysis indicates the presence of two closed and one open states. Closed (left) and open (right) duration histograms for single-channel data recorded with 16 mM cGMP, cIMP, or cAMP. Closed durations were fit to a double and open durations to a single exponential distribution. The time constants are indicated by the arrows. Parameters for the closed duration histograms were as follows: 16 mM cGMP: 1,118 events in histogram, τ(short) = 38 μs (weight, 0.85), τ(long) = 581 μs (weight, 0.15); 16 mM cIMP: 128 events in histogram, τ(short) = 24 μs (weight, 0.69), τ(long) = 4.21 ms (weight, 0.31); 16 mM cAMP: 58 events in histogram, τ(short) = 42 μs (weight, 0.34), τ(long) = 46.4 ms (weight, 0.66). Parameters for the open duration histograms were as follows: 16 mM cGMP: 1,118 events, τ = 3.42 ms; 16 mM cIMP:128 events, τ = 2.04 ms; 16 mM cAMP: 58 events, τ = 102 μs.
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Figure 10. Half-amplitude threshold analysis of currents in the presence of Ni2+. Closed (left) and open (right) duration histograms for single-channel data recorded with 16 mM cGMP, cIMP, or cAMP, and 1 μM Ni2+. Closed durations were fit to a double and open durations to a single exponential distribution. The time constants are indicated by the arrows. Parameters for the closed duration histograms were as follows: 16 mM cGMP: 357 events in histogram, τ(short) = 36 μs (weight, 0.85), τ(long) = 548 μs (weight, 0.15); 16 mM cIMP: 407 events in histogram, τ(short) = 36 μs (weight, 0.96), τ(long) = 3.25 ms (weight, 0.04); 16 mM cAMP: 443 events in histogram, τ(short) = 40 μs (weight, 0.84), τ(long) = 6.3 ms (weight, 0.16). Parameters for the open duration histograms were as follows: 16 mM cGMP: 357 events, τ = 3.57 ms; 16 mM cIMP: 407 events, τ = 3.56 ms; 16 mM cAMP: 443 events, τ = 1.46 ms.
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Figure 12. Model discrimination. Log likelihood ratios from an HMM analysis with five uncoupled generic schemes of single channel data recorded with 16 mM cGMP, cIMP, or cAMP. A convergence criterion of 10−8 was used. The log-likelihoods obtained from the analysis were normalized by subtracting the log-likelihoods obtained for the two-state C ↔ O scheme.
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Figure 15. Errors in the determination of the rate constants and single-channel amplitude from HMM analysis. For this analysis, a 0.73-s segment (or 18,198 sample points) from a single-channel patch activated by cGMP was tested to determine the errors in the determination of the rate constants due to the method (see methods). The approach was applied separately for the (A) C0′ ↔ C1′ ↔ O2′ and (B) C ↔ O ↔ C schemes. The abscissa is the percent change in the value of the parameter away from the maximum-likelihood rate. The ordinate is the change in log likelihood from the maximum-likelihood value. The curves were fit by Eq. 1.
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Figure 17. The effect of Ni2+ on HMM rate constants for cIMP. (A) Comparison of rate constants for cIMP with and without Ni2+. Values for the rate constants were determined by HMM analysis. The horizontal line within each box indicates the median of the data, boxes show the 25th and 75th percentiles of the data, and whiskers show the 5th and 95th percentiles. Extreme data points are also indicated. (B) Comparison of values for ΔG0 for activation by cIMP in the presence of Ni2+ between macroscopic and single-channel experiments.
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Figure 18. The effect of Ni2+ on HMM rate constants for cAMP. (A) Comparison of rate constants for cAMP with and without Ni2+. Values for the rate constants were determined by HMM analysis. The horizontal line within each box indicates the median of the data, boxes show the 25th and 75th percentiles of the data, and whiskers show the 5th and 95th percentiles. Extreme data points are also indicated. (B) Comparison of values for ΔG0 for activation by cAMP in the presence of Ni2+ between macroscopic and single-channel experiments.
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