exponential function (one phase decay with robust fit) graphpad prism v6.0.3  (GraphPad Software Inc)

Journal: The Journal of General Physiology

Article Title: On the Mechanism of MgATP-dependent Gating of CFTR Cl − Channels

doi: 10.1085/jgp.20028673

Figure Lengend Snippet: Burst duration distributions are similar for WT (A–C) and K464A (D–F) channels under comparable conditions, as indicated (PKA present for left column only). Fitted curves (through data points) show single exponentials from maximum-likelihood fits. Improvement of the fit by inclusion of a second exponential component was judged using the algorithm described in . Only for K464A at μM MgATP (F) could the likelihood be significantly increased by including a second component, though with a shorter (but not longer; ) mean: τ 1 = 30 ms, a 1 = 0.17; τ 2 = 263 ms, a 2 = 0.83; increase in log likelihood, ΔLL = 8.3; number of bursts fitted, M = 263; giving (ΔLL − ln(2M) = 2.0). The small differences between means at mM and μM MgATP (B vs. C, E vs. F) may be only apparent, as the mean τb, estimated by multichannel kinetic fits, from these same stretches of record at μM MgATP is not significantly different from that during intervening stretches in 5 mM MgATP (for WT: τb μM /τb 5mM = 1.03 ± 0.07, n = 9; for K464A: τb μM /τb 5mM = 0.95 ± 0.13, n = 7). (G and H) Representative traces showing gating of K464A and D1370N channels at 15 μM MgATP (after PKA removal). Prolonged bursts of K464A channels are not evident. Though variability among the four patches containing sufficiently few D1370N channels precluded pooling the data for burst distribution analysis, in none of those patches (analyzed separately) did introduction of a second component significantly improve the maximum likelihood fit.

Article Snippet: Records ( and ), or sums of records , with several tens of open channels at t = 0 were fitted with single or double exponential decay functions by nonlinear least squares (Sigmaplot; Jandel Scientific).

Techniques:

Journal: The Journal of General Physiology

Article Title: On the Mechanism of MgATP-dependent Gating of CFTR Cl − Channels

doi: 10.1085/jgp.20028673

Figure Lengend Snippet: The K1250A mutation strongly shifts the [MgATP] dependence of P o to higher [MgATP]. (A) steady state level of macroscopic current of prephosphorylated WT CFTR channels was ∼2-fold lower at 50 μM MgATP than during bracketing exposures to 5 mM MgATP (as expected from ); lines below traces mark MgATP applications. Rapid current decay on MgATP washout gave (exponential fit lines superimposed on traces) τ = 0.45 s, τ = 0.40 s, τ = 0.38 s, from left to right (mean τ = 0.54 ± 0.04 s, n = 21, pooled from all [MgATP]). (B) Macroscopic current of K1250A channels was reduced ≥2-fold on lowering [MgATP] from 5 to 1 mM. Superimposed exponential fit lines show slower current decay (note 10-fold contracted time scale relative to A) with, from left to right, τ = 28 s, τ = 30 s, τ = 32 s (mean τ = 39 ± 5, n = 9, from all [MgATP]). (C) Semilog plot of P o versus [MgATP]. Steady currents (averaged over final ≥20 s) at each [MgATP], normalized to the mean bracketing level at 5 mM MgATP, yielded least-squares. Michaelis fit parameters for WT: P o max = 1.04 ± 0.01, K 0.5 = 57 ± 2 μM; for K1250A: P o max = 2.45 ± 0.88, K 0.5 = 6.5 ± 4.8 mM; for display, WT (circles) and K1250A (inverted triangles) data (mean ± SD, 3 ≤ n ≤9) were renormalized to these P o max values. Because 10 mM, the highest [MgATP] used, was still far from saturating for K1250A channels, the fit for this mutant is less accurate, evident from large errors on fit parameters.

Article Snippet: Records ( and ), or sums of records , with several tens of open channels at t = 0 were fitted with single or double exponential decay functions by nonlinear least squares (Sigmaplot; Jandel Scientific).

Techniques: Mutagenesis

Journal: The Journal of General Physiology

Article Title: On the Mechanism of MgATP-dependent Gating of CFTR Cl − Channels

doi: 10.1085/jgp.20028673

Figure Lengend Snippet: Exit from MgAMPPNP-locked burst states is slower when bursts are initiated in the presence of MgATP. Patches with hundreds of prephosphorylated WT CFTR channels were repeatedly subjected to ∼30-s long exposures to nucleotides (as in inset), in varied sequence. Each trace in the main figure is the sum of 21 recordings, synchronized upon nucleotide washout (arrow; also in inset), from 12 patches, each exposed to 0.5 mM MgATP, 5 mM MgAMPPNP, or 0.5 mM MgATP + 5 mM MgAMPPNP alternately, an equal number of times. Exponential decay fit parameters are: after MgATP, a = 33 pA, τ = 0.8 s; after AMPPNP, single a = 8 pA, τ = 6.8 s; double a f = 6 pA, a s = 6 pA, τ f = 0.7s, τ s = 8.8 s; after MgATP + MgAMPPNP, a f = 20 pA, a s = 18 pA τ f = 2 s, τ s = 36.6 s. As solution exchange time was 0.5–1s, fast components do not accurately reflect channel closing.

Article Snippet: Records ( and ), or sums of records , with several tens of open channels at t = 0 were fitted with single or double exponential decay functions by nonlinear least squares (Sigmaplot; Jandel Scientific).

Techniques: Sequencing

Journal: The Journal of General Physiology

Article Title: On the Mechanism of MgATP-dependent Gating of CFTR Cl − Channels

doi: 10.1085/jgp.20028673

Figure Lengend Snippet: The K464A mutation speeds exit from locked open burst states. (A) Macroscopic WT channel current activated by a mixture of 0.5 mM MgATP and 5 mM MgAMPPNP (+PKA) decays slowly upon removal of nucleotides. (B) Current decay is much faster for the K464A mutant in the same conditions. Blue fit lines in A and B show only the slow components of double exponential fits, with τ s = 67.8s, a s = 0.92 for WT, and τ s = 8.7s, a s = 0.79 for K464A. (C and D) Summaries of fractional amplitude, a s (C), and time constant, τ s (D), of the slow component from 18 WT and 16 K464A experiments. In controls with no MgAMPPNP, closure after exposure to MgATP and PKA yielded τ = 1.9 ± 0.2 s ( n = 35) for WT and τ = 1.0 ± 0.1 s ( n = 34) for K464A, and both constructs sometimes showed a small amplitude slower component: for WT, τ s = 7.6 ± 1.7 s, a s = 0.1 ± 0.03 (in 13/35 patches); for K464A, τ s = 5.9 ± 0.8 s, a s = 0.24 ± 0.04 (20/24 patches). (E) Macroscopic K1250A currents, activated by 5 mM MgATP + PKA, decay slowly on nucleotide withdrawal. (F) The additional K464A mutation accelerates channel closure from bursts: for the traces shown, τ = 71.7s (K1250A) and τ = 29.7s (K464A/K1250A). (G) Mean time constants of all 9 K1250A and 9 K464A/K1250A relaxations, each well fit by a single exponential.

Article Snippet: Records ( and ), or sums of records , with several tens of open channels at t = 0 were fitted with single or double exponential decay functions by nonlinear least squares (Sigmaplot; Jandel Scientific).

Techniques: Mutagenesis, Construct