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Figure 1. Sigmoidicity of ShakerBΔ activation is reduced by BrMT. (A) Activation of ShBΔ channels at +40 mV in an outside-out patch in the absence (control condition, thin trace) or presence (thick trace) of 5 μM BrMT. Overlaid on the data are fits of Eq. 1 with the indicated σ values. (B) BrMT IK and the fit of Eq. 1 (same as A) are replotted, and σ from the fit equation was altered to the indicated values. (C) Traces from A scaled in time to such that the time constant of IK rise from Eq. 1 is the same for both traces. After this scaling procedure, the delay before IK rise is shorter in BrMT than control.
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Figure 2. IK activation waveforms from ShBΔ patches were fit with Eq. 1. (A) Fits of Eq. 1 to ShBΔ activation at 0, 20, 40, 70, and 100 mV. (B) Fits of Eq. 1 to activation in 5 μM BrMT. Same voltages as A. (C) Sigmoidicity from fits of Eq. 1 to IK activation. Hollow circles, control condition; filled circles, 5 μM BrMT, n = 4 patches.
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Figure 3. Sigmoidicity of activation approaches a value of 2 as BrMT concentration is increased. (A) ShBΔ IK during voltage steps to +40 mV under control condition (thin trace) or 1, 2, 5, 10, and 20 μM BrMT (thick traces). Experimental IK is average of multiple sweeps. Smooth lines are Eq. 1 fit to IK. (B) Sigmoidicity from fits of Eq. 1 to activation at +40 mV, n = 3–5 patches.
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Figure 4. Divalent zinc reduces ShBΔ sigmoidicity to σ = 4. These experiments used the pH 6.8 external solutions described in Materials and Methods. (A) ShBΔ IK activated at +60 mV in 0, 0.01, 0.1, 1, and 10 mM zinc. Smooth thin lines are fits of Eq. 1 to data. (B) Sigmoidicity under control condition (hollow circle) or with added zinc (gray circles), n = 5–8 patches. (C) Sigmoidicity of IK is constant over a wide voltage range. In 2 mM zinc, sigmoidicity is ∼4 (gray circles), n = 5 patches. Control sigmoidicity is >4 (hollow circles), n = 3 patches.
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Figure 5. BrMT and zinc slow the same activation steps, yet induce different sigmoidicities. The pH 6.8 solutions described in Materials and Methods were used for experiments in this figure. (A) IK at +60 mV during application of BrMT and/or zinc. Traces are scaled to match peak IK. (B) Slowing induced by zinc and/or BrMT was determined from τ in fits of Eq. 1, n = 4. The light gray bar is the multiplicative product of the fold-slowing in 2 mM zinc and 2 μM BrMT. This predicts the degree of slowing expected from both ligands together if they both slow the same activation step. The speckled bar is the degree of slowing expected if BrMT and zinc slow different activation steps: the combined slowing would be no more than the slowest of the two alone, in this case, zinc.
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Figure 6. BrMT does not compete with ligands that block the external pore of ShBΔ channels. All data were measured during 50-ms pulses to +40 mV given every 2 s. Blockers were applied by manually triggering solution switching during the interval between pulses. Solution exchange requires <1 s. (A) Circles are peak ShBΔ IK, measured by averaging over several milliseconds after a steady-state level of IK activation. At time = 0, 50 nM agitoxin-2 is added to the external solution. (B) Same as A, but with 5 μM BrMT in all solutions. (C) Block of ShBΔ IK by 1 mM TEA in the presence of 5 μM BrMT. (D) Mean time constant of block by 50 nM agitoxin-2 with 5 μM BrMT (gray bar, n = 6 patches), and without BrMT (white bar, n = 5 patches). (E) Mean block by 1 mM TEA with 5 μM BrMT (gray bar, n = 6 patches), and without BrMT (white bar, n = 9 patches). (F) Mean fold-slowing of activation by 5 μM BrMT with 1 mM TEA (gray bar) and without TEA (white bar). ShBΔ IK was fit by Eq. 1, and the fold-slowing is the ratio of τ in BrMT to τ before addition of BrMT. (G) Gray bar is sigmoidicity of ShBΔ IK in 5 μM BrMT with 1 mM TEA (gray bar) and without TEA (white bar).
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Figure 7. Schematic depicting the relevant states in an activation path involving one activating transition per subunit. In this model, BrMT simultaneously binds two of the four subunits to slow activation. The forward transition is set by the effect of the BrMT's slowing factor, bx, on the activation rate constant α. The slowing coefficient of each transition (b1–b6) is determined from the probability that BrMT is bound to individual resting subunits. Keq is the binding equilibrium for BrMT.
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Figure 8. Model of negative cooperative inhibition of ShBΔ activation. (A) Depiction of activation in a single subunit. Each subunit completes two activation steps. Forward transitions toward the open state are marked by a darkening of the subunit from white to gray in the first step and then gray to black in the second step. The first forward transition is set by the effect of the BrMT's slowing factor, b, on rate constant α, the reverse by β. The second forward transition has rate γ, and the reverse δ. In model BrMT, the reverse transition, β, is accelerated by a factor 1/b. (B) A model for implementing negatively cooperative binding of BrMT, such that it slows an early step in the Shaker activation pathway. The model is an elaboration of the ShBΔ activation model of Zagotta et al. (1994a). White subunits are available to bind BrMT. Vertical transitions are not affected by BrMT. The open state is demarcated with a hollow circle. The bottom-most is the “flickery” closed state. Equations for the BrMT slowing factors (b1–b6) are shown in Fig. 7. In model BrMT, all reverse transitions (those involving β) are accelerated by the inverse of the factor that slows the forward transition. This model does not attempt to account for the reduction of peak IK by BrMT.
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Figure 9. Effects of BrMT on simulated and experimental IK from ShakerBΔ. The negatively cooperative models used for simulations are depicted in Fig. 8 B. (A) ShBΔ IK from an outside-out patch upon activation to +40 mV. Thin line, control condition (no BrMT); thick lines, 1, 2, 5, and 10 μM BrMT. IK was normalized to match peak current level. (B) Simulated ShBΔ currents from model ZHA. Thin line, control condition; thick lines, 1, 2, 5, and 10 μM BrMT. (C) Simulated ShBΔ currents from model BrMT. Thin line, control condition; thick lines, 1, 2, 5, and 10 μM BrMT. (D) Filled circles, fold slowing of ShBΔ activation at +40 mV by BrMT, n = 4–9 patches; dotted line, model ZHA; solid line, model BrMT. (E) Filled circles, sigmoidicity of ShBΔ IK at +40 mV, n = 3–5 patches; hollow circle is control condition; dotted line, model ZHA; solid line, model BrMT. (F) Sigmoidicity of IK vs. slowing by BrMT. Each data point is a measurement in control solution (hollow circles), or a solution containing 0.5–20 μM of BrMT (filled circles). Dotted line, model ZHA; solid line, model BrMT.
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Figure 10. Voltage dependence of cooperative binding model BrMT. (A) Noisy line, experimental IK at +40 mV in 5 μM BrMT; smooth line, activation of model BrMT at +40 mV in 5 μM BrMT; dashed line, best fit of Eq. 1 to experimental IK. (B) Noisy lines, experimental IK in 5 μM BrMT at −20, −10, 0, 10, 20, 30, 40, and 50 mV; smooth lines, activation of model BrMT under identical conditions, using a reversal potential of −58.2 mV. (C) Lines are sigmoidicity of fits to IK from model BrMT. Circles are sigmoidicity from fits of Eq. 1 to experimental IK. Hollow circles, control condition; filled circles, 5 μM BrMT.
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