Smith-Maxwell CJ , Ledwell JL , Aldrich RW .

NS-23294 NINDS NIH HHS

	Figure 2. Macroscopic ionic currents from S4 chimeras and Shaker. Currents were measured in response to 50-ms positive voltage steps, after 1-s prepulses to −100 mV from a holding potential of −80 mV. Currents were recorded in the voltage ranges indicated in 10-mV increments. The last 6 ms of the prepulse preceding the test pulse is shown for each trace. The beginning of each test pulse is indicated by the left edge of the calibration bars.
	Figure 3. Normalized conductance–voltage curves for S4 chimeras. Means and SEM are shown for Shab S4 (▾), Shal S4 (▪), Shaw S4 (♦), Kv3.2 S4 (▴), and Shaker (•). For Shaker, Shab S4, and Kv3.2 S4, G/Gmax was constructed from the chord conductance as outlined in materials and methods. For Shaw S4, the normalized conductance was constructed from isochronal currents measured at 0 mV at a fixed time after reaching the maximal current, ranging between 0.4 and 1.0 ms after the positive voltage step to activate the channel. Similar measurements of isochronal tail currents were carried out for Shal S4 at −50 mV. Smooth curves through the data represent fits to the mean values for each channel species with a fourth power Boltzmann function, as outlined in materials and methods. The values from these fits are given below, with n representing the number of patches included to calculate each mean. Shaker, V1/2 = −57.4 mV, slope factor = 10.0 mV, n = 8. Shab S4, V1/2 = −58.1 mV, slope factor = 14.9 mV, n = 3. Shal S4, V1/2 = −1.1 mV, slope factor = 19.8 mV, n = 5. Shaw S4, V1/2 = 31.2 mV, slope factor = 28.4 mV, n = 7. Kv3.2 S4, V1/2 = −49.3 mV, slope factor = 25.0 mV, n = 5.
	Figure 4. Model predictions for voltage-dependent channel opening. (top left) The six-state model used for these simulations is a simplified model for Shaker channel activation gating with properties similar to the larger 15-state model previously developed for Shaker channel gating (Zagotta et al., 1994a). Despite the decrease in complexity, the six-state model fits the conductance–voltage relation of Shaker and has kinetic properties similar to Shaker. In the model, a single independent transition in each identical channel subunit is followed by a final concerted transition leading to channel opening. Values for the rate constants α and β are taken from the first set of identical and independent transitions in each subunit of the 15-state model, since they are largely responsible for the voltage-dependent properties of opening in Shaker. Expressions for the voltage-dependent rate constants assume an exponential dependence on voltage where α = α0ez αFV/RT and β = β0e−z βFV/RT, α0 and β0 are values for the rate constants at 0 mV, and zα and zβ are the equivalent charge moved between each state and the transition state. The rate constants for the final concerted transition, γ and δ, are voltage independent. Model parameters for the control simulations with Shaker-like properties are: α0 = 1,120 s−1, β0 = 373 s−1, zα = 0.25, zβ = 1.0, γ = 8,000 s−1, and δ = 100 s−1. (left) Normalized conductance–voltage curves for the control simulations and for the indicated modifications. Conductance–voltage curves predicted for three types of changes in the model are shown. Charge associated with the forward (zα) and backward (zβ) transitions is decreased (top); the 0-mV rate constant (α0) for all forward independent transitions is decreased (middle); and the forward rate constant for the final concerted transition (γ) is decreased (bottom). Normalized conductance–voltage curves were constructed from simulated currents by normalizing isochronal tail currents as outlined in materials and methods. *Values used for the control simulations. (middle) Simulated ionic currents for the control parameters and for the indicated modifications to the control parameters. The simulation with zβ = 0.25 decreases the total charge moved for the channel from 5.0 electronic charges to 2.0 by decreasing zβ from 1.00 to 0.25 electronic charges in each of four subunits. The simulation with α0 = 10 s−1 decreases all 0-mV forward rate constants by two orders of magnitude. The simulation with γ = 10 s−1 decreases the forward rate constant for the concerted final transition by almost three orders of magnitude. (right) Simulated currents from the middle panel scaled for analysis of sigmoidicity. Simulated currents at all voltages were normalized to the same maximum value. Then the slopes at the half maximum current level were made equal by changing scaling along the time axis. This manipulation of the current traces facilitates comparison of the relative delay in the currents at different voltages and from different channel species. For scaled currents that follow a single exponential time course, the time it takes to reach the half maximum current is defined as 1.0. Values >1.0 are indicative of a delay in the activation time course. Arrowheads point to scaled current traces with the smallest and largest relative delays and indicate the voltage range over which currents were scaled.
	Figure 8. Voltage-dependent opening of Shaw S4 and Shaker dimer constructs. (left) Macroscopic ionic current traces recorded from dimer constructs. 1-s prepulses to −100 mV, from a holding potential of −80 mV, preceded each test pulse to the voltages indicated. (right) G/Gmax was determined as outlined in materials and methods from dimer constructs AkBk (○, n = 5), AkBw (♦, n = 8), AwBk (•, n = 6), AwBw (▴, n = 1), and the Shaker (▾, n = 8) and Shaw S4 (⋄, n = 6) monomers. Mean values are plotted as a function of voltage with error bars indicating SEM. Note that data from AwBw superimpose on data from the Shaw S4 monomer and data from AkBk superimpose on data from the Shaker monomer. (top right) Predictions for steady state activation from an independent model. The independent model, based on the model of Hodgkin and Huxley (1952), assumes four identical and independent transitions lead to channel opening. The normalized conductance– voltage curves from AkBk and Shaw S4 were each fit with a fourth power Boltzmann function, as described in results, to determine the voltage-dependent properties of activating a single subunit in the tetrameric channel protein. The following values were obtained from fits to data from the homotetramers: for AkBk, Vk = −52.83 mV and zk = 2.62; for Shaw S4, Vw = 32.29 mV and zw = 0.88. The independent model predicts that the voltage dependence of the conductance–voltage curve will be equal to the product of first power Boltzmann functions for each of the individual subunits making up the channel tetramer. The solid line between the fits is the prediction of the independent model for a channel with two Shaker subunits and two Shaw S4 subunits. (bottom right) Predictions for steady state activation from two cooperative models. Model 1: the first model assumes that Shaker and Shaw S4 channels open from a single closed state to a single open state, and that the forward and backward transitions between the two states involve the concerted movement of all four subunits. Data for AkBk and Shaw S4 were each fit with a single Boltzmann function, as described in results (fits not shown). Values from fits of the homotetramers are: for AkBk, V1/2 = −35.55 mV and z = 3.53; for Shaw S4, V1/2 = +80 mV and z = 1.24. The predicted conductance–voltage curve for channels with two Shaw S4 and two Shaker subunits is represented by the dotted line in the bottom right panel. Model 2: the second model, which includes several independent transitions as well as a cooperative transition, is identical to the six-state kinetic scheme outlined in Fig. 4. Values for transitions in Shaker and Shaw S4 channels were obtained from fits to data from the AkBk dimer and the Shaw S4 monomer constructs, respectively. The probability of opening and the normalized conductance were calculated as outlined in Fig. 4. For Shaker, two variations of the model were used with the same values for the independent transitions, but differing by whether or not the final concerted transition is voltage dependent. The 0-mV rate constants and associated charge used for the independent transitions for both variations are: α0 = 1,120 s−1, zα = 0.25, β0 = 373 s−1, zβ = 1.0. For the voltage-independent concerted transition, γ = 8,000 s−1 and δ = 100 s−1. These values are identical to those used for the control simulations in Fig. 4 and predict the conductance–voltage relation described by the dashed line through the data for AkBk. For the Shaker variation with a voltage- dependent concerted transition, the rate constants γ and δ, like α and β, were assumed to be exponentially related to voltage with γ = γ0e z γF  V/RT, δ = δ0e−z δF  V/RT, γ0 = 10,000 s−1, δ0 = 100 s−1, and zγ = zδ = 0.1. These parameters predict a conductance–voltage relation described by the solid line through the data for AkBk. The Shaw S4 conductance–voltage relation was simulated by slowing the final concerted transition in the activation pathway of the Shaker models and increasing the voltage dependence of the transition. For the Shaw S4 kinetic scheme, the independent transitions have the same values as in the Shaker models and the concerted transition has the following values: γ0 = 1 s−1, zγ = 0.8, δ0 = 50 s−1 and zδ = 0.4. The conductance–voltage curve calculated for the Shaw S4 model is shown by the solid line through the data for Shaw S4. Since the models simulating Shaker and Shaw S4 differ only in the final transition, energy additive predictions for heterodimer opening were calculated, as described in results, by summing the energy contributions of each subunit to this final transition, assuming all other transitions have the same properties as Shaker. The solid line near the heterodimer data shows the prediction for steady state activation of a channel with two Shaw S4 and two Shaker subunits when the concerted transition in Shaker has a small voltage dependence, while the dashed line shows the prediction when the concerted transition in Shaker is voltage independent.
	Figure 5. Macroscopic ionic currents and conductance–voltage curves for Shaker, Shaw S4, and Shaw. (left) Macroscopic ionic currents measured during positive steps to the voltages indicated. For Shaw S4 and Shaker, test pulses to activate the channels followed prepulses to −100 mV from a holding potential of −80 mV. For Shaw, a holding potential of 0 mV was used. (right) Normalized conductance plotted as a function of voltage. Normalized conductance–voltage curves were constructed for Shaker and Shaw S4 as outlined in Fig. 3. For Shaw, isochronal measurements of tail currents were made at −40 mV, between 0.2 and 0.3 ms after the end of the test pulse. Since the maximum probability of opening for Shaw currents was not reached in the voltage range studied, Shaw isochronal currents were normalized to the maximum current obtained at +180 mV. Data shown represent six patches for Shaw, six patches for Shaw S4, and eight patches for Shaker.
	Figure 6. Gating kinetics for Shaker, Shaw S4, and Shaw. (left) Single exponential fits to activation time course. Macroscopic ionic currents typical of each channel type are shown in response to positive voltage steps to the voltages indicated to the right of each trace (millivolts). For Shaker and Shaw S4, the voltage steps followed prepulses to −100 mV from a holding potential of −80 mV. For Shaw, a holding potential of 0 mV was used and positive test pulses were preceded by 10-ms prepulses to −100 mV. Superimposed on the current traces during activation are fits with a single exponential function, as outlined in materials and methods. For Shaw and Shaw S4, each trace was fit over most of the time course of activation, from between 1 and 5% of the maximum current to the maximum current obtained during the test pulse. For Shaker, traces were fit starting at 10–20% of the maximum current and up to the maximum current obtained during the test pulse because of large delays in Shaker opening that are not well fit by a single exponential function. (middle) Relative delay of the activation time course. Current traces measured at the voltages indicated were scaled to compare the relative delay between voltages and channel species as outlined for Fig. 4. The scale bar indicates the time it takes for a channel to activate half maximally when it activates with a single exponential time course and no delay. Arrowheads point to scaled current traces from Shaker with the smallest and largest relative delays and indicate the voltage range over which currents were scaled. (right) Time constants plotted as a function of voltage. Time constants were obtained from fits of single exponential functions to currents during channel opening and closing, as outlined in materials and methods. The time course of channel closing was reasonably well fit by a single exponential function for all three channel types. The time constants for Shaker and Shaw S4 were derived from 7 patches each, while the time constants for Shaw came from 13.
	Figure 7. Single channel openings recorded from Shaker, Shaw, and Shaw S4 during voltage steps to the indicated voltages. Shaw and Shaw S4 records were filtered at 2 kHz. Shaker recordings were taken from Hoshi et al. (1994; see Fig. 1) with filtering ranging from 0.5 kHz at −50 mV to 1.2 kHz at 0 mV. Shaker and Shaw S4 currents were recorded from excised inside-out patches while Shaw currents were recorded from a cell-attached patch. The oocyte used for the cell-attached patch was bathed in the standard intracellular solution with a high concentration of potassium, depolarizing the resting potential to near 0 mV. A holding potential of −80 mV was used in all cases. The patch with Shaw contained at least two channels, the patch with Shaker contained one channel, and the patch with Shaw S4 contained two channels. The intracellular solutions for Shaker and Shaw S4 contained 2 mM MgCl2.
	Figure 9. Sigmoidicity of Shaw S4 and Shaker dimer constructs. Macroscopic ionic current traces from dimer constructs AkBk, AkBw, AwBk, and AwBw were scaled to compare the relative delay between voltages and channel species as outlined in Fig. 4. Currents were measured at the voltages indicated. Currents for the heterodimer prediction were simulated using the six-state model in Fig. 8. Rate constants for the independent transitions were the same as those used for the Shaker and Shaw S4 models, while rate constants for the final cooperative transition were predicted from the rate constants for Shaker and Shaw S4, assuming energy-additive contributions from each of four channel subunits. Rate constants for the final transition in opening of Shaker and Shaw S4 channels are given in Fig. 8. Calculation of rate constants predicted for heterodimer channels was carried out as outlined in results. The Shaker variation without charge movement in the final transition was used for the simulations shown; however, similar results were obtained from the Shaker variation with a small amount of charge movement in the final transition. The simulated currents were scaled for analysis of sigmoidicity in the same way that currents measured from the dimer constructs were scaled. The scale bars indicate the time it takes for a channel with a single exponential time course to activate half maximally.

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