Nano-Positioning System for Structural Analysis of Functional Homomeric Proteins in Multiple Conformations

SUMMARY

Proteins may undergo multiple conformational changes required for their function. One strategy used to estimate target site positions in unknown structural conformations involves single-pair resonance energy transfer (RET) distance measurements. However, interpretation of inter-residue distances is difficult when applied to three-dimensional structural rearrangements, especially in homomeric systems. We developed a novel method using inverse trilateration/triangulation to map target sites within a homomeric protein in all defined states with simultaneous functional recordings. The procedure accounts for probe diffusion to accurately determine the three-dimensional position and confidence region of lanthanide LRET donors attached to a target site (one/subunit), relative to a single fluorescent acceptor placed in a static site. As a first application, the method is used to determine the position of a functional voltage-gated potassium channel’s voltage sensor. Our results verify the crystal structure relaxed conformation and report on the resting and active conformations for which crystal structures are not available.

INTRODUCTION

The growing availability of protein structures has launched a new era of structure-guided functional studies supported by advanced computational tools. In this context we developed a novel technique to quantitatively correlate structure and function by mapping protein sites undergoing conformational change. A crystal structure is a snapshot of the protein in a single conformation, which may be distorted due to the non-native environment or protein-protein contacts necessary for crystallization. In addition, structural resolution is decreased in flexible or dynamic regions, which in many cases are the site of functional relevance. Functional studies are required to confirm or complement the structure in its obtained state and most importantly to model the unknown conformations critical to the protein’s functionality.

There is thus a need for techniques that provide three-dimensional (3D) coordinates of a studied site in multiple conformations. Spectroscopic methods based on fluorescence or lanthanide resonance energy transfer (FRET or LRET respectively) are ideally suited to accurately measure inter- or intra-molecular distances in proteins (Selvin, 2002). It is possible to determine a previously unknown protein site position using trilateration (distance-based version of triangulation) of FRET distance measurements to three or more reference positions provided by a protein structure (for review, see Muschielok et al., 2008). However, flexibility of protein domains in solution may invalidate the required assumption that a structure provides valid reference positions. The FRET-based trilateration method was improved by (Muschielok et al., 2008; Muschielok and Michaelis, 2011) and termed “Nano-Positioning System” (NPS) in analogy to the Global Positioning System (GPS). NPS applies trilateration to single-pair FRET distances measured between three or more reference (structure-derived) “satellite dye molecule” positions and a single “antenna dye molecule” (ADM) to solve for the unknown ADM position. NPS uses probabilistic analysis to account for experimental uncertainty introduced by probe orientation and diffusion at reference positions.

Although many experimental uncertainties inherent to FRET have now been addressed, the accuracy of the antenna position by any trilateration strategy is dependent upon two fundamental criteria. First, accuracy of (known) reference satellite positions must be as high as possible. Common error sources are the length and flexibility of a fluorophore linker, protein distortion in experimental conditions, and change of reference satellite positions in conformational states with no available structure. Second, the ratio of inter-satellite spread to average satellite-antenna distance should be maximized (i.e., trilateration is not possible in the limit where all satellite positions are equivalent), with importance proportional to satellite-antenna distance uncertainties. These criteria establish that trilateration is difficult to apply and/or poorly suited for a homomeric (symmetric) protein system whose conformational change occurs in all subunits on the protein’s periphery rather than central region. In this hypothetical case, satellites must be placed near the (more static) protein center, which causes them to be clustered together, thus violating the 2^nd criterion above.

Our structure-function studies of voltage-gated ion channels prompted us to consider the inverse problem. The inverse trilateration problem is to use a single known antenna position to determine multiple unknown, but symmetrically arranged, satellite positions given the measured distances that exist between them. In voltage-gated ion channels, the tight structural coordination of the selectivity-imparting pore-forming domains, which undergo minimal rearrangement, provides an ideal reference antenna position to predict satellite positions such as the voltage sensing domains (VSDs), which are expected to undergo significant conformational changes. The VSDs are arranged with 4-fold cylindrical symmetry about the channel’s pore, which defines the symmetry axis (Long et al., 2005). Several studies have combined LRET-based distances with a simple geometric model to deduce structural rearrangements of the VSDs (Cha et al., 1999; Posson et al., 2005; Richardson et al., 2006; Posson and Selvin, 2008). However, this topic is still under debate and motivated development of this method.

Here we present a solution to the problem of mapping unknown sites in a symmetrical protein assembly given the knowledge of only one static reference point. For consistency, we named our method “Symmetric Nano-Positioning System” (SNPS). It is a physical model curve fitting procedure that directly fits a geometric model of satellite positions to LRET lifetime measurements. It also introduces numerical and analytical tools to account for donor/acceptor diffusion and evaluates the confidence of fitted satellite positions. The combination of these factors makes SNPS an accurate method for quantitative analysis of 3D conformational change of a specific site within functional proteins arranged with cylindrical symmetry. We demonstrate the technique by mapping 3D coordinates of a donor probe in the VSD of the widely studied Kv channel Shaker in three different functional states. The results demonstrate the potential of the SNPS technique for a K⁺ channel, but it has broad application to multimeric soluble and membrane proteins including homotrimers (e.g., ATP-gated P2X receptors, ASICs), homotetramers (e.g., Kv, Kir, ATP-gated channels), and homopentamers (e.g., GABA receptors, CorA, GLIC channels). Additionally, we generalized the theory for positioning any symmetric system of three or more satellites arranged around one antenna of known position.

RESULTS

LRET Measurements

We studied the VSD S4 segment of the Shaker K⁺ channel expressed in Xenopus laevis oocytes in its three major conformations: resting, active, and relaxed (a state populated after prolonged depolarization (Villalba-Galea et al., 2008; Lacroix et al., 2011)). In general, Kv channels are homotetrameric; each subunit contains a VSD (segments S1-S4) surrounding the ion conducting pore region (segments S5-S6) (Long et al., 2005). The VSDs are responsible for K⁺ conduction by opening the pore and are expected to undergo the most significant conformational rearrangements, especially the arginine-rich S4 segment (Bezanilla, 2008). For LRET distance measurements, we symmetrically placed four “satellite” donor elements in the VSDs (one per subunit) and one “antenna” acceptor element in the pore region, off-center from the pore axis. We used the lanthanide terbium as the donor encaged by a lanthanide binding tag (LBT) (Franz et al., 2003) that was genetically encoded into each subunit of the channel (Sandtner et al., 2007). The LBT motif was inserted at the extracellular end of S4 to optimally report structural rearrangements underlying channel function. The S3-S4 linker was also shortened to partially compensate the LBT insertion (see Experimental Procedures for all channel modifications). The construct is referred to as S4(4) LBT due to its insertion 4 residues above R1, the first gating charge (see Figure S1A available online). The acceptor element was the BODIPY FL maleimide (BFM) fluorophore conjugated to purified agitoxin2 (AgTx2) (Shimony et al., 1994; Posson et al., 2005) at positions which do not affect toxin binding. AgTx2 binds the pore of the channel with 1:1 stoichiometry and high affinity (0.64 nM) (Garcia et al., 1994), insensitive to channel inactivation (Oliva et al., 2005). This complex has been previously modeled, which provided us with coordinates of the acceptor labeling site with respect to the channel’s pore (Eriksson and Roux, 2002). They concluded that two different toxin docking modes (I and II) are possible and we therefore considered both, henceforth referred to as AgTx2(I) and AgTx2(II), respectively. In absence of a Shaker channel structure, we modeled the insertion of the S4(4) LBT into the homologous Kv1.2 structure (Pathak et al., 2007). Figure 1A shows the entire labeled protein system.

Figure 1. SNPS Experimental Design, LRET Instrumentation and Measurements.

(A) Donor and acceptor probe locations in our Kv1.2-based S4(4) LBT model of the Shaker channel; extracellular view. See lower-left subunit for segment labels. Terbium (Tb) atoms transfer energy to a single BODIPY FL maleimide fluorophore (red atoms; linker not shown) conjugated to pore-blocking AgTx2-D20C (yellow). In this case, 4 donor-acceptor distances are simultaneously measured by LRET.

(B) Simplified schematic of the LRET setup. An oocyte expressing Shaker channels under two-electrode voltage clamp (TEVC) rests atop a coverslip. A quadrupled Nd:YAG laser provides a 266 nm excitation pulse upon trigger (T1) by the acquisition/computer system (ACQ/PC). Residual wavelengths are removed by dichroic mirror (DCM), Pellin-Broca prism (PBP), iris diaphragm (ID), and excitation filter (F1). The excitation beam is directed into the objective (L1) by another DCM and defocused to increase illumination area. Emission light is appropriately filtered for SE or DO measurement (F2), optionally filtered by a visible short-pass filter (F3), and focused onto the PMT photocathode by a BK7 lens (L2). The PMT is gated on 10 μs after the laser pulse by trigger (T2). Analog PMT photocurrent is converted to voltage, amplified, low-pass filtered (LPF), and sampled by the ACQ/PC.

(C) Lifetime measurements from the Shaker S4(4) LBT construct in the relaxed state: SE (blue), DO (black). A control/background DO trace from wild-type Shaker-IR is also shown (gray).

(D) SE decays from the same oocyte in the resting (red), active (green), and relaxed (blue) states. All traces were offset-subtracted and normalized in (C-D); note different time scales. See also Figure S1.

Optical measurements were performed using LRET in an inverted microscope configuration (Figure 1B). Briefly, a laser pulse excites the long-lived donors; each donor transfers energy to a single acceptor with rate proportional to 1/r⁶, where r is the separating distance. Sensitized emission (SE) decays, which reflect the donor decay rate in presence of acceptor, were recorded for geometric analysis with SNPS, and donor-only (DO) emission decays were recorded to monitor the integrity of the LBT and adjust for any state-dependent changes of donor emission (Figure 1C-D). We controlled the membrane potential (V_m) with the two-electrode voltage clamp (TEVC) technique (Bezanilla et al., 1982) to set the vast majority of channels into the resting (V_m < −90 mV), active (V_m ≥ 0 mV, short time) and relaxed (V_m ≥ 0 mV, long time) states as we record LRET data.

Geometric Model of the Protein System

The process of mapping donor positions requires a geometric model of M donors (satellites), arranged about the protein’s symmetry axis with cylindrical symmetry, and one acceptor (antenna). The acceptor position must be off-axis to obtain multiple unique distances needed for inverse trilateration. Probe diffusion regions were modeled as a discrete acceptor cloud and spherical donor cloud, discussed in the next section. The model of donors and acceptor cloud, and the protein system (e.g., channel and toxin) must be in the same frame of reference. Calculations are simplified by transformation to a symmetry frame in which the protein’s symmetry axis is collinear with the z-axis, and the origin of protein coordinates corresponds to the membrane center (z = 0), if applicable. In our case of the homotetrameric Shaker channel with M=4 subunits, the donor model is a square (Figure 2A). Donors D₁, D₂, D₃, and D₄ are symmetrically arranged about the z-axis, labeled with donor-acceptor effective distances d₁, d₂, d₃, and d₄, respectively. Distances obtained by time constants of energy transfer do not infer placement within the donor model. Our convention is that distances are sorted in ascending order (d₁ ≤ d₂ ≤ …≤ d_M), which unambiguously places D₁ nearest the acceptor cloud and D₄ farthest from it, while D₂ and D₃ are arbitrarily assigned with an alternating pattern. Donor positions are naturally described using the cylindrical coordinate system where D₁ has circumradius b, azimuthal rotation angle θ, and height h. Rotation is defined as absolute (θ_A) on the unit circle or relative (θ_R) to a stable reference point, such as the Cα of the toxin’s labeled cysteine. Given only the D₁ donor position, all remaining donor positions are directly calculated by M-fold cylindrical symmetry. Note that all model donors lie in the same plane (parallel to the xy-plane) and have equivalent circumradius and height.

Figure 2. Geometric Model and SNPS Curve Fitting of LRET Decays.

(A) Geometric model of the complete distance-geometry configuration. Donors/satellites D₁ through D₄ form a square centered about the z-axis, and are separated from the acceptor/antenna cloud (gray points) by effective distances d₁ through d₄, respectively. The cysteine Cα of the AgTx2-D20C reference position is labeled ‘X’. The D₁ position is described by cylindrical coordinates (b,θ_R,h), with circumradius b, relative rotation angle θ_R, and height h.

(B) Rotational ambiguity exists depending on the relative length of distances d₂ and d₃, yielding rotational solution type 1 {d₂ < d₃, blue} and 1 {d₂ ≥ d₃, red}.

(C) Model of effective distance d between a diffusing donor-acceptor pair in the rapid diffusion limit (not to scale). The acceptor is modeled as a cloud of N discrete points A_i above the fluorophore labeling site (CYS). The donor is modeled as a sphere with radius a_D, with center D(x,y,z) separated from each acceptor point A_i(x,y,z) by distance r_i. Effective distance endpoints do not reach D(x,y,z) or the acceptor cloud mean position due to 1/r⁶ bias.

(D) The geometric model is fit starting from initial donor positions coarsely sampled over the valid geometric parameter space. 25 initial geometries are shown for a fit of solution type 2.

(E) SNPS fits the best geometric model to SE decays. Here, SE decays from 4 different cells were globally fit, but only 1 dataset and its fit (solid line) are shown for clarity, with weighted residuals beneath. The effectiveness of initial donor position sampling is demonstrated by the envelope (dashed lines) of all model decays tested during the fit, which broadly encompasses the measured decay.

(F) Summary scheme of the SNPS curve fitting process. See also Figures S2-S5.

Mapping donor/satellite positions by inverse trilateration of distances in homomeric proteins is accompanied by two ambiguities: vertical and rotational. Since all model donors lie in the same plane (z = h), they can be flipped below or above the plane defined by the mean acceptor z-coordinate $\left({\stackrel{‒}{z}}_A\right)$, yielding lower $\{h<<<{\stackrel{‒}{z}}_A\}$ and upper $\{h\ge {\stackrel{‒}{z}}_A\}$ solutions, respectively. Vertical ambiguity can be easily avoided by experimentally placing the acceptor above or below the range of valid donor heights. The asymmetric position of the toxin/acceptor dictates that distance d₁ is always shortest and d₄ longest. However, the order of intermediate distances d₂ and d₃ is undefined and leads to a rotational ambiguity yielding left-handed {d₂ < d₃} and right-handed {d₂ ≥ d₂} solutions (Figure 2B). We define solution types as (1) lower/left-handed, (2) lower/right-handed, (3) upper/left-handed, or (4) upper/right-handed. In the present case, vertical ambiguity was eliminated by experimental design; therefore only lower solution types 1 and 2 were possible. The donor D₁ rotational parameter space spans 360°/M about the z-axis; each rotational solution can span 360°/(2M). Typically only one solution type is consistent with the protein structure or with proximity measurements in functional states for which no structure is available.

Effective Distance in Presence of Probe Diffusion

A probe attached to a protein labeling site always suffers from inherent uncertainty of probe position, which is proportional to the length of the linker and governed by its surrounding environment. A diffusing donor and acceptor causes apparent shortening of their separation distance as a consequence of the 1/r⁶ distance dependence on Förster energy transfer. We developed measures to correct for this bias by calculating the effective donor-acceptor distance, which corresponds to the diffusion-enhanced energy transfer rate. We derived the effective distance for 4 different single pair donor-acceptor configurations in the rapid diffusion limit (see Supplemental Notes and Figure S2). In the present work, given structural information about the acceptor labeling site, the acceptor diffusion region was modeled as a cloud of discrete points within the fluorophore’s accessible volume (Experimental Procedures and Figure S3). Donor diffusion cannot be modeled as rigorously since the donors undergo yet unknown conformational rearrangements. Given that the LBT is a part of the protein’s backbone and that the expected extent of VSD thermal motion is ±3 Å (Jogini and Roux, 2007), we modeled the donor diffusion region as a sphere with radius a_D= 3 Å centered about a mean donor position D(x,y,z). Points within this donor sphere are assumed continuously distributed and equally probable. The acceptor cloud and donor sphere model pair (Figure 2C) is Case #3 in the derivation (Supplemental Notes). Given an arbitrary mean donor position (with subunit index m), its effective distance d_m to the acceptor cloud is:

$$d_m={\left(\sum _{i=1}^N{p}_i{\left(r_{i,m}^2-a_D^2\right)}^{-3}\right)}^{-1∕6},\forall r_{i,m}>a_D$$ (1)

where each donor cloud has sphere radius a_D, the acceptor cloud hasN discrete points with probability mass function p, and r_i,m is the distance between the mean donor position D_m(x,y,z) and each discrete acceptor cloud point A_i(x,y,z). Equation (1) also applies to simpler cases where the donor or acceptor are considered a static point (i.e., a_D=0 and/or N=1), and demonstrates that a closest approach effective distance is generally not appropriate for single-pair distances measured by LRET with long (i.e., millisecond) donor lifetimes.

Mapping Donor Positions by Curve Fitting LRET Decays

At the core of the SNPS method is a physical model curve fitting procedure to directly fit a geometric model of donor positions to experimentally measured LRET SE decays. To complement this iterative approach, we also derived an analytical solution to the inverse trilateration problem, generalized for satellites in any regular convex polygon geometry with 3 or more vertices (see Supplemental Notes and Figure S4). The analytical solution uses exact distances (no diffusion) and is better suited for more general applications (e.g., robotics, sensor positioning).

SNPS can be applied to SE decays measured in each defined functional state of the protein, where all subunits have high probability of being in the desired state. For the present case of a K⁺ channel, the defined functional states are judged by the gating charge vs. membrane voltage (Q-V) curve. Since the geometric model assumes a single conformation, an LRET measurement of a mixed population of conformations cannot be analyzed by this method. SE decays selected for analysis were shape and amplitude-consistent with lowest possible noise: variance-to-mean ratio (VMR) ≤1. A procedure for robust estimation of VMR from experimental lifetime decays is provided in Supplemental Experimental Procedures. As the fluorophore acceptor and lanthanide donor have excited state lifetimes on the ns and ms timescales, respectively the single acceptor can rapidly cycle to report all energy transfer events from multiple donors. SE is a most accurate readout of τ_DA, the time constant of donor decay in presence of acceptor, due to exclusion of any non-specific donor signal. Using a LBT peptide in external buffer solution, we measured the unquenched donor-only lifetime ${\stackrel{‒}{\tau }}_D$ of the LBT-Tb³⁺ complex as ${\stackrel{‒}{\tau }}_D=2.47\pm 0.03\mathrm{ms}$ (s.d., n=10). Paired with the BFM acceptor fluorophore, we experimentally determined the unquenched Förster distance as ${\stackrel{‒}{\mathit{R}}}_0=42.9\pm 0.2\mathrm{Å}({\kappa }^2=2∕3;n=1.36$ assumed for prominent solution accessibility). Structural rearrangements in the protein and LBT can induce partial donor quenching by water that reduces the donor emission time constant τ_D. The consequence is a slight reduction in R₀, thus we measured DO decays from many cells and fit τ_D in each functional state to calculate a state-dependent (τ_D) and effective R₀ from the partially quenched quantum yield (Gryczynski et al., 1988) according to $R_0={\stackrel{‒}{R}}_0{\left(\langle {\tau }_D\rangle ∕{\stackrel{‒}{\tau }}_D\right)}^{1∕6}$. The method used to fit τ_D from DO decays measured in oocytes is described in Supplemental Experimental Procedures.

At a given donor geometry (b,α_R,h), the effective satellite-acceptor distance d_m is calculated using Equation (1) for each subunit energy transfer pair (with index m; total of M subunits). From Förster theory, the measured SE time constant for each energy transfer pair is:

$${\tau }_{\mathit{DA},m}=\langle {\tau }_D\rangle \frac{d_m^6}{d_m^6+R_0^6}$$ (2)

The corresponding SE decay is monoexponential, defined by only one variable parameter (τ_DA) according to the following amplitude constraint specific to LRET (Heyduk and Heyduk, 2001):

$${\mathit{I}}_m\left(t\right)=\left(\frac{1}{{\tau }_{\mathit{DA},m}}-\frac{1}{\langle {\tau }_D\rangle }\right)\exp \left[\frac{-t}{{\tau }_{\mathit{DA},m}}\right]$$ (3)

where I_m(t) is the luminescence intensity at time t after the excitation pulse. All energy transfer pair intensity signals are then summed to construct the full model luminescence intensity decay defined by the parameter set β = (θ_R,b,h,A,k_ns,τ_ns,c):

$$I_F(t;\beta )=A\sum _{m=1}^M{I}_m\left(t\right)+k_{\mathit{ns}}\exp \left[\frac{-t}{{\tau }_{\mathit{ns}}}\right]+c$$ (4)

Equation (4) also includes non-geometric parameters: the amplitude scaling coefficient A, offset c, and a very fast non-specific exponential term with amplitude k_ns and time constant τ_ns. Instantaneous fluorescence is eliminated by gating the detector on immediately after the laser excitation pulse, but some non-specific delayed fluorescence (or phosphorescence) from the oocyte persists. The typical range for τ_ns is 30-55 μs, which is well separated from (faster than) all energy transfer time constants in our measurements, e.g., τ_DA > 200 μs.

A model decay I_F(t) is easily constructed for a given donor geometry. The task is to search for the parameter set that best fits the model decay to a measured SE decay (in a selected functional state). Perturbation of the geometric parameters causes the donor model to rotate, expand radially, or change height with respect to the acceptor cloud (Figure 2A). Parameters are optimized using nonlinear weighted least-squares (NLWLS) by gradient descent to minimize the reduced chi-square error between the model decay I_F(t) and measured decay I_D(t). In our implementation, we simultaneously fit the same geometric model to SE decays measured from multiple (J) oocytes under the same conditions. This global analysis scheme significantly improves convergence to the correct geometric model. The global parameter set expands to a matrix β and the global reduced chi-square function is:

$${\mathcal{X}}_{\mathit{RG}}^2=\frac{1}{v}\sum _{j=1}^J\sum _{i=1}^n\frac{{\left(I_{F,j}\left(t_i;{\beta }_j\right)-I_{D,j}\left(t_i\right)\right)}^2}{{\widehat{\sigma }}_{D,j}^2\left(t_i\right)}$$ (5)

The j^th decay (of J in total) is defined by parameter set β_j and p_ng non-geometric (unshared) parameters. Globally, there are p_g geometric (shared) parameters and $\nu =\left[{\Sigma }_{j=1}^J(n_j-n_{\mathit{out},j})\right]-{\mathit{Jp}}_{\mathit{ng}}-p_g$ degrees of freedom (d.f.) assuming independent observations, where n and n_out are the number of total and outlier time channels in the fit region, respectively. Each SE decay is weighted by its measurement variance ${\widehat{\sigma }}_D^2\left(t\right)$ based on Poisson statistics. Accurate estimation of ${\widehat{\sigma }}_D^2\left(t\right)$ is a critical step described in Supplemental Experimental Procedures and Figure S5A-C. The following parameter constraints are imposed during the fit to promote accurate convergence: i) the very fast non-specific time constant is constrained such that τ_ns ≤ 55 μs, ii) the offset is constrained within tight bounds $\widehat{c}\pm ({\widehat{\sigma }}_B∕\sqrt[]{2})$, where $\widehat{c}$ and ${\widehat{\sigma }}_B$ are robust estimates of the baseline mean and standard deviation, respectively. See Supplemental Experimental Procedures and Figure S5D.

Nonlinear curve fitting is sensitive to initial parameter values, therefore initial values must be broadly tested to ensure that the global minimum parameter set is reached. For this purpose we generate a set of geometric initial positions that coarsely span the entire donor geometry parameter space (Figure 2D). For each SE decay, initial conditions for non-geometric parameters are obtained by curve fit at each fixed donor initial position. SNPS curve fits are then globally performed (simultaneous parameter optimization of all decays) starting from each of the geometric initial positions. At every function evaluation, subroutines are run to: 1) calculate all donor-acceptor effective distances and 2) optimize all non-geometric parameters at the currently tested geometry. After each coarse SNPS curve fit converges, ${\mathcal{X}}_{\mathit{RG}}^2$ and all parameter values are recorded. After completion, the fit with the minimum ${\mathcal{X}}_{\mathit{RG}}^2$ is assumed to be at the global minimum parameter set $\widehat{\beta }$. To ensure accuracy, a few refinement SNPS curve fits are performed from random initial geometric positions slightly offset (0.5 Å) from $\widehat{\beta }$. If any improvement is made, $\widehat{\beta }$ is updated. Finally, $\widehat{\beta }$ is used to construct all model decays and weighted residuals (Figure 2E). Goodness of fit is judged by the global reduced chi-square value (an optimal fit has ${\mathcal{X}}_{\mathit{RG}}^2=1$), the quality of weighted residuals, and rapid decay of the autocorrelation of weighted residuals. A summary scheme of the SNPS curve fitting procedure is given in Figure 2F.

Confidence of Donor Positions

To evaluate the confidence of fitted donor positions, we applied the likelihood-ratio criterion to obtain the p-dimensional exact 100(1-α)% confidence region contour (Beale, 1960; Seber and Wild, 1989). Since the model decay in Equation (4) is nonlinear, α is an approximate significance level. In terms of the global reduced chi-square:

$${\mathcal{X}}_{\mathit{RG}}^2\left(\beta \right)={\mathcal{X}}_{\mathit{RG}}^2\left(\widehat{\beta }\right)\left\{1+\frac{p}{v}{F}_{\alpha ,p,v}\right\}$$ (6)

where $\widehat{\beta }$ is the global minimum parameter set, F_α,p,ν is the upper critical value of the F_p,ν distribution, and normality of weighted measurement errors is assumed. Equation (6) defines a threshold at which variation of parameters has caused a fractional increase in ${\mathcal{X}}_{\mathit{RG}}^2$ that is statistically significant at level α. To initially estimate the shape and size of the donor position confidence region, we calculated the error surface of each geometric parameter by incremental perturbation away from its global minimum value until reaching ${\mathcal{X}}_{\mathit{RG}}^2$ threshold (Figure 3A). At each fixed parameter step, all other parameters are optimized. This procedure has been termed support plane analysis (Straume M, Frasier-Cadoret SG, Johnson ML, 1991). A minimal bounding box is fit to enclose all error surface points. Next, a grid search is performed by calculating the fit error at fixed geometries within a grid defined by this bounding box, expanded as necessary to fully enclose the confidence region (Figure 3B). Next, error values are linearly interpolated on a 10x higher resolution grid lattice. All points exceeding ${\mathcal{X}}_{\mathit{RG}}^2$ threshold are deleted leaving an egg-shaped uncertainty volume (Figure 3C). The confidence surface of the mean donor position is given by calculation of a smooth isosurface (Figure 3D). The isosurface is written to MRC density file format for viewing in a molecular graphics viewing program with ${\mathcal{X}}_{\mathit{RG}}^2$ values directly mapped to significance level, thus allowing any α ≥ 0.05 to be visualized. The confidence surface of the donor cloud is obtained by convolution of the assumed donor sphere model with the mean donor position confidence surface (Figure 3E). Confidence intervals are obtained by the minimum and maximum parameter values contained within the uncertainty volume (from Figure 3C). The height parameter error surface is analyzed in Figure 3F. To examine geometric correlation, confidence region cylindrical coordinates (from Figure 3C) were plotted pairwise in Figure S6. Moderate correlation exists between the donor circumradius and height, which is a general property of the geometric model. Although our model function is nonlinear, the confidence surface presented in Figure 3D is representative and indicates low nonlinearity, thereby avoiding the need for significance level corrections.

Figure 3. Donor Position Uncertainty: Confidence Surfaces and Intervals.

(A-F) Sequence of calculation steps to obtain 95% confidence surfaces and intervals for the D₁ donor position of the S4(4) LBT construct in the relaxed state.

(A) Error surfaces of D₁ cylindrical coordinates: b (green), θ_R (red), and h (blue), obtained by support plane analysis. A minimal bounding box was fit to the ensemble of scanned points.

(B) Evaluation of ${\mathcal{X}}_{\mathit{RG}}^2$ on a 3D grid oriented according to the initial bounding box in (A).

(C) The ${\mathcal{X}}_{\mathit{RG}}^2$ grid was cubically interpolated at 10x higher resolution. All points above statistical threshold were deleted. Remaining points are within the mean position 95% confidence region.

(D) The 95% confidence surface of the mean donor position is represented by a transparent ${\mathcal{X}}_{\mathit{RG}}^2$ isosurface. The optimal donor position is inside (black).

(E) The 95% confidence surface of the donor cloud. The inner surface is the 95% confidence surface of the mean donor position, from (D). Note that the scale is different from (A-D).

(F) The 95% confidence interval (2σ) of height h is defined by the minimum and maximum values of the height error surface (black contour) from all grid points in (C). The initial error surface from support plane analysis in (A) is shown for comparison (blue contour). See also Figure S6.

Validation of SNPS by Simulation

SNPS was first validated using simulated data to examine its accuracy and convergence properties. SE decays were simulated at defined 3D positions (obtained from AgTx2(II)-D20C datasets in Table 1) to mimic experimentally measured SE decays in the resting, active, and relaxed states. For consistency, non-geometric parameters were identical to fitted values from experimental data. At a known position, Equations (1-4) were applied to generate a simulated SE decay, to which simulated Poisson-distributed noise was added over a wide range of VMR:

$$I_{\mathit{sim}}\left(t\right)=\text{round}\left[I_F\left(t\right)+N\left(0,{\sigma }_{\mathit{sim}}^2\right)\sqrt{I_F\left(t\right)}\right]Q_{\mathit{ADC}}$$ (7)

where ${\sigma }_{\mathit{sim}}^2=\mathrm{VMR}$ is the variance of a 1D Gaussian random variable. The integer rounding operation (round) mimics digitization; multiplication by the resolution of our analog to digital converter $Q_{\mathit{ADC}}$ mimics the scale of experimental decays. This process was repeated to generate an ensemble of simulated SE decays for 4 different cells at 3 different positions, each with 10 different levels of VMR. Simulated data were globally analyzed by SNPS in the same manner as experimental data. We first examined the influence of noise. The convergence rate of coarse sampling fits (Figure 4A) indicates that experimental decays should have VMR < 2.5 for reliable fit convergence (> 50%). The donor position error was excellent (< 0.5 Å) for VMR < 2.5 (Figure 4B). We next examined the fitted time region. Position accuracy was optimal by fitting SE decays between t = 50 μs and the time corresponding to ≈ 99.95-99.99% decay over the remaining amplitude range $\left[I_{\mathit{sim}}(t=50\mathit{us})-\widehat{c}\right]$. Finally, in case the assumption of a static acceptor region fails, we examined the effect of acceptor cloud displacement (Figure 4C). The error (Δd), measured as distance between the calculated and true donor position, is related to acceptor cloud cylindrical displacements as follows: Δd = Δh_acceptor, Δd ~ (b_donor/b_acceptor)Δθ_acceptor, and Δd is nonlinearly related to Δb_acceptor (with maximal sensitivity when donor and acceptor heights are similar).

Table 1.

Donor Coordinates of the Shaker S4(4) LBT Construct Determined by SNPS

Acceptor Label Site	State	Soln	Circumradius b (Å)	Rel. Rotation† θR(°)	Height h (Å)	${\mathcal{X}}_{\mathit{RG}}^2$	⟨ τ D ⟩
AgTx2 D20C n=4	R	1	30.7 (−0.6, +0.6)	−14.2 (−2.4, +2.6)	20.0 (−0.7, +0.8)	1.0914	2.36
	R	2	31.0 (−0.5, +0.6)	23.0 (−2.5, +2.5)	20.1 (−0.7, +0.9)	1.0871	2.36
	A	2	32.4 (−0.6, +0.6)	20.6 (−2.6, +2.1)	21.3 (−0.7, +0.7)	1.0683	2.38
	L	2	36.0 (−0.7, +0.6)	16.1 (−2.5, +1.9)	27.8 (−1.6, +1.8)	1.0214	2.39
AgTx2 N5C n=4	R	2	31.1 (−1.5, +2.1)	−8.6 (−2.2, +2.3)	18.4 (−1.8, +3.1)	1.0472	2.36
	R	1	29.9 (−1.5, +2.1)	0.3 (−3.3, +2.4)	16.3 (−1.5, +2.2)	1.0224	2.36
	A	1	31.7 (−1.5, +1.9)	17.8 (−1.9, +2.0)	18.0 (−1.7, +2.6)	1.0284	2.38
	L	1	36.5 (−1.9, +1.2)	16.4 (−1.4, +1.3)	26.7 (−4.5, +4.6*)	1.0391	2.39

Functional states of the VSD are resting (R), active (A), relaxed (L); Soln is solution type; ${\mathcal{X}}_{\mathit{RG}}^2$ is global reduced chi-square goodness of fit value (a model-free fit has ${\mathcal{X}}_{\mathit{RG}}^2$); n is the number of globally analyzed oocyte datasets; ⟨τ_D⟩ is the donor-only time constant (in ms). Donor cylindrical coordinates are (b,θ_R,h) with negative and positive deviations from the mean given in parentheses at the 95% confidence level. SE decays were fit in the same time region: t = 0.05-6.5 ms after the excitation pulse.

^†Rotation angle is relative to acceptor labeling site cysteine Cα coordinates.

^*Denotes that a physical constraint limit was reached.

Figure 4. Validation of SNPS by Analysis of Simulated Decays.

(A) Convergence to the true donor position as a function of noise for three different simulated SE lifetime datasets, all globally analyzed (n=4). The noise level is described by variance-to-mean ratio (VMR). Percent convergence is the percentage of coarse sampling fits out of the total attempted that reached within a specified distance of the true position: the lower and upper envelope lines represent convergence within 1 or 2 Å, respectively.

(B) Donor position error as a function of VMR.

(C) Donor position error as a function of acceptor cloud cylindrical displacements. Simulated data had VMR=1.

Conformational Changes of the Shaker Channel S4 Segment

We applied SNPS to LRET measurements from our toxin/protein system – the S4(4) LBT construct in the Shaker potassium channel – first using AgTx2 labeled with BFM as an acceptor at residue D20C. We generated and tested acceptor clouds for toxin docking modes I and II, and calibrated each to the (relaxed) reference state donor height (Experimental Procedures). The mode II fit was excellent (${\mathcal{X}}_{\mathit{RG}}^2\left[\mathit{II}\right]=1.0214$) while the mode I fit was poor (${\mathcal{X}}_{\mathit{RG}}^2\left[I\right]=1.2530$), exhibiting systematic oscillations in weighted residuals. Goodness of fit was evaluated by a one-sided F-test of sample variance (s²) with null and alternative hypotheses $H_0:S_1^2=S_2^2$ and $H_A:S_1^2\ast \ast \ast \ast S_2^2$, respectively. For comparison of AgTx2-D20C mode I vs. II fits, the test statistic $F=\left(\frac{{\mathcal{X}}_{\mathit{RG}\left[I\right]}^2}{{\mathcal{X}}_{\mathit{RG}\left[\mathit{II}\right]}^2}\right)=\left(\frac{1.253}{1.021}\right)=1.2272$ significantly exceeded the upper critical value $F\alpha ,\nu ,\nu =F_{0.05,12807,12807}=1.0295$ at α = 0.05, thereby rejecting H₀(p << 0.001). Note that ν is the global d.f. from Equation (5). We thus assumed toxin docking mode II is significantly more probable and used AgTx2(II) in all subsequent analysis. As an internal validation, we next measured the S4(4) LBT construct using AgTx2 labeled with BODIPY FL iodoacetamide (BFI) as an acceptor at residue N5C, and also generated corresponding acceptor clouds. In summary, the mode II fit was again favored (${\mathcal{X}}_{\mathit{RG}\left[\mathit{II}\right]}^2=1.0393$ vs. ${\mathcal{X}}_{\mathit{RG}\left[I\right]}^2=1.0434$), although not statistically significant (p = 0.41) under the same F-test. Due to a shorter linker, the BFI acceptor clouds are significantly smaller than for BFM, which likely explains the lower disparity between mode fits.

The geometrically fitted VSD donor positions in all three functional states are shown in Figure 5 using either AgTx2(II)-D20C or AgTx2(II)-N5C. We tested these two different labeling sites to check that SNPS would report similar results on the donor locations. For visualization, we superimposed the donor coordinates onto our relaxed state model of the channel with the S4(4) LBT construct (Experimental Procedures). Figure 5 also shows 95% confidence surfaces for both the mean donor position and the donor diffusion cloud. Table 1 reports geometric fit results from both toxin labeling sites in cylindrical coordinates. We note that as part of the D20C acceptor cloud calibration, the acceptor cloud was slightly shifted radially by −1.5 Å, towards the pore axis. For consistency in comparing the two acceptor clouds, we identically translated the N5C acceptor cloud along the same vector as for the D20C acceptor cloud. This action can be interpreted as translating the toxin slightly towards the pore axis. Thus, during the N5C acceptor cloud calibration, its position was fixed and only rotameric group probabilities were optimized.

Figure 5. Structural Rearrangements of Shaker S4 Determined by SNPS.

(A-B) Donor positions were determined by SNPS with diffusion modeling for the Shaker S4(4) LBT construct measured in the resting ‘R’, active ‘A’, and relaxed ‘L’ functional states (see key for color scheme and text for solution types). Mapped donor positions are shown for the S4(4) LBT construct measured using 2 different toxin labeling sites: AgTx2-D20C and AgTx2-N5C, superimposed on our relaxed state S4(4) LBT structural model with LBT (yellow) and encaged terbium (black). AgTx2(II) is shown docked to the pore with both calibrated acceptor clouds: D20C (cyan dots) and N5C (deep blue dots); cysteine Cα positions are labeled ‘X’. Mean donor positions are represented as spheres. In one subunit, 95% confidence surfaces are shown for the mean position (solid inner surface) and diffusion cloud (transparent outer surface) of each donor. Viewing angles are extracellular in (A) and side in (B). The hydrophobic thickness of Kv1.2 is depicted by extracellular (EC) and intracellular (IC) lines, obtained from OPM (PDB: 3LUT). Bottom panels: magnified views of one subunit’s VSD; scale bar is 5Å. Note that both rotational solutions 1 and 2 are shown for the resting state. See also Figures S7-S8.

Donor positions reported in Table 1 and Figure 5 use rotational solution types that agree with (i.e., not rejected by) known experimental constraints. For AgTx2(II)-D20C datasets, solution type 2 fulfilled constraints in depolarized states: excellent agreement with the refined (relaxed state) Kv1.2 structures (Pathak et al., 2007; Chen et al., 2010), and active state interaction between Shaker residues A419 (S5 segment) and R362 (S4) (Lainé et al., 2003) as well as equivalent Kv1.2 residues A351 and R294 (Lewis et al., 2008). We presented both resting state solutions as both are supported by the literature. In the resting state, Shaker R362 (S4) interacts with I287 (S2) as well as I241 (S1) (Campos et al., 2007). These interactions indicate that S4 rotates and also tilts tangentially counter-clockwise about the pore axis when going from the resting to active state (extracellular perspective). However, the extent of S4 backbone displacement is highly dependent upon the degree of sidechain rearrangement and helical twisting. A recent model of Na⁺ channel gating supports a large tangential motion indicated by resting state solution 1 (Yarov-Yarovoy et al., 2012). For AgTx2(II)-N5C datasets, both resting state solutions are shown. Consistent positions for active and relaxed states were obtained using solution type 1 (opposite solution scheme).

The first experimental validation of the technique is that SNPS analysis placed the relaxed state donor positions in excellent agreement with the Kv1.2 crystal structure. Furthermore, the positions in unknown conformations (resting and active) agree well with currently available proximity constraints. The second validation is an internal control, repeating the experiment and analysis using a different acceptor labeling site. Donor positions obtained using AgTx2-N5C decays/acceptor cloud were consistent with those obtained using AgTx2-D20C decays/acceptor cloud. Although we globally fit the same number of SE decays for both toxin labeling sites, the AgTx2-N5C fits had a significantly larger uncertainty surface. We reason that this is likely due to closer proximity to the pore axis, thus reinforcing the requirement that the acceptor must be positioned off the symmetry axis. In the limit, with the acceptor set directly on the symmetry axis, LRET would measure one unique distance with donor positions completely undefined.

Finally, as a most similar comparison to previous approaches (Posson and Selvin, 2008), we examined the effect of performing geometric fits of the same data but ignoring donor and acceptor diffusion (Figure S7). Each donor was modeled as a point (a_D = 0 Å). The acceptor was modeled as a point with x- and y-coordinates taken from the toxin’s labeled cysteine Cα, and z-coordinate calculated as the probability-weighted mean of the corresponding acceptor cloud. The acceptor point position was then calibrated to the relaxed reference state, which required a substantial radial shift of −3.3 Å (inward) and +5.76 Å (outward) for AgTx2 labeling sites D20C and N5C, respectively. As expected, the donor’s circumradius decreased as much as 3.2 Å due to bias from 1/r⁶ energy transfer dependence. Although donor height was nearly unaffected, there were systematic differences in rotation, which reflects the loss of information originally present in the acceptor cloud’s asymmetric shape. Importantly, when ignoring diffusion, relaxed state positions agreed less with the relaxed state structural model and the pattern of conformational changes was less consistent between D20C and N5C datasets (see Figure S7, bottom panels). These observations clearly demonstrate the advantage of using diffusion-based effective distance calculations introduced in this work.

DISCUSSION

SNPS uses macroscopic LRET measurements to determine the position and confidence surface of symmetrically arranged protein sites in different functional states. It accounts for diffusion of all probes to compensate for apparent shortening of distances due to energy transfer, thereby reporting more accurate positions. Only one known static antenna/acceptor region within a protein structure is needed to determine 3 or more unknown satellite/donor positions. SNPS therefore serves a different purpose as compared to the trilateration-based mapping technique which requires 3 or more known satellite positions to determine one unknown antenna position. We also presented generalized inverse trilateration (without diffusion) for 3 or more satellites in any regular convex polygon geometry around a single antenna (see Supplemental Notes and Figure S4).

SNPS is intended to facilitate structure-function studies where state-dependent structural rearrangements are expected to occur. Key requirements are i) all proteins must be properly assembled and all target sites (containing donors) must be in the same conformational state during their measurement (precluding analysis of intermediate states), since this is assumed by the donor geometric model, and ii) the acceptor reference site must be placed offset from the protein’s symmetry axis. A minimum value for the average acceptor circumradius (radial distance) is approximately 0.1R₀ Å to provide donor-acceptor distances that are adequately unique, and a maximum value would place the acceptor within a distance of 0.5R₀ Å from the nearest possible donor position (D₁). We suggest that an acceptor circumradius of 0.25R₀ Å should be approximately optimal to evenly distribute distances without allowing the shortest energy transfer pair to overly dominate the SE decay.

SNPS maps absolute coordinates of donors with respect to a reference structure. The accuracy of mapped donor positions primarily depends upon the quality of LRET measurements and accuracy of the acceptor cloud (shape and position). Somewhat similar to other strategies (Sindbert et al., 2011), we have outlined a method to model the acceptor cloud above its known labeling site, which not only defines its accessible volume but also supplies rotameric information useful for coarse estimation of spatiotemporal characteristics of the diffusing acceptor. Regardless of the modeling technique or complexity, the accuracy of the acceptor cloud will dramatically improve as the fluorophore linker length is shortened. We analyzed the accuracy and convergence properties of SNPS using simulated LRET data and the AgTx2(II)-D20C acceptor cloud. Donor positions were reliably recovered within 0.5 Å error of true positions under typical noise levels (assuming a perfectly modeled acceptor cloud). We also demonstrated the extent of donor position error resulting from unexpected acceptor displacement between functional states.

Rigorous uncertainty analysis, fully numerical and without approximation, was applied to calculate the 3D confidence surface of the mean donor position as well as the donor cloud. As expected, confidence region size is reduced as more SE decays are globally analyzed. The mean donor position confidence surface has a thin banana-like shape, which is a general consequence of constraining all distances by a polygonal (symmetric) donor model. We expected that propagation of all measurable uncertainties into the effective R₀ would eliminate this thinness. Surprisingly, confidence surface size was only marginally increased, primarily through elongation rather than thickening. Thus for SNPS, propagation of effective R₀ uncertainty into the donor confidence surface does not readily warrant its extra computational effort.

SNPS can be extended to the situation where no structure is available. Given a general estimate of the acceptor’s circumradius from the protein’s symmetry axis, SNPS can map relative change in donor position between functional states. In this case, selection of solution type will be more difficult, but the same selection strategy applies. In our experience, the reduced chi-square value is not a reliable indicator of the correct solution type.

SNPS can also be applied to study protein sites labeled with conventional cysteine-reactive lanthanide chelates (Selvin, 2002). Through genetic encoding, the LBT has several advantages over cysteine chemistry: all protein subunits contain the LBT, and its labeling by terbium is highly efficient, nearly instantaneous, and highly specific. These factors simplify sample preparation and should also improve the reliability of each protein simultaneously reporting all expected distances, as required for SNPS analysis. Another advantage is that the donor location is more constrained to the backbone because the LBT is part of the protein. However, the LBT size and structure limit its insertion to flexible domains such as linkers (Barthelmes et al., 2011; Sandtner et al., 2011). We therefore carried out extensive modeling and analysis of the LBT and its insertion into the protein, but note that modeling of this sort is not required to use SNPS. We reason that the LBT is appropriate to report large-scale structural rearrangements if one of the LBT termini is directly coupled to the protein target site (e.g., Shaker S4) and the protein region at the opposite end of the LBT is flexible enough to allow the LBT to move (e.g., Shaker S3-S4 linker). Residues 3-15 within the 17 aa LBT are rigidly constrained by coordination of the encaged terbium (the donor time constant shortens significantly if the structure is not maintained), thus leaving only 2 residues available to flex on either end. We assumed that the alpha helical nature of the LBT C-terminus enables rigid connection to the downstream insertion site, and thus directly reports its movement. Although the S4(4) LBT construct was designed in accordance with this hypothesis, note that LBT motion could be dampened by short linkage to the top of S3 (assuming S3 moves less than S4; see (Gonzalez et al., 2005)).

As proof of principle, the SNPS method was applied to the Shaker K⁺ channel with a LBT in a single insertion site, and gave the following new observations. First, as indicated before (Villalba-Galea et al., 2008), the relaxed state of the VSD S4 is shown to be structurally distinct from the active state, primarily separated by an increase in height of several Angstroms. Second, the resting-active and active-relaxed transitions are both radially outward. Third, the resting-active transition is primarily either a large tangential motion about the pore in the counter-clockwise direction (extracellular perspective) or a subtle motion upward and radially outward. Two different toxin labeling sites were used to reproduce these results. Positioning accuracy was demonstrated by overlap of donor position confidence surfaces in each state. More interestingly, confidence surfaces of mean donor positions demonstrated that significant conformational change occurs between all three functional states of the channel. Although one site is clearly not enough to draw general conclusions on the mechanisms of voltage sensor movement, we can make a few tentative comparisons with previous results and simulations. The present results agree with the limited vertical movements reported before (Cha et al., 1999; Posson et al., 2005; Posson and Selvin, 2008) and with the possibility of tangential movement of the VSD as reported by (Posson and Selvin, 2008; Schow et al., 2012) and also observed in long MD simulations by (Jensen et al., 2012). On the other hand, the present results do not agree with a very large vertical translation of the S4 segment (Tao et al., 2010; Henrion et al., 2012; Jensen et al., 2012). The discrepancies in the literature are not expected to be resolved by a single insertion. The results presented here not only indicate that the relaxed state of the VSD is structurally different than the active state, but most importantly they set the stage for future investigation of the entire Shaker VSD using the advances available from the SNPS method.

In conclusion, we have developed, validated, and applied a novel three-dimensional mapping technique to obtain quantitative structural information simultaneously with functional recordings of homomeric proteins in multiple states/conformations. Additionally, we have derived and implemented new mathematical tools to account for donor and acceptor diffusion about their respective labeling sites, resulting in more accurate LRET-derived distances and mapped donor positions.

EXPERIMENTAL PROCEDURES

Software and Availability

All numerical calculations were performed in custom programs written in MATLAB (The MathWorks). The SNPS program for geometric analysis, the DecayAnalysis program for donor-only analysis, instructions, and example datasets are freely available for download at http://memprotein.org/snps. Molecular graphics images were produced with UCSF Chimera (Pettersen et al., 2004).

Acceptor Cloud Generation

Acceptor clouds were generated for both docking modes (I and II) of agitoxin2, and for both labeling sites: BODIPY FL maleimide (BFM) at AgTx2-D20C and BODIPY FL iodoacetamide (BFI) at AgTx2-N5C. The fluorophore’s accessible volume was generated by dihedral angle analysis of the linker (Figure S3A). Technical details and several alternative strategies for generating an acceptor cloud are proposed in Supplemental Experimental Procedures.

Calibration of the Acceptor Cloud to a Reference State

To accurately fit donor positions, minor adjustments were made to the acceptor cloud position. The calibrated AgTx2(II)-D20C acceptor cloud was radially shifted by −1.5 Å, towards the pore axis (xy-translation: Δx = 1.443 Å, Δy = 0.408 Å); fitted rotameric group probabilities were P(−60°) = 0.000096, P(60°) = 0.997209, P(180°) = 0.002695. The calibrated AgTx2(II)-N5C acceptor cloud was xy-translated the same as the D20C acceptor cloud; fitted rotameric group probabilities were P(−60°) = 0.947562, P(60°) = 0.051432, P(180°) = 0.001006. For rationale and details, see Supplemental Experimental Procedures.

LBT Insertion Model and Molecular Dynamics

The LBT structure (PDB: 1TJB) (Nitz et al., 2004) was inserted into a Kv1.2 structural model (Pathak et al., 2007) according to the S4(4) LBT construct design (Figure S1A) using the software package MODELLER v9.8 (Sali, 1993). The LBT insertion was refined and analyzed by molecular dynamics simulation. A symmetric tetrameric S4(4) LBT insertion model was generated by targeted molecular dynamics, with final alignment to the pore (residues 335-395) of the oriented Kv1.2 structure (PDB: 3LUT from OPM database). Details are found in Supplemental Experimental Procedures.

Shaker Potassium Channel Expression in Xenopus laevis Oocyte

The LBT motif (YIDTNNDGWYEGDELLA) was inserted between residues S357-L358 within the coding region of modified Shaker-IR (see Figure S1A). In addition to fast N-type inactivation removal by Δ6-46 (Hoshi et al., 1990), the channel had a shortened S3-S4 linker (ΔV330-S351), and had point mutations (F425G, K427D) to increase agitoxin2 affinity (Goldstein and Miller, 1992; Goldstein et al., 1994). Standard published procedures were used to generate the Shaker S4(4) LBT construct and for transcription and expression of RNA in Xenopus oocytes (Sandtner et al., 2007; Lacroix et al., 2011).

Ionic and Gating Current Recordings

Procedures have been reported previously (Sandtner et al., 2007; Lacroix et al., 2011). Briefly, ionic and gating current recordings were performed using the Cut-Open Oocyte technique under standard recording conditions. Results are shown in Figure S1. For additional details, see Supplemental Experimental Procedures.

Optical and Electrical LRET Measurements

The optical setup for LRET measurements (Figure 1B) has been previously described (Sandtner et al., 2007). Time-resolved luminescence (SE or DO) decays were collected, appropriately filtered, and detected by a gated photomultiplier tube (PMT). During optical measurements, oocytes were under voltage clamp in TEVC mode. For details, including pulse protocols, see Supplemental Experimental Procedures.