Symmetry-constrained analysis of pulsed double electron-electron resonance (DEER) spectroscopy reveals the dynamic nature of the KcsA activation gate

Abstract

Distance determination from an echo intensity modulation obtained by pulsed double electron-electron resonance (DEER) experiment is a mathematically ill-posed problem. Tikhonov regularization yields distance distributions that can be difficult to interpret, especially in a system with multiple discrete distance distributions. Here, we show that by using geometric fit constraints in symmetric homo-oligomeric protein systems, we were able to increase the accuracy of a model-based fit solution based on a sum of Rice distributions. Our approach was validated on two different ion channels of known oligomeric states, KcsA (tetramer) and CorA (pentamer). Statistical analysis of the resulting fits was integrated within our method to help the experimenter evaluate the significance of a symmetry-constrained vs standard model distribution fit and to examine multidistance confidence regions. This approach was used to quantitatively evaluate the role of the C-terminal domain (CTD) on the flexibility and conformation of the activation gate of the K(+) channel KcsA. Our analysis reveals a significant increase in the dynamics of the inner bundle gate upon opening. Also, it explicitly demonstrates the degree to which the CTD restricts the motion of the lower gate at rest and during activation gating.

Figure 1. Distance determination in multimeric proteins

(a) Schematic representation of the expected distance distribution profile as a function of the oligomeric state of a homomeric protein. (b) Cysteine mutation in CorA is shown at position V248 as black spheres at Cβ. For clarity, only 3 subunits are shown. (c) The DEER refocused echo intensity is plotted (open circles) vs. the evolution time. Fits determined from Tikhonov regularization, 2 Rice_3D and symmetry-constrained 2 Rice_3D models are shown in black, blue, and red, respectively. In the inset, the optimal regularization parameter (λ=158) is shown at the corner of the L-curve. (d) Corresponding distance distributions are plotted using the same color code. The vertical dashed lines represent the average spin-spin distances calculated from rotameric libraries of the spin label conjugated to the V248C label site.

Figure 2. Rotamer-based simulation of distance ratio distribution for KcsA and CorA

(a) MTSL rotamers were attached to CorA at position 252 using the program MMM. Nitroxide oxygen coordinates were oversampled (see text) and are displayed as black dots. CorA 252C Cα are represented as red dots and the channel’s symmetry axis is marked as a green cross. MTSL rotamer clouds were independently modified by exclusion of points based on a linear scan of occupancy (step = 0.01), radial distance (step = 0.5 Å, and cylindrical angle (step = ±0.3°). For visualization of occupancy, rotamers in the uppermost subunit were grayscaled (black=high; white=low). The blue circle (dotted) and arrow represent the radial distance scan. The red lines (dashed) and arrows represent the cylindrical angle scan. (b) Distance histograms are shown to exemplify one MTSL cloud modification for one mutant; r₁ is red, r₂ is blue, and their combination is gray. Asterisks represent the mean of the distribution using the same color code; vertical dotted lines represent Cα distances. A 2 Rice_3D fit of the combined distribution is displayed in black. (c) Histogram of <k> from the set of all MTSL cloud modifications for one mutant. (d) Histograms of <k> from the set of all MTSL cloud modifications for 11 KcsA (tetramer) and 15 CorA (pentamer) mutants. For both channels, the average <k> is plotted as a black circle and 1–99% and 5–95% intervals are plotted as tall and short ticks, respectively.

Figure 3. Validation of the symmetry-constrained model fit method

(a) The background-subtracted dipolar evolution (open circles) obtained for the CorA R252C mutant was fit using 3 different methods: Tikhonov regularization (λ=31) is shown in black, a 2 Rice_3D fit with distance ratio <k> = 1.578–1.645 is shown in red, and a 2 Rice_3D fit intentionally misconstrained such that <k> = 1.367–1.433 is shown in blue. The inset is a magnification to better illustrate fit disparities. (b) The corresponding distance distributions are shown using the same color code. The dashed vertical lines correspond to average distances calculated from the X-ray structure.

Figure 4. DEER measurements from the homotetrameric K⁺ channel KcsA R64C and approximate confidence regions

(a) The R64 residue is shown in black on a ribbon representation of the X-ray structure. (b) The background-corrected dipolar evolution is shown as open circles and the fitted dipolar evolution from a 2 Rice_3D model is plotted as a solid line; fit residuals are shown in the inset. (c) The corresponding distance distribution is shown as a solid line together with the expected distances (dashed lines) from the crystal structure. (d) The error surface of the distance ratio <k> from 2 Rice_3D model fits of KcsA R64C (blue) and CorA 252C (black). Distance ratio confidence intervals by F-test at α = 0.32 (1σ), α = 0.05 (2σ), and α = 0.003 (3σ) significance levels are shown as dashed horizontal lines. Shadowed areas represent the 5–95% and 1–99% <k> intervals determined by rotamer simulation. (e) Plots of the 68%, 95%, and 99.7% approximate confidence regions of mean distances (〈r₁〉, 〈r₂〉) obtained by 2 Rice_3D model analysis of DEER measurement from CorA R252C and KcsA R64C. The asterisk is positioned at the optimal parameter set θ̂. Shadowed areas represent the 1–99% <k> intervals.

Figure 5. Influence of the C-Terminal Domain on activation gating of KcsA

(a) Background subtracted dipolar evolution of KcsA-F114C FL and ΔCTD are shown in upper and lower panels, respectively. Data recorded at pH=3 and pH=7 are shown in red and blue respectively. For each construct, the inset displays the fit residuals and the right panel shows the corresponding distance distribution obtained by a symmetry-constrained 2 Rice_3D model fit constrained with <k> = 1.367–1.433. For each dataset <r₁> and <r₂> are shown by asterisks. (b) Plots of the 68%, 95%, and 99.7% approximate confidence regions of mean distances (〈r₁〉, 〈r₂〉), obtained by symmetry-constrained 2 Rice_3D model analysis of DEER measurements from KcsA-F114C FL and ΔCTD. Measurements obtained at pH=7 (closed) and pH=3 (open) are colored blue and red, respectively. An asterisk is positioned at each optimal parameter set θ̂. The two diagonal lines represent the 1–99% <k> interval (1.367–1.433). (c) KcsA closed (3EFF) and open (3PJS) structures are aligned and ribbon-represented using the same color code. The inset represents a lateral magnification of the activation gate where F114 is stick-represented. An analogous representation for the truncated channel is shown in the lower panels using 1K4C and 3F7V PDB accession codes.