Fluorescence Fluctuation Spectroscopy enables quantification of potassium channel subunit dynamics and stoichiometry

Voltage-gated potassium (Kv) channels are a family of membrane proteins that facilitate K+ ion diffusion across the plasma membrane, regulating both resting and action potentials. Kv channels comprise four pore-forming α subunits, each with a voltage sensing domain, and they are regulated by interaction with β subunits such as those belonging to the KCNE family. Here we conducted a comprehensive biophysical characterization of stoichiometry and protein diffusion across the plasma membrane of the epithelial KCNQ1-KCNE2 complex, combining total internal reflection fluorescence (TIRF) microscopy and a series of complementary Fluorescence Fluctuation Spectroscopy (FFS) techniques. Using this approach, we found that KCNQ1-KCNE2 has a predominant 4:4 stoichiometry, while non-bound KCNE2 subunits are mostly present as dimers in the plasma membrane. At the same time, we identified unique spatio-temporal diffusion modalities and nano-environment organization for each channel subunit. These findings improve our understanding of KCNQ1-KCNE2 channel function and suggest strategies for elucidating the subunit stoichiometry and forces directing localization and diffusion of ion channel complexes in general.

Our results reveal that the KCNE2 subunit shows either fast (> 0.02 µm 2 s −1 ) or slow (< 0.02 µm 2 s −1 ) microdiffusion as well as increased diffusive eccentricity when co-expressed with KCNQ1 at short ranges (~ 220 nm). The nanodomain confinement size for the fast population matched that of KCNQ1, suggesting that this population may represent heteromeric KCNE2-KCNQ1 complex whereas the slow diffusive population represents the unbound KCNE2. The N&B analysis confirmed homodimers of KCNE2 proteins in the absence of KCNQ1 and tetramers upon binding to KCNQ1. Overall, we describe a model for KCNE2 with respect to KCNQ1 dynamic interactions at nanometer scale using advanced fluorescence fluctuation analysis.
There are no high-resolution structures or structural models for KCNQ1-KCNE2 channels. However, the Sanders group generated a high-resolution model of KCNQ1-KCNE1 32 , showing KCNE1 in a crevice between the VSD of one KCNQ1 α subunit and the pore module of a neighboring KCNQ1 α subunit (Fig. 2B). Previous stoichiometry studies argue for between two and four KCNE1 subunits in a KCNQ1-KCNE1 complex 33,34 . Using cryo-electron microscopy, the Mackinnon group solved the high-resolution structure of KCNQ1-KCNE3 channels with PIP 2 and calmodulin bound 35 . The structure shows a tetramer of α subunits and four KCNE3 β subunits, positioned again between the VSD and pore modules of neighboring subunits (Fig. 2C). Here, we first expressed KCNQ1-mEGFP alone or with KCNE2-mCherry in Chinese Hamster Ovary (CHO cells) and recorded the currents generated using a standard voltage clamp protocol, with whole-cell patch clamp electrophysiology. KCNQ1-mEGFP expressed voltage-dependent currents with similar properties to those we and others previously observed for untagged KCNQ1, including a "hook" in the − 30 mV tail current that indicates recovery from inactivation 59 . Also similar to previous observations for untagged KCNQ1-KCNE2 channels, KCNQ1-mEGFP/KCNE2-mCherry channels were constitutively active, expressing smaller currents than homomeric KCNQ1-mEGFP (Fig. 2D,E) and with flat − 30 mV tail currents indicative of minimal voltage dependence and an absence of inactivation (Fig. 2F). Thus, the fluorescent tags used in this study did not noticeably perturb KCNQ1-KCNE2 electrical activity.
iMSD provides dynamic fingerprinting of the nano-environment. Lateral modes of mobility at the plasma membrane can significantly impact protein signaling 60 . To this end, we applied iMSD analysis, which exploits spatiotemporal fluorescence fluctuations caused by protein diffusion to obtain various types of protein mobility reported by the iMSD 56,57 curve. This curve can be used to define the diffusion model of a molecule and measure important biophysical parameters to obtain a dynamic picture of proteins diffusing in their nanoenvironment. iMSD is a particularly powerful technique since it yields similar information as single particle tracking (SPT) 61 but is not limited by the need to visualize single molecules. This property allows to extend its applicability to more physiologically relevant applications and to a much larger range of protein concentrations.
In Fig. 3A, we show an example average intensity image of a CHO cell transfected with KCNE2-mEGFP construct. For each condition considered (summarized in Table 1) and for each cell of the dataset we computed its spatial autocorrelation function as a function of time t , we fitted it with a 2D Gaussian and plotted its variance as a function of time σ 2 (t) , namely the iMSD function ( Supplementary Fig. 1, right). The iMSD function was then fitted with three different diffusion models (free, confined or transiently confined diffusion) and calculated their residuals (an example in Supplementary Fig. 1, left) to determine the diffusion modality that best describes the dynamic behavior of the proteins expressed. From this analysis we determined that both KCNQ1 and KCNE2 have a transiently confined mode of diffusion in the membrane, whether expressed independently or co-expressed. The equation describing this diffusion modality is the following equation: where σ 2 0 is an offset defined by the system's optical resolution and τ c is the confinement time. From the equation we were able to extrapolate the size of the domains in which the protein is diffusing (length of confinement,L conf ) as well as the diffusion coefficient inside (micro-diffusion coefficient, D micro = L 2 12τ c + D macro ) and across (macrodiffusion coefficient, D macro ) the nano-domains for each cell.
Interestingly, among the cells where KCNE2 was co-expressed with KCNQ1, we observed two distinct populations in the microdiffusion coefficient distributions ( Supplementary Fig. 2): approximately 46% of the cells analyzed displayed an average D micro slower than 0.02 µm 2 s −1 , while the rest of the cells displayed on average a faster diffusing population. Given this distinct behavior, we separated the cells displaying the slow and the fast micro-diffusion (named E2 s (Q1) and E2 f (Q1), respectively) in order to further investigate this finding.
In Fig. 3B we note that the behavior of E2 s (Q1) largely overlaps with that of E2 alone, whereas E2 f (Q1) has strong similarities with the diffusion behavior of Q1 and Q1(E2). For this reason, we hypothesize that E2 f (Q1) represents the population bound to Q1, whereas E2 s (Q1) represents the unbound population. As it can be appreciated in Table 2, the confinement length measured for E2 f (Q1) and the Q1 conditions are comparable, suggesting that the two units reside in the same microenvironment, therefore supporting our hypothesis. Interestingly, the macro diffusion coefficient of E2 f (Q1) is similar to E2 s (Q1) and E2, suggesting that at longer spatiotemporal range E2 f (Q1) is sensing the same environment of the unbound E2.
The microdiffusion coefficient distributions (Fig. 3C) revealed a similar average D micro for KCNQ1 expressed alone or with KCNE2 co-expression, and a slower D micro for KCNE2. The diffusion coefficient of E2 s (Q1) is similar to that of the E2 samples, while E2 f (Q1) shows a microdiffusion faster than Q1. From the analysis of the length of confinement of the diffusion domains (Fig. 3D), we observe that E2 f (Q1) shows a L conf similar to the Q1 and Q1(E2) samples, and bigger than E2 s (Q1) nano-domains, which have a similar length as E2. As shown in Fig. 3E, E2f(Q1) and E2 s (Q1) have a macro-diffusion similar to that of KCNE2 and statistically different from that of the Q1 samples. Complete tables of the P-values computed for the iMSD parameters are reported in Supplementary Fig. 3. www.nature.com/scientificreports/   58 , which has the capability of mapping anisotropic paths at different spatial locations and therefore barriers to diffusion [62][63][64][65] . Briefly, each pixel in the image contains intensity fluctuations from the proteins occupied within that pixel when the image is captured. Sequential frame sequences are taken to obtain fluctuations as a function of time. To obtain the average time for a protein to move from one position ('a') to another position ('b') separated by a given number of pixels away, the fluctuation from position www.nature.com/scientificreports/ 'a' and position 'b' are cross-correlated by all possible delay times within in the image sequence. If the proteins diffuse into position 'b' , a positive correlation will be detected with a characteristic decays time that took for the protein to reach that spot. To build a map of diffusion across the entire image, pixels are cross-correlated as function of time and in 24 angular directions. For each pixel of an image the pCF is calculated for all adjacent neighbor pixels in a radius around the pixel of interest at a given pCF distance δr. As an example, if a diffusing protein encounters an obstacle while transiting between the two pair-correlating points, its diffusion will no longer be isotropic but it will preferentially diffuse away from that obstacle and this will modify the time delay of the pair-correlation function, as depicted in Fig. 1C. The 2D-pCF analysis can be carried out at different distances in order to infer the presence of obstacle at short or long range.
To evaluate the directionality of diffusion of KCNQ1 and KCNE2, we extrapolated from the 2D-pCF analysis the values of eccentricity for five different pair-correlation distances. The eccentricity describes whether the protein is diffusing isotropically (e = 0) or anisotropically (e > 0).
In Fig. 4A we show the average values of eccentricity as a function of the pair-correlation distance for all the conditions considered. As expected, for all the conditions the values of eccentricity become higher as the paircorrelation distance increase, since at larger distances there is a higher probability for the diffusing molecule to encounter obstacles. Our results show that the KCNQ1 channel, whether independently expressed or coexpressed, displays a low eccentricity, being comparable with that of our inert control membrane bound form of the mEGFP (GAP-mEGFP), which is not a functional protein and therefore its diffusion is solely dictated Table 1. Summary of the experiment conditions and related terminology used throughout the paper.

Acronym
Proteins (co-)expressed  www.nature.com/scientificreports/ by the surrounding environment and is used here as a reference. KCNE2 generally shows a higher eccentricity, therefore a more anisotropic diffusion compared to Q1. At longer pair-correlation distances E2, E2 s (Q1) and E2 f (Q1) show a similar behavior, while at short range (220 nm) E2 f (Q1) eccentricity significantly increases when compared to E2 and E2 s Q1, suggesting a localization in membrane domains in which the directionality of the motion is more pronounced. Complete tables of the P-values computed for the 2D-pCF analysis for the average eccentricity and eccentricity at each distance are displayed in Supplementary Fig. 4. Furthermore, from the 2D-pCF images (shown in Fig. 4B) it is possible to spatially map the eccentricity values for the different conditions and at the different pair-correlation distances. Compared to our inert control (GAP), we can see a strong heterogeneity of behavior in the cell membranes that increases with the distance. In particular we can observe the localization of binding loci at the membrane for both the KCNQ1 and the KCNE2, which appear as rings of high eccentricity 62 , as shown more in detail in Supplementary Fig. 6B.

Number and Brightness analysis of KCNQ1-KCNE2 stoichiometry.
Here, we applied N&B analysis to measure the oligomerization state of the KCNQ1-KCNE2 complex subunits and to further examine the differences between E2 s (Q1) and E2 f (Q1), using the membrane bound form of the mEGFP (GAP-mEGFP) as our monomeric reference. First, we found that the KCNE2 subunit exists on the membrane in the form of a dimer in the absence of KCNQ1 co-expression (Fig. 5A). Upon KCNQ1 co-expression, the E2 f (Q1) results indicated four E2 subunits per KCNQ1-KCNE2 complex, whereas the E2 s (Q1) suggested on average three E2 subunits (Fig. 5A). Since the trimeric form is not thought to be a physiological configuration, we interpreted our result as stemming from a mixture of dimeric (unbound) and tetrameric (KCNQ1-bound) forms of KCNE2. In this scenario, the slow micro-diffusion we measured for the E2 s (Q1) is predominantly driven by the unbound dimeric population, although a small population of bound tetrameric KCNE2 is measured in the N&B analysis. Further indications to support the hypothesis that the E2 f (Q1) represents the component bound to the KCNQ1 is the fact that the cells assigned to the E2 f (Q1) show on average higher expression level of the KCNQ1 with respect to KCNE2 (Fig. 5B, center), compared to the E2 s (Q1). N&B analysis of the KCNQ1 describes the complex as tetrameric with or without co-expression with KCNE2 (Fig. 5A,C). Importantly, from our data we could not correlate any dependence of the oligomerization state on the expression level ( Fig. 5B-C), although it was reported elsewhere for KCNQ1-KCNE1 by some 33 but not others 34 . This may be due to the fact that we are considering a limited range of expression levels, since we did not acquire very dim nor very bright cells in order to avoid low signal and saturation, respectively.
It's worth noting that the width of the distribution is an intrinsic limitation of the N&B technique. In fact, the uncertainty in the determination of the oligomerization state scales with the number of oligomers, as reported elsewhere 36,66 . However, the samples considered were tested for normality and they were determined with high confidence (P > 0.91) to be Gaussian distributions, as expected. Moreover, both the width and the mean of the oligomerization state distribution for E2 f (Q1) (Fig. 5B, right, dark red distribution) is comparable with the distributions shown for Q1 and Q1(E2) (Fig. 5B right, green distributions), which are known to be tetrameric. Complete tables of the P-values computed for the oligomerization state from N&B analysis are provided in Supplementary Fig. 5 and a representative map of brightness is shown in Supplementary Fig. 6C.  (Fig. 6A,B). This plot can provide an immediate quantification of the biophysical properties we can measure with our FFS-based approach. We used this plethora of information to create a graphic model of the membrane environment and homo-and hetero-oligomerization state of the proteins considered for this study (Fig. 6C). A complete table of the parameters used is available in Supplementary Table 1. In our model, the confinement regions are represented as square microdomains with size equal to L conf , the micro-and macro-diffusion as a circular region with diameter d = √ 4Dt where t is 0.5 s for D micro and 60 s for D macro . Directionality is represented as two ellipses with eccentricity equal to the eccentricity calculated from www.nature.com/scientificreports/ 2D-pCF at a distance of 220 nm (inner ellipse) and 660 nm (outer ellipse). KCNQ1 and KCNE2 are represented with their oligomerization state measured from N&B and colored according to the appropriate fluorescent protein tagging. As shown pictorially by the dark blue circle in each panel, KCNE2 dimers diffuse slower and travel a shorter distance than when bound to tetramers of KCNQ1 (E2 f (Q1)), approximately 150-200 nm and 300 nm in 0.5 s, respectively. When KCNE2 dimers are bound to tetramers of KCNQ1, two populations of distinct diffusions emerge as shown in Fig. 3. There are no notable differences in diffusion for complexes of KCNQ1 when bound or not bound to KCNE2.

Discussion
In summary, we showed how the parallel implementation of multiple FFS techniques can give important insights into the diffusion behavior and oligomerization state of ion channels as well as the channel subunits stoichiometry. We provided a demonstration that the fluorescent tagging does not affect the electrophysiology measurements, from which we infer that the diffusional properties are conserved as well, and applied to the same dataset three analysis techniques to obtain information about micro-and macro-diffusion, confinement, directionality of motion, oligomerization state and stoichiometry of the KCNQ1-KCNE2 complex. Analysis with iMSD lead to the discovery of a bimodal distribution in the D micro parameter after co-transfection of the KCNE2 subunit with the KCNQ1 ion channel. We used this information to separate the diffusional behavior of the KCNE2 subunit in a slow and a fast component, which we hypothesized being the unbound and the Q1-bound population, respectively. Our hypothesis is supported by the fact that the slow component has the same length of confinement and oligomerization state as the KCNE2 transfected alone, whereas the fast component shows an increased oligomerization state as well as a confinement length comparable to KCNQ1, suggesting that they reside in a similar microenvironment. Counterintuitively, the bound component displays a faster microdiffusion, which is also associated with an increase in the confinement length, with respect to the unbound component. We attribute this behavior to a segregation of the unbound component in more confined and distinct domains in the cellular membrane, from which KCNE2 is released by binding to KCNQ1 or another intermediary. Interestingly, each cell appeared to contain either the slow or the fast population (but not both), which we showed were independent from (co-)expression levels (Supplementary Figs. 7-9), passage number or transfection. We speculate that other cell-to-cell variability in endogenous factors known to affect KCNQ1 and KCNE surface expression and interaction might explain this cell-specific behavior. Possible examples include Protein Kinase C activity, which regulates KCNQ1-KCNE surface expression and interaction [67][68][69][70] or differential endogenous expression of proteins that interact with KCNE2, such as the focal adhesion protein Testin 71 . Other regulatory influences for diffusion of Kv channels include the underlying cytoskeletal structure, and interactions with other membrane proteins. Specifically, Kv2.1 and Kv1.5 have been detected to co-localize to caveolar and non-caveolar rafts enriched regions in cells 72 . Additional measurements have also shown that the function of Kv1.5 was altered upon cholesterol depletion and inhibition of sphingolipid synthesis. Moreover, lateral diffusion of voltage-gated sodium (Nav) channels is impacted by their ability to bind to the scaffolding protein ankyrin-G (AnkG), as long as the scaffold is in excess concentration versus the ion channel, and may regulate neuronal plasticity 65 . In addition to Nav channels, AnkG retains KCNQ2 and KCNQ3 subunits at the axon initial segment 73 . Further dedicated studies are needed to establish the precise underlying mechanisms controlling the diffusion of the KCNQ1-KCNE2 complex.
Our N&B analysis reported KCNE2 homodimers capable of reaching the plasma membrane without coexpression of KCNQ1. Our finding that KCNE2 reaches the plasma membrane when expressed alone, and forms homodimers in this environment, is in agreement with previous observations that non-fluorescent-tagged KCNE2 is able to traffic alone to the cell surface 74 . This observation is in contrast, however, with prior findings for non-tagged KCNE1, which was reported to be unable to reach the cell surface alone 75 . The KCNE2 regulatory subunit was previously found to traffic to the surface of HEK293 cells much more efficiently than KCNE1 or the hERG alpha subunit with which KCNE1 and KCNE2 can interact. Furthermore, KCNE2 was even found to be secreted into the extracellular medium. Importantly, KCNE2 proteins with the correct mass for dimers were detected in the extracellular fraction by western blot and confirmed by mass spectrometry analysis as being KCNE2 homodimers and the higher mass confirmed as not arising from glycosylation 74 . The dimeric form of KCNE2 reported by Um and McDonald 74 was not tagged with a fluorescent molecule, supporting the premise that dimerization in our study is intrinsic to KCNE2 and not an artifact of tagging.
While the current study represents, to our knowledge, the first assessment of KCNQ1-KCNE2 channel stoichiometry, a number of studies have been conducted on related channels, primarily KCNQ1-KCNE1 (I Ks ) complexes. Initial studies from the Goldstein lab, each employing different counting techniques (site-directed mutagenesis with macroscopic or microscopic functional analysis, and toxin binding), indicated a probable 4:2 KCNQ1-KCNE1 subunit stoichiometry, although the possibility of 4:4 was not entirely dismissed. The rigid 4:2 stoichiometry was also arrived at in a later study using a chemically releasable irreversible inhibitor. The Goldstein lab then subsequently utilized counting of fluorescent tag bleaching to further reinforce the idea of 4:2 KCNQ1-KCNE1 subunit stoichiometry and effectively rule out, in their hands, variable stoichiometry 34,76,77 . However, other labs have contended that they observe a variable stoichiometry with up to 4 KCNE1 subunits per channel complex, depending on KCNE1 expression levels relative to KCNQ1, based on single molecule fluorescence bleaching 33 . More recently, the MacKinnon lab solved a structure of KCNQ1-KCNE3 complexes using cryoelectron microscopy, and found a 4:4 stoichiometry 35 . In addition, using photobleaching, the Felipe lab recently counted 4:4 for KCNA3:KCNE4, although they too reported a variable KCNE4 stoichiometry in the complexes depending on the relative expression level, and concluded that functional attributes varied with stoichiometry 78 . Finally, using photobleaching, the D' Avanzo group concluded that complexes formed by pacemaker (HCN) www.nature.com/scientificreports/ channel alpha subunit and KCNE2, which may contribute to pacemaking in the heart and/or brain, have an expression-level dependent variable stoichiometry of between 4:1 and 4:4 (HCN:KCNE2) 79 . The capability to assess the spatial distribution of multiple structural and functional parameters can have farreaching applications in the study of the spatial organization of membrane channels. As an example, we report in Supplementary Fig. 6 an intensity image together with directionality and brightness maps of a cell displaying the slow KCNE2 population, in which it is possible to appreciate high brightness sites marked by a characteristic high eccentricity ring. Since CHO cells are not polarized and do not display any distinctive spatial feature (such as, e.g., the axon in neurons), the present study was conducted considering the overall median eccentricity and brightness of the whole cell, but may give important insights into the analysis of polarized cells such as gastric parietal cells, thyroid epithelial cells and choroid plexus epithelial cells, all cell types in which KCNQ1-KCNE2 channels play a crucial role.

Conclusions
Our findings herein that KCNQ1-KCNE2 channels likely exist as octamers containing four of each subunit can guide our understanding of how these physiologically important channels function. Furthermore, given their role in several diverse, highly specialized cell types, the enhanced understanding of their movement within the cell membrane produced by this study can be built upon to understand the forces directing and localizing KCNQ1 and KCNE2 subunits in the various polarized cell types in which they are expressed, perturbation of which in vivo has been shown to contribute to complex disease states [23][24][25] .
The biophysical methods used in this work reveal the types of translational motion of molecules at the plasma membrane. Since the biophysical properties of both membrane organization and protein dynamics vary extensively across temporal and spatial scales, it is important to study the diffusion pattern which is dynamically kept out of equilibrium as cells tend to continuously regulate ion channel trafficking 80 . We showed that our multiplexed methods, and in particular iMSD and 2D-pCF analyses, can extract complex diffusion behaviors (Brownian diffusion, confinement/hopping dynamics) without the need to visualize single molecules, greatly simplifying sample preparation and analysis and providing unbiased and user-independent results while avoiding perturbating the correct functionality of the channels, as shown from our electrophysiology results. Furthermore, the N&B method provides information on the oligomerization state of the diffusing proteins, making the approach presented in this study ideal for a system of such complexity. In general, our use of TIRF imaging, a powerful yet relatively common technology, in combination with a series of Fluorescence Fluctuation Spectroscopy techniques allows researchers to determine, in a single acquisition, the oligomerization state, the diffusion modality and the nano-environment organization, making our approach generally suitable for a larger variety of applications in more than one field.

Materials and methods
Cell culture and transfection for whole cell patch-clamp. We seeded CHO cells (ATCC) onto poly-L-lysine treated glass coverslips and transfected using TransIT-LT1 (Mirus Bio LLC, Madison, WI, USA) the following day with CMV-based expression constructs containing cDNA for human KCNE2 (C-terminally mCherry-tagged), and/or KCNQ1 (C-terminally mEGFP-tagged). Cells were cultured in DMEM with 10% FBS and 1% penicillin/streptomycin in a 95% O 2 /5% CO 2 humidified environment at 37 °C for 48-72 h post transfection prior to patch-clamping. We purchased cell culture consumables and reagents from VWR or Fisher Scientific unless otherwise stated.
iMSD. iMSD analysis was performed with a custom code written in MATLAB. From a user-defined rectangular region the spatiotemporal ACF, represented by a 3D matrix, was computed. Each XY plane of this matrix was fitted to a two-dimensional Gaussian function and the σ 2 (t) was stored and fitted with a free diffusion, confined and transient confined models, as described by the following equations: N&B. Number and brightness analysis was performed with a custom code written in MATLAB. The mean and variance along the temporal dimension of the image stack was computed and the brightness was obtained after correcting for the dark noise/offset and the gain of the camera, as described elsewhere 37,53,66 . The oligomerization state was corrected to account for protein maturation and misfolding as described elsewhere 81 . The brightness of the monomers was found to increase linearly with the average intensity; therefore, we performed a fitting of the brightness of all the monomers acquired as a function of the average intensity. The resulting function was used to obtain the oligomerization state for the experiments, scaled with the appropriate average intensity value. Bleaching was not observed and therefore no correction was performed.
Statistical analysis. Electrophysiology. All values are expressed as mean ± SEM. Students' t-test was used for statistical comparisons. All P-values were two-sided. Statistical significance was defined as P < 0.05. violin.m-Simple violin plot using MATLAB default kernel density estimation. INRES (University of Bonn), Katzenburgweg 5, 53,115 Germany." Bandwidth was set as 0.0033 (Fig. 3C), 53.33 (Fig. 3D), 0.0005 (Fig. 3E) and 1.5 (Fig. 5A). Tukey's test was used for multiple comparisons statistics by using the MATLAB function "multcompare" with statistics provided by the "anova1" function, which computes the one-way ANOVA (analysis of variance). Statistical significance is shown as asterisks corresponding to P-values < 0.05 (*), < 0.01 (**) and < 0.001 (***). All distributions have been tested for normality by a single sample Kolmogorov-Smirnov test, yielding high confidence results for all distributions (P > 0.91). Complete diagrams of statistical significance are shown in the Supplementary Figures.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.