Abstract
Crosscorrelation of superresolution images gathered from point localizations allows for robust quantification of protein codistributions in chemically fixed cells. Here this is extended to dynamic systems through an analysis that quantifies the steadystate crosscorrelation between spectrally distinguishable probes. This methodology is used to quantify the codistribution of several mobile membrane proteins in both vesicles and live cells, including Lyn kinase and the Bcell receptor during antigen stimulation.
Introduction
Superresolution localization microscopy techniques such as (direct) stochastic reconstruction microscopy ((d)STORM)^{1,2} and (fluorescence) photoactivation localization microscopy ((f)PALM)^{3,4} can be used to quantitatively investigate the nanoscale coclustering of labelled biomolecules in multicolour fluorescence experiments. In images reconstructed from immobilized probes, the spatial codistributions of spectrally distinct labelled proteins can be quantified using bivariate Ripley’s functions^{5} or by crosscorrelation^{6,7,8}. In live cells, however, single molecules can travel over large distances during the time it takes to reconstruct a single wellsampled image, complicating the interpretation of colocalization results. It is possible to quantify the codistributions of some proteins in live cells when their dynamics are slow compared with the time it takes to reconstruct a superresolved image^{9,10}. However, many proteins undergo fast diffusion making this approximation invalid within the constraints of most image acquisition systems, even considering recent advances^{11} in fast image acquisition and multiemitter fitting.
A robust set of analytical tools has been developed to quantify the timedependent colocalization of components in diffractionlimited images based on image crosscorrelation^{12,13}, although these techniques do not take advantage of the resolution improvement afforded by localizationbased superresolution microscopy. Past work has extended crosscorrelation analysis to localized single molecules through a technique named particle image crosscorrelation spectroscopy^{14}. While powerful, this method was designed to detect colocalization between components over short distances and reports only a singlecorrelation coefficient whose magnitude can vary if the density of observed components changes with time. Here we present an alternate approach that is quantitative, modelindependent and robust to the variations in signal density inherent in superresolution localization measurements. The steadystate crosscorrelation analysis presented here is equivalent to approaches commonly used in statistical mechanics and condensed matter physics, which provide an estimate of the magnitude of interactions between components in units of energy, and the statistical significance of the correlation function can be estimated directly from acquired data.
Here we demonstrate the robustness of the steadystate crosscorrelation approach to quantifying point localized data sets in mobile systems ranging from simulated data, an isolated plasma membrane vesicle, and live Bcell lymphocytes. Using instantaneous crosscorrelation on live twocolour superresolution data, we observe that Lyn kinase is recruited to Bcell receptors (BCRs) soon after clustering with a multivalent soluble antigen, and this recruitment is reduced but not ablated in the presence of the Src kinase inhibitor PP2. The degree of colocalization between Lyn and clustered BCR in the absence of the inhibitor corresponds to an effective interaction potential of ∼1 k_{B}T over the extent of the BCR cluster (∼100 nm), where k_{B}T is the thermal energy, and colocalization decreases with increased stimulation time when short (20 s) steadystate time intervals are used. By combining the steadystate crosscorrelation methodology with a mobility analysis of Lyn, we find that colocalized Lyn proteins diffuse more slowly, consistent with direct binding between Lyn and immobilized components within BCR clusters. We quantify the offrate of this interaction as well of the fraction of Lyn proteins in the immobilized state as a function of stimulation time. Overall, we conclude that this crosscorrelation approach is a powerful tool to probe interactions between labelled proteins in live cell superresolution data sets.
Results
Crosscorrelations quantify mobile and immobile systems
The crosscorrelation function, C(r, τ), measures the probability of finding a pair of differently coloured fluorophores as a function of their separation distance r at a time lag τ. In superresolved data sets of immobile systems, one can quantify colocalization using C(r, <τ>), where <τ> indicates an average over all τ, meaning that all localizations contribute independently of when they were observed^{6,7,8}. C(r,<τ>) is evaluated equivalently by tabulating distances between all localized fluorophores of different colours irrespective of time or by reconstructing images of each fluorophore type followed by image crosscorrelation using Fourier transform methods (Supplementary Fig. 1 and Methods). Generally, the variance in C(r) determines statistical significance, depends on the number of localized molecules in each colour channel as well as the magnitude of correlations, and can be determined directly from acquired data as described in Methods and validated in Supplementary Figs 2,3. Finite localization precision as well as any errors in registering the twoimage channels act to systematically broaden shortrange correlations over longer distances while maintaining the integrated area under C(r)−1^{15}. C(r) can be converted to the density of molecules of one type as a function of separation distance from the average labelled molecule of the other type, ρ(r), by simply multiplying C(r) by the average density of that molecule <ρ(r)>. Several methods have been described to estimate <ρ(r)> from superresolution images^{6,16,17,18,19} or average densities can be obtained using nonimaging methods. Integrating ρ(r) allows for quantification of the average number of interacting proteins^{8,15}. Supplementary Fig. 4 demonstrates how to convert between C(r) and ρ(r) when <ρ(r)> is known for several examples described below.
In mobile systems, crosscorrelations of reconstructed images, C(r, <τ>), may not reflect a meaningful codistribution, as localizations that occur at different times are compared. This is demonstrated using a molecular dynamics (MD) simulation with particles subject to the LennardJones (LJ) potential or through experimental measurements of cholera toxin B subunit (CTxB) in isolated giant plasma membrane vesicles (GPMVs) (Fig. 1). The LJ potential is strongly repulsive for short particle separations (r<σ) and weakly attractive for larger separations (σ<r<2σ). C(r, <τ>) tabulated from reconstructed images acquired over time yields a nearly uniform distribution, with C(r, <τ>) close to 1 for all radii (magenta line in Fig. 1b). The steadystate crosscorrelation produced by tabulating C(r, τ=0) from pairs of particles detected simultaneously (τ=0) reflects the actual codistribution of particles (black line in Fig. 1b), with exclusion at short radii (C(r<σ)<1) and enrichment at intermediate radii (C(σ<r<2σ)>1). A similar observation is made when tabulating crosscorrelation functions between singlemolecule localizations of two spectrally distinct pools of CTxB bound to GPMVs. CTxB partitions strongly into liquidordered domains^{20} and is highly structured in a diffractionlimited image of a phaseseparated GPMV acquired with a short (0.2 s) integration time (Fig. 1c). Reconstructed images of singlemolecule localizations from the bottom surface of the same vesicle appear uniform since domains are mobile over the time frame of the singlemolecule measurement (3 min). C(r, <τ>) tabulated over all Atto 655 CTxB and Alexa 532 CTxB localizations also appears uniform; however, significant crosscorrelation is observed when C(r, τ=0) is calculated using only pairs of probes imaged simultaneously (τ=0) (Fig. 1d top panel). Both C(r, τ=0) and C(r, <t>) reveal a uniform distribution of CTxB for a second GPMV that is in a single liquid phase, since both populations of CTxB explore the entire vesicle surface over both short (0.2 s) and long (3 min) time scales (Fig. 1e,f).
This quantification method also yields a modelindependent measure of the effective interactions between labelled components, frequently referred to as the potential of mean force (PMF) under conditions where it can be reasonably approximated that probe organization is a result of an equilibrium process. The PMF is related to C(r) through PMF(r)=−k_{B}Tln(C(r)), where k_{B}T is the thermal energy. For the case of the MD simulation of Fig. 1, the PMF calculated using C(r, τ=0) reproduces the original LJ potential up to small corrections that arise from manyparticle interactions (Fig. 1b, lower panel). In phaseseparated vesicles, the measured potential well is greater than k_{B}T out to separation distances of nearly 1 μm, consistent with the presence of phaseseparated domains at thermodynamic equilibrium (Fig. 1d, lower panel). No significant PMF is observed between differently coloured CTxB in the singlephase vesicle shown in Fig. 1e,f. We note that the detailed shape of either C(r) or PMF(r) can be used to distinguish models describing interactions between components^{6}.
Quantifying effective protein interactions in live B cells
We have also applied this analysis to quantify the codistribution of Lyn kinase and a geranylgeranylated peptide (GG) with the BCR in the CH27 cell line, which endogenously expresses an IgM isotype of the BCR (Fig. 2a). The BCR is a crucial component of the human adaptive immune system, which is able to bind a wide array of pathogen and selfepitopes. Lyn and other srcfamily kinases phosphorylate conserved tyrosine residues found in intracellular tyrosine activation motifs associated with the receptor^{21,22,23,24}, and Lyn can bind to these phosphotyrosine residues via SH2 domains^{21,24}. The association of Lyn with the BCR has been detected using FRET microscopy in live cells^{25}. However, the initiation of BCR phosphorylation by Lyn is not fully understood. It has been suggested^{26} that Lyn is constitutively associated with BCR, or that Lyn is recruited to BCR only after antigen binding due to either a conformational change or a BCR clusterinduced stabilization of ordered lipid domains.
Lyn and BCR were, respectively, labelled with photoactivatable mEos3.2 (ref. 27) and a f(Ab)_{1} fragment conjugated to both biotin and Atto 655 (ref. 28) as described in Methods. An image reconstructed from all localized singlemolecule positions acquired after the addition of soluble streptavidin indicates that BCR is strongly selfclustered under this condition (Fig. 2a), with streptavidin acting as an antigen against biotinlabelled BCR. Evaluating C(r, τ=0) from a singlecell data set (Fig. 2b, top panel) reveals that Lyn and BCR are weakly crosscorrelated at short radii in the absence of antigen (Ag) and correlations increase significantly in magnitude after antigen addition (+Ag), out to radii corresponding to the largest BCR clusters (200 nm). The PMF obtained from C(r, τ=0) (Fig. 2b, lower panel) indicates a weak attraction (PMF<<k_{B}T) between BCR and Lyn before antigen addition, suggesting that the vast majority of Lyn is not bound to BCR in resting cells. A more significant attractive potential (PMF≈k_{B}T) is found between these proteins after antigen addition, indicating robust Lyn recruitment to BCR clusters following antigen stimulation in agreement with previous reports using FRET^{25}. We note that since our fluorophores do not distinguish between internal states of either protein, such as their phosphorylation state, the PMF should not be interpreted as the interaction strength between specific states of these proteins. Instead, it represents time and populationweighted average over all states that are present in the system.
LynBCR coclustering and the PMF between these components are reduced in cells imaged in the presence of the smallmolecule srcfamily kinase inhibitor PP2 (Fig. 2c,d), also in agreement with previous FRET results^{25}. PP2 inhibits phosphorylation of the BCR by srcfamily kinases, which includes Lyn, attenuating downstream signalling cascades and reducing the number and strength of potential binding sites between Lyn and BCR. Crosscorrelations observed before antigen stimulation are comparable between control and PP2treated cells, suggesting that this weak colocalization is not dependent on srcfamily kinase phosphorylation. To obtain statistically significant correlations under this experimental condition, the curves presented in Fig. 2d are generated by averaging results from five independent cells as shown in Supplementary Fig. 5.
We additionally imaged a GG conjugated to mEos3.2 simultaneously with Atto 655labelled BCR to provide an example of exclusion in this system. GG is weakly excluded from BCR clusters formed after antigen binding, possibly due to steric repulsion from a crowded protein environment, electrostatic repulsion due to the polybasic stretch on this peptide and/or a lipidmediated repulsion due to the disorderpreferring geranylgeranylation modification^{29}, as BCR clusters are hypothesized to stabilize a more ordered local lipid environment^{26}. To obtain statistical significance for this weak repulsion using data collected from a single cell, we evaluated C(r) by averaging over 0<τ<3s, corresponding to 100 image frames. This is appropriate in the case of antigenclustered BCR as the partitioning of GG around BCR does not vary with τ, likely because BCR clusters do not diffuse a significant distance within this time frame. It should be noted that this averaging approach will suppress any structure in the correlation function when C(r, τ) varies quickly with τ. Additional justification for using C(r, τ>0) to better determine C(r, τ=0) in this and alternate circumstances is described in Methods and Supplementary Fig. 6.
There are quantitative differences between C(r, τ=0) compared with timeaveraged C(r, <τ>) in chemically fixed samples, which can be attributed to the presence of fluorophore bleedthrough (Supplementary Figs 7–9). Bleedthrough occurs simultaneously in both channels; therefore, it disproportionally affects C(r, τ=0) compared with C(r, <τ>). A similar increase in simultaneous versus timeaveraged C(r) is observed in simulations including a realistic level of bleedthrough of mEos3.2 from the nearred to farred emission channel, where bleedthrough does not increase in the number of farred localized positions but does bias the position of farred localized centres (Supplementary Fig. 8). Several strategies for reducing the adverse effects of bleedthrough are discussed in Methods and Supplementary Fig. 9.
Quantifying the dynamics of the BCRLyn interaction
The simultaneous crosscorrelation approach described above can also reveal timedependent changes in protein colocalization and dynamics by tabulating C(r, τ=0) over shorter steadystate time intervals (every 20 s in Fig. 3a). By monitoring only correlations for r<50 nm versus time, it is apparent that Lyn becomes correlated with BCR shortly after antigen is added, concurrent with a marked reduction in BCR diffusion and a smaller reduction in Lyn mobility. The shortrange correlations decay over 5 min following antigen stimulation, in good agreement with previous FRET results^{25}, findings in chemically fixed cells (Supplementary Fig. 9) and trends are reproducible over several live cell measurements (Supplementary Fig. 10).
Lyn kinase diffuses on the inner leaflet of CH27 cells at a faster rate than the BCR; thus, a strong and longlived binding of Lyn to BCR should be reflected as a reduced mobility of Lyn. Distributions of single trajectory diffusion coefficients show a reduction in both BCR and Lyn mobility after stimulation (Supplementary Fig. 11). We examined Lyn stepsize distributions only including steps containing localized positions identified as correlated in the C(r, τ=0) analysis, meaning that they are observed within 50 nm of a simultaneously localized BCR. These correlated Lyn steps produce a distribution that closely resembles that observed for all Lyn steps before antigen addition, but shifts to shorter values after antigen addition to more closely resemble the distribution of all BCR steps (Fig. 3b). The majority of correlated Lyn localizations after antigen stimulation are found within sections of Lyn trajectories that are transiently confined (Fig. 3c). These findings indicate that most Lyn do not have longlived (>0.1 s) associations with the BCR in resting cells, but a subset of Lyn becomes associated with BCR after antigen stimulation.
The same data used to tabulate spatial correlations between proteins can also be used to quantify protein mobility. The timeresolved autocorrelation function, G(r, τ), is tabulated from localized positions of the same fluorophore type detected at different times and is a convenient measure of the time evolution of particle motion without the need to identify singleparticle trajectories. This is a localized particle variation of STICS^{13} similar to PICS^{30} but G(r, τ) is normalized to yield the probability density function (PDF) for correlated steps of displacement r in a time interval τ. PDF(r, τ) at fixed τ for a single population of diffusers is a Gaussian with width equal to the mean squared displacement (MSD). PDF(r, τ) of Lyn were fit to models containing slow and fast diffusing populations (Fig. 3d and Methods) yielding the MSD of each population and the fraction of diffusers in the slow population (α) as a function of τ. Diffusion coefficients of Lyn determined by fitting these MSD(τ) are in good agreement with those determined by trajectory MSD analysis (Supplementary Fig. 12). α decreases with τ, with a decay time of 0.3 s before BCR stimulation and 0.7 s following BCR stimulation (Fig. 3e). As the slowly diffusing Lyn population is likely bound to BCR or other slowly diffusing adaptor proteins, this decay likely indicates the offrate of Lyn binding to targets associated with the BCR signalling complex. Finally, the fraction of steps belonging to the slow population extrapolated to zero time lag, α(τ→0), is the fraction of Lyn localizations associated with the slower diffusing pool. Figure 3f shows that this switches from 9±3% before antigen stimulation to 25±6% after stimulation, and does not exhibit the decay at late stimulation times observed for C(r, τ<50 nm) shown in Fig. 3a. This suggests that Lyn associates with other slowly moving components that are spatially distinct from BCR at later stimulation times, consistent with Lyn’s roles in phosphorylating other components during BCR stimulation such as CD19, CD22 and FcγRIIB^{24}.
Discussion
We present an analytical method to quantify the codistribution and dynamics of labelled molecules in superresolution localization measurements without reconstructing images or trajectories, enabling robust measurement of codistributions in single cells exhibiting high mobility. This adds to an existing set of analysis methods based on spatial auto and crosscorrelations^{12,13,14} with specific applicability to point localized stochastically blinking probes commonly used in superresolution fluorescence localization data sets. Here we apply this methodology to quantify interactions between membranebound components, but in principle this methodology could be applied to a range of systems including those imaged in one or three dimensions.
When applied to measurements of the BCR and Lyn kinase in live cells, we find that these proteins are only weakly associated before antigen stimulation, providing evidence against a model where a large fraction of Lyn is constitutively associated with BCR in the resting cell^{26}. Instead, Lyn is observed to transiently colocalize with BCR soon after the addition of multivalent antigen, with single Lyn proteins dwelling with an offrate of 0.7 s. On average, the population of Lyn associating with BCR is greatest at short times after stimulation then decreases over several minutes. This is consistent with Lyn’s role as a mediator of early signalling events and is in excellent agreement with previous findings obtained by FRET^{25}. One advantage of this approach over past FRET measurements in this system is the ability to estimate interaction energies between proteins, and we observe that the potential well attracting BCR and Lyn has depth of roughly the thermal energy over a range of 100 nm. Interestingly, Lyn is still recruited to BCR clusters in the presence of the inhibitor PP2, although to a weaker extent, suggesting that there are interactions between BCR and Lyn beyond SH2 binding to phosphorylated intracellular tyrosine activation motifs within BCR. Overall, this work emphasizes the complexity of LynBCR interactions as well as the power of superresolution localization microscopy to probe the organization and dynamics of protein interactions in intact cells.
Methods
Calculating correlation functions
Crosscorrelation functions are tabulated by first computing the distances between pairs of distinguishable localized molecules, then constructing a histogram with these distances by separating into discrete bins covering different ranges of radii, then finally normalizing this histogram to account for the different areas associated with each bin and effects that arise due to the finite size of the region of interest (ROI) being analysed. These steps are illustrated graphically in Supplementary Fig. S1b for the example of an image reconstructed from BCR and Lyn localizations in a chemically fixed cell, and are described in detail below.
Within a ROI of an image, the total number of distinct pairwise distances between distinguishable localizations is N=n_{1} × n_{2} where n_{1} is the number of localizations of one coloured probe and n_{2} is the number of localizations of the second coloured probe. These N distances are computed, and then discretized into bins centred at radii r with width Δr, which sets the resolution of the crosscorrelation. Here we call this histogram M(r). M(r) tends to increase in magnitude with increasing radius since the two dimensional area associated with each radii bin is a ring with an area of ΔA(r)=2πrΔr. A larger associated area means that there is a greater likelihood of finding pairs separated at larger distances even if particles are randomly distributed. The total area associated with each radii bin also depends on the detailed shape of the ROI being analysed, again with larger area bins being more affected. To account for this, we assemble a normalization factor μ(r), which is the expected M(r) histogram that would be measured if all particles are uniformly distributed over the ROI: μ(r)=ΔA(r)ρ_{0}W(r). The average density of pairwise distances over the whole area is given as ρ_{o}=N/A_{ROI}, where A_{ROI} is the total area of the ROI. W(r) is the radially averaged autocorrelation of the ROI that corrects for the ROI having shape that contributes to the crosscorrelation, and is computed using fast Fourier transforms (FFTs) as described previously^{6}. The crosscorrelation function C(r) is the relative probability of finding a pair separated by a distance r compared with a random distribution, can then be simply expressed as:
Pair crosscorrelation functions describing the codistribution of proteins can also be constructed using FFTs of the reconstructed image^{6,8}. Supplementary Fig. 1e demonstrates that C(r) evaluated by both methods is equivalent.
The steadystate simultaneous crosscorrelation, C(r, τ=0), is tabulated as described above, but M(r) histograms are assembled using only particle localizations that are detected simultaneously over a steadystate time interval. In this case, this histogram is normalized as above, using the total number of pairwise distances between red and green localized particles given by:
where F is the number of image frames included in the steadystate time window, and n_{1,i} and n_{2,i} are the number of localizations of the first and second fluorophore type in the ith image frame. C(r, τ) is tabulated in the same way as for C(r, τ=0), but by measuring pairwise distances between fluorescent localizations separated by a time interval τ. G(r, τ) measures correlations between localizations of the same fluorophore type observed with time lag τ. It is tabulated by the method described above for C(r, τ), but pairwise distances are measured between localizations of the same coloured probe. Note that G(r, τ=0) is a measure of the average density of probes and not a measure of selfclustering and is typically disregarded. Matlab code that tabulates C(r, τ) and G(r, τ) and associated statistical variances from point localization data is included as Supplementary Software.
Determining statistical variance of correlation functions
Variance in C(r, τ) (σ_{C}^{2}) arises from statistical variance in the number of pairs associated with each spatial bin (M(r)) as well as the number of total pairs identified (N) over some integration time. As M and N are independent variables, the σ_{C}^{2} can be determined through simple error propagation:
σ_{M}^{2} and σ_{N}^{2} are given by M and N, respectively, as is expected from Poisson counting statistics and verified in experimental data on chemically fixed cells in Supplementary Fig. 2a. For data sets with reduced sampling, it may be appropriate to approximate σ_{M}^{2} as M+1 to provide a finite estimate of error when spatial bins contain no pairs. Using the definition of C(r) given in equation (1), this becomes
The variance in C(r) is well described by equation (2), as exemplified through data from fixed cells or resampling the MD simulation. Point localization data acquired in chemically fixed cells were resampled after first scrambling the time ordering of frames to remove additional contributions to σ_{C} that arise from probe photobleaching and/or fluorophores localizations being otherwise correlated in time. Values of M(r) and N were recorded and C(r,τ=0) was tabulated over steadystate time windows with constant number of scrambled frames. The s.d. of M(r) is well described by the square root of M(r), as shown in Supplementary Fig. 2a. In addition, the s.d. of C(r) is well described by the variance given in equation (2), which holds independent on the values of C(r), as evidenced by examining a cell chemically fixed without antigen as well as a cell chemically fixed after incubation with antigen for 1 min (Supplementary Fig. 2b). We performed a similar validation using a simulated superresolution experiment of the LennardJones MD simulation by assigning a probability that a particle is on, P_{on}, as illustrated in Supplementary Fig. 2c. σ_{C} is estimated by resampling the simulation 15 times for each P_{on}, changing the identity of red and green particles for each resampling. C(r, τ=0) is tabulated from each resampled simulation and the s.d. is used to estimate variance. We find good agreement between the measured variance and the predicted variance determined in equation (2), as illustrated in Supplementary Fig. 2d.
Using equation (2), the predicted relative error in a measurement, σC(r)/C(r), is given by
Quantifying singlemolecule mobility with correlation functions
Normalizing G(r, τ) such that the total two dimensional area under the curve is set to one produces a probability distribution function (PDF) describing singlemolecule displacements r over a time lag τ.
The PDF for 2 dimensional Brownian diffusion is a normalized Gaussian function with center at zero with a width equal to the mean squared displacement (MSD(τ)=<r(t+τ)−r(t)^{2}>) which defines the diffusion coefficient, D, according to MSD(τ)=4Dτ.
The PDF for two populations of diffusers can be written as a summation of two independent normalized Gaussians with associated diffusion coefficients D_{1} and D_{2}, and a parameter α describing the fraction of segments associated with the diffusion coefficient D_{1}.
Matlab software for calculating C(r, τ) and G(r, τ) and associated statistical variances from point localization data are available online as a Supplementary Material.
MD simulation
A MD simulation was performed utilizing the LJ potential with particle motions constrained to two dimensions. A system of 64 atoms was created with a reduced density of 0.05 atoms per unit area, giving a side length close to 36σ. Periodic boundary conditions were enforced, and the temperature of the simulation was adjusted by setting the initial velocities to a Gaussian distribution of magnitudes. Positions were propagated using the Verlet algorithm, and a time step of 0.005 (reduced time) was used. The starting configuration maximized space between atoms, and the simulation was allowed to equilibrate for 40,000 steps before molecular positions were tracked. A total of 200,000 time steps were taken in each simulation run, and the positions of atoms were saved every five time steps, giving 40,000 snapshots of atomic positions to use in the TRXC analysis. The atoms were randomly divided into two equal groups displayed as green and red fractions. Simulation and analysis were carried out in MATLAB (The MathWorks).
f(Ab)_{1} and cholera toxin subunit B modification
f(Ab)_{1} fragment goat antibody to mouse IgM, μ chain specific (Jackson Immuno Research, West Grove, PA, item number 115007020) was simultaneously chemically modified with Atto 655 NHS ester (Sigma, St Louis, MO) and BiotinX, SSE, 6((Biotinoyl)Amino)Hexanoic Acid, Sulfosuccinimidyl Ester, Sodium Salt (SulfoNHSLCBiotin) (Invitrogen, Grand Island, NY). Modifications were carried out in aqueous solution buffered by 0.01 M NaH_{2}PO_{4} with 0.01 M NaH_{2}CO_{3}, with 23 μM f(Ab)_{1} in the presence of 47 μM Atto 655 NHS ester and 140 μM Biotin–X SSE, at pH 8.2 for 30 min at room temperature. Reaction products were separated by gel filtration on Illustra NAP5 columns (GE Healthcare, Piscataway, New Jersey) to remove unbound dye from labelled protein. Labelled f(Ab)_{1} was conjugated to additional Atto 655 in the same manner as above using 10 μM f(Ab)_{1} in the presence of 140 μM Atto 655, and unbound dye was again separated using gel filtration. Labelled f(Ab)_{1} fragment was then spun down at 20,000 × g for 90 min at 4 °C to remove any protein aggregates. We determined the average number of Atto 655 dye molecules per f(Ab)_{1} fragment to be 1.6 from absorbance measurements using a NanoDrop 2000 (Thermo Scientific, Rockford, IL). The average number of biotin per f(Ab)_{1} was determined to be 0.8 using the FluoReporter Biotin Quantification Kit (Invitrogen).
Cholera toxin subunit B (CTxB) (Sigma Alderich, St Louis, MO) modifications were carried out in aqueous solution buffered by 0.01 M Na_{2}B_{4}O_{7} with 0.150 M NaCl, with 19 μM CTxB in the presence of 80 μM reactive dye, either Atto 655 NHS ester or Alexa 532 NHS ester, at pH 8.2 for 30 min at room temperature. Reaction products were separated by gel filtration on Illustra NAP5 columns (GE Healthcare, Piscataway, New Jersey) to remove unbound dye from labelled protein. Labelled CTxB was then spun down at 20,000 × g for 90 min at 4 °C to remove any protein aggregates. We determined the average number of dye molecules per CTxB to be around 3 for both Atto 655 and Alexa 532 conjugated CTxB.
GPMV preparation
GPMVs were prepared through incubation of RBL2H3 cells with low concentrations of dithiothreitol (DTT, 2 mM) and formaldehyde (25 mM) in the presence of calcium (2 mM) for 1 h at 37 °C consistent with previous work^{31}. Before GPMV formation, cells were labelled with two distinct pools of CTxB for 10 min at room temperature, 0.4 μg ml^{−1} conjugated to Atto 655 and 0.1 μg ml^{−1} conjugated to Alexa 532.
Cells, transfection and fixation
CH27 cells were a generous gift from Neetu Gupta (Cleveland Clinic, Lerner Research Institute) and were maintained in lowglucose DMEM (Life Technologies, Carlsbad, CA) containing 15% FBS (Mediatech, Manassas, VA), 10 mM HEPES, 110 mg l^{−1} sodium pyruvate, 50 μM BME and 1% Pen/Strep in 5% CO_{2} at 37 °C. CH27 cells were transiently expressing either Lyn protein containing a Cterminal fusion to the mEos3.2 photoactivatable fluorescent protein or a 20 aminoacid sequence, here called GG, coding for a polybasic stretch and Cterminal geranylgeranylation and Nterminal fusion to mEos3.2. A total of 500,000 CH27 cells were transfected with 0.5 μg mEos3.2tagged plasmid DNA in Clontech N1 or C1 vector (Clontech, Mountain View, CA) using Lonza Nucleofector electroporation (Lonza, Basel, Switzerland). Plasmid DNA encoding for fulllength Lyn protein and mEos3.2 have been described previously^{32}, and the GG plasmid described previously^{29} was cloned to include mEos3.2. Cells were plated at 100,000 ml^{−1} and grown overnight on glass bottom wells (MatTek Corporation, Ashland, MA). Endogenous BCR in the plasma membrane was labelled with a modified f(Ab)_{1} fragment conjugated to both Atto 655 and biotin by staining with 10 μg ml^{−1} labelled f(Ab)_{1} for 10 min at room temperature in growth media followed by extensive washing with phosphatebuffered saline (Life Technologies) before imaging. Cells were stimulated by clustering f(Ab)_{1} biotin Atto 655 conjugatelabelled IgM with with 5 μg ml^{−1} soluble streptavidin. This labelling and activation scheme preserves signalling functionality under our imaging conditions, as indicated by increased tyrosine phosphorylation and calcium mobilization after the addition of antigen (Supplementary Fig. 3). For fixed cells, CH27 cells were transfected with LynmEos3.2 and BCR was stained with modified f(Ab)_{1} fragment as described above before holding in control buffer (135 mM NaCl, 5 mM KCl, 1 mM MgCl_{2}, 1.8 mM CaCl_{2}, 5.6 mM glucose, 20 mM HEPES) at room temperature during addition of streptavidin (Life Technologies) at 5 μg ml^{−1} to stimulate cells. Cells were then washed extensively in phosphatebuffered saline before chemical fixation with 4% formaldehyde and 0.01% gluteraldehyde (Ted Pella Inc, Redding, CA) for 10 min at room temperature.
TIRF microscopy
Imaging was performed on an Olympus IX81XDC inverted microscope with a cellTIRF module, a 100 × UAPO TIRF objective (NA=1.49), active Zdrift correction (ZDC) (Olympus America, Center Valley, PA). Images were acquired on an iXon897 EMCCD camera (Andor, South Windsor, CT). Excitation of Atto 655 was accomplished using either a 647nm diode laser for livecell measurements (OBIS 647 LX100FP, Coherent, Santa Clara, CA) or a 641nm diode laser for GPMV measurements (CUBE 64075FP, Coherent). Excitation of Alexa532 was accomplished using a 532nm diode laser (150 mW Samba, Cobolt, Sweden), and excitation of mEos3.2 constructs was accomplished using a 561nm diode laser (Sapphire 561 LP, Coherent). Photoactivation of mEos3.2 was accomplished with a 405nm diode laser (CUBE 40550FP, Coherent). Laser intensities were adjusted such that single fluorophores could be distinguished in individual images. Excitation and emission were filtered using the quadband filter cube set ET405/488/561/647 (Chroma, Bellows Falls, VT) for both mEos3.2/Atto 655 and mEos3.2/Dyomics 654 fluorophore pairs or filtered using ET405/488/532/640 for Alexa 532/Atto 655 fluorophore pair. Emission was split into two channels using a DV2 emission splitting system (Photometrics, Tuscon, AZ) using a T640lpxr dichroic mirror to separate emission, ET605/52m to filter nearred emission, and ET700/75m to filter farred emission (Chroma).
Live cells were imaged in a live cell compatible imaging buffer: 30 mM Tris, 100 mM NaCl, 5 mM KCl, 1 mM MgCl_{2}, 1.8 mM CaCl_{2}, 50 mM glucose, 12 mM glutathione, 40 μg ml^{−1} catalase (Sigma), 500 μg ml^{−1} glucose oxidase (Sigma), pH 7.5. Where noted, cells were treated with 40 μM PP2 (Invitrogen) in live cell compatible imaging buffer for 5 min before and during antigen stimulation. Fixed cells were imaged in buffer with higher buffering capacity, glucose concentration and pH: 50 mM Tris, 550 mM glucose, 10 mM NaCl, 12 mM glutathione, 40 μg ml^{−1} catalase, 500 μg ml^{−1} glucose oxidase, pH 8.5. GPMVs were diluted 1:1 into live cell compatible imaging buffer. A small quantity of water (5%) was also added to better match the osmolarity of the GPMV and imaging buffers. GPMVs were imaged using offTIR excitation between two #1.5 coverslips with a vacuum grease spacer and attached to a homebuilt Peltierbased temperature stage coupled to a PID controller (Oven Industries, Mechanicsburg, PA), consistent with previous work^{31}.
Western blots and Ca^{2+} mobilization
CH27 cells were incubated with 10 μg ml^{−1} of goat antimouse IgM μchain specific f(Ab)_{1}biotin fragment (Jackson) for 10 min to label the IgM with biotin and then subsequently washed twice by centrifugation. One million CH27 cells were each suspended in either control buffer (defined above), live cell imaging buffer (defined above) or imaging buffer without oxygen scavenging enzymes glucose oxidase and catalase. Some cells were stimulated by the addition of 5 μg ml^{−1} streptavidin. Cells were lysed at room temperature using RIPA buffer (EMD Millipore, Billerica, MA) in the presence of Halt Phosphatase Inhibitor Cocktail (Thermo Scientific) and Complete Mini Protease Inhibitor Cocktail (Roche, Basel, Switzerland). Cell lysates were centrifuged at 16,000 × g for 15 min at 4 °C. Supernatants were run on a denaturing sodium dodecyl sulfate–PAGE (SDSPAGE) gel, 7.5% MiniPROTEAN gel (BioRad, Hercules, CA) and then transferred to an ImmobilonP PVDF transfer membrane with 0.45 μm pore size (Millipore). Blots were stained with a 1:2,000 dilution of mouse IgG2b 4G10 Platinum antiphosphotyrosine antibody (Millipore, catalogue number 05321) and subsequently stained with a 1:5,000 dilution of peroxidaseconjugated goat antimouse IgG2b specific secondary antibody (Jackson Immuno research, catalogue number 115035207). Blots were sensitized using SuperSignal West Pico chemiluminescent substrate and developed on Amersham Hyperfilm ECL (GE Healthcare Biosciences, Piscataway, NJ). Ca^{2+} mobilization assays were performed by incubating three million CH27 cells per ml with 2 μg ml^{−1} Fluo4, AM (Life Technologies) in the presence of 0.25 mM sulfinpyrazone for 5 min at room temperature and then diluting to 0.2 million cells per ml in the same buffer for 30 min at 37 °C. Cells were washed twice by centrifugation and resuspended in either control buffer or imaging buffer. CH27 IgM was labelled with biotin as above and then cells were loaded into wells 96well black plates at a concentration of two million per ml, and fluorescence was assayed by exciting the cells with 485 nm light and collecting 520 nm light in the Omega PolarStar (BMG Labtech, Ortenberg, Germany).
Singlemolecule analysis
Singlemolecule fluorescent events were localized by fitting local maxima in background subtracted images to Gaussian functions, and images were reconstructed^{6}. In brief, background subtracted raw images were bandpass filtered and local maxima above a threshold were used as starting locations for twodimensional Gaussian fitting to unfiltered background subtracted images. The width and errors of the Gaussian fits as well as the sum of intensity in the fluorescent spot were used to cull outliers in each distribution of parameters. Stage drift was corrected for every 500 frames by finding the maximum in the 2D cross correlation produced by all localizations between successive groups of frames.
Localizations in the nearred channel were registered with the farred channel using fiducial markers with adapted methodology^{33}. In brief, 100 nm diameter Tetraspeck beads with fluorescence emission in both near and farred channels (Invitrogen) were adhered to glass slides, excited by both 561 nm (or 532 nm) and 647 nm lasers, and 70 fluorescent images of 20–40 beads were collected before and after the acquisition of each data set. These diffractionlimited fluorescent beads were used as control points to create a polynomial transform from the nearred channel to the farred channel, and this polynomial transform was applied to mEos3.2 localizations in the nearred channel.
Stagedriftcorrected and emission channelregistered point localizations were used to reconstruct a multicolour superresolution image by incrementing pixels corresponding to 25 nm for each localization falling into that pixel for each emission channel. C(r,<τ>) was determined from images, I_{1} and I_{2}, reconstructed from point localizations collected from each emission channel over time as follows consistent with previous work^{6}.
Here, conj[] indicates a complex conjugate, ρ_{1} and ρ_{2} are the average surface densities of images I_{1} and I_{2}, respectively, and Re{} indicates the real part. C(r,τ) was determined using stage driftcorrected and emission channelregistered point localizations. Both C(r, τ) and C(r, <τ>) were computed from point localizations falling within a userdefined ROI, and this ROI was used to determine normalization factor W(r).
Singlemolecule trajectories were determined using a tracking algorithm that searches for localizations within 500 nm in subsequent frames and terminates ambiguous trajectories^{34}. The average MSD as a function of time interval (τ) was tabulated for all trajectories and diffusion coefficients were extracted through a linear fit to the second through fourth time point of the MSD(τ), and error bounds reflect s.e. determined directly from this fit to determine the average diffusion coefficient D. Single trajectory diffusion coefficients were obtained by tabulating MSDs from single long trajectories (greater than 10 segments), and fitting the second through fourth point of MSD versus τ in the same manner to obtain individual diffusion coefficients D.
Strategies to reduce the effects of bleedthrough
As demonstrated in Supplementary Figs 7, 8, and 9, fluorescent bleedthrough of one fluorophore into the other image channel leads to additional spatial correlations at short distances that are also correlated in time. While the most reliable method to reduce the adverse effects of bleedthrough are to choose probe pairs that minimize this artefact, several analytical approaches can be used to correct for bleedthrough under specific circumstances. For example, if dynamics are slow compared with both the acquisition time for singlemolecule detection and the characteristic ontime of fluophoroes, then it is possible to extrapolate C(r, τ) to τ=0 while excluding the small τ points that are affected by bleedthrough. An application of this can be seen in Supplementary Fig. 6, where C(r, τ =0) is systematically higher than C(r, τ → 0) for the first spatial bin (r<50 nm for Lyn and r<100 nm for GG). For instances where colocalization dynamics are fast compared with acquisition time or fluorophore ontimes, then it may be possible to estimate the magnitude of a bleedthrough correction to C(r, τ=0) by first calibrating with a fixed cell sample, where the effects of bleedthrough can be directly measured (Supplementary Fig. 9). Under conditions where it can be assumed that bleedthrough properties are not altered by fixation, then in principle this correction could be applied to live cell data. It should be noted that chemical fixation can alter the quantum yield of some fluorophores^{35}, so there is limited applicability of this method. Finally, it may be possible to correct for bleedthrough directly, by first measuring the magnitude of the bleedthrough signal, then subtracting the predicted bleedthrough signal directly from acquired data before image processing. In our hands, we found this method to be computationally expensive, as it requires that fluorophores be first localized, then a spatial transform computed to properly localize the bleedthrough signal on the second image channel. We also found this method to be only moderately effective for reducing the magnitude of C(r, τ=0) in cases of known bleedthrough, likely due to the uncertainty in intensity and localization inherent to this treatment.
Code availability
Matlab code for calculating correlation functions is available as Supplementary Software through Nature Communications website.
Additional information
How to cite this article: Matthew B. Stone and Sarah L. Veatch. Steadystate crosscorrelations for live twocolour superresolution localization data sets. Nat. Commun. 6:7347 doi: 10.1038/ncomms8347 (2015).
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Acknowledgements
We thank Barbara Baird, David Holowka, Jonathan Grover and Akira Ono for constructs; Benjamin Machta, Sarah Shelby and Brian DeVree for helpful discussions; and Jing Wu and Jason Karslake for assistance with experiments. Research was funded by the NIH (R01GM110052).
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The work is the intellectual product of both M. S. and S. V., both authors prepared the manuscript and figures, and M. S. carried out the experiments.
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Supplementary information
Supplementary Information
Supplementary Figures 113. (PDF 1935 kb)
Supplementary Software
A MATLAB function to compute C(r,) and G(r,) from superresolution point localization data sets. (TXT 14 kb)
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Stone, M., Veatch, S. Steadystate crosscorrelations for live twocolour superresolution localization data sets. Nat Commun 6, 7347 (2015). https://doi.org/10.1038/ncomms8347
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DOI: https://doi.org/10.1038/ncomms8347
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