Topic Introduction

Image Correlation Spectroscopy: Principles and Applications Paul W. Wiseman

Image correlation spectroscopy (ICS) was developed as the imaging analog of ﬂuorescence correlation spectroscopy. Using standard ﬂuorescence microscopy image series as input, different versions of ICS can be used to extract parameters on the molecular transport properties (diffusion and ﬂow) and oligomerization state for ﬂuorescently labeled species in cells. This review introduces the various forms of spatial and temporal ICS and discusses application of these methods to reveal properties of the biomolecules that can be measured from standard ﬂuorescence image time series sampled from cells and neurons.

INTRODUCTION TO IMAGE CORRELATION SPECTROSCOPY Background

Image correlation spectroscopy (ICS) was originally introduced as the imaging analog of the temporal ﬂuctuation method called ﬂuorescence correlation spectroscopy (FCS; see Fluorescence Correlation Spectroscopy: Principles and Applications [Bacia et al. 2014]) as a method to measure membrane receptor densities and oligomerization states in the plasma membranes of cells (Petersen et al. 1993). In its original guise, ICS was entirely a spatial domain technique; however, the base method has been extended for measurements in the spatial and temporal domains via ﬂuorescence microscopy image time series. The method has also been extended to analysis in k-space and time. This discussion introduces the background theory of ICS and provides a guide for the types of measurements that can be made with the variants of these methods for applications on cells. Principles of ICS

All forms of ICS are based on the analysis of ﬂuctuations in intensity from pixels that compose ﬂuorescence microscopy images. However, it is important to understand that the intensity recorded in a given pixel (or voxel) represents an integrated light intensity from a focal volume deﬁned by the laser beam focus for a laser scanning microscope (LSM) or the effective optical resolution element or point-spread function (PSF) for a ﬂuorescence microscope in general (see Figs. 1 and 2). Temporal domain ﬂuctuation methods like FCS rely on the measurement and analysis of ﬂuorescence ﬂuctuations as a function of time. These temporal ﬂuctuations arise from spontaneous changes in the number of ﬂuorescent molecules within the focus of a stationary excitation laser beam as a result of molecular transport or chemical reactions (Fig. 1). Both the amplitude of the ﬂuctuation (size of the deviation from the mean) and the duration of the ﬂuctuation in time contain important information about the ﬂuorescently tagged macromolecules. In contrast to FCS, ICS relies on the characterization of ﬂuorescence ﬂuctuations as a function of space across an image (Fig. 2) or space and time from a ﬂuorescence microscopy time series (Fig. 3). In Adapted from Imaging: A Laboratory Manual (ed. Yuste). CSHL Press, Cold Spring Harbor, NY, USA, 2011. © 2015 Cold Spring Harbor Laboratory Press Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086124

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Image Correlation Spectroscopy

4

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0

–2

–4 –1

–0.5

0

0.5

1

B

δi(t) δi(t) = i(t) –

τf

FIGURE 1. Temporal fluorescence fluctuations. (A) Schematic depicting that the intensity in any pixel in the image is an integration of fluorescence photons emitted by fluorophores within an optical focal volume (beam focus). The volume of the focal volume can be on the order of a femtoliter. (B) Schematic showing that transport of fluorescent molecules in and out of the focal volume leads to changes in occupation number, which are recorded as intensity fluctuations. The fluctuation magnitude (δi) and the characteristic fluctuation time (t) are the important measureable observables for fluctuation spectroscopy.

any form of correlation spectroscopy, it is assumed that the ﬂuorescence intensity is proportional to the number of ﬂuorophores within the focal volume contributing to the integrated signal intensity. We must deﬁne the pixel intensity ﬂuctuation as this is the basic input datum for all forms of ICS, and we will assume an x–y–t image time series. Any given pixel in the image time series will have an intensity value ia( p, q, s), where “a” represents the detection channel (e.g., green channel) for the image series, p and q represent the discrete spatial coordinates in x–y space, and s is the discrete time point (image number) when the value was recorded. Following convention, we deﬁne the ﬂuorescence intensity ﬂuctuation at this pixel as simply the difference between the pixel intensity value and the mean intensity: dia ( p, q, s) = ia ( p, q, s)−,ia..

(1)

The mean intensity can be calculated in several different ways depending on which variant of image correlation is applied, as will be outlined below. Given an x–y–t image time series as an input data set from a ﬂuorescence microscope, it is possible to calculate a corresponding matrix of ﬂuctuations using Equation 1, which can then be analyzed by one of the variants of ICS. Generalized Spatiotemporal Correlation Function

We can deﬁne a fully general spatiotemporal ﬂuctuation correlation function, r(ξ, η, t) using the following equation: rab (j, h, t) =

kkdia (x, y, t)dib (x + j, y + h, t + t)lxy lt

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kia lt kib lt+t

,

(2)

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P.W. Wiseman

A

B D z

C

FIGURE 2. Spatial fluorescence intensity fluctuations. (A) Schematic showing the molecular basis for spatial fluctuations is the distribution of fluorescent molecules in space. This case depicts a distribution of fluorescently tagged proteins in the membrane with some found in the beam focal area where they are excited and emit fluorescence. (B) This shows that the optical focal volume from which fluorescence intensity is integrated is larger than the pixel dimensions in the image. This leads to spatial correlation between adjacent pixels in an image that are exploited for spatial ICS. (C ) Image level showing the region of interest and approximate focal area size scale outlined by the circle. (D) The optical focal volume (defined by the laser beam focus for an LSM) dimensions define the system in which correlations are measured in space and time.

A

r 11(ξ,η)

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y t

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FIGURE 3. Spatial ICS. (A) Schematic of an image series showing that for spatial ICS, a region of interest (ROI) in x–y space in a single image is selected, and a spatial correlation function is calculated from the chosen pixels. (B) A spatial correlation function calculated in spatial ICS showing the peak central amplitude at zero spatial lags. This amplitude is inversely proportional to the mean number of independent fluorescent entities in the focal volume/area. (C ) Schematic of a molecular aggregation event that changes the mean number of independent fluorescent entities in the focal area that is measurable by spatial ICS.

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Image Correlation Spectroscopy

where ξ and η are spatial lag variables that represent shifts of the image in x–y space for calculation of spatial correlation xy, whereas t is a temporal lag variable representing shifts in time in the x–y–t image series for calculation of the temporal correlation t. The angular brackets in the denominator simply represent calculation of a mean intensity, and the subscripts a and b stand for detection channels a and b for image series collected for two ﬂuorophores of different emission wavelengths. Equation 2 represents a general spatiotemporal ﬂuctuation cross-correlation function when a and b are different (two-color collection), whereas it becomes a spatiotemporal autocorrelation if a and b are identical (single-detection-channel image series). In addition, it represents a correlation function that is continuous in the spatial and temporal lag variables. In fact, the image series data sets are discrete pixels and represent a sampling of the underlying molecular distribution by the diffraction limited focus modeled by the microscope’s PSF (see Fig. 2). So, in practice, we actually calculate a discrete approximation to this correlation function from the input image series, where the symbols are the same as deﬁned in Equations 1 and 2: rab (Dp, Dq, Ds) =

kkdia ( p, q, s)dib ( p + Dp, q + Dq, s + Ds)lxy lt kia ls kib ls + Ds

,

(3)

and the lag variables represent discrete (integer) pixel shifts in x, y, or t. The discrete pixel shifts can always be converted to spatial and temporal lags using the pixel spatial dimension (δp = δq) and image frame time step (δt) by simple multiplication (e.g., ξ = Δx = Δpδp, and t = Δsδt). There are now several variants of ICS that differ in how the image data set or sets are analyzed and consequently on the information that they provide in terms of output. Most can be considered as variations of Equations 2 and 3 in some limit, and these will be described in turn. Spatial ICS

The original form of ICS was exclusively the spatial autocorrelation variant (Petersen et al. 1993). A spatial autocorrelation function is calculated from an image or region of interest (ROI) within an image by correlating the ROI with itself as a function of pixel shifts in the x and y directions (Fig. 3). This is equivalent to taking Equation 2 or 3 in the limit that the time lag or shift variable goes to 0 for a single detection channel a: raa (j, h, 0) =

kdia (x, y, t)dib (x + j, y + h, t)lxy kia l2t

.

(4)

An equivalent, and more computationally efﬁcient, way to calculate the discrete spatial correlation function is using fast Fourier transforms (FFTs): raa (j, h, 0) = FFT−1 {FFT[ImageROI]·FFT∗ [ImageROI]},

(5)

where FFT indicates the forward fast Fourier transform operation, FFT−1 indicates the inverse fast Fourier transform, and the ∗ indicates the complex conjugate operation. In practice, Equation 5 is usually preferred over the brute force calculation of Equation 4 as it is much faster computationally. Once the raw spatial autocorrelation function is calculated from the image ROI, a Gaussian function is then ﬁt to it by nonlinear least squares: 2 j + h2 raa (j, h, 0) = g aa (0, 0, 0)exp + g 1, v2

(6)

where the ﬁtting parameters are shown in bold and represent the zero-lags amplitude of the correlation function gaa(0, 0, 0); the correlation radius ω that is related to the e −2 radius of the laser beam Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086124

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focus; and g1, which is an offset at large spatial lags to take into account incomplete decay of the correlation function. The laser beam has a Gaussian intensity proﬁle that acts as the correlator in spatial ICS. As the beam excites ﬂuorescence from ﬂuorophores throughout the illumination region, the integrated intensity reﬂects the underlying distribution of ﬂuorescent entities, and there will be intensity correlations between nearby pixels in the image as the beam area is larger than the pixel area (Fig. 2). The zero-lags amplitude is equal to the inverse of the mean number of independent ﬂuorescent entities, , within the beam focal area: gaa (0, 0, 0) =

1 . kNl

(7)

If the beam radius is known (through calibration measurement), it is possible to calculate the beam area and hence the surface density of ﬂuorescent molecules from the zero-lags autocorrelation amplitude. If the ﬂuorescently tagged molecules change their oligomerization state (see Fig. 3), the number of independent entities in the beam focus changes, and this is measurable as a change in the amplitude of the correlation function (Wiseman and Petersen 1999). Temporal ICS

Temporal ICS (TICS) is the variant of ICS that is closest to FCS. Intensity ﬂuctuations are correlated in time through the image series, and a time correlation function is calculated from the time series. The rate of decay of the correlation function reﬂects the average decay time of the ﬂuctuations as ﬂuorescent entities move in and out of the area deﬁned by the beam focus (Fig. 4). Any process that contributes to ﬂuorescence ﬂuctuations on the timescale of the sampling will contribute to the decay of a correlation function, and each dynamic process will have a mean characteristic ﬂuctuation time. To measure transport with TICS, the labeled macromolecules must have a characteristic ﬂuctuation time that is longer than the image frame time. In other words, the ﬂuorophores have to be within the x

A

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y t

r11(0,0,τ)

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τ (sec)

FIGURE 4. Temporal ICS (TICS). (A) Schematic of an image series showing that for TICS, pixels are correlated in time. (B) A temporal correlation function calculated by TICS. The decay shape and rate reflect the transport dynamics of the underlying molecules. (C ) Schematic of molecular diffusion that changes the mean number of independent fluorescent entities in the focal area in time that is measureable by TICS.

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Image Correlation Spectroscopy

same general beam focal area when the raster scan returns the beam to the same position to acquire the next frame to preserve molecular correlations. With standard imaging rates 1 Hz, the slower transport of membranes proteins is measurable, but the faster diffusion of cytoplasmic components is not (Wiseman et al. 2000). The temporal autocorrelation function is calculated from the image series using an equation that follows from the general correlation function, Equation 2 (continuous) or Equation 3 (discrete pixels), evaluated with zero spatial lags variables or zero pixel shift variables for a single channel:

raa (0, 0, t) =

raa (0, 0, Ds) =

kkdia (x, y, t)dia (x, y, t + t)lxy lt kia lt kia lt + t

,

kkdia (p, q, s)dia (p, q, s + Ds)lxy lt kia ls kia ls + Ds

(8)

.

(9)

With temporal correlation, we are presented with a choice in terms of order of correlation in space and time. Although Equations 8 and 9 show spatial correlation (at zero lags) being performed in time, it is also possible to perform temporal correlation on a given pixel location ﬁrst and then average the correlation functions for each pixel position. For the former, the average intensity in the denominator is the mean intensity for the entire image region of interest. In the case of the latter (temporal correlation at given pixel positions), the average intensity is the mean intensity calculated in time for the pixel stack at i(x, y, t). In practice, we usually choose the ﬁrst approach of spatial correlation in time because it tends to converge more quickly for limited time stacks inherent in imaging and is also sensitive to immobile populations of the labeled species (see below). The decay of the temporal correlation function essentially records the average time decay of ﬂuctuations for any dynamic process that contributes to changes in the number of ﬂuorescent species in the beam volume in time (Fig. 4). However, to extract molecular transport or kinetic properties for the system, the correlation function must be ﬁt with an appropriate physical decay model for the process(es) that causes the ﬂuctuations in occupation number in the focus. For each dynamic process, there will be an associated characteristic ﬂuctuation time that represents an average lifetime of the ﬂuorescent species within the beam focus. Transport parameters can then be calculated from the characteristic ﬂuctuation time obtained from the decay model best ﬁt and the beam focal volume radii in x–y and z (obtained by calibration measurement of the microscope system PSF usually using ﬂuorescent microspheres). For a system with 3D diffusion of the ﬂuorescent species, the correlation function can be ﬁt using a decay model that assumes a laser beam with a Gaussian intensity proﬁle in x–y and z (Aragon and Pecora 1976): g aa (0, 0, 0) 2 1/2 + g 1 , t v t 1+ 2 1+ td z0 td

raa (0, 0, t) =

(10)

where gaa(0, 0, 0) is the zero time lag best-ﬁt amplitude, td is the best-ﬁt characteristic diffusion time, and g1 is a ﬁtting offset parameter that accounts for cases in which the correlation function does not decay to 0 at longer lag times because of the presence of an immobile population (if spatial correlation is performed before temporal correlation). The e −2 beam radii in x–y and z are ω and z0, respectively, and are ﬁxed as constants for the ﬁtting using values obtained from a beam focus calibration measurement. The gaa(0, 0, 0) is the inverse of the mean number of independent ﬂuorescent entities in the focal volume, as was the case for spatial correlation (Eq. 7). Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086124

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If the system is restricted to 2D diffusion, as is the case for membrane proteins, the ﬁt model above reduces to the following hyperbolic decay assuming a Gaussian intensity beam proﬁle in 2D: g (0, 0, 0) + g1 . raa (0, 0, t) = aa t 1+ td

(11)

The diffusion coefﬁcient can then be calculated from the best-ﬁt characteristic diffusion time knowing the laser beam radius at focus: D=

v2 . 4td

(12)

Calibration for TICS diffusion measurements may be done using ﬂuorescent microspheres of known radius (r) suspended in a ﬂuid of known viscosity (η) such as glycerol or concentrated sucrose solutions in water using the Stokes–Einstein relationship (Wiseman et al. 2000): Dtheory =

kT , 6p hr

(13)

where k is Boltzmann’s constant and T is the absolute temperature in kelvins. For systems in which there is ﬂow, the appropriate ﬁt mode for the temporal correlation function is a Gaussian, as has been shown for FCS (Magde et al. 1978): |v|t 2 raa (0, 0, t) = g aa (0, 0, 0) exp + g 1, v

(14)

where gaa(0, 0, 0) and g1 are the same ﬁt parameters as described above for the diffusion case and |v| is the best-ﬁt speed of the ﬂowing population. The ratio of |v| to w is simply the inverse of the characteristic ﬂow time: 1/tf. A single population undergoing ﬂow with superimposed diffusion is ﬁt by a combined model that is the product of each dynamic contribution: |v|t t −1 g aa (0, 0, 0) exp − raa (0, 0, t) = 1+ + g 1. t v td 1+ td

(15)

If there is a mixture of two ﬂuorescent populations having different dynamics, then the decay ﬁt model is a linear combination of each dynamic contribution: |v|t 2 t raa (0, 0, t) = A 1 + + B exp − + g 1. td v

(16)

It is important to note that TICS analysis is sensitive to ﬂow speed; that is, magnitude but not direction as the spatial correlation is calculated only for zero lags (no pixel shift). So the method is able to measure how quickly the ﬂuorescent species traverse the focal volume but is blind to the direction of ﬂow. An extension of TICS to full spatial and temporal correlation permits measurement of true ﬂow velocities, as is outlined in the next section. 342

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Image Correlation Spectroscopy

Spatiotemporal ICS

Spatiotemporal image correlation spectroscopy (STICS) (Hebert et al. 2005) effectively calculates the generalized autocorrelation limit of Equation 2 for a single detection channel: raa (j, h, t) =

kkdia (x, y, t)dia (x + j, y + h, t + t)lxy lt kia lt kia lt + t

.

(17)

If there is a ﬂowing ﬂuorescent population in the sample, it may be revealed by spatial correlation as a function of time lag (Fig. 5). Spatial correlation at zero time lag effectively averages the spatial correlation of each image in the series with itself so there can be no movement; hence, raa(ξ, η, 0) maps as a Gaussian spatial correlation function with its peak centered at the origin (ξ = 0, η = 0). At longer time lags, the mobile ﬂuorescent species will move, and this will affect the shape and decay of the spatiotemporal correlation function. If the population is diffusing, the particles undergo Brownian motion, which is isotropic. In this case, the Gaussian spatial correlation peak will remain centered at the origin and decay in amplitude and increase in width at a rate that depends on D in accordance with the laws of diffusion. For a single uniformly ﬂowing population, the ﬂuorescent species will spatially correlate in time in a direction determined by the ﬂow. Thus at longer time lags, the spatiotemporal correlation function can show a Gaussian peak that moves from the central origin at a uniform rate in a speciﬁc direction (see Fig. 5). This correlation peak due to ﬂow can be ﬁt and tracked in time to calculate a ﬂow vector (magnitude and direction). In practice, the presence of an immobile or slowly diffusing population complicates the measurement of ﬂow at short time lags (when the peak due to ﬂow is in the vicinity of the origin). It is possible to ﬁlter the immobile population to fully reveal the dynamic populations. The immobile population contribution to the spatiotemporal correlation function can be removed by Fourier ﬁltering in

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FIGURE 5. Spatiotemporal ICS (STICS). (A) Schematic of an image series showing that for STICS, image ROIs are spatially correlated in time. (B) The time evolution of the spatial correlation function for a system where there is flow showing directed movement of the correlation peak. (C ) Example of a cellular vector map obtained by STICS measurement on a chick dorsal root ganglion with fluorescently labeled microtubule tips. (Image series courtesy of the Fournier Laboratory, Montreal Neurological Institute.) Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086124

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frequency space the DC component for every pixel trace in time before running the space–time correlation analysis. For each given pixel location, the corrected intensities are given by ia ′ (x, y, t) = Ff−1 {Ft {ia (x, y, t)} × H1/T ( f )},

(18)

where T is the total acquisition time of the image series; H 1/T( f ) is the Heaviside function, which is 0 for f1/T; F−1 i denotes the (inverse) Fourier transform with respect to variable i; and f is the pixel temporal frequency variable. It is also possible to apply a moving average ﬁlter to remove dynamics on a range of timescales. Edge boundaries will also perturb spatial correlation analysis because of the sharp discontinuity in intensity at the periphery of the cell. This issue can be especially problematic for dendritic morphologies characteristic of neurons. However, there is a way to circumvent this issue if we remember that we are correlating ﬂuctuations and that ﬂuctuations are simply the difference between an intensity value and the average intensity. If we measure the on-cell average intensity for a region near an edge that we wish to measure, we can pad this average value in image pixels for areas outside the cell and effectively create a carpet of zero ﬂuctuations that masks the boundary (Comeau et al. 2008). This requires application of image processing routines to identify cell boundaries; however, spatiotemporal correlation can then be performed across the boundary (see Fig. 5 for an example on a growth cone).

Image Cross-Correlation Spectroscopy

The previous sections dealt with applications of image correlation in which a single protein species was labeled with a ﬂuorophore and spatial autocorrelation was performed to reveal number densities and dynamics. It is also possible to extend these approaches to measurements on cells in which two protein species are labeled with two different ﬂuorophores. It is simply a matter of collecting the ﬂuorescence image data in detection channels a and b and performing image cross-correlation analysis between ﬂuctuations in each image channel. The equations are simply obtained using the fully general correlation functions deﬁned in Equations 2 and 3 with a=b (which by deﬁnition is cross-correlation). The cross correlation is sensitive to the presence of interacting species (heterooligomers) that carry both color ﬂuorophores and will be nonzero when such species are present in the sample (see Fig. 6). In the ideal case, the focal volumes for the lasers used to excite both ﬂuorophores should be the same size and overlap in space. For single-photon excitation, this is difﬁcult to achieve without careful alignment and specialized adjustment of the optics. For two-photon excitation, a single wavelength can often be used to excite multiple ﬂuorophores to avoid this problem. However, it is also possible to apply a focal area mismatch correction for 2D systems (membrane proteins) for regular single-photon excitation. The average number of interacting particles ab in the focal area for a 2D system is given by the cross-correlation function ﬁt zero-lags amplitude normalized by the two autocorrelation

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B

FIGURE 6. Image cross-correlation spectroscopy (ICCS). (A) Schematic of a two-channel image series showing that for ICCS, cross correlation is performed between the two detection channels in space and/or time to detect interacting species. (B) Schematic of the molecular distribution of two species labeled with different fluorophores showing interacting heterodimers in the focal area that would be detectable by ICCS.

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Image Correlation Spectroscopy

function ﬁt zero-lags amplitudes multiplied by a ratio of the focal areas for the two channels to correct for small mismatches in focal overlap (Comeau et al. 2006): kNlab =

gab (0, 0, 0) Ab , gaa (0, 0, 0)gab (0, 0, 0) Aa

(19)

where Ai = πω2i is the beam area for channel i. The fraction of interacting particles to total number of particles with a given ﬂuorophore within a focal area may also be calculated from the ratio of the bestﬁt cross-correlation amplitude to the best-ﬁt autocorrelation amplitude: kNlab gab (0, 0, 0) kNlab gab (0, 0, 0) = = and . kNlaa gbb (0, 0, 0) kNlbb gaa (0, 0, 0)

(20)

Transport information (diffusion coefﬁcients, ﬂow speeds, and vectors) on the interacting species may be obtained by temporal or spatiotemporal cross-correlation calculations using the two channel variants of the generalized correlation functions (Eqs. 2 or 3).

Other Variants of ICS

The temporal resolution for the measurement of transport dynamics using TICS or STICS is set by the frame time between images. For standard confocal imaging this is typically 1 sec and is too slow to measure the diffusion of free molecules in the cytoplasm of cells. An extension that takes into account the actual sampling of the raster scan permits measurement of the faster dynamics used on standard laser scanning microscopes (confocal or two photon). The method is called raster image correlation spectroscopy (RICS) and essentially breaks the analysis down in terms of spatial correlations along the fast scan direction of the raster scan (microsecond pixel dwell times) and slow scan direction (microsecond line times) (Digman et al. 2005). With RICS, image correlation measurements can be performed on freely diffusing molecules in solution just as is the case for FCS. Another extension of ICS has been introduced as k-space image correlation spectroscopy (kICS) (Kolin et al. 2006b). This reciprocal space variant relies on calculation of a time correlation function after each image in the time series has been converted to k-space by a 2D FFT. The kICS approach allows measurement of diffusion coefﬁcients and ﬂow directions, but offers the advantage of separating time-dependent photophysics ﬂuctuations (such as ﬂuorophore blinking and bleaching) from the transport ﬂuctuations that are space/time-dependent. This allows measurement of transport coefﬁcients that are not biased by blinking or photobleaching, as well as allowing separate measurement of the photophysics ﬂuctuations. Another advantage of kICS is that it does not require calibration of the beam radii for transport measurements as the beam parameters separate out because of the mathematics of the transforms. Further details on both RICS and kICS can be found in a recent review (Kolin and Wiseman 2007).

INSTRUMENTATION AND ANALYSIS Instrumentation for ICS

ICS analysis can be applied to ﬂuorescence images obtained using a variety of microscopes. The method has been applied to images obtained using laser scanning microscopes, both with twophoton excitation (Wiseman et al. 2000; Hebert et al. 2005) and conventional single-photon confocal microscopy (Wiseman and Petersen 1999; Hebert et al. 2005). Image series collected using evanescent wave excitation by total internal reﬂection ﬂuorescence (TIRF) microscopy have also been analyzed using ICS (Brown et al. 2006; Comeau et al. 2008). Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086124

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P.W. Wiseman

Sampling, Signal-to-Noise Ratio, and Photobleaching

The signal-to-noise ratio in any ﬂuorescence ﬂuctuation measurement will depend on several variables including the molecular brightness of the species of interest (number of photons collected per sampling time), the density or concentration in the beam volume, and the number of characteristic ﬂuctuations sampled for the dynamic process of interest. As image correlation is usually performed using analog detection, we will assume that the user has a sample that is bright enough to be imaged above background. In practice, it is useful to deﬁne an ROI that is off cell and calculate the average intensity of this region to deﬁne a background. This mean background value is then subtracted from every pixel in the image before carrying out image correlation analysis. This assumes that the background is relatively constant in space and time so a control measurement may be performed to conﬁrm this assumption. The relative magnitude of a ﬂuctuation varies inversely with the square root of the number of labeled particles in the beam volume or area. This sets an upper limit on concentrations that are accessible to ICS. If the density or concentration is too high, then the ﬂuctuations become too small to be measured (uniform intensity in the image), and ICS cannot be performed. Simulation results show that a density of 100 particles per beam focal area still yields ﬂuctuations of reasonable magnitude for such measurements. Fortunately, expression levels in cells often result in densities that are on the order of 1–10 particles per beam focal area for many membrane proteins. At the other extreme, the concentration has to be high enough such that the ROI actually contains a sampling of the species of interest. If the signal-to-noise ratio is sufﬁciently high for imaging and the density of the species of interest falls in the proper range, then ICS measurements can be performed with an uncertainty that is established by the sampling. The uncertainty for any ﬂuctuation method will vary inversely with the square root of the number of characteristic ﬂuctuations sampled. For example, if the characteristic diffusion time for a membrane protein is 1 sec, then sampling one point for 100 sec would yield 100 ﬂuctuations in the measurement, and the uncertainty would be 10% (assuming sufﬁcient intensity). The ability to sample in both space and time provides ICS methods with a sampling advantage because limited time sampling can be compensated by spatial sampling in the image ROI. The number of independent spatial ﬂuctuations sampled is given by the image ROI area divided by the beam area of the focus (A = πω2). So a user can adjust the ROI size and the size of the time window to optimize measurements and map processes across a cell. Typical values used for TICS would be an ROI of 32 × 32 pixels and 50–100 images in the time series, and for STICS an ROI of 16 × 16 pixels and 10–50 images in the time series (assuming a 1 sec image frame time). These values are a rough guide only and, of course, depend on the rate of the transport process of interest and the sampling time for the imaging in a given experiment. Photobleaching of the ﬂuorophore is a major perturbation for most forms of ICS (but not for kICS). As photobleaching changes the number of detectable species on the focal volume over time, it will affect both spatial and temporal ICS measurements. For TICS, it is possible to determine the decay form of the photobleaching from the image series. If the characteristic timescale for the bleaching is longer than that for molecular transport, then it can be neglected. If the decay form of the photobleaching can be ﬁt by an exponential or biexponential, then the perturbation of the photobleaching can be corrected in the TICS analysis (Kolin et al. 2006a). Photobleaching will introduce a signiﬁcant systematic error to any measurement of number densities as a function of time by spatial correlation of each image. It is best to adjust the imaging conditions to minimize bleaching while still obtaining sufﬁcient signal. Software for Image Correlation

Several stand-alone graphical user interface ICS programs for the PC have been developed by our research group at McGill University. These programs are available for download from the Wiseman Research group (choose the software link) and are continually extended (http://wiseman-group.mcgill .ca/). The programs allow users to open and load image data sets, select regions of interest to analyze in 346

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Image Correlation Spectroscopy

FIGURE 7. The graphical user interface (GUI) for the STICS analysis program showing a loaded image data set of a cell and some of the range of operations accessible in the program.

the image frame, perform ﬁltering operations, run various forms of ICS analysis, and save and output the results. A screen capture of the interface for STICS is shown in Figure 7. In addition, Enrico Gratton of the Laboratory for Fluorescence Dynamics (LFD) has developed an extensive SimFCS software package that includes RICS analysis and is available for download from the LFD website (http://www.lfd.uci.edu/).

CONCLUSION

Image correlation methods offer a new window to analyze images obtained using standard forms of ﬂuorescence microscopy. As such, they can reveal information about biological molecule transport, oligomerization, and interactions that are entirely accessible in standard measurements performed in many biomedical laboratories. New developments and graphical user interface (GUI)-based analysis programs are extending the range of applications, making them accessible to nonexperts. REFERENCES Aragon SR, Pecora R. 1976. Fluorescence correlation spectroscopy as a probe of molecular dynamics. J Chem Phys 64: 1791–1803. Bacia K, Haustein E, Schwille P. 2014. Fluorescence correlation spectroscopy: Principles and applications. Cold Spring Harb Protoc doi: 10.1101/pdb.top081802. Brown CM, Hebert B, Kolin DL, Zareno J, Whitmore L, Horwitz AR, Wiseman PW. 2006. Probing the integrin-actin linkage using high-resolution protein velocity mapping. J Cell Sci 119: 5204–5214. Comeau JW, Costantino S, Wiseman PW. 2006. A guide to accurate ﬂuorescence microscopy colocalization measurements. Biophys J 91: 4611–4622. Comeau JW, Kolin DL, Wiseman PW. 2008. Accurate measurements of protein interactions in cells via improved spatial image cross-correlation spectroscopy. Mol Biosyst 4: 672–685.

Digman MA, Brown CM, Sengupta P, Wiseman PW, Horwitz AR, Gratton E. 2005. Measuring fast dynamics in solutions and cells with a laser scanning microscope. Biophys J 89: 1317–1327. Hebert B, Costantino S, Wiseman PW. 2005. Spatiotemporal image correlation spectroscopy (STICS) theory, veriﬁcation, and application to protein velocity mapping in living CHO cells. Biophys J 88: 3601– 3614. Kolin DL, Wiseman PW. 2007. Advances in image correlation spectroscopy: Measuring number densities, aggregation states, and dynamics of ﬂuorescently labeled macromolecules in cells. Cell Biochem Biophys 49: 141–164. Kolin DL, Costantino S, Wiseman PW. 2006a. Sampling effects, noise, and photobleaching in temporal image correlation spectroscopy. Biophys J 90: 628–639.

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Kolin DL, Ronis D, Wiseman PW. 2006b. k-space image correlation spectroscopy: A method for accurate transport measurements independent of ﬂuorophore photophysics. Biophys J 91: 3061–3075. Magde D, Webb WW, Elson EL. 1978. Fluorescence correlation spectroscopy. III. Uniform translation and laminar ﬂow. Biopolymers 17: 361–376. Petersen NO, Höddelius PL, Wiseman PW, Seger O, Magnusson KE. 1993. Quantitation of membrane receptor distributions by image

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correlation spectroscopy: Concept and application. Biophys J 65: 1135–1146. Wiseman PW, Petersen NO. 1999. Image correlation spectroscopy. II. Optimization for ultrasensitive detection of preexisting platelet-derived growth factor-β receptor oligomers on intact cells. Biophys J 76: 963–977. Wiseman PW, Squier JA, Ellisman MH, Wilson KR. 2000. Two-photon image correlation spectroscopy and image cross-correlation spectroscopy. J Microsc 200: 14–25.

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