Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells

Abstract

We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.

FIGURE 1

Schematic illustration of the algorithm used to compute the discrete approximation to a generalized spatiotemporal correlation function for a simulated system with flow and diffusion. The Gaussian autocorrelation peaks for each image are shown in the left column (Δt = 0), the cross-correlation for a lag-time of 1 time-unit in the middle column (Δt = 1), and for the second longest lag-time of N–1 time-units in the right column (Δt = N−1, where N is the number of frames in the image series). The open arrows on the simulation images represent the direction of the flow. The averaged Gaussian correlation functions r′_aa(ξ, η, Δt) are shown at the bottom for Δt = 0,1 and N–1. The separation of the Gaussian correlation peak due to flow (FG) from the Gaussian correlation peak arising from the diffusing population (DG) is clearly seen.

FIGURE 2

STICS and ICS analysis results for computer-generated simulations. (A) A contour plot of the STICS correlation functions for the case of i), flow (v_x = −0.12 μm/s and v_y = 0.08 μm/s); ii), diffusion (D = 0.01 μm²/s); and iii), two-populations' flow and diffusion (v_x = −0.12 μm/s, v_y = 0.08 μm/s, and D = 0.01 μm²/s). (B) The ICS temporal autocorrelation functions (Eq. 4) and best fits for the same simulations. (C) Plots of the peak position of the STICS Gaussian correlation peaks from A as a function of time. The peak position versus time gives an estimate of the concerted velocity of the particles in case i, of v_x = −0.119 ± 0.002 μm/s and v_y = 0.0792 ± 0.0005 μm/s and in case iii, of v_x = −0.096 ± 0.007 μm/s and v_y = 0.068 ± 0.006 μm/s, respectively. All simulations were 128 × 128 pixels with 500 frames at a density of 50 particles/μm², using 0.02 s/frame, 0.06 μm/pixel, and an e⁻² radius of 0.4 μm.

FIGURE 3

STICS analysis results for computer simulations of two populations, one flowing (v_x = −0.12 μm/s and v_y = 0.08 μm/s) and one diffusing (varying diffusion coefficients). (A) The x velocity as resolved by STICS with and without the immobile population filtering. (B) The y velocity as resolved by STICS with and without the immobile population filtering. On both graphs, each point and error bar represents the average result of 100 simulations with standard deviation. The shaded regions show the set velocities in the simulation with an acceptable error of ±10%. The computer simulations were 128 × 128 pixels with 100 frames at a density of 100 particles/μm², using 0.1 s/frame, 0.06 μm/pixel, and an e⁻² radius of 0.4 μm.

FIGURE 4

(A) A composite image of fluorescent microspheres consisting of two different fluorescent particle populations (red and green) and an added interacting particle population (yellow overlap). The composite image was made by adding an independent image of fluorescent spheres (our artificial interacting population) to both detection channel images. For each image time-series constructed, the velocities of the non-interacting populations remained constant whereas the interacting fraction's direction of flow was systematically changed. (B) A plot of the interacting population velocity magnitudes in x and y measured by STICS in the composite image series (i.e., with the added population and the red and green microspheres present) versus the velocity magnitude of the introduced interacting population measured by STICS in its original image series (i.e., without the red and green particles present).

FIGURE 5

Two-photon LSM images of the basal membrane of CHO cells expressing EGFP-labeled α-actinin. The regions analyzed with ICS and STICS are shown as open squares and the STICS analysis results are shown in Figs. 5–7. (A) A 64² pixel region where the temporal autocorrelation function is best fit to a single-population diffusion model (Eq. 5). (B) A 128² pixel region where the temporal autocorrelation function is best fit to a two-population flow/diffusion model (Eq. 8). (C) A 128² pixel region where the temporal autocorrelation function is best fit to a two-population flow/diffusion model (Eq. 8). All images are 512 × 480 pixels at a resolution of 0.118 μm/pixel, and a total of 180, 360, and 120 frames at a resolution of 5, 5, and 15 s/frame for A–C, respectively.

FIGURE 6

In vivo ICS and STICS analysis of protein diffusion in a peripheral basal membrane region of a CHO cell (Fig. 5 A) expressing EGFP-labeled α-actinin. (A) Contour plots of space-time correlation functions from STICS analysis (Eq. 11) as a function of lag-time for i) with and ii) without the immobile population contribution present. (B) A plot of the ICS temporal autocorrelation function and best fit to a single-population diffusion model (Eq. 5). The recovered diffusion coefficient was D = (9 ± 1) × 10⁻⁴ μm²/s. (C) Peak tracking plot of the STICS correlation peaks reveals that they stay centered at zero spatial lags, within the precision of our measurement.

FIGURE 7

In vivo ICS and STICS analysis of protein flux in random directions in a peripheral basal membrane region of a CHO cell (Fig. 5 B) expressing EGFP-labeled α-actinin. (A) Contour plots of space-time correlation functions from STICS analysis as a function of time for i) with and ii) without the immobile population contribution present. (B) A plot of the ICS temporal autocorrelation function and best fit to a two-population flow/diffusion model (Eq. 8). The recovered ICS velocity and diffusion were v_ICS = (13 ± 1) × 10⁻³ μm/s and D = (8 ± 1) × 10⁻⁴ μm²/s. (C) Peak tracking plot of the STICS correlation peaks reveals that they stay centered at zero spatial lags, within the precision of our measurement, yielding a very small velocity of v_STICS = (1.1 ± 0.7) × 10⁻³ μm/s.

FIGURE 8

In vivo ICS and STICS analysis of directed protein flow in a peripheral basal membrane region of a CHO cell (Fig. 5 C) expressing EGFP-labeled α-actinin. (A) Contour plots of space-time correlation functions from STICS analysis as a function of time for i) with and ii) without the immobile population contribution present. (B) A plot of the ICS temporal autocorrelation function and best fit to a two-population flow/diffusion model (Eq. 8). The recovered velocity was v_ICS = (7.7 ± 0.8) × 10⁻³ μm/s and a small diffusion coefficient was measured: D = (6 ± 1) × 10⁻⁵ μm²/s. (C) Peak tracking plot of the STICS correlation peaks (after the immobile population removal) shows a net displacement of the Gaussian center, yielding velocities of v_x = (1.8 ± 0.3) × 10⁻³ and v_y = (5.5 ± 0.2) × 10⁻³ μm/s.

FIGURE 9

Two-photon STICS velocity map image of EGFP/α-actinin flux in the vicinity of a retracting lamellar extension in a CHO cell plated on fibronectin. The original image-series reveals that the extended lamellar protrusions are retracting. Selecting regions of 16 × 16 or 32 × 32 pixels and performing the STICS analysis reveals a net flow of the α-actinin toward the cell interior (arrows). The spatial scale is shown as a bar and the velocity scale is shown as an arrow. The original image-dimensions are 512 × 480 pixels at 0.118 μm/pixel and a total of 120 images at 5 s/frame.

FIGURE 10

Two-photon auto- and cross-correlation STICS velocity map images of ECFP/α-actinin and EGFP/α5 integrin at the basal membrane of a CHO cell on a fibronectin substrate. (A) STICS velocity map for ECFP/α-actinin (channel 1); (B) STICS velocity map for EYFP/α5 integrin (channel 2); and (C) two-color STICCS velocity map of channel 1 with channel 2 showing flow vectors for co-transported ECFP/α-actinin and EGFP/α5 integrin. The spatial scale is shown as a bar and the velocity scale is shown as an arrow. The original image dimensions are 512 × 480 pixels at 0.118 μm/pixel and a total of 120 images at 5 s/frame.