A Random Motility Assay Based on Image Correlation Spectroscopy

Abstract

We demonstrate the random motility (RAMOT) assay based on image correlation spectroscopy for the automated, label-free, high-throughput characterization of random cell migration. The approach is complementary to traditional migration assays, which determine only the collective net motility in a particular direction. The RAMOT assay is less demanding on image quality compared to single-cell tracking, does not require cell identification or trajectory reconstruction, and performs well on live-cell, time-lapse, phase contrast video microscopy of hundreds of cells in parallel. Effective diffusion coefficients derived from the RAMOT analysis are in quantitative agreement with Monte Carlo simulations and allowed for the detection of pharmacological effects on macrophage-like cells migrating on a planar collagen matrix. These results expand the application range of image correlation spectroscopy to multicellular systems and demonstrate a novel, to our knowledge, migration assay with little preparative effort.

Introduction

The potential of specialized cell types to migrate within an organism is playing a central role in embryonic development (1), wound healing (2), inflammation (3), and tumor metastasis (4–6). Thus, it is fundamental in basic cell biophysics research and drug discovery alike to investigate the constituents of the cell migration machinery, such as cytoskeleton (7,8), cell-extracellular matrix interactions (9), cell adhesion (10), and their modulators. A number of cellular assays are available to analyze different aspects of cell migration (11), e.g., chemotaxis assays for directed motion along a gradient (12,13), scratch assays for void repopulation (wound healing) (14), or porous membrane invasion assays (12,15). They are designed to determine the degree of bulk motility from the number of cells that passed from one area or compartment to another within a certain period of time. Hence, their purpose is to capture the collective or directional part of cell migration (16).

Random cell migration is the prevalent mode of migration of immune cells and metastatic cancer cells in the absence of external cues and can be quantified by localization of the centroid of the cells and single particle trajectory analysis (17). This is often a nontrivial task and requires the contrast and brightness of the image to be sufficiently high to localize the cells and the cell density to be sufficiently low to reconstruct trajectories. For cases where these requirements are not fulfilled, we propose, in this report, to use image correlation spectroscopy (ICS) to quantify the speed and modes of randomly migrating cell populations (18). With ICS, the characteristic features of cell motility can be extracted from time-lapse phase contrast images without the need for identifying individual objects or for reconstructing their traces. The entire toolbox of ICS, developed to study molecular dynamics inside living cells, can be utilized to analyze different motion patterns of whole cells, e.g., directed motion, free or confined Brownian-type random walk, anomalous sub- or superdiffusion. The in vitro ICS random motility assay (RAMOT) has been established and validated using macrophage-like THP1 cells and known modulators of the cytoskeleton and cell adhesion. Furthermore, Monte Carlo simulations provide a basis for the detailed characterization of the potential and the pitfalls of this approach.

Materials and Methods

All simulations and data analysis algorithms were implemented in the free R software for statistical programming (19).

Cell migration experiment

The migration of THP-1 cells (human acute monocytic leukemia cell line, ATCC ID:CL000004; American Type Culture Collection, Manassas, VA) which were used as a model system for monocytes/macrophages was investigated on a collagen gel in a 12-well format. Collagen gels were prepared from rat tail collagen I (Gibco, Invitrogen, Carlsbad, CA), as suggested by the manufacturer. Briefly, 2000 μL collagen, 500 μL 10× RPMI medium, and 125 μL NaOH were mixed in 2375 μL distilled water. A quantity of 350 μL of the collagen suspension was given to each well to achieve ∼1-mm thickness of gel per well (area 3.5 cm²), and was allowed to polymerize for 1 h at 37°C. The gel was then rinsed with serum-free medium before seeding the cells. The THP-1 cells were starved in serum-free RPMI 1640 medium (Gibco) overnight, adjusted to 1 × 10⁵ cells in 1500 μL, which was added to the wells and incubated for 2–3 h at 37°C to allow the cells to adhere to the collagen surface. They were subsequently incubated with the respective compounds (4 μM Cytochalasin D, 5 μM Nilotinib, 15 μg/mL Substance F (proprietary)) and additionally stimulated with 10 nM phorbol myristate acetate.

Random cell migration was recorded by capturing phase contrast images on an inverted microscope (Axiovert; Carl Zeiss, Jena, Germany) with 20× magnification every 20 min in a climatized chamber at 37°C containing 5% CO₂. For each time-lapse movie, 50 images were taken within 14 h at two defined locations in the well. The pixel resolution was 220 nm.

Image correlation spectroscopy

Similar to other fluctuation techniques such as fluorescence correlation spectroscopy (20,21), ICS can be used to characterize dynamical processes that induce fluctuations in the intensity between or within images. The intensity I(x,y,t) at each pixel (x,y) of the frame recorded at time t is decomposed into a constant part I_avg and a fluctuating part δI(x,y,t):

$$I\left(x,y,t\right)=I_{\text{avg}}+\delta I\left(x,y,t\right).$$

In general, the complete spatiotemporal correlation function of the fluctuating part of the intensity is

$$\text{Cor}\left(dx,dy,\tau \right)=\frac{1}{N_{\text{frames}}}\sum _t\frac{1}{N_{\text{pixels}}}\sum _{x,y}\delta I\left(x,y,t\right)\cdot \delta I\left(x+dx,y+dy,t+\tau \right).$$

The summation runs over all pixels of the image, which is padded with zero-valued pixels to avoid missing neighbor inconsistencies. The convolution operation is a simple product in Fourier space, leading to

$$\text{Cor}(dx,dy,\tau )=\frac{1}{N_{\text{frames}}}\sum _t{F}^{-1}\left(F\left[\delta I\left(x,y,t\right)\right]\cdot \overline{F\left[\delta I\left(x+dx,y+dy,t+\tau \right)\right]}\right),$$

which is computationally much more attractive using the fast Fourier transform algorithm than actually calculating the sum over the two spatial dimensions explicitly (F[⋅] denotes the Fourier transform and the horizontal bar complex conjugation). In the simplest case of a point particle moving randomly in two dimensions and imaged by a Gaussian point spread function (PSF), the correlation function is derived using the propagator for normal diffusion and can be found in the relevant literature (22–25):

$$\begin{array}{c}\text{Cor}\left(dx,dy,\tau \right)=g_0+\left(\frac{1}{1+4D\tau /{\omega }_0^2}\right)\text{exp}\left\{-\frac{d{x}^2+d{y}^2}{w{\left(\tau \right)}^2}\right\}\\ w{\left(\tau \right)}^2={\omega }_0^2+4D\tau .\end{array}$$ (1)

The offset g₀ of this two-dimensional Gaussian was introduced to account for nonvanishing long-range spatial correlations. The width w(τ)² is composed of the time-independent width of the point-spread function ω²₀, and the time-dependent mean-square displacement (MSD) of a population of Brownian particles, 4Dτ. The correlation function for extended objects has only recently been published (24). In brief, the total correlation contains convoluted contributions of the particle shape, the particle motion, and the PSF:

$$\text{Cor}\left(dx,dy,\tau \right)\propto {\zeta }_{\text{PSF}}\left(dx,dy\right)\circ \Phi \left(dx,dy,\tau \right)\circ {\phi }_{\text{shape}}\left(dx,dy\right),$$

with ζ_PSF, Φ(τ), and φ_shape, the correlation function of the PSF (time-independent), the object dynamics (time-dependent), and the object shape (time-independent), respectively, and where the hollow dot (∘) denotes the convolution operation. The time-independent shape correlation is averaged over all particle orientations at any given moment in time, and therefore might increase the width of the total correlation function but not its decay time. For Gaussian-shaped objects it is useful to combine φ_shape and ζ_PSF to a single template correlation function (see Kurniawan and Rajagopalan (24)). Assuming Gaussian particles of size d²₀, the width of the correlation function (Eq. 1) becomes

$$w{\left(\tau \right)}^2={\omega }_0^2+d_0^2+4D\tau ,$$

where ω²₀ and d²₀ can be combined to a template width. This description is exact for the analysis of the simulated images described later, where the particle shape is Gaussian. For the analysis of the cell migration images, it represents a first approximation of the shape contribution to the correlation function.

From the analysis of the Gaussian width, w(τ)² as a function of the time-lag knowledge about the underlying motility mode and its dynamic behavior can be obtained. Of particular interest are the two expressions (26,27)

$$\begin{array}{c}w{\left(\tau \right)}^2=w_0^2+K{\tau }^{\alpha }\\ w{\left(\tau \right)}^2=w_0^2+\frac{L^2}{3}\left(1-e^{-12D\tau /L^2}\right)\end{array}$$ (2)

for anomalous and confined diffusion, respectively. As just described, w₀(τ)² includes contributions of the PSF and the particle shape correlation, as well as fast particle motion that leads to motion blur (broadening of the PSF) rather than resolvable steps (28) and position measurement uncertainty or mechanical jitter of the setup. The expression for anomalous diffusion describes unconfined random motion which can be slower (α < 1) or faster (α > 1) than free diffusion (α = 1, K = 4D), but also directed motion or drift with velocity $\overrightarrow{v}$ (α = 2, K = v²). The transport coefficient K is used in Eq. 2 to differentiate cases where K = 4D (α = 1) from the other cases (α ≠ 1), where K even has different units. The expression for confined diffusion in a square box of length L is a good description for motion that does not exceed a certain maximum range L ≪ (4Dt_max)^1/2 within the observation time.

Before two images from a time-lapse series acquired at different time points were correlated with each other, the background was subtracted using a median polish (29). The correlograms of all image pairs for a particular time lag were averaged, implicitly assuming stationary motion. Similarly, isotropic motion as assumed and therefore a radial averaging was performed as well, resulting in a correlation function Cor(r,τ) that depends only on one spatial dimension and time. Nonlinear least-square regression of the expressions in Eq. 2 finally yields the apparent transport coefficient K_ano and the anomaly exponent α, or the confinement size L and the apparent diffusion coefficient D_conf.

Single cell tracking

As an alternative method to characterize cell motility a single particle tracking (SPT) approach was chosen. Individual cells were identified using the image segmentation algorithm implemented in the Nuclei Detection Module of Acapella, the image analysis and workflow scripting language integrated in the Opera-QEHT High-Content Screening System (PerkinElmer Cellular Technologies, Hamburg, Germany). The software discriminates bright objects in front of a dark background using a global threshold. Individual objects are separated using the watershed algorithm and smoothed using binary opening and closing operations (30). The detected objects are filtered for a typical range of area and intensity to exclude segmentation artifacts; the quality of the segmentation and the filtering is monitored by visual inspection. For each of the valid two-dimensional objects, the center of mass is calculated as

$${\overrightarrow{R}}_{\text{CoM}}=\sum _{\text{i}}{\overrightarrow{r}}_{\text{i}},$$

where the sum includes all pixels belonging to the object.

Using the centroid positions extracted from the segmented object lists, single cell trajectories were reconstructed as described in Jacquier et al. (31). Briefly, each cell/particle localized in frame i and belonging to trajectory j is connected with the closest cell/particle in frame i+1 inside a circle with radius r_max = 50 pixels, which is thus added to trajectory j. If no cell is found within r_max, trajectory j is terminated. Likewise, all localized cells not connected to a previously existing trajectory are starting points of new trajectories.

Next, for each trajectory the distribution of square displacements was computed for each time lag and later averaged. The so-derived MSD can be biased by extreme displacements coming from localizations erroneously assigned to a trajectory. For small-scale experiments with only a small number of trajectories and only a few conditions it is feasible and most useful to curate the data by visual inspection and to exclude misassociations manually. This is no longer possible in a screening environment with hundreds of conditions, thousands of trajectories each. We therefore implemented an automated curation algorithm based on nonparametric statistical testing. The algorithm simulates the human decision-making by excluding object localizations from a trajectory when the distance to its neighboring localizations is much larger than expected, in light of all other displacements of the same trajectory. To this end, the empirical square displacement distribution for time-lag 1 frame (including the extreme displacement) was compared to the exponential distribution Exp(mean = 1/MSD) expected from theory, using Kolmogorov-Smirnov’s test. Recursively, the location producing the largest displacement was deleted from the trajectory, until the type-1 error rate p > 0.01. This criterion ensures that among the valid trajectories that lead to displacements consistent with expectation, only one in a hundred is falsely corrected. If the final trajectory contained <20 points, it was discarded from further analysis. For the remaining trajectories, the MSD for each time lag was computed. Two important statements shall be made here:

• 1.Only extremely large displacements are corrected whereas small displacements are unmodified; and
• 2.The estimation is conservative because the extreme displacement is included in the calculation of the mean, leading to a potential overestimation, thus introducing a bias to the expected distribution.

A brief illustration of the effect of this curation algorithm is shown in Fig. S3 in the Supporting Material.

Standard errors on the MSD(t) profiles were calculated taking into account the correlation structure of the residuals (32):

$$SE\left(MSD\left(n\Delta T\right)\right)=MSD\left(n\Delta T\right)\cdot \sqrt{\frac{\left(2n^2+1\right)}{\left[3n\left(N-n+1\right)\right]}}.$$

The MSD(t) profile of each trajectory was fitted to the model equations of both confined diffusion,

$$MSD\left(t\right)=c+\frac{L^2}{3}\left(1-e^{-12Dt/L^2}\right)$$

and anomalous diffusion,

$$MSD\left(t\right)=c+K{t}^{\alpha },$$

where the constant offset c includes the uncertainty of the position determination (26,31–33). This is done to avoid artifacts coming from a wrong model selection. It was a conscious decision not to attempt a model selection because here, as in many other cases, the quality of the data (presence of extreme observations; too-short trajectories; too-short observation time) does not allow a powerful decision in favor or against a particular model. Population summary statistics over objectwise data was calculated using robust estimators, i.e., median for the sample average, median absolute deviation (MAD)

$$MAD\left(x\right)={\text{median}}_i\left(\left|x_i-{\text{median}}_j\left(x_j\right)\right|\right)\cdot 1.4826$$

for the sample standard deviation, and MAD of the median

$$MAD\left(x\right)/\sqrt{n}$$

for the standard error of the mean.

Simulations

Two-dimensional Monte Carlo simulations were performed to validate the image correlation algorithm. For each time-lapse movie, 40 images of 512 pixels square were simulated containing 50 Gaussian-shaped particles. All particles had the same radius (expressed by the Gaussian width s) ranging from 1 to 10 pixels. The particles’ initial positions were chosen at random with uniform probability and the dynamics followed a Markovian random walk with reflecting boundary conditions. Increments from frame to frame were sampled from a normal distribution with mean zero and variance 2D in each direction, where D was ranging from 1 to 100 pixel²/frame. To match the signal/noise ratio and signal/background ratio in the experimental situation of typically 30 and 8, respectively, the mean particle peak signal amplitude a was adjusted to be eight times the mean background intensity b, which was set to 20. Taking all this together, the expected intensity at each pixel is

$$\langle i\left(x,y\right)\rangle =b+a\cdot \sum _k\exp \left\{-\frac{\left[{\left(x-x_k\right)}^2+{\left(y-y_k\right)}^2\right]}{2s^2}\right\},$$

where the sum runs over all objects. To arrive at the final intensity at each pixel i(x,y), the values were sampled from the corresponding Poissonian distribution

$$p\left(i,\langle i\rangle \right)=\frac{{\langle i\rangle }^{\text{i}}}{i\text{!}}{e}^{-\langle i\rangle }.$$

For images obtained by fluorescence photon counting this signal generation procedure is exact and for transmission light images it is a useful approximation.

Results and Discussion

Image correlation spectroscopy has been proven to be a powerful tool to investigate isotropic and anisotropic, random and directed motion of fluorescently labeled proteins inside living cells (23). Despite the strength to detect and quantify protein recruitment and trafficking, ICS is used today mainly by a few experts with biophysics background. It is the purpose of this work to expand the use of ICS in two ways: first, by focusing on the motion of whole cells as the object of investigation instead of proteins within cells; and second, by translating the area of application of ICS from the basic biophysical sciences toward medium throughput compound screening in the pharmaceutical industry.

The amount of correlation between pairs of images in a time-lapse movie of migrating THP-1 cells is illustrated in Fig. 1, a–c, by the yellow intensity compared to the sum of the green and red intensity (color figures online). As the delay between the two images increases from Fig. 1, a–c, more red and green regions appear due to cells moving laterally in the image plane. This loss of correlation is reflected in the decreasing amplitude and the increasing width of the central peak of the two-dimensional spatial image correlation functions (Fig. 1, d–f). Assuming that the cellular motion is isotropic, the ICF is univariate and can be radially averaged (Fig. 1 g).

Figure 1.

Image correlation spectroscopy analysis of migrating THP1 macrophage cells. (a–c) False color two-channel RGB overlay of image pairs with time-lag 0, 5, and 10 frames. (a) The red and green channel images are identical (time-lag 0 frames) resulting in a pure black and yellow overlay image. (b and c) Cells migrating in the image plane lead to a relative shift of the green channel image (time-lag 0) and the red channel image (time-lag 5 and 10 frames, respectively). The amount of yellow intensity compared to the red and green intensity is related to the correlation between the two image pairs. (d–f) Two-dimensional spatial correlation functions for the image pairs in panels a–c. (g) Radially averaged univariate correlograms from the same time-lapse series. Increasing time lags show decreasing amplitudes.

As a first step in the development of the RAMOT assay, this implementation of the ICS algorithm was tested on simulated images where particles of known size and shape randomly walked in a two-dimensional plane with known diffusion coefficient. The same procedure was then applied to microscopic phase-contrast images of migrating THP-1 cells to discriminate treatment effects of different compounds. Finally, the ICS-based RAMOT assay was compared to the gold standard of population motility assays, single particle tracking (SPT).

Simulations

It is good scientific practice to test novel data analysis algorithms and their implementation on simulated data to study the sensitivity of the method on system parameters that can be varied in a controlled way. Here, time-lapse image series were simulated as described in the Materials and Methods comprising realistic signal and noise levels, two-dimensional freely diffusing particles, and a Gaussian-shaped instrument response. One frame of such a time series is displayed later in Fig. 3 a and an example movie is available as the Supporting Material (Movie S1, D_in = 10). ICS was applied to retrieve the diffusion coefficient D_out for a range of input values D_in and a set of four particle sizes.

Figure 3.

Single particle tracking (SPT) analysis of simulated random cell trajectories. (a) Simulated image with segmentation results indicated as colored circumferences. (b) SPT mean-square displacement (MSD) time course for different input diffusion coefficients D and (c) different particle radii s. The median MSD(t) trends (lines) are calculated from the objectwise data (see Fig. S1 and Table S1 in the Supporting Material). Error bars represent the median absolute deviation (MAD) of the population median, a robust estimator for the standard error of the mean.

The MSD time courses are derived as described for the five input diffusion coefficients D_in = 1, 5, 10, 30, 100 pixel²/frame and displayed in Fig. 2 a as indicated. In Fig. 2 b, for a fixed D_in = 5, the particle size was varied (color scale, Gaussian width σ = 1, 2, 4, 8 pixel). In all cases the MSD grows linearly with time, reflecting correctly the simulated free Brownian motion. From the properties of the correlation function it is clear that the noise in ICS depends on the number of available image frames, the signal/noise ratio of the moving features, the mean free path length, and the number of pixels actually changing between frames. For this reason, small particles consisting of only a few pixels exhibit more noisy curves than larger particles do (Fig. 2 b, solid line, σ = 1), and fast particles more than slow ones do (Fig. 2 a, dashed-dotted blue line, D = 30, and solid orange line, D = 100). Error bars represent the standard error of the fit parameter.

Figure 2.

Image correlation spectroscopy analysis of simulated random cell trajectories. Error bars represent the standard error of the fit coefficient. (a) ICS mean-square displacement (MSD) time course for different input diffusion coefficients D_set and a constant particle radius four pixels. (b) MSD(t) for different particle radii s and constant input diffusion coefficient D_set = 5. (c) Comparison of simulation input D_in with the derived D_out. (Dashed lines) Twofold difference.

A strong increasing trend of the initial MSD(lag = 1) with increasing particle velocity (Fig. 2 a) and with increasing particle size is visible (Fig. 2 b). The first is due to the fast particle motion that leads to a significant displacement already between consecutive image frames (lag = 1). The finite extrapolated intersect at lag = 0 of ∼60 px² is a result of the particle size (s = 4) and the signal/noise ratio (SNR = 30). The second is due to the finite particle size contribution to the width of the correlation function. In fact, the identity between the e⁻² radius of the simulated particles and the MSD(0) offset w₀² = 4s² is confirmed (see Fig. S4).

Fig. 2 c shows the correlation plot between D_in and D_out, where the error bars indicate the standard error of the fit parameter. In all of the eight cases the ICS-derived diffusion coefficient is correct within less than a factor of two, although there might be a slight bias to underestimate the true value. No systematic trend was observed that would be related to the size of the particle. This comparison provides evidence that even with a small number of moving objects (50 objects) and a short observation period (40 frames), reasonable accuracy and precision can be obtained.

Apart from comparing ICS-derived quantities with theoretical values used in the simulation, a further comparison with the gold standard of particle motion analysis, SPT, was performed. Fig. 3 a shows a representative simulated image (grayscale) together with results from an image segmentation and object identification procedure (colored contours). The homogeneous, convex shape and the high signal/noise ratio allow for a reliable determination of the objects’ outline and their center provided they are well separated. In situations where two objects lie close to each other they are recognized as one large dumbbell-shaped object, which has two consequences: First, the object identification algorithm delivers one center position for the combined object instead of two center positions for the individual objects; and Second, the SPT connectivity analysis will assign the position of the combined object to one of the two trajectories whereas the other one is terminated. Once the two objects move apart, a new trajectory is started. As a result, one long trajectory is split into two parts with a few frames missing in between. Although this has little effect on the precision of the small time-lag MSDs, valuable information about the large time-lag MSDs is lost. The position of the combined object within a trajectory deviates from the true object position roughly by the mean of the two objects’ radii. As long as the between-frame step-size of an object is large compared to the size of the object, this error can be neglected. In contrast, if the object misidentification leads to an unexpectedly large displacement vector, the correction procedure outlined in the Materials and Methods was implemented to eliminate it, although at the cost of trajectory length and sampling statistics.

The MSD time courses of individual objects (see Fig. S1, dots) exhibit a high degree of variability compared to the ICS-derived MSD(t) (Fig. 2 a) despite small errors on the individual MSD(t) profile (an example is shown in Fig. S2). This is a result of the random nature of the diffusion process, the relatively short observation period, and the small sample size. Nevertheless, the details of the distribution of observed objectwise MSD time courses can report on the presence of multiple distinguishable species—for instance, fast and slow moving objects or freely and confined moving objects. Here, the object population is homogeneous by design; the distribution of the object properties is homogeneous and, hence, the MSD curves can be averaged (Fig. 3 b). As expected, and in agreement with ICS-derived MSDs and with the simulation input, the ensemble median MSD increases approximately linearly with time and there is no systematic trend with particle size (Fig. 3 c). Here, the error bars represent the robust version of the standard error of the mean, the median absolute deviation (MAD) of the population median.

Instead of averaging the MSD reads of all objects to one average MSD time course and subsequent fitting of anomalous and confined diffusion models, SPT uniquely allows extraction of the objectwise diffusion parameters for both models by nonlinear regression to the objectwise MSD(t) and subsequent analysis of the ensemble statistics (Fig. S2 and Fig. S3).

The median diffusion coefficients D_SPT derived from anomalous and confined diffusion models from SPT analysis of all valid object trajectories compare well within a factor of 2 with the simulation D_set (Fig. 4, solid symbols) as well as with the ICS-derived diffusion coefficients D_ICS (open triangles). Even though four out of five D_ICS are smaller than their simulation input, no systematic difference can be inferred (Wilcoxon signed rank test p > 0.3). In contrast, D_SPT systematically deviates from the input values in two different ways—anomalous diffusion-derived D_ano = K/4 underestimates and confined diffusion-derived D_conf overestimates the true value. This is most likely an artifact of the regression procedure, as explained in the next paragraph.

Figure 4.

Comparison of simulation input D-set with the derived D-measured. The MSD(t) profiles were analyzed by fitting a normal diffusion model to the ICS-derived curves (green/open triangles) and anomalous (pink/solid squares) or confined diffusion model to the SPT-derived curves (blue/solid circles). Error bars show standard errors of the fit parameter (ICS) or median absolute deviations (MAD) of the population median of the fit parameter (SPT).

Let us assume the average linear MSD trend is a superposition of identically distributed anomalous diffusion modes with 〈α〉 = 1 and some allowed variation ±δα. The corresponding diffusion coefficient will then be correlated with the exponent: α < 1 is connected to a steep slope, i.e., a large D, and α < 1 is connected to a shallow slope. The confined diffusion model expects MSD(t) to approach a plateau and to have negative curvature. Hence, regression to data that are positive in curvature will not converge, effectively eliminating traces with α > 1 before averaging, leading to a small but significant overestimation of D_set. The anomalous diffusion model expects experimental MSD(t) curves to increase strictly monotonically, neither reaching a plateau nor decreasing. Because diffusion is a random process and there is considerable noise in the detection process, some objects will give rise to a plateau or even a bell-shaped MSD(t) with a steep slope for low t. In these cases the fit will not converge, effectively eliminating the large D part of the distribution before averaging, leading to a small but significant underestimation of D_set.

Random motility of THP-1 cells on collagen

A THP-1 cell RAMOT assay was established to characterize pharmaceutical compounds for their potency as migration modulators. The setup described in Materials and Methods allows label-free detection of cell migration on a planar two-dimensional collagen substrate. Compared to traditional assays, such as the scratch assay or the invasion assay, no additional preparative steps are necessary. Therefore, the RAMOT assay constitutes a particularly comfortable and easy-to-use method.

In the previous chapter, the ICS-based RAMOT assay was shown to recover correctly the dynamics of identical Gaussian objects in simulated images. Application of ICS to study random cell motility in phase contrast recordings will be discussed in the following paragraphs.

Macrophage-like THP-1 cells on a collagen matrix appear as spherical objects, giving rise to a doughnut-shaped intensity distribution in phase-contrast images (Fig. 5 a and b). Time-lapse video recording at a 3 h⁻¹ frame rate nicely captures their erratic motion (see Movie S2 in the Supporting Material). Addition of cytochalasin D, a known inhibitor of cell migration and actin polymerization, results in a pronounced slowdown of most cells (see Movie S3). The effect is clearly visible to the naked eye and can be quantified systematically using ICS as described above.

Figure 5.

THP1 macrophage cell motility assay. (a) Segmentation of phase contrast images. The raw images were background-subtracted and contrast-enhanced for better visibility. The segmentation results are indicated as colored circumferences in the magnified section. (b) Trajectories of 50 randomly selected cells as derived from the custom connectivity algorithm are painted in color on top of the first frame of a time-lapse series. Comparison of ICS (c) and SPT results (d) of the THP1 cell migration assay. Error bars show standard errors of the fit parameter (ICS) or median absolute deviations (MAD) of the population median of the fit parameter (SPT). The diffusion coefficient is given in units of pixel²/frame⁻¹ = 0.2 μm²/h. SPT also allows the construction of single-cell distributions of the diffusion coefficient (e). The error on the diffusion coefficient of the individual cell is ∼0.2 on the log scale.

ICS measures the sum of all dynamic changes in an image series in a time-resolved fashion. At a given timescale, the ICF is dominated by the strongest change, i.e., the largest population of objects undergoing the change, the highest frequency of the change to occur, and the largest amplitude of the change. Apart from cell migration, a number of dynamic changes can occur during the data acquisition period that this theory does not account for, such as changes in the cell number (cell division, cell death) or the cell shape (cell growth, cell differentiation). Both can be separated from migration if they occur at different timescales, or neglected if they occur infrequently, or have to be excluded by design. In our experimental situation, none of these processes is contributing to the observed dynamics. For instance, the THP-1 cells are partially differentiated, resulting in a very low proliferation rate and a stable morphology; visual inspection of the movies presented in the Supporting Material did not reveal a single cell division event. Individual THP-1 cells exhibit little or no morphological change in phase contrast recording. And finally, experiments were done under environmentally controlled conditions, providing sustained viability and a low rate of detachment and cell death.

The RAMOT assay was designed to fill the gap among migration assays to quantify independent, random cell motility with little collective motion. These preconditions are fulfilled at low cell density far below confluency. Two consequences of an increased cell density shall be discussed here:

• 1.The theoretical description according to the theory of Brownian motion is no longer valid because cells cannot move independently but have to pass each other. Although it may be difficult to establish a more accurate theoretical description for such a coupled multiparticle dynamic problem, even at high confluency the motion of the individual cells can be captured by the correlation analysis.
• 2.In the crowded environment of a highly confluent monolayer the motility of the cells becomes increasingly slow, anomalous, and hindered. It is more determined by the availability of empty space and cell-to-cell communication than by the inherent migration capacity of the individual cells. These aspects are better characterized by the classical scratch assay mentioned in the Introduction.

Compound effect detected by the ICS-based RAMOT assay

Assigning an effective diffusion coefficient to the erratic cell motion allows the differentiation of treatment effects (Fig. 5 c). The statistical significance was determined by a linear mixed effect model on the log-transformed diffusion coefficients as the target variable, with the treatment as the main fixed effect and the location inside the microwell plate as a random effect. Addition of the reference compounds cytochalasin D (green) or nilotinib (yellow) reduces the effective cell motility significantly (p < 0.01), approximately threefold compared to untreated cells (black). This was expected as cytochalasin D is known to disrupt the cytoskeleton by interference with actin polymerization and nilotinib is a known inhibitor of a number of tyrosine kinases, some of which are important components of the cell adhesion and migration machinery (34). The additional negative controls (i.e., azide control, human IgG) did not change the diffusion coefficient significantly. Azide was present in the IgG solution, and IgG was included as a control for the proprietary human monoclonal antibody Substance F. The effect of Substance F on macrophage motility was not significant as determined by ICS under this experimental design.

Comparison with single cell tracking

Single particle tracking is based on the reliable detection of the coordinates of a moving object either by interferometric position sensing in optical traps (35) or, most commonly, in time-lapse video microscopy (32,36). In cases where the object is much smaller than the resolution limit of the microscope, the position of the object can be derived by least-square fitting of the PSF (37,38), or by deconvolution. This approach, while being the most accurate, is often time-consuming and has been replaced in the past by the determination of the intensity centroid (39,40). For extended objects of arbitrary shape and intensity distribution, the intensity centroid may not correspond to the true center of the object. Then, the geometric center obtained from object recognition based on watershed segmentation of the image may reflect the position of the object more accurately (Fig. 5 a).

Following the described procedure, single-cell trajectories were reconstructed (Fig. 5 b) and the effective cell diffusion coefficient was obtained by fitting the anomalous diffusion model equations to the MSD(t) curve of each cell (examples are shown in Fig. S5). The population median of D_SPT for the six treatments is displayed in Fig. 5 d and resembles closely the D_ICS pattern in Fig. 5 c. The error bars amount typically to ∼10% of the determined diffusion coefficient. Multiple linear mixed-effect modeling reveals that now, in addition to cytochalasin D and nilotinib (p < 0.001), also the proprietary Substance F (p = 0.02) and IgG (p = 0.04) but not the azide control (p = 0.31) weakly but significantly reduces macrophage motility, as determined by SPT. There is no significant difference, however, between Substance F and IgG (p = 1). A plausible reason for this increased sensitivity might be the fact that, in SPT, each moving object has the same influence on the median motility whereas, in ICS, brighter objects have more weight. Therefore, a few relatively bright but relatively slow objects might dominate the average dynamics obtained with ICS and thus reduce the overall D_ICS.

In SPT, knowing D_SPT for each moving object independently allows a focus upon the population median or in fact the whole distribution of D_SPT (Fig. 5 e). Here the width of the distributions is 10 times larger than the uncertainty for the individual diffusion coefficient of ∼0.2 on the log scale. The existence of small subpopulations or inhomogeneous broadening is much more easily detected on the distribution level and can be distinguished from a pure homogeneous broadening. This obvious limitation of the ICS-based RAMOT is balanced by the advantage that it still works for conditions in which object identification or trajectory reconstruction is no longer possible.

Random motion of a sparse cell population is a common feature, for instance, of immune cells or metastatic cancer cells but cannot be quantified using traditional migration assays that rely on some kind of collective or directed motion (2). Therefore, if random cell migration could be quantified with ICS, this would address an unmet need and add considerable value to fields like immunology or oncology.

ICS allows quantification of dynamical processes in two ways—either phenomenologically, by reading a correlation half-life time, for instance, after nonparametric regression, or, preferably, model-based by assuming a specific dynamical mode, such as normal or anomalous diffusion, and deriving parameters by (non)linear regression of the corresponding mathematical expression. The latter gives the most powerful results provided the model is true, whereas the former is more robust and does not require understanding of the underlying dynamical processes.

Visual inspection of the time-lapse movies suggested that the cell trajectories can be described sufficiently well with a model based on a random walk. Hence, we conducted an exploratory study that revealed that the vast majority of macrophage cells migrate randomly in a Brownian motion-type fashion on the timescale of observation and exhibit a mean-square displacement characteristic of normal or subdiffusion kind. This is in contrast to migration of fibroblast cells or Dictyostelium, for which a more complex migration pattern has been observed (41,42). Given our observation of randomly hopping cells, it is valid to characterize their dynamics by an effective diffusion coefficient, where the term “effective” indicates that the cellular hopping only appears to be independent, isotropic, and randomly distributed on an hour timescale, but is expected to be correlated at shorter timescales.

Upon closer inspection of the movies, it becomes clear that some cells are moving particularly fast whereas some cells tend to be very slow or even immobile. In principle, ICS theory should allow for differentiation of several diffusing subpopulations by fitting a two-component decay function (25). In this study, it was not possible to resolve a slow and a fast moving population, either because the number of slow cells was not large enough to significantly contribute to the pixel dynamics or because the observation time was not long enough.

This is a general limitation of ICS compared to SPT when dealing with heterogeneous populations due to the ensemble averaging process. For example, the appearance of a small subpopulation of cells with a slightly higher migration speed than the majority cannot be distinguished from a small increase of the migration speed of the whole population. Moreover, the effect of this small subpopulation on the average diffusion coefficient may only lead to an insignificant change while at the same time its appearance can still lead to a significantly different distribution of diffusion coefficients. It is the ability to resolve distributions and detect rare events/species where the advantage of single cell tracking appears to be most striking.

Conclusion

We have applied an image correlation spectroscopy approach to determine a population-averaged cell motility score in the RAMOT assay. Monte Carlo simulated images under realistic conditions provide evidence that ICS-derived diffusion coefficients of randomly walking objects are in quantitative agreement with input values and with SPT-derived results. Moreover, the ICS-derived diffusion coefficients in a THP-1 cell RAMOT assay under standard conditions are in quantitative agreement with single cell tracking and allowed to monitor pharmacological effects of known migration inhibitors. These laboratory and computer experiments extend the range of application of ICS analysis from protein dynamics inside living cells to moving cell populations.

A more detailed analysis of the image correlation function of extended objects including the influence of the cell shape and the z-dependence of the phase contrast images will give deeper insight in the future. Although the ICS-RAMOT assay was demonstrated here using label-free (phase contrast) microscopy of planar motion on an hour timescale there is no known limitation toward fluorescence microscopy on shorter timescales or in three dimensions. The faster computer algorithm of ICS compared to object identification and tracking, especially for large cell numbers, facilitates online analysis and automated high-throughput screening without specialized software.

In summary, the ICS-based RAMOT assay is a unique tool to investigate cell migration under conditions where traditional approaches fail. Application of the RAMOT assay to other cellular models for the immune response or for tumor metastasis promises new insights into the weakly interacting regime of cell migration.