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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Methods Enzymol. Author manuscript; available in PMC 2011 August 20.
Published in final edited form as:
PMCID: PMC3158948
NIHMSID: NIHMS318094

Single mRNA Tracking in Live Cells

Abstract

Asymmetric distribution of mRNA is a prevalent phenomenon observed in diverse cell types. The posttranscriptional movement and localization of mRNA provides an important mechanism to target certain proteins to specific cytoplasmic regions of their function. Recent technical advances have enabled real-time visualization of single mRNA molecules in living cells. Studies analyzing the motion of individual mRNAs have shed light on the complex RNA transport system. This chapter presents an overview of general approaches for single particle tracking and some methodologies that are used for single mRNA detection.

1. Introduction

Localization of mRNA is an important mechanism to generate cell polarity crucial in diverse cellular functions from motility to differentiation (for reviews, see Condeelis and Singer, 2005; Martin and Ephrussi, 2009; Shav-Tal and Singer, 2005). The asymmetrical distribution of mRNA provides a means for a cell to regulate the protein synthesis at high spatial and temporal resolution. Localized mRNAs can be translated repeatedly to produce high concentrations of proteins in specific subcellular compartments in response to local stimuli. To date, thousands of mRNAs are found to exhibit spatially distinct patterns in many different cell types, including budding yeast, fruit fly oocyte, fibroblasts, and neurons (Martin and Ephrussi, 2009).

Technical developments in intracellular RNA imaging have been indispensable to increase our knowledge about the mechanisms of mRNA localization. When the localization of ß-actin mRNA was first observed in the lamellipodia of fibroblasts (Lawrence and Singer, 1986), the mRNAs were hybridized with radioactive DNA probes and visualized by autoradiography, which required exposure times in the range of weeks. Now, it is possible to observe the movement of single mRNA molecules in living cells in real time (Bertrand et al., 1998; Fusco et al., 2003; Shav-Tal et al., 2004).

Single particle tracking (SPT) is used in many different research fields to investigate the dynamics of individual objects by regarding them as punctate points while ignoring the internal conformations. By following the trajectories of particles, we can characterize the types of motion and measure the velocity or diffusion coefficient. Jean Perrin, probably in the first SPT akin to modern methods, observed the movements of gamboges with submicron precision (Perrin, 1913). His quantitative analysis of the trajectories supported Einstein's microscopic theory of Brownian motion (Einstein, 1905). In cell biology, the use of SPT was pioneered by Barak and Webb (1982). They observed the motion of fluorescently labeled low-density lipoprotein (LDL) receptors on plasma membrane. De Brabander et al. (1985) microinjected colloidal gold particles of 20–40 nm in living cells, and visualized their motion using transmitted light To date, SPT has been extensively used to study complex cellular dynamics, including ligand–receptor interactions, membrane organization, secretory granules, locomotion of motor proteins, and transport within nuclei (reviewed in Kusumi et al., 2005; Levi and Gratton, 2007; Saxton and Jacobson, 1997; Wieser and Schutz, 2008). There are other optical techniques for measuring the lateral mobility. In the technique of fluorescence recovery after photobleaching, or FRAP (Axelrod et al., 1976), a region of interest is irreversibly photobleached by intense laser irradiation and then, recovering fluorescence in the area is recorded in time. From the recovery curve, one can derive the fraction and the diffusion coefficient D of mobile fluorescent molecules. Caution is required, however, in the presence of multiple species with distinct characteristics of mobility: FRAP data are an ensemble average of the total population, and the specific dynamics of a subpopulation may be hidden. SPT overcomes this limitation of FRAP by directly observing individual particles. Furthermore, the spatial resolution of SPT exceeds that of FRAP by more than an order of magnitude. SPT considers only the center of particles which can be determined with a precision of one to tens of nanometers, whereas the diffraction-limited focal volume dictates the minimum area in FRAP or fluorescence correlation spectroscopy (FCS). Consequently, SPT is suitable for high-resolution studies, far below the diffraction limit, of nanometer-scale displacements and structures, such as motor proteins and membrane microdomains.

Here, we describe SPT techniques that have been applied to the studies of mRNA trafficking in living cells. Methods to label, visualize, and track single mRNA molecules are reviewed. The “MS2 system” (Beach et al., 1999; Bertrand et al., 1998) for labeling mRNA is emphasized, which has been established in our laboratory. Various analysis techniques are reviewed and the information obtained by combining SPT with the MS2 system is discussed toward the end of the chapter.

2. Significance of Tracking mRNA

Many aspects of mRNA transport and localization have been discovered by single mRNA imaging and tracking. Whereas in situ hybridization shows the distribution of mRNA fixed at different stages, tracking of single mRNAs can reveal the in vivo dynamics that occur in the native environment. Tracking single mRNA particles in the cytoplasm of COS cells revealed that the movement of a reporter mRNA in the cytoplasm could be diffusive, static, corralled, and directed, with diffusive motion dominating (Fusco et al., 2003). The authors of this study were also able to show for the first time the movement of mRNA along cytoskeletal fibers. Interestingly, the addition of the ß-actin 3’ UTR to the construct, which contains a localization sequence necessary for the localization of ß-actin mRNA, increased in the relative amount of directed movements and their average length. In a related study, single molecule tracking allowed the measurement of the diffusion coefficient of ß-actin mRNA in different regions of the COS cells. ß-actin mRNA was found to diffuse freely in the leading edge of the cell, however, in the perinuclear region, mRNA diffusion was restricted. Disruption of the actin cytoskeleton delocalized mRNA and increased the diffusion coefficient of mRNA in the perinuclear region, indicating that cytoskeletal barriers may play a role in the localization of ß-actin mRNA (Yamagishi et al., 2009).

In an additional study where SPT was critical to probing a mechanism of mRNA localization, Bertrand et al. (1998) employed single mRNA tracking to address the question of how ASH1 mRNA travels to the bud tip in yeast. It was known that SHE1/MYO4, a type V myosin, as well as an intact actin cytoskeleton were necessary for ASH1 mRNA localization, however, it was not clear whether ASH1 mRNA was actively transported to the bud tip or if myosin was transporting another protein necessary for ASH1 mRNA anchoring at the bud tip. Real-time imaging and particle tracking indicated that ASH1 was transported from mother to daughter yeast cell with a velocity consistent with motor-based transport and that mRNA particles colocalized with myosin.

Single mRNA tracking in the nucleus was used to address the controversial question of how mRNA travels in the nucleus, revealing movements indicative of corralled diffusion (Shav-Tal et al., 2004). In this study, it was shown that mRNAs are not actively transported in the nucleus but passively diffuse. Zimyanin et al. (2008) also used live cell visualization and tracking of mRNA to address a controversy in the field of oskar mRNA localization in Drosophila oocytes. Prior to their study, it had been known that kinesin was necessary for posterior oskar mRNA localization, so seemingly oskar mRNA localization depended on kinesin-based transport; however, paradoxically, the microtubule network in the Drosophila oocyte lacks uniform polarity. Other theories postulated that cytoplasmic flow or exclusion from specific regions are responsible for oskar mRNA localization, with kinesin playing an indirect role. By direct observation of the mRNA, the authors showed that the mRNA moves along microtubules in many directions with a 14% bias toward the posterior region. Over time, this is sufficient to localize the mRNA to the correct region in the appropriate time frame.

An interesting cellular model for active transport of mRNA is the study of mRNA localization in neuronal processes, as diffusion alone is insufficient to transport mRNA into long dendritic processes, thus, active transport is a necessity for mRNA to reach the distal regions of neurons. Live imaging of calcium/calmodulin kinase II alpha reporter mRNA revealed a kinesin and microtubule-dependent oscillatory movement of the mRNA in the dendrites. Following stimulation, there is an increase of mRNA movement in the anterograde direction, bringing mRNA granules into dendrites and increasing the probability of arriving at activated synapses (Rook et al., 2000). These representative examples emphasize the significant discoveries in the field of mRNA trafficking where live mRNA imaging and tracking played a pivotal role in understanding the mechanisms of mRNA localization.

3. Labeling mRNA in Living Cells

3.1. Selection of probes for SPT

A wide variety of probes have been used in SPT, including gold particles, quantum dots, small organic dyes, and fluorescent proteins. Colloidal gold particles of 20–40 nm in diameter have been used with bright field microscopy (De Brabander et al., 1985) or differential interference contrast (DIC) microscopy (Sheetz et al., 1989). A small number of ligands or Fab fragments of the antibody IgG for target molecules are conjugated to the gold particles. Labeling by gold is advantageous for longer duration of tracking because there is no photobleaching and little saturation. Also, it allows the manipulation of single particles by using an optical trap (Edidin et al., 1991; Kusumi et al., 1998). However, gold probes have artifacts such as nonspecific charge interactions and crosslinking (Kusumi et al., 2005) and have not been yet applied successfully to mRNA labeling in living cells.

Fluorescent probes are more amenable to specific labeling. Simultaneous tracking of different species is readily achieved by multicolor imaging with diverse fluorescent tags. When using fluorescent probes, photostability and brightness are the primary figures of merit for SPT. Quantum dots have been widely used for SPT since they are 10 to 100-times brighter and 100 to 1000-times more photostable than organic dyes (Smith et al., 2008). Another advantage of semiconductor nanocrystals is that the emission wavelength can be tuned by the size; larger quantum dots emit redder fluorescence. However, quantum dots exhibit intermittent emission, or “blinking” (Nirmal et al., 1996), which can complicate the analysis of SPT data. Using quantum dots, Ishihama and Funatsu observed the movement of single mRNAs for over 60 s with a time resolution of 30 ms (Ishihama and Funatsu, 2009). Organic dyes and fluorescent proteins have been predominantly used for labeling mRNAs (for reviews, see Querido and Chartrand, 2008; Rodriguez et al., 2007; Tyagi, 2009). To image total mRNA in live cells, nonspecific nucleic acid stains such as SYTO 14 can be used (Knowles et al., 1996). Visualization of specific mRNA has been typically achieved through the microinjection of fluorescently labeled RNAs (Ainger et al., 1993; Shan et al., 2003; for a review of fluorescent RNA cytochemistry, see Pederson, 2001). An alternate technique that allows the labeling of endogenous mRNA is a variation of FISH performed on live cells. Santangelo et al. (2009) describe a technique where the membranes of live cells are reversibly permeabilized with the Streptolysin O, which delivers fluorescently labeled oligonucleotides into cells. Finally, molecular beacons have also been used to visualize endogenous mRNAs in live cells (Bratu et al., 2003), where delivery also typically involves microinjection.

3.2. The MS2-GFP system

To label native mRNA with GFP in living cells, the MS2-labeling technique has been devised (Bertrand et al., 1998). High autofluorescence in the cytoplasm can significantly confound tracking single molecules in a live cell. In order to enhance the signal-to-background ratio, the system expresses mRNAs that contain multiple MS2 stem loops, to each of which a dimer of fluorescent protein-fused MS2 coat proteins (FP-MCP) specifically binds. We have empirically determined that 24 copies of the MS2 binding sites (MBS) binding up to 48 FPMCPs are sufficient to visualize single mRNA molecules (Fusco et al., 2003; Shav-Tal et al., 2004). Plasmids containing multiple MBS cassettes and FP-MCP are available upon request at http://singerlab.aecom.yu.edu/requests/.

The benefit of using genetically encoded fluorescent proteins to label mRNAs is that the mRNA is transcribed and labeled in the nucleus, which should ensure proper binding of mRNA binding proteins, necessary for proper export, transport, and translation (Farina and Singer, 2002). Additionally, the MS2 system involves minimal perturbation to the cellular structure as opposed to other methods of delivery of exogenous mRNA such as microinjection of fluorescently labeled mRNAs or delivery through the perturbation of the plasma membrane. Many previous chapters have addressed the methodology using the MS2 system to fluorescently label mRNAs (Chao et al., 2008a; Grunwald et al., 2008b). This chapter will focus on technical considerations as opposed to specific instructions.

An MS2-GFP labeling system should be designed properly with several considerations. It is important that the MS2-GFP construct includes appropriate untranslated regions (UTR), which play an essential role in the mRNA localization by regulating the mRNA's interaction with the cytoskeleton or RNA binding proteins. Moreover, the MS2 repeats must be inserted in a carefully selected location. It is highly recommended to verify proper trafficking of mRNA using FISH in order to avoid potential problems. Other unknown elements not included in the reporter construct may be important for correct localization. Or the MS2 repeats may interfere with trafficking or induce nonsense-mediated degradation of the mRNA.

Secondly, appropriate levels of expression are crucial. If both the reporter mRNA and the FP-MCP are overly expressed, they may form fluorescent aggregates in the cytoplasm of the cell. Overexpression of mRNA may also lead to abnormal localization, because RNA-binding proteins and transport machinery may exist in limiting amounts. Therefore, it is most desirable that the reporter constructs are expressed under their own promoters. Retrovirus or lentivirus infection is widely used for creating stably expressing cells. Because each cell will only contain a few copies of the transgene, this method not only eliminates the concern of overexpression but also reduces the cell-to-cell variations in expression.

When performing live cell imaging using the MS2 system, multiple controls are essential to perform to verify the correct trafficking of the mRNA. MS2-tagged mRNAs should be visualized in combination with FISH to measure the relative abundance of labeled mRNAs, as in Fusco et al. (2003). Furthermore, FISH should be performed on cells that express the stem-loop-tagged mRNA in the absence and presence of the FP-MCP to ensure proper targeting of the mRNA with the stem loops and while bound to multiple fluorescent proteins. An additional necessary control is to express the FP-MCP in cells that do not contain the stemloop-tagged mRNA for the purpose of verifying that the expression of the coat protein does not lead to artifactual aggregation of fluorescent protein in the cells.

In our laboratory, a transgenic mouse line with 24 MS2 repeats inserted into the 3’ UTR of the ß-actin gene has been created recently (manuscript in preparation). This system will allow the visualization and tracking of endogenous ß-actin mRNA in various cell types, and moreover in vivo, which has not been achieved before. An orthogonal system for RNA labeling has also been developed using PP7 bacteriophage coat protein (Chao et al., 2008b), which will enable the tracking of multiple mRNA species.

3.3. Minimizing photobleaching and phototoxicity

Ultimately, long time-lapse imaging experiments are limited by photobleaching and phototoxicity. The average number of photons emitted by a dye molecule before photobleaching is approximately 10,000–100,000. Photobleaching occurs by several complex mechanisms and strongly depends on the environmental conditions such as solvent polarity and temperature (Eggeling et al., 2005). The most notable mechanism for photobleaching is photooxidation. Fluorophores in triplet excited state react with groundstate triplet oxygen and generate singlet oxygen (1O2). The highly reactive singlet oxygen causes both photobleaching and phototoxicity. Several reagents such as ascorbic acid and enzymatic deoxygenation systems have been used to reduce the detrimental effects. However, the removal of oxygen can enhance or reduce the photobleaching effect depending on the experimental condition. This is because photooxidation processes cause both the ground-state recovery of the dyes and the formation of irreversible photoproducts. Therefore, the concentration of oxygen scavengers needs to be optimized for sufficiently long tracking experiments. Addition of triplet quenchers such as Trolox (a water-soluble analog of vitamin E) and mercaptoethylamine can also improve the photostability (Rasnik et al., 2006; Widengren et al., 2007).

4. Imaging mRNA Movements

4.1. Experimental considerations

In order to track single mRNA movement in real time, it is important to achieve high sensitivity for single molecule detection and fast image acquisition. In fluorescence microscopy, photobleaching phenomena inherently limit the number of photons available from the probe. Therefore, one needs to find a good balance in the image-acquisition protocol.

First, the camera exposure time needs to be optimized to detect single molecules in motion. The precision to locate the center of a particle is proportional to the total number of collected photons (Bobroff, 1986). Once the imaging system is optimized for the highest signal-to-noise ratio, the exposure time needs to be long enough to locate particles with a desirable precision. On the other hand, the camera exposure has to be short enough to capture an image of a highly mobile object. If the particle travels a significant distance during the exposure time, it will show up as a streak or a blurred object, which impairs the detection of the object.

Secondly, a high frame rate is desired to follow the trajectory of a diffusing particle. In order to identify the same particle in two successive image frames, it is ideal to meet the Nyquist criterion in temporal sampling, that is, the displacement during the time interval should be less than half the spatial resolution. The previously measured diffusion coefficients of messenger ribonucleoprotein particles (mRNPs) in living cells are 0.1–0.8 μm2/s (Fusco et al., 2003; Shav-Tal et al., 2004), thus, the sampling time interval needs to be 5–40 ms. This requirement can be relaxed when the particle density in the image is sufficiently low. If the average distance between particles is much larger than the average particle displacement between frames, two successive images of an object can be linked to each other unambiguously. However, with increasing particle density, it becomes more difficult to solve the motion correspondence problem.

Lastly, a sufficient tracking range is crucial to identify the type of motion. The total number of frames in the image sequence determines the statistical accuracy of the analysis (Qian et al., 1991; Saxton, 1997). Monte Carlo simulations can be performed without limitation on the tracking period to quantitatively estimate the deviations from Brownian motion. For instance, Saxton examined the statistical variation of the diffusion coefficient D by simulations (Saxton, 1997). In addition, longer observation enables the detection of motion-type transitions. Since it is difficult to meet all of these requirements with a limited number of photons, one needs to find a good compromise between the high acquisition rate and the total duration of the experiment.

4.2. Instrumentation

SPT may be performed in various forms of light microscopy, including widefield, confocal, and total internal reflection microscopy (TIRFM). A standard wide-field epi-illumination microscope has been successfully used to visualize single mRNA molecules labeled by the MS2 system. The microscope system should be optimized to observe single molecule dynamics in living cells. For a sensitive detection of weak fluorescence, the photon collection efficiency needs to be maximized while the background noise is minimized.

Microscope objectives with higher NA are desirable to obtain a higher photon collection efficiency and tighter point-spread function. Large magnification may be beneficial to minimize the pixelation noise, as long as the particle under study does not travel beyond the field of view. When using multiple fluorophores with different emission colors, chromatic aberration must be appropriately corrected by using achromat or apochromat objectives. For colocalization of single molecules labeled with different fluorophores, multichannel image registration is also necessary (Churchman and Spudich, 2007).

The most common light source for wide-field microscopy is either a mercury or xenon arc lamp. If the power of the lamp at the excitation wavelength is not sufficient to detect single molecules, a laser light source can be employed. Laser illumination provides not only higher power but also narrower excitation bandwidth in the subnanometer range, which reduces the excitation background (Grunwald et al., 2008b). Since the viability of the cell also needs to be ensured, the illumination power must be balanced to protect the specimen against photodamage and photobleaching.

For single-molecule detection, there are many different types of cameras and spot detectors. The most commonly used detector for SPT is the electron-multiplying chargecoupled device (EMCCD). The electronmultiplying shift register increases the gain while keeping the noise level low. In order to achieve shot noise-limited detection, it is desirable to obtain maximum quantum efficiency and minimum camera noise. For higher quantum efficiency, back-illuminated type CCD chips are preferable. The dark noise of the CCD is due to the thermal fluctuation in the amount of charge in total darkness and can be reduced by cooling the chip down to -80°C. The readout noise increases approximately with the square root of the readout speed (Rasnik et al., 2007). Therefore, there is a tradeoff between the acquisition rate and the noise level. A frame-transfer feature alleviates this constraint and is highly desirable for sufficiently frequent acquisition.

Finally, cells must be kept in physiological conditions to ensure that the dynamics observed is an appropriate representation of the behavior in vivo. For mammalian cells, the temperature should be maintained at 37 °C.

There are several commercial systems to keep the sample warm during imaging sessions. A simple economical method is to use heating elements for the specimen and the objective lens. However, there can be a thermal drift due to the cycles of heating and cooling. A more reliable method is to build an incubator around the microscope body. A custom-designed incubator that can enclose the majority part of the microscope can keep the system at a stable temperature and prevent thermal drift. Also, incubators are desirable to control the CO2 level and humidity for extended periods of time.

4.3. 3D tracking

SPT has been mainly employed in two-dimensional systems such as cell surface or immobilized cytoskeletons in vitro. It is highly desirable to extend the technology into three-dimensional imaging since most biological processes occur within the 3D space of the cell. Kao and Verkman (1994) introduced a weak cylindrical lens in the detection optics of an epifluorescence microscope, which caused astigmatism in a particle image. Images of fluorescent beads are circular in the focus but become ellipsoidal when out of the focus. The major axis of the ellipsoid is rotated by 90° above and below the focus. They retrieved the x, y, and z positions by analyzing the shape, orientation, and position of the particle's image.

Simple defocusing methods have also been used for 3D tracking. Speidel et al. (2003) calibrated the radii of the ring patterns in the defocused image of a particle as a function of the axial position of the object. They found a linear dependence of the ring radii on the z-offset within an axial range of ~ 3 mm. Toprak et al. (2007) employed a similar method but with simultaneous imaging of the focused and defocused planes, and improved the localization accuracy in 3D. 3D tracking is also demonstrated using a two-photon microscope by tracing the laser beam in four circular orbits surrounding the object (Levi et al., 2005). The position of the particle is calculated on the fly, and those coordinates are used to set the next scanning position.

5. Analyzing mRNA Motions

A number of ideas and techniques for tracking objects in a sequence of images can be found in the context of fluid mechanics, computer vision, and radar surveillance. In cell biological applications, two types of tracking algorithms have typically been used. The first category detects the changes in particle positions by crosscorrelating consecutive frames. The second category generally consists of two steps: find the center of each particle in timelapse images, and connect the positions to reconstruct the trajectory. Cheezum et al. (2001) compared the tracking algorithms quantitatively by simulations. They concluded that the crosscorrelation method performs better for particles larger than the wavelength. Conversely, for particles that are smaller than the emission wavelength, it is more accurate and precise to perform particle detection followed by trajectory linking. Since the size of the mRNPs is smaller than the visible light wavelength, we will consider the second category of the tracking method here.

5.1. Localization algorithms

In light microscopy, an object that is smaller than the dimension of wavelength appears as a diffraction-limited spot. Because of the limited resolution, the details of the object cannot be discerned. However, the center of the object can be determined with a much better precision when a sufficient number of photons are collected from the particle. There are two major categories of algorithms to identify the location of single particles: searching for the intensity-weighted center of mass (centroid) or fitting image intensities by point-spread function.

In a centroid method, the image is filtered to remove high-frequency noise, a binary mask is applied to exclude the background below threshold intensity, and the weighted center of mass of contiguous pixels is calculated (Ghosh and Webb, 1994). Gelles et al. (1988) demonstrated a localization precision of 1–2 nm by usingDIC images of plastic beads. They crosscorrelated the sequence of images with a kernel segment of a single bead image and computed the centroid of each particle. The centroid method is computationally efficient and valid for asymmetric particles. However, the precision and accuracy of the particle position found by centroid methods are highly dependent on the background threshold level (Cheezum et al., 2001).

Alternatively, the fluorescent intensity distribution of a single particle can be fit with a 2D Gaussian function. It provides a higher localization precision and an accurate measure of the intensity (Anderson et al., 1992). Cheezum et al. (2001) compared the efficacy of the centroid and Gaussian fitting routines and concluded that a direct Gaussian fit to the intensity profile is superior in terms of both accuracy and precision.

Thompson et al. (2002) derived an approximate equation for the localization precision:

equation M1
(equation 1)

where s is the standard deviation of the point-spread function, a is the pixel size, b is the background noise, and N is the photon number. In the shot noise limit (the first term in Eq. (1)), the localization error is inversely proportional to the square root of the number of photons. When the background noise dominates (the second term in Eq. (1)), the uncertainty scales as the inverse of the number of photons. They also introduced a simplified fitting algorithm called “Gaussian mask,” which is equivalent to a nonlinear least-squares fit to a Gaussian distribution ignoring the shot noise. In this method, the centroid is calculated in convolution with a Gaussian distribution around the candidate position, and iterated until the centroid position converges. When the number of photons originating from the molecule of interest is small, the Gaussian mask algorithm can be more robust than the full least-squares fit.

5.2. Tracking algorithms

After the particles are located in a sequence of frames, the next step is to link a position in each frame with a corresponding position in the next frame. In general, the particles are not distinguishable from one another. With increasing particle density, it becomes more difficult to determine the next position of a given particle. Therefore, an important parameter to gauge the difficulty of particle tracking is the spacing-displacement ratio, which is the average distance between particles divided by the average particle displacement between two successive frames (Malik et al., 1993). If the spacing-displacement ratio is much larger than one, tracking can be reliably done by simple nearest-neighbor approaches (Anderson et al., 1992; Ghosh and Webb, 1994).

However, it becomes more difficult to connect the trajectories as the spacing-displacement ratio becomes smaller. Because there are many possible pairs of particles between two images, it is necessary to find the most probable set of connection. Various algorithms have been developed to seek a unique solution to the motion correspondence problem, and they can be divided into two broad categories: deterministic and statistical methods (Yilmaz et al., 2006).

Deterministic methods are also called combinatorial optimization techniques. They define a cost function of associating each spot in the previous frame to a single spot in the next frame. By minimizing the cost function, an optimal assignment can be obtained. For example, Crocker and Grier (1996) described a simple cost function to track noninteracting Brownian particles. If we consider an ensemble of indistinguishable noninteracting M particles, the most probable set of linkages between two frames is obtained when

equation M2

is minimized. If the particles can be distinguished by additional information such as size, color, and intensity, these data can be treated as another dimension of the particles in the cost function. The algorithm is available at http://www.physics.emory.edu/~weeks/idl. If the scope of the tracking is extended to more than two image frames, it becomes a multidimensional optimal assignment problem (Sbalzarini and Koumoutsakos, 2005; for the associated Im age J plug in, see http://www.mosaic.ethz.ch/Downloads/ParticleTracker). Most multiframe tracking algorithms are based on heuristic assumptions such as smoothness of the particle trajectories motion (Sage et al., 2005; for the associated Im age J plug in, see http://bigwww.epfl.ch/sage/soft/spottracker/; Vallotton et al., 2003). By tracking objects across multiple frames, the history of the particle movement is considered. Therefore, these methods can resolve problems arising from crossing trajectories, temporary occlusion, blinking, and detection failure. However, multiframe tracking is computationally expensive and becomes difficult to solve as the frame number increases. Therefore, greedy search techniques and heuristic approaches are used to obtain approximate solutions (reviewed in Jähne et al., 2007; Yilmaz et al., 2006).

Statistical data association methods take the uncertainty of the position measurements into account and assign a probability density function for a particle state. The probability distribution propagates over time and is updated by the measurements in each frame. The simplest statistical tracking method is the Kalman filter. In a Kalman filter, the initial particle state and noise have a Gaussian distribution. The next position of a particle is predicted by a linear model of motion, and the actual observation in the predicted search region is used to adjust the particle state. Kalman filtering can also be extended to multiple frame processing. The multiple hypotheses tracking (MHT) algorithm defers the correspondence decision until several frames are examined (Reid, 1979). Probabilities for multiple hypotheses are calculated, and the most likely set of track is chosen. The MHT algorithm seeks the globally optimal solution by considering all particle positions at all time frames. However, it is computationally intense both in time and memory. Thus, various approximate solutions to MHT were developed and applied to SPT in living cells (Jaqaman et al., 2008; Serge et al., 2008).

5.3. Categories of single particle motion

It is not known whether molecular motion in biology is finite, but the effort to categorize it is well worthwhile for SPT. Random walk is one of a few simple and universal models in physics, which analytically describes unobstructed, or “normal,” diffusion. Therefore, it is natural in SPT that normal diffusion serves as a reference while complicated motions are treated as deviations from this null model. A molecule may exhibit one of the five modes of motion, depending on the nature of interactions; stationary, normal diffusion, anomalous subdiffusion, corralled diffusion, and directional movement by active transport. Moreover, it is also possible that an mRNA molecule makes transitions between the modes (Fusco et al., 2003). It was only after SPT was applied that researchers began to recognize the significance of nonBrownian microscopic motions in biology (Feder et al., 1996; Kusumi et al., 1993).

A measurable parameter most commonly employed in SPT analysis is the mean-squared displacement (MSD) as a function of time. If we consider a trajectory r(t) recorded every δt for N time steps, the MSD for a given time lag nδt is calculated by:

equation M3

The MSD curves for the different types of motion are shown in Fig. 1 and the analytical forms can be expressed as follows:

equation M4

When fitting experimental MSD data with these analytical functions, one needs to add a constant to the fit-function because the localization precision Dx leads to an offset in the MSD plot (Wieser and Schutz, 2008).

Figure 1
Mean-squared displacement as a function of time for various modes of motion.

Another approach to analyze SPT trajectories is obtained by looking at the statistics of displacements, rather than the average. The probability distribution (Anderson et al., 1992), or equivalently, the jump-distance distribution (Grunwald et al., 2008a; Siebrasse et al., 2008), permits different perspectives from MSD. While ensemble MSD analysis measures an average of a population, jump-distance histogram detects different mobility populations. Jump distance analysis measures the probability P to find a particle recorded within a distance of r(i+1) from the initial position r(t) after time t according to the following equation:

equation M5

The probability distribution is suited to distinguish subpopulations with multiple diffusion coefficients, which can be nontrivial to identify in MSD plots.

5.4. Interpretation of mRNA tracking data

Upon successful labeling, imaging, and tracking of mRNAs, SPT data provide a rich source of information. Linking the quantitative analysis of mRNA movement to a biological process or function is another big challenge. SPT often yields observational information about the nature of mRNA movement. Observational reports about the travels of mRNA in the nucleus have utilized mean-squared displacement (Politz et al., 2006; Shav-Tal et al., 2004) as well as jump-distance histograms (Grunwald et al., 2008a; Siebrasse et al., 2008) to describe the nuclear environment that the mRNA encounters. In these reports, MSD measurements yielded an average diffusion coefficient, while mean jump distance was used to calculate the mean diffusion coefficient of discernable populations in unique compartments.

While nuclear SPT of mRNA usually yields diffusion coefficients of mRNA in the various nuclear compartments or the entire nucleus, utilization of SPT of mRNA in the cytoplasm needs to distinguish between diffusing mRNAs and ones that are transported along cytoskeletal elements. The use of MSD to analyze SPT data is capable of comparing the distribution of distinct motility populations of mRNA in the cytoplasm of cells. For example, MSD has been used to compare the relative population of diffusing mRNAs compared to transported or static mRNAs of reporter constructs with and without the ß-actin 3’ UTR (Fusco et al., 2003).

Alternatively, a specific aspect of active transport may be measured, such as the average velocity, maximum velocity, or the average length of transport path. Rook et al. (2000) measured a variety of aspects of active transport of CamKII alpha mRNA in the neuronal dendrites preand post-potassium chloride (KCl) stimulation. They measured the percent motile mRNA granules, distance traveled, average rate, and the maximum rate of active transport. The comparison of the motility of mRNA prior and following a treatment or knockdown of RNA-binding proteins is a direct way to measure cellular elements responsible for mRNA localization or means in which mRNA localization can be induced. In this study, it was shown that following KCl stimulation, there was a shift of movement from oscillatory to anterograde. In a more recent study of CamKII mRNA in dendrites, MSD was used to compare the relative abundance of actively transported and nonmotile mRNAs in wild type and FMRP knockout neurons. SPT of mRNA also allowed the measurement of the maximal and mean granule velocity in both the anterograde and retrograde directions in dendrites (Dictenberg et al., 2008). The measurement of mRNA velocity along the cytoskeleton is an important stepping stone toward understanding more about the nature of active transport in different cell types and situations. Because cytoskeletal filaments are required for active transport, studying the contribution of cytoskeletal elements and molecular motors on mRNA localization is often accomplished by chemical disruption of the cytoskeleton or overexpression of the dominant negative motors (Mingle et al., 2005; Sundell and Singer, 1991; Zhang et al., 1999). Conversely, live measurements of mRNA being actively transported can provide an insight into how cells actively facilitate the localization of mRNA to discrete locations.

6. Conclusions

SPT is a useful tool for monitoring the behavior of individual molecules in living cells, providing new information about dynamic heterogeneity. Current technological advances in SPT used in conjunction with the MS2-labeling system have allowed more accurate and extended tracking of mRNAs in cells. Single mRNA tracking studies are now elucidating the mechanisms of mRNA transport and localization in various cell types. Despite the remarkable recent progress, many important questions remain to be answered. A clear picture of the cause-and-effect relationship between mRNA localization and cell physiology will likely emerge as the in vivo dynamics of mRNA is revealed. Furthermore, multicolor imaging of single mRNAs interacting with their diverse binding partners will provide a more comprehensive picture of the molecular pathways in live cells.

ACKNOWLEDGMENTS

This work was supported by National Institutes of Health grant EB2060. H. Y. P. was also supported by National Research Service Awards 5T32 HL007675 and 1F32 GM087122.

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