INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Understanding the relationship between the dynamics of intracellular processes and their biological function is a problem of emerging fundamental importance in cell biology and biophysics. The processes that occur in living cells are complex because they involve interrelated motion of myriad intracellular species on a broad range of spatial and temporal scales. On the scale of small biological molecules (the scale of nanometers), substrates and second messengers diffuse from one enzymatic site to another. On the scale of large molecules (~10-30 nm), protein complexes are assembled and disassembled. Examples are the formation (and destruction) of replication complexes in the nucleus, of translation complexes in the cytosol, and of the permeability transition pore complex in mitochondria. Another important class of cell dynamics involves motion on the scale of the cellular and subcellular levels (0.1-10 µm); organelles may move in response to the timing of the cell cycle or to changes in metabolic conditions. A complete understanding of this complex picture in terms of biological function ultimately requires a detailed understanding of the dynamics of the processes involved.

Because the volumes associated with the intracellular compartment are extremely small, experimental methods for characterizing the movements of intracellular species must use a high degree of signal sensitivity. Traditionally, the most powerful tools are based on measurements of fluorescently labeled specimens due to the inherent sensitivity associated with the detection of optical signals emitted against a dark background. In recent years, fluorescence methods have undergone resurgence as a consequence of technological innovations in optical imaging and detection hardware. State-of-the-art detection equipment is capable of monitoring ultra-low fluorescence signals, in some cases from single isolated molecules (Xie and Trautman, 1998).

Digital video fluorescence microscopy (DVFM) (Saxton and Jacobson, 1997; Marcus, et al., 1996), fluorescence recovery after photobleaching (FRAP) (Chazotte and Hackenbrock, 1991; Partikian et al., 1998; Davoust et al., 1982), and fluorescence correlation spectroscopy (FCS) (Thompson, 1991; Keitling et al., 1998) are three well-established methods that have been successfully used to study intracellular motion. When applied individually, each method has both advantages and disadvantages. DVFM is a means to obtain detailed microscopic dynamical information. However, beyond qualitative interpretations, the meaning of DVFM measurements requires extensive image and computational analysis. Interpretation of FRAP and FCS experiments is more straightforward; collective or self-diffusion coefficients are measured directly, although their values are based on highly model-dependent analyses. Because FRAP and FCS measure ensemble average quantities, it is often difficult to interpret their meaning in terms of the underlying microscopic dynamics that give rise to them.

Here we introduce a new form of correlation spectroscopy, Fourier imaging correlation spectroscopy (FICS), which does not require a model-dependent analysis to extract dynamical information and is designed to fully characterize the dynamics of complex-fluid systems. We apply FICS together with DVFM to study the behavior of a structurally complex intracellular organelle: the mitochondrion.

Recent studies using fluorescence imaging have supported previous electron microscopy work in showing that the mitochondrial fraction of the cell can exist as a single interconnected tubular network, or reticulum (Bereiter-Hahn and Voth, 1994; Rizzuto et al., 1999). Typically, a reticulate mitochondrion extends throughout the cellular interior, filling approximately 20% of the cell volume. The tube-like filaments (~0.5 µm diameter cross-section) are plastic and constantly undergo changes in shape. The details of these motions and their physiological significance are poorly understood, although important functions of the organelle's plasticity have been speculated upon (Bereiter-Hahn and Voth, 1994; Rizzuto et al., 1998). Until now, detailed measurements of these dynamics have not been carried out.

In our FICS measurements, intracellular motion, such as that observed in a fluorescently labeled mitochondrial reticulum, can be detected through time-dependent fluctuations on an experimentally determined length scale, d_G, corresponding to an interference fringe pattern created by two intersecting laser beams. By changing the intersection angle of the laser beams, the wavelength of the detected fluctuations can be varied. The advantage of the FICS method over conventional FCS is that movements can be systematically studied as a function of spatial scale. In this way, it is possible to distinguish normal Fickian diffusion from anomalous diffusion, confined motion, or directed motion, all of which are believed to be important modes of intracellular transport (Saxton and Jacobson, 1997; Luby-Phelps, 1994; Madden and Herzfeld, 1993; Han and Herzfeld, 1993). The FICS measurements directly probe mitochondrial fluctuations over a wide dynamic range (~10⁴-10² sec). These measurements yield the time- and wave number-dependent diffusion coefficient and mean-square displacement through analysis of the dynamic structure function. The DVFM measurements generate mitochondrial filament trajectories. We show that Fourier analysis of the trajectories can be used to reconstruct the dynamic structure function, which is found to be in quantitative agreement with the measurements performed using FICS. By using both methods to study the same system, we directly compare statistically averaged dynamical quantities with their microscopic counterparts. Thus, we obtain a microscopic interpretation of the observed rates. The two methods used in combination are a powerful tool to study the dynamics of a complex intracellular organelle such as the mitochondrion.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Osteosarcoma cells (143B) were grown in 5-mm-diameter wells created by attaching a perforated layer of sylgard polymer to a glass coverslip. The cells were cultured using HG-DMEM medium supplemented with 10% fetal calf serum, and incubated in 5% CO₂ atmosphere until they reached a 60-80% confluency. For each measurement, the cells were stained for 20 min with 0.25 µM MitoTracker Orange or 0.25 µM JC-1 (Molecular Probes, Eugene, OR). Immediately before data acquisition, another coverslip was placed on top of the sylgard polymer to make a perforated sample chamber. This chamber was sufficient for maintaining the cells in good condition over the duration of a typical measurement (~45 min). For both DVFM and FICS measurements the temperature was maintained at 37 ± 0.5°C using a water-circulating heating stage equipped with active feedback.

Fourier imaging correlation spectroscopy

The FICS method is described in detail by Knowles et al. (2000). FICS is a new technique that we recently implemented to measure the dynamics of fluorescently labeled complex fluids over a wide dynamic range (~10⁴-10² sec) and as a function of spatial scale (~5 × 10⁷-10⁴ m). Although related methods have been used to study liquid-state dynamics (Hattori et al., 1996; Davoust et al., 1982; Hanson, et al., 1998), this is the first application of a fluorescence experiment that directly measures the time-dependent trajectory of a spatial Fourier component of the fluid density distribution. In our FICS measurements, the experimental observable is the time correlation function (the statistical-mechanical dynamic structure function) that reflects the growth and decay of fluctuations in a spatial Fourier component of the mitochondrial filament areal density profile with wavelength 2k_G¹. Here k_G (= 2d_G¹) is the optically detected wave number. Roughly speaking, the decay time associated with a particular value of k_G is given by ₀ = [D₀k_G²]¹, which is the time required for an unhindered fluorescently labeled filament to diffuse (with diffusion coefficient D₀) the distance k_G¹. The range of k_G probed is significant when compared to key structural features of the mitochondrial reticulum. Although the cross-sectional diameter of a typical filament is ~0.5 µm, the average contour length and the average separation between inter-filament connections is on the order of several microns. For the FICS measurements reported in this work, the range of wave numbers probed is 0.5  2k¹  1.2 µm. Thus, our measurements probe the microscopic dynamics of local filament regions.

We show in Fig. 1 a schematic of the FICS apparatus that we assembled and have used in this study. The sample chamber is held on the stage of a microscope and placed at the focus of two intersecting laser beams. The excitation source is the continuous wave frequency doubled output of a Spectra Physics Nd:YAG laser (_ex = 532 nm); its output power (measured just before sample incidence) is typically set to 1 mW. The laser beam is divided into two optical paths by a Fresnel-rhomb prism and polarizing beam splitter. The transmitted S-polarization component of the beam is rotated 90° using a periscope to match the P-polarization of the reflected beam. The transmitted beam is further passed through an electro-optic phase modulator (Conoptics, Danbury, CT), and then focused onto the sample using a long focal length lens (f = 40 cm). The second beam is reflected by a corner cube mirror mounted on a translation stage before being directed through an identical lens onto the sample chamber. The two beams produce an intensity interference fringe pattern, with adjustable spatial period d_G, inside the sample. The fringe spacing depends on the intersection angle, , between the two beams (Fleming, 1986):

(1)

The fringe spacing, d_G, can be adjusted continuously between tens of microns (for the case of small ) and _ex/2 (for the case of counter propagating beams).

View larger version (48K): [in this window] [in a new window]   FIGURE 1   Schematic illustration of the FICS apparatus used in the reported studies.

The fluorescence emitted from the overlap of the labeled filaments and the oscillatory excitation fringe pattern is imaged onto a detector using a fused silica objective lens (Plan Fluotar, 100×, N.A. = 1.3, oil immersion, Leica, Deerfield, IL) and eyepiece (5×, Zeiss, Thornwood, NY). The image depth-of-field is limited by placing an adjustable aperture (~50 µm) at the focal plane conjugate to the sample. For the FICS measurements, the emission is coupled into a multimode optical fiber (3M). The emission from the transmitting end of the fiber is imaged onto a thermoelectrically cooled photomultiplier tube (R3896, Hamamatsu, Bridgewater, NJ) after filtration by an interference filter (central wavelength 590 nm, bandwidth 10 nm, transmission efficiency 90%, CVI Laser, Livermore, CA) and an excitation barrier filter (532 nm). At any instant in time, the oscillatory excitation profile picks out a small set of spatial Fourier components of the labeled particle distribution. There is a primary component at wavenumber k_G = |k_G| = 2d_G¹, in addition to a |k| = 0 component associated with the mean fluorescent light level, and a band of small-k contributions associated with the Gaussian envelope of the illuminated region. Temporal fluctuations in the integrated fluorescence intensity, I(t) = I(t)  I, reflect the growth and decay of the spatial Fourier components represented by the image. Slow fluctuations of the chromophore distribution associated with the small-k spatial components arise from filaments moving in and out of the illuminated Gaussian envelope and from slow drifts in the alignment of the laser spots. Other components of the signal include low-frequency mechanical vibrations and 1/f shot-noise in the detection electronics.

Fluctuations of the signal due solely to number density fluctuations at wavenumber k_G are selectively measured using the method of lock-in detection. A frequency generator (Keithley) is used to send an amplified saw-tooth waveform to the phase modulator to drive the relative phases of the two beams from 0 to 2 at a frequency, _G, of 10 kHz. The excitation fringe pattern is thus swept across the illuminated sample region at a velocity, _G (=_G/k_G), greater than that with which a filament can travel the distance 2k_G¹. The modulated signal output of the photomultiplier tube is detected using a lock-in amplifier (Stanford Research Systems) that is referenced to the signal waveform used to drive the phase modulator. A personal computer records separately (1) the average background fluorescence intensity, I₀(0) (DC signal component, defined below), (2) the instantaneous fluorescence modulation amplitude, A(t) = I₀|(k_G, t)| (AC signal component, defined below), which arises due to the sweeping of the fringe pattern and whose magnitude varies as a result of filament fluctuations at k = k_G, and (3) the laser excitation power. All contributions to the noise that are not correlated with the modulation frequency (including filament fluctuations corresponding to k  k_G) are suppressed.

FICS was used to study the dynamics of mitochondria in cells stained with JC-1 and MitoTracker Orange. Multiple experiments were performed at three different fringe spacings (d_G = 0.55, 0.82, and 1.0 µm). For each experiment, 16,000 data points were collected at an acquisition frequency of 8 Hz. Under these conditions, the signal-to-background ratio of the modulated fluorescence amplitude, A^21/2/(0), was found to be ~50%. The extent of photodegradation over the duration of a 30-minute test measurement represented less than 20% loss of the total fluorescence signal. In practice, the total fluorescence intensity, after being corrected for drifts in laser power (less than ±1%), was used to normalize the time-dependent modulation amplitude, effectively removing the influence of photodegradation on the overall fluctuation signal. To determine the effects of laser-induced photodamage on our measurements, we performed a power-dependence study. Laser excitation intensities up to 10 mW resulted in identical autocorrelation functions to those obtained using 1 mW. However, the amount of photodegradation was significantly increased, resulting in a 90% signal loss. Thus, at the relatively low excitation powers used in these studies, photodamage did not affect our measurements of mitochondrial dynamics.

The total instantaneous fluorescence intensity emitted from the excitation grating, I_G(t), is proportional to the spatial overlap of the time-dependent oscillatory excitation profile and the time-dependent distribution of fluorescently labeled filaments, C(r, t) [see Eq. 9, below] (Knowles et al., 2000). In the limit where the laser beam diameter is much larger than d_G, the excitation profile can be well approximated by an infinite two-dimensional fringe pattern modulated in the direction of the x-axis, and the signal can be written

(2)

where _G is the velocity with which the fringe pattern travels across the sample, (k_G, t) is the spatial Fourier transform of the filament distribution, C(r, t), evaluated at k = k_G and  is the phase angle associated with , namely  = tan¹[Im /Re ]. The vectors k_G and _G are antiparallel and indicate the propagation direction of the fringe pattern. The constants  and I₀ represent the luminescence efficiency and incident laser intensity, respectively. Eq. 2 shows that the total signal is composed of a stationary and modulated component. The stationary component, I₀(0), corresponds to the mean fluorescence background, whereas the modulated component contains information about the distribution (k_G, t) through its modulus, ||, and phase angle . The time-dependent fluctuations of I_G(t) [I_G(t) = I_G(t)  I_G] arise for two reasons. As the fringe pattern is swept across the sample with velocity _G, the total fluorescence signal is modulated at the angular frequency k_GG. The modulation amplitude, A(t) = ||, depends on the extent to which the heterogeneous spatial distribution of filaments contains some periodicity with wavelength d_G. The velocity _G is set to an arbitrary value greater than the average velocity of the mitochondrial filaments. As C(r, t) fluctuates in time due to the "slow" motion of the labeled filaments, its periodicity with wavelength d_G also fluctuates, resulting in slow variation of the modulation amplitude from its average value [A(t) = A(t)  A]. The time-dependence of A(t) contains the k-dependent dynamical information we wish to study.

Using a diffusion equation of motion, we obtain the normalized autocorrelation function of I_G(t) (Hattori et al., 1996),

(3)

The first term in Eq. 3 represents the background motion of filaments entering or leaving the Gaussian envelope of the two intersecting laser beams, with b ( 100 µm) the 1/e beam radius and D_b the characteristic diffusion coefficient of this process. The second term in Eq. 3, which oscillates at the angular frequency k_GG, describes the local filament mobility characterized by the so-called "effective" diffusion coefficient, D_eff = (k = k_G, ), observed on the length scale d_G and incremental time .

To selectively measure the second term in Eq. 3, we use lock-in amplification. The lock-in amplifier rejects the relatively large DC component of I_G(t) and measures its relatively small instantaneous modulation amplitude, A(t). Because fluctuations in A(t) reflect the motion of the mitochondrial filaments at wave number k_G, we can write the normalized autocorrelation function of A²(t) (Hattori, 1996)

(4)

G_k() is a wave number-dependent time-correlation function whose decay is characterized by the same effective diffusion coefficient that appears in the second term of Eq. 3. The connection between G_k() and the microscopic motion of mitochondrial filaments can be understood in terms of liquid state theory (Balucani and Zoppi, 1994). According to Eq. 2, the detected fluorescence signal can be interpreted as an instantaneous Fourier component of the filament distribution,
at wavevector k_G. The temporal autocorrelation function of (k_G, t) is proportional to the microscopic dynamic structure of the mitochondrial filaments,

(5)

where k = |k|. Because we are interested in high-k measurements applied to semidilute systems of entangled filaments, the cross terms in Eq. 5 do not contribute to their respective sums, leaving only the self terms. Thus, Eq. 5 reduces to (Berne and Pecora, 1976)

(6)

where F_S(k, ) is the self-part of the intermediate scattering function.

To relate Eq. 6 to the effective diffusion coefficient, we use the Gaussian model for single particle motion (Berne and Pecora, 1976). The Gaussian model makes use of the fact that the time scale associated with observation of the local filament displacements is large compared to the relaxation time of the velocity autocorrelation function of the local filament positions. In this case, [r(t)  r(t + )] may be treated as a Gaussian random variable, which leads Eq. 6 to take the following form for two dimensions,

(7)

where W() = [r(t)  r(t + )]²/4 is the effective two-dimensional mean square displacement of a local filament region and _S(k, ) = W()/ is the effective self-diffusion coefficient measured at wave number k. Comparison between Eqs. 4 and 7 leads to

(8)

We conclude that the experimental observable measured in our FICS experiments is directly related to the self-displacements of local mitochondrial filaments as described by Eq. 8.

The similarity between Eqs. 4 and 7 is not coincidental. In each case, the assumption of Fickian dynamics was made. For a system that strictly obeys Fickian dynamics, the effective self-diffusion coefficient is expected to be constant whereas the mean square displacement is a linear increasing function of time. For a system that does not obey Fickian dynamics, the diffusion coefficient is time-dependent. The extent to which _S(k, ) deviates from Fickian behavior is an indication of the system exhibiting, on average, a mode of motion more complex than pure diffusion.

Digital video fluorescence microscopy

DVFM is a powerful technique that has been applied to the study of biological systems (Rizzuto et al., 1998b; Saxton and Jacobson, 1997) and to complex fluids (Crocker and Grier, 1996; Marcus et al., 1996, 1999).

We perform DVFM measurements on mitochondria samples using a Zeiss UEM fluorescence microscope with a 100×, numerical aperture 1.3, oil immersion objective lens (Ultrafluar, Zeiss). The excitation source is a Coherent Nd:YAG laser operating in continuous wave (cw) mode at 532 nm; its output power is typically set to below ~1 mW (as detected at the sample). Samples are exposed to the excitation light by epi-illumination and the fluorescence emission is relayed to the camera eyepiece via a dichroic beamsplitter (550-615-nm transmission). Fluorescence images of the sample are collected using an image intensified charge coupled device (CCD) digital video camera mounted to the camera eyepiece (16 bit, Gen V, Princeton Instruments, Trenton, NJ). The frame speed of the CCD is adjustable; images are acquired at a rate ranging between 0.05 and 1 Hz. Exposure times for each image is typically set within the range 0.8-1.0 sec. During the time intervals between successive frames, a mechanical shutter is used to block the laser excitation such that the total sample exposure time does not exceed 1 sec per captured image. The Princeton Instruments frame grabber supplied with the CCD is used to digitize sequences of 512 × 512 square pixel frames. A typical run consists of 100 frames in sequence, corresponding to roughly 250 Mbytes of data. All image-processing procedures are implemented using IDL (Research Systems, Inc.), a programming language optimized for visual data analysis. The pixel length is calibrated by imaging a transmission electron microscope grid of known scale. The aspect ratio is determined to be 1 ± 0.1 and the calibrated pixel dimension is 1 pixel = 0.178 µm for 100× magnification and 1 pixel = 0.0699 µm for 250× magnification.

Unlike FICS, the observable in a DVFM experiment is a complete set of two-dimensional N filament position trajectories,

(9)

Here we designate the filament positions as a locus of points that define the instantaneous configuration of all filaments visible in the image. In DVFM, the minimum sampling time interval is determined by the time step between consecutive configurations. The experimental procedure is to image a representative area of the sample onto the detector face of a high resolution CCD video camera. The video signal is subsequently converted into storable digitized information using a frame grabber. The process of transforming the information contained in a sequence of digitized images into the time-dependent density profile described by Eq. 9 is given by a prescription involving five logical steps. Here we provide a rough outline of the procedure.

1.	Image restoration: The raw data images usually contain various defects that hinder immediate analysis. These include long wavelength contrast gradients and random pixel noise. The background artifacts are nominally due to uneven illumination or sensitivity of the camera pixels, whereas pixel noise is associated with the instrument response of the CCD camera and the frame grabber. Because pixel noise is nearly random with a correlation length n equal to one pixel, it is greatly reduced by convolving the raw data image with a Gaussian surface of half-width n. This operation suppresses the noise without noticeably decreasing the contrast. The resulting "noise reduced" image is further enhanced by subtracting off the "background" image. This background is constructed by performing a boxcar average of the raw data with a step size equal to 2w + 1, where w is the apparent feature radius measured in pixels. The end result is an estimate of an ideal image that can be further processed.
2.	Location of filament positions: The filtered images are analyzed to determine the locations of local brightness maxima. A pixel position is designated as a local maximum if only one other pixel within a distance w has a larger value. Typically, the number of candidate local maxima found is larger than the number of filament positions in the frame. Because the maxima corresponding to the filament positions are the brightest of those found, only the brightest 30% of the candidates are accepted.
3.	Refining candidate positions: The local maximum algorithm described by steps 1 and 2 is sufficient to resolve filament positions to within half a pixel. The spatial resolution is improved by calculating the brightness-weighted centroid positions from the spatial integral of circular areas with radius w centered at the original uncorrected positions. This correction is smaller than 0.5 pixel and has the overall effect of improving the resolution to 0.1 pixel.
4.	Candidate filament position discrimination: In addition to the integrated brightness within a circular area of radius w centered about each candidate position (m0), the second moment of the brightness distribution (m2) is also calculated. It is found that filament and nonfilament candidates form two distinct well-separated distributions in the (m0, m2) plane. The candidates corresponding to the true filament positions are selected based on this criterion.
5.	Linking sequential configurations into filament position trajectories: In this final step, it is necessary to determine which filament positions in a given image correspond to subsequent positions in later images. For dilute suspensions, the mean separation is much larger than single-filament position displacements, which are typically much smaller than the dimensions of a filament diameter. Therefore, all trajectory displacements of interest are easily identified because they fall within an empirically determined cutoff range.

Several properties can be calculated from the trajectory data (Eq. 9) using the methods of statistical mechanics (Marcus, et al., 1996, 1999). Here we focus on the intermediate scattering function to compare with our FICS results. In principle, it is possible to calculate F_S(k, ) directly from the trajectory data. This is accomplished in two ways. First, we consider the microscopic definition,

(10)

where (k, t) is the Fourier transform of the spatial filament position density Eq. 9 given by

(11)

For nonzero k, the combination of Eqs. 11, 9, and 10 results in an expression for F(k, ) that is an explicit function of r(t) given by the statistical average Eq. 5. This expression is evaluated numerically using standard computer simulation techniques (Allen and Tildesley, 1987). Alternatively, image-processing algorithms are used to calculate F(k, ) from "idealized" images constructed from the filament trajectories. These ideal images are numerically Fourier transformed in two dimensions using standard fast Fourier transform algorithms. Eq. 10 is evaluated by calculating the time autocorrelation function of the Fourier space images for a particular time interval, averaged over many filament configurations.

Using these two independent methods of evaluating F(k, ) from the microscopic data, we were able to check for self-consistency of the results for a single set of filament trajectories. We also examined the differences between the full intermediate scattering function and the self part, F_S(k, ). As discussed above, neglecting the cross terms (j  i) in Eq. 5 leads to an expression (Eq. 6) for F_S(k, ). For the microscopy data presented in this work, the filament concentrations were small enough that the self and full intermediate scattering functions were indistinguishable by the methods described above. Therefore, the previous assertion that these measurements correspond to the microscopic regime was experimentally verified.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In Fig. 2 we show three-dimensional reconstructions of confocal fluorescence micrographs of an osteosarcoma cell transfected with green fluorescent protein targeted to the matrix space (Fig. 2 A) and a high-power magnification image of mitochondria stained with JC-1 (Fig. 2 B). In both images, the mitochondrion of the cell is fluorescently labeled and appears as a single interconnected tubular network of filaments (i.e., a reticulum). Additional work using serial-sectioning techniques and transmission electron microscopy confirms that the mitochondrion exists as a reticulum in these cells (Gilkerson, et al., 2000). JC-1 is a positively charged carbocyanine dye that is known to be a quantitative fluorescence indicator of membrane potential, (Reers et al., 1991, 1995; Salvioli et al., 1997). Under favorable physiological conditions and above a critical threshold concentration, JC-1 forms a concentration-dependent fluorescent nematic phase consisting of J-aggregates. When excited at 488 nm, the monomers exhibit an emission maximum at 527 nm (green regions) and J-aggregates at 590 nm (red regions). Increasing JC-1 concentration results in a proportionate rise in J-aggregate fluorescence without affecting monomer fluorescence. The membrane potential of energized mitochondria is polarized such that the matrix space has a net negative charge. Local regions of the membrane that are energized promote an uptake of JC-1 into the matrix with subsequent formation of J-aggregates.

View larger version (93K): [in this window] [in a new window]   FIGURE 2   (A) Three-dimensional reconstruction of a confocal fluorescence image of an osteosarcoma cell labeled with a green fluorescent protein construct targeted to the mitochondrial matrix space. The reticulate structure of the mitochondria is evident. (B) High-magnification image of reticulate mitochondrial filaments stained with JC-1 dye.

It is evident from Fig. 2 B that the spatial distribution of in reticulate mitochondria, as visualized by JC-1 monomer/J-aggregate emission, appears heterogeneous under control physiological conditions. This spatial heterogeneity is sensitive to the metabolic state of the cell. In Fig. 3, we show fluorescence micrographs of JC-1-labeled cells after exposure to various drugs (listed in Table 1). Nigericin is an ionophore that exchanges K⁺ and H⁺ across the mitochondrial inner membrane, resulting in uncoupling of respiration from adenosine triphosphate production. The net effect of Nigericin treatment is the hyperpolarization of the mitochondrial inner membrane. The spatial distribution of becomes uniformly large throughout the reticulum after ~30 min incubation with Nigericin (Fig. 3 B). Inhibition of respiration can be achieved with Antimycin A, which inhibits the activity of mitochondrial respiratory chain complex III. Cells treated with Antimycin A (~10-min incubation) show a progressive decrease in local membrane regions with high (Fig. 3 C). Staurosporine is a protein kinase inhibitor that induces apoptosis (programmed cell death). Dramatic changes in mitochondrial membrane morphology are observed in cells that have been treated with Staurosporine (~4-h incubation). This drug has the initial effect of hyperpolarizing the mitochondrial membrane accompanied by membrane swelling, followed by the disruption of mitochondria structure with the formation of mega-mitochondria and cell blebbing (Fig. 3 D).

View larger version (63K): [in this window] [in a new window]   FIGURE 3   Osteosarcoma cells stained with JC-1. Orange regions have a higher mitochondrial membrane potential than green regions. (A) Control physiological state; (B) Uncoupling of respiration induced by Nigericin (10 µM); (C) Inhibition of respiration induced by Antimycin (10 µg/ml); (D) Apoptosis induced by Staurosporine (5 µM).

We studied the motion of hyperpolarized regions of the mitochondrial membrane under various conditions by detecting only those regions of the images that emit at 590 ± 5 nm. Control experiments were also performed on cells treated with MitoTracker Orange (CM-H₂TMRos), a rhodamine-based dye that becomes fluorescent after it is oxidized in actively respiring regions of the mitochondria and irreversibly binds to mitochondrial proteins. MitoTracker Orange is insensitive to transient behavior of . For cells treated with either JC-1 or MitoTracker Orange, the excitation and detection wavelengths were 532 and 590 nm, respectively.

When these cells are visualized in the fluorescence microscope, movements of the reticulum filaments can be observed. In Fig. 4, we show a single restored image frame taken from a DVFM data set of a cell treated with MitoTracker Orange under control physiological conditions. Also shown are the assignments of local filament positions and the associated trajectories of the full 100-frame sequence (1 frame s¹). The pathways taken by individual filament regions appear to be unbiased by the possible presence of net flows in the cytosol or cytoskeletal activity. This assertion was tested by constructing displacement histograms for all N filament positions as a function of time (see Fig. 10, below) and observing that the resulting time-dependent spatial probability distributions are well described as symmetric distributions with a mean value equal to zero.

View larger version (54K): [in this window] [in a new window]   FIGURE 4   (A) Digitally processed fluorescence image of osteosarcoma cells labeled with MitoTracker Orange. Filament positions are determined by local pixel brightness and shape (inset) according to the prescription given in the text. (B) Trajectories of filament positions are computed from 100 sequential frames acquired at 0.172 frame s1.

The movement of the reticulum results in complicated spatial trajectories and multiexponential k-dependent time-correlation functions. We now examine this behavior systematically through the results of FICS and DVFM experiments. Our microscopic interpretation of these processes is summarized in the Discussion section.

To fully characterize the dynamic state of reticulate mitochondria, we use both FICS and DVFM. Using FICS, the fluctuations of the modulated fluorescence amplitude, A(t), are used to construct time-correlation functions, G_k(), for specific fringe spacings. These correlation functions are simply related to the self-intermediate scattering function, F_S(k_G, ), according to Eq. 8. The correlation function is determined by averaging the fluctuations of the square amplitude of the modulated fluorescence signal over t_max time origins,

(12)

The decay time of the autocorrelation function is a measure of the time required for a labeled region to move the distance k_G¹. The information contained in G_k() is a measure of the complexity of the motion. If G_k() is a multiexponential decay, more than one type of motion is responsible for the fluorescence fluctuations detected at wave number k and time . Figure 5 displays plots of F_S(k, ) for JC-1-labeled cells under control physiological conditions (Fig. 5 A) and after incubation with Nigericin (Fig. 5 B). In each case, measurements were performed at three different wave numbers corresponding to the fringe spacings d_G = 0.55, 0.82, and 1.0 µm.

View larger version (30K): [in this window] [in a new window]   FIGURE 5   Wave number-dependent time-correlation functions, Gk(), obtained from FICS experiments performed on JC-1 labeled cells. Measurements correspond to three different fringe spacings. (A) Control physiological conditions; (B) After exposure to Nigericin.

From the autocorrelation functions, we construct the time-dependent effective mean square displacement, W(), by inverting Eq. 8:

(13)

In Fig. 6, A and B, we display plots of W_eff() corresponding to the data shown in Fig. 5. As noted previously, the mean square displacement is an independent function of k_G for systems undergoing purely diffusive motion. For a purely diffusive system, W_eff() = D, and all measurements made at different fringe spacings yield a single line with slope D. Our measurements of W_eff() taken at fixed wave number are clearly k-dependent and exhibit time windows with distinctly different slopes. For both control (Fig. 6 A) and Nigericin-treated cells (Fig. 6 B), the mean square displacement corresponding to d_G = 0.55 µm is distinctly smaller at all times than for 0.82 and 1.0 µm. At very short times ( < 1 s), local filament regions primarily undergo independent motion with short-time self-diffusion coefficient D_S^S. For intermediate times (1 s <  < 20 s) and for short-range displacements (d_G  0.55 µm) the local filament regions begin to experience interactions with their surroundings. The effect of these short-range interactions is to modify the self-diffusion coefficient on the time scale that these interactions occur (_I ~ 15 s) to a smaller value than D_S^S. Here we define the time scale of this transition in dynamic behavior as _I. At these intermediate time and length scales, the time- and k-dependent functional form of W_eff() is indicative of a kinetic transition from short-time filament motion to a modified long-time diffusion, _S^L, that is effectively "dressed" by collective interactions. Such collective interactions are the mechanism that gives rise to long-range filament displacements, which are probed by large fringe-spacing measurements. In the limit of sufficiently large fringe spacing (short wave number) and time scales long compared to _I, the effective diffusion coefficient is no longer a "self" quantity, but rather a reflection of the decay of fluctuations in the collective filament distribution of large spatial extent. In this "hydrodynamic" limit, _S(k  0,   ) = D_C can be identified as the same collective diffusion coefficient as would be measured in conventional gradient-diffusion measurements (Boon and Yip, 1980).

View larger version (31K): [in this window] [in a new window]   FIGURE 6   Time-dependent effective mean-square displacement, Weff() = ln[Gk()]/2k2, constructed from FICS data. (A) Control physiological conditions; (B) After exposure to Nigericin.

The kinetic behavior of the mitochondrion can be examined directly from the time- and wave number-dependent effective diffusion coefficient. We calculate _S(k, ) from W() according to Eq. 7. In Fig. 7, A and B, we display plots of _S(k, ) corresponding to the data shown in Figs. 5 and 6. For intermediate times (1 s <  < 60 s) and fixed k, _S(k, ) decreases continuously, which is consistent with our interpretation that the time-dependence of W_eff() is the signature of a kinetic transition from local filament short-time motion to a dressed collective long-time diffusion. The values for _S(k, ) lie in the range 3.5-0.5 × 10¹² cm² s¹ and are listed in Tables 2 and 3. We now examine the k-dependence of _S(k, ) at fixed . In Fig. 7, A and B, the effective diffusion coefficient at all times is consistently smaller for large k (or small filament probe volume, d_G ~ 0.55 µm) than it is for progressively decreasing k (or incrementally large filament probe volumes, d_G ~ 0.55 µm) than it is for progressively decreasing k (or incrementally large filament probe volumes, d_G ~ 0.82, 1.0 µm). This behavior is a well-known property of the dynamics of complex fluids where the rates of collective particle fluctuations, as a consequence of local structure, may be greater than the corresponding rates of single-particle motion (Boon and Yip, 1980; Berne and Pecora, 1976). We note that for all k, _S(k, ) reaches its long-time asymptotic value for  > 60 s. From the available data, we observe that, for long times and small k, the diffusion coefficient appears to approach a limiting value, _C^L. Our observations suggest that the kinetic transition from short- to long-time dynamic behavior is the result of a structural rearrangement of the local mitochondrial filament environment in the range of length scales 0.55 µm < d_G < 0.82 µm for Nigericin-treated cells (Fig. 7 B), and 0.82 µm < d_G  1.0 µm for cells under control physiological conditions (Fig. 7 A). We show below that this long-time long-range motion is related to the structural reorganization of cytoskeletal filaments and to the metabolic state of the cell. We further examine the microscopic details of this process in our discussion of the DVFM data below.

View larger version (31K): [in this window] [in a new window]   FIGURE 7   Wave number and time-dependent effective diffusion coefficient, S(k, ), constructed from FICS data according to Eq. 7. (A) Control physiological conditions; (B) After exposure to Nigericin.

To examine the effects of metabolic activity on mitochondrial dynamics, we used FICS to measure W_eff() (Eq. 13) for JC-1-labeled cells after incubation with drugs known to alter metabolism. Figure 8 displays direct comparisons between measurements of W_eff() for control cells and for those treated with the drugs listed in Table 1. We note that the slopes of the corresponding curves define the effective diffusion coefficient. The fringe spacing for these measurements was set to 0.82 µm. In Fig. 8 A, we examine Nigericin-treated cells. Nigericin is an uncoupler of respiration. Although Nigericin has the effect of hyperpolarizing the mitochondrial membrane (see Fig. 3 B), ATP synthesis through the respiratory chain pathway is effectively turned off. There is, however, some ATP production through glycolysis. For short times ( < 15 s) the data for the Nigericin-treated cells is indistinguishable from the corresponding control-cell measurement. For long times ( > 15 s), the slope of W_eff() is a factor of 1.5 smaller for Nigericin in comparison to control cells. We note that the transition time (~15 s) is the same as the interaction time scale, _I, obtained from our k-dependent study. Hence, uncoupling of respiration causes the collective interactions that lead to long-range filament displacements to be significantly slowed but not eliminated.

View larger version (27K): [in this window] [in a new window]   FIGURE 8   The effect of the metabolic state on reticulate mitochondrial motion observed by FICS. The effective mean-square displacement, Weff() = ln[Gk()]/2k2, is plotted against  for fixed wave length 2kG1 = 0.82 µm. Each panel represents a comparison between measurements performed in the presence and absence of drug. (A) Uncoupling of respiration induced by Nigericin (10 µM); (B) Inhibition of respiration induced by Antimycin (10 µg/ml); (C) Actin filament depolymerization induced by Latrunculin A (10 µM); (D) Apoptosis induced by Staurosporine (5 µM).

In Fig. 8 B, we examine the effects of Antimycin A. Antimycin A is an inhibitor of respiration and induces the progressive loss of mitochondrial membrane potential (see Fig. 3 C). Similar to Nigericin, for cells treated with Antimycin A, mitochondrial ATP production is completely halted. Measurements begun after 10-min incubation with Antimycin A show almost identical behavior at short and long times to that observed from Nigericin-treated cells. Both Nigericin- and Antimycin-treated cells show a decreased rate of long-range filament motion. This finding is consistent with the hypothesis that the origin of the long-range filament motion is due to the action of ATP-driven cytoskeletal filaments. Because both Nigericin and Antimycin A affect the energetic level of the cell by inhibiting the production of mitochondrial ATP, this observation suggests that cytoskeletal-assisted motion of mitochondria depends on normal respiration.

In general, we find that the short-time ( < _I) short-range motion of mitochondrial filaments is independent of metabolic activity. Figure 8 C shows our results for cells treated with Latrunculin A that depolymerizes actin filaments, a major component of the cytoskeleton. Our findings are similar to those for Antimycin A- and Nigericin-treated cells. For short times, the data corresponding to control and actin-depleted cells are indistinguishable, whereas for  > 50 s _I, the long-range motion is completely turned off. Our observation that short-range motion is independent of metabolic state, and the normal activity of cytoskeletal filaments suggests that this motion is a consequence of the mechanical properties of the reticulate structure. We expect the short-time motion to exhibit sensitivity to temperature that depends on the elastic properties of the membrane.

Our interpretation of the short-time dynamical behavior of the reticulum having a purely elastic origin is further supported by our measurements using Staurosporine (5 µM), a protein kinase inhibitor that induces apoptosis. As shown in Fig. 3 D, this drug dramatically affects mitochondrial structure with the initial swelling and eventual disruption of the membrane. Our comparison between control cells and those treated with Staurosporine are shown in Fig. 8 D. In this case, both short- and long-time mitochondrial motions are dramatically reduced. The reduction of the effective mean square displacement at short times is consistent with the expected behavior of a swelled membrane because its surface tension is much larger than that for control cells. The absence of motion at long times is consistent with the fact that oxidative phosphorylation becomes uncoupled early in the programmed cell death process (Mignotte and Vayssiere, 1998). The lack of long-time motion is an indication that cytoskeletal activity is shut down under apoptotic conditions.

As mentioned previously, we performed DVFM measurements so that a microscopic mechanism could be assigned to the rates observed by FICS. For this purpose, it is important to establish that the same processes are probed using the two techniques. Figure 9 displays a direct comparison of F_S(k, ) determined from the FICS data of control cells (solid lines) and from the DVFM data (circles) as a function of  for three different wave numbers. The FICS data were obtained using Eq. 8, whereas the microscopy data were calculated as described in the Methods section. There is very good agreement between the FICS and DVFM data for all three fringe spacings.

View larger version (27K): [in this window] [in a new window]   FIGURE 9   Comparison between JC-1 stained mitochondrial filament dynamic structure function, FS(k, ), computed from FICS data (solid lines) and from DVFM (circles). The latter were obtained by Fourier inversion of DVFM trajectories. The comparison is made for three wave numbers as indicated.

For the DVFM experiments, Osteosarcoma cells (143B) were cultured and stained with either MitoTracker Orange or JC-1. Before and after each measurement, the cell morphology was observed in transmitted light to ensure that experimentally induced cell death had not occurred. In Fig. 10, we display histograms of mitochondrial filament displacements in JC-1 labeled cells constructed from DVFM trajectories. To avoid possible image-processing artifacts such as pixel biasing, we required that consistent and reproducible results were obtained from measurements performed at 100× (Fig. 10 A) and 250× (Fig. 10 B) magnification. We note that the time-dependent shape of the distributions is independent of magnification. These distributions are formally described as the space-time correlation function G_S(x, ), which is the probability that a given filament position suffers a positive or negative displacement projected onto the x-axis during a time interval . This is the self part of the van Hove correlation function, defined as

(14)

For the case of a system undergoing purely diffusive motion, G_S(x, ) is a single-mode Gaussian distribution with a second moment (given by W() = [x₁(t)  x₁(t + )]²/2) that increases as a linear function of time. The spatial probability distributions shown in Fig. 10 are symmetric and well behaved. Nevertheless, they cannot be described as simple Gaussian distributions. For intermediate times ( ~ _I), a broad but distinct secondary peak can be seen to develop in G_S(x, ) centered at x = ±0.8 µm. At long times (  _I), the distribution becomes single mode. We see that the primary peak (centered at x = 0) represents randomly oriented short-range displacements, and the secondary peaks are due to the occurrence of long-range cooperative hops. The maximum value of the secondary peaks is most pronounced when  ~ _I = 15 s. The two types of dynamic processes identified in the distributions G_S(x, ) correspond to the short-time thermally activated process and the long-time ATP-driven process observed in our FICS experiments. The interaction time and distance scales measured by FICS (_I ~ 15 s, d_I ~ 0.8 µm) are in close agreement with the characteristic time and length scales associated with the secondary peak in G_S(x, ). Thus, cooperative dynamics are the collective interactions that give rise to the observed kinetic transition from short-time local motion to long-time dressed collective diffusion, as discussed above. It is known that the secondary peaks in the distributions G_S(x, ) would not be present unless the long-range hops occur in a cooperative fashion (Marcus et al., 1999). That is, within a time period in which a labeled filament position undergoes a long-range displacement, there is a high probability that another nearby filament position will also undergo a long-range displacement. This is consistent with the interpretation that the majority of long-range hopping displacements occur along the contour length of a given mitochondrial filament.

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