Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy1

doi:10.1006/jmbi.2000.3692 available online at http://www.idealibrary.com on

J. Mol. Biol. (2000) 298, 677±689

Anomalous Diffusion of Fluorescent Probes Inside Living Cell Nuclei Investigated by Spatially-resolved Fluorescence Correlation Spectroscopy Malte Wachsmuth, Waldemar Waldeck and JoÈrg Langowski* Division Biophysics of Macromolecules, German Cancer Research Center, Im Neuenheimer Feld 280 D-69120 Heidelberg Germany

We have investigated spatial variations of the diffusion behavior of the green ¯uorescent protein mutant EGFP (F64L/S65T) and of the EGFP-bgalactosidase fusion protein in living cells with ¯uorescence correlation spectroscopy. Our ¯uorescence correlation spectroscopy device, in connection with a precision x-y translation stage, provides submicron spatial resolution and a detection volume smaller than a femtoliter. The ¯uorescence ¯uctuations in cell lines expressing EGFP are caused by molecular diffusion as well as a possible internal and a pH-dependent external protonation process of the EGFP chromophore. The latter processes result in two apparent non¯uorescent states that have to be taken into account when evaluating the ¯uorescence correlation spectroscopy data. The diffusional contribution deviates from ideal behavior and depends on the position in the cell. The ¯uorescence correlation spectroscopy data can either be evaluated as a two component model with one fraction of the molecules undergoing free Brownian motion with a diffusion coef®cient approximately ®ve times smaller than in aqueous solution, and another fraction diffusing one or two orders of magnitude slower. This latter component is especially noticeable in the nuclei. Alternatively, we can ®t the data to an anomalous diffusion model where the time dependence of the diffusion serves as a measure for the degree of obstruction, which is large especially in nuclei. Possible mechanisms for this long tail behavior include corralling, immobile obstacles, and binding with a broad distribution of binding af®nities. The results are consistent with recent numerical models of the chromosome territory structure in the cell nucleus. # 2000 Academic Press

*Corresponding author

Keywords: anomalous diffusion; EGFP; ¯uorescence correlation spectroscopy; intracellular diffusion; nuclear structure

Introduction The architecture of the interphase nucleus and its physical properties have become a subject of major interest in recent years. However, the threedimensional arrangement of chromatin, functional, and structural components is still largely unknown, although evidence for the existence of chromosomal territories has emerged (Cremer et al., 1993; MuÈnkel et al., 1999). The structure inside these domains vitally in¯uences for example molecular transport and diffusion, which play an Abbreviations used: EGFP, enhanced green ¯uorescent protein; FCS, ¯uorescence correlation spectroscopy; ACF, autocorrelation function. E-mail address of the corresponding author: [email protected] 0022-2836/00/040677±13 $35.00/0

important role for processes like transcription, replication, or repair. In particular the combination of high-resolution, high-sensitivity optical microscopy techniques with in vivo labeling of speci®c compounds of the cellular protein machinery by green ¯uorescent protein (GFP)-tagging has opened the possibility to observe the dynamics of single macromolecules directly in the living cell (Pierce & Vale, 1999). The spatial resolution of such studies is limited by the resolving power of the microscope system used which is typically 0.3 mm in the lateral and 1 mm in the vertical direction for the best lenses available today (Langowski & Tewes, 1999). The time resolution in video microscopy is limited by the sample rate of the video system, which is typically 50 Hz and as many as 300 frames per second for very fast systems (Gabriel & Teissie, 1997). On the other # 2000 Academic Press

678 hand, the diffusion coef®cient of a medium size protein with radius R ˆ 2.5 nm in aqueous solution is D ˆ kBT/6pZR ˆ 86 mm2/s, thus the average dwell time in a 0.3 mm wide focus is t ˆ hr2i/ 6D ˆ 170 ms, much shorter than the limit given by the time resolution of video microscopy. For characterizing intracellular motions on length scales equal to or smaller than the resolution of the microscope, we therefore have to resort to other techniques. One possibility is not to observe the motion of individual molecules directly, but their concentration ¯uctuations in the focal volume of the microscope by ¯uorescence correlation spectroscopy (FCS); such measurements can be done on a much faster time scale. Today, FCS (Magde et al., 1972) is a well-established method to measure ¯uorescence intensity ¯uctuations from a microscopic illuminated volume (of the order of a femtoliter and smaller) containing only a few ¯uorochrome molecules (Eigen & Rigler, 1994; Rigler et al., 1993). The molecules traverse the observation volume by Brownian motion, leading to ¯uorescence ¯uctuations; another source of ¯uctuations are the photophysics of the ¯uorophore, because ``switching'' between ¯uorescent and non¯uorescent states will also lead to ¯uctuations. Through a time correlation analysis of the ¯uorescence ¯uctuations, the hydrodynamic and photophysical properties of the molecules are then accessible. Many recent FCS studies were focused on the investigation of interactions between biomolecules free in solution by measuring changes of hydrodynamic properties upon binding (Rigler & Widengren, 1993). However, since FCS is generally performed using confocal microscope optics (Qian & Elson, 1991; Rigler et al., 1993), it is also possible to probe cellular microenvironments that in¯uence the diffusion and intramolecular dynamics with high spatial resolution. This makes FCS an intrinsically calibrated, noninvasive sensing tool for intracellular properties which could also be extended into a powerful imaging technique. Since GFP and its mutants experience a growing interest as noninvasive ¯uorescent markers (Tsien, 1998), a number of studies have investigated its structure and the biochemical and photophysical properties (Brejc et al., 1997; Chattoraj et al., 1996; Ormo et al., 1996; Palm, 1998; Palm et al., 1997; Yang et al., 1996): A possible internal and a pH dependent external protonation process of the mutant EGFP (F64L/S65T) results in ``blinking'' and a strong pH-dependence of the ¯uorescence, and combined with the diffusion coef®cient, this can help to identify the ¯uorescence of EGFP expressing cells and to probe the local viscosity and pH with FCS. Diffusion processes in the cytoplasm have been investigated for several years, e.g. in (Kao et al., 1993; Seksek et al., 1997), but only a few studies applied FCS (Berland et al., 1995; Brock et al., 1998) or focused on the nucleus (Politz et al., 1998). The authors of (Schwille et al., 1999), e.g. found very

Intracellular Diffusion of EGFP

recently anomalous diffusion both for GFP and for small marker dyes in the cytoplasm and near the plasma membrane; the diffusion properties in the cell nucleus were not studied in particular. In this work, we analyze the spatially dependent diffusion of EGFP and the EGFP-b-galactosidase fusion protein in the cytoplasm and in the nucleus. This analysis also includes a detailed treatment of the effect of GFP blinking on the ¯uorescence correlation behavior. Our results show that the diffusion shows a substantially greater anomaly in the nucleus than in the cytoplasm. This indicates that for proteins of the size studied here, the fraction of obstacle-free accessible space is signi®cantly smaller in the nucleus. We compare our results with estimates of the volume occupancy of the nucleus by the chromatin ®ber and with our own recent model calculations (MuÈnkel et al., 1999; MuÈnkel & Langowski, 1998). The results con®rm a view of the nucleus as a network of chromatin and other intranuclear components surrounded by a cytosollike ¯uid rather than a homogenous viscous compartment.

Theory General FCS theory The conceptual and theoretical basis of FCS has been well established for years (e.g. Elson & Magde, 1974; Qian & Elson, 1991). Here, we only summarize those speci®c theoretical considerations that are necessary when dealing with FCS of EGFP in a cellular environment. Any dynamic process that affects the emission of ¯uorescent molecules in a solution causes ¯uctuations in the ¯uorescence signal F(t) that can be characterized by a normalized autocorrelation function (ACF): …1†

where d stands for the deviation from the mean value and t for the lag time.

Unobstructed diffusional contribution Free Brownian motion of molecules of a species s in the solution causes local concentration ¯uctuations that can be observed as ¯uorescence ¯uctuations in small laser illuminated sample volumes. We assume that the combined illumination and detection pro®le in a diffraction limited focus of a microscope objective lens is a three-dimensional Gaussian distribution (Qian & Elson, 1991; Rigler et al., 1993) and consider the local ¯uctuations to be governed by Fick's second law of diffusion:

679

Intracellular Diffusion of EGFP

…2†

Solving equation with appropriate initial and boundary conditions results in the diffusion propagator:

butions, dw is related to their fractal dimension on the considered length scale (Bunde & Havlin, 1995). The exponent also appears in the propagator, and the one-species ACF transforms into:

…7†

…3†

This function generates the analytical ACF:

…4†

where Ns denotes the mean number of molecules in the focal volume, ts ˆ w20/4Ds is related to the beam waist w0 and the diffusion coef®cient Ds, and k ˆ z0/w0 is the ratio of w0 and the axial radius z0 of the focus. If the solution contains more than one distinct species, the resulting ACF is a sum of normalized single species ACFs Ns
Gdiff,s(t) weighted with the relative concentrations rs ˆ cs/ctot and the square of the quantum yields Zs of ¯uorescence excitation at the wavelengths used: …5†

Obstructed diffusion, corralling, and long tail kinetics In the presence of immobilized inert obstacles with a concentration co below the percolation threshold co,p that obstruct molecular motion by an excluded volume interaction, the mean square displacement of a diffusing species is found to be (Bunde & Havlin, 1995; Saxton, 1994): …6†

This behavior, called obstructed diffusion or anomalous (sub-)diffusion, governs the Brownian motion on length scales r(t) < rcrossover(co, co,p). Above this crossover length, the mean square displacement is again proportional to time. The anomaly parameter dw is equal to 2 for free diffusion, and increases with increasing obstacle concentration (thus Ds is the diffusion coef®cient without obstacles). In self-similar obstacle distri-

The only effect of additional binding to obstacles with uniform energies for a thermally equilibrated system is to decrease the apparent diffusion coef®cient Ds (Saxton, 1996). If the obstacles form cages, dead ends, and cavities smaller than the focal volume which can be characterized by an escape time tesc > ts, we expect to observe a fast component due to free diffusion and an additional slower component of trapped molecules that take longer to leave the focus (Saxton, 1995). If a system can be approximated locally as twodimensional (e.g. obstacles delimiting a layer) or one-dimensional (channel-like), the ACF shows a smoother shape. This is known as long-tail kinetics (Qian et al., 1999) and means in the context of Brownian motion that a tracer molecule will return to its starting position with non-zero probability before it has visited all accessible sites. The analytically available 1D or 2D ACF can be ®tted with a 3D model with either additional slow components, equation (5), or anomalous behavior, equation (7). Nagle has proposed another model accounting for long-time tail effects (Nagle, 1992; Scher et al., 1991). Here, binding with a broad distribution of energies is represented by a distribution of waiting times:

…8†

that stands for the probability that a tracer having jumped at t ˆ 0 will jump at time t; the algebraic decay is more stretched than an exponentially decaying c that would describe normal diffusion. With the approximations for the number of jumps versus time given in (Nagle, 1992) we have calculated the ACF numerically, and the resulting function is very similar to equation (7). Background signal An uncorrelated background signal U(t) (e.g. due to immobilized auto¯uorescence in cells) added to the signal of all species s according to F(t) ˆ sFs(t) ‡ U(t) results in a smaller ACF amplitude and an apparently larger number of molecules. Multiplying the ACF with a correction factor:

680

Intracellular Diffusion of EGFP

…9†

accounts for this (Koppel, 1974).

lifetime and much smaller than the diffusion times ts, the ACF can be corrected to good approximation with two additional exponential decays (Haupts et al., 1998). The required correction factor (cf. equation (10)) is then:

Triplet state correction An additional contribution to the ¯uorescence ¯uctuations is the population of metastable non¯uorescent triplet states of the ¯uorophores with a time constant tt ˆ 1/lt resulting in an equilibrium fraction  of molecules in the triplet state. To account for this, an approximated correction factor can be applied (Widengren et al., 1995):

…13†

The apparent fractions c,1..2 and time constants tc,1..2 are related to the reaction constants according to:

…10† …14†

Influence of changes in chromophore protonation and conformation of EGFP EGFP is known to have non-¯uorescent ground state conformations. The proposed models can explain very well many spectroscopic properties on a molecular level, including the dependence of the absorption and the ¯uorescence excitation and emission spectra on pH, temperature, or ionic strength (Haupts et al., 1998; Palm, 1998; Tsien, 1998) as well as the observed blinking of other GFP mutants (Dickson et al., 1997; Garcia-Parajo et al., 1999; Pierce et al., 1997). It has been proposed (Palm et al., 1997) that the ¯uorescence emission at wavelengths above 500 nm with an excitation at 488 nm can be assigned to a deprotonated state Aÿ of the chromophore. Moreover, the chromophore can be protonated either by internal proton transfer due to a conformational change or from the solvent, the latter process being pH dependent: …11†

In the forms AH and Nÿ ¯uorescence emission is suppressed, and the equilibration of the three conformations causes ¯uctuations similar to triplet state population. The ¯uorescence yield is therefore linear in the equilibrium population [Aÿ] of the deprotonated state and pH dependent: …12†

Here pKa characterizes the protonation reaction. With the reaction constants kprot,e, kdeprot,e, kprot,i, kdeprot,i (equation (11)) and assuming for simpli®cation that the time constants of the (de-) protonation processes are much larger than the ¯uorescence

Application of FCS to subcellular structures In general, living cells do not provide the stationary conditions required for FCS. All parameters that can induce or change local ¯uorescence ¯uctuations need to be suf®ciently independent of time in order to ensure a local equilibrium. The total volume must be signi®cantly larger than the sample volume, which is in the order of a femtoliter in a typical FCS setup (Langowski & Tewes, 1999), to compensate photodestruction of the ¯uorophores. This holds for the application of FCS to total volumes of 10-100 ml as well as for photobleaching based methods (Kao et al., 1993; Luby-Phelps et al., 1986; Wedekind et al., 1996) but not necessarily within cells that have a volume of a few picoliters in a spherical approximation with a 10 mm radius. Then a time dependent decrease of the number of molecules can affect the ACF, and experimental parameters (laser intensity, irradiation time) have to be adjusted to reduce this in¯uence. Investigating binding reactions (ligand-receptor or hybridization) with FCS requires reaction time constants much faster or much slower than the diffusion time or the triplet lifetime; in that case, binding-induced changes of the diffusion coef®cient, of the quantum yield, or of the triplet parameters of ¯uorescently marked molecules will not signi®cantly bias the ACF. These constraints taken into account, all stationary spatial variations can serve as an interesting signal, e.g. the impact of immobilized subcellular structures on diffusion properties, or of pH variations on spectroscopic properties.

681

Intracellular Diffusion of EGFP

Results Characterization of cellular EGFP Beyond its ¯uorescence spectrum, EGFP can be characterized by the strong pH dependence of its ¯uorescence emission, by the two exponential decays for small lag times in the ACF that are due to protonation (see above), and ®nally by its diffusion coef®cient. In order to ensure that the ¯uorescence observed in EGFP expressing cells belongs to EGFP we have screened these properties in a solution that was prepared from cell extracts (see methods). Both the emission and the excitation spectrum (Figure 1(a) and (b)) are in good agreement with other results (Haupts et al., 1998; Tsien, 1998): at pH 7.5 an excitation at 488 nm results in an emission maximum at 510 nm and a shoulder at 540 nm. The excitation of the 510 nm emission shows a pronounced peak at 490 nm and decreases monotonously with decreasing wavelength. Shapes and maxima of the spectra are pH-independent (data not shown). However, extracts from nontransfected cells have a much smaller signal at pH 7.5 (Figure 1(a) and (b)) and all other pH values studied (not shown). The total signal amounted to less than 10 % of that of the EGFP-containing cells in the spectral range of the detection bandpass ®lter (Figure 1(a)). The pH-dependence of the emission intensities from several FCS measurements can be ®tted according to equation (12) (Figure 1(c)). The obtained pKa of 6.0(0.4) agrees well with other results (Haupts et al., 1998; Palm, 1998) indicating the expected single step protonation process (Brejc et al., 1997; Chattoraj et al., 1996). In Figure 2 the ACF of EGFP free in solution at pH 7.5 acquired with the UPlanFl 20  /0.5NA lens is presented. It is evident that the simple expression for the ACF (equation (4)) is not suf®cient to describe the data, and one needs to take into account two non¯uorescent states according to equation (13), as demonstrated in Figure 2. In the cytosol, we expect the pH to vary moderately between 7 and 8 (Darnell et al., 1990). Therefore we averaged the parameters c,1..2 and tc,1..2 over several FCS measurements at pH between 6.2 and 8.6, obtaining a fast decaying fraction of 16(1) % with an apparent lifetime of 9(1) ms and a slower fraction of 14(3) % with a time constant of 310(20) ms. The diffusion time of the protein with the UPlanFl 20  /0.5NA lens was 810(90) ms. For ®tting the data from intracellular FCS measurements, we applied these values for c,1..2 and tc,1..2 as ®xed parameters. From additional FCS data of EGFP in the same pH range taken with the UPlanApo 60  /1.2NA lens (not shown) we obtained a diffusion time of 144(10) ms. Compared to ¯uorescein (Swaminathan et al., 1996) this yields a diffusion coef®cient of D ˆ 87  11 mm2/s as expected (Swaminathan et al., 1997; Terry et al., 1995).

Figure 1. (a) Fluorescence emission and (b) excitation spectra, of extracts from EGFP expressing AT-1 cells ( Ð ) and nontransfected cells (





). The hatched interval in (a) is the transmission range of the detection ®lter, the vertical line in (b) represents the 488 nm excitation line. (c) Fluorescence intensity at different pH from several FCS measurements of extracts from EGFP expressing AT-1 cells in isotonic (&) and hypotonic (*) Tris buffer and the ®tted function equation (12) ( Ð ) with pKa ˆ 6.0(0.4).

FCS line scans in cells In this section, we present the results of intracellular FCS line scans, i.e. ACFs taken in a cell at equidistant positions along a straight line. First, FCS scans in nontransfected cells were carried out as a control to account for the cellular auto¯uorescence background. Figure 3(b) shows the ¯uorescence intensity along a line scanned in an EGFP-expressing AT-1 cell compared to a nontransfected one, normalized to the signal of the medium. Inside the nontransfected cell the signal is two to three times smaller than in the medium, the ¯uorescence of EGFP-expressing cells, however, is

682

Figure 2. Normalized ACF of EGFP free in solution at pH 7.5: Measured function ( Ð ) and theoretical functions with one ( ± ± ) and two ( Ð ) non-¯uorescent states ®tted to the measured data with corresponding residuals.

at least 40 times brighter than that of non-transfected cells. This holds as well for the COS-7 cells studied under the same conditions. ACFs taken in nontransfected cells (Figure 3(a)) are always very noisy and often do not show any correlation, indicating mainly immobilized ¯uorescence. Every assumed ratio U(t)/F(t) (equation (9)) results in particle numbers for the non-transfected cells similar to those found in EGFP cells. Therefore, the intensity ratio of 40 and larger is caused by very different ¯uorescence ef®ciencies Zs at a similar ¯uorophore concentration. According to equations (5) and (9), this allows us to neglect the impact of auto¯uorescence on the ACFs in EGFP expressing cells. Visual inspection of the position of the laser focus in the cell allowed us to distinguish cellular compartments (indicated by the letters ``m'' for membranes, ``c'' for the cytoplasm, and ``n'' for nuclei) and to de®ne their lateral position as plotted in Figures 4-7. The difference of the EGFP mobility at different positions in a cell is apparent in the FCS data, as shown in Figure 3: the ACF taken at position 1 in the cytoplasm (open circles) can be ®tted with a single component, while the ACF recorded at position 2 in the nucleus (®lled circles) requires either two freely diffusing species or obstructed diffusion of one species for interpretation. In this particular case, the diffusion in the cytoplasm can be described by a diffusion coef®cient

Intracellular Diffusion of EGFP

Figure 3. (a) Normalized ACF at pos. 1 (Figure 4(a)) in the cytoplasm (*) and at position 2 in the nucleus (*) of an EGFP expressing AT-1 cell and in the nucleus of a nontransfected cell, ( Ð ). (b) Fluorescence intensity line scans along straight lines through an EGFP expressing AT-1 cell (*) and through a non-transfected cell ( Ð ).

Ds ˆ 12.5(1.3) mm2 sÿ1, while the two components in the nucleus have diffusion coef®cients of Ds ˆ 9.8(1.6) mm2 sÿ1 and D2 ˆ 1.0(0.6) mm2 sÿ1. For the obstructed diffusion model, we have Ds ˆ 8.7(1.0) mm2 sÿ1 and dw ˆ 2.3(0.1). The position-dependence of EGFP diffusion in an AT-1 cell is further illustrated by the FCS line scan in Figure 4. The fast-diffusing component can be found everywhere in the cell: the twocomponent ®ts were performed with the average value for the fast ts from this scan. In addition, the slow component appears with a fraction r2 depending on the position (Figure 4(a)), showing remarkable structure especially in the nucleus. The slow diffusion times display a broad distribution between 10 ms and 100 ms. Since each FCS measurement took 40 s, the total number of particles in the cell decreased from step to step approximately exponentially due to bleaching. Therefore the relative particle number Nfocus, rel in the focal volume (Figure 4(b)) is the parameter N (equation (5)) divided by an exponential decay with a relaxation time between 30 and 90 minutes for cells in this study. The average EGFP monomer and fusion protein concentrations in the cells varied between 10 and 150 nM. This was obtained from the ACF amplitude and the size of the detection volume, derived from FCS of ¯uorescein in solution. Nfocus, rel also shows variations with the position, which in a microscopic image would correspond to variations in ¯uorescence intensity.

Intracellular Diffusion of EGFP

683

Figure 4. FCS scan through an EGFP expressing AT-1 cell. (a) Fraction of a slow component and (b) relative number of molecules, found with a free diffusion two-component ®t; (c) anomaly parameter and (d) relative number of molecules found with an obstructed diffusion model as a function of the position in the cell.

Interpreting the data with the obstructed diffusion model, we found similar structures (Figure 4(c) and (d)): especially in the nucleus, the anomaly parameter is greater than 2. We have obtained similar results in COS-7 cells expressing EGFP, an example of which is shown in Figure 5. Again, the diffusion is more obstructed in the nucleus than in the cytoplasm, or the amplitude of the slow component is larger than in the cytoplasm. Moreover, similar to the AT-1 cells, variations of the anomaly parameter (or the slow fraction) inside the nucleus, as well as structures in the cytoplasm that induce a deviation from ideal one-component diffusion, can be discerned. We

could not decide here whether the structures in the cytoplasm corresponded to speci®c organelles; this will be the subject of future work. An FCS scan through an AT-1 cell expressing the EGFP-b-galactosidase fusion protein is presented in Figure 6. Again, the FCS data can be interpreted either as free diffusion of two components or as obstructed diffusion. Both ways of treating the data reveal (intra-)cellular structures like membranes, the cytoplasm, or the nucleus. For this example, the diffusion shows a non-vanishing anomalous behavior even outside the nucleus. In order to test the reproducibility we have scanned a second time along the ®rst line but now crossing

Figure 5. FCS scan through an EGFP expressing COS-7 cell. (a) Fraction of a slow component and (b) relative number of molecules found with a free diffusion twocomponent ®t; (c) anomaly parameter and (d) relative number of molecules, found with an obstructed diffusion model as a function of the position in the cell.

684 the whole cell (Figure 6(e)-(h)). The structures are qualitatively reproduced; deviations are probably due to slow internal motions in the cell. An even stronger distinction between cytoplasm and the nucleus as well as remarkable variations in the diffusion properties can be found in COS-7 cells expressing the fusion protein (Figure 7). Nevertheless, in both cell types and with both tracer proteins we have also found cells where the proteins exhibited the same diffusive behavior in the nucleus and in the cytoplasm without larger areas of obstruction (not shown). These cells are probably in a different phase of the cell cycle where the chromosomes are more highly condensed. In further studies, this could be systematically investigated using synchronized cells or constructions where histones labeled with ¯uorescent proteins of different spectral signatures

Intracellular Diffusion of EGFP

allow visualization of the condensation state of the chromatin (Kanda et al., 1998). Table 1 gives an overview of the ratio of diffusion coef®cients in vivo and in aqueous solution of EGFP, averaged over wide spatial ranges of several cells (®rst and third row). This is the inverted ratio of the corresponding diffusion times and represents relative viscosities. Thus, the apparent viscosity sensed by a tracer of the size of EGFP ( a few nm) is approx. ®vefold higher in the cell than in water. The ratio of intracellular diffusion coef®cients of EGFP monomers and fusion proteins (second and fourth row) is comparable to the predicted factor 1.4 (assuming spheres, the molecular mass ratio of 3 corresponding to a ratio of the radii and diffusion coef®cients p  3 3  1:4).

Figure 6. FCS scan through an EGFP-b-galactosidase fusion protein expressing AT-1 cell. (a) Fraction of a slow component and (b) relative number of molecules, found with a free diffusion twocomponent ®t, (c) anomaly parameter and (d) relative number of molecules, found with an obstructed diffusion model as a function of the position in the cell. (e-h) Results from the repeated FCS scan (*) along the same axis, but now crossing the whole cell, compared to the scan from (a-d) ( Ð ).

685

Intracellular Diffusion of EGFP

Figure 7. FCS scan through an EGFP-b-galactosidase fusion protein expressing COS-7 cell. (a) Fraction of a slow component and (b) relative number of molecules, found with a free diffusion twocomponent ®t, (c) anomaly parameter and (d) relative number of molecules, found with an obstructed diffusion model as a function of the position in the cell.

Discussion Our results show that FCS can be used to study the diffusion characteristics of ¯uorescent proteins in compartments of living cells, in particular in nuclei. The spatial resolution is similar to a confocal microscope, with the advantage of very small ¯uorophore concentrations in the nanomolar range. The application of FCS to the intracellular environment is an emerging ®eld of interest (Berland et al., 1995; Brock et al., 1998; Politz et al., 1998; Schwille et al., 1999) and its usage as an imaging tool has been recently proposed (Brock & Jovin, 1998). FCS is suited for characterizing the dynamics of dyes on the molecular level (Haupts et al., 1998); through this route, we can distinguish EGFP from possible cellular auto¯uorescence. Moreover, we show for the ®rst time the detection of structures in the nucleus of living cells through their dynamics that would be hardly distinguishable by ¯uorescence intensity alone: The use of different models for diffusion obstruction (Bunde & Havlin, 1995; Nagle, 1992; Qian et al., 1999; Saxton, 1996) to FCS in three-dimensional systems

leads to quantitative predictions for the microstructure of the nucleus. In order to ensure that the intracellular ¯uorescence is mainly emitted by EGFP, we have analyzed the spectra and pH dependence of the cellular ¯uorescence as well as the ¯uorescence ¯uctuations in FCS. Our observations agree well with results from previous studies (Brejc et al., 1997; Chattoraj et al., 1996; Haupts et al., 1998; Palm, 1998; Swaminathan et al., 1996, 1997; Terry et al., 1995; Tsien, 1998), and intensity line scans in transfected and nontransfected cells prove that the major part of the observed ¯uorescence is in fact emitted by EGFP. The viscosity of the cytosol of other cell lines has been investigated in a variety of experiments (Kao et al., 1993; Luby-Phelps et al., 1986, 1987, 1993; Partikian et al., 1998; Seksek et al., 1997; Swaminathan et al., 1996, 1997) and was found to be 2.6 to tenfold higher than in aqueous solution. Only few studies were carried out in nuclei, and the most recent reported a diffusive behavior very similar to the cytoplasm (Politz et al., 1998; Seksek et al., 1997). Here we observe (Table 1) that in the

Table 1. Ratio of diffusion coef®cients in vivo and in aqueous solution of EGFP and ratio of diffusion coef®cients of EGFP and of the EGFP-b-galactosidase fusion protein in vivo, obtained from the given number of cells of each cell line for both ®t models AT-1 Dmonomer, Dmonomer, COS-7 Dmonomer, Dmonomer,

Two components

Obstructed diffusion

Number of cells

aq./Dmonomer, cell

5.3(0.6) 1.4(0.2)

5.5(0.6) 1.5(0.4)

9 6

aq./Dmonomer, cell

4.7(0.5) 1.2(0.1)

4.5(0.7) 1.3(0.3)

8 4

cell/Dfus.prot., cell

cell/Dfus.prot., cell

686 two-component diffusion interpretation the fast component shows a constant diffusion coef®cient everywhere in the cell with moderate variations, and the same holds for the derived diffusion coef®cient for obstacle-free motion in the framework of anomalous subdiffusion. Both are about ®ve times smaller than in water. Moreover, water amounts to approx. 70 % (w/w) of typical cell lines (Darnell et al., 1990). Therefore, we think that a large volume fraction of the nucleus contains a cytosollike liquid with macromolecules and larger complexes diluted in a ¯uid phase, both contributing to the apparent viscosity (Kao et al., 1993). The remaining space is ®lled with chromatin and associated macromolecules organized in chromosomes and forming a distribution of obstacles. In metaphase nuclei, the chromosomes are highly condensed, and the diffusion behavior is supposed to be nearly the same as in the cytoplasm. This can be assigned to those cells where no differences between the two compartments were observed. Cells with noticeably different mobility properties of the EGFP tracers in nucleus and cytoplasm (see Figures 4-7) are presumably in interphase. If the non-ideal diffusion behavior was due to a true two-component system, this would require a rather inhomogeneous density distribution with high local concentrations in order to form cages for the trapping of tracers (Saxton, 1995). This is not necessary for obstructed diffusion which is therefore expected to appear even in the presence of low concentrations of stochastically distributed obstacles (Saxton, 1994). In addition, long-tail kinetics due to binding (Nagle, 1992) or local geometrical restrictions (Qian et al., 1999) lead to anomalous diffusion (Saxton, 1996), and the anomaly parameter can be related to the geometrical fractal dimension of this distribution on the length scale of the observation volume (Bunde & Havlin, 1995). Therefore, we take anomalous subdiffusion as the more suitable interpretation of our FCS data. Consequently, in systems with diffusion obstacles and more than one real component present, e.g. in vivo hybridization assays (Paillasson et al., 1997; Politz et al., 1998), it might be helpful to observe the probe and inert tracers simultaneously. Several models for the chromatin structure in the interphase nucleus have been suggested and can be applied to predict the intranuclear diffusion: The phenomenological ICD (interchromosomal domain) model (Cremer et al., 1993; Zirbel et al., 1993) postulates a network of channels, especially between chromosomal domains, where transport takes place. From a more quantitative point of view, the MLS (multi-loop subcompartment) model (MuÈnkel et al., 1999; MuÈnkel & Langowski, 1998) developed in our laboratory describes the interphase nucleus as ®lled with chromosome territories of a typical diameter of 3 mm that intermingle only moderately but allow interchromosomal as well as intrachromosomal transport. From the

Intracellular Diffusion of EGFP

numerical simulations it is anticipated that the remaining space forms a network of not too densely packed obstacles that can be characterized by its local fractal dimension and mass density. Numerical predictions of diffusion data inside this simulated network are in progress.

Materials and Methods FCS instrument The FCS instrument is based on an Olympus IX70 inverted microscope (Olympus Optical, Hamburg, Germany). A compact module which was constructed in our laboratory (Langowski & Tewes, 1999) is attached to the video port, consists of confocal optical paths for one excitation and two detection channels, and provides a diffraction limited focus. For the excitation we used a low noise Omnichrome Ar-Kr gas laser with variable output power whose 488 nm Ar line is coupled via a monomode ®ber (both Laser 2000, Wessling, Germany) into the module and with a dichroic mirror 505DRLP through a ®lter 485DF22 into the microscope. For the detection of EGFP ¯uorescence we used a 515-545 nm ®lter 530DF30 (all Omega Optical, Brattleboro, VT) and an actively quenched avalanche photodiode SPCM-AQ141 (EG&G, Vaudreuil, Canada) behind a pinhole with a diameter of 50 mm. The laser intensity in the focus was measured with a Nova Display power meter (Ophir Optronics, Jerusalem, Israel) and did not exceed 1.32 kW/cm2 in living cells. For intracellular measurements we used an Olympus UPlanApo 60  /1.2NA water immersion and for some bulk measurements an Olympus UPlanFl 20  /0.5NA water immersion objective lens. Sample solutions as well as adherently grown cells were situated in chambered coverglasses with a thickness of 0.14 mm (Nalge Nunc, Naperville, IL). Three dimensional positioning with a mechanical resolution of about 200 nm but a reproducibility of worse than 1 mm is obtained with a x-y stage (MaÈrzhaÈuser, Wetzlar, Germany) and a stepping motor moving the objective lens along the z axis (local design). Data acquisition and analysis The autocorrelation data were directly obtained with the ALV-5000/E two channel correlator board (ALV, Langen, Germany) in a PC, and the model functions were ®tted to the data with a program written in our laboratory based on the Marquardt-Levenberg algorithm (Press et al., 1992). A control program coordinates positioning and data acquisition. Cells AT-1 and COS-7 cells were transfected with a vector expressing EGFP (28 kDa; Figure 8(a); Clontech, Heidelberg, Germany) and an EGFP-b-galactosidase fusion protein (80 kDa; Figure 8(b)) and grown in a 5 % CO2 humidi®ed atmosphere at 37  C in RPMI medium (Life Technologies, Karlsruhe, Germany) without phenol red, but supplemented with 10 % fetal calf serum. Transfection was carried out by Lipofectin as proposed by Clontech. For the FCS measurements, cells were grown subcon¯uently on chambered coverglasses and mounted on the scanning stage at room temperature. The same procedure was followed for non-transfected AT-1 and COS-7 cells.

687

Intracellular Diffusion of EGFP

10,000 rpm and then transferred with dilutions of 1:10 and 1:100 into isotonic Tris buffer with pH varying from 5.5 to 9.5. All ¯uorescence spectra were collected in 1 cm  1 cm quartz cuvettes (Hellma, MuÈllheim, Germany) on a SLMAminco 8100 spectro¯uorimeter (SLM Instruments, Urbana, IL) with double monochromators for the excitation and emission channels.

Acknowledgments We thank G. MuÈller for cell culture and cloning and T. Weidemann and T. A. Knoch for helpful discussions. This work was supported by BMBF grant # 01 KW 9602/2.

References

Figure 8. Restriction maps of the vectors used for synthesis of EGFP and the fusion protein in transfected cells. (a) The basic plasmid expressing EGFP-C3. (b) Vector expressing the EGFP-b-galactosidase fusion protein, derived from vector pCH 110 (Amersham Pharmacia Biotech, Freiburg, Germany). The b-galactosidase gene was excised at the HindIII and the BamHI restriction sites and ligated in the same direction into the multiple cloning site of plasmid (a).

EGFP in solution Identically treated EGFP expressing and nontransfected AT-1 cells that were con¯uently grown on 145 mm petri dishes were washed twice with ice-cold hypotonic Tris buffer (20 nM Tris-HCl (pH 7.5)) and then swollen on ice in this buffer for ®ve minutes. After removing the buffer the cells were scraped together, homogenized in a Dounce type S homogenizer, and the volume was adjusted to 2.5 ml per plate with isotonic Tris buffer (20 mM Tris-HCl (pH 7.5), 130 mM NaCl). The samples were centrifuged for ®ve minutes at

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Edited by W. Baumeister (Received 15 December 1999; accepted 28 February 2000)