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3518 Biophysical Journal Volume 87 November 2004 3518–3524
Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells
Matthias Weiss,* Markus Elsner,y Fredrik Kartberg,y and Tommy Nilssony *MEMPHYS-Center for Biomembrane Physics, Physics Department, University of Southern Denmark, Campusvej 55, Odense M, Denmark; and yDepartment of Medical Biochemistry, Go¨teborg University, Medicinaregatan 9A, Go¨teborg, Sweden
ABSTRACT Macromolecular crowding dramatically affects cellular processes such as protein folding and assembly, regulation of metabolic pathways, and condensation of DNA. Despite increased attention, we still lack a definition for how crowded a heterogeneous environment is at the molecular scale and how this manifests in basic physical phenomena like diffusion. Here, we show by means of fluorescence correlation spectroscopy and computer simulations that crowding manifests itself through the emergence of anomalous subdiffusion of cytoplasmic macromolecules. In other words, the mean square displacement of a protein will grow less than linear in time and the degree of this anomality depends on the size and conformation of the traced particle and on the total protein concentration of the solution. We therefore propose that the anomality of the diffusion can be used as a quantifiable measure for the crowdedness of the cytoplasm at the molecular scale.
INTRODUCTION At first glance the cytoplasm of mammalian cells appears to with a , 1. This kind of diffusion is known as anomalous be an unstructured, aqueous liquid in which proteins, sugar subdiffusion and has been found in many different contexts; molecules, and other solvents are dissolved. Taking a closer e.g., for the movement of lipids on model membranes (Schutz look, one realizes that the cytoplasm is in fact structured on et al., 1997), integral membrane proteins on organellar mem- many length scales: on the mm-scale we find organelles like branes (Weiss et al., 2003) and proteins in the nucleoplasm the mitochondria, endosomes, and the Golgi apparatus. On (Wachsmuth et al., 2000), solute transport in porous media a smaller scale (;100 nm) the endoplasmic reticulum (ER) (Drazer and Zanette, 1999), and the translocation of polymers imposes a random reticular network (Marsh et al., 2001) (Metzler and Klafter, 2003; Kantor and Kardar, 2004). together with the cytoskeletal elements, such as microtubuli In the case of obstructed diffusion, the emergence of a tran- and actin filaments. Together, these yield a higher order sitional subdiffusive regime is observed when the concen- structure of the cytoplasm (see, for example, Alberts et al., tration of obstacles is increased. This transient subdiffusive 1994 for a more detailed introduction). As a consequence, behavior collapses back to normal diffusion after a timescale diffusional movement of particles, such as macromolecules, T which diverges in the limit c / c*. At c ¼ c* (the so- can be obstructed. In fact, it has been reported that the called percolation threshold), subdiffusion is observed on all diffusional mobility in the cytoplasm strongly decreases with timescales. Whereas T grows with increasing obstacle con- an increasing radius of the tracked particle, leaving particles centration, the (transient) anomality parameter a decreases with a radius .25–30 nm immobile (Luby-Phelps et al., concomitantly from unity to a finite value a*atc*, which is 1986, 1987; Seksek et al., 1997; Arrio-Dupont et al., 2000). given by a* 0.697 and a* 0.526 for two- and three- Extensive computer simulations also have shown that the dimensional environments, respectively (Havlin and Ben- molecular mobility is reduced when a particle diffuses in Avraham, 1987; Bouchaud and Georges, 1990). These a maze-like environment (Saxton, 1993): When increasing values were obtained for continuum percolation in a ‘‘Swiss- the concentration c of obstacles in the maze, the tracer cheese’’ model (see Havlin and Ben-Avraham, 1987 for particles appeared to diffuse slower and slower until complete details) and presumably represent the best approximation to immobilization occurred beyond a certain value, c*. In- the actual values in nature. However, other mechanisms can terestingly, when approaching c* the characteristics of the also lead to anomalous subdiffusion where the entire range diffusional motion changed dramatically. The mean square 0 , a , 1 may be observed (see, for example, Bouchaud displacement v(t) of the monitored particles did no longer and Georges, 1990; Metzler and Klafter, 2000). Regardless grow linearly in time but, rather, showed a power law v(t) ; ta of its microscopic origin, anomalous subdiffusion has been shown to strongly influence the formation of spatiotemporal patterns (Weiss, 2003) as well as kinetic rates (Saxton, 2002) and the time course of enzymatic reactions (Berry, 2002). Submitted April 9, 2004, and accepted for publication August 16, 2004. When neglecting the higher-order structuring of the Matthias Weiss and Markus Elsner contributed equally to this work. cytoplasm by cytoskeletal elements and membranes, one Address reprint requests to Matthias Weiss, MEMPHYS-Center for Bio- could anticipate from the above that one deals with an membrane Physics, Physics Department, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Tel.: 45-6550-3686; unstructured aqueous solution in which normal diffusion E-mail: [email protected]. 2004 by the Biophysical Society 0006-3495/04/11/3518/07 $2.00 doi: 10.1529/biophysj.104.044263 Subdiffusion Due to Molecular Crowding 3519 should be observed. Yet, the assumption of the cytoplasm as in the presence of 100 nM nocodazole (Sigma Chemical, St. Louis, MO) being a homogenous viscous solution is somewhat mis- (Zieve et al., 1980). leading as differently sized proteins, lipids, and sugars con- For subcellular fractionation, HeLa cells were scraped off the culture dish and collected by centrifugation (500g, 5 min.). Cells were washed with stitute up to 40% of the cytoplasmic volume (Fulton, 1982). phosphate-buffered saline (PBS) twice and once with homogenization This phenomenon is commonly referred to as molecular buffer. The homogenization buffer consisted of 20 mM HEPES-KOH crowding and has recently received increased attention (Ellis (pH 7.4), 1 mM DTT (both Biomol, Hamburg, Germany), 250 mM sucrose and Minton, 2003; Rivas et al., 2004) since, for example, (USB, Cleveland, OH), 1 mM EDTA (Merck, Hamburg, Germany), plus enzymatic reactions and protein folding appear to be strongly protease inhibitors (1 mg/ml aprotinin, 1 mg/ml leupeptin, 1 mg/ml pepstatin, 1 mg/ml antipain, 1 mM Benzamidine-HCl, 40 mg/ml phenylmethylsulfonyl affected by the crowdedness (for reviews see Ellis, 2001; Hall fluoride). Cell pellets were resuspended in 4 volumes of homogenization and Minton, 2003). Also, crowding seems to contribute buffer in the presence of protease inhibitors and homogenized using a ball- significantly to the high viscosity of the cytoplasm which has bearing homogenizer (10 passages with a 16 mm clearing). The homogenate 3 4 5 been determined to be three- to fourfold higher than that of was then centrifuged sequentially at 10 g (P1), 10 g (P10), and at 10 g water (Verkman, 2002; Elsner et al., 2003). Despite the (P100), retaining the supernatant at each subsequent centrifugation step. The final 105g supernatant (S100) was boiled in equal volume sample buffer and increased interest in the phenomena associated with molec- various amounts (0.1–10 mg) of protein were resolved on a 12.5% SDS- ular crowding, the term ‘‘crowdedness’’ so far has been used polyacrylamide gel. Protein bands were visualized by Coomassie Brilliant without a quantitative definition of what it actually means. In blue G250 (Merck, Darmstadt, Germany). other words, we lack a definition of a quantity which summarizes how crowded an environment really is and also Fluorescence microscopy and FCS states in which primary physical property of the heteroge- FCS measurements were carried out on a LSM510/ConfoCor 2 (Carl Zeiss, neous fluid the crowdedness is manifested. As basic criterion, Jena, Germany) using a 488-nm laser line for illumination. The fluorescence a quantitative measure of crowdedness should be independent was detected with a bandpass filter (505–550 nm) and the objective of influences imposed by the cytoskeletal and membrane (Apochromat 403/1.2 W) was heated to 37 C using an objective heater obstacles discussed above. Rather, it should reflect a basic and (Bioptechs, Butler, PA). The pinhole for all shown measurements was 1 Airy unambiguous physical quantity which can be assigned to the unit. We verified that for free diffusion in water, the autocorrelation function of the fluorescence was well fitted by Eq. 1 with a ¼ 1. Thus, our analysis highly, yet heterogeneous, concentrated protein/sugar solu- does not suffer from deviations of the confocal volume from a three- tion called cytoplasm. dimensional Gaussian point-spread function (see also discussions in Hess Here we utilize fluorescence correlation spectroscopy and Webb, 2002; Weiss et al., 2003). For each cell and condition, at least 30 (FCS) to show that inert tracer particles show anomalous fluorescence time series of 10 s duration were recorded, autocorrelated, and subdiffusion in the cytoplasm of living cells over a wide superimposed for fitting with XMGRACE (see http://plasma-gate.weizmann. ac.il/Grace/). range of particle sizes. This behavior is found to occur Autocorrelation times tD were translated into apparent hydrodynamic irrespective of the stage of the cell cycle or the presence of radii by comparison with green fluorescent protein (EGFP, Molecular ER membrane structures and cytoskeletal scaffolds. Using Probes) in PBS: From the diffusion coefficient D 85 mm2/s of GFP in ¼ computer simulations, we demonstrate that this effect most buffer (Terry et al., 1995) and the determined diffusive time tD 130 ms, we obtained via the Einstein-Stokes equation D ¼ kBT/(6phr) a mean radius likely arises due to molecular crowding, e.g., diffusing 21 r ¼ 2.6 nm for GFP (kBT 4.3 3 10 J is the thermal energy and h particles are scattered by nearby particles due to excluded- 10 3 kg/(m 3 s) is the viscosity of water). This value agrees well with the volume interactions. We verify our hypothesis in vitro by dimensions derived from the crystal structure of GFP (Yang et al., 1996). determining the degree of anomalous diffusion of tracer particles in highly concentrated dextran solutions. Fitting anomalous diffusion
To determine if the experimentally observed autocorrelation function C(t)is MATERIALS AND METHODS governed by anomalous subdiffusion one has to generalize the well-known expression for the autocorrelation decay due to normal diffusion. Knowing Cell culture the illumination profile (which is usually approximated by a three- dimensional Gaussian), this task is essentially done when the propagator HeLa cell lines were grown in DMEM supplemented with 10% fetal calf Gð~r1;~r2; tÞ of the density of the (sub)diffusing particles is known. This serum, 100 mg/ml penicillin, 100 mg/ml streptomycin, and 10 mM function simply tells the probability to find a particle at position ~r2 after glutamine (Gibco, Eggenstein, Germany). FITC-labeled dextrans of a time t when it was initially at position~r1: For normal diffusion Gð~r1;~r2; tÞ different molecular masses (10, 40, 500, 2000 kDa: Molecular Probes, is simply a Gaussian which satisfies the diffusion equation and it is easy to Eugene, OR; 150 kDa: Sigma, Germany) were either injected with an derive the appropriate expression for C(t) (for details see, for example, Hess Eppendorf microinjection system (Eppendorf, Hamburg, Germany) or and Webb, 2002; Weiss et al., 2003). In contrast, the propagator for incorporated by electroporation. Microtubules were disrupted by incubating subdiffusion is somewhat more difficult to obtain. Bearing in mind that cells with 20 mM nocodazole at 37 C for one hour. To disrupt the ER subdiffusion is commonly defined via the asymptotic power-law increase of network, cells were treated with 5 mg/ml Filipin III (Sigma, Germany) for the mean square displacement v(t) ; ta (a , 1), a straight-forward (yet 30 min at 37 C and 45 min at 30 C. The efficiency of the treatment was approximative) approach to determine Gð~r1;~r2; tÞ is to assume a time- confirmed by examining the change of the fluorescence pattern of HeLa cells dependent diffusion coefficient D(t) ¼ Gta 1 so that v(t) ¼ D(t) 3 t. Clearly, expressing the ER marker Sec61 fused to CFP (see Axelsson and Warren, this interpretation is problematic for small times as D(t) diverges for t / 0. 2004 for details). Experiments using mitotic cells were accomplished by Yet, assuming that one still can use this approximation for all times, one arresting HeLa cells in the metaphase of mitosis by incubating them for 16 h obtains the propagator
Biophysical Journal 87(5) 3518–3524 3520 Weiss et al.
ð j~ ~ j2=ðG aÞÞ exp rp1 ffiffiffiffiffiffiffiffiffiffiffir2 t Gð~r1;~r2; tÞ¼ ; pGta which satisfies the modified diffusion equation
@Gð~r ;~r ; tÞ 1 2 ¼ DðtÞDGð~r ;~r ; tÞ: @t 1 2
Using this expression in conjunction with a Gaussian illumination profile, we obtain