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Rapid Hop Diffusion of a G-Protein-Coupled Receptor in the Plasma Membrane as Revealed by Single-Molecule Techniques

Kusumi Membrane Organizer Project, Exploratory Research for Advanced Technology Organization, Department of Biological Science and Institute for Advanced Research, Nagoya University, Nagoya 464-8602, Japan

Correspondence: Address reprint requests to Akihiro Kusumi, PhD, Dept. of Biological Science, Nagoya University, Nagoya 464-8602, Japan. Tel: 81-52-789-2969; Fax: 81-52-789-2968; E-mail: akusumi{at}bio.nagoya-u.ac.jp.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Diffusion of a G-protein coupled receptor, µ-opioid receptor (µOR), in the plasma membrane was tracked by single-fluorescent molecule video imaging and high-speed single-particle tracking. At variance with a previous publication, where gold-tagged µOR was found to be totally confined within a domain, which in turn underwent very slow diffusion itself, we found that µOR undergoes rapid hop diffusion over membrane compartments (210-nm and 730-nm nested double compartments in the case of normal rat kidney cell line), which are likely delimited by the actin-based membrane-skeleton "fence or corrals" and its associated transmembrane protein "pickets", at a rate comparable to that for transferrin receptor (every 45 and 760 ms on average, respectively), suggesting that the fence and picket models may also be applicable to G-protein coupled receptors. Further, we found that strong confinement of gold-labeled µOR could be induced by the prolonged on-ice preincubation of the gold probe with the cells, showing that this procedure should be avoided in future single-particle tracking experiments. Based on the dense, long trajectories of µOR obtained by high-speed single-particle tracking, the membrane compartments apposed and adjoined to each other could be defined that are delimited by rather straight boundaries, consistent with the involvement of actin filaments in membrane compartmentalization.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The structure of the cell membrane at a very basic level can be described by the fluid-mosaic model proposed by Singer and Nicolson more than 30 years ago (1972). However, membrane proteins and lipids undergo diffusion in the plasma membrane at a rate 5–50 times slower than those found in artificial reconstituted membranes (Chang et al., 1981; Lindblom et al., 1981; Peters and Cherry, 1982; Swaisgood and Schindler, 1989; Lee et al., 1993; Ladha et al., 1997; Schütz et al., 2000), and such a vast reduction cannot be explained by the presence of the physiological levels of membrane proteins and cholesterol (Peters and Cherry, 1982; Fujiwara et al., 2002). Clearly, there must be some long-range ordering mechanisms that retard the diffusion of membrane molecules in the plasma membrane (Saxton, 1989a,b, 1990; Sheetz, 1993; Jacobson et al., 1995; Kusumi and Sako, 1996; Fujiwara et al., 2002; Edidin, 2003). Furthermore, many membrane molecules exhibit large reductions in the diffusion rate upon clustering (Iino et al., 2001; Suzuki and Sheetz, 2001; Shvartsman et al., 2003), which cannot be explained by a two-dimensional continuum model of the cell membrane: as predicted by Saffman and Delbrück (1975), and later experimentally confirmed by Peters and Cherry (1982) and Vaz et al. (1982), in the two-dimensional continuum liquid, clustering should only exert very minor effects on the translational diffusion rate. Again, some higher-order organizing mechanisms for the plasma membrane that do not exist in protein-lipid reconstituted membranes are clearly required for explaining the extensive slowing effect of clustering on membrane molecules. Elucidating mechanisms for such slowing effects would be important for understanding the signal transduction mechanism in the cell membrane (Murakoshi et al., 2004). Upon the ligand binding, many receptor molecules form clusters and subsequently induce the binding of cytoplasmic signaling molecules. The diffusion rates of these signaling complexes are often greatly reduced as compared to those for the receptors before ligation (Felsenfeld et al., 1996; Holowka and Baird, 1996; Bray, 1998).

Recently, Fujiwara et al. (2002) investigated this issue by using both single-fluorescent molecule video imaging (SFVI) (Schütz et al., 2000; Iino et al., 2001; Sako et al., 2001; Vrljic et al., 2002, 2005; Lommerse et al., 2004) and single-particle tracking (SPT) (Saxton and Jacobson, 1997) with time resolutions of up to 25 µs. They found that both an unsaturated phospholipid, 1,2-dioleoyl-sn-glycero-3-phosphorylethanolamine (DOPE), and a transmembrane protein, transferrin receptor (TfR), are confined within compartments of 230 nm on average for short timescales. On longer timescales, both molecules undergo hop movements among adjacent compartments, which were termed hop diffusion. The average residency time of DOPE in a compartment was 13 ms, which is shorter than that of TfR (65 ms) by a factor of 5 (Fujiwara et al., 2002, reported an 11-ms residency time, but recently, it turned out that 13 ms may be a better value (T. Fujiwara, unpublished observation)). They found that the membrane skeleton is primarily responsible for such temporary confinement, although the DOPE marker lipid that they observed was located in the outer leaflet of the membrane and could not directly interact with the membrane skeleton. Based on these observations, they proposed the anchored membrane-protein "picket" model (Fig. 1 a, right), in which various transmembrane proteins anchored to the actin-based membrane skeleton effectively act as rows of pickets lined up along the membrane skeleton, due to the effects of steric hindrance and hydrodynamic frictionlike effects (Bussell et al., 1995; Dodd et al., 1995). Such compartmentalization of the cell membrane and hop diffusion of the phospholipid molecules among the compartments were found in all of the eight cultured cell lines we examined thus far (Murase et al., 2004).

View larger version (35K): [in this window] [in a new window]   FIGURE 1  Proposed mechanism for the compartmentalization of the plasma membrane for the translational diffusion of transmembrane proteins and lipids in the membrane: corralling by the membrane-skeleton "fences" and the anchored-protein "pickets". (a, left) The membrane-skeleton "fence" or "corral" model in which transmembrane proteins are confined within the mesh of the actin-based membrane skeleton. Transmembrane proteins protrude into the cytoplasm, and in this model, their cytoplasmic domains collide with the membrane skeleton, which induces the temporary confinement of transmembrane proteins in the membrane-skeleton mesh. (a, right) Anchored-protein "picket" model. Various transmembrane proteins anchored to and lined up along the actin-based membrane skeleton effectively act as rows of pickets against the free diffusion of lipids and proteins in the cell membrane due to steric hindrance and the hydrodynamic frictionlike effects of immobilized proteins. Fences would act on transmembrane proteins, whereas pickets would act on both lipids (including lipid-anchored proteins) and transmembrane proteins. Therefore, transmembrane proteins are corralled by both fences and pickets. In both models, membrane proteins and lipids can hop from a compartment to an adjacent one, probably when thermal fluctuations of the membrane and the membrane skeleton create a space between them large enough to allow the passage of integral membrane proteins, when an actin filament temporarily breaks, and/or when membrane molecules have sufficient kinetic energy to cross the barrier when they are in the boundary region. (b) A model of nested double compartmentalization of the NRK cell membrane. DOPE and TfR undergo free diffusion inside a 210–260-nm compartment (for the simplicity of the presentation, we simply use 260 nm here) for an average of 13 and 65 ms, respectively, and then hop to an adjacent compartment. Besides these 210-nm compartments, larger 710–750-nm compartments (we use 710 here) containing the 210-nm compartments exist, although the confining effect is weaker (Murase et al., 2004). The residency time within the 710-nm compartment is 0.41 s for DOPE and 0.53 s for TfR on average, respectively. In this article, we found that the same mechanism works for a GPCR, µ-opioid receptor (µOR), hopping over 210- and 730-nm nested double compartments with residency times of 45 ms and 0.76–1.6 s, respectively. This gives further support for the fence and picket models, with average compartment sizes of 210 nm and 730 nm. Therefore, the larger compartment may contain 11 smaller compartments, on average.

Therefore, the diffusion in the cell membrane is slow, not because the diffusion per se is slow (the diffusion rates within a compartment are as large as those found in artificial (cholesterol-free) reconstituted membranes, which excludes the presence of the further smaller compartments within the 30–250-nm compartments and the direct involvement of cholesterol for the large reduction of the diffusion coefficients in the cell membrane from those found in artificial membranes, see Pralle et al., 2000; Kenworthy et al., 2004; and Vrljic et al., 2005), but because it takes time to hop across the compartment boundary between adjacent compartments. Slowing of receptor diffusion upon clustering can also be explained by the presence of these "rows of pickets" and the membrane skeleton "fences". Hence, monomeric receptors may hop across the compartment boundaries quickly, whereas receptor clusters would take much longer to hop due to their increased size (for the cluster to hop across the boundary, all of the molecules have to hop at the same time), which would dramatically decrease the macroscopic diffusion rate with an increase in the cluster size ("oligomerization-induced trapping" as proposed by Kusumi and Sako, 1996, Iino et al., 2001, and Kusumi et al., 2005).

However, Daumas et al. (2003) recently reported that a G-protein coupled receptor (GPCR), µ-opioid receptor (µOR), was almost totally confined within a domain (with almost no probability of escape, i.e., no hop movements) that itself underwent very slow diffusion. This observation was made using SPT (at 25 Hz or 40-ms time resolution, a European video rate) of a colloidal gold probe with a 40 nm diameter, by way of a T7-tag fused to µOR at its N-terminus (extracellular domain) and an anti-T7 monoclonal IgG antibody. They proposed a "walking confined diffusion model", in which the long-term confinement of µOR may be caused by the "long-range attractive interaction between membrane proteins", with the form of a quadratic potential, rather than by the membrane-skeleton-based "pickets" and "fences".

Their results raised a number of important questions. Since basically all of the molecules incorporated in the membrane should sense the presence of rows of pickets anchored and lined up along the membrane skeleton, how can their long-range attractive interaction model be reconciled with the anchored-protein picket model? Are the total confinement and the confinement mechanism characteristic of GPCRs, or are they unique to µOR, in that most of the molecules are stationary, or undergo extremely slow diffusion in the cell membrane? How can these results be reconciled with the fact that GPCRs rapidly move to the internalization apparati in the cell membrane and become internalized upon ligation (Laporte et al., 1999; Santini et al., 2002)?

Our investigation was undertaken to critically investigate these questions, using the same receptor and the same cell type (normal rat kidney cell line) used by Daumas et al. (2003). We paid special attention to the probe preparation and the method of attaching these probes to the cells. Furthermore, in addition to carrying out SPT at video rate (in our case at 30 Hz or at a 33-ms resolution), we performed SFVI at video rate, as well as high-speed SPT at 40 kHz (25-µs resolution, enhanced from the video rate by a factor of 1350).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Cell culture, drug treatment, and transfection
Normal rat kidney fibroblasts (NRK, a cell line) and Chinese hamster ovary (CHO) cells were grown in Ham's F12 medium (GIBCO, Grand Island, NY) supplemented with 10% fetal bovine serum. Cells used for the experiment were transfected with the cDNA encoding rat µOR tagged with green fluorescent protein (GFP, a gracious gift from Dr. Schülz, Institute of Pharmacology, University of Munich, Germany; Schülz et al., 2002) that bears the monomeric mutation of A206K (mGFP) at the C-terminus of µOR (µOR-mGFP), or with myc or T7 epitopes at the N-terminus (myc-µOR or T7-µOR, respectively). Cells transiently expressing these fusion proteins were cultured on 18 x 18-mm coverslips for 1 day after plating. The treatment of cells with latrunculin B was done by incubating the cells in Hanks' balanced salt solution medium containing 50 nM latrunculin B (Spector et al., 1983) under the microscope observation at 37°C for 2 min and the observation was continued for up to 10 min.

Preparation of colloidal gold probes
The myc-tagged µOR expressed on the NRK cell surface was first labeled with anti-myc-Fab, and then the cells were further incubated with protein G-coated colloidal gold particles (40 nm) to label the complex of the anti-myc-Fab and the myc-tagged µOR on the NRK cell surface (see the next section for further details). The anti-myc-Fab was prepared from anti-myc-IgG (9E10). The T7-tagged µOR was labeled by colloidal gold particles conjugated with anti-T7 antibody (whole) IgG. The minimal protecting amounts (MPA, defined as the minimum concentration of the protein needed to stabilize colloidal gold particles in suspension) of protein G (Sigma, St. Louis, MO) and anti-T7-antibody IgG (Novagen, Darmstadt, Germany) were determined to be 1.0 and 2.5 µg/ml, respectively (De Mey, 1983; Leunissen and De Mey, 1989). For the preparation of colloidal gold coated with the MPA of protein G, a 50 µl aliquot of 10 µg/ml protein G in 2 mM phosphate buffer (pH 7.2), was mixed with a 500 µl suspension of colloidal gold (pH 7.4) on a slowly tumbling shaker overnight at 4°C. Colloidal gold probes coated with 1/100 MPA of the anti-T7-antibody (Daumas et al., 2003) were prepared in a similar way. The gold probes were further stabilized with 0.02% Carbowax 20M (Sigma). After three washes by sedimentation and resuspension in 0.02% Carbowax 20M, in 20 mM phosphate buffer (pH 7.0), the gold probe was resuspended in Hanks' balanced salt solution buffered with 2 mM PIPES at pH 7.2, sterilized by filtration with a 0.22-µm filter (Millipore, Bedford, MA), and then used within 3 h.

SPT of gold-tagged µOR and SFVI of µOR-mGFP
For the observations of the myc-µOR, first, the anti-myc Fab (2 µg/ml final concentration) was incubated with NRK cells expressing the myc-tagged µOR, which were cultured on coverslips, and then after washing the cells, gold probes conjugated with protein G were applied to the cells. Note that protein G can monovalently bind to a Fab fragment of the anti-myc antibody (IgG1) (Derrick and Wigley, 1994; Perosa et al., 1997). All observations of the gold probes were carried out at 37°C within 15 min after the application of the gold probes to the cells. Generally, limiting the period from the application of gold probes until the microscope observation to within 15 min, and carrying out all experiments at 37°C, were very effective for reducing the number of gold particles exhibiting slow diffusion or immobilization. Under these conditions, an average of 10 protein G-gold particles/cell were attached to the cell membrane. In contrast, only 1.5 gold particles/cell were found on the cell surface on average, when gold particles without protein G conjugation were used or when the anti-myc Fab incubation step was omitted. These results indicate that specific labeling of myc-µOR molecules was achieved under these conditions.

For the observations of T7-µOR, gold probes conjugated with the 1/100 MPA of anti-T7 antibody were applied to NRK cells expressing T7-µOR at room temperature, and the observations of the gold probes on the cell membrane were immediately started at 37°C. To examine the outcome of the protocol employed by Daumas et al. (2003), we also followed their experimental procedure, which basically differs from ours in only one key point: they employed a prolonged (45 min), on-ice preincubation of the cells with anti-T7 gold particles. After this incubation period, the gold particles were observed at 37°C during next 30 min. The instrumentation and actual observation methods for SPT and SFVI are described in the Supplementary Material.

Obtaining the trajectories of membrane molecules and the plots of mean-square displacement versus time
Positions (x and y coordinates) of the selected gold particles were determined by a computer that employs the method developed by Gelles et al. (1988). For each particle's trajectory, the mean-square displacement (MSD), r(t))², for every time interval (Eq. 1) was calculated according to the formula (Sheetz et al., 1989; Qian et al., 1991; Kusumi et al., 1993):

(1)

where t is the video frame time and x(jt + nt), y(jt + nt) describes the particle position following a time interval t_n = nt after starting at position (x(jt), y(jt)), N is the total number of frames in the video recording sequence, n and j are positive integers, and n determines the time increment.

To keep the statistical spread in the MSD within reasonable levels, µOR-mGFP trajectories >1 s (30 video frames) and gold-tagged µOR trajectories over 300 frames were used for the quantitative analysis (Saxton, 1994, 1996).

Analysis of high-speed SPT trajectories
Statistical classification of each trajectory into either simple Brownian type or confined + hop type diffusion was carried out as described (Kusumi et al., 1993; Fujiwara et al., 2002). Note that all of the statistical and quantitative analyses were performed without any arbitrary or intentional subdivisions of the obtained trajectories. For example, the results shown in Fig. 4 c obtained for 4000-step trajectories were directly obtained from the raw 4000-step trajectories, or when a part of a longer trajectory was used, the trajectory for the first 4000 steps was used.

View larger version (39K): [in this window] [in a new window]   FIGURE 4  Gmyc-µOR observed at a 25-µs resolution undergoes hop diffusion over 210-nm compartments. (a) Representative trajectories of Gmyc-µOR. Each color (purple, blue, green, yellow) represents a plausible compartment detected by computer software (Fujiwara et al., 2002). The residency time within each compartment is shown. It is comparable to the frame time of normal video rate (33 ms), exemplifying why such hop movements cannot be visualized by normal video observations. (b, left) An MSD-t plot (25-µs resolution) for the trajectory shown in a, left. It was fitted to a theoretical curve representing hop diffusion (Powles et al., 1992). The fit parameters include L, Dmicro, and DMACRO, and the residency time can be calculated from L and DMACRO (L2/4DMACRO). X, Y, and R indicate diffusion in the x and y directions and in a two-dimensional plane, respectively. The software always selects the direction of the longest overall movement as the x axis. For further details of the analysis, see the subsection of "Analysis of high-speed SPT trajectories" in the Materials and Methods section. (b, right) An example of a MSD-t plot (25-µs resolution) for the trajectory with short total observation periods (300 frames = 7.5 ms) and the short analysis time window (150 frames = 3.75 ms). This indicates that the analysis of diffusion in such a short time range may not be adequate for the detection of hop diffusion of membrane molecules (average compartment size = 210 nm; average residency time = 45 ms). (c) The distributions of RD(N, n) for Gmyc-µOR (bottom) are quite different from those expected from simple Brownian particles (generated by Monte Carlo simulations, top). Here, N is fixed at 4000 and n is varied (2000, 1000, 500, and 200 steps corresponding to analysis time windows of 50, 25, 12.5, and 5 ms, respectively). For the classification of the trajectories into different diffusion modes, RD(4000, n) values that give 2.5% of the particles from both ends of the distribution, referred to as RDmin(4000, n) and RDmax(4000, n), as shown by vertical blue and magenta lines, respectively, were used (Kusumi et al., 1993; also see the text). When a particle exhibits an RD(4000, n) smaller than RDmin(4000, n), its trajectory is classified into the confined + hop diffusion mode. The majority of Gmyc-µOR trajectories are classified into this mode as seen in these histograms. (d) Histograms of Deff(25 µs)75 µs (determined by the linear fit between the second (50-µs) and the fourth (100-µs) points based on the data of 25-µs/frame, first box), DMACRO (D(25 µs)100 ms, second box), the compartment size (third box), and the residency time (fourth box) (n = 34)(shaded bars) (the latter three determined by the hop fit). The average residency time within a compartment for each trajectory was calculated based on DMACRO and the compartment size determined for each trajectory, using the equation of L2/4·DMACRO. To further confirm the involvement of the membrane skeleton, the cells were very mildly treated with latrunculin B (50 nM final concentration for 2–12 min; during this period, all the measurements were performed) to slightly increase the actin-based membrane skeleton mesh (open bars). Arrowheads indicate the median values.

The determination of the diffusion coefficients for membrane molecules in the cell membrane is complex because they strongly depend on the total length of the observation, the timescales used for the analysis, and the time resolution employed for the observation in complex ways. This already strongly indicates the anomaly in the molecular diffusion in the cell membrane. In our investigation, the above experimental parameters are systematically varied.

For the analysis of the trajectories obtained by using high-speed SPT (with 25-µs or 8-ms resolutions), the MSD-t plots were fitted with a home-made program based on the hop diffusion theory of Powles et al. (1992; termed "hop fit" in this article; Fujiwara et al., 2002; Murase et al., 2004). All the parameters for the hop diffusion were evaluated by the computer program using the theory developed by Powles et al., who determined the exact solution of the time evolution of the probability distribution due to diffusion through an infinite array of equally spaced, semipermeable barriers. In their analysis, the time evolution of the probability distribution depends on three parameters: the distance between barriers, L, the true diffusion coefficient in the absence of barriers, D_micro, and the permeability of the barriers, P. They also derive a relationship between the permeability and the long-term diffusion coefficient, D_MACRO, D_MACRO/D_micro = [1 + (PL)^–1]^–1, which puts their solution into measurable quantities.

The second moment of the probability distribution gives the mean-squared displacement of a particle diffusing through the infinite array of barriers, which is further averaged over all possible starting positions between two barriers. Fitting to experimental data, independently in two orthogonal directions, reveals estimates for the compartment size ( where and are the compartment sizes determined in each direction), microscopic (short-term) diffusion coefficient (D_micro = (1/2)(D_{micro, x} + D_{micro, y}), where D_{micro, x} and D_{micro, y} are the short-term diffusion coefficients determined in each direction) and the macroscopic (long-term) diffusion coefficient (D_MACRO = (1/2)(D_{MACRO, x} + D_{MACRO, y}), where D_{MACRO, x} and D_{MACRO, y} are the long-term diffusion coefficients determined in each direction). The average residency time is determined from the average compartment size, and the average macroscopic diffusion coefficient, as

Compartment detection was performed through the following algorithm. Consider a starting point in the trajectory at frame m extending over a window of the next n frames. Within this window, the center of geometry of the distribution of the recorded locations is determined and the maximum radial displacement from this center in this window is determined. This maximum displacement is used to produce an apparent diffusion coefficient for this window of data through where is the time differential between consecutive points in the trajectory. For free Brownian diffusion, is constant (allowing for statistical variations) independent of m or n. If a molecule is temporarily trapped in a finite compartment, then as the window size n increases, decreases due to the confinement within a compartment. When the window size increases enough to include a hop to an adjacent domain, there is a sharp increase in due to the extended range of diffusion. By scanning all possible m and n pairs over the trajectory, a map of can be produced. Hops are flagged by persistent sharp increases in for both a given starting position (e.g., if position m is before a hop and is after a hop, then for all window sizes n, will be greater than ) or for the combination of starting position and window size (e.g., if the trajectory starting from position m with a window size n, ending at a point is wholly within one compartment and if extending the window size by 1 includes a hop to an adjacent compartment is included, then will be greater than for all m and n such that ).

One might wonder if the computer program developed by Simson et al. (1995) for the detection of "transient confinement zones" can be used to detect the membrane compartments described in this article. This software detects the part of the trajectory where a molecule stays much longer than expected from the overall average diffusion coefficient. We tried to use or modify this program in the hope to detect the membrane compartments described here. However, it has never worked for the detection of these compartments that may exist everywhere in the trajectory: the temporal fraction of the transient confinement zone that µOR exhibited at a 25-µs resolution was <0.1%, much less than that found in simple Brownian trajectories generated by Monte Carlo simulations (our computer program was made based on the program obtained from Jacobson (Simson et al., 1995) and tested for the trajectories obtained by Dietrich et al. (2002) for its proper implementation and usage). This result is somewhat expected: in the trajectories obtained at higher time resolutions, the molecule is basically confined everywhere, which is reflected in the long-term diffusion coefficient. Therefore, if this long-term diffusion coefficient is used for the detection of membrane compartments, because this diffusion coefficient already includes the confinement effect of the compartments, the program detects only the compartments where the molecule stays much longer than in others. For the differences between the membrane compartments and the transient confinement zones, the readers are referred to a review published by our group (Box 1 in Kusumi et al., 2004).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
µOR diffusion observed by SPT and SFVI at video rate
All of the microscopic observations were carried out at 37°C, unless otherwise stated. Fig. 2, a and b, show typical trajectories of gold-tagged myc-µOR (Gmyc-µOR) and gold-tagged T7-µOR (GT7-µOR), respectively, observed at video rate in the NRK cell membrane using SPT. We employed these two methods for gold labeling (via myc and T7 tags) for the following reasons:

1. If the same results are obtained with different methods of labeling, then the credibility of the data is greatly enhanced.
   
2. For a direct comparison with the data generated by Daumas et al. (2003), the same T7-epitope and the same anti-T7-antibody IgG had to be used.
   
3. However, since the affinity of the anti-T7 antibody for T7 is extremely high, with a dissociation constant on the order of 2 pM (Daumas et al., 2002, 2003), we were afraid that such a high-affinity antibody could easily cause cross-linking of µOR, leading to receptor aggregation and long-term confinement within a single compartment. However, the affinity of the Fab fragment of the anti-myc antibody to the myc epitope is close to the average level (on the order of 80 nM, Schiweck et al., 1997), and thus we decided to additionally use the myc epitope for the present research.
   

View larger version (41K): [in this window] [in a new window]   FIGURE 2  Typical trajectories of gold-tagged µOR obtained by SPT and those of µOR-mGFP obtained by single fluorescent molecule video imaging (SFVI), both recorded at a 33-ms resolution (video rate) (a–c) SPT trajectories for 10 s. (a) Gmyc-µOR. (b) GT7-µOR. (c) GT7-µOR after attaching the gold probes to the cell surface by a preincubation with the cells on ice for 45 min, and then washing away the unbound gold particles (microscope observation at 37°C, as in all other experiments). This procedure was adopted following Daumas et al. (2003). In a and b, gold probes were added to the NRK cells expressing µOR at room temperature, and were instantly observed under the microscope at 37°C (without removing the unbound gold particles, which may later bind to the cell surface during the observation. Since the gold particles in the cell-culture medium are moving rapidly in the medium, they do not form distinct images on the camera, and thus do not block observations of the cell surface), which is the standard protocol in our laboratory and the Sheetz laboratory at Columbia University, New York (personal communication, 2004; Felsenfeld et al., 1996). d SFVI of µOR-GFP. The lengths of the trajectories are indicated beneath them in seconds (video frames). They vary due to mGFP-photobleaching. (e) Mean-square displacement (MSD) of the gold-µOR complex, averaged over all particles in the full scale of 10 s (left) and 0.3 s (right). Blue circles, Gmyc-µOR; green circles, µOR-mGFP; red circles, GT7-µOR, including a prolonged cold preincubation period. In the left figure, due to the presence of many small circles (spots), they almost look like lines.

Quantitative analysis of single-molecule diffusion of µOR observed at video rate
Plots of the MSD averaged over all observed particles (of the same kind) against time are shown in Fig. 2 e (SPT data during 10 s are on the left, and the comparison of SPT and SFVI data during 0.3 s is on the right). Fig. 2 e on the right shows that Gmyc-µOR (blue) and µOR-mGFP (green) exhibited very similar MSD-t plots during 0.3 s. This result indicates that as long as we remain in a timescale <0.3 s, the possible detrimental slowing effect of gold particles, perhaps due to nonspecific interactions with membrane lipids, proteins, and extracellular matrices, cross-linking µOR molecules, and cross-linking µOR and other molecules, is undetectable (as shown later in Fig. 3, as long as we remain in a timescale <0.5 s (rather than 0.3 s), the effects of gold are undetectable). This result is consistent with our earlier observations using trypsin to remove the extracellular domains of membrane-associated proteins and extracellular matrix proteins (Fujiwara et al., 2002; Murase et al., 2004).

View larger version (48K): [in this window] [in a new window]   FIGURE 3  Distributions of the effective diffusion coefficients in time windows of 67–133 ms (Deff(33 ms)100 ms, left column), 67–500 ms (Deff (33 ms)250 ms, middle column), and 67 ms-3 s (Deff(33 ms)1.5 s, right column) based on video-rate observations; 33 ms is not shown in this figure to avoid too much crowding in labels. Note that all of the determinations here were done by linear fitting in the MSD-t plot for given durations. Each row shows the results with different probes: from the first row to the fourth row, SPT data on Gmyc-µOR, GT7-µOR, and GT7-µOR after a prolonged cold preincubation, as done by Daumas et al. (2003), and SFVI data for µOR-mGFP. In all cases, the trajectories >30 frames (1 s) were analyzed for better statistics of the diffusion coefficient (Saxton, 1994, 1996, i.e., µOR-mGFP trajectories <1 s were not used for analysis). Arrowheads indicate the median values (the numbers of inspected particles or molecules are shown in the histograms for Deff(33 ms)100 ms). Long black arrows in the histograms in the third row indicate the results reported by Daumas et al. (2003) for the mean values of Deff(40 ms)40 ms or DMACRO for GT7-µOR using a prolonged cold incubation for the attachment of gold particles on the cell surface. In the histogram for Deff(33 ms)100 ms of µOR-mGFP (fourth row, green), the distribution of Deff(33 ms)100 ms of mGFP fixed on the coverglass surface is also shown (open histogram). Most of the mGFP molecules on the glass showed the nominal D100 ms values distributed in the range of <0.02 µm2/s, with a median value of 0.0052 µm2/s. Therefore, the diffusion coefficients <0.02 µm2/s were (operationally) classified as being immobile, as indicated in yellow. The lower-limit of the diffusion coefficients that can be evaluated by SPT was 0.0003 µm2/s (at video rate, Kusumi et al., 1993).

View larger version (64K): [in this window] [in a new window]   FIGURE 5  A long-term trajectory of Gmyc-µOR obtained at a 25-µs resolution indicated the nested double compartmentalization of the NRK cell membrane and enabled determination of membrane compartments. (a) A typical long-term trajectory of Gmyc-µOR, recorded at a 25-µs resolution for a period of 1.77 s (70,800 frames). Larger compartments were identified in b and reproduced here. After the blue compartment, the particle went back to the purple compartment, but this part was omitted here because the trajectory would become very complicated. (b) A time-lapse trajectory at a frame rate of 8 ms/frame, produced from the trajectory in a by selecting a point out of every 325 consecutive points. Plausible compartments were identified by a computer program, and are shown in different colors: purple, 1.44 s; and blue, 0.33 s. The instance of the hop is shown in black. (c) In these larger 730-nm compartments (for this size, see Fig. 6 and the related text), smaller nested compartments (210-nm subcompartments) can be detected. The trajectory in a, containing 70,800 frames, was divided into 11 subtrajectories. For easier inspection, time-lapse trajectories at a frame rate of 0.5 ms are shown (sampling every 20 frames). Individual plausible compartments are color-coded (the full trajectory at a 0.5 ms resolution is shown in light gray and blue), and the residency time within each compartment is indicated beneath each subtrajectory in the same color (color coding in the order of purple-blue-green-yellow-red and then purple again; note that the plausible compartments were determined using the raw 25-µs resolution subtrajectories). Individual smaller (210-nm) compartments are indicated by dashed black ellipses in the upper row, which we propose based on the trajectory and the hopping points detected by computer software. Note that even in compartments where the determined points appear sparse, there are actually 20 times more determined points based on the 25-µs/frame data. The problems in determining these compartments are summarized in the text. Based on these elliptic compartments, compartment boundaries with slightly, gradually curved lines are proposed (in the bottom two rows of subtrajectories). Since this could be done reasonably well (see the far right figure in the bottom row, where both the elliptic compartments and the proposed mesh structure are superimposed), individual compartments are indexed using the quasi x and y coordinates (see the text for details). Thicker broken lines are proposed boundaries for larger compartments. The thick black line between the yellow [2, 2] and the red [1, 1] indicate the hop trajectory between two large compartments. The hop trajectory is not exactly located on the proposed boundary, but is located closely to the boundary line. (d) The third subtrajectory in c reproduced in full detail (25-µs resolution).

View larger version (48K): [in this window] [in a new window]   FIGURE 6  Gmyc-µOR observed at an 8-ms resolution exhibited hop diffusion over the larger 730-nm compartments. (a) Representative trajectories of Gmyc-µOR recorded at an 8-ms time resolution for a period of 4 s. Different colors (purple, blue, and green) indicate different plausible compartments. These compartments were detected by computer software we developed (see the Materials and Methods section; Fujiwara et al., 2002). (b) The distribution of the microscopic diffusion coefficient within larger compartments (also representing the hop diffusion rate over smaller compartments), Deff(8 ms)100 ms, the compartment size (L), and the residency time () determined for the larger compartments using 4-s trajectories at the time resolution of 8 ms (a total of 55 particles were examined). Deff(8 ms)100 ms was determined in the MSD-t plot (for the trajectories obtained at an 8-ms resolution) by linear fitting between the eighth (64-ms) and 17th (136-ms) points. The compartment size and the residency time were determined for each trajectory using the same methods described for the 25-µs trajectories using the equation of L2/4·DMACRO.

View larger version (26K): [in this window] [in a new window]   FIGURE 7  The plot of log(MSD/time) against log(time), covering over five orders of magnitude in time. Trajectories used for this plot were obtained at time resolutions of 25 µs (4,000-frame long, blue circles), 8 ms (500-frame long, orange circles), and 33 ms (300-frame long, red circles). The mean values of log(MSD/time) averaged over all of the trajectories obtained at the same time resolution were plotted as a function of log(time). The standard error is shown for each point. The fit using the five lines is based on the assumption of nested double compartmentalization (see the text).

Since many fluorescence recovery after photobleaching (FRAP) studies have been conducted based on the theory of simple Brownian diffusion (+ immobile component), the diffusion coefficients obtained by FRAP must be thought to be "effective diffusion coefficient". For the further details of the problems of FRAP diffusion measurements, particularly the issue of long tails that may be difficult to be distinguished from the immobile component, see Nagle (1992), Feder et al. (1996), and Saxton (1994, 1996, 2001).

In Fig. 3, D^eff(33 ms)_{100 ms}, D^eff(33 ms)_{250 ms}, and D^eff(33 ms)_{1.5 s} are used, which were determined by the linear fit in the time range between 67 ms (the second point in the MSD-t plot) and 133 ms (the fourth point), 500 ms (15th point), or 3 s (90th point), respectively; but to save the space in the figure, (33 ms) was omitted in the figure label. Fig. 3 shows the distributions of effective diffusion coefficients determined for single particles of gold-µOR (from SPT data) and single molecules of µOR-mGFP (from SFVI data) for video-rate observations (note that these distributions contain, in addition to the measurement noise, the true distributions of the diffusion coefficient reflecting the local environment and interactions as well as unavoidable statistical fluctuations; Saxton, 1997). A common feature for all of these probes is that the effective diffusion coefficient decreases with the lengthening of the time window. Although a complete explanation requires the high-speed SPT data described below, and thus full details will be given later, here, to advance the argument, we simply state our interpretation (which will be justified later): "This common feature is consistent with the short-term confinement within a compartment and the long-term hop diffusion over compartments (at an average hop rate of once every 45 ms, as described later). Furthermore, we assume that the diffusion coefficient within a compartment is comparable to the fast diffusion rate found in artificial reconstituted membranes, which is on the order of 3–10 µm²/s (Murase et al., 2004; also see below). Therefore, the effective diffusion coefficients obtained at time windows of 0.1, 0.5, and 3 s are mixtures of the fast diffusion within a compartment and slow hop diffusion between the compartments, with the weight of the fast diffusion coefficient within a domain decreasing (thereby the averaged effective diffusion rate decreasing) with an increase of the time window (consistent with the results shown in Fig. 3). Thus, a comparison of effective diffusion coefficients shown in Fig. 3 only makes sense when it is made with the same time window, and thus we pay special attention to this point (if the diffusion observed here were truly simple Brownian diffusion, then the time window would not matter)".

Comparison of µOR's long-term diffusion coefficients obtained by different probes and methods
The effective diffusion coefficients determined in the time ranges of 100 ms, 500 ms, and 3 s are shown in Fig. 3 and Table 1, which should be compared with those obtained by Daumas et al. (2003).

Second, in Fig. 3, compare the distributions of D^eff (33 ms)_{100 ms} and D^eff(33 ms)_{250 ms} (first and second columns) for gold-tagged µOR (first and second rows) with those for µOR-mGFP (bottom row, green histograms). The distributions are practically the same (statistically insignificant differences), suggesting that, in our hands, the gold probes are not causing serious reductions in the diffusion of µOR molecules in NRK cells, as long as we remain in the analysis time range in the MSD-t plot <0.5 s.

Third, compare the diffusion rate of µOR-mGFP with the rates of other GPCRs reported previously (Table 1). The immobile fractions of GPCRs in the FRAP experiments are 20%, except for the case of luteinizing hormone receptor 3 expressed in CHO cells (57%). In the case of µOR, Daumas et al. (2003) did not explicitly report the immobile fraction in their FRAP experiment. The SFVI results for µOR-mGFP obtained here suggest the presence of 5–10% of an immobile fraction (estimated from the distributions of D^eff(33 ms)_{100 ms} and D^eff(33 ms)_{250 ms}), in the sense that their apparent movement cannot be distinguished from the fluorescent spots of immobile mGFP molecules adsorbed on the glass surface, due to the observation noise, for which D^eff(33 ms)_{100 ms} is <0.02 µm²/s (see the yellow region in the bottom row of figures in Fig. 3, and the Materials and Methods section).

The diffusion coefficients for the mobile component of GPCRs in the previous FRAP experiments (Table 1), which are likely to represent the macroscopic diffusion coefficient measured over a micron domain in the time window of 0.5–10 s, are between 0.12 and 0.48 µm²/s, 24–100 times greater than the FRAP diffusion coefficient measured by Daumas et al. (2003). However, the FRAP diffusion coefficients for other GPCRs are consistent with the present µOR data for D^eff(33 ms)_{250 ms} and D^eff(33 ms)_{1.5 s} in both the SPT and SFVI results (Fig. 3), further supporting the results obtained in our investigation.

Daumas et al. (2003) somehow compared the SPT data obtained in NRK cells with the FRAP data obtained in CHO cells, finding that, as described above, the diffusion of µOR is also very slow in CHO cells. Therefore, we also observed the diffusion of µOR-mGFP expressed in CHO cells and compared the results with those in NRK cells, examining the possibility that the diffusion of µOR-mGFP is slow in CHO cells. The diffusion coefficients were only slightly smaller in CHO cells than those in NRK cells (Table 1).

The diffusion coefficients found in the plasma membrane of cultured cells summarized in Table 1 are smaller, by a factor of 10–15, than those reported for bacteriorhodopsin (a GPCR-like protein with seven transmembrane domains) in reconstituted membranes in the liquid-crystalline phase (Peters and Cherry, 1982). This suggests that there may be a slowing mechanism in the cell membrane that does not exist in reconstituted membranes of lipids and transmembrane proteins, and that could not be observed by video-rate observations (see the high-speed SPT results presented later).

Effect of prolonged on-ice preincubation of colloidal gold probes with the cells
Next, we carefully looked for differences between our protocol and that employed by Daumas et al. (2003). According to their protocol, for gold labeling of µOR on the NRK cell surface, the cells were incubated with the gold particles conjugated with anti-T7 antibody (we followed their procedure exactly for the preparation of gold probes) on ice for 45 min, and then the temperature was raised to 37°C (22°C in some cases) for microscopic observations. In most cases, we start our microscopic observations at 37°C right after the addition of gold particles at room temperature, in the presence of gold particles in the medium, and as new gold particles become bound to the cell surface, we tend to observe the newly attached particles (Fujiwara et al., 2002; Nakada et al., 2003; Murase et al., 2004). This procedure is the same as that employed in the Michael Sheetz laboratory at Columbia University, New York (personal communication, 2004; Felsenfeld et al., 1996). Therefore, we thought that the prolonged cold preincubation of the gold probes with the cells might have caused the artifactual cross-linking and/or nonspecific binding. To test this hypothesis, we also carried out on-ice preincubation of gold probes with the cells for 45 min, and observed the movement of GT7-µOR.

Typical trajectories of GT7-µOR observed after the cold preincubation are shown in Fig. 2 c (red trajectories). Compare these trajectories with those shown in Fig. 2 b. Those obtained after the prolonged cold preincubation exhibited much less mobility. The MSD-t curves in the time windows of 10 s (left) and 0.3 s (right) displayed in Fig. 2 e also show the very limited mobility of GT7-µOR (note the very shallow slopes of red circles) after the cold preincubation. Likewise, D^eff(33 ms)_{100 ms}, D^eff(33 ms)_{250 ms}, and D^eff(33 ms)_{1.5 s} for the cold-preincubated GT7-µOR shown in Fig. 3 (third row) exhibited greatly reduced diffusion coefficients, with the mean values reduced from those for GT7-µOR without cold preincubation by factors of 8, 12, and 14, respectively, and from those for µOR-mGFP by factors of 11 and 17, respectively (p < 0.0001 for all of the above cases. Also see Table 1 and in Fig. 3, third row and third column). These results indicate a prolonged on-ice incubation step likely causes slowed diffusion and immobilization of µOR.

These results strongly suggest that the prolonged cold preincubation of gold probes with the cells is at least partially responsible for the artifactual long-term confinement of µOR found previously. Based on these observations, we strongly recommend that prolonged cold incubations of gold probes with the cells be absolutely avoided, and that the observations of gold particles on the cell surface be carried out and finished quickly (for example, within 15 min after the application of the gold probes) in the presence of gold particles in the medium (without washing unbound gold particles away), which are in dynamic equilibrium with those attached on the cell membrane.

High-speed SPT of gold-tagged µOR revealed its hop diffusion over the plasma membrane compartments, consistent with the results found for DOPE and TfR
The µOR diffusion coefficients in the NRK cell membrane measured at video rate were smaller than those measured for bacteriorhodopsin (another seven-path transmembrane protein) in reconstituted membranes (Peters and Cherry, 1982) by a factor of as large as 10–15, suggesting the presence of slowing mechanisms in the cell membrane that could not be resolved by video-rate observations. Since single molecules of µOR-mGFP cannot be observed at very high time resolutions, we had to depend on SPT with gold tags, and thus used Gmyc-µOR. The use of such large gold particles can be justified (in the time window of 500 ms or shorter) because, as described, Gmyc-µOR gave the same effective diffusion coefficient as µOR-GFP in these time windows. Therefore, the diffusion of Gmyc-µOR on the cell surface was observed at a 25-µs resolution (1350-fold enhanced from the normal video rate). The precision of the particle's coordinate determination at this time resolution was 17 nm (Fujiwara et al., 2002).

Typical trajectories of Gmyc-µOR observed at a 25-µs resolution are shown in Fig. 4 a, which suggest the occurrence of hop diffusion, as described previously (Fujiwara et al., 2002). From the trajectory on the left (slightly >100 ms, containing more than 4,000 positions determined every 25 µs), the MSD-t curve in the time range up to 37.5 ms was obtained using Eq. 1 (Fig. 4 b, left). It increases rapidly near time 0, but the slope appears to gradually decrease to a certain value.

A statistical method for classifying each trajectory into simple Brownian, confined, directed, or stationary modes, based on the MSD-t plot, has been described by Kusumi et al. (1993), and used here. This method employs a parameter RD(N, n), which describes the long-term deviation of MSD(N, n) from the expected MSD at time nt (n = number of frames, t = frame exposure time) from the initial slope of the MSD-t plot, assuming that the trajectory is a simple Brownian one (4D_micront), i.e., RD(N, n) = MSD(N, n)/4D_micront. Here, N is the full length (in image frames) of the trajectory being examined. In the case of molecules undergoing simple Brownian diffusion, the average value of RD(N, n) is 1, but the individual trajectories of Brownian particles would show a statistical spread around 1. Using Monte Carlo simulation, we generated 500 4000-step trajectories (here N is 4000), and the distributions of the RD(4000, n) were obtained for various n values (time windows used for the analysis; see the Materials and Methods section for further details). These distributions are shown in Fig. 4 c (top) for n values of 2000, 1000, 500, and 200 (analysis time windows of 50, 25, 12.5, and 5 ms, respectively). For the classification of the trajectories into different diffusion modes, RD(4000, n) values that give 2.5% of the particles from both ends of the distribution, referred to as RD_min(4000, n) and RD_max(4000, n), were determined as described by Kusumi et al. (1993) (shown in Fig. 4 c by vertical blue and magenta lines, respectively; note that N is fixed to 4000 for the convenience of the presentation, but as long as it is sufficiently long to include at least one hop event within the trajectory on average, the exact value of N does not matter as much as n, as shown by Kusumi et al., 1993)).

See Fig. 4 c, bottom. The histograms show the distributions of RD(4000, n) for Gmyc-µOR trajectories. Note that trajectories observed longer than 4000 frames were used for the analysis (the initial 1–4000 steps were used for the analysis for all the trajectories), without any arbitrary or intentional subdivision of the trajectory (which would defeat the whole purpose of this statistical analysis). These distributions are totally different from those established for simulated simple Brownian trajectories shown on the top row. Based on the numerical criterion using RD_min(N, n) and RD_max(4000, n), it was found that >90% of the Gmyc-µOR trajectories were categorized into the confined mode. Readers must be aware that, in our trajectory classifications protocol, we have never intentionally preselected portions of the trajectories or subdivided the longer trajectories into pieces of subtrajectories that appear to represent the motion within a compartment, since such a preselection of a part of the trajectory would totally defeat the purpose of the statistical analysis: when the trajectories of (for example) 4000 frames were needed for the analysis, 4000-step trajectories were experimentally obtained, or when longer trajectories were used, the initial 1–4000 steps were used.

One might wonder why such a straightforward classification method works even for hop diffusion trajectories (and not limited to totally confined diffusion; of course, the trajectories used for the analysis have to be sufficiently long to sense the presence of the compartment boundaries). This is likely due to a direct consequence of two characteristics of Gmyc-µOR diffusion in the plasma membrane:

1. The plasma membrane is compartmentalized everywhere, and if one has the right time resolution and sufficient number of points at that time resolution, every part of the trajectory (again, N has to be sufficiently long to detect the confinement as described by Kusumi et al., 1993) should exhibit the confinement.
   
2. The residency time within a compartment is sufficiently long to be statistically differentiated from simple Brownian diffusion cases. In fact, successful statistical detection of temporary confinement of Gmyc-µOR within a compartment was expected in a simplistic way: as described below, since the ratio of D_micro versus D_MACRO for 210-nm compartments is as large as 20 for Gmyc-µOR, detection of diffusion anomaly should not be difficult.
   

Due attention should be paid to the time resolution (the observation density in time) and the time window used for analysis (as well as the total period for the observation) when the MSD-t curve is used for the analysis of trajectories. For example, a MSD-t curve based on the experiments employing conditions like a time resolution of 0.30 ms and an analysis time window of 3.75 ms out of a 7.5-ms trajectory is not uncommon in the literature. Such a display was simulated in Fig. 4 b, right, using the initial 300-step part of the trajectory shown in Fig. 4 a, left. Finding any indication of leveling off may be difficult in this display (thus the linear fit appears sufficient as shown): the time window used for the analysis is too short and the plot is too coarse for the detection of leveling off or confinement of a molecule in a compartment. This indicates that to detect the confined or hop diffusion characteristics of single molecules or particles diffusing in the plasma membrane, one has to carefully vary the time resolution and the analysis time window before reaching any conclusions.

To quantitatively analyze the trajectories obtained at a 25-µs resolution (like those shown in Fig. 4) for the evaluation of the compartment size and the residency time within a compartment, the "hop fit" for the MSD-t plots in the time range (time window) between 0.05 and 25 ms (1000 frames) was performed with the total observation period of 100 ms (4000 frames) as described in the Materials and Methods section. The adjustable parameters for the hop fit were D_micro (the diffusion coefficient within a compartment), D_MACRO (the macroscopic rate of diffusion hopping over many compartments), and the compartment size L. Note that for the successful hop fitting, the time window has to be chosen so that the contributions from D_micro and D_MACRO are balanced; although the time range used for the curve fitting here is 25 ms in the MSD-t plot, the curve in this time range contains information for the whole 100-ms trajectory because in the MSD calculation, all possible pairs of the determined points in the trajectory are used (see the Methods section, Kusumi et al., 1993), and therefore, residency times within a compartment >25 ms can be detected. If the residency time is much >25 ms, D_MACRO will hardly contribute to the determination of the MSD-t curve, which makes the accuracy of the evaluation of D_MACRO much worse, and thus the time window for the fitting has to be lengthened.

Since D_MACRO is a generic term and may refer to the diffusion coefficient in various time scales in different contexts (note that the term D_MACRO is only used when it was estimated using the hop fit; in our study, D_MACROS were determined based on the observations made at time resolutions of 0.025, 2, and 8 ms, by using trajectories with durations of 0.1, 3, and 4 s, respectively; see Table 2), we use a D(time resolution)_{the length of the full trajectory} like D (25 µs)_{100 ms} in this article to indicate the time resolution and the length of the trajectory whenever the meaning of D_MACRO might be confusing.

Fig. 4 d (third box, shaded bars) shows the distribution of the compartment size (L), which was determined for each Gmyc-µOR particle from the MSD-t plot (like the one shown in Fig. 4 b, left). The median compartment size is 210 nm for NRK cells, which is consistent with the 230 nm found for an unsaturated phospholipid (DOPE) and with the 260 nm determined for TfR (a transmembrane protein, native dimer) in the same NRK cell line (also see Supplementary Material, Text 2). This result strongly supports the membrane skeleton "fence" and "picket" models.

The average residency time within a compartment for each trajectory was calculated based on D_MACRO and the compartment size determined for each trajectory, using the equation of L²/4D_MACRO. The distribution of the µOR's residency time within a compartment is shown in Fig. 4 d (fourth box, shaded bars). The median residency time was 45 ms, which is between that for DOPE (13 ms) and TfR (65 ms) (Fujiwara et al., 2002), and thus is generally consistent with our previous observations.

µOR diffusion data after mild latrunculin treatment further support the GPCR hop diffusion over the membrane compartments
To further confirm the involvement of the membrane skeleton in the hop diffusion of µOR, the cells were very mildly treated with latrunculin B (50 nM final concentration) (Spector et al., 1983). The treatment was carried out under microscopic observation at 37°C, and after incubating the cells for 2 min, the collection of single-molecule dynamics data on Gmyc-µOR was initiated and continued for up to another 10 min. Note that these conditions are substantially milder than those employed in most other biochemical, biophysical, or cell biological studies, because our intention was not to wipe out the F-actin from the cytoplasmic surface of the membrane, but to modestly increase the compartment size by inducing slight actin depolymerization (see Supplementary Material, Fig. S1 and its caption).

The distributions of D^eff(25 µs)_{75 µs} (its distribution and the average value is basically the same as those for D_micro determined by the hop fit), D_MACRO (D(25 µs)_{100 ms}], the ^</