INTRODUCTION

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Domain structure in membranes has been postulated for 20 years or more (Jain and White, 1977), and large domains are well known in differentiated cells such as epithelium and cells of the reproductive system. However, there is less evidence for lateral heterogenity in the undifferentiated cell surface, and that which exists derives mainly from interpretations of various fluorescence studies. The large range of values obtained from typical fluorescence recovery after photobleaching (FRAP) studies (see, for example, Jacobson et al., 1987) has been taken as evidence for lateral heterogenity; and the presence of domains has been inferred from the dependence of the FRAP mobile fraction on laser beam diameter in the specimen plane (Yechiel and Edidin, 1987; Edidin, 1996). More directly, micron-sized lipid enrichments have been imaged by fluorescence in red cell ghosts (Rodgers and Glaser, 1993). The application of single-particle tracking (SPT) and laser trapping to plasma membrane components allows submicron domains to be investigated (see Jacobson et al., 1995; Kusumi and Sako, 1996). SPT permits observation of the movements of single or very small groups of proteins on a distance scale of tens of nanometers and on a time scale of tens of milliseconds. Based on SPT measurements of a major CAM, E-cadherin (Kusumi et al., 1993), the transferrin receptor and ₂-macroglobulin (Sako and Kusumi, 1994), as well as elegant laser trap and SPT measurements on the transferrin receptor (Sako and Kusumi, 1995), Kusumi and co-workers have proposed the membrane skeleton fence (Kusumi and Sako, 1996) as a general restraint to the mobility of membrane proteins.

Using SPT, the goal of this work was to determine the lateral mobility of various isoforms of another prominent cell adhesion molecule, the neural cell adhesion molecule (NCAM). The NCAM family consists of nearly 30 isoforms of cell adhesion molecules, which arise from a single gene that is alternatively spliced during transcription (Doherty et al., 1989, 1990a,b, 1992a,b; Pollerberg et al., 1986; Walsh and Doherty, 1991). Major isoform differences result either from various forms of membrane anchorage, including a membrane-spanning peptide with different sized cytoplasmic domains or a glycosylphosphatidyl-inositol (GPI) linkage. Cell type-specific ectodomain differences include a 37-amino acid insert, called the muscle-specific domain (MSD) (Walsh and Doherty, 1991), and a 10-amino acid insert derived from the VASE exon (Small et al., 1988; Doherty et al., 1992a). In addition to its role in cell adhesion, NCAM is involved in regulating neurite outgrowth (Doherty et al., 1989, 1990a,b, 1992a,b). The GPI-linked 120-kDa isoform and the 140-kDa isoform of NCAM, which contains a small cytoplasmic domain, are much more effective at promoting neurite outgrowth than the 180-kDa large cytoplasmic domain isoform (Doherty et al., 1992b).

The classification and analysis of NCAM SPT data revealed, in addition to free diffusion, the widespread existence of both corralled and very slow diffusing fractions for all isoforms. NCAM in these zones experienced a type of diffusion that can be interpreted as being strongly hindered by dense obstacle fields. These measurements indicate that the membrane is a mosaic containing regions that permit free diffusion as well as regions in which NCAM is confined for a range of times. Our measurements can be contrasted to those for E-cadherin (Kusumi et al., 1993). Such a comparison reveals significant differences between the lateral mobility of these two CAMs and indicates that either the membrane skeleton fence (Kusumi and Sako, 1996) is not a general restraint for all plasma membrane proteins, or that the way in which it restricts mobility depends on the particular protein.

	MATERIALS AND METHODS

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Cells and reagents

C2C12 mouse muscle cells and National Institutes of Health 3T3 fibroblasts were transfected with various isoforms of human NCAM as described elsewhere (Doherty et al., 1989; Peck and Walsh, 1993). Cells were routinely cultured in DMEM-H (Dulbecco's modified Eagle's medium, with D-glucose, L-glutamine, and sodium bicarbonate; H is for high glucose (9 g/liter)), supplemented with 10% fetal bovine serum, and plated on 22 mm × 22 mm coverslips for the SPT measurements 2 days before experiments. The anti-human NCAM (ERIC-1) is a mouse monoclonal antibody (mAb) IgG1 (Bourne et al., 1991); it was obtained from an ascites (Vector Labs, Burlingame, CA) and purified by ammonium sulfate precipitation, followed by a protein G column using the mAb Trap G11 Kit (Pharmacia). To label endogenous NCAM on C2C12 cells, anti-NCAM mAb H28 was employed (Gennarini et al., 1986). Fourty nanometer gold particles were conjugated to the antibody as previously described (Lee et al., 1991).

SPT measurements

SPT studies were performed essentially as described by Lee et al. (1991). Plated cells were incubated for 20 min with gold-conjugated antibody at 37°C in a CO₂ incubator and were examined on a Zeiss Axiovert 10 microscope with bright-field optics (100×, 1.3 NA oil-immersion objective and a 1.4 NA oil-immersion condenser). Cells were used for less than 1 h after labeling, and usually no evidence for internalization of gold-labeled antibody was found during this period, as judged by the fact that with bright-field optics, internalized gold probes are lower in contrast than gold probes on the cell surface.

Images were projected with a 4× adapter onto a Hamamatsu C2400 video camera and recorded on a Panasonic TQ-2028F optical disc recorder after real-time background subtraction and contrast enhancement, using Image 1 (Universal Imaging Corp., West Chester, PA). The data were analyzed by Image 1 to obtain the centroids of gold particles in each recorded frame, using a threshold function or cross-correlation analysis. Thresholding the diffraction pattern of gold tags yielded a pixel-size spatial resolution (~48 nm at the magnification used). Centroids could be localized to an accuracy of 20-30 nm by using a cross-correlation analysis as described by Gelles et al. (1988). The mean squared displacement (MSD) was calculated for every time interval previously described (Gross and Webb, 1988; Lee et al., 1991; Quian et al., 1991). Two-dimensional Brownian motion exhibits a linear relationship between the MSD and time (r² = 4Dt), yielding a straight line of slope 4D in a plot of MSD versus time; regression analysis was used to obtain D from the initial slope of this plot.

Classification of short-term trajectories

The movements of the GPI-anchored NCAM120 and the transmembrane NCAM180 were examined in National Institutes of Health 3T3 fibroblasts over durations of 6.6 s (called short-term observations). Data sets consisting of 200 frames were recorded at video rate (33 ms/frame). Trajectories of NCAM observed on this time scale exhibited several distinct behaviors. Because just one mobility parameter would not have sufficed in separating different diffusional modes, we classified the data based on a combination of parameters. Trajectories could be separated into various classes based on D, the shape of the MSD-versus-time plot, and certain characteristics derived from the radius of gyration tensor (Saxton, 1993). The criteria that defined a given mobility class were chosen in a way that made it possible to assign each trajectory to one of the classes with little overlap. The selection of particular criteria was checked by comparision to simulated data (see below).

The shape of the MSD-versus-time plot allows different lateral transport modes to be distinguished. For example, if diffusion is confined to a corral of radius a, the MSD approaches a limiting value of a², reflecting the size of the corral. Following work by Saxton (1993), parameters derived from the radius of gyration tensor T (Eq. 1) were employed to characterize the shape, size, and asymmetry of trajectories:

(1)

Here x and y are the coordinates of points that make up a trajectory, and the brackets denote an averaging over all points in the trajectory. The eigenvalues of T determine the major (R₁) and minor (R₂) semiaxes of an ellipse that approximates the size and shape of a trajectory. A standardized measure for the size of the trajectory is therefore provided by the squared radius of gyration, Rg² = R₁² + R₂². In the case of confined diffusion, Rg² also provides a measure for the size of the corral with r²(t  ) = 2Rg² (Saxton, 1993). Two other parameters, a₂ = R₂²/R₁² and A₂ = (R₁²  R₂²)/(R₁² + R₂²), allow characterization of the asymmetry of the trajectory (Saxton, 1993). Although a₂ and A₂ are trivially related for a single trajectory, when averaged over a large set of tracks, they emphasize different parts of the asymmetry distribution. For a perfectly symmetrical trajectory, T describes a circle with R₁ = R₂, yielding a₂ = 1 and A₂ = 0. For a more asymmetrical trajectory, R₁ > R₂, and therefore 0  a₂, A₂ < 1. In the extreme asymmetrical case of the trajectory being a straight line, R₁ =  and R₁ = 0, and therefore a₂ = 0 and A₂ = 1.

Short-term trajectories were divided into four classes, based on the following characteristics. The mobile class was defined by a linear MSD-versus-time curve, with D > 1 × 10¹⁰ cm²/s, Rg² > 0.07 µm², and a₂ < 0.5. The MSD-versus-time plot of the slowly diffusing class was approximately linear, but with D < 1 × 10¹⁰ cm²/s, Rg² < 0.07 µm², and a₂ < 0.5. The corralled class had a MSD-versus-time curve that approached a limiting value, Rg² < 0.07 µm² and a₂ > 0.5. The immobile class also exhibited a MSD-versus-time curve that plateaued, but with D < 0.1 × 10¹⁰ cm²/s and Rg² < 0.015 µm² with a₂ > 0.5. These criteria reflect the fact that the area covered by the trajectory within a certain time period, as characterized by Rg², will be greater for rapidly diffusing particles than for those with low diffusivity. Furthermore, immobilized or corralled diffusants usually produce more symmetrical trajectories that yield higher values for a₂, when compared to freely diffusing particles. Less than 3% of all trajectories did not fit perfectly into one of these categories. These trajectories were assigned to the class that best accounted for their characteristic parameters as defined above. In all cases, D was calculated from the initial slope of the MSD-versus-time plot.

Long-term trajectories and their classification

The diffusion of gold-labeled NCAM in C2C12 mouse muscle cells was examined on a longer time scale of 90 s, over which sets of 300 frames were recorded, at a frequency of one frame every 300 ms. A rigorous separation of trajectories into different classes as accomplished on the shorter time scale was not possible, because a significant fraction of NCAMs switched between confined and free diffusion modes during the observation time. Because random diffusion can account for a wide variety of trajectory shapes and may temporarily mimic confinement (Berg, 1983), a comparison with simulated Brownian motion is necessary to determine if these apparent switches in diffusion mode cannot be accounted for by the large family of random walks. Accordingly, we developed a method for detecting temporary confinement that is not due to random diffusive behavior (Simson et al., 1995). Briefly, the probability  of small segments of a trajectory arising from Brownian motion is calculated according to the method of Saxton (1993):

(2)

where R is the radius of a circle circumscribing the area covered by a segment of a trajectory during the time period t, and D is the diffusion coefficient. These probabilities are compiled to form a probability profile of that trajectory, in which regions exceeding a threshold level, L_c, denote periods of confinement due to nonrandom origins. The particular value of L_c chosen (3.16) corresponds to a probability of less than 1 × 10⁴ that the underlying NCAM behavior arises from Brownian motion. Key parameters, including L_c, the segment size, and confinement time, have been optimized to minimize the detection of transient confinement in simulated random walks (Simson et al., 1995). For trajectories exhibiting more than one confinement event, the interconfinement zone distance was measured as the separation of the centers of successively visited confinement zones.

Trajectories switching between confined and free diffusion were combined in a new class termed hybrid. Furthermore, when observed at this longer time scale, practically no particle proved to be immobile according to the definition used for the short-term observations. All trajectories characterized by a value of D < 0.1 × 10¹⁰ cm²/s were therefore combined in a slow class. The remaining unconfined and rapidly diffusing proteins were again classified as mobile.

Detection of anomalous diffusion

NCAM trajectories have also been analyzed to determine whether diffusion is normal or anomalous. Motion through a dense field of obstacles can cause diffusion to be anomalous, in which case the MSD is no longer linear in time, but it is proportional to a power of time of less than 1, r²  t^2/d_w, where d_w is the anomalous diffusion exponent. A plot of log(MSD/time) versus log(time) for normal diffusion yields a straight line of slope 0, whereas anomalous diffusion results in an initially negative slope given by 2/d_w  1 (Saxton, 1994). Anomalous diffusion is therefore characterized by a value of d_w > 2, whereas normal diffusion yields d_w = 2. For obstacle concentrations below the so-called percolation threshold, a cross-over to normal diffusion can be observed after a cross-over time t_c. Above this threshold, however, no long-range diffusion is possible, so no cross-over to normal diffusion can be observed (Saxton, 1994).

	RESULTS

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Lateral mobility of NCAM isoforms expressed in 3T3 cells

On a time scale of 6.6 s, both the GPI-anchored 120-kDa and the transmembrane 180-kDa isoforms of NCAM expressed in 3T3 cells exhibited four distinctly different subpopulations when examined by SPT, and were classified according to the criteria presented in Materials andMethods. Differences between characteristic trajectories of the four classes (mobile, slow, corralled, and immobile) can be seen in Fig. 1 and can be readily identified in a plot of the MSD versus time for each class (Fig. 2). Roughly 50% of the population for both isoforms exhibited rapid Brownian diffusion (the straight line of highest slope in Fig. 2). This fraction, called mobile, was characterized by a mean diffusion coefficient of 3.7 × 10¹⁰ cm²/s, about four- to sixfold lower than that measured by FRAP (Jacobson et al., 1997). Smaller fractions underwent corralled diffusion (the MSD approaching a limiting value with increasing time) or slow diffusion, or were classified as immobile. The average diffusion coefficients for each class were taken from the initial slope of their MSD curves in Fig. 2 and are listed in Table 1.

View larger version (5K): [in this window] [in a new window]   FIGURE 1   Representative trajectories of the various classes (NCAM 180 transfected into 3T3 cells) of short-term (6.6 s) measurements. (A) Mobile; (B) slow; (C) corralled; (D) immobile.

View larger version (23K): [in this window] [in a new window]   FIGURE 2   Different modes of diffusion (classes) detected in a plot of mean squared displacement (MSD) versus time interval for NCAM120 (a) and NCAM180 (b). The fastest diffusing class (mobile) is characterized by the steepest slope. The MSD for the corralled fractions approaches a limiting value with increasing time, which is a measure of corral size.

The quantities a₂ and A₂, although not independent, are both measures of the asymmetry of the trajectory, emphasizing different parts of the distribution. Simulations of unobstructed random walks yield, on average, a₂ = 0.28 and A₂ = 0.39 (Saxton, 1993), reflecting the fact that Brownian motion typically produces asymmetrical trajectories (Berg, 1983). NCAM classified as mobile come closest to these values (Table 1), consistent with the presumed Brownian nature of NCAM diffusion in this class. Proteins classified as slow, corralled, or immobile, however, yield different values for a₂ and A₂, reflecting a deviation from Brownian motion (Table 1). Trajectories in the classes corralled or immobile are more symmetrical, yielding higher values for a₂, whereas trajectories in the slow category are more asymmetrical as compared to trajectories for Brownian motion. Differences in the values for Rg² reflect the fact that trajectories from rapid diffusing proteins cover a larger membrane area within a certain time period than slowly diffusing proteins (Table 1). For corralled NCAM, however, exhibiting a diffusivity comparable to that of NCAM in the class mobile, Rg² simply corresponds to an average corral diameter of ~300 nm.

The classification scheme was checked for self-consistency for the mobile and slow classes by simulating random walks characterized by the experimentally obtained D values for NCAM 120 and 180, respectively, and then calculating the fraction of trajectories that would be misclassified as corralled according to our criteria (Table 2). These simulations show that the probability of wrongly classifying a trajectory as corralled increases as the D value decreases. For example, for the fastest diffusing class, mobile, only ~3% of the simulated trajectories would have been classsified as corralled. In the case of the slow class, the trajectories failing to match the condition in a₂ for slow Brownian diffusion would necessarily satisfy the condition for corralled because the criteria for slow and corralled differ only in a₂. In this case 11.5% of the trajectories would have been misclassifed as corralled. On the other hand, if we simulate Brownian diffusion for the range of D values obtained for the corralled diffusion of NCAM 120 and 180, only 8.4% and 5.6%, respectively, would have qualified as corralled (last two rows of Table 2). As discussed in Materials and Methods, movements through a dense field of obstacles can cause diffusion to become anomalous; this phenomenon yields an initially negative slope in a plot of log(MSD/time) versus log(time) and an anomalous diffusion exponent d_w > 2. On the same plot, normal diffusion yields a straight line of slope 0, or d_w = 2. We applied this test to both NCAM180 and NCAM120 for the 6.6-s observation times. Linear regression yields an initial slope of ~ 0.07, or d_w  2.1, for the mobile fractions of both isoforms (Fig. 3 a), indicating that diffusion is indeed normal for NCAM in this class. For the classes slow and corralled, however (Fig. 3, b and c, respectively), the results suggest that diffusion is anomalous, with anomalous diffusion exponents between d_w  4 and d_w  7 (Table 3).

View larger version (16K): [in this window] [in a new window]   FIGURE 3   Tests for anomalous diffusion for mobile (a), slow (b), and corralled (c) classes for both NCAM 120 and 180 expressed in 3T3 cells. Fitting parameters are given in Table 3.

Lateral mobility of NCAM isoforms expressed in C2C12 muscle cells

The behavior of transfected isoforms (NCAM125, NCAM140) and endogenous isoforms (predominantly NCAM140) was examined in muscle cells on the longer time scale of 90 s; endogenous NCAM was also investigated on the short-term time scale (Table 1). The predominant NCAM expressed in the myoblast stage is the transmembrane 140-kDa isoform, whereas the 125-kDa isoform is more prevalent in myotubes (Moore et al., 1987). Although NCAM125 is a GPI-anchored protein and NCAM140 is a transmembrane protein, all isoforms showed roughly similar behavior in the long-term observations. The mobile class for the endogenous NCAM140 was characterized by a lateral diffusion coefficient somewhat greater than that for the two transfected isoforms (Table 4). Furthermore, endogeneous NCAM showed appreciably more corralled diffusion in the long term (hybrid, Table 4) and in the short term (Table 1) than did the isoforms expressed by gene transfer.

A considerable fraction (15-40%) of all isoforms exhibited free Brownian diffusion interspersed with periods of transient confinement, and are referred to as the hybrid class. Periods of transient confinement were identified by probability profile analysis (Simson et al., 1995) (Fig. 4); they have a likelihood of less than 1 × 10⁴ of arising from Brownian motion. By the same analysis, confined periods were detected in only 1.5% of 1100 simulated random walks (Table 5; Simson et al., 1995). The range of confinement times, confinement zone radii, and interconfinement zone separations is given by the histograms in Fig. 5 for NCAM 125 (Fig. 5, a-c) and endogenous NCAM (Fig. 5, d-f). NCAM in the hybrid class typically exhibited one or two confined periods, each lasting ~7 s and occurring within a region with a diameter of ~300-400 nm (Table 4). The interconfinement zone separations were distributed over a range of distances from less than 0.5 µm to over 2 µm. A large fraction, ~50%, had only one confinement zone per trajectory, which suggests a large separation of successive confinement zones.

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Trajectory and the corresponding probability profile are shown for a lipid linked NCAM125, observed for 90 s in C2C12 muscle cells. The probability level L is given as log()  1, where  is the probability that the underlying NCAM behavior is Brownian. Transient confinement is defined to occur in regions of the profile (b) where L rises above a threshold level Lc = 3.16, corresponding to a probability of less than 1 × 104 that the NCAM behavior was Brownian. In this example, three periods of confinement were detected in the probability profile (b), corresponding to the circled and numbered regions in the trajectory (a). Note that confinement zone 3 has a probability of less than 1 × 1022 of arising from Brownian motion, because peak 3 reaches a level L  21 (b).

View larger version (57K): [in this window] [in a new window]   FIGURE 5   (a, b, d, e) Histograms of the distribution of confinement times and confinement zone radii. (a, b) Human NCAM 125 expressed in C2C12 muscle cells. (d, e) Endogenous NCAM (predominantly NCAM140) in C2C12 muscle cells. (c, f) Histograms of interconfinement zone separations. (c) Human NCAM 125 expressed in C2C12 cells; (f) endogenous NCAM (predominantly NCAM 140) in C2C12 muscle cells. In both histograms, the tallest bar to the right represents the fraction of trajectories with only one confinement zone detected.

The remaining fraction of the NCAM could be separated into a mobile class, exhibiting unconfined Brownian diffusion, and a slowly diffusing class, that contained proteins with D values less than 0.1 × 10¹⁰ cm²/s (Table 5). Although they diffused very slowly, these proteins were not immobile by the standards set for the 6.6-s studies.

Tests for anomalous diffusion were also conducted for NCAM diffusion in muscle cells. For all three isoforms, NCAM125, NCAM140, and the endogenous NCAM140, the log-log plot for the unconfined diffusing proteins in the mobile class yields values of d_w between 1.9 and 2.2, indicating that diffusion is normal (Table 3). NCAMs in the slow class exhibit anomalous diffusion, with d_w between 3 and 4 (Table 3). The same analysis for only the confined parts of the hybrid trajectories suggests that diffusion within the confinement zones is anomalous, with d_w  6 for all NCAM isoforms (Table 6, "corralled"), whereas diffusion appears normal during the unconfined periods (data not shown).

	DISCUSSION

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SPT results demonstrate the existence of transient confinement and slow diffusion zones

These SPT results expand our understanding of membrane protein mobility by increasing both the time and spatial resolution of the mobility determination. They indicate that a significant fraction of NCAM exhibits confined, hindered diffusion. Short-term SPT results could be classified into mobile (Brownian) diffusion, corralled diffusion, slow diffusion, and immobile fractions. On this time scale, proteins maintained a single diffusion mode during the entire period of observation. Notably, only ~50% of the labeled population exhibited normal, Brownian diffusion. Neither the D value for the mobile class nor the distribution of trajectories into the various classes depended significantly on the mode of membrane anchorage (GPI anchorage for NCAM 120 versus membrane-spanning peptide with large cytoplasmic domain for NCAM 180). The similarity of SPT-derived D values for the mobile classes of NCAM 120 and 180 in particular is consistent with earlier FRAP results on vesicular stomatitis G glycoprotein membrane anchorage mutants (Zhang et al., 1991) and various NCAM isoforms with different membrane anchors (Jacobson et al., 1997). In these cases, the D value characterizing the mobile fraction showed little dependence on the mode of membrane anchorage when mutants or isoforms with similar or identical ectodomains were compared. To examine whether proteins within corrals can ever leave them, two transfected NCAM isoforms, NCAM125 and NCAM140, and an endogenous isoform, NCAM140, were examined on a much longer time scale of 90 s in C2C12 muscle cells. Roughly 20-40% of the populations of both the transfected GPI-anchored 125 kDa and the transmembrane 140-kDa isoforms as well as the endogenous NCAM isoforms exhibited hybrid trajectories in which the particle switched between unrestricted Brownian and confined diffusion. Although the size of the confinement zones and duration of confinement may vary, this behavior is not unique to NCAM (for a review, see Sheets et al., 1995). The remaining NCAM exhibited either rapid Brownian or slow, anomalous diffusion.

NCAM diffusion within transient confinement zones and slow diffusion zones is anomalous

Within confinement zones, diffusion was anomalous for both the GPI and transmembrane NCAM isoforms expressed in muscle and 3T3 cells. These results suggest that a high concentration of obstacles exists within the confinement zones. A dense field of obstacles on the cell surface could entrap both transmembrane and lipid-linked proteins like the ball in a pinball machine. However, diffusion was normal for the mobile NCAM, both in fibroblasts and in muscle cells. These results indicate that some regions of the plasma membrane exhibit diffusion unhindered by obstacles, reflecting a marked heterogeneity of the membrane structure.

Models for slow diffusion and transient confinement zones

A way to think about the NCAM results is to assume that both TCZs and slow diffusion regions are both obstacle-rich regions, but of different sizes. In the smaller TCZs, the particle is confined, but only temporarily, whereas in the larger slow diffusion regions, the particle experiences constrained, anomalous diffusion for the entire period of observation.

What molecular structures might give rise to this constrained diffusion? Current concepts for the restraints to lateral mobility have been reviewed recently (Sheetz, 1993; Zhang et al., 1993; Edidin, 1996; Saxton and Jacobson, 1997). These range from the membrane skeleton fence model (Kusumi and Sako, 1996; see below) to lipid lateral domain structure (see, for example, Sheets et al., 1995), to a generalized system of fluctuating barriers with no fixed time or length scale (Feder et al., 1996). The latter concept includes the possibility of transient associations between the diffusant and other membrane components, and such associations could occur in the extracellular, bilayer, or cytoplasmic regions. One noteworthy result is that confinement parameters (percentage confined in the short-term data and the size and duration of the confinment zones from the long-term data) were similar for both transmembrane and GPI-anchored isoforms; this suggests that one mechanism could apply to both forms of membrane anchorage.

Confinement based on the membrane-apposed cytoskeleton

View larger version (33K): [in this window] [in a new window]   FIGURE 6   Models for confined diffusion zones. (a) Confinement-based membrane skeleton fence (Kusumi and Sako, 1996). In this version, anomalous diffusion is caused by protein obstacles tethered to the cytoskeleton and/or the cytoskeletal filaments themselves. (b) Confinement based on largely impenetrable lipid microdomains (shaded regions), which provide the obstacle field, giving rise to anomalous diffusion.

Confinement based on lipid domains

Comparison of SPT results for NCAM and E-cadherin: general applicabilty of the membrane skeleton fence model

The membrane skeleton fence model (Kusumi and Sako, 1996) is a conceptually straightforward basis for transient confinement of diffusing proteins. This model is based on earlier work on the erythrocyte membrane (Golan and Veatch, 1980; Sheetz et al., 1980; Tsuji and Ohnishi, 1986). The fence structure consists of spectrin, actin, and ankyrin or their analogs, forming a meshwork apposed to the cytoplasmic leaflet. Confinement of transmembrane proteins occurs when their cytoplasmic domains are entrapped by this meshwork. Thermally induced fluctuations or dissociation of the cytoskeleton meshwork are proposed to account for the transient nature of the confinement by allowing movement of the membrane protein from one confinement zone to an adjacent one (Kusumi and Sako, 1996).

It is instructive to compare the mobility results for two members of two prominent CAM families: NCAM 140 and E-cadherin. Both are single spanning transmembrane proteins of similar molecular weight and cytoplasmic domain size: NCAM 140 has a cytoplasmic domain size of ~13 kDa versus ~16 kDa for E-cadherin. Some of the cytoplasmic domain binding partners for E-cadherin, the catenins, are known (Ranscht, 1994; Kemler, 1993).

Inspection of Table 6 reveals that the data for NCAM 140 do not fit the membrane skeleton fence model as nicely as do the results for E-cadherin (Kusumi et al., 1993). First, as measured by FRAP, the long-range lateral diffusion coefficient for NCAM 140 is nearly 30 times greater than that for E-cadherin. This large difference is presumbably due to the constraints the membrane skeleton fence confers on E-cadherin diffusion. SPT studies reveal that over half of NCAM undergoes rapid Brownian diffusion, whereas only 10% of the E-cadherin does. About one-third of both proteins are transiently confined, and roughly speaking, the confinement times and domain diameters are similar, although in high-Ca²⁺ medium fully two-thirds of E-cadherin is confined (Kusumi et al., 1993). But the interdomain distances are different: NCAM 140 interdomain separations are broadly distributed from <0.5 µm to over 2 µm, with the largest fraction of trajectories showing only one transient confinement zone (Fig. 5, c and f). In contrast, E-cadherin is thought to move from one confinement zone to the adjacent one, a distance of 300-600 nm (Kusumi et al., 1993). Last, there are no immobile NCAM on the 90-s time scale, but ~20% of the E-cadherin is immobile; and no NCAM shows directed motion, but 37% of E-cadherin does.

How can these discrepencies be interpreted? If we take the membrane skeleton fence model as providing the preferred length and time scales for confinement, some revision of the model is required to incorporate the NCAM data. It is important to note that this generalized restraint must be at least temporarily inoperative to permit half of the labeled NCAM 140 to diffuse normally and rapidly. This could mean that in certain regions of the plasma membrane, the skeleton-membrane distance is too great to constrain the mobility of some or all membrane proteins or, alternatively, that membrane regions exist that have no skeleton intimately associated with them. One reason that the skelton-membrane distance is too great to regulate mobility could be that the size of the NCAM domain may be too small to interact with the skeleton except occasionally, and as a result, the intercorral distance is greater for NCAM. Because E-cadherin can have its cytoplasmic domain further expanded by association with catenins, it may interact more continously with the skeleton, leading to its hopping from one domain to an adjacent one. Indeed, Kusumi and co-workers have shown by both SPT and laser trapping that mutants of E-cadherin truncated in their cytoplasmic domain have considerably larger confinement zones (Kusumi et al., personal communication). Such truncation may abolish the association with cytoplasmic molecules.

It is also possible that whereas proteins such as the cadherins are directly confined by the cytoskeletal network underlying the membrane, proteins with smaller cytoplasmic domains or GPI anchors are confined indirectly by interacting via their ecto- or membrane anchorage domains with other membrane proteins that are bound to the cytoskeleton (Sheets et al., 1995).

Gold particle effects on lateral diffusion

In general, diffusion coefficients measured by SPT for the highly mobile fraction of a given membrane component are a factor of 2 to 6 lower than those measured by FRAP for that membrane component without a particle attached (for a review, see Saxton and Jacobson, 1997). For NCAM, we have recorded similar differences in comparing the SPT and FRAP values (see Table 6). The size of the gold particle (40-nm diameter) and its potential to link to one or several NCAMs make it plausible that the D values measured for the mobile fractions by SPT would be smaller than those measured by FRAP. In general, the effect of these two factors on the measured mobility properties has not been completely resolved. However, work by Sheets et al. (1997) from this laboratory shows that the classification of trajectories as well as the size and duration of the transient confinement zones for particles attached to the membrane protein Thy 1 are independent of the apparent valency of the particle.

	CONCLUSIONS

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Although it is tempting to accept the membrane skeleton fence model as a plausible general extension of the red cell membrane structure to other mammalian cells, there are a number of features of the NCAM data that do not immediately fit into this paradigm. These include a large fraction of randomly diffusing particles, similar confinement of GPI-anchored and transmembrane proteins, and larger interdomain distances for NCAM compared to E-cadherin. Furthermore, that a significant fraction of particles diffuse slowly and anomalously is not directly accounted for by the membrane skeleton fence model. The strength of the model will ultimately be judged on its capability to accommodate such apparently discordant results.