Single-particle Tracking Measurements Research Articles

DNA damage induces differentiated response of chromatin motion across temporal scales.

Movement of chromatin in human cells is complicated. Emerging evidence from single particle tracking (SPT) of chromatin loci have shown that chromatin motion is highly dependent on molecular size and time lag in SPT measurements. The physical foundations behind these observations are unclear. Most theoretical studies of chromatin dynamics that are based on the polymer model fail to explain this behavior. We have proposed a single molecule imaging strategy that can track the dynamics of the single nucleosomes in the human cell. By conducting the temporal-varying imaging, we have identified that the measured chromatin motion includes two types of movements, i.e. the fast local fluctuation of the nucleosome, and the slow chromatin chain movement. This conclusion was further validated by the theoretical modeling through ChromoShake. Furthermore, we investigated the response of nucleosome dynamics to the DNA damage. Interestingly, the bleomycin induces the accelerated motion of nucleosomes at short time scale (interval ∼ 30 ms), while the motion of nucleosomes at long time scale (interval ∼seconds) is reduced. This disparity discloses that the DNA damage accelerates the local chromatin motion, while slows down the chromatin chain movement.

Protein overexpression can induce the elongation of cell membrane nanodomains

In cell membranes, proteins and lipids are organized into submicrometric nanodomains of varying sizes, shapes, and compositions, performing specific functions. Despite their biological importance, the detailed morphology of these nanodomains remains unknown. Not only can they hardly be observed by conventional microscopy due to their small size, but there is no full consensus on the theoretical models to describe their structuring and their shapes. Here, we use a combination of analytical calculations and Monte Carlo simulations based upon a model coupling membrane composition and shape to show that increasing protein concentration leads to an elongation of membrane nanodomains. The results are corroborated by single-particle tracking measurements on HIV receptors, whose level of expression in the membrane of specifically designed living cells can be tuned. These findings highlight that protein abundance can modulate nanodomain shape and potentially their biological function. Beyond biomembranes, this mesopatterning mechanism is of relevance in several soft-matter systems because it relies on generic physical arguments.

Measurement error correction in particle tracking microrheology

In diverse biological applications, single-particle tracking (SPT) of passive microscopic species has become the experimental measurement of choice, when either the materials are of limited volume or so soft as to deform uncontrollably when manipulated by traditional instruments. In a wide range of SPT experiments, a ubiquitous finding is that of long-range dependence in the particles’ motion. This is characterized by a power-law signature in the mean squared displacement (MSD) of particle positions as a function of time, the parameters of which reveal valuable information about the viscous and elastic properties of various biomaterials. However, MSD measurements are typically contaminated by complex and interacting sources of instrumental noise. As these often affect the high-frequency bandwidth to which MSD estimates are particularly sensitive, inadequate error correction can lead to severe bias in power law estimation and, thereby, the inferred viscoelastic properties. In this article we propose a novel strategy to filter high-frequency noise from SPT measurements. Our filters are shown theoretically to cover a broad spectrum of high-frequency noises and lead to a parametric estimator of MSD power-law coefficients for which an efficient computational implementation is presented. Based on numerous analyses of experimental and simulated data, results suggest our methods perform very well compared to other denoising procedures.

Localization Error and Fitting Model Evaluation in Single Particle Tracking

Single Particle Tracking (SPT) is a powerful technique for uncovering molecular dynamics in lipid membrane biophysics, as well as in many other fields. Thus far, it has been successfully used to discover non-Brownian motion phenomena such as transient confined (also known as hop) diffusion of lipids and membrane proteins in the plasma membrane by accessing high framerates (103-104 fps) and claimed localization accuracies in the nanometre range. However, most of literature reporting high-speed SPT data relies on analysis protocols that are very susceptible to underestimations of the effects of localization errors; whose consequences are particularly pronounced at high framerates. Therefore, we propose a different approach to estimate such errors, and a statistically-driven procedure for determining the appropriate mode of motion fitting model. Using Interferometric Scattering (iSCAT) microscopy, we were able to collect high sampling frequency data of immobile and moving particles in different situations, to use for our analysis. First, we compare the effect of Signal-to-Noise Ratio on the localization precision of different immobile particles (gold nanoparticles, single proteins). Next, we show the effect of camera blur and localization error on the same particles diffusing on quasi-homogeneous Supported Lipid Bilayers (SLB), to develop an error correction method and a fitting goodness discrimination method of fitting SPT data. These last results are compared to Fluorescence Correlation Spectroscopy (FCS) measurements as a control for the values of diffusion rate. Finally, we acquired data of gold nanoparticle-tagged lipids diffusing on epithelial cell membranes, and apply the newly developed method to these data, to determine which model is the best statistical fit for cell membrane dynamics. In conclusion, the analysis workflow we propose, based on statistical methods rather than previous knowledge, could increase reliability and accuracy of future SPT measurements at high spatiotemporal resolution.

Dynamics of Nanoparticles in Entangled Polymer Solutions.

The mean square displacement ⟨r2⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (Rg), are investigated. In simple fluids and for polymer solutions in which d ≫ Rg, long-time particle dynamics obey random-walk statistics ⟨r2⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < Rg, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Single-molecule tracking of small GTPase Rac1 uncovers spatial regulation of membrane translocation and mechanism for polarized signaling

Polarized Rac1 signaling is a hallmark of many cellular functions, including cell adhesion, motility, and cell division. The two steps of Rac1 activation are its translocation to the plasma membrane and the exchange of nucleotide from GDP to GTP. It is, however, unclear whether these two processes are regulated independent of each other and what their respective roles are in polarization of Rac1 signaling. We designed a single-particle tracking (SPT) method to quantitatively analyze the kinetics of Rac1 membrane translocation in living cells. We found that the rate of Rac1 translocation was significantly elevated in protrusions during cell spreading on collagen. Furthermore, combining FRET sensor imaging with SPT measurements in the same cell, the recruitment of Rac1 was found to be polarized to an extent similar to that of the nucleotide exchange process. Statistical analysis of single-molecule trajectories and optogenetic manipulation of membrane lipids revealed that Rac1 membrane translocation precedes nucleotide exchange, and is governed primarily by interactions with phospholipids, particularly PI(3,4,5)P3, instead of protein factors. Overall, the study highlights the significance of membrane translocation in spatial Rac1 signaling, which is in addition to the traditional view focusing primarily on GEF distribution and exchange reaction.

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

Single-particle tracking (SPT) has been extensively used to obtain information about diffusion and directed motion in a wide range of biological applications. Recently, new methods have appeared for obtaining precise (10s of nm) spatial information in three dimensions (3D) with high temporal resolution (measurements obtained every 4 ms), which promise to more accurately sense the true dynamical behavior in the natural 3D cellular environment. Despite the quantitative 3D tracking information, the range of mathematical methods for extracting information about the underlying system has been limited mostly to mean-squared displacement analysis and other techniques not accounting for complex 3D kinetic interactions. There is a great need for new analysis tools aiming to more fully extract the biological information content from in vivo SPT measurements. High-resolution SPT experimental data has enormous potential to objectively scrutinize various proposed mechanistic schemes arising from theoretical biophysics and cell biology. At the same time, methods for rigorously checking the statistical consistency of both model assumptions and estimated parameters against observed experimental data (i.e., goodness-of-fit tests) have not received great attention. We demonstrate methods enabling (1) estimation of the parameters of 3D stochastic differential equation (SDE) models of the underlying dynamics given only one trajectory; and (2) construction of hypothesis tests checking the consistency of the fitted model with the observed trajectory so that extracted parameters are not overinterpreted (the tools are applicable to linear or nonlinear SDEs calibrated from nonstationary time series data). The approach is demonstrated on high-resolution 3D trajectories of single ARG3 mRNA particles in yeast cells in order to show the power of the methods in detecting signatures of transient directed transport. The methods presented are generally relevant to a wide variety of 2D and 3D SPT tracking applications.

Probing the Influence of the Particle in Single Particle Tracking Measurements on Lipids

We present a systematic study of the influence of the nanoparticle used as a probe in Single Particle Tracking experiments with a supported lipid bilayer as a model system. Quantum Dots, 40 nm and 200 nm diameter fluorescent latex spheres, and 40 nm diameter gold colloids were attached to headgroup-labeled lipid molecules in the bilayer by means of an antibody. The percentage of the particle's surface covered with antibody was also varied. We argue that the best estimate of the diffusion coefficient is derived from the first two points of the particle's mean square displacement. The accuracy of this estimate is equivalent to a more rigorous analysis based on the cumulated probability function. We show that, under optimal conditions, Quantum Dots and also 40 nm latex beads have a negligible influence on the lipid diffusion. The diffusion coefficient of gold colloids and 200 nm diameter latex particles was systematically reduced 2- to 3-fold compared to the reference value obtained by Fluorescence Recovery After Photobleaching. Unexpectedly, the diffusion coefficient of Quantum Dots and 40 nm latex beads depended on the percentage of the nanoparticle's surface covered with antibody: at very low percentage the perturbation to the lipid diffusion due to the particle increased. We speculate that in this regime subtle details of antibody binding to the nanoparticle become important.In an alternative system using particles tethered with 30 or 90 bp DNA strands, particles attached with the longer tether showed the highest diffusion coefficient. We propose that the proximity of the nanoparticle to the membrane may modify lipid dynamics.ReferenceP. Mascalchi et al. 2012. Probing the influence of the particle in Single Particle Tracking measurements of lipid diffusion. Soft Matter, 2012,8, 4462-4470.

Ensemble and single particle fluorimetric techniques in concerted action to study the diffusion and aggregation of the glycine receptor α3 isoforms in the cell plasma membrane

The spatio-temporal membrane behavior of glycine receptors (GlyRs) is known to be of influence on receptor homeostasis and functionality. In this work, an elaborate fluorimetric strategy was applied to study the GlyR α3K and L isoforms. Previously established differential clustering, desensitization and synaptic localization of these isoforms imply that membrane behavior is crucial in determining GlyR α3 physiology. Therefore diffusion and aggregation of homomeric α3 isoform-containing GlyRs were studied in HEK 293 cells. A unique combination of multiple diffraction-limited ensemble average methods and subdiffraction single particle techniques was used in order to achieve an integrated view of receptor properties. Static measurements of aggregation were performed with image correlation spectroscopy (ICS) and, single particle based, direct stochastic optical reconstruction microscopy (dSTORM). Receptor diffusion was measured by means of raster image correlation spectroscopy (RICS), temporal image correlation spectroscopy (TICS), fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT). The results show a significant difference in diffusion coefficient and cluster size between the isoforms. This reveals a positive correlation between desensitization and diffusion and disproves the notion that receptor aggregation is a universal mechanism for accelerated desensitization. The difference in diffusion coefficient between the clustering GlyR α3L and the non-clustering GlyR α3K cannot be explained by normal diffusion. SPT measurements indicate that the α3L receptors undergo transient trapping and directed motion, while the GlyR α3K displays mild hindered diffusion. These findings are suggestive of differential molecular interaction of the isoforms after incorporation in the membrane.

Probing the influence of the particle in Single Particle Tracking measurements of lipid diffusion

We present a systematic study of the influence of the nanoparticle used as a probe in Single Particle Tracking experiments with a supported lipid bilayer as a model system. Quantum Dots, 40 nm and 200 nm diameter fluorescent latex spheres, and 40 nm diameter gold colloids were attached to headgroup-labeled lipid molecules in the bilayer by means of an antibody. The percentage of the particle's surface covered with antibody was also varied. We made the choice to extract the diffusion coefficient from the first two points of the mean square displacement of the particle after demonstrating that the accuracy of this method is equivalent to a more rigorous but less prevalent analysis based on the cumulated probability function. We show that, under optimal conditions, Quantum Dots and also 40 nm latex beads have a negligible influence on the lipid diffusion, whereas the diffusion coefficient of gold colloids and 200 nm diameter latex particles was systematically reduced 2- to 3-fold compared to the reference value obtained by Fluorescence Recovery After Photobleaching. Interestingly, the diffusion coefficient of Quantum Dots and 40 nm latex beads depended on the percentage of the surface of the nanoparticle covered with antibody in an unexpected manner: at very low percentage the perturbation to the lipid diffusion due to the particle increased. We speculate that in this regime subtle details of antibody binding to the nanoparticle become important.

Aquaporin-4 (AQP4) Associations and Array Dynamics Probed by Photobleaching and Single-molecule Analysis of Green Fluorescent Protein-AQP4 Chimeras

The plasma membrane assembly of aquaporin-4 (AQP4) water channels into orthogonal arrays of particles (OAPs) involves interactions of AQP4 N-terminal domains. To study in live cells the site of OAP assembly, the size and dynamics of plasma membrane OAPs, and the heterotetrameric associations of AQP4, we constructed green fluorescent protein (GFP)-labeled AQP4 "long" (M1) and "short" (M23) isoforms in which GFP was inserted at the cytoplasm-facing N or C terminus or between Val-141 and Val-142 in the second extracellular loop of AQP4. The C-terminal and extracellular loop GFP insertions did not interfere with the rapid unrestricted membrane diffusion of GFP-labeled M1 or the restricted diffusion and OAP assembly of GFP-labeled M23. Photobleaching of brefeldin A-treated cells showed comparable and minimally restricted diffusion of M1 and M23, indicating that OAP assembly occurs post-endoplasmic reticulum. Single-molecule step photobleaching and intensity analysis of GFP-labeled M1 in the absence versus presence of excess unlabeled M1 or M23 with an OAP-disrupting mutation indicated heterotetrameric AQP4 association. Time-lapse total internal reflection fluorescence imaging of M23 in live cells at 37 degrees C indicated that OAPs diffuse slowly (D approximately 10(-12) cm(2)/s) and rearrange over tens of minutes. Our biophysical measurements in live cells thus reveal extensive AQP4 monomer-monomer and tetramer-tetramer interactions.

Analysis and interpretation of two-dimensional single-particle tracking microscopy measurements: Effect of local surface roughness

Methodological advances in light microscopy have made it possible to record the motions of individual lipid and protein molecules resident in the membrane of living cells down to the nanometer level of precision in the x, y plane. Such measurement of a single molecule’s trajectory for a sufficiently long period of time or the measurement of multiple molecules’ trajectories for a shorter period of time can in principle provide the necessary information to derive the particle’s macroscopic two-dimensional-diffusion coefficient—a quantity of vital biological interest. However, one drawback of the light microscopy procedures used in such experiments is their relatively poor discriminatory capability for determining spatial differences along the z axis in comparison to those in the x, y plane. In this study we used computer simulation to examine the likely effect of local surface roughness over the nanometer to micrometer scale on the determination of diffusion constants in the membrane bilayer by the use of such optical-microscope-based single-particle tracking (SPT) procedures. We specifically examined motion of a single molecule along (i) a locally planar and (ii) a locally rough surface. Our results indicate a need for caution in applying overly simplistic analytical strategies to the analysis of data from SPT measurements and provide upper and lower bounds for the likely degree of error introduced on the basis of surface roughness effects alone. Additionally we present an empirical method based on an autocorrelation function approach that may prove useful in identifying the existence of surface roughness and give some idea of its extent.

K-Space Image Correlation Spectroscopy: A Method for Accurate Transport Measurements Independent of Fluorophore Photophysics

We present the theory and application of reciprocal space image correlation spectroscopy (kICS). This technique measures the number density, diffusion coefficient, and velocity of fluorescently labeled macromolecules in a cell membrane imaged on a confocal, two-photon, or total internal reflection fluorescence microscope. In contrast to r-space correlation techniques, we show kICS can recover accurate dynamics even in the presence of complex fluorophore photobleaching and/or “blinking”. Furthermore, these quantities can be calculated without nonlinear curve fitting, or any knowledge of the beam radius of the exciting laser. The number densities calculated by kICS are less sensitive to spatial inhomogeneity of the fluorophore distribution than densities measured using image correlation spectroscopy. We use simulations as a proof-of-principle to show that number densities and transport coefficients can be extracted using this technique. We present calibration measurements with fluorescent microspheres imaged on a confocal microscope, which recover Stokes-Einstein diffusion coefficients, and flow velocities that agree with single particle tracking measurements. We also show the application of kICS to measurements of the transport dynamics of α5-integrin/enhanced green fluorescent protein constructs in a transfected CHO cell imaged on a total internal reflection fluorescence microscope using charge-coupled device area detection.

Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells.

We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.

3D single-particle tracking and optical trap measurements on adhesion proteins

A three-dimensional single-particle tracking system was combined with an optical trap to investigate the behavior of transmembrane adhesion proteins. We exploited this setup to investigate which part of the cell adhesion protein LFA-1 forms a connection to the cytoskeleton after binding to its ligand ICAM-1. LFA-1 is an integrin consisting of an α and a β chain. Thus far, only the cytoplasmic tail of the β chain is known to form a connection to the cytoskeleton. We investigated cells that express a mutant form of LFA-1 that lacks the complete β cytoplasmic tail and therefore is not thought to bind to the cytoskeleton. Interestingly, single-particle tracking measurements using beads coated with the ligand ICAM-1 indicate that this mutant form of LFA-1 does not move freely within the cell membrane, suggesting that LFA-1 is still connected to the cytoskeleton network. This finding is strongly supported by the observation that LFA-1 exhibits a more diffusive motion when the cytoskeleton network is disrupted and confirmed by the optical trap measurements used to force the proteins to move through the membrane. Collectively, our findings suggest that the interaction of LFA-1 with the cytoskeleton cannot solely be attributed to the cytoplasmic part of the β chain. Cytometry 36:189–194, 1999. © 1999 Wiley-Liss, Inc.

3D single-particle tracking and optical trap measurements on adhesion proteins.

A three-dimensional single-particle tracking system was combined with an optical trap to investigate the behavior of transmembrane adhesion proteins. We exploited this setup to investigate which part of the cell adhesion protein LFA-1 forms a connection to the cytoskeleton after binding to its ligand ICAM-1. LFA-1 is an integrin consisting of an alpha and a beta chain. Thus far, only the cytoplasmic tail of the beta chain is known to form a connection to the cytoskeleton. We investigated cells that express a mutant form of LFA-1 that lacks the complete beta cytoplasmic tail and therefore is not thought to bind to the cytoskeleton. Interestingly, single-particle tracking measurements using beads coated with the ligand ICAM-1 indicate that this mutant form of LFA-1 does not move freely within the cell membrane, suggesting that LFA-1 is still connected to the cytoskeleton network. This finding is strongly supported by the observation that LFA-1 exhibits a more diffusive motion when the cytoskeleton network is disrupted and confirmed by the optical trap measurements used to force the proteins to move through the membrane. Collectively, our findings suggest that the interaction of LFA-1 with the cytoskeleton cannot solely be attributed to the cytoplasmic part of the beta chain.

Compliance of actin filament networks measured by particle-tracking microrheology and diffusing wave spectroscopy

We monitor the time-dependent shear compliance of a solution of semi-flexible polymers, using diffusing wave spectroscopy (DWS) and video-enhanced single-particle-tracking (SPT) microrheology. These two techniques use the small thermally excited motion of probing microspheres to interrogate the local properties of polymer solutions. The solutions consist of networks of actin filaments which are long semi-flexible polymers. We establish a relationship between the mean square displacement (MSD) of microspheres imbedded in the solution and the time-dependent creep compliance of the solution, <Δr 2(t)>=(k B T/πa)J(t). Here, J(t) is the creep compliance, <Δr 2(t)> is the mean-square displacement, and a is the radius of the microsphere chosen to be larger than the mesh size of the polymer network. DWS allows us to measure mean square displacements with microsecond temporal resolution and Angstrom spatial resolution. At short times, the mean square displacement of a 0.96μm diameter sphere in a concentrated actin solution displays sub-diffusion. <Δr 2(t)>∝t , with a characteristic exponent =0.78±0.05, which reflects the finite rigidity of actin. At long times, the MSD reaches a plateau, with a magnitude that decreases with concentration. The creep compliance is shown to be a weak function of polymer concentration and scales as J p ∝c –1.2±0.3. This exponent is correctly described by a recent model describing the viscoelasticity of semi-flexible polymer solutions. The DWS and video-enhanced SPT measurements of the compliance plateau agree quantitatively with compliance measured independently using classical mechanical rheometry for a viscous oil and for a solution of flexible polymers. This paper extends the use of DWS and single-particle-tracking to probe the local mechanical properties of polymer networks, shows for the first time the proportionality between mean square displacement and local creep compliance, and therefore presents a new, direct way to extract the viscoelastic properties of polymer systems and complex fluids.

Structural Mosaicism on the Submicron Scale in the Plasma Membrane

The lateral mobility of the neural cell adhesion molecule (NCAM) was examined using single particle tracking (SPT). Various isoforms of human NCAM, differing in their ectodomain, their membrane anchorage mode, or the size of their cytoplasmic domain, were expressed in National Institutes of Health 3T3 cells and C2C12 muscle cells. On a 6.6-s time scale, SPT measurements on both transmembrane and glycosylphosphatidylinositol (GPI) anchored isoforms of NCAM expressed in 3T3 cells could be classified into mobile (Brownian diffusion), slow diffusion, corralled diffusion, and immobile subpopulations. On a 90-s time scale, SPT studies in C2C12 cells revealed that 40–60% of transfected NCAM was mobile, whereas a smaller fraction (∼10–30%) experienced much slower diffusion. In addition, a fraction of ∼30% of both transfected GPI and transmembrane isoforms and endogenous NCAM isoforms in C2C12 cells experienced transient confinement for ∼8 s within regions of ∼300-nm diameter. Diffusion within both these and the slow diffusion regions was anomalous, consistent with movements through a dense field of obstacles, whereas diffusion outside these regions was normal. Thus the membrane appears as a mosaic containing regions that permit free diffusion as well as regions in which NCAM is transiently confined to small or more extended domains. These results, including a large, freely diffusing fraction, similar confinement of transmembrane and GPI isoforms, a significant slowly diffusing fraction, and relatively large interdomain distances, are at some variance with the membrane skeleton fence model (Kusumi and Sako, 1996). Possible revisions to the model that incorporate these data are discussed.