Single Partical Tracking Review

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Annu. Rev. Biophys. Biomol. Struct. 1997. 26:373–99 c 1997 by Annual Reviews Inc. All rights reserved Copyright

Annu. Rev. Biophys. Biomol. Struct. 1997.26:373-399. Downloaded from arjournals.annualreviews.org by National Taiwan University on 03/13/07. For personal use only.

SINGLE-PARTICLE TRACKING: Applications to Membrane Dynamics Michael J. Saxton Institute of Theoretical Dynamics, University of California, Davis, California 95616; email: [email protected]

Ken Jacobson Department of Cell Biology and Anatomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599; email: [email protected] KEY WORDS:

single-particle tracking, fluorescence recovery after photobleaching, lateral diffusion, membrane dynamics, cell membrane

ABSTRACT Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.

CONTENTS PERSPECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capabilities of SPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modes of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EXPERIMENTAL TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Modes of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anomalous and Normal Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confined Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Directed Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SPT and FRAP: Effects of the Label . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WHAT DIFFUSION TELLS US ABOUT MEMBRANE STRUCTURE . . . . . . . . . . . . . . . . TECHNICAL PRIORITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

374 375 375 376 376 377 380 380 381 385 389 390 391 393

373 1056-8700/97/0610-0373$08.00

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PERSPECTIVES

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In single-particle tracking (SPT), computer-enhanced video microscopy is used to track the motion of proteins or lipids on the cell surface. Individual molecules or small clusters are observed, with a typical spatial resolution of tens of nanometers and a typical time resolution of tens of milliseconds. Some general questions addressed by the technique are as follows: (a) How do particles move on the cell surface? To what extent does the motion of various particles deviate from pure diffusion? How is that motion controlled, and what is its function? (b) How is the cell surface organized? To what extent do membranes deviate from the fluid mosaic model? Is a fractal time model a useful description of the cell surface (36, 63)? How are structures on the cell surface assembled? Does compartmentation prevent crosstalk of receptors (30)? What regional or global control over cell membrane dynamics exists (85)? (c) What are the effects of heterogeneous motion in a heterogeneous environment on kinetics and equilibrium (3, 20, 44, 91, 99)? More specifically, SPT may help to answer questions about particle motion raised by fluorescence recovery after photobleaching (FRAP) measurements. First, FRAP experiments show that diffusion coefficients for proteins in a cell membrane are 5–100 times lower than the values for proteins in an artificial bilayer (28, 103). Many mechanisms may be involved: obstruction by mobile or immobile proteins, transient binding to immobile or mobile species, confinement by membrane skeletal corrals, binding or obstruction by the extracellular matrix, and hydrodynamic interactions. These mechanisms have been difficult to sort out, in large part because some or all of them may occur simultaneously, and their relative importance may depend on the protein and the cell type (30). Second, a significant fraction of protein and lipid is immobile on the time scale of a FRAP experiment. For artificial bilayers and rhodopsin in the rod outer segment, recovery is close to 100%, but in the plasma membrane, recovery is typically 25% to 80% (30). The increased resolution of SPT ought to make it possible to understand the FRAP immobile fraction. Third, in FRAP experiments, the distribution of observed diffusion coefficients D is much broader than expected from experimental error (28, 51, 98). Values of D vary around twofold among different points on a single cell, and tenfold among cells (51). This suggests significant heterogeneity in the membrane, a view supported by other evidence (7, 28, 29).

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Capabilities of SPT SPT has several advantages over FRAP measurements. The spatial resolution is approximately two orders of magnitude higher than FRAP, so that with sufficient time resolution (65) motion in small domains can be characterized. Typically the time resolution is similar to FRAP, so the minimum detectable diffusion coefficient is lowered by approximately two orders of magnitude. Furthermore, FRAP averages over hundreds or thousands of diffusing molecules, but SPT measures individual trajectories. Thus, different subpopulations indistinguishable by FRAP can be resolved. SPT provides the ultimate specificity in measurement of motion of membrane components, particularly if the individual particle tracked could be characterized in terms of, for example, its phosphorylation state.

Modes of Motion A major advantage of SPT is the ability to resolve modes of motion of individual molecules, and a major result of the technique is that motion in the membrane is not limited to pure diffusion. Several modes of motion have been observed: immobile, directed, confined, tethered, normal diffusion, and anomalous diffusion. In an ensemble average, the time dependence of the mean-square displacement (MSD) for pure modes of motion is much different (Figure 1) so the motion can be classified readily.

Figure 1 The mean-square displacement hr 2 i as a function of time t for simultaneous diffusion and flow, pure diffusion, diffusion in the presence of obstacles, and confined motion.

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Two important phenomena have been observed that are related to the classification of modes of motion. First, correlated motion can provide convincing evidence that apparently non-Brownian motion is in fact non-Brownian motion and not merely a fluctuation in Brownian motion. Second, practically all experimental results show apparent transitions among modes of motion. If a transition is real, it could result from partition of the mobile species into different microdomains or from an active control mechanism such as transient binding to a cytoskeletal motor (76, 90).

History In the first SPT experiment on cell membranes, Barak & Webb (5) tracked a fluorescent-labeled low density lipoprotein receptor (see also 42, 45). De Brabander et al developed the technique of nanovid microscopy, in which a highly scattering colloidal gold label is used with bright-field microscopy (24). They applied the technique to endocytosis and protein motion on the cell surface (25). Sheetz and collaborators developed techniques using differential interference contrast microscopy to determine particle coordinates with nanometer resolution, and applied this to the motion of motor molecules and membrane proteins (41, 81, 89). This combination of techniques led to current SPT work on gold-labeled membranes.

EXPERIMENTAL TECHNIQUES Video microscopy is reviewed in (48, 49, 92), and SPT techniques, resolution, and error analysis are discussed in several reviews (6, 41–43, 65, 78, 81, 88, 89). Nanometer-scale SPT is possible because the center of a small particle can be located with a precision well below the wavelength of light, even though two particles at that separation cannot be resolved (43, 81, 88). The particle is much smaller than the wavelength of light, so its image is an Airy disk, and two nearby particles give partially overlapping Airy disks. According to the Rayleigh criterion (49), if the particles are too close, the pair cannot be resolved. But this unresolved spot is more intense than the spot for a single particle, so the number of particles can be determined, at least well enough to distinguish multiple particles from a single particle. For a wavelength of 546 nm and a numerical aperture of 1.4, the radius of the Airy disk is 238 nm. The limiting spatial accuracy in an SPT measurement is set by the mechanical stability of the apparatus and is obtained from trajectories of stationary particles. The scatter in position is 1–30 nm, yielding a minimum observable D of 5 × 10−14 to 5 × 10−13 cm2 s−1 . For mobile particles, the spatial accuracy is decreased by the motion of the particle during the acquisition time of the image, and it is therefore a function of D (81). The acquisition time depends on the

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label. For gold labels, images are usually obtained at the standard video rate, so the image is integrated over 1/30 or 1/25 s. For fluorescent labels, typical acquisition times are 1–10 s, although the fastest reported so far is 5 ms (78). Camera lag and interlacing must also be considered because they degrade the time resolution (21a, 48, 88, 100). Colloidal gold, latex beads, and fluorescent particles have been used as labels. Colloidal gold is a strong light scatterer that acts as a light sink rather than a light source. Light is scattered out of the objective, so, after background subtraction and contrast enhancement, the label appears darker than the surrounding image. The diameter d of the gold particle is much less than the wavelength of light, so the particle is a Rayleigh scatterer, for which the scattering ∝ d 6 . The minimum detectable diameter is ∼15 nm and the typical diameter used is 30–40 nm. Gold particles are much stronger scatterers than organelles are, so the organelles are almost invisible in bright-field microscopy (93). The use of gold labels is reviewed in References 21 and 23. Fluorescent labels used include fluorescent microspheres, typically of diameter 30–100 nm (37, 46); phycobiliproteins (104); virus labeled with fluorescent lipid analogs (2); low-density lipoprotein labeled with the carbocyanine lipid analog diI (diI-LDL) (4, 42, 43); diI-LDL conjugated to immunoglobulin E (IgE) (95); and tetramethylrhodamine conjugated to individual lipid molecules (78, 79). Advantages and disadvantages of the labels are discussed in the references. There are several potential difficulties associated with different labels. First, most labels are large, so that drag from the interaction of the label with the extracellular matrix may be significant (59, 60, 95). Second, labels are often multivalent and can crosslink binding sites. Crosslinking lowers D through hydrodynamic effects (1) and may trigger biological responses such as transmembrane signaling and interactions with the cytoskeleton. Furthermore, if diffusion is restricted by corrals, crosslinking yields aggregates less likely to cross corral walls (34, 68). Third, perturbations caused by antibody binding can affect interactions of the labeled protein with other proteins (19, 52). Finally, during a measurement, a particle may disappear as a result of moving out of the focal plane, endocytosis, detachment from the membrane, or photobleaching (2). (For a detailed quantitative discussion of photobleaching of single fluorophores, see 78.)

DATA ANALYSIS The goal of SPT data analysis is to sort trajectories into various modes of motion and to find the distribution of quantities characterizing the motion, such as the diffusion coefficient, velocity, anomalous diffusion exponent, corral size, and escape probability. The difficulty is that in a pure random walk

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the randomness yields trajectories that suggest other modes of motion. This problem is made worse by the experimental limits on the duration of trajectories measured (65, 72). It is instructive to calibrate (or uncalibrate) one’s intuition by writing a simple random walk program and looking at a few dozen pure random walks. One will see apparent diffusion, directed motion, trapping, and transitions (66, 70) because our nervous systems are wired to see patterns. But observation of multiple trajectories with the same apparently nonrandom behavior provides strong evidence that the nonrandom behavior is real. The most striking experimental examples are of directed motion (43) and motion among corrals (67). In addition to the usual cellular, biochemical, and instrumental controls, it is necessary to do controls for data analysis using a pure random walk as a reference. The minimum test for a classification algorithm is to try it on pure random walks of the appropriate number of time steps. A more rigorous test requires both experiment and simulation. For example, consider the case of corralled motion. First, the experimental corralled trajectories are identified by some criterion. Then the criterion is applied to pure random walks to see how many pure random walks are falsely classified as corralled, and to corralled random walks to see how many corralled random walks are falsely identified as free. Some corralled trajectories are necessarily rejected because their residence times are by chance very low, so the average escape time is biased toward higher escape times. To be able to do such tests, it is necessary to use some algorithm to find quantities such as the initial slope, rather than finding them by eye. When reporting classifications of trajectories based on some parameter, inclusion of a histogram of the parameter for the experimental data and pure random walks (57, 67) is useful to show whether the classification is based on a somewhat-arbitrary dividing line in a unimodal distribution or a minimum in a multimodal distribution. Similarly, if multiple parameters are used, it is useful to show them as a scatter plot (68). To reduce the noise in an experimental trajectory, the data points within a single trajectory are averaged, yielding the mean-square displacement (MSD) for that trajectory (65). The MSD for a given time lag can be defined as the average over all independent pairs of points with that time lag (42), or all pairs of points with that time lag. These averages are discussed in detail elsewhere (MJ Saxton, manuscript submitted). Briefly, for time lags less than ∼ 14 of the total number of points in the trajectory, the two averages agree, but the average over all points is less noisy. When the time lag is a substantial fraction of the length of the trajectory, neither average is useful because there are simply not enough data points, as shown by the formulas for the standard deviations (see 65). The short-range MSD is accurately determined, but the long-range MSD is noisy, yielding good short-range diffusion coefficients but highly scattered

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long-range ones. Averaging should not be done automatically because it may obscure transitions between diffusive and nondiffusive segments of a trajectory. The analytical forms of the curves of MSD versus time for the different modes of motion (Figure 1) form the basis of various classification methods.

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hr 2 i = 4Dt

normal diffusion

(1)

anomalous diffusion

(2)

directed motion with diffusion hr i = 4Dt + (V t) ­ ¡ ±­ ®¢¤ ®£ corralled motion hr 2 i ' rC2 1 − A1 exp −4A2 Dt rC2

(3)

hr 2 i = 4Dt α 2

2

(4)

In Equation 2, α < 1, so strictly speaking this is anomalous subdiffusion (11, 36). In Equations 3 and 4, V is velocity, hrC2 i is the corral size, and A1 and A2 are constants determined by the corral geometry. Equation 4 is based on the first two terms of the exact series solutions for square corrals (57) and circular corrals (70). The probability density p(r, t)dr is the probability that a particle at the origin at time zero is at position r at time t. For pure diffusion in two dimensions (65), 1 (5) exp(−r 2 /4Dt)2πr dr, 4π Dt and for diffusion with simultaneous flow along the x-axis with velocity V , p(r, t)dr =

1 (6) exp([−(x − V t)2 + y 2 ]/4Dt)d x d y. 4π Dt For corralled motion, the probability density depends on the initial position in the corral, and is complicated (57, 70). Webb and collaborators (36, 95) assume that the probability density is the standard two-dimensional form of Equation 5 but with a time-dependent diffusion coefficient: p(x,y, t,V )d x d y =

D = (1/4)0t α−1 ,

(7)

or, equivalently, hr 2 i = 4Dt = 0t α ,

(8)

with α < 1. Diffusion is free at short times but slowed at longer times as the effect of barriers becomes dominant. The physical basis for Equation 7 is the idea of the membrane as a random array of continuously changing traps with a distribution of energies so broad that there is no average residence time (36). The continuous-time random walk (CTRW) model (63) gives the same form for hr 2 i at long times.

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Next, we summarize methods used to classify trajectories. Whatever the method, the longer the run, the more reliable the classification unless the particle changes its mode of motion. Cherry and colleagues (2, 104) use the shape of the hr 2 (t)i curve to classify trajectories. They calculate the experimental MSD and determine which analytical expression yields the best fit. These workers also construct an experimental probability density and fit sums of standard forms of p(r ) to it. Kusumi and colleagues (57) characterize the shape of the hr 2 (t)i curve in terms of the relative deviation (RD). In effect, one draws a straight line through the origin with the observed initial slope, which is known precisely and is not affected significantly by nondiffusive motion. Then one extrapolates the MSD to a prescribed time and takes RD to be the ratio of the observed MSD to the extrapolated MSD. If RD > 1, then the motion is directed; if RD < 1, the motion is confined. This approach reduces the shapes of the different curves of Figure 1 to a single parameter. The distribution of RD can then be calculated for a pure random walk and non-Brownian motion. The overlap of the distributions is a measure of how well non-Brownian motion can be distinguished from pure Brownian motion when using this parameter (57, 72). Webb and collaborators (36, 95) use the anomalous diffusion exponent from Equation 8. For each trajectory, log hr 2 i is plotted versus log t, α is found from the initial slope, and the trajectory is classified according to α. The radius of gyration tensor is a well-known tool to characterize random walks (66), which yields the asymmetry parameter a2 and the radius of gyration 2 2 , a measure of the extent of the random walk. The joint distribution of Rgyr Rgyr and a2 may be used to classify trajectories (70). A related approach (93) combines the observed D, the shape of the hr 2 (t)i curve, and the values of 2 and a2 to sort trajectories into mobile, slowly diffusing, corralled, and Rgyr immobile.

APPLICATIONS Results of SPT experiments, and the corresponding FRAP experiments when available, are summarized in the tables. Table 1 includes artificial bilayers; Table 2, lipids and GPI-linked (glycosylphosphatidylinositol) proteins in cells; and Table 3, selected transmembrane proteins in cells. We believe the tables include all the results to date for which both SPT and FRAP data are available.

Classification of Modes of Motion FRAP measurements are generally interpreted as showing only mobile and immobile fractions. SPT makes a much more detailed classification possible. Practically all experimentalists report different modes of motion and transitions

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SPT IN MEMBRANES Table 1 Artificial bilayersa Membrane component

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Lipid analogs TMR-POPE Fi-PE Biotin-PE GPI-linked proteins DAF (CD55) Fcγ RIIIB (CD16)

Label

Bilayer composition

None 30 nm Au Ab-Fl 30 nm FM St 30 nm FM St-biotin-Ab same

D(SPT)b

D(FRAP)

Ref.

POPC 87% egg PC 13% Chol 80% egg PC 20% Chol

140 ± 23 30 (MV) 70 (PV) 30

77 ± 13 133 ± 33

78 58

80% egg PC 20% Chol same

—

37

25

—

37

56

—

37

a

Ab, antibody; Chol, cholesterol; Fl, fluorescein; FM, fluorescent microsphere; GPI, glycosylphosphatidylinositol; MV, multivalent; PC, phosphatidylcholine; PE, phosphatidylethanolamine; POPC, palmitoyloleoyl PC; POPE, palmitoyloleoyl PE; PV, paucivalent; St, streptavidin; TMR, tetramethylrhodamine. b All diffusion coefficients D in units 10−10 cm2 s−1 .

among the modes. Often, simple diffusion is observed in only a minority of trajectories. Some data on modes of motion are given in the tables, but methods of classification differ enough among laboratories that a table of modes of motion is not useful.

Anomalous and Normal Diffusion One of the most important results of SPT to date is the observation and measurement of anomalous diffusion in cell membranes. Anomalous diffusion can be used as a probe of membrane organization. Furthermore, anomalous diffusion implies slow diffusional mixing and therefore affects reaction rates in the membrane (3). What is the cause of this nonclassical behavior? In the most general terms, anomalous diffusion results from a deviation from the central limit theorem, resulting from pathologically broad distributions of jump times or jump lengths, or strong correlations in diffusive motion (11). In cell membranes, anomalous diffusion is most likely the result of both obstacles to diffusion and traps with a distribution of binding energies or escape times. For diffusion in the presence of random point obstacles (71), diffusion is anomalous at short times and normal at long times: hr 2 i ∼ t α for t  tC R and hr 2 i ∼ t for t  tC R , where tC R is the crossover time and α < 1. As the obstacle concentration approaches the percolation threshold, α decreases and tC R increases, that is, diffusion becomes more anomalous for a longer time. At the percolation threshold there is no crossover, and diffusion is anomalous at all times because the percolation cluster is self-similar. For diffusion in the

b

HEPA-OVA cells

MHC I (Qa2)

40 nm Au Ab

30 nm Au Ab

∼30–40 (∼50% mobile) —

3.7 ± 0.4 ∼70% mobile 2–4

6.1 (corralled) 7.2 ± 1.0

0.89 ± 0.18

2.1 ± 0.3

—

7.1 ± 1.3

See footnotes a and b of Table 1. NCAM, neural cell adhesion molecule; MHC, major histocompatibility complex. R Simson, SE Moore, P Doherty, FS Walsh & KA Jacobson, submitted.

Myoblasts

NCAM 125

40 nm Au Ab

100 nm FM Ab

—

24 ± 6.8

33% slow diffusion D(slow) ∼ 0.04 28% hybrid

31% slow diffusion D(slow) ∼ 0.2 38% corralled

39% slow diffusion D(slow) = 0.057

18% slow diffusion with D ∼ 1 38% corralled diffusion

Analyzed as 1d diffusion along axon length

Unspecified fraction stationary and not extractable by detergent

23% with D < 4 (lamella) 71% with D < 4 (nucleus)

33

b

84

46 50

84

22

46

60

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Fibroblasts

Thy-1

Fibroblasts

40 nm Au cholera toxin B

500 nm latex Ab-Fl

—

8

54 ± 27 (69% mobile)

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Fibroblasts

Neurons

Fi-PE

100 nm FM avidin

12 ± 7 lamella

Comments

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Fibroblasts

biotin-PE

30 nm Au Ab

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Table 2 Lipids and GPI-linked proteins in cellsa

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a

R-phycoerythrin Ab

0.001–0.05

—

2–4

1.3 ± 0.2

40 nm Au Ab

See footnotes a and b of Table 1 and footnote a of Table 2. LDL, low-density lipoprotein.

Fibroblasts

5.4 80% mobile

≈1 (see comment)

diI-LDL

Also corralled diffusion and directed motion

Time-dependent D evaluated at 1 s

Most receptors confined to ≈500 nm for ≈30 s durations

22% slow diffusion D(slow) = 0.06 14% hybrid

14% slow diffusion D(slow) = 0.5 21% corralled

104

33

36

68

93

93

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HLA-DR Class II

Rat basophilic leukemia cells Major histocompatibility antigens H-2Da Class I HEPA-OVA cells

—

4.7 ± 0.5 70% mobile

1.1 ± 0.1

10 (short-range) 0.24 (long-range)

40 nm Au transferrin

30 nm Au Ab

18.3 ± 3.1 60% mobile

3.7 ± 0.18

57

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Fibroblasts

Muscle

NCAM140

30 nm Au Ab

High Ca+2 medium 28% random diffusion 64% corralled ensemble average D(SPT)

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Receptors Transferrin receptor

Fibroblasts

0.34 75% mobile

D(FRAP)

0.16

Apparent D(SPT) for mobile fraction

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Cell

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Table 3 Transmembrane proteins in cellsa

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presence of traps, or obstacles that bind the mobile species, the behavior is complex (11, 74). Other anomalous diffusion models, such as those discussed in the next paragraph, have no crossover, so determining whether a crossover time exists restricts possible models of anomalous diffusion. The effect of anomalous diffusion on FRAP experiments has been examined. Nagle (63), using a one-dimensional CTRW model with no crossover, found that if a FRAP recovery curve is generated from the CTRW model but fit by the standard FRAP recovery equation, the diffusion coefficient and the mobile fraction change dramatically depending on the time scale of the FRAP experiment. Feder et al (36) used a time-dependent D (Equation 7) in the usual two-dimensional probability density function (Equation 5) to obtain a FRAP recovery equation of standard form but with t replaced by t α . For the experimentally accessible time range, FRAP data could be fit equally well by the anomalous diffusion equation (parameters 0 and α) and the standard equation (parameters D and mobile fraction), but no statistically significant improvement in the fit was obtained with the anomalous diffusion equation (36). SPT is more sensitive to anomalous diffusion than FRAP is because in SPT every tracer is tested for anomalous diffusion individually, but FRAP averages over many tracers, some of which may be diffusing normally, and others anomalously. To analyze SPT trajectories, log hr 2 i or log hr 2 i/t is plotted against log t (42, 71, 93). The initial slope yields the exponent α, but simulations suggest that it is difficult to see the crossover in an individual trajectory (MJ Saxton, in preparation). One is more likely to see a crossover from anomalous diffusion to noise than a crossover from anomalous diffusion to normal. Various factors can cause crossovers, which suggests caution in interpreting observed crossovers. Experimental results suggest that anomalous and normal diffusion may occur in distinct domains, producing an apparent crossover when the tracer leaves a domain. An apparent crossover might also occur as a result of biological modulation, such as a change in phosphorylation state. SPT data for various proteins and cells show a significant amount of anomalous diffusion. Ghosh (42, 43) was the first to observe anomalous diffusion in cell membranes, in measurements on the LDL receptor labeled with diILDL. Trajectories were classified according to α, and ∼ 50% of the trajectories showed anomalous diffusion, with values of α between 0.2 and 0.9. Transitions were observed from anomalous to normal to anomalous diffusion in the trajectory of an individual particle. If anomalous diffusion in this system were caused by random point obstacles, diffusion would remain normal after the crossover. The observed behavior suggests domain structure in the membrane. Slattery (95) measured diffusion of the high-affinity IgE receptor FcRI in rat basophilic leukemia cells, using an antibody-conjugated diI-LDL label elegantly shown not to crosslink receptors under experimental conditions. The

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average α was 0.22–0.48, and for 48–60% of the trajectories, α was between 0.1 and 0.9. The FRAP results of Feder et al (36) were obtained in the same system. Interestingly, Ghosh (42) found that if the cells were treated with azide and 2-deoxyglucose, the fraction of particles showing normal diffusion increased from 26% to 43%, which suggests that the constraints to diffusion require metabolic energy. But Slattery (95) found no effect of metabolic inhibitors in similar experiments on his system. It will be important to determine whether the structures that produce anomalous diffusion generally require metabolic energy. Simson (93) examined the mobility of neural cell adhesion molecules (NCAM) labeled with antibody adsorbed to 40-nm gold particles. Short-term (6.6 s total) SPT measurements were made on fibroblasts, which have no endogenous NCAM. For both GPI-linked and transmembrane isoforms, 50% of the particles were classified as mobile and showed normal diffusion, but the slow (15%) and corralled (20%) fractions showed anomalous diffusion with α = 0.29–0.50. GPI-anchored and transmembrane isoforms of human NCAM were expressed in cultured mouse muscle cells, along with endogenous NCAM, predominantly a transmembrane isoform. Long-term trajectories (90 s) showed that no particles were actually stationary and that corralled particles escaped and diffused normally before being corralled again, yielding hybrid trajectories. For both transfected and endogenous isoforms, the mobile fraction (40%–60%) diffused normally, but diffusion was anomalous in the slow fraction and the confined portions of the hybrid trajectories. Diffusion was also found to be anomalous for the GPI-linked protein Thy-1, the lipid analog Fl-PE (fluorescein-conjugated phosphatidylethanolamine), and the glycolipid GM1 in those trajectories that exhibited transient confinement or slow diffusion (84). It will be important to see whether anomalous diffusion occurs in fixed regions of the cell surface, and if so, the lifetimes of those regions.

Confined Motion Confined motion may result from corrals formed by cytoskeletal proteins near the membrane (56, 85a), from tethering to immobile species, or from restrictions to motion imposed by lipid domains. Evidence for confined motion comes from the interpretation of FRAP (29, 31), SPT, and laser trap experiments. In SPT measurements, several workers have reported a significant fraction of confined motion, with corral sizes in the range of 250–1500 nm, and average residence times in the range of 3–35 s (85). The range of sizes reflects instrumental factors and should not be taken as real lower or upper limits. To see small corrals, high resolution in space and time is needed; to see large corrals, trajectories must be measured for long times before confinement becomes apparent (65, 67).

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Some of the strongest experimental evidence for confined motion comes from the work of Kusumi and collaborators (56). A remarkable figure of Sako & Kusumi (67) shows long-term trajectories (1000 images at 3 images/s) of the transferrin receptor in fibroblasts. Each trajectory was divided into segments by eye, each segment corresponding to a compartment. The particle appeared to diffuse within a compartment, escape to an adjacent compartment and diffuse there, and so on. Quantitative analysis showed that the average compartment radius was 280 nm, the average escape time was 29 s, and the short-range diffusion coefficient was 0.1 µm2 s−1 (67). The relation hr 2 i = 4Dt gives a root-mean-square displacement for a freely diffusing particle of 3400 nm in 29 s, which suggests confinement. A test for confined motion yields a probability ∼10−20 that a freely diffusing particle with the observed D would remain in a region of that size for that time (73). Kusumi and collaborators (57, 67) used their RD parameter to classify trajectories, reporting histograms of RD for their experimental values and Monte Carlo values for a pure random walk. The distributions are clearly different. Furthermore, the criterion for confined motion was chosen so that only 2.5% of pure random walks are falsely classified as confined, and the observed fraction of confined motion was much greater: 30–65% for E-cadherin in keratinocytes and 80–90% for the transferrin and α2 -macroglobulin receptors in fibroblasts. These results clearly established that for a significant fraction of trajectories, motion was non-Brownian. Analysis of the hr 2 (t)i curves showed distinct plateaus for 80–90% of the transferrin receptors (A Kusumi, private communication), which implies confined motion, not anomalous diffusion. Simson et al (94) analyzed subtrajectories of experimental trajectories using a test (70) to see whether a diffusing particle stays in one region longer than a freely diffusing particle is expected to do. Subtrajectories were classified as confined if they were not likely to have resulted from a pure random walk and the residence time was above a prescribed minimum (94). In measurements of two GPI-linked proteins, Thy-1 in fibroblasts (84) and NCAM-125 in cultured muscle cells (94), 28% of the experimental trajectories showed periods of transient confinement, but only 1.5% of pure random walks were scored as showing transient confinement. Similar results were obtained for transmembrane isoforms of NCAM in muscle cells. Schmidt et al (80) developed a related subtrajectory test and showed confinement of lipids in an artificial bilayer, which they attributed to defects in the supported planar bilayer. Others have argued for the existence of corrals using various tests: by fitting the hr 2 (t)i curve to various functional forms (2), by probability density tests (25, 104), and by the RD parameter (46). Some results are summarized in the Tables above. A key SPT experiment would be to test for permanent corrals

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by trying to observe two particles in the same corral at different times and to observe two distinctly labeled particles in the same corral simultaneously. Further experimental evidence on corrals is obtained from laser trap experiments that measure the barrier-free path (BFP), the distance a labeled particle can be moved by the trap before it encounters a barrier strong enough to force it to escape the trap (33). The laser trap (laser tweezers) provides a controlled, movable potential well with nanometer dimensions and piconewton forces (8, 96, 97). The forces used in the BFP experiments are in the range 0.05–1 pN, which are sufficient to stretch a polymer, less than the force exerted by a motor molecule, and insufficient to break even a single hydrogen bond (35). Boal (9, 10) has used Monte Carlo calculations to evaluate the BFP for a model membrane skeleton consisting of a network of flexible, nonpenetrating polymer chains attached to the membrane. Edidin et al (33) measured the BFP for the class I major histocompatibility complex (MHC), comparing homologous GPI-linked and transmembrane isoforms. At 34◦ C, the transmembrane isoform had a BFP of 3.5 µm, and the GPI-linked isoform, 8.5 µm, which is much larger than the typical corral size measured by SPT. A temperature decrease from 34◦ C to 23◦ C led to a large change in BFP but a small change in D, which suggests that the measured barriers do not control diffusion. Experiments on truncated forms of class I MHC showed a doubling in the BFP for a sufficiently short cytoplasmic domain (34). To characterize the barriers, Sako & Kusumi (68) measured the BFP as a function of trap strength for the transferrin receptor in fibroblasts. Corralling and tethering can be distinguished by laser trap measurements but not necessarily by SPT (68). Approximately 10% of the particles were classified as tethered, with a BFP < 300 nm and a low diffusion coefficient. The remainder were classified as confined and had a larger diffusion coefficient. At the highest trap force, these particles had a BFP ≥ 2 µm, the maximum displacement attempted, but at lower trap forces they often escaped at distances corresponding to the corral size measured by SPT for free diffusion. Particles were also observed to escape the trap and rebound, implying that the boundaries are elastic. The force required to move a particle across the boundary was 0.1 pN for a 40-nm gold label and 0.6 pN for a 210-nm latex label. The increase in force was attributed to increased crosslinking of receptors by the larger label. If the width of the corral boundary is 10 nm and the force is 0.5 pN, then the energy required for a particle to cross the boundary (68) is 5 × 10−21 J ' 2.5( 12 kT ). The BFP measurements are highly interesting, but there are some complications in their interpretation. First, the trap may exert forces perpendicular to the membrane, in addition to the in-plane forces (WW Webb, private communication), though the BFP is still sensitive to truncation of the cytoplasmic domain of the protein (34; M Edidin, private communication). Second, moving a labeled

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protein may stretch the barrier (68; MJ Saxton, in preparation). Third, the measurements involve energies of order kT, and the number of particles measured is limited, so the results are inherently noisy. The hindrances constraining lateral diffusion are thought to fluctuate in space and time (27, 36, 56), but there is disagreement about the length scale of the barriers. Kusumi and collaborators (56) consider a network of membrane skeleton barriers to be a basic feature of plasma membranes. Long-range diffusion occurs by crossing corral walls as a result of fluctuations in the separation between the membrane and the membrane skeleton, and as a result of the associationdissociation equilibrium of membrane skeleton proteins. The corral walls impose a preferred length scale of 300–600 nm, and the fractal time model (63) applies only to diffusion over shorter lengths. In contrast, the time-dependent diffusion coefficient of Webb and collaborators (36) requires barriers on all length scales and no preferred length. Hindrances fluctuate in space and time over the full range of experimental values, 0.3 to ∼600 s and 30 nm to ∼5 µm, as determined by SPT (42, 95) and FRAP (36). It may be possible to reconcile these views. The distribution of escape times from corrals is wide (around 1.5 orders of magnitude), as shown by Monte Carlo calculations for uniform circular corrals with a fixed escape probability for each collision with the wall (73). Presumably the distribution would be even broader for a more realistic corral model, such as a membrane skeleton of polymers with conformational fluctuations (9, 10), especially when associationdissociation equilibria are included. Fluctuations in association are likely to occur on longer time scales than fluctuations in conformation would because the energies involved are greater. The distribution of escape times would be further broadened by the distribution in corral sizes. The corrals would thus contribute to a time-dependent diffusion coefficient over times greater than the corral escape time. Establishing a connection between a domain as defined by SPT trajectories and a biochemically defined domain is of great interest. One possible example involves local lipid compositional differences in the membrane. Many GPIlinked proteins preferentially co-isolate at 4◦ C with a detergent-inextractable fraction enriched in glycosphingolipids and cholesterol (14, 64). The more ordered lipids of this fraction may optimally accommodate the highly saturated acyl chains of the GPI anchor (83). Schnitzer et al (82) have isolated from lung tissue detergent-resistant vesicles with diameters that are consistent with the size of the SPT confinement regions observed for several GPI-anchored proteins (93) (ED Sheets, R Simson, GM Lee & K Jacobson, unpublished data). The gel-like microphases existing within these putative lipid domains may be the obstacles producing anomalous diffusion within such regions.

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Directed Motion Directed motion has been observed frequently in SPT experiments. In the uniform flow model (72, 90), the entire membrane moves with a constant velocity, and the particle diffuses with respect to the membrane. In the conveyor belt model (39, 62, 72, 76, 90), the mobile particle is reversibly attached to a cytoskeletal motor. When the particle is bound, it moves with a constant velocity along the cytoskeletal element; when it is unbound, it diffuses freely. In the similar “conveyor rope” model, when a particle is bound to the conveyor rope, it moves with constant velocity along the rope. But it also diffuses over a short distance in the perpendicular direction due to the flexibility of the cytoskeletal element (42, 57), or it diffuses isotropically over short distances from its attachment point due to the flexibility of the attachment (90). The uniform flow model describes directed bulk flows within the cell frame of reference, but no such flow could be measured by SPT with gold-labeled lipids in keratocytes (60) or by FRAP in leukocytes (61). These studies suggested that the bilayer moves forward passively with the cell, most likely using membrane accumulated as the cell retracts its trailing edge. In these experiments, most of the gold-labeled lectin receptors in the plasma membrane also moved forward with the keratocyte, showing no net directed movement in the cell frame of reference (55). These studies seem to rule out a retrograde lipid flow, at least in non-neuronal cells, although the original proponent remains unconvinced (13). In contrast, retrograde lipid flow does occur in some axons as membrane is added at the growth cone and retrieved at the neuronal cell body (12, 40). Under certain conditions, vesicular transport along the axon and insertion at the growing tip appears to be the most efficient way to get material to the site of growth. Recent SPT experiments support this view. In dorsal root ganglia, membrane lipid flows rearward along the axon as determined by SPT of Fl-PE labeled with latex beads (22). When a laser trap was used to pull membrane tethers from bead-labeled axons, the beads moved a significantly greater distance on the growth cone side of the tether than on the cell body side. The results of this elegant experiment suggest that the source of the membrane was at the base of the growth cone. Although it is well known that various membrane components that are sufficiently crosslinked will move rearward in motile fibroblasts, lymphocytes, macrophages and neuronal growth cones, SPT studies have shown unexpected forms of directed transport, which may be attributed to a conveyor belt mechanism. Bead-labeled neuronal antigens were transported forward to the leading edges of growth cones (87). Similarly, concanavalin A–coated beads were moved to the leading edge of locomoting fish keratocytes (54), as were integrins in motile fibroblasts (77). In cells undergoing cytokinesis, fluorescent

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beads connected to the actin cytoskeleton are drawn to the cleavage furrow (102). The conveyor belt model was used by Schmidt et al (76, 77) to analyze the motion of integrin in moving fibroblasts. Observed trajectories fitted to Equation 3 yielded the instantaneous velocity and D. The rate constants for binding and unbinding were obtained from computer simulations in which the calculated average velocity and the fraction of directed transport were required to match the observed values.

SPT and FRAP: Effects of the Label No general, quantitative correspondence has yet been found between SPT modes of motion and the FRAP immobile fraction, although efforts have been made to reconcile the data from measurements on the same system (57, 93). An alternative approach uses a time-dependent D with no immobile fraction to fit both experiments (36). Some striking differences between FRAP and SPT measurements suggest that our understanding of the effects of the label is incomplete. For lipid components in supported planar bilayers, D(FRAP) values are a factor of two to four times larger than D(SPT). A notable exception is the elegant work of Schmidt et al (78–80), tracking individual rhodamine-labeled lipid analogs in planar supported bilayers. Here no gold or fluorescent bead is used, and the agreement between FRAP and SPT is much closer, with the SPT values higher. This result is attributed to lateral heterogeneity in the bilayer. SPT detects free, rapid diffusion within small regions, but FRAP measurements sample both free diffusion and diffusion obstructed by defects in the bilayer. The general diminution of D values in SPT relative to FRAP is attributable to the valency and size of the label. The effect of these two factors has not yet been resolved. However, Lee et al (58) measured the diffusion of Fl-PE labeled with 30-nm gold microspheres in planar supported bilayers, using both a multivalent label, coated completely with relevant (anti-Fl) antibodies, and a paucivalent label, coated with a 20:1 mixture of irrelevant and relevant antibodies. Compared with D(FRAP) for Fl-PE, D(SPT) was reduced by a factor of ∼4 for the multivalent label but only by a factor of 2 for the paucivalent label. Moreover, increasing the viscosity of the aqueous phase by a factor of 2 did not change D, which suggests that it was the higher valency that reduced D. Valency affects D because it affects both the cluster size and the distance between the lipids anchoring the label. Depending on the degree of penetration by the lipid solvent into the gold-tagged lipid cluster, hydrodynamic effects lower D by a factor of 1.5–2.0. Measurements on gold-labeled avidin-biotin-phosphatidylethanolamine (PE) by scanning concentration correlation spectroscopy (53) gave D values between those found by Lee et al (58) for the two antibody labels. Fein et al (37) found similar D values for PE derivatives and GPI-linked proteins in planar

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supported bilayers, but in this work only 10–50% of the particles were mobile. Whether this is due to the label or to structural irregularities in the bilayer is not known. When SPT and FRAP values for the highly mobile fraction of various lipids and GPI-anchored proteins in plasma membranes are compared, again the FRAP values are 2- to 7-fold greater than the SPT values (Table 2). Table 3 lists transmembrane proteins measured by SPT and FRAP. The label can have a large effect on mobility measurements. FRAP measurements on FcRI labeled with fluorescent antibody gave D values of 5 × 10−10 cm2 s−1 , with an 80% mobile fraction. Measurements using the antibody conjugated to diI-LDL gave similar D values, but a mobile fraction of <20%, perhaps due to interaction of the label with the extracellular matrix (36). Mobility measurements on the LDL receptor itself also reveal a pronounced effect of the label (95). LDL bound to its receptor in the plasma membrane has a diffusion coefficient two orders of magnitude lower than that of the unliganded receptor in the plasma membrane or the liganded receptor in a bleb. Presumably, the bleb membrane is not tethered to the cytoskeleton and has little associated extracellular matrix material. In the plasma membrane, the label could cause drag by interacting with the extracellular matrix, or its binding could cause the receptor to engage the membrane-associated cytoskeleton, markedly reducing diffusion. For the class II MHC antigen, D(SPT) (104) is two orders of magnitude less than D(FRAP) (101). The cause could be biological: Different MHCs are expressed in different cells and may have different interactions with the cytoskeleton. But particles that move as slowly as those observed in the SPT experiments would clearly be part of the immobile fraction in standard FRAP experiments. This work is the first step in examining the dynamics of the FRAP immobile fraction and shows that even in the immobile fraction, different modes of motion are observed.

WHAT DIFFUSION TELLS US ABOUT MEMBRANE STRUCTURE One can take two approaches to modeling diffusion in the membrane. In the mechanistic approach, one starts with some biological structure and tries to model its effects on diffusion. It is ultimately necessary to identify and model all the structures and processes, and to find their combined effect. To test the model it is necessary to unravel these processes experimentally. Alternatively, in the phenomenological approach of Feder et al (36), photobleaching and SPT experiments are analyzed in terms of the parameters of the time-dependent diffusion coefficient (Equation 7). To see how the lateral diffusion of membrane proteins is controlled (86), one must consider three regions of the protein: cytoplasmic, transmembrane, and

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extracellular. The influence of these regions may vary among proteins and cell types. In some cases, a major factor affecting diffusion is the cytoplasmic domain of the membrane protein and the membrane skeleton with which the domain interacts. Truncation of the cytoplasmic domain of the class II MHC receptor or erythrocyte band 3 increases the diffusion coefficient (27, 105). Kusumi and collaborators (56) argue that the membrane skeleton is a universal feature of cells, which defines short-range diffusion and controls long-range diffusion. Webb and collaborators (103) have shown for a variety of proteins that lateral diffusion in blebs is much faster than in intact membranes, suggesting direct or indirect control of diffusion by the cytoskeleton. For a number of other proteins, however, the membrane skeleton has little effect on diffusion. Severe truncation of the cytoplasmic domain, or replacement of the transmembrane segment by a GPI linkage, has little effect on diffusion coefficients (27, 105). In such cases, either the membrane skeleton has little effect or the effect is indirect, involving other membrane proteins that do interact with the membrane skeleton directly (85). In the transmembrane region, the area fraction of protein is likely to be well below the percolation threshold, because many membrane proteins have large cytoplasmic and extracellular domains, but only a single transmembrane helix. Hammer, Koch, and collaborators (15–18, 26) evaluated the combined effect of obstruction (68a) and hydrodynamic interactions with the obstacles. They showed that low concentrations of immobile protein reduce the diffusion coefficient of mobile proteins significantly. Their model assumes a macroscopic object moving in a fluid continuum. The model is therefore restricted to proteins with multiple membrane-spanning regions to ensure that the protein solute is larger than the lipid solvent that forms the continuum. It will be important to see whether the hydrodynamic model can be extrapolated to proteins with a single transmembrane domain. In an unobstructed system, the SaffmanDelbr¨uck model predicts little difference in D for large and small proteins (1), so it will be interesting to see whether or not there is a significant difference in D as a result of hydrodynamic interactions with immobile obstacles. If these interactions are significantly different, the diffusion of multichain proteins may be controlled by hydrodynamic effects in the bilayer, but the diffusion of singlechain and GPI-linked proteins in the same membrane may be controlled by the extracellular domains. The effect of immobile domains of gel-phase lipid would be similar to that of immobile proteins. In some cases, there is compelling evidence of the importance of extracellular domains in diffusion (31, 86, 105). Given the large size of the extracellular domains, obstruction and percolation effects are likely to be dominant in this region and are determined by the area fraction of extracellular domains and

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extracellular matrix. More precisely, the effect of obstructions is determined by the excluded area fraction, which depends on the radius of the particular mobile protein (69). If the protein-protein interaction is simple electrostatic repulsion, the effective excluded area fraction increases as either temperature or ionic strength decreases. However, there may be specific complications. Removal of charge can lower D, presumably by allowing association (32). In addition to steric and hydrodynamic effects, protein-protein interactions (62a) in any of the regions are likely to have a major effect on diffusion. Transient association is favored in membranes (32, 105), and diffusion is hindered by the association of mobile species with either mobile or immobile species. Anomalous diffusion is emerging as a key property in membrane dynamics, both because it is a probe of membrane microstructure and because it has a major influence on reaction kinetics within the membrane. Anomalous diffusion has been observed by SPT, at least in local domains (42, 93, 95). It has not yet been established experimentally whether anomalous diffusion in cell membranes shows a crossover to normal diffusion at large times, or is anomalous at all times. If diffusion is anomalous at all times, it could be the result of a single mechanism, such as a singular distribution of trap depths as found in amorphous semiconductors (75). Alternatively, it could originate from various biological structures and processes with different length and time scales. For example, over short distances, anomalous diffusion could result from obstruction and binding. Over intermediate distances, it could result from corrals with a broad distribution of escape times. Over long distances and times, it could result from biological modulation, such as turnover of membrane components by cycles of endocytosis and exocytosis (86), or changes in phosphorylation state. In summary, the main factors controlling diffusion in the plasma membrane are likely to be fluctuations in the membrane skeleton, obstruction and hydrodynamic interaction in the transmembrane region, and obstruction and percolation in the extracellular region. These interactions depend on the structure of the protein, including its size, charge, mode of membrane anchorage, degree of oligomerization, and degree of glycosylation. All of these factors may combine to produce the non-Brownian behavior that characterizes much of the lateral motion in the membrane.

TECHNICAL PRIORITIES If SPT is to reach its full potential, several technical issues need to be addressed: (a) Calibration. Further work on the relation of FRAP and SPT is important. A systematic study of D as a function of label size and valency in welldefined synthetic bilayers and in cells would provide a firmer basis for the interpretation of experimental results in cells.

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(b) Cross-calibration. One of the problems in the field is that each laboratory uses different cell types, membrane proteins, labels, and methods of data analysis. It is therefore difficult to compare results among laboratories. Experiments in all laboratories should include measurements of one standard protein with one standard label in one standard cell line. In addition, where possible, the motion of the standard protein and label should be measured in the cell lines used in each laboratory, to provide a basis for comparison among cell lines of the mechanisms that constrain diffusion. Similar measurements with a standard lipid label should also be made. Laboratories should exchange data analysis programs and use one anothers’ methods in addition to their own. It would also be useful for the laboratories to agree on standard methods for classifying modes of motion and report the results of those methods in addition to their own classification. (c) Hydrodynamic interactions. Hammer, Koch, and colleagues (15–18, 26) have shown theoretically that hydrodynamic interactions have a major effect on lateral diffusion coefficients. A small area fraction of immobile protein reduces the diffusion coefficient significantly. The hydrodynamic effect of immobile protein is much greater than that of mobile protein, just as for obstruction (68a). Both effects are therefore much greater in plasma membranes than in organelle or artificial membranes. An experimental test of these results in a model system is crucial to our understanding of membrane dynamics and would involve both FRAP and SPT. (d) Improved data analysis and modeling. One area of particular interest is lateral diffusion of proteins obstructed by the membrane skeleton, modeled as a network of flexible polymers (9, 10). Another is Brownian dynamics calculations of the hydrodynamic interactions just mentioned, to see their effect on SPT trajectories and anomalous diffusion. Development of new methods of data analysis and systematic comparison of existing methods are also essential. (e) Multiple-labeling experiments. The use of distinct fluorophores may make it possible to track two reactants simultaneously, or a diffusing species and an obstacle or receptor. This approach could also be used to examine whether corrals or regions of anomalous diffusion are semipermanent features of the cell surface that different proteins can enter. ACKNOWLEDGMENTS We thank our colleagues for helpful discussions of various aspects of SPT and membranes, and for supplying preprints, answering questions about their

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results, and criticizing parts of this review: BG Barisas, K Berland, DH Boal, RJ Cherry, M Edidin, H Geerts, DA Hammer, A Kusumi, DA Pink, H Qian, Th Schmidt, ED Sheets, MP Sheetz, R Simson, and WW Webb. This work was supported by National Institutes of Health grants GM38133 (MJS) and GM41402 (KJ).

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Annual Review of Biophysics and Biomolecular Structure Volume 26, 1997

CONTENTS

Annu. Rev. Biophys. Biomol. Struct. 1997.26:373-399. Downloaded from arjournals.annualreviews.org by National Taiwan University on 03/13/07. For personal use only.

WHATEVER HAPPENED TO THE FUN? An Autobiographical Investigation, Frederic M. Richards

1

STRUCTURAL AND MECHANISTIC DETERMINANTS OF AFFINITY AND SPECIFICITY OF LIGANDS DISCOVERED OR ENGINEERED BY PHAGE DISPLAY, Bradley A. Katz

27

CALCIUM IN CLOSE QUARTERS: Microdomain Feedback in Excitation-Contraction Coupling and Other Cell Biological Phenomena, Eduardo Ríos, Michael D. Stern

47

HISTONE STRUCTURE AND THE ORGANIZATION OF THE NUCLEOSOME, V. Ramakrishnan

83

HIERARCHY AND DYNAMICS OF RNA FOLDING, Philippe Brion, Eric Westhof

113

FLEXIBILITY OF RNA, Paul J. Hagerman

139

STRUCTURAL PERSPECTIVES OF PHOSPHOLAMBAN, A HELICAL TRANSMEMBRANE PENTAMER, Isaiah T. Arkin, Paul D. Adams, Axel T. Brünger, Steven O. Smith, Donald M. Engelman

157

BIOMOLECULAR DYNAMICS AT LONG TIMESTEPS: Bridging the Timescale Gap Between Simulation and Experimentation, Tamar Schlick, Eric Barth, Margaret Mandziuk

181

MOLECULAR MECHANISM OF PHOTOSIGNALING BY ARCHAEAL SENSORY RHODOPSINS, Wouter D. Hoff, KwangHwan Jung, John L. Spudich

223

MODULAR PEPTIDE RECOGNITION DOMAINS IN EUKARYOTIC SIGNALING, John Kuriyan, David Cowburn EUKARYOTIC TRANSCRIPTION FACTOR-DNA COMPLEXES, G. Patikoglou, S. K. Burley NANOSECOND TIME-RESOLVED SPECTROSCOPY OF BIOMOLECULAR PROCESSES, Eefei Chen, Robert A. Goldbeck, David S. Kliger LESSONS FROM ZINC-BINDING PEPTIDES, Jeremy M. Berg, Hilary Arnold Godwin SINGLE-PARTICLE TRACKING: Applications to Membrane Dynamics, Michael J. Saxton, Ken Jacobson BACTERIOPHAGE DISPLAY AND DISCOVERY OF PEPTIDE LEADS FOR DRUG DEVELOPMENT, H. B. Lowman SOLVATION: HOW TO OBTAIN MICROSCOPIC ENERGIES FROM PARTITIONING AND SOLVATION EXPERIMENTS, Hue Sun Chan, Ken A. Dill THE STRUCTURAL AND FUNCTIONAL BASIS OF ANTIBODY CATALYSIS, Herschel Wade, Thomas S. Scanlan

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327 357 373 401

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Annu. Rev. Biophys. Biomol. Struct. 1997.26:373-399. Downloaded from arjournals.annualreviews.org by National Taiwan University on 03/13/07. For personal use only.

ADVANCED EPR SPECTROSCOPY ON ELECTRON TRANSFER PROCESSES IN PHOTOSYNTHESIS AND BIOMIMETIC MODEL SYSTEMS, H. Levanon, K. Möbius

495

USE OF SURFACE PLASMON RESONANCE TO PROBE THE EQUILIBRIUM AND DYNAMIC ASPECTS OF INTERACTIONS BETWEEN BIOLOGICAL MACROMOLECULES, Peter Schuck

541

OPTICAL DETECTION OF SINGLE MOLECULES, Shuming Nie, Richard N. Zare

567

PROTEIN FOLDS IN THE ALL-ß AND ALL alpha- Classes, Cyrus Chothia, Tim Hubbard, Steven Brenner, Hugh Barns, Alexey Murzin

597

SITE-SPECIFIC DYNAMICS IN DNA: Experiments, Bruce H. Robinson, Colin Mailer, Gary Drobny

629