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8/15/2019 Single Partical Tracking Review
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Annu. Rev. Biophys. Biomol. Struct. 1997. 26:37399
Copyright c 1997 by Annual Reviews Inc. All rights reserved
SINGLE-PARTICLE TRACKING:Applications to Membrane Dynamics
Michael J. SaxtonInstitute 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 ChapelHill, Chapel Hill, North Carolina 27599; email: [email protected]
KEY WORDS: single-particle tracking, fluorescence recovery after photobleaching, lateraldiffusion, membrane dynamics, cell membrane
ABSTRACT
Measurements of trajectories of individual proteins or lipids in the plasma mem-
brane of cells show a variety of types of motion. Brownian motion is ob-
served, but many of the particles undergo non-Brownian motion, including di-
rected motion, confined motion, and anomalous diffusion. The variety of motionleads 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
Capabilities of SPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Modes of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
EXPERIMENTAL TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
Classification of Modes of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380Anomalous and Normal Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381Confined Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Directed Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389SPT and FRAP: Effects of the Label . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
WHAT DIFFUSION TELLS US ABOUT MEMBRANE STRUCTURE . . . . . . . . . . . . . . . . 391
TECHNICAL PRIORITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
373
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374 SAXTON & JACOBSON
PERSPECTIVES
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 generalquestions addressed by the technique are as follows:
(a) How do particles move on the cell surface? To what extent does the mo-
tion 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 environ-
ment 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 5100 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, confine-
ment 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 scaleof 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 exper-
iments, 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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SPT IN MEMBRANES 375
Capabilities of SPT
SPT has several advantages over FRAP measurements. The spatial resolu-
tion 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 detectablediffusion coefficient is lowered by approximately two orders of magnitude. Fur-
thermore, FRAP averages over hundreds or thousands of diffusing molecules,
but SPT measures individual trajectories. Thus, different subpopulations indis-
tinguishable by FRAP can be resolved. SPT provides the ultimate specificity
in measurement of motion of membrane components, particularly if the in-
dividual particle tracked could be characterized in terms of, for example, its
phosphorylation state.
Modes of MotionA major advantage of SPT is the ability to resolve modes of motion of in-
dividual 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 r2 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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376 SAXTON & JACOBSON
Two important phenomena have been observed that are related to the classi-
fication of modes of motion. First, correlated motion can provide convincing
evidence that apparently non-Brownian motion is in fact non-Brownian mo-
tion and not merely a fluctuation in Brownian motion. Second, practically all
experimental results show apparent transitions among modes of motion. If atransition is real, it could result from partition of the mobile species into dif-
ferent 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 differen-
tial 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, 4143, 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 parti-
cles. The scatter in position is 130 nm, yielding a minimum observable D of
5 1014 to 5 1013 cm2s1. 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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SPT IN MEMBRANES 377
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 110 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 d6. The minimum
detectable diameter is 15 nm and the typical diameter used is 3040 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 isreviewed in References 21 and 23.
Fluorescent labels used include fluorescent microspheres, typically of diam-
eter 30100 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 trans-
membrane 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 ofthe focal plane, endocytosis, detachment from the membrane, or photobleach-
ing (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, cor-ral size, and escape probability. The difficulty is that in a pure random walk
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378 SAXTON & JACOBSON
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) ones intuition by writing a simple
random walk program and looking at a few dozen pure random walks. Onewill see apparent diffusion, directed motion, trapping, and transitions (66, 70)
because our nervous systems are wired to see patterns. But observation of mul-
tiple 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 testrequires 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 themby eye.
When reporting classifications of trajectories based on some parameter, in-
clusion 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 aver-
age 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 MSDis noisy, yielding good short-range diffusion coefficients but highly scattered
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SPT IN MEMBRANES 379
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.
r2 = 4Dt normal diffusion (1)
r2 = 4Dt anomalous diffusion (2)
r2 = 4Dt + (V t)2 directed motion with diffusion (3)
r2
r2C
1 A1 exp4A2Dt
r2C
corralled motion (4)
In Equation 2, < 1, so strictly speaking this is anomalous subdiffusion (11,
36). In Equations 3 and 4, V is velocity, r2C 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),
p(r, t)dr =1
4Dtexp(r2/4Dt)2r dr, (5)
and for diffusion with simultaneous flow along the x-axis with velocity V,
p(x ,y, t,V)d x d y =1
4Dtexp([(x V t)2 + y2]/4Dt)d x d y. (6)
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 diffu-
sion coefficient:
D = (1/4)t
1, (7)
or, equivalently,
r2 = 4Dt = t , (8)
with < 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 formfor r2 at long times.
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380 SAXTON & JACOBSON
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 r2(t) curve to classify
trajectories. They calculate the experimental MSD and determine which analyt-ical 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 r2(t) 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 ofFigure 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 r2 is plotted versus log t, is found from
the initial slope, and the trajectory is classified according to .
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 gyrationR2gyr, a measure of the extent of the random walk. The joint distribution of R2gyr
and a2 may be used to classify trajectories (70). A related approach (93)
combines the observed D, the shape of the r2(t) curve, and the values of
R2gyr and a2 to sort trajectories into mobile, slowly diffusing, corralled, and
immobile.
APPLICATIONS
Results of SPT experiments, and the corresponding FRAP experiments whenavailable, 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 381
Table 1 Artificial bilayersa
Membrane Bilayer
component Label composition D(SPT)b D(FRAP) Ref.
Lipid analogs
TMR-POPE None POPC 140 23 77 13 78
Fi-PE 30 nm Au 87% egg PC 30 (MV) 133 33 58
Ab-Fl 13% Chol 70 (PV)
Biotin-PE 30 nm FM 80% egg PC 30 37
St 20% Chol
GPI-linked proteins
DAF (CD55) 30 nm FM 80% egg PC 25 37
St-biotin-Ab 20% Chol
FcRIIIB (CD16) same same 56 37
aAb, antibody; Chol, cholesterol; Fl, fluorescein; FM, fluorescent microsphere; GPI, glycosylphos-
phatidylinositol; MV, multivalent; PC, phosphatidylcholine; PE, phosphatidylethanolamine; POPC,palmitoyloleoyl PC; POPE, palmitoyloleoyl PE; PV, paucivalent; St, streptavidin; TMR, tetramethyl-rhodamine.bAll diffusion coefficients D in units 1010 cm2s1.
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 DiffusionOne of the most important results of SPT to date is the observation and mea-surement of anomalous diffusion in cell membranes. Anomalous diffusion can
be used as a probe of membrane organization. Furthermore, anomalous diffu-
sion 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, anomalousdiffusion 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: r2 t for t tC Rand r2 t for t tC R , where tC R is the crossover time and < 1. As the
obstacle concentration approaches the percolation threshold, 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
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382 SAXTON & JACOBSON
Table2
LipidsandGPI-linkedproteinsincellsa
Membrane
ApparentD(SPT)
component
Cell
Label
formo
bilefraction
D(FRAP)
Comments
Ref.
Lipidanalogs
Fi-PE
Fibroblasts
30nmAu
12
7
54
27
23%withD