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In a mirror dimly: tracing the
movements of molecules in living
cellsq
Matthias Weiss1 and Tommy Nilsson2,3
1
MEMPHYS-Center for Biomembrane Physics, Physics Department, University of Southern Denmark, DK-5230 Odense M, Denmark
Department of Medical Biochemistry, Gothenburg University, 413 90 Gothenburg, Sweden
3
Swegene Centre for Cellular Imaging, Gothenburg University, 413 90 Gothenburg, Sweden
2
The random movement of molecules (diffusion) is fundamental to most cellular processes, including enzymatic reactions, signalling, protein –protein interaction,
as well as domain and pattern formation. Despite playing a central role, diffusion is, to a large extent, underappreciated in the cell biology community. One reason
for this is that diffusion is rather challenging to study in
living cells. This article is intended to explain, at least in
part, how we can go about studying diffusion of molecules in living cells, why it is important and how it provides us with important clues about biological systems.
As the title ‘In a mirror dimly’ suggests, we do this by
monitoring faint light emitted by fluorescent probes or
proteins using advanced optics (e.g. mirrors) and electronics. The data are then fitted and interpreted with
mathematical and physical models, providing a glimpse
into the world of molecules.
In 1827, Robert Brown observed through his microscope
that small pollen particles exhibit a rather erratic motion
in aqueous solution, an effect now known as Brownian
motion or, simply, diffusion (for an explanation of diffusion,
see later). Since then, many studies have been devoted to
the process of diffusion (i.e. how molecules or particles
move in response to thermal noise), and in a seminal
article Einstein developed an elegant theoretical basis to
describe diffusion [1]. Our everyday experience tells us
that diffusion is an irreversible process that flattens out
existing concentration gradients (e.g. an ink droplet
spreading in water). Diffusion, therefore, acts according
to the second law of thermodynamics [2] (i.e. the molecules
spread to achieve a state of maximum entropy, or
maximum disorder). It is often overlooked, however, that
diffusion can also bring order into a system by destabilizing homogeneity. Such a drive towards self-organization
tends to happen when a reaction does not take place in a
well-stirred mixture so that components have to seek each
q
The title ‘in a mirror dimly’ refers to how we must often extrapolate from indirect
representations (such as fluorescent light) to construct a more complete picture. The
quote is taken from the New Testament, I Corinthians 13.12: ‘…di’esoptrou en
ainigmati…’ (‘Now we see in a mirror dimly, but then face to face. Now I know in part,
but then I shall understand fully.’)
Corresponding authors: Matthias Weiss (mweiss@memphys.sdu.dk),
Tommy Nilsson (tommy.nilsson@medkem.gu.se).
other out with the help of Brownian motion (diffusion). It is
under these conditions that the emergence of selforganizing spatiotemporal patterns, so-called Turing
patterns, can be observed [3]. In such cases, local domains
are enriched in a particular chemical, whereas others are
devoid of it. Despite its tendency to flatten out any
concentration gradient, diffusion promotes the appearance
of these domains because of its poor ‘self-mixing’ property
[4,5]. Diffusive mixing on interfaces such as membranes,
for example, is far less efficient than in bulk solution [6,7].
Thus, when molecules that react or otherwise interact
with each other diffuse on membranes, they will selforganize more readily into patterns or domains than when
diffusing in solution. In any event, it is clear that
quantifying the diffusion of molecules in solution and on
membranes is of major importance when studying
biological processes. In this article, we will attempt to
highlight important features of diffusion, why diffusion is
highly relevant to cell biological processes and how it can
be accessed experimentally in vivo using light microscopy
techniques.
Diffusion as a facilitator for pattern and domain
formation
In 1952, Turing discussed in the context of embryonal
morphogenesis [8] a set of simple chemical reactions (socalled reaction-diffusion systems), one of which we will
explain in more detail (Figure 1a): namely, a spontaneously synthesizing and autocatalytically reproducing
morphogen X (the activator) produces its own inhibitor Y,
which tries to prevent the production of X. Both species are
subject to degradation and are also capable of diffusing to
another location, albeit with different mobilities (i.e. the
inhibitor Y diffuses faster than the activator X). Despite its
apparent simplicity, this reaction scheme yields an
interesting phenomenon when the diffusional mobilities
of X and Y are sufficiently different. Instead of observing a
uniform distribution of both chemicals, X and Y appear to
segregate and form domains where either X or Y
dominates. The emergence of this self-organized Turing
pattern relies crucially on the diffusional mobility of the
reagents and can be understood as follows: as inhibitor Y
quickly diffuses out of regions where the slowly diffusing
activator X is more dominant, the Y-induced degradation
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Local activation
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Figure 1. The concept of Turing-pattern formation. (a) Schematic representation of a reaction-diffusion system involving two particle species, activator X and inhibitor
Y. The activator X is synthesized at a certain rate and catalyses its own production, as well as participating in creating Y molecules, which in turn inhibit the production of
X. Additionally, both species are subject to degradation and can diffuse to other loci, although inhibitor Y diffuses faster than activator X. (b) Because of the difference in
diffusion, a local (autocatalytically driven) activation is obtained (i.e. enrichment of X and a long-range inhibition where Y dominates). (c) An example of Turing-pattern
formation on a membrane. For simplicity, only the colour-coded activator concentration is displayed (blue to yellow represents low to high concentration). Starting from a
random initial concentration profile (i), a ‘patchy’ steady-state pattern is obtained (ii) when assuming that the number of reacting molecules is huge. Using small amounts
of reacting molecules, the pattern does not become stable (iii) because strong concentration fluctuations oppose pattern formation. However, even in the presence of these
concentration fluctuations, the pattern formation can be stabilized when the activator species X is slightly subdiffusive (iv). (d) The mean square displacement (MSD) values
of the activator molecules, as used in panels (i)– (iv), are displayed as broken and unbroken lines, respectively. Note the qualitative difference in the increase of the MSD
(solid line: normal diffusion, MSD , t; broken line: subdiffusion, MSD , t 0.9).
of X molecules slows down. Via autocatalytic feedback, this
locally enhances the number of X molecules, while the
spreading inhibitor Y suppresses the production of
activator molecules in the surrounding region, resulting
in local activation and long-range inhibition (Figure 1b).
An example of the formation of such a Turing pattern on a
membrane is shown in Figure 1c, where for simplicity only
the concentration profile of activator X is shown. Starting
from a random initial configuration [Figure 1c (i)], a stable,
patch-like array of domains [Figure 1c (ii)] is obtained at
steady-state, assuming that the number of reacting
molecules is sufficiently high that a meaningful concentration can be defined (in the physics literature this is
called the mean-field limit). Of course, this surprising
effect depends very much on the nature of the (nonlinear)
type of reactions involved [3] and their kinetic parameters
(reaction rates). Importantly, the stability of the pattern is
very sensitive to the values of the diffusion coefficients [3]
and even to the type of diffusional motion [9] [see later and
Figures 1c (iii) and (iv)].
The concept of Turing patterns has helped to elucidate
many forms of pattern formation, especially in physics and
chemistry (see, for example, Refs [3,10] for reviews). A
classical example of reaction-diffusion systems that display Turing patterns is the Belousov-Zhabotinskii reaction
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(see, for example, Ref. [11] for a recent experimental
realization). In biology, a famous example is the GiererMeinhard model [12], which describes the self-organized
development of the freshwater polyp Hydra. More
recently, studies on pattern formation in cell biology
have also been addressed using Turing’s concept. A nice
example is the positioning of the septum in dividing
bacteria [13– 15] or in the slug formation of Dictyostelium
discoideum [16 – 18]. Many more Turing-like self-organizing systems in cell biology will undoubtedly be discovered
in the future.
Not a simple matter of diffusion
As noted before, the formation and maintenance (or
stability) of patterns depends crucially on the reaction
rates and diffusion involved. Investigating pattern formation such as Turing-pattern mechanisms is therefore
only possible if relevant in vivo parameters can be
accessed. Before attempting this, however, it is important
to understand a bit more about diffusion. In its simplest
form, diffusion is the very same behaviour that a person
displays when trying to get back home after an extensive
pub-crawl (for the uninitiated, a pub-crawl involves the
sometimes arduous task of frequenting as many pubs or
bars as is physically possible in one night, always
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consuming at least one alcoholic beverage in each place).
Staggering from street lamp to street lamp, the drunk
person instantly forgets from which of the two neighbouring lamps he or she came from and hence will stagger
randomly to either one of them; in other words, having a
complete lack of any sense of direction. This lack of
direction is an intrinsic property of diffusion and it is
obvious that such movement is a much less efficient way to
move compared with directed motion (simply to go straight
home). Nevertheless, the mean square displacement
(MSD) of the person as seen from his or her starting
position will grow linearly with time (Figure 1d); that is,
MSD(t) , Dt, with a prefactor that measures the diffusional mobility. This factor is known as the diffusion
coefficient, D. Let us now suppose that, as soon as reaching
one lamppost, the person does not immediately move on to
the next one. Instead, he or she will remain at each
lamppost for a certain time (e.g. hugging the lamppost or
admiring its beauty). Such ‘resting’ times might not only
be random but also sometimes quite long; that is, one can
still define a mean resting time, but the standard deviation
from it might become arbitrarily large. In this case, the
MSD will grow qualitatively more slowly than for normal
diffusion (i.e. MSD , ta, where a , 1; Figure 1d). In other
words, although we still observe an ‘unbiased’ random
walk, the efficiency of moving away from the starting point
(the last pub) has decreased qualitatively as it now takes
more and more time to explore the same area. Whereas the
random movement without the rests is called normal
diffusion (a ¼ 1), diffusional movement with long rests is
called anomalous subdiffusion (a , 1).
There are several reasons for subdiffusion, such as
obstructed diffusion imposed by molecular crowding or by
almost immobile obstacles such as membrane domains
[19]. Another possible mechanism giving rise to subdiffusion has already been outlined above (i.e. particles take
long rests between periods of free diffusional motion). The
reason for these rests can be manifold, such as special
binding or trapping events with immobile partners, where
the properties of the ‘trap’ can be time-independent
(binding without memory) or time-dependent (binding
with some memory). Readers are referred to Refs [20– 22]
for details.
Regardless of the underlying reason for subdiffusion, its
mere occurrence has major implications for biological
processes. The degree of subdiffusion dramatically influences the rate at which biological reactions take place [23],
the time-course of enzymatic reactions [24] and, most
importantly, the efficiency with which spatiotemporal
patterns form [9]. The latter is demonstrated in Figure
1c, where a well-characterized reaction-diffusion system,
the so-called Schnakenberg model [25], is simulated on a
membrane (see Ref. [9] for technical details). Initially, the
reacting molecules (activator X and inhibitor Y) are
distributed randomly on the membrane [Figure 1c (i)].
Using the mean-field limit (i.e. assuming that a huge
number of X and Yparticles make up the reaction-diffusion
system), we end up with the stationary Turing pattern
shown in Figure 1c (ii). When using the same reaction
rates and diffusion coefficients but reducing the number of
particles to a few thousands (a realistic number in
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biological processes), the observed pattern disappears
[Figure 1c (iii)]. This is because the low particle number
locally leads to strong concentration fluctuations, which
counteract and overcome the drive towards pattern
formation. When one of the reagents is made slightly
subdiffusive (a ¼ 0.9), however, the pattern is restored
[Figure 1c (iv)]. This demonstrates that subdiffusion
promotes the formation and maintenance of patterns,
enabling improved efficiency, a higher degree of compartmentalization and, consequently, increased specificity of
biological processes (e.g. signalling).
Determining (sub)diffusion using light microscopy
Several excellent studies exploring the nature of subdiffusion, both theoretically and experimentally, already exist
in the physics field (see Refs [26 – 28] for extensive
reviews). Despite its powerful and important implications,
however, subdiffusion has largely been neglected by the
cell biology community. This is now about to change.
Elegant single-particle tracking experiments have already
revealed subdiffusion of neural adhesion molecules [29]
and the major histocompatibility complex [30] on the
plasma membrane of neurons and HeLa cells, respectively.
This approach, however, is limited to studies on the plasma
membrane or reconstituted systems and is not yet really
applicable to intracellular events. Intracellular movements are instead more easily accessed by monitoring
fluorescent proteins, most commonly the green fluorescence protein (GFP), fused to the protein of interest.
We outline below two techniques that are particularly
useful when studying diffusion in living cells: fluorescence
recovery after photobleaching (FRAP) and fluorescence
correlation spectroscopy (FCS). As will be explained, FCS
is well suited to determining the degree of subdiffusion.
The FRAP method was introduced in its basic form in
the late 1970s [31,32] and was applied to the study of
diffusion of lipids and proteins in living cells [33]. The
concept is straightforward: after bleaching an area of
interest with high laser intensity (i.e. irreversibly destroying all fluorophores in this region), the temporal recovery
of fluorescence in the bleached region is monitored under
low laser power. This recovery can be due to the simple
diffusional influx of particles into the region and/or the
binding of particles to a structure (e.g. an intracellular
membrane) in the bleached area. The experimentally
obtained time-course of the fluorescence recovery FðtÞ is
then fitted with an appropriate theoretical formula to
extract the desired information about reaction rates and/or
diffusion coefficients. For example, binding kinetics of a
peripheral membrane protein to a membrane of interest
can be assessed by bleaching the membrane-bound pool
and then monitoring the recovery due to new binding
events. This approach has recently been used to explore
the membrane-binding kinetics of peripheral Golgi proteins such as ARF-1 and coatomer, which are involved in
the formation of COPI vesicles [34,35]. In such studies,
diffusion-limited binding events such as that observed for
coatomer have to be taken into account [35]. In other
words, any recovery rate observed by FRAP might not be
determined just by the particular binding kinetics but
might also be influenced by the diffusion of molecules into
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the region. Another aspect worth emphasizing when
performing FRAP is that the shape of the bleached region
plays a crucial role because the functional form of the
recovery depends on the shape. In other words, bleaching a
circular region and fitting experimental data with a
theoretical expression derived for a narrow strip will
give an incorrect value for the diffusion coefficient, thus
invalidating the entire study. Despite these caveats, FRAP
has been applied frequently, and usually successfully, to
assess the mobility of soluble proteins in the cytoplasm and
nucleus [36] and of membrane proteins, for example, in
both the endoplasmic reticulum (ER) and the Golgi
apparatus [37].
When using FRAP, it is important to remember that it is
rather challenging and imprecise to determine the diffusion coefficients of membrane proteins (this also applies to
FCS, see below). First, the unknown geometry of the
membrane leads to uncertainty in protein mobility by a
factor of two or more [38,39]. Second, the diffusion
coefficient of a protein diffusing in a membrane depends
only logarithmically on the size of its membrane-penetrating domain [40], whereas the diffusion coefficient of a
(globular) protein in bulk solution is inversely proportional
to its size [2]. This is crucial to understand when
attempting to translate the measured mobility (i.e. the
diffusion coefficient) into particle or complex size. If there
is uncertainty in the mobility by a factor of two (caused, for
example, by the particular but hidden geometry of the
membrane or variability in measurements), this translates into uncertainty regarding the size of the traced
particle or complex by a factor of ten. To give a concrete
example, the diffusional mobility of glycosylation enzymes
on the ER and Golgi membranes was determined by FRAP
and shown to be rather high [37]. A conclusion that could
be drawn from these studies (e.g. by the cell biology
community) is that this would negate the possibility that
enzymes exist as larger complexes (kin complexes [41]) in
the Golgi cisternae. In fact, in that study, it was impossible
to distinguish a dimer from complexes of at least 400
molecules [39]. Third, the diffusion of membrane proteins
is often anomalous; that is, the MSD does not increase
linearly with time (see above) and must therefore be
interpreted with the help of a generalized diffusion
coefficient. With regard to this last point, FRAP can
potentially be used to determine anomalous diffusion [42],
but the measurement usually does not permit one to
distinguish between subdiffusion or a mixture of fastdiffusing monomers and slow-moving complexes
(i.e. multiple populations having different diffusional
mobilities).
It is here that FCS has proved to be more valuable. The
origins of FCS can be traced back to the early 1970s [43],
but it was not until the 1990s that the technique became
feasible and sufficiently sensitive [44]. In FCS applications, a laser beam with a bell-shaped (gaussian)
intensity profile is focused onto a spot of interest inside a
living cell and a pinhole is then used to discriminate the
fluorescent light emitted from different focal planes
(Figure 2a). In this way, the collection of photons is
effectively constrained to a confocal volume of , 1 mm3, the
minimum size the diffraction limit permits for. In contrast
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to FRAP, it is not the average fluorescence but rather the
fluctuations around the mean that are of interest because
the fluorescence signal rises or falls when a fluorescent
molecule enters or leaves the confocal volume (Figure 2b).
The Brownian movement of the particles is thereby
reflected in the fluctuations of the fluorescence signal
FðtÞ and the fluorescence fluctuations become stronger and
more easily visible when fewer labelled particles are in the
confocal volume. In other words, FCS works best at very
low overexpression concentrations (1 nM is sufficient).
This is at the level of single molecules in the confocal
volume and cells can therefore be studied almost in their
native state without perturbing them. The fluctuations of
the fluorescence time series FðtÞ (Figure 2b) are then
evaluated by calculating the autocorrelation function C(t),
which essentially describes the decreasing average probability that a particle inside the confocal volume will stay
in the focus for at least the time period t. A typical example
of what C(t) looks like is given in Figure 2c. Depending on
its mobility, size and interaction with other molecules, the
labelled molecule will dwell for shorter or longer time
periods inside the confocal volume until it leaves. Using
some simplifying assumptions, C(t) can be calculated
analytically for different diffusion types (e.g. for diffusion
in the cytoplasm or on membranes [39,44,45]) and fitted to
the experimental data to obtain the time point tD at which
the autocorrelation function C(t) has dropped to half of its
value (Figure 2c). This half-time is inversely proportional
to the diffusion coefficient of the traced protein, which is
the desired quantity. Furthermore, the mean number of
particles in the confocal volume (i.e. the local concentration of particles) can be deduced from the maximum
value C(t ¼ 0).
FCS has several advantages over FRAP. It works at
much lower levels of overexpression, there is no destruction or bleaching of the dye (GFP), the time resolution is in
the microsecond range (this will also soon be possible with
FRAP, thanks to a new generation of confocal microscopes)
and local concentrations on the scale of single molecules
can be determined. The range of FCS applications so far
includes in vitro studies on the hybridization kinetics of
DNA probes to RNA [46]; the real-time kinetics
of enzymatic reactions [47]; the spatiotemporal changes
of signalling proteins involved in regulating bacterial
motors [48]; in vivo studies on the diffusion of fluorescent
probes in the nucleus [49]; the dynamics of the COPI
vesicle machinery [35]; and the occurrence of anomalous
diffusion of Golgi-resident proteins [39]. Subdiffusion has
also been found and characterized using FCS for membrane proteins of the plasma membrane [50], as well as for
proteins in the nucleoplasm [49]. In most cases, the degree
of subdiffusion was simply calculated by fitting the
autocorrelation decay C(t) with a model for anomalous
diffusion. This is not very precise because a two-component
system (e.g. a mixture of fast-diffusing monomers and
slow-diffusing complexes) might exhibit a subdiffusive
‘signature’ and vice versa; thus an alternative approach is
required. It turns out that the fluctuating fluorescence
seen by the FCS detector is actually a fractal curve (i.e. it
appears to have a similar appearance on all scales when
zooming into the curve; see successive magnifications in
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Confocal volume
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Figure 2. The concept of fluorescence (cross)-correlation spectroscopy. (a) A green laser beam is focused into a living cell, and the fluorescence from the focus (the confocal
volume, yellow) is collected by highly sensitive detectors. A second (red) laser beam can also be applied and discriminated by appropriate filters. Ideally, the confocal
volumes of the red and green laser light should be congruent. (b) Time series of the fluorescence as measured by the detectors fluctuates strongly around a well-defined
mean (the average intensity). On zooming into the fluorescence curve, it can be seen that it has a similar appearance on several scales (see successive magnifications of the
green fluorescence time series). In other words, the curve is neither a line nor a plane, but rather a fractal object [39] in between. The fluctuations in the fluorescence arise
from the ‘dancing’ of fluorescently labelled molecules to the ‘music’ of thermal noise (i.e. they diffuse into and out of the focus). A departing particle reduces the
fluorescence and an incoming particle leads to increased fluorescence. (c) By calculating the autocorrelation curve of the fluorescence fluctuations, one obtains a sigmoidally decaying curve in a semilogarithmic plot (shown in red and green for the different laser beams). The half-time tD of the decay (broken line) is related to the diffusional
mobility of the dancing molecules. If red- and green-labelled molecules form complexes, the cross-correlation curve of the red– green fluorescence can be calculated
(shown in black). Not only is the decay of the curve somewhat slower than that of the separate red and green molecules (the dancing couple experiences more friction
during the dance; i.e. the diffusional mobility is lower) but also, from the offset of the curve at t ¼ 0, the fraction of couples and red or green individuals can be estimated. In
other words, the affinity of the reaction [red] þ [green] $ [red–green] can be determined.
Figure 2b). Characterization of this fractal property of the
fluorescent signal in more detail reliably revealed subdiffusion of membrane proteins in both the Golgi and the
ER [39].
Although FCS is a valuable tool to assess subdiffusion, it
suffers from the same drawbacks as FRAP when it comes
to calculating particle size (i.e. the degree of oligomerization) from the measured diffusion coefficient: geometrical
constraints (e.g. the shape of the host membrane) can
considerably influence the diffusion and thus hinder
estimation of the size of the tracked protein [38,39]. A
recent FCS development, however, circumvents this
problem. Termed fluorescence cross-correlation spectroscopy (FCCS), two differently labelled particle species
are monitored at the same time. FCCS effectively
eliminates the uncertainties imposed by the geometrical
constraints using FCS and FRAP. Here, two laser beams
are superimposed to yield a congruent confocal volume to
monitor, for example, a red- and a green-labelled protein
species at the same time (Figure 2). The recorded
fluorescence time series, Fr ðtÞ and Fg ðtÞ; of the two dyes
can be used to determine, for example, the diffusion
coefficient, as described for FCS. When the erratic motion
of some particles of the red species influences the diffusion
of some particles of the green species (i.e. when some of
them form a complex), the cross-correlation function G(t)
between Fr ðtÞ and Fg ðtÞ can be calculated. This function
essentially describes the average probability that a green
particle will stay for at least a time period t in the confocal
volume when a red particle is currently in it. Similar to
C(t), G(t) is a decaying curve with a typical half-time tD
that is determined by the diffusion coefficient of the red –
green complexes (Figure 2c). As long as red and green
particles do not form complexes, G(t) is always zero,
whereas it becomes non-zero when complexes form. The
fraction of complexes can be determined from the red and
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green autocorrelation curves and the cross-correlation
curve (i.e. the affinity between protein species on the level
of single molecules) can be estimated in vivo. So far, FCCS
has been used to demonstrate the cleavage of DNA by
endonucleases [51]: upon cleavage, the differently labelled
parts of the DNA diffused away from each other and the
cross-correlation approached zero. Also, the output of the
polymerase chain reaction was studied on the level of a few
molecules by observing the emergence of a non-zero crosscorrelation when a double-labelled piece of DNA was
constructed [52]. The application of FCCS to membrane
systems was further demonstrated by monitoring the
association of a labelled IgE receptor with differently
labelled raft domains [53]. More recently, FCCS has
been applied to the endocytic pathway of living cells to
study the passage of the cholera toxin along the
endocytic pathway [54].
Another very new and exciting development that should
be mentioned is the combination of FCS or FCCS and total
internal reflection microscopy [55,56]. This approach
makes use of the fact that incident laser light is almost
totally reflected at the glass– water interface and only a
very thin layer (, 100 nm) of the sample (i.e. the cell) is
illuminated. The fluorescent light is then collected in the
same way as in conventional FCS. This approach enables a
reduction of the illuminated volume (i.e. the lateral
resolution stays the same while the ‘height’ of the confocal
volume is decreased approximately tenfold). With this
promising approach, diffusion and reactions near to and on
the plasma membrane can be studied with very high
sensitivity, a technique perhaps ideally suited to explore
lipid domains.
Concluding remarks
We hope that we have managed to highlight some
important aspects of diffusion and explain why it is
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important that we study it, as well as how we can access it
experimentally. For cell biologists considering embarking
on more-advanced imaging and the necessary data-fitting
or modelling, it is worth pointing out that there are highly
competent people in the fields of (bio)physics who already
know a great deal. What is important for the cell biologist
is to have some level of appreciation of the complexity
involved. In turn, for (bio)physicists, cell biologists have a
lot to offer in terms of formulating important questions
that await the curious. Therefore, we hope that our article
will help to stimulate cross-disciplinary work on fascinating problems in cell biology.
Acknowledgements
The MEMPHYS-Center for Biomembrane Physics is supported by the
Danish National Research Foundation (M.W.). The Centre for Cellular
Imaging is supported by the Swegene Postgenomic Research and
Technology Programme in South Western Sweden (T.N.).
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