The method of fluorescence recovery after photobleaching (FRAP) utilizes the phenomenon of photobleaching of fluorescent probes to measure parameters related to molecule mobility. It was initially designed by Axelrod and coworkers to measure

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The method of fluorescence recovery after
photobleaching (FRAP) utilizes the phenomenon of
photobleaching of fluorescent probes to measure
parameters related to molecule mobility. It was
initially designed by Axelrod and coworkers to
measure two-dimensional diffusion of
membrane-bound molecules (see applications of
photobleaching techniques for further application
details ). Frequently photobleaching interferes
with image acquisition in fluorescence microscopy
by fading the fluorescent probes, resulting in a
lower signal/noise ratio. However in FRAP
experiments, it is used to selectively
photobleach a specific area by high intensity
laser pulses. Subsequently the kinetics of
fluorescence recovery are recorded by sampling
images at regular time intervals with low
intensity illumination. Closely related to FRAP
is fluorescence loss in photobleaching (FLIP). In
FLIP experiments a specified region of the cell
is repetitively photobleached and the loss of
fluorescence in non-bleached parts of the cell is
measured. Another variant of photobleaching
techniques is iFRAP (inverse FRAP) where all the
fluorescent molecules in a cell except for a
small region are bleached . The loss of
fluorescence from the unbleached region in the
postbleach images is then analyzed. With this
technique qualitative information about mobility
and equilibration time can be gained. Because of
the time needed to bleach large areas, this
method is especially suited to analyze the
dissociation parameters of molecules which are
bound to an immobile structure for several
seconds.
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How FRAP works In unbleached cells fluorescent molecules are in equilibrium. Bleaching a fraction of the total fluorescent molecules in a region of interest (ROI) disturbs this equilibrium. Under optimal conditions the recovery kinetics are dependent only on the mobility (effective diffusion coefficient and binding kinetics to macromolecular structures) of the investigated molecule.Thus by measuring the recovery kinetics, following properties of the molecule can be characterized the ratio between mobile and immobile fraction the effective diffusion coefficient Deff the binding time (as well as assembly/disassembly) of proteins to macromolecular structures continuity of intracellular organelles (FLIP) formation of protein complexes (resulting in lower Deff)
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Photobleaching Absorbtion of light by a fluorophore elevates electrons from the ground state to an excited singlet state. Fluorescence arises from the emission of a photon during relaxation to the ground state.The exact mechanism of photobleaching is not known, but it is assumed to be linked to a transition from the excited singlet state to the excited triplet state. The excited triplet state is relatively long-lived and is chemically more reactive. Each fluorophore has different photobleaching-characteristics. For FRAP experiments it is important to choose a dye which bleaches minimally at low illumination power (to prevent photobleaching during image acquisition) but bleaches fast and irreversibly at high illumination power.
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According to the Stokes-Einstein equation

• the diffusion coefficient D for a particle in a
  free volume depends on the Boltzmann constant
  (k), the absolute temperature (T), the viscosity
  of the solution (h), and the hydrodynamic radius
  (R) of the particle.
• The mobility of a molecule in the cellular
  environment is affected by the following
  parameters
• The size of the moleculean eightfold increase of
  the size of a soluble sperical protein decreases
  D by factor 2.
• the viscosity of the cellular environment e.g.
  membranes have a much higher viscosity than
  cytoplasm
• protein-protein-interactions and binding to
  macromolecules can also slow down the diffusion
• if flow or active transport is involved in the
  movement of the probed molecule, the measured
  movement rate can become significantly higher
  than the theoretical diffusion rate
• The diffusion coefficient D of the probed
  molecule can be measured via the halftime of the
  recovery (thalf). This coefficient is influenced
  by the above stated parameters. Therefore this
  value is often termed as the effective diffusion
  coefficient (or apparent diffusion coefficient)
  Deff (in µm2 s-1) and reflects the mean squared
  displacement explored by the proteins through a
  random walk over time.
• Changes of the effective diffusion coefficient,
  e.g. due to binding to a larger molecule, can be
  exploited to study the function of the protein of
  interest. For instance the endonuclease ERCC1/XPF
  is binding to DNA when damages are induced by UV
  light resulting in a decreased Deff (Houtsmuller
  et al. 1999).
• By performing the FRAP experiment at different
  temperatures (e.g. 27 and 37 C) it is possible
  to determine if energy-dependent processes are
  involved in the mobility of the investigated
  molecule. While the difference in molecular
  diffusion due to a 10 K change in absolute
  temperature is too small to be resolved by FRAP
  (D decreases only 3, Phair Misteli 2000),
  energy-dependent processes are more sensitive to
  temperature (Hoogstraten et al. 2002).

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For qualitative determination of the recovery
dynamics, e.g. to compare differences of one
molecule at different conditions, a simple
exponential equation can be used as a first
approximation
   After determination of t by fitting the above
equation to the recovery curve the corresponding
halftime of the recovery can be calculated with
the following formula
 If the molecule binds to a slow or immobile macromolecular structure it is very likely that the recovery curve does not fit a single exponential equation. To overcome this problem, a biexponential equation can be used. Depending on the investigated molecule the amount of interaction with other molecules will be variable. For example proteins which associate with relatively immobile cellular structures such as the cytoskeleton have a significantly reduced recovery compared to a freely mobile molecule. Using kinetic modeling the binding characteristics of the examined molecule can determined by the ratio between mobile and immobile fraction.
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An idealized plot of a FRAP recovery curve. II
initial intensityI0 intensity at timepoint t0
(first postbleach intensity)I1/2 half recovered
intensity (I1/2 (IE - I0) / 2)IE endvalue of
the recovered intensitythalf Halftime of
recovery corresponding to I1/2 (t1/2 - t0) 
Mobile fraction Fm (IE - I0) / (II -
I0)Immobile fraction Fi 1 - Fm
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The optimal fluorophore should be bright and stable under low intensity illumination during image acquisition (pre- and postbleach). Under high intensity illumination it should bleach fast and irriversibly. Another prerequisite is that the used fluorophore must not inhibit the function of the investigated molecule.
   

Fluorophores for FRAP-experiments (according to Ellenberg and Rabut) Fluorophores for FRAP-experiments (according to Ellenberg and Rabut)
fluorophore comment
fluorescein and derivatives probably the most used chemical fluorophore, tends to bleach too easily and photoleaching is partly reversible (Periasamy 1996)
fluorescent proteins mostly irreversible photobleachingEGFP tends to multimerize  at high concentrations
                                                                                                                     
Regardless of fluorophore, it is important to test its photobleaching characteristics under the imaging condition used.
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The classical approach for FRAP measurements
utilizes a widefield epi-fluorescence microscope
to monitor the fluorescence intensity during pre-
and postbleach acquisition. For bleaching a laser
beam is focused onto a small diffraction limited
spot (1µm) in the region of interest. These
systems are not of the shelf and have to be
custom-build. In principal the standard
commercially available confocal laser-scanning
microscope (CLSM) equipped with acousto-optical
tuneable filter (AOTF) is suitable for FRAP,
iFRAP and FLIP experiments. The AOTF is needed to
switch the laser power rapidly between the low
intensity imaging and the high intensity
bleaching modes. The higher the diffusion
constant of the investigated molecule, the more
imaging speed and laser power is required. Read
more about useful confocal equipment for FRAP
experiments.
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Standard features of typical CLSM necessary for
FRAP experiments AOTF to attenuate the laser
power between high intensity illumination for
bleaching and low intensity for imaging mode
Interactive definition of the bleaching area by
regions of interest (ROI) or spots including
saving parameters of the ROI(s) or spot(s) for
evaluation The software should be as flexible as
possible to define prebleach-, bleach- and
postbleach-settings either by special routines or
by macro-programming, e.g. number and frequency
of frames scan speed and zoom factor laser
intensity (AOTF settings) Depending on the
required resolution and the desired depth of
bleaching, different objectives are suitable for
FRAP experiments. For homogenous bleaching in
z-direction objectives with a lower magnification
like a 20x 0.7 NA lens are suitable, but result
in a lower resolution. Higher resolution with
increased light intensity in the focal plane but
incomplete bleaching in z-direction can be
achieved using lenses with a high numerical
aperture like a 63x 1,4NA objective. The thinner
the structure subjected to bleaching the higher
the NA should be.
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If molecules with rapid kinetics are
investigated, advanced features can be necessary
for FRAP experiments higher laser power to
bleach faster (to minimize diffusion during
bleaching) time optimized FRAP modules
(switching delays between bleach and postbleach
image aquisition should be minimized) small
formats and fast acquisition speed Long-term
FRAP-experiments which explore molecules with
very slow recovery characteristics also requires
additional properties of the imaging system To
correct for laser-fluctuations the laser
intensity can be quantified by monitor diodes
or transmission images. Tracking of the mobile
photobleached cells using autofocus routines
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There is no universal protocol for FRAP experiments since the design of a FRAP experiment always has to take into account the bleaching and recovery characteristics of the molecule under investigation. The visualized cells should not be affected by high illumination conditions. Therefore the optimal conditions have to be empirically tested for each biological system. The information in this section intends to provide general rules and hints applicable to most photobleaching experiments. One general consideration in FRAP experiments is to minimize the bleaching during acquisition instead of acquiring nice images. The data has to be averaged over the selected area anyway to diminish statistical distributed noise.
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Preconditions Before meaningful FRAP data can be
measured the following experiments should be
carried out First when using fluorescent
protein constructs the cells should be checked
for physiological and morphological alterations
compared to control cells. Only cells which are
normal should be used for further analysis by
FRAP. Bleaching characteristics have to be
checked in fixed cells to determine bleach rates
without movement of the probed molecule
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To minimize photobleaching during acquisition
these parameters should be adjusted decreasing
the pixel resolution by zooming out or by
lowering the pixel number (e.g. 128x128 instead
of 512x512) decreasing the pixel dwell time
using a faster scan speed (this is also
preferable to monitor rapid recovery kinetics)
decreasing the laser power during image
acquisition to a minimum using fluorophores
which are less susceptible to photobleaching at
low laser intensities frame or line averaging
should be avoided to reduce undesired
photobleaching in the imaging mode opening the
pinhole leads to a brighter signal with less
laser power
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The imaging in a FRAP experiment generally
consists of 3 steps The sample is first imaged
at low intensity illumination in a prebleach
series (usually about 10 images) to measure the
fluorsecence equilibrium before disturbance. The
second step is to bleach one or more spots or
regions of interest (ROI) with high intensity
illumination to disturb the fluorescence
equilibrium. In the last imaging step a series
of postbleach images is acquired to record the
fluorescence recovery kinetics. Finally several
data evaluation steps reveal mobility-related
parameters of the molecule of interest.
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The prebleach series is used to determine the
(total) fluorescence intensity at low intensity
illumination prior to bleaching to provide a
reference point for fluorescence recovery
typically 3-10 images.(If fluorescent proteins
(FP) are imaged with more than 1 image/s a
prebleach series of 50-100 images is needed to
reach a steady state of FPs in dark states (Weber
et al. 1999)). calculate the fluorescence loss
due to acquisition photobleaching To prevent
artefacts from pixel saturation, the maximum
intensity (255 in 8-bit images) should be reached
only in very few pixels. The offset should be
adjusted that the background pixels show
grayvalues slightly above zero (otherwise
information can be lost). To increase the dynamic
range it can be advantageous to employ the 12-bit
mode. In the pre- and postbleach-series laser
intensity should be attenuated as low as possible
to get a sufficient signal - for FRAP experiments
minimized acquisition photobleaching is more
important than nice images. In the data
evaluation step the fluorescence intensity during
recovery will be normalized with the prebleach
values.
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In the bleaching step one or more spot(s) or region(s) of interest (ROI) are irradiated with high intensity illumination. Ideally the bleaching event should be instantaneous, in practice it should not exceed a tenth of the half time of the recovery. Therefore for analysing rapid kinetics, more powerful lasers as well as time optimized acquisition routines are essential. Parameters that influence the bleaching process Laser power More laser power enables faster bleaching but also can harm the cells. Zoom Zooming in increases the effective irradiation of the scanned area. Thus zooming in speeds up the bleaching, but the response time for switching back to the unzoomed imaging mode can delay the acquisition of the postbleach series. Which is especially undesirable when analysing rapid kinetics. Scan speed The slower the scan speed the more energy is radiated (longer pixel dwell time) It is important to calibrate the bleached volume for each set of parameters (laser power, objective, zoom, speed, etc.) which is best done using fixed samples. A more precise definition of the bleached volume along the optical axis can be achieved using two-photon excitation.
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The postbleach series monitors the dynamics and extent of the fluorescence recovery. The following hints help to improve the accuracy of the recovery detection The acquisition frequency should be adjusted to resolve the dynamic range of the recovery with good temporal resolution (rule of thumb at least 20 data points during the time required for the half of the recovery). Acquisition photobleaching should be minimized to record the recovery dynamics as precisly as possible. The ideal postbleach acquisition duration is 10 to 50 times longer than the halftime (Axelrod 1976). In practice initial experiments should be conducted until no noticeable further increase in fluorescence intensity is detected. When using FPs the imaging frequency should not be altered during an experiment because the fraction of FPs driven into dark states could be altered complicating the analysis of the data.
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• Depending on the experiment there are several
  data evaluation steps which have to be carried
  out before meaningful results can be achieved
• Alignment of the images (only necessary if the
  regions of interest moved over time).
• Fluorescence intensity quantification (obtaining
  the raw data)
• Background subtraction
• Correct for laser fluctuations, photobleaching
  during acquisition (postbleach) and total
  fluorescence loss caused by the bleaching step
• Normalization
• Mobile/immobile fraction
• T½ halftime of the equilibration of bleached and
  unbleached molecules
• Theoretical models to additionally determine
  binding characteristics of the analysed molecule

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Image Alignment During longer FRAP experiments,
e.g. analyzing very slow molecules or molecules
which bind to immobile structures, the bleached
ROI can move over time. In order to obtain the
right data in these cases it is essential to
correct for this movement by alignment prior to
the intensity quantification. Image Alignment can
be done with ImageJ TurboReg (freeware) or the
commercial tool Autoaligner (Bitplane AG,
Switzerland).
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Obtaining the raw data To determine the raw
FRAP data the total or average pixel values in
the bleached ROI has to be determined for each
timepoint. This can be done with the most
confocal operating software (e.g. Zeiss LSM,
Leica LCS) or with other image processing
software which can handle time series (e.g. the
freeware ImageJ).
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Background subtraction The image brightness not
only originates from fluorescence of the
fluorescently labelled molecules of interest. For
example detector readout noise, autofluorescence
(medium, glass...), and reflected light
contribute to the total detected intensity.
Therefore the average background value
(background measurement in an area outside the
cell) should be subtracted from the average pixel
value in the bleaching region for each
timestep. The background quantification can be
carried out with the confocal operating software
(e.g. Zeiss LSM, Leica LCS) or with other image
processing software which can handle time series
(e.g. the freeware ImageJ).
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Further necessary corrections Laser fluctuations,
acquisition photobleaching, and fluorescence loss
during photobleaching leads to intensity changes
during image acquisition. In order to obtain data
with a linear relationship between the measured
fluorescence intensity and the concentration of
fluorescent molecules, the raw data has to be
corrected for these changes. One straightforward
possibility to do so is to divide the background
subtracted fluorescent measurement by the total
cell intensity at each time point. If this is not
possible, e.g. when only a part of the cell can
be imaged, alternative correction methods are
available Acquisition photobleaching can be
corrected for by measurement of the fluorescence
intensity of neighboring cells, in control
experiments or the prebleach series. The
fluorescence measurement at each timepoint can be
divided by a function representing the
acquisition photobleaching y(n) exp(-n/x) with
n  image number can be easily determined by
measuring the total fluorescence intensity of an
unbleached neighboring cell or the gradual
fluorescence decrease in the prebleach or
postbleach images. Laser intensity fluctuations
can be compensated for by dividing the
fluorescence measurement at each timepoint by the
corresponding value of the laser monitor diode or
the averaged intensity of the transmission
channel outside the cell (corrected for the
nonzero offset of the diode or transmission
detector, respectively).
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Normalization To compare different experiments
usually the fluorescence intensity of the average
prebleach intensity is normalized to one by
dividing the intensity of all timepoints by the
average prebleach intensity. This can be easily
done with common spreadsheet programs. It is also
possible to normalize to numbers of fluorophores
by using fluorophore calibration standards
(Ellenberg and Rabut).
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Determination of the Mobile / Immobile
Fraction If the whole population of the
investigated molecule is freely mobile the
fluorescence intensity (background subtracted and
corrected for loss of fluorescence due to the
bleaching pulse) recovery curve should reach a
plateau at 100 of the initial fluorescence of
the prebleach. Binding of a fraction of the
molecules of interest to slow or immobile
structures (e.g. Nuclear envelope) reduces the
recovered level of the fluorescence, the
fractions can be calculated with the following
equations. Mobile fraction Fm (IE - I0) / (II
- I0)Immobile fraction Fi 1 - Fm With IE
Endvalue of the recovered fluorescence
intensity         I0 first postbleach
fluorescence intensity         II Initial
(prebleach) fluorescence intensity An additional
method to measure the mobile and immobile
fractions exemplified for the nucleus is
described by Houtsmuller 2001. A spot in the
compartment of interest is bleached over an
extended period of time with relatively low laser
intensity. During this extended bleaching time a
large percentage of mobile molecules passes
through the bleaching spot and partially will be
bleached. Subsequently, the mobile molecules are
allowed to completely redistribute through the
nucleus (depending on their diffusion
coefficient). The ratio of fluorescence intensity
of confocal images before and after this
procedure is then plotted against distance to the
laser spot. To accurately calculate the immobile
fraction from this plot one should obtain two
reference curves, representing the situations in
which all molecules are immobile (fixed sample)
and in which all molecules are mobile (e.g. in an
inducible system).
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Determination of the halftime of the recovery
(thalf) The halftime (thalf) of recovery is the
time from the bleach to the timepoint where the
fluorescence intensity reaches the half (I1/2) of
the final recovered intensity (IE). Fitting the
recovery data to an exponential equation can be
used to determine thalf If the investigated
molecule freely diffuses in the cell or
compartment a simple exponential formula should
be used
                                                                           
Where A is the endvalue of the recovered
intensity (IE), t is the fitted parameter and t
is the time after the bleaching pulse. After
determination of t by fitting the above equation
to the recovery curve the corresponding halftime
of the recovery can be calculated with the
following formula
                                               
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If the molecule binds to slow or immobile
macromolecular structures or the diffusion is
partially hindered it is very likely that the
recovery curve cannot fit properly by a single
exponential equation. The use of a biexponential
equation can often overcome this problem. To
compare the halftimes of a molecule under
different experimental conditions (e.g. during
interphase and mitosis) it is essential to use
bleaching regions with the same size, relative
position in the cell and scanning parameters.
An idealized plot of a FRAP recovery curve. II initial intensityI0 intensity at timepoint t0 (first postbleach intensity)I1/2 half recovered intensity corresponding to t1/2        (I1/2 (IE - I0) / 2)IE endvalue of the recovered intensitythalf Halftime of recovery (t1/2 - t0)Mobile fraction Fm (IE - I0) / (II - I0)Immobile fraction Fi 1 - Fm
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Kinetic modelling FRAP experiments contain
information about the diffusional properties of
the studied molecule, but also about its binding
characteristics. Using kinetic modeling and
computer simulation, this information can be
extracted and hypotheses can be evaluated in
comparison with experimental data (Phair
2001). The lifetime of different molecular states
(e.g. freely diffusing or bound) can be simulated
by calculating their rates of formation and decay
(e.g. kon and koff). Two kinds of kinetic models
are used by cell biologists for this
purpose Compartmental model Biological
processes are described by a finite number of
compartments that contain a chemical species at a
cellular location. Each compartment is defined as
well mixed (the dynamics are not diffusion
limited). The crossover of molecules between
compartments represents exchange processes
between different places (e.g. cytoplasm and ER),
chemical states (e.g. phosphorylation) or
chemical interactions (e.g. binding to
receptormolecules). The transfer rates can be
determined by fitting to best match the
experimental data. Time is the only variable in a
compartmental model. Spatial modelThe cell is
divided into a number of spatial elements. In
each element the investigated molecule can
transfer between different molecular states.
Additionally these different molecular states can
exchange with neighboring elements by diffusion.
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Programs for kinetic modelling Programs for kinetic modelling Programs for kinetic modelling
Program Link Comment
SAAM II www.saam.com Easy compartmental model setup
Berkeley Madonna www.berkeleymadonna.com compartmental model
Mathlab www.mathworks.com Good graphic output possibilities
Gepasi www.gepasi.org Spatial modelFreeware
Virtual Cell www.nrcam.uchc.edu Easy way to write spatial modelsfreeware (academical use)
WinSAAM www.winsaam.com freeware