Fluorescence recovery after photobleaching
Fluorescence recovery after photobleaching (FRAP) is a method for determining the kinetics of diffusion through tissue or cells. It is capable of quantifying the two dimensional lateral diffusion of a molecularly thin film containing fluorescently labeled probes, or to examine single cells. This technique is very useful in biological studies of cell membrane diffusion and protein binding. In addition, surface deposition of a fluorescing phospholipid bilayer (or monolayer) allows the characterization of hydrophilic (or hydrophobic) surfaces in terms of surface structure and free energy. Similar, though less well known, techniques have been developed to investigate the  3-dimensional diffusion and binding of molecules inside the cell; they are also referred to as FRAP. Experimental setup. The basic apparatus comprises an optical microscope, a light source and some fluorescent probe. Fluorescent emission is contingent upon absorption of a specific optical wavelength or color which restricts the choice of lamps. Most commonly, a broad spectrum mercury or xenon source is used in conjunction with a color filter. The technique begins by saving a background image of the sample before photobleaching. Next, the light source is focused onto a small patch of the viewable area either by switching to  a higher magnification microscope objective or with laser light of the appropriate wavelength. The fluorophores in this region receive high intensity illumination which causes their fluorescence lifetime to quickly elapse (limited to roughly 10 photons before extinction). Now the image in the microscope is that of a uniformly fluorescent field with a noticeable dark spot. As Brownian motion proceeds, the still-fluorescing probes will diffuse throughout the sample and replace the non-fluorescent probes in the bleached region. This diffusion proceeds in an ordered fashion, analytically determinable from the diffusion equation. Assuming a Gaussian profile for the bleaching beam, the  diffusion constant "D" can be simply calculated from: where "w" is the radius of the beam and "t" is the "Characteristic" diffusion time. Applications. Supported lipid bilayers. Originally, the FRAP technique was intended for use as a means to characterize the mobility of individual lipid molecules within a cell membrane. While providing great utility in this role, current research leans more toward investigation of artificial lipid membranes. Supported by hydrophilic or hydrophobic substrates (to produce lipid bilayers or monolayers respectively) and incorporating membrane proteins, these biomimetic structures are potentially useful as analytical devices for determining the identity of unknown substances , understanding cellular transduction, and identifying ligand binding sites. Protein binding. This technique is commonly used in conjunction with green fluorescent protein (GFP) fusion proteins, where the studied protein is fused to a GFP. When excited by a specific wavelength of light, the protein will fluoresce. When the protein that is being studied is produced with the GFP, then the fluorescence can be tracked. Photodestroying the GFP, and then watching the repopulation into the bleached area can reveal information about protein interaction partners, organelle continuity and protein trafficking. If after some time the fluorescence doesn't reach the initial level anymore , then some part of the fluorescence is caused by an immobile fraction (that cannot be replenished by diffusion). Similarly, if the fluorescent proteins bind to static cell receptors, the rate of recovery will be retarded by a factor related to the association and disassociation coefficients of binding. This observation has most recently been exploited to investigate protein binding. Similarly, if the GFP labeled protein is constitutively incorporated into a larger complex, the dynamics of fluorescence recovery will be characterized by the diffusion of the larger complex. Applications outside the membrane. FRAP can also be used to monitor proteins outside  the membrane. After the protein of interest is made fluorescent, generally by expression as a GFP fusion protein, a confocal microscope is used to photobleach and monitor a region of the cytoplasm, mitotic spindle, nucleus, or another cellular structure. The mean fluorescence in the region can then be plotted versus time since the photobleaching, and the resulting curve can yield kinetic coefficients, such as those for the protein's binding reactions and/or the protein's diffusion coefficient in the medium where it is being monitored. Often the only dynamics considered are diffusion and binding/unbinding interactions, however, in principle proteins  can also move via flow, i.e., undergo directed motion, and this was recognized very early by Axelrod et al. This could be due to flow of the cytoplasm or nucleoplasm, or transport along filaments in the cell such as microtubules by molecular motors. The analysis is most simple when the fluorescence recovery is limited by either the rate of diffusion into the bleached area or by rate at which bleached proteins unbind from their binding sites within the bleached area, and are replaced by fluorescent protein. Let us look at these two limits, for the common case of bleaching a  GFP fusion protein in a living cell. Diffusion-limited fluorescence recovery. For a circular bleach spot of radius formula_2 and diffusion-dominated recovery, the fluorescence is described by an equation derived by Soumpasis (which involves modified Bessel functions formula_3 and formula_4) with formula_6 the characteristic timescale for diffusion, and formula_7 is the time. formula_8 is the normalized fluorescence (goes to 1 as formula_7 goes to infinity). The diffusion timescale for a bleached spot of radius formula_2 is formula_11, with "D" the diffusion coefficient. Note that this is for an instantaneous bleach with a step function profile, i.e., the fraction formula_12  of protein assumed to be bleached instantaneously at time formula_13 is formula_14, and formula_15, for formula_16 is the distance from the centre of the bleached area. It is also assumed that the recovery can be modelled by diffusion in two dimensions, that is also both uniform and isotropic. In other words, that diffusion is occurring in a uniform medium so the effective diffusion constant "D" is the same everywhere, and that the diffusion is isotropic, i.e., occurs at the same rate along all axes in the plane. In practice, in a cell none of these assumptions will be strictly true . Thus, the equation of Soumpasis is just a useful approximation, that can be used when the assumptions listed above are good approximations to the true situation, and when the recovery of fluorescence is indeed limited by the timescale of diffusion formula_6. Note that just because the Soumpasis can be fitted adequately to data does not necessarily imply that the assumptions are true and that diffusion dominates recovery. Reaction-limited recovery. The equation describing the fluorescence as a function of time is particularly simple in another limit. If a large number of proteins bind to sites in a small volume such  that there the fluorescence signal is dominated by the signal from bound proteins, and if this binding is all in a single state with an off rate k, then the fluorescence as a function of time is given by Note that the recovery depends on the rate constant for unbinding, "k", only. It does not depend on the on rate for binding. Although it does depend on a number of assumptions If all these assumptions are satisfied, then fitting an exponential to the recovery curve will give the off rate constant, "k". However, other dynamics can give recovery curves similar  to exponentials, so fitting an exponential does not necessarily imply that recovery is dominated by a simple bimolecular reaction. One way to distinguish between recovery with a rate determined by unbinding and recovery that is limited by diffusion, is to note that the recovery rate for unbinding-limited recovery is independent of the size of the bleached area "r", while it scales as formula_21, for diffusion-limited recovery. Thus if a small and a large area are bleached, if recovery is limited by unbinding then the recovery rates will be the same for the two sizes of bleached area, whereas  if recovery is limited by diffusion then it will be much slower for the larger bleached area. Diffusion and reaction. In general, the recovery of fluorescence will not be dominated by either simple isotropic diffusion, or by a single simple unbinding rate. There will be both diffusion and binding, and indeed the diffusion constant may not be uniform in space, and there may be more than one type of binding sites, and these sites may also have a non-uniform distribution in space. Flow processes may also be important. This more complex behavior implies that a model with several parameters  is required to describe the data; models with only either a single diffusion constant "D" or a single off rate constant, "k", are inadequate. There are models with both diffusion and reaction. Unfortunately, a single FRAP curve may provide insufficient evidence to reliably and uniquely fit (possibly noisy) experimental data. Sadegh Zadeh " et al." have shown that FRAP curves can be fitted by "different" pairs of values of the diffusion constant and the on-rate constant, or, in other words, that fits to the FRAP are not unique. This is in three-parameter (on-rate constant, off-rate constant and  diffusion constant) fits. Fits that are not unique, are not generally useful. Thus for models with a number of parameters, a single FRAP experiment may be insufficient to estimate all the model parameters. Then more data is required, e.g., by bleaching areas of different sizes, determining some model parameters independently, etc.