Fluorescence photobleaching recovery using total internal reflection interference fringes

Lateral diffusion measurements on cell membrane molecules, most commonly accomplished through fluorescence photobleaching recovery (FPR or FRAP), provide information on such molecules' size, environment, and participation in intermolecular interactions. However, difficulties arise in FPR measurements of lateral dynamics of materials, such as visible fluorescent protein (VFP) fusion proteins, where fluorescent intracellular species contribute to the fluorescence recovery signal and thus distort measurements intended to reflect surface molecules only. A new method helps eliminate these difficulties. In total internal reflection interference fringe FPR, interfering laser beams enter a 1.65-numercial aperture (NA) Olympus objective at the periphery of the back focal plane where the NA exceeds 1.38. This creates an extended interference pattern totally internally reflected at the coverslip-medium interface which excites fluorescence only from fluorescent molecules located where the cell contacts the coverslip. The large illuminated area interrogates many more membrane receptors than spot methods and hence obtains more diffusion information per measurement while rejecting virtually all interfering intracellular fluorescence. We report successful measurements of membrane dynamics of both VFP-containing and conventionally labeled molecules by this technique and compare them with results of other FPR methods.     

Lateral diffusion of rhodopsin in photoreceptor cells measured by fluorescence photobleaching and recovery.

Frog rod outer segments were labeled with the sulfhydryl-reactive label iodoacetamido tetramethylrhodamine. The bulk of the label reacted with the major disk membrane protein, rhodopsin. Fluorescence photobleaching and recovery (FPR) experiments on labeled rods showed that the labeled proteins diffused rapidly in the disk membranes. In these FPR experiments we observed both the recovery of fluorescence in the bleached spot and the loss of fluorescence from nearby, unbleached regions of the photoreceptor. These and previous experiments show that the redistribution of the fluorescent labeled proteins after bleaching was due to diffusion. The diffusion constant, D, was (3.0 +/- 10(-9) cm2 s-1 if estimated from the rate of recovery of fluorescence in the bleached spot, and (5.3 +/- 2.4) x 10(-9) cm2 s-1 if estimated from the rate of depletion of fluorescence from nearby regions. The temperature coefficient, Q10, for diffusion was 1.7 +/- 0.5 over the range 10 degrees--29 degrees C. These values obtained by FPR are in good agreement with those previously obtained by photobleaching rhodopsin in fresh, unlabeled rods. This agreement indicates that the labeling and bleaching procedures required by the FPR method did not significantly alter the diffusion rate of rhodopsin. Moreover, the magnitude of the diffusion constant for rhodopsin is that to be expected for an object of its diameter diffusing in a bilayer with the viscosity of the disk membrane. In contrast to the case of rhodopsin, FPR methods applied to other membrane proteins have yielded much smaller diffusion constants. The present results help indicate that these smaller diffusion constants are not artifacts of the method but may instead be due to interactions the diffusing proteins have with other components of the membrane in addition to the viscous drag imposed by the lipid bilayer.     

Total internal reflection/fluorescence photobleaching recovery study of serum albumin adsorption dynamics.

The total internal reflection/fluorescence photobleaching recovery (TIR/FPR) technique (Thompson et al. 1981. Biophys. J. 33:435) is used to study adsorbed bovine serum albumin dynamics at a quartz glass/aqueous buffer interface. Adsorbed fluorescent labeled protein is bleached by a brief flash of the evanescent wave of a focused totally internally reflected laser beam. The rates of adsorption/desorption and surface diffusion determine the subsequent fluorescence recovery. The protein surface concentration is low enough to be proportional to the observed fluorescence and high enough to insure that the observed recovery rates arise mainly from adsorbed rather than bulk protein dynamics. The photobleaching recovery curves for rhodamine-labeled bovine serum albumin reveal both an irreversibly bound state and a multiplicity of reversibly bound states. The relative amount of reversible to irreversible adsorption increases with increasing bulk protein concentration. Since the adsorbed protein concentration appears to be too high to pack into a homogeneous surface monolayer, the wide range of desorption rates possibly results from multiple layers of protein on the surface. Comparison of the fluorescence recovery curves obtained with various focused laser beam widths suggests that some of the reversibly bound bovine serum albumin molecules can surface diffuse. Aside from their relevance to the surface chemistry of blood, these results demonstrate the feasibility of the TIR/FPR technique for measuring molecular dynamics on solid surfaces.     

Diffusion of molecules on biological membranes of nonplanar form. A theoretical study.

Lateral mobility of molecules on cell membranes has been recently studied by fluorescence photobleaching recovery (FPR) techniques. The interpretation of these results in terms of diffusion along the membranes is based on the assumption that the surface is planar, although biological membranes may have blebs and microvilli. To study the effect of nonplanarity on the diffusion rate, the diffusion equation along curved surfaces was derived and was solved numerically for a "wavy" surface of the form A cos kx cos ky. Calculations show that for k = 10 pi micrometer-1 and a bleached spot of 1 micrometer in diameter, the time dependence of the intensity of fluorescence in the bleached spot depends on A at A less than 0.5 micrometer, while at higher values of A (a and 2 micrometer) the dependence is weak. If one calculates diffusion coefficients from FPR measurements and assumes that the membrane is planar, the resulting diffusion coefficient is not less than about half of the real one. Because of the tortuous shape of the spot boundary, increasing the microvilli length from 0.5 micrometer to 1 or 2 micrometer does not change the diffusion rates. These considerations are valid for times when the diffusion is dominated by molecules that were initially located close to the spot boundary.     

Lateral diffusivity of lipid analogue excimeric probes in dimyristoylphosphatidylcholine bilayers.

The lateral mobility of pyrenyl phospholipid probes in dimyristoylphosphatidylcholine (DMPC) vesicles was determined from the dependence of the pyrene monomeric and excimeric fluorescence yields on the molar probe ratio. The analysis of the experimental data makes use of the milling crowd model for two-dimensional diffusivity and the computer simulated random walks of probes in an array of lipids. The fluorescence yields for 1-palmitoyl-2-(1'-pyrenedecanoyl)phosphatidylcholine (py10PC) in DMPC bilayers are well fitted by the model both below and above the fluid-gel phase transition temperature (Tc) and permit the evaluation of the probe diffusion rate (f), which is the frequency with which probes take random steps of length L, the host membrane lipid-lipid spacing. The lateral diffusion coefficient is then obtained from the relationship D = fL2/4. In passing through the fluid-gel phase transition of DMPC (Tc = 24 degrees C), the lateral mobility of py10PC determined in this way decrease only moderately, while D measured by fluorescence photobleaching recovery (FPR) experiments is lowered by two or more orders of magnitude in gel phase. This difference in gel phase diffusivities is discussed and considered to be related either to (a) the diffusion length in FPR experiments being about a micrometer or over 100 times greater than that of excimeric probes (approximately 1 nm), or (b) to nonrandomicity in the distribution of the pyrenyl probes in gel phase DMPC. At 35 degrees C, in fluid DMPC vesicles, the diffusion rate is f = 1.8 x 10(8) s-1, corresponding to D = 29 microns2 s-1, which is about three times larger than the value obtained in FPR experiments. The activation energy for lateral diffusion in fluid DMPC was determined to be 8.0 kcal/mol.     

Disparate modulation of plasma membrane protein lateral mobility by various cell permeabilizing agents

The mobility of a cell surface protein on cells osmotically swollen by treatment with several different cell permeabilizing agents retains specific restraints despite detachment of the plasma membrane from the cortical cytoskeleton. Fluorescence photobleaching recovery experiments indicate that the lateral diffusion constants of immunoglobulin E (IgE)-receptor complexes on the surface of rat basophilic leukemia cells increase 2–5 × following permeabilization with streptolysin O or digitonin, with little change in their mobile fractions. Swelling by hypo-osmotic treatment in water enhances lateral diffusion of IgE-receptor complexes and raises the mobile fractions to near 100%. In contrast, swelling by treatment with filipin arrests lateral diffusion, although rotational mobility remains unhindered. Lateral mobility of a fluorescent lipid analogue remains unchanged under these conditions. Crosslinking by anti-IgE antibodies redistributes the IgE-receptor complexes into large patches on untreated cells and on cells swollen by permeabilization with streptolysin O or digitonin, but rot on cells swollen by treatment with filipin. The results indicate a diversity of effects of the various permeabilizing agents on the mobility of membrane proteins. In particular, treatment with filipin appears to reorganize the plasma membrane into a network of fluid domains on a scale smaller than the bleaching spot size used (～1.5 μm). © 1994 Wiley-Liss, Inc.     

Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy.

The theoretical basis of a new technique for measuring equilibrium adsorption/desorption kinetics and surface diffusion of fluorescent-labeled solute molecules at solid surfaces has been developed. The technique combines total internal reflection fluorescence (TIR) with either fluorescence photobleaching recovery (FPR) or fluorescence correlation spectroscopy (FCS). A laser beam totally internally reflects at a solid/liquid interface; the shallow evanescent field in the liquid excites the fluorescence of surface adsorbed molecules. In TIR/FPR, adsorbed molecules are bleaching by a flash of the focused laser beam; subsequent fluorescence recovery is monitored as bleached molecules exchange with unbleached ones from the solution or surrounding nonilluminated regions of the surface. In TIR/FCS, spontaneous fluorescence fluctuations due to individual molecules entering and leaving a well-defined portion of the evanescent field are autocorrelated. Under appropriate experimental conditions, the rate constants and surface diffusion coefficient can be readily obtained from the TIR/FPR and TIR/FCS curves. In general, the shape of the theoretical TIR/FPR and TIR/FCS curves depends in a complex manner upon the bulk and surface diffusion coefficients, the size of the iluminated or observed region, and the adsorption/desorption/kinetic rate constants. The theory can be applied both to specific binding between immobilized receptors and soluble ligands, and to nonspecific adsorption processes. A discussion of experimental considerations and the application of this technique to the adsorption of serum proteins on quartz may be found in the accompanying paper (Burghardt and Axelrod. 1981. Biophys. J. 33:455).     

Fringe pattern photobleaching, a new method for the measurement of transport coefficients of biological macromolecules.

The conventional method of studying mass transport in membranes by spot photobleaching and then following the recovery of fluorescence has disadvantages. Among them, the need for a high density of fluorescent molecules, the measurement of the beam profile, and a knowledge of the photobleaching processes are of a crucial importance. The application of a planar fringe pattern of light both for the bleaching and the monitoring of the fluorescent molecules solves these three major difficulties. Brownian diffusion coefficients and flow velocities can be measured independently and are averaged over the whole fringe pattern volume. These transport coefficients are explored over the wide range of experimentally accessible distances (from an interfringe spacing 0.5-50 micron). The quantification of the mobile and immobile components is further simplified by scanning the fringe pattern and detecting only a modulated fluorescence recovery signal. The fringe pattern photobleaching method is particularly adapted to the measurements of diffusion coefficients and flow velocity of membrane components, as well as of cytoplasmic proteins. The theoretical results and the test experiments with fluorescent bovine serum albumin are described.     

Micrometer-scale domains in fibroblast plasma membranes

We have used the technique of fluorescence photobleaching recovery to measure the lateral diffusion coefficients and the mobile fractions of a fluorescent lipid probe, 1-acyl-2-(12-[(7-nitro-2-1, 3-benzoxadiazol-4-yl)aminododecanoyl]) phosphatidylcholine (NBD-PC), and of labeled membrane proteins of human fibroblasts. Values for mobile fractions decrease monotonically with increasing size of the laser spot used for the measurements, over a range of 0.35-5.0 microns. Values for NBD-PC diffusion coefficients increase in part of this range to reach a plateau at larger laser spots. This variation is not an artifact of the measuring system, since the effects are not seen if diffusion of the probe is measured in liposomes. We also find that the distribution of diffusion coefficients measured with small laser spots is heterogeneous indicating that these small spots can sample different regions of the membrane. These regions appear to differ in protein concentration. Our data strongly indicate that fibroblast surface membranes consist of protein-rich domains approximately 1 micron in diameter, embedded in a relatively protein-poor lipid continuum. These features appear in photographs of labeled cell surfaces illuminated by the expanded laser beam.     

Fluorescence recovery after photobleaching of suspensions of vacuoles

In this work we derive theoretical expressions for the FRAP measured on a liquid suspension of vacuoles labelled by a fluorescent probe bound to the surface membrane of these vacuoles. The bleaching laser beam creates an inhomogeneity in the surface concentration of the probe molecules. We consider the case in which the randomization of these probe molecules on the vacuole surface occurs much faster than the fluorescent recovery due to the vacuole diffusion. For a given value of the bleaching parameter K, we found that the bleaching fraction of the fluorescent molecules and the fluorescence recovery rate are decreasing functions of the square ratio of the vacuole to the laser beam radius of the FRAP instrument.     

Membrane receptor mobility changes by sendai virus

Treatment with Sendai virus does affect the lateral mobility of cell surface components on cultured human cells (KB) and cultured mouse cells (3T3). Diffusion coefficients and mobile fractions of a fluorescent lipid analog, tetramethyl rhodamine-succinyl concanavalin A (ConA) and tetramethyl rhodamine-anti human β₂ microglobulin antibodies on the cell surface were measured by fluorescence photobleaching recovery (FPR). Diffusion coefficients of receptors for ConA and for antibodies to β₂ microglobulin (presumably histocompatibility antigens) were increased 2- to 3-fold by exposure to the ultraviolet inactivated virus at virus doses from 250 to 2 500 HAU/ml, regardless of whether the particular cells measured had been fused. No mobility enhancement was induced with trypsinized Sendai virus, nor by influenza virus, indicating a probable requirement for the Sendai virus F protein. Virus treatment reduced the diffusion coefficient of a lipid analog in 3T3 cells. The results are compatible with the hypothesis that the Sendai virus disrupts a mobility restraint system, perhaps cytoskeleton-membrane connections.     

Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

cAMP regulated membrane diffusion of a green fluorescent protein-aquaporin 2 chimera

To study the membrane mobility of aquaporin water channels, clones of stably transfected LLC-PK1 cells were isolated with plasma membrane expression of GFP-AQP1 and GFP-AQP2, in which the green fluorescent protein (GFP) was fused upstream and in-frame to each aquaporin (AQP). The GFP fusion did not affect AQP tetrameric association or water transport function. GFP-AQP lateral mobility was measured by irreversibly bleaching a spot (diameter 0.8 microm) on the membrane with an Argon laser beam (488 nm) and following the fluorescence recovery into the bleached area resulting from GFP translational diffusion. In cells expressing GFP-AQP1, fluorescence recovered to >96% of its initial level with t(1/2) of 38 +/- 2 s (23 degrees C) and 21 +/- 1 s (37 degrees C), giving diffusion coefficients (D) of 5.3 and 9.3 x 10(-11) cm(2)/s. GFP-AQP1 diffusion was abolished by paraformaldehyde fixation, slowed >50-fold by the cholesterol-binding agent filipin, but not affected by cAMP agonists. In cells expressing GFP-AQP2, fluorescence recovered to >98% with D of 5.7 and 9.0 x 10(-11) cm(2)/s at 23 degrees C and 37 degrees C. In contrast to results for GFP-AQP1, the cAMP agonist forskolin slowed GFP-AQP2 mobility by up to tenfold. The cAMP slowing was blocked by actin filament disruption with cytochalasin D, by K(+)-depletion in combination with hypotonic shock, and by mutation of the protein kinase A phosphorylation consensus site (S256A) at the AQP2 C-terminus. These results indicate unregulated diffusion of AQP1 in membranes, but regulated AQP2 diffusion that was dependent on phosphorylation at serine 256, and an intact actin cytoskeleton and clathrin coated pit. The cAMP-induced immobilization of phosphorylated AQP2 provides evidence for AQP2-protein interactions that may be important for retention of AQP2 in specialized membrane domains for efficient membrane recycling.     

Reduced lateral mobility of a fluorescent lipid probe in cholesterol-depleted erythrocyte membrane

The effect of cholesterol depletion of the human erythrocyte membrane on the lateral diffusion rate of a fluorescent lipid probe is reported. At low temperatures (?5 to 5°C), the diffusion of the probe is 50% slower in the cholesterol-depleted membrane than in non-depleted membrane. At high temperatures (30 to 40° C), probe mobility is not affected by cholesterol depletion. These results suggest that cholesterol suppresses aspects of phospholipid phase changes in animal cells in a manner consistent with its behavior in artificial bilayers and multilayers.Whole erythrocytes were depleted of 30–50% of their cholesterol by incubation with a sonicated dispersion of dipalmitoyl phosphatidylcholine. Cells were then labeled with 3,3′-dioctadecylindocarbocyanine (diI), a phospholipid-like fluorescent dye, and hemolyzed into spherical ghosts. The rate of lateral motion of diI was measured by observing the fluorescence recovery after local photobleaching with a focused laser spot.The diffusion rate of the lipid probe in both control and cholesterol-depleted erythrocyte membrane is substantially smaller than in any cell or model membrane previously measured.     

Lateral regionalization and diffusion of a maturation-dependent antigen in the ram sperm plasma membrane

We have used a monoclonal antibody ESA 152 in fluorescence recovery after photobleaching (FPR) studies of a maturation-dependent surface antigen of ram sperm. The antibody is an immunoglobulin G secreted by a hybridoma derived from NS1 mouse myeloma cells. The ESA 152 antigen is not detectable in testicular sperm. It is localized on the surface of ejaculated sperm where it is present on all regions of the surface, but tends to be concentrated on the posterior region of the head. The ESA 152 antigen can be extracted by detergents or chloroform-methanol. The extracted antigen is sensitive to proteases and migrates with an apparent Mr approximately 30,000 in SDS-containing 10-20% polyacrylamide gradient gels. FPR measurements of ESA 152 lateral mobility in the membrane yield diffusion coefficients in the range 10(-9)-10(-8) cm2/s, values typical of lipids but observed for proteins only at the fluid dynamic limit where diffusion is controlled by lipid fluidity. Immobile fractions, typical of membrane proteins, are observed on all regions. When the antigen is stained by a fluoresceinated Fab fragment of the ESA 152 antibody, the diffusibility is highly regionalized, with particularly low, but rapid, recovery on the midpiece. Cross-linking of the antigen with the intact ESA 152 antibody induces a redistribution in which the antigen is excluded from the posterior head region. This cross-linking is accompanied by increases in ESA 152 diffusibility on both the anterior head and the midpiece.     

Dynamics of fluorescence marker concentration as a probe of mobility.

We have developed an effective experimental system for the characterization of molecular and structural mobility. It incorporates a modified fluorescence microscope geometry and a variety of analytical techniques to measure effective diffusion coefficients ranging over almost six orders of magnitude, from less than 10(-11) cm2/s to greater than 10(-6) cm2/s. Two principal techniques, fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR), are employed. In the FPR technique, translational transport rates are measured by monitoring the evolution of a spatial inhomogeneity of fluorescence that is produced photochemically in a microscopic volume by a short burst of intense laser radiation. In contrast, FCS uses laser-induced fluorescence to probe the spontaneous concentration fluctuations in microscopic sample volumes. The kinetics are analyzed by computing time-correlation functions of the stochastic fluctuations of the measured fluorescence intensity. The optical system and digital photocount correlator designed around a dedicated minicomputer are described and discussed. The general power of these techniques is demonstrated with examples from studies conducted on bulk solutions, lipid bilayer membranes, and mammalian cell plasma membranes.     

Measurement of molecular diffusion in solution by multiphoton fluorescence photobleaching recovery

Multiphoton fluorescence photobleaching recovery (MP-FPR) is a technique for measuring the three-dimensional (3D) mobility of fluorescent molecules with 3D spatial resolution of a few microns. A brief, intense flash of mode-locked laser light pulses excites fluorescent molecules via multiphoton excitation in an ellipsoidal focal volume and photobleaches a fraction. Because multiphoton excitation of fluorophores is intrinsically confined to the high-intensity focal volume of the illuminating beam, the bleached region is restricted to a known, three-dimensionally defined volume. Fluorescence in this focal volume is measured with multiphoton excitation, using the attenuated laser beam to measure fluorescence recovery as fresh unbleached dye diffuses in. The time course of the fluorescence recovery signal after photobleaching can be analyzed to determine the diffusion coefficient of the fluorescent species. The mathematical formulas used to fit MP-FPR recovery curves and the techniques needed to properly utilize them to acquire the diffusion coefficients of fluorescently labeled molecules within cells are presented here. MP-FPR is demonstrated on calcein in RBL-2H3 cells, using an anomalous subdiffusion model, as well as in aqueous solutions of wild-type green fluorescent protein, yielding a diffusion coefficient of 8.7 x 10(-7) cm(2)s(-1) in excellent agreement with the results of other techniques.     

Reduced lateral mobility of a fluorescent lipid analog in cell membranes of rat fibroblasts transformed by simian virus 40

In order to study the difference between normal and transformed cells, lateral motion of fluorescent molecules embedded into cell membranes of rat clonal fibroblasts and its SV40-transformed derivative cells was measured by the FPR technique. The lateral diffusion coefficient of a fluorescent fatty acid analog, F18, was smaller in transformed cells than normal cells. This indicates that the lipid phase of membranes from transformed cells is less fluid than that from normal cells. On the other hand, the lateral diffusion coefficient of S-F-concanavalin A was identical in both cells. These results suggest that the mobility of different molecules on the membranes is controlled by different mechanisms.     

Analysis of simulated and experimental fluorescence recovery after photobleaching. Data for two diffusing components.

Fluorescence recovery after photobleaching has been a popular technique to quantify the lateral mobility of membrane components. A variety of analysis methods have been used to determine the lateral diffusional mobility, D. However, many of these methods suffer from the drawbacks that they are not able to discern two-component diffusion (i.e., three-point fit), cannot solve for two components (linearization procedures), and do not perform well at low signal-to-noise. To overcome these limitations, we have adopted the approach of fitting fluorescence recovery after photobleaching curves by the full series solution using a Marquardt algorithm. Using simulated data of one or two diffusing components, determinations of the accuracy and reliability of the method with regard to extraction of diffusion parameters and the differentiation of one- versus two-component recovery curves were made under a variety of conditions comparable with those found in actual experimental situations. The performance of the method was also examined in experiments on artificial liposomes and fibroblast membranes labeled with fluorescent lipid and/or protein components. Our results indicate that: 1) the method was capable of extracting one- and two-component D values over a large range of conditions; 2) the D of a one-component recovery can be measured to within 10% with a small signal (100 prebleach photon counts per channel); 3) a two-component recovery requires more than 100-fold greater signal level than a one-component recovery for the same error; and 4) for two-component fits, multiple recovery curves may be needed to provide adequate signal to achieve the desired level of confidence in the fitted parameters and in the differentiation of one- and two-component diffusion.