The lateral mobility of the (Na+,K+)-dependent ATPase in Madin-Darby canine kidney cells.

Fluorescence microphotolysis (recovery after photobleaching) was used to determine the lateral mobility of the (Na+,K+)ATPase and a fluorescent lipid analogue in the plasma membrane of Madin-Darby canine kidney (MDCK) cells at different stages of development. Fluorescein-conjugated Fab' fragments prepared from rabbit anti-dog (Na+,K+)ATPase antibodies (IgG) and 5-(N-hexadecanoyl)aminofluorescein (HEDAF) were used to label the plasma membrane of confluent and subconfluent cultures of MDCK cells. Fractional fluorescence recovery was 50% and 80-90% for the protein and lipid probes, respectively, and was independent of developmental stage. The estimated diffusion constants of the mobile fraction were approximately 5 X 10(-10) cm2/s for the (Na+,K+)ATPase and approximately 2 X 10(-9) cm2/s for HEDAF. Only HEDAF diffusion showed dependency on developmental stage in that D for confluent cells was approximately twice that for subconfluent cells. These results indicate that (Na+,K+)ATPase is 50% immobilized in all developmental stages, whereas lipids in confluent MDCK cells are more mobile than in subconfluent cells. They suggest, furthermore, that the degree of immobilization of the (Na+,K+)ATPase is insufficient to explain its polar distribution, and they support restricted mobility of the ATPase through the tight junctions as the likely mechanism for preventing the diffusion of this protein into the apical domain of the plasma membrane in confluent cell cultures.

Mobility of surface proteins on normal rat macrophages and on a "macrophagelike" rat tumor.

Peritoneal macrophages endocytosed their histocompatibility antigens (RT1), Fc receptors (FcR), and concanavalin A (Con A) receptors after cross-linking by ligands, but did not cap these membrane proteins. The 323N cell, a "macrophage like" tumor cell, under identical conditions capped its surface proteins. Experiments measuring fluorescence recovery after photobleaching showed that the mobile fraction of RT1 was significantly greater in 323N cells than in normal peritoneal macrophages. Presumably, the membrane proteins of 323N are not as tethered to the cytoskeleton, or, if so, are in a nexus that is not the same as that which occurs between membrane proteins of normal macrophages and the cytoskeleton. The mobility of RT1 on normal lymphocytes was also different from that of macrophages. These observations suggest that the movement of membrane molecules is determined by cell type and is regulated by the cytoskeleton which varies in structure and function from cell type to cell type.

Fluidity in the membranes of adult and neonatal human erythrocytes.

Several antigens and receptors are mobile in the plane of the membrane of the intact neonatal human erythrocyte but not in the membrane of the normal adult cell. In this report, measurements of the fluorescence polarization of perylene dissolved in isolated erythrocyte membranes are reported, which are indistinguishable for the two kinds of cells. This result indicates that the viscosities of the membrane interiors of the two cells are the same. The observed mobility differences, therefore, cannot be attributed to different lipid viscosities in the two membranes.

The relationship between plasma membrane lipid composition and physical-chemical properties. I. Fluorescence polarization studies of fatty acid-altered EL4 tumor cell membranes.

EL4 cels were cultured with exogenous fatty acids under conditions that resulted in their incorporation into membranes phospholipids. The behavior of the fluorescent lipid probes diphenylhexatriene and perylene was monitored in intact EL4 cells and in isolated EL4 plasma membranes. In whole cells substituted with unsaturated fatty acids, there was always a marked decrease in the P value of both probes compared to the P value of the probes in unsubstituted cells. In whole cells substituted with saturated fatty acids, on the other hand, P values for both probes were unchanged compared to unsubstituted cells. In plasma membrane isolated from EL4 cells, no difference in P values for either probe was observed among membranes from unsubstituted, saturated fatty acid substituted or unsaturated fatty acid substituted cells, even when the degree of fatty acid substitution was quite substantial. Most of the fluorescent signal for both probes in whole cells appeared to come from cytoplasmic lipid droplets. The value of techniques such as fluorescent polarization from monitoring physical properties of membranes (such as 'fluidity') is discussed.

Rotational dynamics of immunoglobulin G antibodies anchored in protein A soluble complexes.

The rotational dynamics of rabbit IgG anti-dansyl antibodies anchored in staphylococcal protein A (SpA) soluble complexes were studied by both steady-state and nanosecond fluorescence spectroscopy. To aid in the interpretation of the anisotropy data, the results of recently reported hydrodynamic and electron microscopic studies of IgG-SpA complexes were used to calculate global tumbling times of the various complexes and to estimate the steric hindrance of the antibody Fab segments. The anisotropy decays, fitted to the sum of two exponentials, indicated that the Fab arms of antibodies bound to SpA by their Fc regions exhibit considerable flexibility. For the different IgG-SpA mixtures examined, changes in the IgG preexponential anisotropy weighting factors, fS and fL, and the short rotational correlation time, phi S, were relatively small. On the other hand, the long rotational correlation time, phi L, increased systematically when the percentage of larger IgG-SpA complexes in a mixture was increased. The greatest restriction of Fab flexibility was observed for antibodies anchored in the exceptionally compact IgG4-SpA2 complexes. Available electron microscopic data suggest that increases in phi L correlate with increased steric hindrance of the antibody segments. Both native and hinge-disulfide-cleaved IgG experienced similar percentage increases in phi L when bound in SpA complexes. In agreement with our earlier interpretation, the results of this study provide rather striking evidence that phi L mainly represents flexible motions of the Fab segments and not global tumbling: the phi L-values of IgG bound in the various SpA complexes ranged from 101 to 162 nsec, whereas the calculated global tumbling times of the different complexes ranged from about 300 to 3000 nsec.

Mutants of ETS domain PU.1 and GGAA/T recognition: free energies and kinetics.

The ETS family members display specific DNA binding site preferences. As an example, PU.1 and ETS-1 recognize different DNA sequences with a core element centered over 5'-GGAA-3' and 5'-GGAA/T-3', respectively. To understand the molecular basis of this recognition, we carried out site-directed mutagenesis experiments followed by DNA binding studies that use electrophoretic mobility shift assay (EMSA) and surface plasmon resonance methods. EMSA experiments identified amino acid changes A231S and/or N236Y as being important for PU.1 recognition of both 5'-GGAA-3' and 5'-GGAT-3' containing oligonucleotides. To confirm these data and obtain accurate binding parameters, we performed kinetic studies using surface plasmon resonance on these mutants. The N236Y substitution revealed a weak protein-DNA interaction with the 5'-GGAA-3' containing oligonucleotide caused by a faster release of the protein from the DNA (k(off) tenfold higher than the wild-type protein). With the double mutant A231S-N236Y, we obtained an increase in binding affinity and stability toward both 5'-GGAA-3' and 5'-GGAT-3' containing oligonucleotides. We propose that substitution of alanine for serine introduces an oxygen atom that can accept hydrogen and interact with potential water molecules or other atoms to make an energetically favorable hydrogen bond with both 5'-GGAA-3' and 5'-GGAT-3' oligonucleotides. The free energy of dissociation for the double mutant A231S-N236Y with 5'-GGAA-3' (delta deltaG((A231S-N236Y) - (N236Y)) = -1.2 kcal mol confirm the stabilizing effect of this mutant in the protein-DNA complex formation. We conclude that N236Y mutation relaxes the specificity toward 5'-GGAA-3' and 5'-GGAT-3' sequences, while A231S mutation modulates the degree of specificity toward 5'-GGAA-3' and 5'GGAT-3' sequences. This study explains why wild-type PU.1 does not recognize 5'-GGAT-3' sequences and in addition broadens our understanding of 5'-GGAA/T-3' recognition by ETS protein family members.

Theory for establishing proximity relations in biological membranes by excitation energy transfer measurements.

In a previous publication (Shaklai et al., 1977a) the present author developed a theory for evaluating proximity relations and surface densities sigma in biological membranes by measurements of excitation energy transfer from a donor attached to a specific site of a membrane protein and an acceptor attached to a specific carbon on a membrane lipid. It was assumed that the protein and lipid are randomly distributed in the plane of the membrane and that the donor and acceptor groups are confined to different planes in the membrane separated by a distance Rp. In this article several aspects of the theory presented in the previous paper are clarified, especially noting that the previous theoretical expressions for the time-dependent and steady state fluorescence intensities assumed that the labeled protein molecule is cylindrically symmetric with the symmetry axis perpendicular to the plane of the membrane and that the donor is positioned on the symmetry axis of the protein. This assumption is also implicitly or explicitly made in subsequent formulations by other investigators. In this article we generalize the theory to include the case where the donor is not on the symmetry axis of the labeled protein. Equations for calculating the time-dependent and steady state fluorescence intensities for this more general case are presented, and methods for applying these theoretical expressions to the analysis of steady state fluorescence intensity data and evaluation of proximity parameters are discussed. It is also shown in this article that the linear relation l/lo = 1 + Kq sigma previously derived for simple analysis of excitation transfer data for the condition rc/Ro 1 can be modified to apply to almost all practical ranges of rc/Ro without much affecting its simplicity in the analysis of experimental data.

Quantitative fluorescence method for continuous measurement of DNA hybridization kinetics using a fluorescent intercalator.

We present a quantitative fluorescence method for continuous measurement of DNA or RNA hybridization (including renaturation) kinetics using a fluorescent DNA intercalator. The method has high sensitivity and can be used with reaction volumes as small as 1 microliter and amounts of DNA around 1 ng. The method is based on the observations that (i) for the usual hybridization conditions, intercalators such as ethidium bromide bind (intercalate) to double-stranded DNA (dsDNA) but not single-stranded DNA or RNA and (ii) there is a large increase in fluorescence intensity when intercalators such as ethidium bromide bind to dsDNA. In this application, the intercalator can be considered as a quantitative indicator of dsDNA concentration. When a small amount of intercalator is added to a hybridizing solution, the fluorescence intensity of the intercalators increases with increase in dsDNA. The hybridization reaction can thus be monitored by continuously recording fluorescence intensity vs time. Because the amount of intercalator bound to dsDNA is not necessarily proportional to dsDNA concentration, the time-dependent fluorescence intensity graph is not identical to the kinetic graph [dsDNA] vs t. However, the fluorescence intensity vs time graph can easily be converted to the true [dsDNA] vs t graph by means of an experimental calibration graph of fluorescence intensity vs [dsDNA]. This calibration graph is obtained in a separate experiment using samples containing known amounts of dsDNA in the ethidium bromide buffer used in the kinetic measurement. We present results of experimental tests of the intercalator technique using ethidium bromide as an intercalator and DNA from Escherichia coli and lambda-phage and Poly(I)-Poly(C) RNA hybrids. These DNA and RNA samples have Cot1/2 values that cover a range of 10(6). Our experimental results show that (i) the kinetics of hybridization are not significantly perturbed by the intercalator at concentrations where no more than 10% of the binding sites on DNA or RNA hybrids are occupied, (ii) the kinetic graphs obtained by the intercalator fluorescence method and corrected with the calibration graph agree with kinetic graphs obtained by optical absorbance measurements at 260 nm, and (iii) the intercalator technique can be used in the different salt environments often used to increase the velocity of the hybridization reaction and at the hybridization temperatures (35-75 degrees C) normally used to minimize nonspecific hybridization.

Fluorescence spectroscopy of an oriented model membrane.

We have devised a simple method that makes it feasible to apply fluorescence techniques to lipid bilayer membranes to elucidate aspects of their structure and dynamics. Fluorescence excitation, emission, and polarization spectra were obtained from a single spherical bilayer membrane consisting of oxidized cholesterol and fluorescent probe. The emission transition moments of N,N'-di(octadecyl)oxacarbocyanine and 12-(9-anthroyl)-stearic acid were found to be aligned parallel to the plane of the bilayer, whereas that of p-bis-[2-(4-methyl-5-phenyloxazolyl)]-benzene was aligned in a perpendicular direction. All three probes exhibited appreciable rotational mobility, parallel to the plane of the bilayer, in durations of nanoseconds. An attractive feature of this model membrane is that fluorescence measurements can be made at the same time as electrical measurements and perturbations. Also, it may be possible to incorporate functional protein assemblies into this model and to use fluorescence spectroscopy to delineate some aspects of their assembly and function.

Membrane dynamics of differentiating cultured embryonic chick skeletal muscle cells by fluorescence microscopy techniques.

Changes in membrane fluidity during myogenesis have been studied by fluorescence microscopy of individual cells growing in monolayer cultures of embryonic chick skeletal muscle cells. Membrane fluidity was determined by the techniques of fluorescence photobleaching recovery (FPR), with the use of a lipid-soluble carbocyanine dye, and by fluorescence depolarization (FD), with perylene used as the lipid probe. The fluidity of myoblast plasma membranes, as determined from FPR measurements in membrane areas above nuclei, increased during the period of myoblast fusion and then returned to its initial level. The membrane fluidity of fibroblasts, also found in these primary cultures, remained constant. The fluidity in specific regions along the length of the myoblast membrane was studied by FD, and it was observed that the extended arms of the myoblast have the highest fluidity on the cell and that the tips at the ends of the arms had the lowest fluidity. However, since the perylene probe used in the FD experiments appeared to label cytoplasmic components, changes in fluidity measured with this probe reflect changes in membrane fluidity as well as in cytoplasmic fluidity. The relative change in each of these compartments cannot yet be ascertained. Tips have specialized surface structures, filopodia and lamellipodia, which may be accompanied by a more immobile membrane as well as a more rigid cytoplasm. Rounded cells, which may also have a more convoluted surface structure, show a lower apparent membrane fluidity than extended cells.

Resonance light scattering particles as ultrasensitive labels for detection of analytes in a wide range of applications.

We have developed a new detection technology that uses resonance light scattering (RLS) particles as labels for analyte detection in a wide range of formats including immuno and DNA probe type of assays in solution, solid phase, cells, and tissues. When a suspension of nano sized gold or silver particles is illuminated with a fine beam of white light, the scattered light has a clear (not cloudy) color that depends on composition and particle size. This scattered light can be used as the signal for ultrasensitive analyte detection. The advantages of gold particles as detection labels are that (a) their light producing power is equivalent to more than 500,000 fluorescein molecules, (b) they can be detected at concentrations as low as 10(-15) M in suspension by eye and a simple illuminator, (c) they do not photobleach, (d) individual particles can be seen in a simple student microscope with dark field illumination, (e) color of scattered light can be changed by changing particle size or composition for multicolor multiplexing, and (f) they can be conjugated with antibodies, DNA probes, ligands, and protein receptors for specific analyte detection. These advantages allow for ultra-sensitive analyte detection with easiness of use and simple and relatively inexpensive instrumentation. We have shown that our RLS technology can indeed be used for ultra-sensitive detection in a wide range of applications including immuno and DNA probe assays in solution and solid phases, detection of cell surface components and in situ hybridization in cells and tissues. Most of the assay formats described in this article can be adapted for drug fast throughput screening.

Photoreversible conductance changes induced by phytochrome in model lipid membranes.

The plant protein phytochrome induces photoreversible conductance changes when added to a black lipid membrane made from oxidized cholesterol. The conductance of the phytochrome-modified membrane is increased by red-light illumination but is decreased by illumination with far-red light. Denatured phytochrome does not affect the conductance of the model membrane.

Solute accessibility to N epsilon-fluorescein isothiocyanate-lysine-23 cobra alpha-toxin bound to the acetylcholine receptor. A consideration of the effect of rotational diffusion and orientation constraints on fluorescence quenching.

To obtain information on the disposition of alpha-toxin when bound to the acetylcholine receptor (AChR), we evaluated the accessibility of solutes to fluorescein isothiocyanate (FITC) conjugated to alpha-toxin (siamensis 3) at lysine 23 (FITC-toxin) by measuring the rate constants for iodide quenching of the fluorescence of fluorescein free in solution and FITC-toxin free in solution and bound to AChR. Relative to the free fluorescein, we observed a 55% reduction in the quenching rate constant for the unbound FITC-toxin and 80% reduction for the AChR-bound FITC-toxin. It is tempting to interpret a decrease in the quenching rate constant as due to an increase in the masking of the labeling fluorophore, which in our case would then be indicative of masking of fluorescein conjugated to the free toxin and masking of FITC-toxin, in the region of lysine 23, when bound to AChR. However, elementary considerations indicate that the quenching rate depends not only on geometrical masking factors but also on the translational and rotational mobilities of the labeled molecules as well as orientational constraints. To evaluate these effects we have established quantitative relations between the rate of fluorescence quenching, the degree of masking of fluorophore, translational and rotational rates, and orientational constraints of the labeled macromolecules, using recent formulations for the rate of reaction between asymmetric molecules (Shoup et al., 1981, Biophys. J., 36:619-714). These relations predict that the decrease in quenching constant observed for the labeled FITC-toxin as well as the AChR-bound FITC-toxin is largely due to differences in translational and rotational rates and orientational constraints and not to significant increases in geometrical masking. Our theoretical formulation shows that the quenching rate can be decreased by a factor of 2-5 merely by immobilizing a fluorophore on the surface of a large protein without any significant increase in geometrical masking.

Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications.

Submicroscopic gold particle suspensions scatter colored light when illuminated with white light, and we have observed that a light-scattering gold particle suspension has the same appearance as a fluorescing solution. Thus, when illuminated by a narrow beam of white light, a 40-nm gold sol displays a clear (not cloudy), green scattered light (Tyndall) beam and has the same appearance as a fluorescing fluorescein solution. These, as well as other, observations have suggested to us that, in general, light-scattering particles can be treated as fluorescent analogs and used as fluorescent analog tracers in immuno- and DNA probe assays as well as in cell and molecular biology studies. Light-scattering particles are advantageous in these applications because particles such as gold and silver have very high light-scattering powers, which allows these particles to be easily detected, by light-scattering, at particle concentrations as low as 10(-16) M. The scattered light can be detected by the unaided eye for qualitative measurements or with a simple light-sensitive detector for quantitative measurements. Moreover, individual particles can be easily detected by eye or a video camera using a simple light microscope with a proper illuminating system. In addition, submicroscopic particles which scatter blue, green, yellow, orange, or red light can be readily synthesized. Antibodies, DNA probes, and other tracer substances can be readily attached to gold and other particles without altering their light-scattering properties. In this article we present the theory which allows one to predict the light-scattering properties of particles of different sizes and compositions and identify those particle sizes and compositions which appear most adequate for particular applications. Furthermore, we calculate molar extinction coefficients and emission efficiencies for particles of different sizes and compositions which allows us to compare the light-producing powers of these particles with those of well known fluorescent tracers. A 60-nm gold particle, for example, is equivalent to about 3 x 10(5) fluorescein molecules. Very simple, easy to use, low-cost, ultrasensitive immuno- and DNA probe assays can be developed using light-scattering particles as fluorescent analog tracers. Single particles can be detected on cell surfaces and inside cells using light microscopy techniques with proper illumination as described in the article. At high particle densities, particle-labeled cells have the same appearance as fluorescent cells.

Light-scattering submicroscopic particles as highly fluorescent analogs and their use as tracer labels in clinical and biological applications.

In a companion article we present the idea that submicroscopic light-scattering particles, such as gold and silver particles, can be used as fluorescent analog tracers in biological and clinical applications. The light-emitting power and scattered light color of the particles can be adjusted by changing particle composition or diameter. Using Rayleigh and Mie light-scattering theory, we calculated the absorbance and light-scattering properties and power of particles of different diameters and selected compositions and compared them to the properties of fluorophores. In the present article, we evaluate experimentally the optical properties of particles of selected compositions and sizes and compare the results with the theoretically calculated values. We also discuss the methods which we use to measure the light-scattering properties of particles in suspension and to view individual particles by light microscopy. We also outline examples which demonstrate the use of light-scattering particles as fluorescent analogs in biological and clinical applications.

Transient response of retinal rod outer segment phosphodiesterase to actinic light pulses. I. Simple quantitative kinetic model.

We present a quantitative kinetic model for the transient velocity (microM of cGMP hydrolyzed/s) response of retinal rod outer segment (ROS) cGMP phosphodiesterase (v(t) versus t) to a stimulating light pulse in the linear response range. The model gives an excellent fit to experimental v(t) versus t data for ROS suspensions at different concentrations of GTP and GDP and clarifies experimental results which are difficult to understand in the absence of such a model. It contains the minimum number of steps required to fit our experimental data and consists of one rate-limiting step with specific rate kL for the production of active phosphodiesterase (PDE), PDE*, by photoactivated rhodopsin, R*, and deactivation processes for R* and PDE* with lifetimes tau R and tau P, respectively. The experimental graphs of v(t) versus t at each concentration of GTP and GDP are characterized by a fast rise to a peak value, vpeak, followed by a slow decay to zero level. The minimal kinetic model allows us to characterized completely the effects of GTP and GDP, and any other pertinent species, in terms of their effects on the parameters kL, tau R, and tau P. Our kinetic model indicates that for "washed" ROS preparations (a) the risetime of v(t) is determined by tau P which has a value of about 2 s and is insensitive to [GTP]. (b) The decay of v(t) is determined by tau R which decreases with [GTP] and has a value greater than 300 s at low [GTP] and a limiting value of 50 s at high [GTP]. We attribute the greater than 300 s lifetime to the complex R*G (where G is ROS G protein) and the 50-s lifetime to free R*. (c) The rate kL increases hyperbolically with [GTP] with a half-maximal value of 56 microM and kL.max = 22-45 s-1. (d) Peak velocity is given by the expression vpeak alpha kL tau P which is consistent with the dependence of kL on [GTP] and the experimental finding that vpeak varies hyperbolically with [GTP]. The minimal model has also allowed us to (a) develop clear definitions of amplification for the light-triggered enzymatic cascade and (b) clarify experimental methods for measuring gain.(ABSTRACT TRUNCATED AT 400 WORDS)

Transient response of rod outer segment cGMP phosphodiesterase to actinic light pulses. II. Detailed quantitative kinetic model.

In the accompanying article (Schmidt, J.A., and Yguerabide, J. (1989) J. Biol. Chem. 264, 19790-19803), we presented a minimal quantitative kinetic model with one rate-limiting step for the transient response of rod outer segment (ROS) phosphodiesterase (PDE) to stimulating light pulses of low fractional bleach (linear response range) and showed that the model was in excellent quantitative agreement with experimental results. The model characterizes the PDE response in terms of the specific rate constant of the rate-limiting step, kL, the lifetime of photoactivated rhodopsin, tau R, and the lifetime of activated PDE, tau P, but makes no predictions on how these kinetic parameters should depend on the concentrations of the various reactive species involved in the PDE response to light and does not reveal the nature of the rate-limiting step. However, we established by curve fitting experimental data to theoretical expressions from the model that kL increases hyperbolically with [GTP], tau R decreases with [GTP], and tau P is independent of GTP. In this report we present three detailed kinetic models which make specific quantitative predictions on how the kinetic parameters of the minimal model should depend on nucleotide and G protein concentrations and test the models against experimental data. Each model consists of one rate-limiting step. The first detailed model postulates that the rate-limiting step is the dissociation of R*GT into R* and GT (T stands for GTP). The second model postulates that the rate-limiting step is the binding of GTP to R*G, and the third model postulates that the rate-limiting step is the encounter rate of R* and G on the ROS disc membrane. We find that only the first detailed model is consistent with the experimental results as characterized by the minimal model. Using this detailed model we (a) define kL and tau R in terms of more fundamental equilibrium and rate parameters, (b) develop a theory for the systematic evaluation of amplification or gain of the PDE light response from light-stimulated GTP-binding data as well as v(t) versus t graphs, and (c) clarify methods which have been used in the past to evaluate gain experimentally.

Lateral mobility in membranes as detected by fluorescence recovery after photobleaching.

The evaluation of lateral diffusion coefficients of membrane components by the technique of fluorescence recovery after photobleaching (FRAP) is often complicated by uncertainties in the values of the intensities F(O), immediately after bleaching, and F(infinity), after full recovery. These uncertainties arise from instrumental settling time immediately after bleaching and from cell, tissue, microscope, or laser beam movements at the long times required to measure F(infinity). We have developed a method for precise analysis of FRAP data that minimizes these problems. The method is based on the observation that a plot of the reciprocal function R(tau) = F(infinity)/[F(infinity)-F(tau)] is linear over a large time range when (a) the laser beam has a Gaussian profile, (b) recovery involves a single diffusion coefficient, and (c) there is no membrane flow. Moreover, the ratio of intercept to slope of the linear plot is equal to tau 1/2, the time required for the bleached fluorescence to rise to 50% of the full recovery value, F(infinity). The lateral diffusion coefficient D is related to tau 1/2 by tau 1/2 = beta w2/4D where beta is a defined parameter and w is the effective radius of the focused laser beam. These results are shown to indicate that the recovery of fluorescence F(tau) can be represented over a large range of percent bleach, and recovery time tau by the relatively simple expression F(tau) = [ F(o) + F(infinity) (tau/tau 1/2)]/[1 + tau/tau 1/2)]. FRAP data can therefore be easily evaluated by a nonlinear regression analysis with this equation or by a linear fit to the reciprocal function R(tau). It is shown that any error in F(infinity) can be easily detected in a plot of R(tau) vs. tau which deviates significantly from a straight line when F(infinity) is in error by as little as 5%. A scheme for evaluating D by linear analysis is presented. It is also shown that the linear reciprocal plot provides a simple method for detecting flow or multiple diffusion coefficients and for establishing conditions (data precision, differences in multiple diffusion coefficients, magnitude of flow rate compared to lateral diffusion) under which flow or multiple diffusion coefficients can be detected. These aspects are discussed in some detail.