INTRODUCTION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS DISCUSSION APPENDIX REFERENCES

The fluorescence anisotropy (r) of intrinsic or extrinsic fluorophores provides valuable information about the state and environment of the corresponding biomolecular carrier on or within a cell. The steady-state anisotropy, , of a distinct molecular species undergoing isotropic rotational diffusion is related to the excited state lifetime  and the rotational correlation time  according to the Jablonski equation (Jablonski, 1960),

(1)

where r_o is a limiting value (in the absence of rotation) given by the relative orientation of the absorption and emission transition moments, and  is the ratio /. From Eq. 1, it follows that the anisotropy is a parameter with the capability of revealing changes in orientational distribution and in the excited state lifetime with great sensitivity. Such a circumstance arises readily in cell biology, e.g., from alterations in local microviscosity or other restrictions to diffusional motion, biochemical environment, complex formation, and molecular proximity manifested by hetero- or homo-transfer of electronic energy. Furthermore, the fluorescence anisotropy and lifetime are both intrinsic parameters, unlike the intensity signals used to determine them, and are thereby relatively insensitive to experimental factors such as light path and geometry. This fortunate circumstance permits more reliable comparisons between data obtained from different experiments and from different laboratories.

The measurement of fluorescence anisotropy in a microscope offers the possibility for characterizing very small domains on the surface or in the interior of the cell. For example, the cytoplasmic viscosity of living cells was determined by anisotropy imaging of fluid-phase fluorophores (Dix and Verkman, 1990). In addition, highly oriented samples, such as labeled protein constituents of the plasma membrane, can be readily visualized by anisotropy microscopy, as documented in the pioneering study by Axelrod (1979) of the orientational distribution of dyes bound to erythrocyte ghost membranes.

Measurements of dynamic depolarization or anisotropy decay provide additional and complementary information, such as rotational correlation times sensitive to the rotational volume and shape of the fluorophore. Anisotropy decay can reveal the multiplicity of rotational correlation times reflecting heterogeneity in the molecular population and in the size, shape, and internal motions of the fluorophore-biomolecule conjugate. Real molecules often exhibit molecular asymmetry, anisotropic rotational modes, and multiple lifetimes, and, in the cellular milieu, molecular heterogeneity is the rule rather than the exception. An adequate mathematical formulation of such systems is necessarily complex, as is already evident from Eq. 1 due to the dependence of on three other parameters. The need to image the dynamic depolarization of fluorophores in cellular environments directly prompted the present investigation.

Determinations of rotational correlation times are performed either in the time or frequency domain. For example, using an excitation pulse as a forcing function, Eq. 1 is transformed into a decay process in which the fluorescence lifetime  is no longer linked to the correlation time  

(2)

where i(t) is the instantaneous emission intensity, normalized to a unit integrated value. In Eq. 2, the parameter r reflects the extent to which the rotational reorientation is hindered. An example is the case of a transmembrane protein undergoing molecular rotation in a lipid bilayer (Lipari and Szabo, 1980; Kinosita et al., 1982; Thevenin et al., 1994; Martin-Fernandez et al., 1998). For this case, is obtained by integrating the intensity-weighted r(t) (Eq. 3); the same approach applies to heterogeneous systems and more complex (multiexponential, nonexponential) time courses for the decay of the excited state or rotational diffusion,

(3)

By itself, the fluorescence lifetime is of great value for the generation of contrast in fluorescence microscopy. Fluorescence lifetime imaging microscopy (FLIM) provides pixel-by-pixel discrimination among fluorophores differing in excited state kinetics due to distinct photophysical characteristics or microenvironments. FLIM has been implemented with time-domain (Wang et al., 1991; Ghiggino et al., 1992; Scully et al., 1997; Cole et al., 2000) and frequency-domain (Marriot et al., 1991; Lakowicz et al., 1992; Piston et al., 1992; Gadella et al., 1993; Squire et al., 2000; Verveer et al., 2000; Hanley et al., 2001) techniques.

We have undertaken the extension of the FLIM technology to include the generation of images based on the dynamic depolarization of fluorescence, and denote the approach featured in this report as anisotropy FLIM (rFLIM). rFLIM complements standard steady-state polarization microscopy (Axelrod, 1979) and corresponding static and dynamic polarization measurements performed in solution or suspension. It adds the imaging capability to previous systems that were limited to single-point anisotropy decay measurements in the microscope (Verkman et al., 1990; Martin-Fernandez et al., 1998; Tramier et al., 2000).

The implementation of rFLIM with two-dimensional (2D) image detection using a sensitive charge-coupled device (CCD) camera provides wide-field imaging of dynamic depolarization, e.g., with the intent of simultaneously interrogating different compartments of a cell. To this end, we modified a frequency-domain FLIM apparatus (Gadella et al., 1993; Schneider and Clegg, 1997; Hanley et al., 2001) by the introduction of linear polarizers in the excitation and emission paths (Fig. 1). In this report, we first describe our experimental implementation of rFLIM and then the theory of frequency-domain rotational dynamics extended to rFLIM. The latter is illustrated with dynamic depolarization measurements of fluorescein in glycerol/water mixtures and of enhanced green fluorescent protein (EGFP) in bacteria. Finally, we discuss other applications, limitations, and future perspectives of rFLIM.

View larger version (28K): [in this window] [in a new window]   FIGURE 1   Schematic of rFLIM apparatus. The microchannel plate intensifier was modulated at the photocathode. The signal generators driving the image intensifier and the acousto-optical modulator (AOM) were phase locked to a 10-MHz frequency standard. The relative phase ( phase) between the two was adjusted under computer control, cycling through a series of n phase steps of 360°/n. An image was recorded at each phase step. The zero-order light exiting the AOM was isolated from the higher orders by an iris and relayed to the microscope illumination system through a multimode optical fiber. The optical modulation frequency was double the AOM driving frequency.

	EXPERIMENTAL

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS DISCUSSION APPENDIX REFERENCES

rFLIM apparatus

A schematic of the rFLIM instrument is shown in Fig. 1. The frequency domain fluorescence lifetime and rotational dynamics imaging instrument was built as an add-on to a standard research grade fluorescence microscope (E-600, Nikon, Düsseldorf, Germany). The FLIM system used as the basis for the measurement of rotational dynamics was similar to previously described instruments (Gadella et al., 1993; Schneider and Clegg, 1997; Hanley et al., 2001). A modulated image intensifier (model C5825, Hamamatsu Photonics, Herrsching, Germany) was installed on the camera port of the microscope. The modulation frequency and phase were set with a computer-controlled signal generator (model 2030; Marconi Instruments, St. Albans, UK). The intensified image was relayed to a 14-bit cooled CCD camera (model KX-2 containing a Kodak KAF-1600 CCD with 9-µm square pixels in a 1536 × 1024 format; Apogee Instruments, Tucson, AZ) using a tandem pair of f/1.8 (AF Nikkor, Nikon) camera lenses. The 488-nm line of an Ar⁺ ion laser (Innova 90-5; Coherent, Santa Clara, CA) was used to illuminate the microscope field. The laser light was modulated by an acousto-optic modulator (AOM) (model SWM-10044; IntraAction Corp., Belwood, IL). A second signal generator (model 2023; Marconi) was frequency and phase locked to the intensifier signal generator. Its output signal was amplified with a 37-dB broadband linear power amplifier (model 403LA; Electronic Navigation Industries, Rochester, NY) and used to drive the AOM at a frequency in most experiments of 28.84 MHz, leading to optical modulation at f = 57.68 MHz. The zero-order light from the AOM was selected and relayed through a multimode optical fiber (model CU-3578 UV-vis; Multimode Fiber Optics, East Hanover, NJ) to the microscope illumination port. The optical fiber was vibrated mechanically at audio frequencies to scramble modes and thus reduce speckle. The dichroic filter was a 505 DRLP02 and the emission longpass filter (>515 nm) a 515EFLP (Omega Optical, Brattleboro, VT).

Anisotropy measurements were implemented by the addition of a sheet polarizer (Y-FA, Nikon) to the excitation light source and an analyzer (PW44, Schott, Mainz, Germany; or a Polaroid film polarizer) on the emission path of the microscope oriented either parallel or perpendicular to the excitation beam polarizer. Three data sets were taken; a conventional lifetime image with both excitation and emission polarizers removed; a 0°/0° (excitation/emission) polarization image; and a 0°/90° polarization image. A lifetime and anisotropy standard, 1 µM aqueous rhodamine 6G (Hanley et al., 2001), was also measured to provide a pixel-by-pixel calibration of relative modulation depth, phase shift, and polarization dependent transmissions (G-factor, Eq. 4 below).

Polarization confocal laser scanning microscopy

Confocal polarization-dependent images of the EGFP-expressing bacteria were acquired with a modified LSM 310 confocal laser scanning microscope (model LSM310; Zeiss, Göttingen, Germany), equipped with an external Ar⁺ ion laser (80 mW, 488 nm) as a photobleaching source. Fluorescence images of the parallel and perpendicular emission of the bacterial embedded in agarose were recorded with a 63× (1.2 NA) C-Apochromat water immersion objective, using excitation at 488 nm and emission at >515 nm. The unpolarized emission of a 0.2 µM fluorescein solution served to calculate the instrument G-factor (1.23) under the same conditions.

The total fluorescence and anisotropy images were generated with Scil-Image (TNO TPD, Delft, The Netherlands) software after background subtraction and pixel registration of the two polarized emission images by cross-correlation analysis. The final anisotropy image was smoothed by a 3 × 3 uniform filter function. Background pixels were excluded by threshold masking. The mean r for each anisotropy image was calculated from the mean intensity-weighted pixel values. Measurements were performed at ambient temperature (23°C).

Data acquisition and processing in rFLIM

In our implementation of rFLIM, the excitation light and the detector (intensifier) gain were modulated by the same radial frequency . A series of images was acquired while adjusting the relative phase between the AOM and the intensifier (Fig. 1) over one period (2 radians, 360°). The images were taken in sets of n (n = 4, 8, or 16) such that each successive image was measured with an incremental phase shift of 360°/n. Each series of images was accompanied by a corresponding blank image acquired with all shutters open except for the laser source. Acquisition proceeded with a reversal of the sequence of phase shifts for achieving a first-order photobleaching compensation; the second data series was processed as a second period of the sampled sinusoidal waveform. Acquisition was the same for sample, standard, and all polarization states. Two sets of measurements were made with the emission polarizer oriented either parallel or perpendicular. Each data set was processed (Hanley et al., 2001) to yield frequency-dependent amplitudes, and a phase shift between the excitation and the emitted light. The two resulting polarized emission components are modulated at the same frequency but phase shifted relative to each other; I_,AC leads I_,AC by . In addition, the AC amplitude of the perpendicular component is reduced relative to that of the parallel component. These signals are characterized by the ratio Y_AC = I_,AC/I_,AC, and the corresponding ratio of DC ( = 0) magnitudes by Y_DC = I_,DC/I_,DC.

Processing of the data involved five steps. 1) The lifetime images were computed from data obtained for the sample and lifetime reference in the absence of polarization optics. 2) The , Y_AC, and Y_DC images were calculated for the sample data sets. 3) The equivalent standardization images were computed for use as diagnostics and for determining G-factor corrections. 4) The latter were applied to the Y_AC, and Y_DC images according to the procedures given below. 5) Images of the anisotropy parameters (, r_o, r) were generated according to the formalism developed in the Results section (Eqs. 14, 18-20, 24-27).

The pixel-by-pixel corrections to the amplitude images (Y_AC, Y_DC) were based on measurements of a reference solution with known anisotropy. G-factors (G_i) accounting for differences in system response for the two polarized emission components were computed at each (ith) image pixel using a reference solution of known anisotropy (usually ~0), according to

(4)

where _ref is the steady-state anisotropy of the reference solution measured in a spectrofluorometer and Y is the DC intensity ratio (I_,i/I_,i) of the polarized emission measured in the microscope (see also Dix and Verkman, 1990). The reference measurements were made either directly before or after the sample measurement with identical optical configuration (objective, dichroic filter, etc.). The values of G_i were 1.15 ± 0.08 [Plan 2× (NA 0.06) air objective] and differed by less than 0.02 among the different objectives tested [Plan 2×, PlanFluor 20× (NA 0.75) air, PlanFluor 40× (NA 0.75) air, Plan Apo 60× (NA 1.2) water]. The corrected AC and DC ratios of the sample were obtained from

(5)

We observed a zero phase shift (within experimental error) for excitation with unpolarized light. Consequently, no corrections for instrumental effects on the phase shift were required. The programs Scil-Image (TNO TPD) and Mathematica 4.0 (Wolfram Research, Champaign, IL), including the Digital Imaging Processing add-on, were used for further image processing (segmentation and masking), generation of frequency histograms, and statistical analyses. Regions of interest (corresponding to individual cuvettes in a dual cuvette image or a particular cellular compartment in the cells) were isolated using an image intensity threshold mask.

Reference measurements in a spectrofluorometer

The fluorescence anisotropies of fluorescein solutions in glycerol-buffer mixtures and of rhodamine 6G in water were determined at 23°C with a commercial spectrofluorometer (enhanced model C-60, Photon Technology International, Monmouth Junction, NJ). The excitation wavelength was 488 nm, the emission wavelength 540 nm, and the slit spectral bandwidth 5 nm. For the rhodamine 6G solution, _ref was 0.012.

The fluorescence anisotropy and relative peak intensities of EGFP solutions were determined at 20°C with a Cary Eclipse spectrofluorometer (Varian Australia Pty, Melbourne) equipped with motorized excitation and emission polarizers. The excitation wavelength varied between 450 and 480 nm, and the emission spectra were measured up to 600 nm with a 5-nm bandwidth. A Suprasil cuvette with a 0.25-mm square cross section (<1 µL fill volume) was used to minimize inner filter and reabsorption effects. The intensity values were corrected for absorption A along the lightpath by the factor A ln[10]/(1  10^A). Anisotropy values determined in the two spectrofluorimeters agreed within 5%.

Materials and EGFP-expressing bacteria

Glycerol-buffer solutions over a range of glycerol concentrations from 10 to 80% (w/w) were prepared gravimetrically using spectroscopic grade glycerol (Aldrich, Milwaukee, WI) and 10 mM Tris-HCl, pH 8.0. Solutions for rFLIM rotational correlation time measurements contained 10, 61, and 70% glycerol by weight. The viscosities (, 23°C) of these solutions (1.2, 10.6, 21.3 cP, respectively) were estimated from published tables (Weast, 1979). Solutions for viscosity-dependent fluorescence measurements were prepared by addition of a small volume (<50 µL) of ~2 mM fluorescein in ethanol to a cuvette containing the glycerol/buffer mixture. The solutions were not deoxygenated. EGFP solutions were prepared volumetrically in 0.1 M Tris-HCl, 0.1 M NaCl, pH 8.5 buffer by dilution from a stock solution of known concentration, based on the extinction coefficient at 490 nm of 55 mM¹cm¹ (Patterson et al., 1997); we used _480nm = 50 mM¹.

Escherichia coli bacteria expressing EGFP were cultured at 37°C as described previously (Jakobs et al., 2000). Before rFLIM measurements, the bacteria were suspended in 1% agarose to minimize movement and mounted between a microscope slide and a coverslip. Some of the EGFP leaked into the extracellular medium. A sample from the same bacterial culture was centrifuged and the supernatant was found to contain free EGFP, the spectral properties of which were identical to those obtained by deliberate lysis of the bacteria via repeated freeze-thaw cycles. The mean concentration of intracellular EGFP was estimated by filtration of the bacterial suspension over a Millipore HA 0.45 µ nitrocellulose filter. The weight of the packed cells corresponding to a given volume of culture medium was determined and the EGFP fluorescence of the suspension and filtrate compared to a known (2.8 µM EGFP) reference solution.

	RESULTS

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS DISCUSSION APPENDIX REFERENCES

Theory

We first examine the theory of anisotropy and dynamic depolarization as applied to standard cuvette-based measurements of randomly orientated fluorophores using a homodyne measurement scheme. In conventional instruments, the sample is excited with linearly polarized light. The emission is detected perpendicular to the excitation propagation direction and viewed through an analyzing polarizer oriented either parallel (I) or perpendicular (I) to the excitation beam polarizer. These two signals differ in general because the polarized incident beam generates an anisotropic distribution of excited state fluorophores, i.e., by photoselection (Albrecht, 1961). Rotational diffusion of the fluorophores during the excited state lifetime reduces the disparity between I and I, resulting in dynamic depolarization of the emitted light according to Eq. 2. The fluorescence anisotropy r(t) at any time point is defined as (Jablonski, 1960)

(6)

The theory underlying the determination of rotational correlation times, differential polarized phase fluorometry, a method introduced by Weber and coworkers, is found in several excellent papers and reviews (Weber, 1977, 1978; Mantulin and Weber, 1977; Lakowicz et al., 1979; Lakowicz 1983; Jameson and Hazlett, 1986). The three measured parameters (, Y_AC, Y_DC) reflect the excited state lifetime and/or the intrinsic rotational diffusion properties of the fluorophore (and its conjugate) (Eq. 2), and an experimental variable (the modulation frequency ) that can be manipulated at will.

For the hindered rotator represented by Eq. 2 and using our nomenclature, one obtains

(7)

(8)

(9)

Note that we have used the dimensionless variables and , incorporating  and . That is, the rotational correlation time is expressed relative to the lifetime and the latter serves to scale the radial frequency. Our parameters differ from those used in the early publications (R = 1/(6), Weber, 1977, 1978; Lakowicz et al., 1979). The relationships of Eqs. 7-9 are depicted in Fig. 2 as a function of and . The phase difference approaches 0 at both extremes of frequency ( = 0, ) and passes through a maximum, whereas Y_AC increases monotonically with , albeit to a degree dependent on ; Y_DC is not a function of frequency. The maximal value of , for any given parameter set (r_o, r, ), is given by (Weber, 1978)

(10)

View larger version (56K): [in this window] [in a new window]   FIGURE 2   Dependence of rFLIM measured parameters (, YAC, YDC) and their partial derivatives on and . See text for discussion.

with

(11)

and, for any given parameter set (r_o, r, ), by

(12)

with

(13)

The approximations of Eqs. 11 and 13 hold well (±10%) over a large range of r_o and r values. Thus, a frequency sweep of can provide an estimate of  (Eq. 11) and, thereby, of .

The dependence of , Y_AC, and Y_DC on  is also featured in the three-dimensional (3D) representations of Fig. 2. is a bell-shaped function of  (a limited region of parameter space is shown in Fig. A1). Y_DC and Y_AC decrease monotonically with . (These properties apply for r_o > r > 0.) Important features of these parametric functions are revealed by the partial derivatives of , Y_AC, and Y_DC with respect to and , which are also functions of the same two parameters (Fig. 2). The greatest measurement sensitivity is achieved for the largest magnitudes of the derivatives, i.e., at low values of  and . However, the optimal conditions for determining  are not necessarily the same as those for . It follows that a judicious choice of experimental conditions is required for the most sensitive determination of .

The expressions corresponding to an isotropic rotator are given by setting r to 0 in Eqs. 7-9 (and in Eqs. 14-19 below). In the practical application of Eqs. 7-9,  is obtained from independent measurements, and  is derived from various strategies for achieving solutions for  (and thus  via the definition  = /). The approaches depend on the model and differ according to the degree of prior knowledge about the other depolarization parameters (r_o and r) and the selection of signals (Eqs. 7-9) to be used alone or in combination.

The general solutions of Eqs. 7-9 for  (and thus for ) consist of the following expressions (Eqs. 14-19). The program Mathematica was used to perform extensive symbolic manipulations and simulations of these functions. The solution derived from difference phase measurements is given by

(14)

with

(15)

(16)

(17)

In experimental practice, it is best to select a frequency for which _max is not close to  because b, the argument of the square root function of Eq. 14, vanishes for this condition. Experimental error in the determination of can lead to fluctuations of b about 0, including negative values, and thus render evaluations of Eq. 14 problematical due to the presence of complex numbers. However, a good approximation holds for |b|  0:   /_max. For _max  , b can still be driven negative in the event that experimental noise generates a recorded exceeding the value of _exact (given by Eq. 7) by a factor > [(_max,/_exact)  1]. In such cases, is mathematically and physically indeterminate, inasmuch as all solutions are imaginary.

The solutions derived from the AC and DC components of the relative polarized signals are given by

(18)

(19)

(20)

(21)

(22)

(23)

(24)

Composite expressions for rotational diffusion parameters

Equations related to those presented above have appeared in the literature in different forms. They share the disadvantage of requiring some prior knowledge of r_o and/or r, information that may not be readily available in microscope-based studies. However, combining all three parameters (, Y_AC, Y_DC; Eqs. 7-9) and  leads to independent "composite" expressions (Eqs. 25-27) for the three rotational diffusion parameters.

(25)

(26)

(27)

Note that r does not depend explicitly on either the fluorescence lifetime or the modulation frequency; an implicit dependence is via , Y_AC, and Y_DC (Eqs. 7-9). This parameter may well be invariant in a given system under investigation, suggesting that a global analysis over an entire image would provide a constant mean value for use in Eq. 20. This procedure also minimizes quantitative discrepancies by ensuring that the same optical configuration applies to all parameters. Others have noted that distortions to the anisotropy decay induced by high NA objectives are mainly manifested in changes in the r_o and not  (Tramier et al., 2000). Thus, independent self-consistent measures of r_o and  are desirable.

In this study, the above formalism was applied to images acquired in the fluorescence microscope and with pixel-by-pixel resolution. The apparent correlation times computed according to the above formalism were used to characterize the system and detect heterogeneity with respect to the correlation time and degree of hindered rotation. In the presence of heterogeneity, including that of the intensity decay function (multiple lifetimes), one must resort to more complex models and multi-frequency measurements, as has been described for FLIM (Squire et al., 2000). If some, but not all, parameters are constant over the sample, a global analysis can also be implemented, as in the case of single-frequency FLIM determinations (Verveer et al., 2000). It is evident that the influence of propagated measurement error will vary among the various approaches represented in Eqs. 14-27.

The above equations are valid provided a unique or appropriate mean fluorescence lifetime can be defined. Fluorophores with monoexponential decays yield equivalent phase and modulation lifetimes. This condition does not hold for more complex decay functions, requiring a more elaborate formalism for the selection of an appropriate lifetime average (e.g., a combination of phase and modulation values) for use in the above equations. However, the latter approach fails if molecular association(s) leads to a coupling of multicomponent intensity and anisotropy decay processes (Szmacinski et al., 1987; Jameson and Sawyer, 1995).

Concentration depolarization due to homotransfer Fluorescence Resonance Energy Transfer (emFRET)

In addition to depolarization by rotational diffusion, the emission anisotropy decreases in the event that excitation energy is transferred between nearby molecules during the excited state lifetime. Concentration depolarization due to FRET between identical molecules is a well-documented phenomenon (Bojarski and Sienicki, 1989) that occurs in concentrated solutions of fluorophores exhibiting a finite excitation-emission overlap integral, i.e., a relatively small Stokes shift. In cell biological studies, homotransfer FRET (which we designate here as emFRET) has been applied to the analysis of protein oligomerization on the plasma membrane (Varma and Mayor, 1998; Blackman et al., 1998; Bene et al., 2000) and within the cell (Gautier et al., 2001). In the latter case, emFRET of EGFP fused to viral thymidine kinase was measured by time-correlated single photon anisotropy decay.

We sought to implement emFRET by the wide-field rFLIM imaging technique. To do so, we extended the phase-modulation frequency domain formalism presented above to include provision for the excited state process (Lakowicz and Balter, 1982) of energy migration. For the specific experimental case treated here, that of emFRET involving EGFP in free solution, the extent of rotational depolarization during the excited state lifetime is limited ( < 1) and a good approximation for the apparent composite anisotropy decay (diffusion + energy migration) is given by the product of the terms representing the two processes (see Fig. 4 of Engstrom et al., 1992). In this case, the impulse response functions (Eq. 1) corresponding to the parallel and perpendicular emission components and for the case of an unhindered spherical rotator are given by

(28)

where  = 2 and  = 1, c is the fluorophore concentration (in mM units), and , the coefficient of the c(t/)^1/2 term accounting for energy migration, is given (in mM¹ units) by

(29)

where R_o is the characteristic Förster transfer distance (50% transfer efficiency for a single donor-acceptor FRET pair; units, nm), N_av is Avogadro's constant, and || (= 0.69) is the orientation-averaged square root of the Förster orientation factor ². This formulation assumes a random initial static distribution of molecular transition moments and a completely depolarized emission from any but the initially excited molecule. The ensemble excited state lifetime remains unaltered in emFRET.

The steady-state anisotropy is obtained by integration of Eq. 28, yielding

(30)

where

(31)

The convolution of Eq. 28 with a sinusoidal modulating function leads to analytical equations for the difference phase and modulation corresponding to Eqs. 7-9 but including the effect of energy migration, represented by the parameter . A detailed analysis will be given elsewhere. However, the effect of emFRET on and Y_AC can be summarized as follows: increases and then decreases with c, particularly for high modulation frequencies and low values of ; and Y_AC decreases at all frequencies.

Determination of fluorescence anisotropy in the microscope

Conventional descriptions of fluorescence anisotropy apply most readily to standard solution measurements of fluorophores with random orientations in the ground state and detection of the emission with the conventional 90° narrow-aperture configuration, i.e., orthogonal to the propagation direction of the excitation beam. In the microscope, one has to deal with the particular excitation/detection configurations including epi-illumination, high numerical apertures, nonrandom orientations in the ground state (Axelrod, 1979; Florine-Casteel, 1990; Fushimi et al., 1990), polarization distortions produced by biases or birefringence in the optical components (i.e., objectives, apertures, reflectors, filters, prisms: Axelrod, 1979; Florine-Casteel, 1990; Dix and Verkman, 1990; Bahlmann and Hell, 2000; Tramier et al., 2000) and detectors, and photobleaching under conditions of high irradiance.

The perturbation by high numerical aperture (NA) illumination/collection optics of polarization states characteristic of plane waves is manifested by mixing of polarization components along the three optical axes (Jovin, 1979; Axelrod, 1979, 1989; Florine-Casteel, 1990; Dix and Verkman, 1990; Sheppard and Torok, 1997; Bahlmann and Hell, 2000; Tramier et al., 2000). According to Axelrod (1989), the contribution of the observed polarization components of the emission can be formulated as linear sums of products of axial distributions dependent on sample properties and weighting factors that are functions of the NA. We have examined these effects empirically by assessing the influence of NA on the steady-state anisotropies and phase-shifts of known samples.

	EXPERIMENTAL RESULTS

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS DISCUSSION APPENDIX REFERENCES

Microscope validation

Steady-state anisotropies of fluorescein solutions of varying viscosity (achieved by addition of glycerol) were measured in the imaging microscope and compared to the corresponding values obtained in a spectroflurometer. In general, the two sets of measurement were in good agreement and could be accounted for by a single G-factor (Eq. 4). Tests for a systematic depolarization bias due to wide-aperture excitation-detection via the objective lens were also carried out. Using solutions of fluorescein in 80% glycerol, a small depolarizing effect, manifested as slight decreases in Y_AC and , was observed as the magnification and NA of the objective lens increased (Table 1). Similar results have been reported by others (Dix and Verkman, 1990; Verkman et al., 1990; Tramier et al., 2000). According to the theoretical results of Axelrod (Fig. 2 in Axelrod, 1989), the steady-state anisotropy corresponding to an isotropic rotator with r_o = 0.4 and  = 0.6 should decrease from 0.25 to ~0.21 as the NA/ value varies from 0.06 to 0.88. The variation documented in Table 1 was somewhat smaller, probably due to a contribution from out-of-focus light from the relatively thick solutions. Recent rFLIM data from cultured cells expressing GFP-tagged receptors and calibrated microspheres have revealed more pronounced NA effects (Subramaniam et al., 2002).

View this table: [in this window] [in a new window]   TABLE 1   Effect of objective lens numerical aperture on rFLIM parameters (, YAC, ) for fluorescein in 80% (w/w) glycerol/buffer

It is interesting that the corresponding values of in Table 1 were independent of the aperture, in accordance with the observations of Verkman et al. (1990). As expected, removal of the excitation polarizer yielded a  = 0 within experimental error, implying the absence of an instrumental phase lag between the parallel and perpendicular components of emission. Thus, no correction for instrumental phase shift was required.

Single-frequency rFLIM measurements of fluorescein-glycerol solutions

As a model system for demonstrating the ability of rFLIM to image regions differing in and , we imaged two adjacent cuvettes containing fluorescein solutions of different viscosity (10% glycerol/90% buffer,  = 1.2 cP; 61% glycerol/39% buffer  = 10.6 cP) and FLIM and rFLIM measurements. Figure 3 illustrates the acquired polarization data (, Y_AC, and Y_DC), the fluorescence lifetime values (_phase and _mod), and the corresponding derived quantities: the rotational correlation times [(, _YAC, _YDC; Eqs. 14-19, with r_o = 0.35, r = 0) and (_,, r; Eqs. 20-24, with r_o = 0.35)] determined at a single optical modulation frequency of 58 MHz. The mean values and standard deviations of the lifetime and anisotropy parameter distributions are collected in Table 2. Standard errors have been included as an indication of the errors in the means. The large number of pixels in the distribution led to reasonably precise estimates of the mean, and to standard errors that were typically two orders of magnitude smaller than the standard deviations. Consideration of the standard deviations and standard errors also allows an estimate of the number of pixels required to discriminate between given differences in rotational parameters. The minimal detectable difference between the means of two distributed parameters x and y is given by |  | = st, where t is the Student's test, s is the pooled standard deviation and n_x, n_y are the population sizes. Anisotropy decay parameters computed from the means of the entire distributions (, Y_AC, and Y_DC) for each condition are also given in Table 2.

View larger version (59K): [in this window] [in a new window]   FIGURE 3   Spatially-resolved FLIM and rFLIM of fluorescein solutions containing 10% and 61% glycerol. Solutions in adjacent cuvettes: 10% glycerol, left in images and red in histograms; 61% glycerol, right in images and blue in histograms. Top and bottom rows, histograms corresponding to the images in the two center rows. Symbols, all of the binned data points; solid lines, Gaussian fits. Both original measured signals (, YAC, YDC) and derived anisotropy parameters are shown. The objective was a Plan 2× air (NA 0.06). See text for nomenclature and discussion.

Several points emerge from the images and histograms displayed in Fig. 3. First, spatial resolution was achieved with both acquired data and derived par