Rotational relaxation of the "microviscosity" probe diphenylhexatriene in paraffin oil and egg lecithin vesicles.

The rotational relaxation of the widely used "microviscosity" probe, 1,6-diphenyl-1,3,5-hexatriene, was examined by the technique of nanosecond time-resolved fluorescence depolarization. The decays of the emission anisotropy were determined at five temperatures in the range 3-31 degrees both in a reference paraffin oil and in sonicated egg lecithin vesicles. These decays were complex in both media. Marked qualitative as well as quantitative differences were observed in the rotational behavior of the probe in the complex bilayer medium as opposed to the homogeneous reference solvent. The results are discussed in relation to the structure of the hydrophobic bilayer membrane interior and the concept of its "microviscosity".

The decays of the emission anisotropy were determined at five temperatures in the range 3-31" both in a reference paraffin oil and in sonicated egg lecithin vesicles. These decays were complex in both media. Marked qualitative as well as quantitative differences were observed in the rotational behavior of the probe in the complex bilayer medium as opposed to the homogeneous reference solvent. The results are discussed in relation to the structure of the hydrophobic bilayer membrane interior and the concept of its "microviscosity." In recent years, the technique of fluorescence depolarization which, following the classic work of Weber (1,2), had found wide application in determination of the shape and size of labeled biological macromolecules in aqueous solution (3,4), has been utilized to study the fluidity of a variety of bilayer membranes (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The method has provided information regarding phase transitions and phase separations in liposomes (8)(9)(10)(11)(12)(13)(14) and with more complex cell membrane systems (15)(16)(17)(18)(19).
The fluidity of the hydrocarbon bilayer interior has been described in terms of an apparent "microviscosity" by comparing the steady state fluorescence depolarization of the probe in a reference oil with that observed in the membrane system. Phase transitions are readily identified from the behavior of the depolarization or of the derived "microviscosity" as a function of temperature.
In some cases, it has been possible to define a thermodynamic parameter for the system, the "fusion activation energy," e.g. Refs. 5,7,8,11,15,19. The extent of depolarization of the emission of a fluorophore reflects the degree to which a population of photoselected excited fluorophores loses its initial selective orientation and * This work was SUDDOrted bv National Institutes of Health Grant GM 11632 and National Science Foundation Grant GB 37555. Contribution No. 921 from the McCollum-Pratt Institute. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked 'hduertisement" in accordance with 18 U.S.C. Section 1734 solelv to indicate this fact.
$ Supported by National Institutes of Health Career Award Development Grant GM 10245. becomes randomized.
In these applications, a modified form (16) of the Perrin equation (20) has been used to describe the reference oil data and, by implication, also that of the membrane system: F) = 1 + C((r)) y where (r) is the observed steady state emission anisotropy (21, 22) defined by: Ill -I, (r) = ~ I,, + 21, (2) in which I,, and IL are the intensities of components of the emission polarized parallel and perpendicular to the electric vector of plane polarized excitation. The zero-point emission anisotropy r,) is the limiting value observed in the absence of rotational motion on the nanosecond time scale, while n represents the "microviscosity" of the system and r the excited state lifetime at temperature T. C((r)) contains volume and shape factors for the fluorophore plus any associated solvent shell and also, as will be indicated below, any other factor contributing to curvature in the Perrin plot of the reciprocal of the emission anisotropy against the factor (Tr/n) in Equation 1.
When the decays of both the emission anisotropy and the total emission are monoexponential, C((r)) is a constant and the Pert-in plot is linear. The former obtains for a spherical rotor or any solid of revolution in which the absorption and/or emission transition dipole is oriented along the symmetry axis. If the latter also holds then, in the first case, the constant is equal to K, the Boltzmann constant, divided by the volume of the spherical rotor; in the second it is also a function of the axial ratio (23-25). However, the rotational relaxation is usually more complicated than indicated above and may in general be represented by a multiexponential decay law, e.g. Ref. 26: r(t) = C P, ev-t/&l (3) where di are the rotational correlation times and the zero point emission anisotropy is determined as the sum of the pre-exponentials pi. In addition, the decay of the emission itself may be complex, again generally representable as a sum of exponentials: where the average lifetime is defined by: (7) = j= tI(t)dt/ j-zwt = 7 cY,T,li~ a$-, (4 = 7 P, (7 w4,1j-' Thus, only in the range of (T/n) for which 7, < 4, will the Perrin plot be linear. Outside this range, the nonlinearity will depend not only on the complexity of the rotational process but also on that of the emission kinetics.  the nanosecond time scale could be detected (4 > 700 ns). The latter effect was attributed to binding of the probe to relatively immobile proteins present in the membrane, but the origin of the ultra-rapid phase of the depolarization was not clear. One of the more popular fluorescent "microviscosity" probes has been diphenylhexatriene' (8,(11)(12)(13)(14)(16)(17)(18)(19) were tuned in by a computer-controlled stepper motor mounted on a Bausch and Lomb 0.5-m monochromator. The Gfactor, which here incorporates fluctuations in excitation intensity, was obtained by summation of the counts collected in the two decay curves and normalization to the steady state emission anisotropy of the same sample measured as described above. As seen by comparison with Equation 9 : Reproducibility of a single exponential decay and determination of the wavelength-dependent time shift between excitation and emission wavelengths (46, 47), as well as fidelity of zero emission anisotropy at all observable times for effectively completely depolarized fluorescence (431, were determined with the single exponential decay standard 9-cyanoanthracene in ethanol using the same excitation and emission conditions.

Analysis of Polarized
Decay Data -Impulse response functions for total emission s(t) and emission anisotropy r(t) decays were recovered from experimental sum and difference decays, S(t) and D(t), respectively, which were constructed from the data as: and S(t) = I,,(t).G + 21,,,(t) (11) An experimental emission anisotropy decay curve may also be constructed from the data according to Equations 11 and 12 together with the identity: The sum curve was fitted to a mono-or multiexponential decay law convolved onto the excitation profile using a nonlinear least squares search (45,48).
Two analyses of the difference curve were considered, corresponding to two different models for the emission anisotropy decay. The first associated the different components of the total emission with different mono-or multiexponential emission anisotropy decays (microheterogeneity) according to: In the second it was assumed that the decay course of the emission anisotropy was the same for all the kinetic components in the decay of the total emission (rotational homogeneity of sites) so that (34,491: In each case, one of the exponential terms describing r,(t) or r(t) could be replaced by a constant (equivalent to a decay term with an infinite correlation time). Modifications of the nonlinear least squares search in which the sum parameters were held constant and only the parameters of the emission anisotropy decay adjusted (49) were used to accomplish these analyses.
As with the sum analysis, the impulse response functions were convolved onto the excitation profile and compared with the data for both these models. The correct statistical (photon-counting) weights in the least squares analysis of the composite sum and difference decay curves are not linear functions of the counts collected in the two polarized decays I&t) and I&t). However, using synthetic test data to which photon-counting noise was added, the test parameters were recovered to good accuracy for the sum curve using the normal weighting factors, i.e. the reciprocal of the apparent number of counts in S(t). For the difference curves, however, it was found that application of equal weighting to all points led to good recovery of the test emission anisotropy parameters from D(t), while the normal weighting procedure consistently returned incorrect parameters and poor fits as judged by the residuals and their autocorrelation functions (45,48).

RESULTS
Steady state emission anisotropies (r) were measured at five temperatures in the range 3-31" both for DPH in the reference paraffin oil and in the vesicle suspension. A background fluorescence of the oil contributing less than 1.5% to any of the polarized components of emission was subtracted. The error that would have been introduced by neglecting this correction was smaller than the standard error of the measurements. The background due to vesicles was always less than 0.2% and could safely be entirely neglected. These results are given in Fig. 1. The error bars on the vesicle data are the standard errors for 6 to 10 determinations on the same vesicle suspension used in the time-resolved studies.
The nanosecond time dependence of the emission anisotropy r(t) was determined at the same five temperatures for both the reference oil and vesicle suspension. Subtractions of the appropriate small blanks for each of the orthogonally polarized decay curves in the case of the reference oil did not have any significant effect on the final decay parameters obtained.

Relaxation of DPH in Oil & Egg Lecithin Vesicles
The decay of the total emission of DPH in paraffin oil did not vary significantly over the temperature range investigated. The impulse response function s(t) was close to, but tally unusual fluorophore (36, 50).
The decay course of the total emission in the vesicle system was far from consistent with first order kinetics at any of the temperatures examined. The decays were decidedly biexponential at all temperatures.
Both lifetimes decreased somewhat with increasing temperature as seen in Table I, in  qualitative agreement with relative yield measurements in the literature (8). The ratio of the pre-exponential factors remained remarkably constant, and (23.4 + 0.6) % of that part of the excitation giving rise to fluorescence was associated with the shorter decay time. Comparative fits for the single and double exponential decay model to one of the 16" total emission decay curves are displayed in Fig. 3. Whether the biexponentiality of these decay kinetics arises from two excited state populations differing in their quenching interactions (microheterogeneity), from reversible formation of a dark, i.e. nonfluorescent, photoproduct in the excited state or has a more complex origin is an open question. not quite, monoexponential as judged by fitting criteria and comparison with the monoexponentially decaying standard, 9-cyanoanthracene in ethanol, measured under the same conditions.
The major decay component, which comprised (98.5 2 0.5)% of the emission, had a lifetime of 9.65 + 0.02 ns, the minor one 3.3 f 0.7 ns. The average lifetime, defined in Equation 6 was 9.55 + 0.03 ns compared with 9.54 r 0.03 given by the best single exponential fits to the data. A comparison of the fits for single and double exponential decay laws convolved with the excitation profile E(t) is presented in Fig. 2 for one of the 16" data sets along with the fractional residuals and autocorrelation function of the weighted residuals (45). These, together with the reduced x2 values for the fits and fidelity of the monoexponential hypothesis for decay of the standard, suggest that a single exponential decay model is not adequate for DPH in the reference oil. It seems possible that the apparent biexponentiality of the decay process may be connected with a reversible excited state reaction e.g. formation of a nonfluorescent isomer of this spectroscopi-$ 0. 25c   I  ,  I  I  I  I  I  0  5  IO  15  Taking the viscosity of a refractometrically determined (90.5 2 0.2)% glycerol/water (w/w) solution (42) as 170 cp at 25" with an estimated uncertainty of *lo cp (42) for calibration, the viscosity of the reference oil was found to be 145 f 10 cp at 25" with a fusion activation energy of 12.3 + 0.2 kcal/ mol determined from the linear Arrhenius plot obtained over the range 1.5 to 42.5". These values are very similar to those in the literature for American White Oil U.S.P. 35, i.e. 155 cp and 12.7 kcal/mol, respectively (27). From the steady state emission anisotropies for DPH in the reference oil (Fig. 1) and the above determined viscosity/temperature profile, the value of C((r)) was calculated from Equation 1 at the five temperatures examined between 3 and 31", setting the zero point emission anisotropy r0 at 0.362 (see below) and using the average emission decay time of 9.55 ns. As seen in the Perrin plot of Fig. 4, C((r)) did not approximate a constant in this temperature range. Its value varied from (14.6 f 1) lo5 poise degree-' s-l at 3" to (10.4 c 1).105 poise degree-' s-l at 31". These results appear to be at variance with a previous report that the Perrin plot for DPH in purified American White Oil U.S.P. 35 was essentially linear with a value for C((r)) of (8.6 ? 0.4).105 poise degree-' s-l (16). Using the values of C((r)) obtained here along with the steady state emission anisotropies for DPH in egg lecithin vesicles displayed in Fig. 1 Fig. 2. (a), difference decay D(t) = I,,(t).G -I,,&) compared with the product of the optimal double exponential decay function for total emission defined in the legend to    Table   III) appropriately reconvolved with the excitation pulse profile E(t).
(b), emission anisotropy decay R(t) defined in the same way as in difference data curves D(t) is displayed in Fig. 6a together with the impulse response d(t) obtained from the responses recovered for r(t) and s(t) as described in Equation 15, convolved with the excitation profile E(t). The equivalent comparison with R(t) is made in Fig. 66 which also shows the best but unacceptable mono-and biexponential emission anisotropy fits obtained in the same way, along with a semilogarithmic representation of S(t) for reference. The emission anisotropy decay parameters recovered from the duplicate data sets collected at each temperature are presented in Table  III.
The mean value of the zero point emission anisotropy determined in the vesicle system, r,) = 0.337 2 0.017 is somewhat lower than that found in the reference oil, but again no definite trend with temperature can be discerned. The difference in r,, value between reference and vesicle systems may reflect the summation of small depolarizing effects in the latter, i.e. randomization of the polarization planes of excitation and emission due to scattering and birefringence in the vesicle suspension as also optical activity of asymmetric bilayer components (53). These effects are not linear in r (53), so the whole course of the emission anisotropy decay will be changed. However, since the maximum error (that in r,J is small, the errors in relative partial anisotropies /3 and correlation times C#J due to this will be second order at most.
There is a slight trend towards shorter rotational correlation times for DPH in the vesicle system as the temperature increases and, as in the reference oil, the ratio of longer to shorter correlation times decreases somewhat. However, the similarity does not carry over to the pre-exponential factors whose ratio shows at most a small trend in the oil but changes by a factor of about 10 in the vesicle system. The relative values of the partial emission anisotropies associated with the longer and shorter rotational correlation times change from about 3 or 4 at the lowest temperature to about 0.5 to 0.2 at the highest.
Attempts were also made to analyze the vesicle data in terms of the associative model described by Equation 14. Adequate fits to the difference curves D(t) could be obtained in several of the associative models tested. However, in no case were the emission anisotropy decay parameters recovered physically realistic. As an example the data displayed in Fig.  6 could be adequately fitted to an emission anisotropy decay described by rl(t) = 0.800 exp [-t/1.39] and rZ(t) = 0.197 expl-t/5.671 + 0.032 associated, respectively, with the shorter and longer components of the total emission decay. It was also fitted equally well by r,(t) = 0.110 exp[+t/5.47] + 0.677 and r2(t) = 0.233 expl-t/l.401 and a total of six other associative models containing three components. In all cases, the pre-exponential factors of one of the emission anisotropy decays were impossibly large (e.g. in the above rol = 0.800 or 0.787) and/or negative correlation times were obtained (e.g. in the second example above, & = -5.47 ns).
The effects of rotation of the spherical vesicle as a whole and of lateral diffusion of the excited probe around the curved vesicle interior are both included in the correlation times determined here which represent harmonic addition of the appropriate correlation times for these motions to the correlation times for rotation of the probe in absence of these additional depolarizing processes (54). The Brownian rotational correlation time for the spherical vesicles under consideration: where V is the volume of the vesicle, q the viscosity of the suspending medium, and k the Boltzmann constant, is on the order of 1 to 2 ps. The equivalent correlation time correspond- for the decays are given in Table II for (a) and in Table III  ing to lateral diffusion of the probe is given by: that might be expected for any given emission anisotropy value, i.e. within about 0.005 to 0.01 of each other at all except the very earliest times. It is worthwhile pointing out that no attempt should be made to compare the (convolved) experimental emission anisotropy decay curves R(t) for the reference oil and vesicle systems directly, Figs. 5b and 6b respectively, both because the excitation pulse widths E(t) differ considerably and, no less importantly, because the total emission impulse responses s(t) convolved into these data are far from similar. This does not apply to the impulse responses r(t) obtained within the framework of the models so far considered and the apparent quantitative differences between these decay laws in the reference oil and vesicle systems are qualitatively well demonstrated in Fig. 7, where it is readily seen that an initially faster rate of depolarization in the vesicle system at any given temperature is compensated to some extent by the negligible depolarization rate at later times. The latter represents the appearance of a constant term in the decay law, i.e. a term with an apparently infinite decay time as indicated in Table III. (17) where R is the radius of the spherical vesicle and D the lateral diffusion coefficient (55). D may be as high as about 2 x 10-O cm2/sec (56) which sets a lower limit of about 100 ns on &,,,. Any motion leading to correlation times of 100 ns or more will not have appreciably influenced the results obtained here. Neither will resonance energy transfer have had any significant effect, since the mean fluorophore separation is about 90 A or more for the two or three probes found on average per vesicle (40) under the conditions utilized in the experiments described here, compared with a critical transfer distance (57) of about 18 A (58).
The constant term and its evident temperature dependence could represent a temperature-variable fraction of the fluorophore population that is held immobile on the nanosecond time scale. This hypothesis has been invoked to explain observable differences in the "microviscosity"/temperature profile between small single bilayer vesicles and multilamellar forms of phospholipids that exhibit gel-liquid crystalline transitions (13). An alternative explanation involves the existence of temperature-variable barriers preventing rotations of the probe beyond some angular limit about the mean position, a kind of cage effect. These possibilities correspond to limiting cases of the microheterogeneity and anisotropic solvent hypotheses outlined in the introduction to the text. Although the final duplicate parameters recovered for r (t) In view of the known structure of the bilayer, a cage effect seem rather variable in both reference oil (Table II) and would imply orientational anisotropy of the fluorophore with vesicles (Table III), the corresponding impulse responses can respect to the bilayer and this has indeed been observed for be seen, in Fig. 7, a and (12,31,32) and interpreted for planar egg lecithin multibilayers in terms of such a cage restricting the possible range of rotational reorientation (31). These studies on oriented systems show that, if the constant term in the emission anisotropy decay law is in fact due to immobilization of some of the fluorophores, this population must be at least partially oriented with respect to the bilayer. In the light of possible stacking of part of the linear aliphatic side chains of the bilayer phospholipids near their head groups, such an effect would not be unexpected. The much more dramatic orientational anisotropy observed for DPH in dipalmitoyllecithin bilayers below the gel-liquid crystalline transition temperature (12) and the extremely high value of the constant term, about 0.25, in the emission anisotropy decay of DPH in dimyristoyllecithin vesicles below its transition temperature reported recently from this laboratory (431, strongly support the present observations although, as in those cases, a definitive interpretation of the results in terms of immobilization or restricted range of motion is not possible. In view of this uncertainty, it would be premature to attempt an analysis of the rotational motion of the probe in the bilayer system according to the detailed model proposed recently for fluorescence depolarization in planar arrays of oriented fluorophores (59). However, it may be pertinent to note that the complex rotational relaxation of spin-labeled probes in membranes reflected in the details of their ESR spectra have also been widely interpreted in terms of models including restricted anisotropic motions (60-64). Considering by way of example the wobble or restricted tumbling or random walk model (61, 641, the cone half-angle for the volume corresponding to such restricted motion of DPH in egg lecithin vesicles on the nanosecond time scale changes from -55 to -70" in the temperature range 3-31" (65). This compares with the equivalent angle of about 30" reported previously for DPH in dimyristoyllecithin vesicles below the transition temperature (43) and about 15 and 20" for the subnanosecond motions of DPH in the reference oil and egg lecithin vesicles respectively calculated utilizing the same model.

DISCUSSION
The concept of a fluid bilayer lipid membrane has been supported by studies conducted on a variety of model membrane systems as well as with true biological membranes (66). A number of different physical techniques have been employed in this connection and, among others, steady state fluorescence depolarization measurements have provided useful information (67,68). In general, fluorescence depolarization data obtained with embedded aromatic fluorophores such as diphenylhexatriene have been interpreted in terms of a "microviscosity" for the hydrocarbon interior of the bilayer by comparison with depolarizations observed for the probe in a reference hydrocarbon oil of known bulk (macroscopic) viscosity. The nanosecond time-dependent depolarization data reported here for DPH in paraffin oil and in egg lecithin vesicles suggest a more complicated picture than that implied by this interpretation. It is quite certain that the fluorescence depolarizations observed in both reference and bilayer systems reflect the rates of rotation of the fluorophore. It is also true that these rates depend on the viscous opposition of the solvent to rotation of the probe. However, it is necessary to define in this connection precisely what is meant by a term such as "microviscosity." The bulk viscosities of homogeneous reference solvents can, of course, be determined and the steady state fluorescence depolarization of a dissolved probe may then be correlated with this viscosity scale. In terms of such a calibration, the "microviscosity" inferred from the depolarization observed for the probe embedded in the interior of the lipid bilayer, actually represents the apparent macroviscosity of a microscopic volume element which is unobtainable by direct measurement. A more physically realistic definition of microviscosity would have to take into account the local viscous opposition of the solvent to rotations of the probe in its microenvironment.
This viscous opposition may differ, not only for different rotational modes of the probe (anisotropic probe) but also vary as a function of the direction of a given rotational mode in the coordinates of the medium (anisotropic solvent). It may or may not be simply related to the bulk viscosity.
The time-dependent fluorescence depolarization data presented in this communication show that the rotational motion of DPH dissolved in a reference paraffin oil or embedded in the interior of egg lecithin single bilayer vesicles is complex. Moreover, as indicated by comparing the emission anisotropy decays depicted in Fig. 7 for these systems, the rotational characteristics of DPH are not only quantitatively but also qualitatively different in the two media. The most striking difference observed is that, whereas in the homogeneous reference oil the emission anisotropy tends to zero indicating that complete randomization of orientations is attained at long times, it decays not to zero but to a finite constant level (on the nanosecond time scale) in the vesicle system.
Two extreme models may be advanced to interpret the complex rotational behavior observed for DPH in the bilayer environment.
In one, a rotationally homogeneous population of probes in an anisotropic fluid membrane interior is assumed. The probes tumble on the nanosecond time scale over a range restricted by the confines of a cage formed by partial radial alignment of the fatty acid chains in the spherical bilayer vesicle. In the other extreme, a microheterogeneous population of probe sites in which DPH rotates at different rates is assumed. In a fraction of the sites, the probe is completely immobilized.
It would hardly be surprising if the observed complexity reflected the details of both models in part. The data reported here also indicate that the decay of the total fluorescence intensity of DPH in the vesicle system cannot adequately be described as a single first order process. On the other hand, they are consistent with a double exponential decay of the excited state population, which may indicate that the probe occupies two different sites in the membrane interior. However, it was not found possible to associate these postulated sites with physically realistic emission anisotropy decay laws, so that a simple two-state model for heterogeneity of both emission and rotation appears to be ruled out. In connection with this it should be emphasized that, although it is tempting to attribute a double exponential excited state decay law to two sites for the probe, a homogeneous probe population undergoing a reversible excited state reaction may also exhibit biexponential, or even more complex, decay behavior.
In view of the results presented here, no matter what the precise interpretation of them may be, inferences drawn as to the "microviscosity" (i.e. apparent bulk. viscosity of a microscopic volume element) of membrane bilayer interiors by comparison of steady state depolarizations of DPH in these and reference media should be viewed with caution. Furthermore, the problem of defining true local viscosities opposing the rotation of this probe in the bilayer interior, and for that