Quantitation of Hindered Rotations of Diphenylhexatriene in Lipid Bilayers by Differential Polarized Phase Fluorometry

Abstract

Diffusional motions of 1,6-diphenyl-1,3,5-hexatriene (DPH) were observed by diferential polarized phase fluorometry. The measurements indicated that the depolarizing rotations of DPH in propylene glycol are isotropic. The results in vesicles of dimyristoyl-L-α-phosphatidylcholine indicated that diffusional rotations of DPH are dominated by hindered torsional motions. Combined use of both differential phase and steady-state anisotropy measurements showed that the average rotational angle of DPH, at times long compared to the fluorescence lifetime, is limited to about 23° at temperatures below the transition temperature of the lipid and that these rotations become less hindered above the transition temperature. The evidence that the depolarizing rotations of DPH in a lipid bilayer are different from those in an isotropic solvent calls into question the meaning of membrane microviscosity as determined by fluorescence anisotropy.

Measurements of the fluorescence polarization of probes embedded in lipid bilayers have been widely used to estimate the microviscosity of the hydrophobic regions of both natural and model cell membranes (1–6). In these microviscosity measurements it is assumed that the depolarizing rotational motions of the probe in lipid bilayers are equivalent to those in isotropic solvents.

1, 6-Diphenyl-1,3, 5-hexatriene (DPH) has become widely used in microviscosity studies because of its favorable fluorescence polarization and spectral properties (7), but perhaps more importantly because of the dramatic changes in fluorescence polarization that occur at the solid-liquid phase transition temperature of phospholipid bilayers (8, 9). These strongly temperature-dependent polarization changes are sharper with DPH than with other fluorophores, such as 12-anthroyl stearate, I-anilino-8-naph-thalenesulfonic acid, perylene, and N-phenyl-1-naphthylamine. A presumed advantage of DPH is the fact that the absorption and emission oscillators both lie along the long axis of the fluorophore. As a result, only rotations perpendiculart o this long axis will be effective in depolarizing the fluorescence emission. For these reasons, steady-state polarization measurements with DPH are considered to accurately describe the microviscosity of lipid bilayers.

Recent studies involving time-resolved decays of fluorescence anisotropy have demonstrated that DPH undergoes only hindered torsional motions below the phase transition temperature of dimyristoyl-l-α-phosphatidylcholine (DMPC) vesicles and that there is a highly nonexponential decay of anisotropy above the transition temperature (10). These phenomena reflect a hindered environment for DPH in lipid bilayers and illustrate the need to understand the types of probe motion that are responsible for fluorescence depolarization so that polarization data can be interpreted in terms of the membrane microviscosity.

In the work reported here we used differential polarized phase fluorometry to investigate the rotational diffusion of DPH in an isotropic solvent and in DMPC vesicles. This technique was used recently (11, 12) to study the rotational rates of fluorophores in isotropic solutions. Differences in the phase angle of the vertical and horizontal components of the emitted light are measured when the fluorescence sample is irradiated with polarized, sinusoidally modulated light. The tangent of the phase difference between the vertical and horizontal components of the fluorescence emission (tan Δ) is a function of the fluorescence lifetime (τ), the fluorescence anisotropy (13) value in the absence of rotational diffusion (r₀), the rotational rate in radians per second (R), and the circular modulation frequency (ω), as shown by Eq. 1

$$\text{tan} \mathrm{\Delta }=\frac{(2R\tau )\omega \tau r_0}{m\left(1+{\omega }^2{\tau }^2\right)+(2R\tau /3)\left(2+r_0\right)+{(2R\tau )}^2}$$ (1)

where

$$m=\frac{1}{9}\left(1+2r_0\right)\left(1-r_0\right)$$ (2)

The quadratic form of Eq. 1 may be used to obtain R from measurements of tan Δ.

$${(2R\tau )}^2+(2R\tau )\left(\frac{2+r_0}{3}-\left|\frac{r_0}{\text{tan} \mathrm{\Delta }}\right|\omega \tau \right)+m\left(1+{\omega }^2{\tau }^2\right)=0$$ (3)

For isotropic rotations the maximum value possible for tan Δ (tan Δ_max) is a function of only r₀, ω, and τ.

$$\text{tan} {\mathrm{\Delta }}_{\text{max}}=\frac{3\omega \tau r_0}{\left(2+r_0\right)+6{\left[m\left(1+{\omega }^2{\tau }^2\right)\right]}^{1/2}}$$ (4)

Equations 1 to 4 apply to spherical molecules or isotropic rotators. If the rotational motions are isotropic the tan Δ_max values will agree with that predicted by Eq. 4. Anisotropic rotations, a heterogeneous population of isotropic rotators, or hindered torsional motions result in a tan Δ_max less than that predicted by Eq. 4. Studies of Mantulin and Weber (12) demonstrated the usefulness of differential polarized phase fluorometry in the detection of anisotropic rotations.

Figure 1 shows the fluorescence lifetimes and differential phase lifetimes of DPH in propylene glycol (ω) Δτ = tan Δ). The precise agreement of the maximum value of the differential tangent with the theoretical value (Table 1) demonstrates that the depolarizing rotations of DPH in propylene glycol are isotropic. Additional evidence for this is provided by the precise agreement between the rotational rates calculated from the differential phase measurements and those calculated from the steady-state polarization measurements using the Perrin-Weber equation (Fig. 2; see the legend of Table 1 for a description of the experimental procedures).

Fig. 1.

Fluorescence lifetimes and differential polarized phase lifetimes of DPH in propylene glycol.

Table 1.

Differential polarized phase measurements of 1,6-diphenyl-1,3,5-hexatriene. Fluorescence lifetimes and differential phase lifetimes were measured by the phase shift method (12, 16), using a modulation frequency of 30 MHz. To obtain lifetimes unbiased by depolarizing Brownian rotations the excitation and emission polarizers were set 0° and 55° from the vertical, respectively (17). The instrumental conditions were: excitation wavelength, 360 nm; excitation filter, Coming 7–54; emission filters, Coming 3–73 and 2 mm of 1M NaNO₂. All equipment was from SLM Instruments, Inc. Steady-state anisotropy and anisotropy values in the absence of rotational diffusion (r₀) were obtained directly in a subnanosecond spectrofluorometer with the radio-frequency electronics and light modulation turned off. Rotational rates of DPH in propylene glycol were determined both by solving Eq. 3 and by steady-state anisotropy measurements. In the latter case we used the Perrin-Weber equation, r₀/r = 1 + 6Rτ. We found r₀ = 0.392 at −57°C and used this value in all our calculations. The lifetimes shown in this table are those observed at the temperature corresponding to the maximum value of tan Δ. The synthetic lipid DMPC (Sigma) was used without further purification. Chromatography of the phospholipid on silica with chloroform, methanol, and water (65:25:4) and ethyl ether, benzene, ethanol, acetic acid, and water (40:40:20:8:4) showed a single spot by both phosphate and dichromate char staining. The DMPC vesicles were prepared by adding benzene solutions of the probe and lipid to a stainless steel beaker, with a probe/lipid molar ratio of 1:500. The benzene was evaporated by gently warming the solution while maintaining a constant flow of argon over the materials. Buffer (0.01M tris, 0.05M KC1, pH = 7.5) was added to the dried lipid to establish a concentration of 0.17 mg of lipid per milliliter of buffer. Solutions were sonicated with a Heat Systems model 350 sonicator at 200 W, using a 0.5-inch-diameter tip. The temperature of the solution was maintained near 40°C during the 15-minute sonication period. This preparation was annealed for 1 hour at 40°C and then centrifuged at 48,000g for 90 minutes. No significant fluorescent impurities were observed in unlabeled vesicles prepared in an identical manner. No scattered light at the excitation wavelength or at the Raman wavelength was observed through the filters used for the lifetime and differential lifetime measurements. The absorbance of DPH in propylene glycol was 0.4 at 360 nm. A blank solution of propylene glycol showed no significant fluorescence at equivalent instrumental conditions.

Sample	τ (nsec)	tan Δmax		Percentage of tan Δmax observed
		Observed	Calculated
Propylene glycol	4.5	0.185	0.195	95
DMPC vesicles	8.7	0.159	0.278	57

Fig. 2.

Rotational rate of DPH in propylene glycol. Rotational rates were calculated by both steady-state polarization mea surements (A) and differential polarized phase fluorometry (B). The duplicate points between the bars in (B) result from the two possible solutions to Eq. 1. Near Δτ = Δτ_max the choice of the proper solution is not clear. However, the value chosen is often unimportant since the rotational rates are similar.

Figure 3 shows the differential polarized phase measurements of DPH-la-beled DMPC vesicles. Similar results were obtained with unsonicated liposomes (14). These results demonstrate an increase in the rotational or torsional motions of DPH at the phase transition temperatures, but in contrast to the results with DPH in propylene glycol the maximum differential tangent is only 57 percent of the theoretical value predicted by Eq. 4. This 43 percent tangent defect is greater than that predicted by Mantulin and Weber (12) for any degree of rotational anisotropy in the depolarizing motions. Since the depolarizing rotations of DPH are likely to be isotropic (7) and a similar tangent defect was observed in unsonicated liposomes of DMPC (which provide a more homogeneous population of probe molecules), we concluded that the tangent defect we observed was a result of hindered torsional motions of the probe when located in the lipid bilayer.

Fig. 3.

Fluorescence lifetimes (○) and differential polarized phase lifetimes (□) of DPH in DMPC vesicles. he Δτ_max indicates the maximum differential lifetime predicted for a free isotropic rotator with r₀ = 0.392 and τ = 8.7 nsec.

Recently, Weber (15) obtained solutions for the differential tangent under conditions where the rotational motions of the probe are limited to a nonzero anisotropy value (r_∞) at times long compared to τ. Under these conditions the parallel [I_‖(t)] and perpendicular [I_⊥(t)] components of the fluorescence emission are given by

$$I_{\Vert }(t)=\left(1+2r_{\infty }\right)\text{exp}(-t/\tau )+2\left(r_0-r_{\infty }\right)\text{exp}\left[-\left(\frac{1}{\tau }+6R\right)t\right]$$ (5)

$$I_{\perp }(t)=\left(1-r_{\infty }\right)\text{exp}(-t/\tau )-\left(r_0-r_{\infty }\right)\text{exp}\left[-\left(\frac{1}{\tau }+6R\right)t\right]$$ (6)

From these equations Weber (15) obtained

$$\text{tan} \mathrm{\Delta }=\omega \tau \left(r_0-r_{\infty }\right)(2R\tau )/\left\{m\left(1+{\omega }^2{\tau }^2\right)+(2R\tau /3)\left[2+r_0-r_{\infty }\left(4r_0-1\right)\right]+{(2R\tau )}^2\left(1+2r_{\infty }\right)\left(1-r_{\infty }\right)\right\}$$ (7)

and

$$\text{tan} {\mathrm{\Delta }}_{\text{max}}=\omega \tau \left(r_0-r_{\infty }\right)/\left\{1/3\left[\left(2+r_0\right)-r_{\infty }\left(4r_0-1\right)\right]+2{\left[m\left(1+2r_{\infty }\right)\left(1-r_{\infty }\right)\left(1+{\omega }^2{\tau }^2\right)\right]}^{1/2}\right\}$$ (8)

For r_∞ = 0, Eqs. 7 and 8 reduce to forms applicable to free isotropic rotations.

Since r_∞ is a measure of the degree to which the depolarizing rotations of DPH are restricted, we wished to use our measurements to obtain r_∞, in DMPC bilayers at various temperatures. Differential phase measurements alone do not yield r_∞,. However, in a hindered environment both the steady-state anisotropy and the differential tangent are functions of r_∞, and R. With these measurements and the fluorescence lifetime it should be possible to determine r_∞, and R. By integrating and normalizing Eqs. 5 and 6 over times from 0 to infinity we obtained

$$r_{\infty }=r+\frac{\left(r-r_0\right)}{6R\tau }$$ (9)

Substituting Eq. 9 into Eq. 7 gives

$$(C\text{tan} \mathrm{\Delta }){(2R\tau )}^2+(D\text{tan} \mathrm{\Delta }-A)(2R\tau )+(E\text{tan} \mathrm{\Delta }-B)=0$$ (10)

where

$$\begin{gathered} A=3B=\omega \tau \left(r_0-r\right) \\ C=(1+2r)(1-r) \\ D=1/3\left(2r-4r^2+2\right) \\ E=C/9+m{\omega }^2{\tau }^2 \end{gathered}$$ (11)

By measuring tan Δ, r, and τ, one can obtain R from Eq. 10. This value of R may then be substituted into Eq. 9 to calculate r_∞,. The values for r_∞ so obtained are presented in Fig. 4. It is apparent from these data that DPH is highly hindered at temperatures below the transition temperature of the bilayer (r_∞ ≃ 0.3) and that DPH rotates freely above the transition temperature (r_∞ ≃ 0). The midpoint of the change in r_∞, occurs at 24°C, which is near the phase transition temperature (8).

Fig. 4.

Limiting anisotropy values for DPH in DMPC vesicles. Limiting anisotropy values (□) were calculated from Eqs. 9 to 11, using data from Fig. 3 at regular temperature intervals, and from the steady-state anisotropy values (○). By using data read off Fig. 3, we effectively smoothed the data and minimized errors resulting from single data points. There are two solutions for r_∞. at each point because Eq. 11 is quadratic. However, in each in stance one of the rotational rates was negative and thus inadmissible.

Using time-resolved decays of fluorescence anisotropy, Chen et al. (10) found r_∞ ≃ 0.25 below the transition temperature and r_∞ ≃ 0.01 above the transition temperature. Our results are in excellent agreement with those of Chen et al. However, the rapidity with which differential tangents may be measured allowed us to obtain a complete temperature profile for r_∞ (Fig. 4). Thus differential phase fluoreometry will be a powerful method for investigating hindered motions of fluorophores in lipid bilayers.

The detection of restricted diffusional motions of DPH in lipid bilayers illustrates the difficulties inherent inr the extrapolation of DPH fluorescence anisotropy data to estimate membrane microviscosity. In such extrapolations it is assumed that the depolarizing rotations of DPH in the bilayers are identical to those in the reference solvent, which is usually a mixture of branched-chain alkanes. Our data demonstrate that this assumption is not valid, a result that calls into question the definition of membrane microviscosity from anisotropy measurements. Combined steady-state anisotropy measurements and differential phase fluorometry more accurately describe the rotational motions of probes in lipid bilayers and provide a better understanding of the constraints imposed by an anisotropic lipid bilayer. By such experiments it should also be possible to select fluorescence probes whose rotational motions in lipid bilayers are similar to those in homogeneous solutions, and thereby provide a better method for estimating membrane microviscosities.