Biological membranes are the sites of various biochemical processes in a cell.1,2 Characterizing the structural and dynamical properties of biological membranes is important to understand the kinetics and mechanisms of such cellular processes. Especially, lateral mobility of membrane components has attracted much attention since the introduction of the classical fluid mosaic model,3 where membrane proteins float freely in lipid bilayer membranes. The more recent lipid-raft model proposed that biological membranes are heterogeneous in structure and contain local ordered micro domains called lipid rafts.4,5 It has been a subject of interest for chemists and biologists to investigate the influence of the heterogeneous structure on the lateral mobility of the membranes.
To date, the lateral mobility of biological membranes has been extensively studied by measuring translational diffusion coefficients of molecules in model biological membranes or membrane viscosities, which are related to diffusion coefficients by the Stokes-Einstein relation. Various techniques have been developed for the measurement of diffusion coefficients in model membranes, such as fluorescence correlation spectroscopy (FCS),6 fluorescence recovery after photobleaching (FRAP),7 time-resolved fluorescence spectroscopy,8–10 fluorescence lifetime correlation spectroscopy11,12 and electron spin resonance (ESR) spectroscopy.13 Most of them are based on fluorescence measurements of fluorescent probe molecules solubilized within model membranes. Holmes et al. conducted time-resolved fluorescence measurements of trans-stilbene solubilized within a dipalmitoylphosphatidylcholine (DPPC) liposome, a spherical-shaped lipid bilayer membrane.8 They observed the bi-exponential fluorescence decay of the trans-stilbene in the liposome, suggesting the existence of two solvation environments in the DPPC bilayer. Nojima et al. estimated membrane viscosities by performing picosecond time-resolved fluorescence measurements of trans-stilbene in five kinds of phospholipid liposomes.10 They reported that all the phospholipid bilayers they examined have two solvation environments with different viscosities.
The fluorescence-based methods are powerful and widely used for diffusion measurements in model membranes. It is, however, difficult to distinguish whether the heterogeneity of membranes detected by fluorescence measurements reflects that of membrane viscosities or that of the dielectric constants because fluorescence characteristics can be influenced also by the local dielectric properties of surrounding media.14 To gain insight into the question, it is desirable to develop alternative methods other than fluorescence measurements. In this letter, we applied transient grating (TG) method with an interface-sensitive total internal reflection (TIR) geometry for a probe light (TIR-TG)15,16 to diffusion coefficient measurements in lipid bilayer membranes.
The TG method has several advantages in measuring diffusion coefficients over other conventional techniques.17 This method has high sensitivity and high time resolution, it does not require fluorescent probes, and the physical interpretation of the signal is rather straightforward. In this method, spatial modulations of the concentrations of reactant and product molecules are induced by an interference pattern between two excitation laser pulses. Diffusion of the molecules across the modulation (grating) is detected by diffraction of a probe laser beam. The decay process of the diffracted light intensity (TG signal) directly reflects molecular diffusion processes. Thus, this method can provide direct information on the influence of membrane environments on molecular diffusion processes.
Despite its potential usefulness, the TG method has not been applied to diffusion measurements in membranes. The major obstacle to applying this method to membrane samples is light scattering from the samples. The scattered light seriously interferes with the TG signal, making reliable measurements difficult. To solve this problem, we prepared a planar supported bilayer membrane of phospholipids at a silica prism/water interface and measured it with the TIR-TG method. By observing the sample localized at the interface with the interface-sensitive TG method, we suppressed the problematic background light scattering from membrane samples in the solution phase without loss of the signal intensity. Here, we report TIR-TG measurements of trans-stilbene solubilized within a dimystoylphosphophatidylcholine (DMPC, Figure 1) membrane supported at a silica/water interface. We obtained two different diffusion coefficients for stilbene molecules in the DMPC lipid bilayer. This result indicates that the DMPC lipid bilayer consisted of two kinds of domains with different viscosities, as previously suggested by the time-resolved fluorescence study.10
3. Results and Discussion
Figure 3a shows a TIR-TG signal of trans-stilbene in a DMPC bilayer membrane at a silica/water interface observed at a grating wavenumber q2 of 5.8 × 1012 m−2. Following the pulsed laser irradiation, the TIR-TG signal quickly rose within the time-resolution of the apparatus (∼30 ns) and decayed in the sub microsecond time range (Figure 3a (inset)). The signal then showed monotonous decay in the time range from 1 µs to 100 ms to reach the baseline. We tried to measure the TG signal of the same sample under the transmission conditions. However, we were not able to obtain the signal under the transmission conditions. The main cause was the light scattering from the liposomes which remained in the aqueous solution phase. The scattering light seriously fluctuated in intensity with time, making it almost impossible to detect the signal. We think that the measurements under the TIR conditions effectively suppressed the light scattering, allowing us to obtain the TG signal from the lipid membrane sample.
In principle, the intensity of a TG signal is proportional to the square of photo-induced refractive index change (δn), which mainly comes from thermal energy releasing (thermal grating) and creation and depletion of chemical species (species grating) upon the photoexcitation.20,21 In a previous TIR-TG study on a liquid crystal molecule at a solid/liquid interface, it was reported that the decay rate of the thermal grating signal at the solid/liquid interface was much faster than that observed in the bulk liquid phase.16 The acceleration of the decay rate was explained by the assumption that the thermal conduction from the liquid to solid phase is much faster than that across the grating. Since the rate of the initial large decay component observed in this study was similar to that observed in the previous TIR-TG study, we attribute the initial decay signal to the decay of the thermal grating signal due to the thermal conduction from the DMPC membrane to the silica prism.
The other decay components observed after the thermal grating signal were attributed to the species grating signal. We found that the temporal profile of the species grating signal was reproduced by a sum of three exponential functions: the total TIR-TG signal was expressed as a following equation:
\begin{align}
I_{\text{TG}}(t) &= \{a_{\text{th}}\exp(- k_{\text{th}}t) + a_{1}\exp (- k_{1}t) + a_{2}\exp (- k_{2}t) \\
&\quad + a_{3}\exp (- k_{3}t)\}^{2}.
\end{align}
(1)In this equation, kth is the decay rate constant of the thermal grating signal, whereas k1, k2, and k3 (k1 > k2 > k3) denote those of the other signal components, respectively. By using a least square fit of the signal, contributions of the individual exponential terms to the TIR-TG signal were separated out as shown in Figure 3b. It is important to note that the observed TIR-TG signal did not drop to the baseline before it finally decayed to the baseline. From this observation, together with the fact that the thermal grating signal at this temperature is negative (ath < 0), the signs of all the pre-exponential factors ai were unambiguously determined to be negative.
The three decay components observed in the species grating signal can reflect reaction kinetics and species diffusion processes. To assign these components, we measured TIR-TG signals under various q2 conditions. The change in q2 corresponds to that in the spatial dimension of the grating interval, i.e., the effectively probed length for the molecular diffusion. Therefore, if the rate linearly depends on q2, this component should be assigned to diffusion processes. If not, it should be due to reaction kinetics. We found that the TIR-TG signals at all the q2 were reproduced by the eq (1). The obtained rate constants k1, k2, and k3 are plotted against q2 in Figure 4a, 4b, and 4c, respectively. The rate of k1 did not depend on q2 and its value was always (7.5 ± 0.6 µs)−1. In this paper, confidence bands are shown by ± standard deviations. The k1-component should represent some reaction kinetics of trans-stilbene. This kinetics might be related to a process occurring specifically in the membrane because trans-stilbene does not show reactions in this time range in organic solutions. A possible candidate for such a process is structural changes of lipid molecules around photoexcited stilbene molecules. Such structural changes could be induced by the temperature increase due to the heat energy released from the photoexcited stilbene and persist after the temperature becomes uniform. The k1-kinetics might be interpreted as a reverse process of such structural changes or further conformational rearrangement of the lipid molecules. In this report, however, we focus on diffusion processes in membranes and do not discuss the origin of this kinetics further. In contrast to k1, k2 and k3 clearly depended on q2. The q2 dependence indicates the existence of two distinguishable molecular diffusion processes (diffusion signal) with different diffusion constants after the photoexcitation of trans-stilbene in the DMPC membrane.
Then what were the two diffusion components? Since cis-stilbene was produced upon the photoexcitation of trans-stilbene and their diffusion coefficients could be different from each other in the DMPC membrane, one may consider a possibility that the two diffusion components reflect diffusion processes of cis-stilbene and trans-stilbene. However, this possibility is excluded when we consider the signs of the diffusion signal components. If the diffusion coefficients of cis- and trans-stilbene were appreciably different, the diffusion processes of the two isomers would manifest themselves as two exponential components in the analysis. In this case, however, their pre-exponential factors should have the opposite signs because cis-stilbene is generated while trans-stilbene is depleted upon the photoexcitation. This is not the case; the negative sign was obtained both for a2 and a3 in the experiment. Accordingly, the k2- and k3-kinetics cannot be attributed to the diffusion processes of cis- and trans-stilbene.
The observation of the two diffusion components in the TIR-TG signals are reasonably understood when we consider inhomogeneous structures of the membrane. The previous time-resolved fluorescence studies suggested the presence of two solvation environments with different viscosity values within the lipid bilayer membranes.8–10 It is natural to consider that stilbene molecules dissolved in a fluid environment would show higher mobility than those in a viscous environment. We analyzed the observed TIR-TG signals with a model where the stilbene molecules in the DMPC bilayer show two different diffusion coefficients of Dfast and Dslow, which characterize the fluid and viscous environments, respectively. In this model, the temporal profile of the species diffusion signal, δndif (t), is expressed as the following equation:
\begin{align}
\delta n_{\text{dif}}(t) &= \delta n_{\text{fluid}}\exp (- D_{\text{fast}}\,q^{2}t) \\&\quad+ \delta n_{\text{viscous}}\exp (- D_{\text{slow}}\,q^{2}t),
\end{align}
(2)where δ
nfluid and δ
nviscous are the refractive index changes upon the photoisomerization of
trans-stilbene in the fluid and viscous environments, respectively. By comparing the third and fourth terms in the eq (
1), we obtain
k2 =
Dfast q2 and
k3 =
Dslow q2. From the slope of the
k2-
q2 and
k3-
q2 plots, we obtained the values of the two diffusion coefficients as
Dfast = (5.7 ± 1.0) × 10
−10 m
2s
−1 and
Dslow = and (2.8 ± 0.5) × 10
−12 m
2s
−1.
It should be noted that the value of the smaller one (Dslow) is comparable to those of diffusion coefficients in lipid bilayer membranes obtained by previous FCS and FRAP studies,6 and the larger one (Dfast) is ∼100 times larger than that usually observed. This fact does not support other possible interpretations of the observed large difference in the diffusion coefficients. For example, one might consider the possibility that the observed large difference may come from free and aggregated stilbenes. However, it is unlikely, because the aggregated stilbene, if exists, would have smaller D as compared to Dslow. One may also consider that interactions of stilbene molecules with the silica surface could explain the large difference in the diffusion coefficients. The interaction would, however, decelerate translational motions of the stilbene. Thus, it is difficult to consider that the interaction explains the observed large difference. In contrast, the interpretation by the inhomogeneous structures of the membrane is consistent with that in the previous fluorescence study as discussed below.
We here applied the Stokes-Einstein equation to the conversion of the obtained diffusion coefficients into the membrane viscosities for the purpose of comparison with the previous study10 though the theoretical description of molecular diffusion in supported lipid bilayer membranes is still in debate. According to the Stokes-Einstein equation, diffusion coefficients are inversely proportional to the viscosity of the surrounding media. Assuming the hydrodynamic radius of stilbene is approximately the same both in chloroform and the DMPC membrane, we obtained the viscosity of the membrane, ηDMPC by using the following equation:
\begin{align}
&\eta_{\text{DMPC}} \\&\quad= \eta_{\text{chloroform}} \times (D_{\text{stilbene in chloroform}}/D_{\text{stilbene in DMPC}}),
\end{align}
(3)where
Dstilbene in chloroform and
Dstilbene in DMPC are the diffusion coefficients of stilbene in chloroform and DMPC, respectively.
Dstilbene in chloroform was estimated by TG measurements of
trans-stilbene in chloroform, of which viscosity value,
ηchloroform is 0.537 mPa·s.
22 The obtained viscosities,
ηfluid and
ηviscous, which correspond to the fast and slow diffusion coefficients in the DMPC membrane, are 1.8 ± 0.3 and 375 ± 70 mPa·s, respectively.
The viscosities of the DMPC membrane obtained in this study, together with those reported in the previous time-resolved fluorescence study,10 are summarized in Table 1. In the previous study, Nojima et al. estimated viscosities by two different methods: one method was based on the photoisomerization rates and the other was on the rotational relaxation time of trans-stilbene within the phospholipid bilayer membranes. By both methods, they obtained two viscosity values, ηfluid and ηviscous with ∼100-fold difference. The values estimated from the photoisomeriation rates were 1.5 and 97 mPa·s, while those from the rotational relaxation time were 2.2–7.6 and 41–150 mPa·s. The order of magnitudes of lower and higher viscosities obtained by the different methods are each well correlated though the values themselves are appreciably different depending on the methods. The difference may be due to different spatial sample dimensions that each method probes. The TIR-TG method monitors translational diffusion processes across the grating spacing with typically a micrometer order, which are long-range motion as compared to the molecular motion involved in the photoisomerization and rotational relaxation. Consequently, this method detects longer-range inhomogeneity than the fluorescence measurements. The two different diffusion coefficients detected in the TIR-TG measurements implies that the DMPC membrane has micrometer-scale inhomogeneity that can be described with two different effective viscosities. At this time, we do not have a specific molecular picture of such long-range inhomogeneity. It might originate from structural variation across the membrane; the viscosity of lipid bilayer membranes at the center, away from the lipid head groups, could be significantly lower than that at the edges as suggested by a previous ESR study.13 It is also possible that the dynamics in the proximal and distal leaflets of the supported bilayer membrane could be different. Further investigations are required to obtain a detailed picture of the long-range inhomogeneity.
 | Table 1. Viscosity values in the DMPC bilayer membrane estimated from the diffusion measurements by the TIR-TG method, together with those estimated by the previous time-resolved fluorescence study.10 |
|
Table 1. Viscosity values in the DMPC bilayer membrane estimated from the diffusion measurements by the TIR-TG method, together with those estimated by the previous time-resolved fluorescence study.10 | ηfluid/mPa·s | ηviscous/mPa·s | Probed molecular motion |
| 1.8 ± 0.3 | 375 ± 70 | Translational diffusion |
| 1.5 | 97 | Photoisomerization |
| 2.2–7.6 | 41–150 | Rotational relaxation |
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