Configuration to Determine Donor-to-Acceptor Ratio-Dependent

on the donor-to-acceptor (D-A) ratio, by using a new type of microchannel ... a method for determining the FRET efficiency between NBD (donor) and Tex...
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Langmuir 2008, 24, 921-926

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Novel “Lipid-Flow Chip” Configuration to Determine Donor-to-Acceptor Ratio-Dependent Fluorescence Resonance Energy Transfer Efficiency Kazuaki Furukawa,* Hiroshi Nakashima, Yoshiaki Kashimura, and Keiichi Torimitsu NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, Japan 243-0198 ReceiVed September 1, 2007. In Final Form: October 17, 2007 We report on the determination of fluorescence resonance energy transfer (FRET) efficiency, which is dependent on the donor-to-acceptor (D-A) ratio, by using a new type of microchannel device called a “lipid-flow chip”. The chip comprises two supported lipid bilayers (SLBs) that self-spread from either side of 10 µm wide straight lines and carry molecules embedded in them. We first show that the diffusion process that occurs when the two SLBs collide with each other in the channel and form a unified SLB can be expressed by a one-dimensional diffusion equation. Next we describe a method for determining the FRET efficiency between NBD (donor) and Texas Red (acceptor) from observations using the lipid-flow chip by employing a one-dimensional diffusion model. The advantages of our method are that all the D-A ratios are achieved in one chip, and a large number of data are recorded in one chip. The FRET efficiency varies depending on the D-A ratio under conditions whereby the concentration of the sum of the donors and acceptors is constant. The Fo¨rster radius is also estimated from our results using a known model describing two-dimensional FRET systems, which yields a radius consistent with the previously reported value for NBD and Texas Red.

Introduction A lipid bilayer supported on a solid surface (referred to as a supported lipid bilayer, SLB) has been attracting considerable attention with respect to fundamental research on, for example, model cell membranes1,2 and biosensor applications.3-6 We are interested in a unique set of dynamic properties possessed by the SLB, namely, self-spreading7-9 and molecular diffusion within the SLB.10-12 Self-spreading is a lipid wetting process at a solidliquid interface, where a single SLB is formed by a self-organizing process at the rim of a lipid spot adhering to a hydrophilic surface.7 The membrane grows concentrically to a greater than millimeter scale.13-15 Molecular diffusion is driven by position exchange processes that occur between the lipid molecules within an SLB. It is known that the number of exchanges in animal cell membranes reaches about 107 per second, which corresponds to * To whom correspondence should be addressed. E-mail: furukawa@ nttbrl.jp. (1) Sackmann, E. Science 1996, 271, 43-48. (2) Kasemo, B. Surf. Sci. 2002, 500, 656-677. (3) Cornell, B. A.; Braach-Maksvytis, V. L. B.; King, L. G.; Osman, P. D. J.; Raguse, B.; Wieczorek, L.; Pace, R. J. Nature 1997, 387, 580-583. (4) Fertig, N.; Meyer, Ch.; Blick, R. H.; Trautmann, Ch.; Behrends, J. C. Phys. ReV. E 2001, 64, 040901. (5) Grane´li, A.; Rydstro¨m, J.; Kasemo, B.; Ho¨o¨k, F. Langmuir 2003, 19, 842850. (6) Suzuki, H.; Tabata, K.; Kato-Yamada, Y.; Noji, H.; Takeuchi, S. Lab Chip 2004, 4, 502-505. (7) Ra¨dler, J.; Strey, H.; Sackmann, E. Langmuir 1995, 11, 4539-4548. (8) Nissen, J.; Gritsch, S.; Wiegand, G.; Radler, J. O. Eur. Phys. J. B 1999, 10, 335-344. (9) Nissen, J.; Jacobs, K.; Ra¨dler, J. O. Phys. ReV. Lett. 2001, 86, 1904-1907. (10) Salafsky, J.; Groves, J. T.; Boxer, S. G. Biochemistry 1996, 35, 1477314781. (11) Kung, L. A.; Groves, J. T.; Ulman, N.; Boxer, S. G. AdV. Mater. 2000, 12, 731-734. (12) Groves, J. T.; Boxer, S. G. Acc. Chem. Res. 2002, 35, 149-157. (13) Suzuki, K.; Masuhara, H. Langmuir 2005, 21, 537-544. (14) Suzuki K.; Masuhara, H. Langmuir 2005, 21, 6487-6494. (15) Furukawa, K.; Sumitomo, K.; Nakashima, H.; Kashimura, Y.; Torimitsu, K. Langmuir 2007, 23, 367-371.

the diffusion constant D ∼ 1 µm2 s-1.16 The fluidity is also maintained for an SLB, as shown by the fluorescence recovery after photobleaching (FRAP).10 We have developed a method for controlling the position and direction of a self-spreading SLB that uses a photoresist micropattern fabricated on a hydrophilic SiO2 surface.17 We have used this technique in our proposal of a new type of microchannel device called a “lipid-flow chip”, which employs a lipid bilayer membrane as a molecule carrier. Figure 1 is a schematic illustration of our lipid-flow chip.17 The chip is equipped with 10 µm wide and 400 µm long microchannels, and has a well on each side. A self-spreading SLB grows from the rim of a small spot consisting of lipid molecules adhering to the inside well surface (Figure 1A) when the chip is gently immersed in a buffer solution (Figure 1B). Lipid molecules are not soluble in aqueous media; instead, they form an SLB on a solid surface by selforganization. The self-spreading proceeds only on hydrophilic surfaces once the SLB has reached the pattern. The SLB can be regarded as a 5 nm high microchannel, in which the molecules of interest are embedded and transported to the place of collision as shown in Figure 1C. After the collision, the two SLBs combine to form a unified SLB, and molecular diffusion from one side to the other begins. This also means that the two kinds of molecules embedded in each SLB are mixed within the unified SLB. If there is any intermolecular interaction between the two molecules, it occurs in the mixed region. We have reported the observation of fluorescence resonance energy transfer (FRET), as one example of intermolecular interaction.17 FRET is an intermolecular interaction that occurs when two molecules are close to each other, typically within 10 nm. This makes FRET a powerful and useful technique for biological applications.18-21 It is used in the field of fundamental research, (16) Alberts, B.; Bray, D.; Lewis, J.; Raff, M.; Roberts, K.; Watson, J. D. Molecular Biology of the Cell, 2nd ed.; Garland Publishing: New York, 1990. (17) Furukawa, K.; Nakashima, H.; Kashimura, Y.; Torimitsu, K. Lab Chip 2006, 6, 1001-1006. (18) Miyawaki, A. DeV. Cell 2003, 4, 295-305.

10.1021/la702695f CCC: $40.75 © 2008 American Chemical Society Published on Web 12/22/2007

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Figure 1. Schematic drawing of a lipid-flow chip during operation. (A) Spots of L-R-PC with or without dye-conjugated lipids adhering in the wells. (B) When the chip is immersed in buffer solution, the self-spreading lipid bilayer starts to grow. (C) A magnified view of part of a microchannel during operation. Arrows indicate the self-spreading direction.

including studies of protein-protein interactions, which usually occur within distances of 10 nm, as well as for practical applications such as commercially available assay kits. In these cases, FRET is used solely for judging whether or not the two molecules are in close proximity. If we can observe and discuss the results while taking the FRET efficiencies into consideration, it may lead to a paradigm shift in the types of experiments that will be undertaken in the future.22 However, this is currently very difficult because the FRET efficiencies differ when measured with different experimental setups.23-25 This may be overcome by using a good FRET standard, although we have not yet obtained such a standard.22 In addition, a number of donors and acceptors are involved in many of the observations with different donorto-acceptor (D-A) ratios. Therefore it is important to determine the FRET efficiency dependence on the D-A ratio. In this paper, we report on a simple method for determining the FRET efficiency from FRET observations that employs our lipid-flow chip. First, we observe the diffusion of dye-conjugated lipid molecules into a label-free SLB. By comparing experimental and simulated results, we show that the diffusion of dyeconjugated lipids in our lipid-flow chip configuration is expressed by an ideal one-dimensional diffusion process. Next we show that our system can be employed to determine the FRET efficiency between NBD (donor) and Texas Red (acceptor) embedded within an SLB. We provide an example FRET observation, and analyze the result using the one-dimensional diffusion model. We discuss the FRET efficiency dependence on the D-A ratio and the Fo¨rster radius between the two dyes. Materials and Methods A micropattern was fabricated on a SiO2 or a Si wafer with a 300 nm SiO2 layer by a conventional photolithographic technique using TSMR-V3 (Tokyo Ohka Kogyo) photoresist. The metal pattern (approximately 5 nm Ti and 45 nm Au) was fabricated with a conventional lift-off process. L-R-Phosphatidylcholine (L-R-PC) extracted from egg yolk was purchased from Sigma-Aldrich. Dye-conjugated lipids NBD-DHPE and Texas Red-DHPE were purchased from Avanti Polar Lipid, Inc. and Invitrogen, respectively. Chloroform and sodium chloride were (19) Ueno, T.; Taguchi, H.; Tadakuma, H.; Yoshida, M.; Funatsu, T. Mol. Cell 2004, 14, 423-434. (20) Lin, Z.; Rye, H. S. Mol. Cell 2004, 16, 23-34. (21) Murakoshi, H.; Iino, R.; Kobayashi, T.; Fujiwara, T.; Ohshima, C.; Yoshimura, A.; Kusumi, A. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 7317-7322. (22) Vogel, S. S.; Thaler, C.; Koushik, S. V. Sci. STKE 2006, 331, re2. (23) Berney, C.; Danuser, G. Biophys. J. 2003, 84, 3992-4010. (24) Zal, T.; Gascoigne, N. R. J. Biophys. J. 2004, 86, 3923-3939. (25) Corry, B.; Jayatilaka, D.; Rigby, P. Biophys. J. 2005, 89, 3822-3836.

purchased from Kanto Chemical Co., Inc. A 1 mol/L Tris-HCl buffer (pH ) 7.6) was purchased from Nacalai Tesque. Deionized water (Millipore, >18 MΩ) was used throughout the work. A mixture of L-R-PC (99 mol %) and dye-conjugated lipid (1 mol %) was prepared according to our previously reported method.17 A small amount of a solid was stuck on the inside surface of each well. The solids we used to observe molecular diffusion were L-R-PC/ NBD-DHPE and label-free 100% L-R-PC. For FRET, the solids were L-R-PC/NBD-DHPE and L-R-PC/Texas Red-DHPE. The buffer solution consisted of 100 mM NaCl and 10 mM Tris-HCl (pH ) 7.6). An Olympus BX51-FV300 confocal laser-scanning microscope equipped with 488 and 543 nm laser light sources for excitation was used for observing images. We used a 505-525 nm filter with a 488 nm light source for the NBD observations and a 610 nm high-pass filter with a 543 nm light source for the Texas Red observations. We chose the minimum excitation laser power (0.1% of the full power of our system) and set the photomultiplier voltage and gain within a range that avoided saturating the output signals so that the photomultiplier output can be considered as fluorescence intensity that is proportional to the number of dye molecules in the observation area. A Plan Apo 40×WLSM water-immersion objective lens (Olympus) was used for all the observations. The space between the chip and the objective lens was filled with buffer solution throughout the observations. All observations were carried out at room temperature.

Results and Discussion One-Dimensional Diffusion Model for Lipid-Flow Chip. Figure 2 shows NBD-DHPE diffusing into a label-free SLB within the micropattern. At the top of Figure 2A, an SLB of L-R-PC/NBD-DHPE is growing from the left and an SLB of L-R-PC is growing from the right. Since the latter contains no dye molecules for visualization, it cannot be observed with a fluorescence microscope. However, our system enables us to obtain images before and after collision by employing timelapse observations of the micropattern area because the labelfree SLB is certainly growing along the micropattern. This is a unique and important advantage of our experimental setup. Since the label-free SLB is invisible, we have to perform time-lapse observations for the L-R-PC/NBD-DHPE at 10 s intervals in order to find the collision point in practice. The number of scans is thus 6 times as many as that in the FRET observations, which may cause the slight photobleaching. At the top of Figure 2A, we show an image we obtained shortly before the collision (referred to as t ) 0, where t refers to the time after the collision) together with images obtained 60, 120, 180, and 600 s after the collision. It is clear that the NBD-

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Figure 3. (A) The hexagonal packing with 0.4 nm-edge hexagons used for the simulation model. (B) An x-axis projection of a twodimensional distribution of a molecule after 106 exchanges (top). The distribution is identical to the Gaussian distribution of the solution of the diffusion equation, where D ) 1.2 µm2 s-1 (bottom). Figure 2. (A) Time evolution of confocal laser scanning microscope images showing NBD-DHPE diffusing into L-R-PC. From top to bottom, t ) 0, 60, 120, 180, and 600 s (the time shortly before the collision is set at 0 s.). The white arrows indicate the point of contact between the two SLBs. Scale bar: 20 µm. (B) Averaged fluorescence intensities at each x position. The intensities are normalized by using the intensities at a position where the two dyes have not faced each other at t ) 0. The abscissa scale is set so that it is the same as the scale bar in panel A.

DHPE is diffusing into the label-free SLB. We take an x-axis parallel to the direction of the line pattern. The fluorescence intensities averaged for a width of 10 µm at each x position are plotted in Figure 2B. The plot corresponds to a numerical expression of the NBD-DHPE diffusing into the SLB from the collision point shown by the arrow. As the NBD-DHPE molecules diffuse into the label-free L-R-PC region, the fluorescence intensity from the NBD on the left-hand side decreases. This is due to the diffused molecules that are provided from the left-hand side where NBD-DHPE originally existed. The observations show that the molecular diffusion processes become dominant after the collision of two self-spreading SLBs. This is also supported by the observation of the isosbestic point shown in Figure 2B. Although it does not affect the discussion in the present article, the isosbestic point seems to shift slightly toward the label-free SLB region. There are several possible reasons for this, namely, the difference between the real collision time and the time set at t ) 0 owing to the scans with 10 s intervals in the time-lapse observations and the slight photobleaching because of the large number of scans needed for Figure 2. We compared these experimental results with those we obtained using a simulation. The simulation model is shown in Figure 3. The model employs hexagonal packing, although the molecules would be much more loosely packed in a real SLB. The unit hexagon has a 0.4 nm edge, which corresponds to an area of 0.42 nm2 per unit. This value was selected on the basis of the known lipid molecule density in a cell membrane of 5 × 106 µm-2,16 which gives an area of 0.4 nm2 for one lipid. In addition, the

model assumes that the Ti/Au walls are elastic and that the top and bottom monolayers in an SLB behave in the same way. The latter is generally acceptable for analyzing many FRAP experiments.10 We think the former assumption is also plausible for the following reason. The top image in Figure 2A shows L-RPC/NBD-DHPE after it had self-spread more than 100 µm in the pattern. The front edge of the SLB is almost linear and vertical to the channel direction. This means that the friction between the self-spreading SLB and the Ti/Au wall is negligible in our present experimental setup. We place one dye-conjugated lipid at position x ) 0 at t ) 0 and start the diffusion (Figure 3A). The dye-conjugated lipid is set to exchange its position with one of its six nearest neighbors with an equal probability of 1/6. It reaches an isotropic concentric probability after a certain period of time, according to our simple model. If we take an x-axis projection of the probability after 106 exchanges, it yields a distribution as shown at the top of Figure 3B. The projection profile corresponds to the solution of the onedimensional diffusion equation, eq 1:

∂C(x,t) ∂2C(x,t) )D ∂t ∂x2

(1)

whose solution is given by

C(x,t) )

1

x4πDt

exp

[ ] -x2 4Dt

(2)

We use the known lipid exchange number per second of 107 to compare the simulation and the solution of the diffusion equation. When t is set at 0.1, we found that the simulation result corresponds to the distribution for D ) 1.20 µm2 s-1 in eq 2 (Figure 3B). This D value is in good agreement with values determined by FRAP experiments.10 In order to simulate the experiments in Figure 2, we take the initial conditions by distributing dye-conjugated lipid molecules homogeneously in the region at x e 0 and none at x > 0 at t )

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Figure 4. Dye-conjugated molecule distributions at t ) 60, 120, 180, and 600 s resulting from the initial condition at t ) 0 of the homogeneous distribution of dyes at x e 0 and none at x > 0 calculated by using D ) 1 µm2 s-1.

0. Note that the concentration of the dye-conjugated lipid is not a parameter in the present simulations. It is set at 1 mol %, which is the same as the concentration in our present experiments. Because we disregard the collision between dye-conjugated molecules in our model, a lower concentration makes better agreement to the assumption. Under these conditions, the projection of dye-conjugated lipid distributions onto the x-axis after a certain period of time is the sum of the Gaussian functions at the bottom of Figure 3B. Figure 4 shows the results at each time. The calculations reproduce the experimental resultssthe shape and the time and length scalessvery well. In the present simulations, we did not consider any specific or complicated assumptions such as the friction between an SLB and the Ti/Au wall or collisions between dye molecules. Despite this, the results obtained with our experimental system agree with both simulation and theory. Thus we have realized an ideal one-dimensional diffusion system for the molecule diffusion that occurs after the collision of two SLBs self-spreading within a micropattern. Determination of FRET Efficiency. When one SLB contains donors and the other contains acceptors, FRET between the molecules can be observed in the area where the two dyes are mixed together by lateral diffusion.17 Figure 5 shows several frames from time-lapse observations of such a case. The observation was performed before and after the collision with the interval of 60 s, and the time when two SLBs collide is set as t ) 0. Figure 5A shows images taken at t ) 0, 60, 120, 180, and 600 s. The fluorescence from NBD (donor) and Texas Red (acceptor) is shown in green and red, respectively. After the collision, for instance at t ) 120, the red fluorescence is observed in the area where the green fluorescence was observed at t ) 0. In contrast, the green fluorescence does not appear to spread into the red fluorescence area. Figure 5B plots averaged fluorescence intensities at each x position. The intensities are normalized so that they represent the relative number of dye molecules that yield fluorescence. For the normalization, the fluorescence intensities of donors and acceptors before the collision are used, respectively, as the unique normalization factors. Possible photobleaching from the observations is not further corrected because it is negligible in the present FRET experiments. This is also clarified in Figure 5, which shows that the fluorescence intensities from donors in the x < -40 µm region remained constant after several observations. It becomes clearer that the red fluorescence area continues to spread over time, while the green area continues to decrease. This is attributed to FRET occurring between NBD and Texas Red, as we have already demonstrated using another pair of dyes.17 Our present purpose is to estimate the FRET efficiency from the results in Figure 5 by using the one-dimensional diffusion model. Two points must be considered regarding the estimation: one is the distribution of dye-conjugated lipid molecules in the area in which they are mixed after the collision, and the other

Figure 5. (A) Time evolution of confocal laser scanning microscope images showing FRET between NBD and Texas Red. Each image is composed of two independent scans: fluorescence over 610 nm under 543 nm laser excitation is shown in red, that from 505 to 525 nm under 488 nm laser excitation is shown in green. From top to bottom, t ) 0, 60, 120, 180, and 600 s (the time shortly before the collision is set at 0 s.). The white arrows indicate the point of contact between the two SLBs. Scale bar: 20 µm. (B) Averaged fluorescence intensities at each x position. The intensities are normalized by using the intensities at a position where the two dyes have not faced each other at t ) 0. The abscissa scale is set so that it is the same as the scale bar in panel A.

is the relationship between the number of dyes and the observed fluorescence intensity. The mixing of the two dye molecules after the collision is driven by lateral diffusion processes. The two kinds of dyeconjugated lipids change their distributions over time, as described in Figure 4. Since the two dye-conjugated lipids used in the present experiments have similar structures and similar bulkiness, their diffusion constants do not differ much. Thus the distribution profiles of NBD and Texas Red lipids are bilaterally symmetric with x ) 0, and the sum of the two dye-conjugated lipids is constant at any x. The D-A ratio at the collision point (x ) 0) is independent of time and always maintained at 1:1. In other words, this means that no concentration distribution appears after two SLBs collide and mix. It would be natural for this to occur in the present case, where the mixing is dominated by thermodynamically driven random walk processes. We also confirmed the diffusion of NBD-DHPE to the L-R-PC/Texas Red-DHPE region by observing the donor fluorescence recovery after acceptor photobleaching (see Supporting Information). The fluorescence intensity from the dye molecules is proportional to the number of dye molecules when emitting light is the dominant process for the relaxation of excited energy. This is not satisfied by the donors, because they lose excited energy as a result of FRET. However, the acceptors satisfy the condition. In addition, we considered several other conditions supporting this idea. A typical problem is that we observe crosstalk or fluorescence from the donors when we excite the acceptors. We

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did not observe such unfavorable crosstalk in Figure 5, which showed almost zero level fluorescence in the donor region when we observed acceptor fluorescence at t < 0. In addition, the laser power used in our experiments is within the normal excitation conditions, where the density of the excited dyes is limited. Thus we can take the fluorescence intensity from acceptors as the quantitative index for the number of acceptors existing at each x. The experiments also support this, as the profiles over time are in good agreement with those in Figure 2, if we look at the acceptor fluorescence in Figure 5. The fluorescence intensities are normalized in Figure 5, and this enables us to discuss the concentration of each dye molecule in terms of these values. In our present experiments, this means that the fluorescence intensities become 1 and 0 when the SLB contains 1 and 0 mol % of acceptor molecules, respectively. In the region where the donors and acceptors are mixed, it provides intermediate values that are proportional to the concentrations of each (however, this is not the case for donors when they exhibit FRET). The present discussion is not dependent on the quantum yield of each dye because the FRET efficiency can be determined simply from the relative changes in the fluorescence intensities of each dye. In our experiments, the D-A ratio at the collision point (x ) 0) is independent of time, with a ratio of 1:1. Thus the relative intensities from both the donors and acceptors at the collision point must be 0.5 if there is no FRET. Our experiments agree well with the above for the acceptor, but at the same time show a significant reduction in donor fluorescence. The fluorescence from the donor at x ) 0 is about 0.15, which means that the FRET efficiency EFRET reaches about 70% under our experimental conditions. The above discussion is formularized as follows. The ideal one-dimensional diffusion system is expressed by using the normalized fluorescence intensities from the donor, fD, and acceptor, fA, as

fD + fA ) 1

(3)

obs Let f obs D and f A be the observed fluorescence intensities from obs the donor and acceptor, respectively. f obs D and f A should also be normalized. For an acceptor, eq 4 is given as follows:

fA ) f obs A

(4)

Equation 4 cannot be used to determine fD in the present case because donors exhibit FRET. Instead, using eqs 3 and 4, fD is given by

fD ) 1 - fA ) 1 - f obs A

(5)

obs f obs D is always less than fD under FRET conditions.f D /fD is the ratio of donors that give fluorescence by escaping the FRET process. The FRET efficiency EFRET is given by

f obs f obs D D )1EFRET ) 1 fD 1 - f obs

(6)

A

We can thus calculate the FRET efficiency from eq 6 using the obs experimental values of f obs D and f A . FRET Efficiency Depending on D-A Ratio. The FRET efficiency determined by eq 6 is plotted in Figure 6 with the D-A ratio as the abscissa. The D-A ratio, fD/fA, can be determined at each x using f obs A from eqs 4 and 5. Figure 6 indicates that the FRET efficiency varies depending on the D-A

Figure 6. D-A ratio-dependent FRET efficiency between NBD (donor) and Texas Red (acceptor). EFRET, calculated by eq 6, is plotted by using the D-A ratio, calculated by eq 5, as the abscissa. The data are obtained from the observations shown in Figure 5 at t ) 60, 120, 180, and 600 s.

ratio; however, the total dye lipid concentration, and thus the average dye lipid distance, should not change. This is understood in the high and low limits of the D-A ratio. The donor is surrounded by many other donors and a few acceptors at a high donor ratio of over 30, and it is difficult for the donors to find a FRET partner. Thus the FRET efficiency approaches 0. At a small D-A ratio of less than 0.3, the donors are surrounded by many acceptors, and this results in a maximum efficiency that depends on the D-A distance. Figure 6 shows that all the data trace a unique curve, independent of the observation time. This supports the idea that the FRET efficiency is determined by the D-A ratio. We should mention that time is not a parameter with respect to determining FRET, but only contributes to changing the distribution of the D-A ratio to the x direction. Thus it is sufficient to obtain an observation at a certain time to discuss the relationship between the FRET efficiency and the ratio. However, another observation obtained at a different time using the same lipid-flow chip gives an independent set of data. This enables us to collect a large number of data for statistical analysis. Observations at a different time are easy to obtain, and they provide a great advantage in regards to determining the FRET efficiency with a high degree of accuracy. This allows us to undertake a quantitative discussion of FRET efficiency. The observation of the unique curve in Figure 6 further supports the validity of our assumption in eq 3 that the concentration of the sum of the donors and acceptors is constant. If this is not true and the dye distribution changes with time, it cannot give the time-independent unique curve shown in Figure 6. The unique characteristic of the method that determines the FRET efficiency by using a lipid-flow chip is that all the ratios are realized at the same time on one chip. Such a device has never previously been reported. This method can be applied to all dye-conjugated lipids, and we can determine the FRET efficiencies of any combination. We have, for example, already demonstrated FRET observations using different combinations of the dye molecules coumarin and fluorescein.17 The way in which the FRET efficiency varies depending on the D-A ratio is in good agreement with a recent Monte Carlo simulation.23 The simulation was performed on a multiple-donormultiple-acceptor system by extending an earlier simulation on a single-donor-multiple-acceptor system.26 The authors also reported their experimental results and discussed the way in which the experimentally determined efficiencies corresponded to the simulation. They found that the FRET efficiency strongly (26) Wolber, P. K.; Hudson, B. S. Biophys. J. 1979, 28, 197-210.

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depended on the calculation methods, although the data used for the calculations were obtained from the same sample, and that the efficiency did not correspond with the simulation results in some cases. It is certain that their experiments were well designed for examining the D-A ratio dependence of FRET in two dimensions. However, the D-A ratios that they were able to vary were still limited and discrete. In contrast, the D-A ratios that we can vary in our experiments cover a wide range almost continuously. The excellent coincidence between our experimental data and the simulation supports the validity of the Monte Carlo simulation. We can also estimate the Fo¨rster radius R0 from our results. However, we cannot estimate it by using a simple equation for single-donor-single-acceptor with the distance R

EFRET )

R06

(7)

R06 + R6

Instead we have to consider a multiple-donor-multiple-acceptor system confined within a two-dimensional space. Theoretical and numerical treatments of the system have been reported over many years.27 They include a variety of cases that depend on whether the donor/acceptor distribution in the membrane is random28 or nonrandom,29 in the absence or presence of diffusion during the lifetime of the excited-state of the donor.30 The following equation gives the FRET efficiency based on the simplest model that assumes the completely random distribution of acceptors within the membrane and no diffusion during the excitation lifetime:27

[

()]

t t IDA(t) ) I0D exp - - 2β τD τD

1/3

(8)

where

β)

Γ(2/3) C 1 ,C ) 2 C0 0 πR

2

0

Here, IDA(t) and I0D are the fluorescence intensities from donors in the presence/absence of acceptors, respectively. The parameters τD, C, and C0 are the fluorescence lifetime for donors in the absence of acceptors, the inverse of the average area occupied for one acceptor, and that of a circular area with a Fo¨rster radius R0. Γ represents a gamma function, and Γ(2/3) ) 1.354177. Integrating IDA(t)/I0D by t over 0 to infinity gives the total fluorescence from donors that escape the FRET process. Thus the FRET efficiency EFRET is the rest of the calculated value:

IDA(t) dt I0D ∞ t t ) 1 - 0 exp - - 2β τD τD

EFRET ) 1 -

∫0∞ ∫

[

()] 1/3

dt

(9)

(27) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 3rd ed.; Springer: New York, 2006. (28) Koppel, D. E.; Fleming, P. J.; Strittmatter, P. Biochemistry 1979, 18, 5450-5457. (29) Fung, B. K.-K.; Stryer, L. Biochemistry 1978, 17, 5241-5248. (30) Kusba, J.; Li, L.; Gryczynski, I.; Piszczek, G.; Johnson, M.; Lakowicz, J. R. Biophys. J. 2002, 82, 1358-1372.

Figure 7. Calculated FRET efficiency using eq 9 as a function of Fo¨rster radius with an acceptor concentration of 0.005 (half the value of the total dye concentration of 1%). We assume the area occupied by one lipid molecule to be 0.4 nm2, yielding C ) (0.4/ 0.005)-1 ) 80 nm-2 in eq 8.

We can estimate the Fo¨rster radius by using the experimental value EFRET ) 0.7 with a D-A ratio of 1. However, eq 9 cannot be solved analytically. Thus we calculated IDA(t)/I0D numerically with different R0 values, and plotted the results in Figure 7. From Figure 7, a FRET efficiency of 0.7 corresponds to a Fo¨rster radius of about 5.3 nm. This value is in good agreement with the known value for the NBD and Texas Red pair.31 This indicates that our lipid-flow chip is also valuable in regards to obtaining the Fo¨rster radius in a two-dimensional membrane system.

Conclusion We have described a new approach for determining the FRET efficiency between dye molecules embedded in a lipid bilayer membrane by using a lipid-flow chip. This was based on the idea that the molecular diffusion in an SLB confined within the microchannel of the lipid-flow chip can be modeled by a onedimensional diffusion process. The validity of the model was confirmed by comparing experimental and simulation results. We also described a method for determining the FRET efficiency by employing our model. We employed the method to analyze FRET observations that we undertook using our lipid-flow chip. We determined the relationship between FRET efficiency and the ratio of the donor and acceptor precisely by collecting a large number of data for all possible D-A ratios. Furthermore, we estimated the Fo¨rster radius by analyzing the data using a known model that describes a multiple acceptor system in two dimensions. The value we obtained agreed well with the known Fo¨rster radius between the pair of dyes. We expect this work to trigger detailed quantitative discussions of the relationship between FRET efficiency and D-A distance, in addition to the D-A ratio. The approach we described is promising because we can perform experiments with various D-A distances by controlling the D-A concentrations. The new method also enables us to determine the FRET efficiency of various pairs of dyes, because the method is applicable to all dye-conjugated lipid molecules. Supporting Information Available: The donor fluorescence recovery after acceptor photobleaching. This information is available free of charge via the Internet at http://pubs.acs.org. LA702695F (31) Kaizuka, Y.; Groves, J. T. Biophys. J. 2004, 86, 905-912.