J. Phys. Chem. B 2000, 104, 6103-6107
6103
Diffusion Bias and Photophysical Dynamics of Single Molecules in Unsupported Lipid Bilayer Membranes Probed with Confocal Microscopy Daniel L. Burden* and John J. Kasianowicz National Institute of Standards and Technology, Biotechnology DiVision, Gaithersburg, Maryland 20899-8313 ReceiVed: March 3, 2000; In Final Form: April 26, 2000
We use scanning confocal fluorescence microscopy to study the dynamic properties of single fluorescent lipid molecules in unsupported planar bilayers. Specifically, we characterize the emission saturation and diffusive behavior of lipids that have been covalently modified at various locations. By analyzing the time interval between fluorescent bursts, we observe a large deviation from theoretical prediction that indicates a substantial 2D diffusion bias. Interestingly, a correlation between the emission saturation and the power dependency of the deviation suggests that the resonantly enhanced polarizability of the fluorescent label plays a role in the biasing mechanism. Incorporation of the measured fluorescence rate constant into a model for particle escape from a shallow potential well indicates that the well depth is ≈kT. These results are in agreement with the calculable laser/membrane interaction potential and are consistent with previous reports concerning diffusion biases in free solution caused by weak optical traps.
Introduction Advances in fluorescence microscopy have led to a variety of techniques that enable single-molecule detection in solution and on supportive substrates.1-3 More recently, single molecules have been visualized in free-standing and pseudo-supported lipid membranes by utilizing either direct wide-field4,5 or total internal reflection6 illumination at relatively low excitation intensities. In contrast, the strong laser focusing and high light throughput of confocal microscopy enable a single fluorescent molecule to be interrogated with a large photon flux and excellent detection efficiency. Strong focusing also produces a sizable electric-field gradient that can confine dielectric particles in a single-beam optical trap.7 Our confocal measurements in lipid bilayers are consistent with the hypothesis that a shallow singlemolecule optical trap is generated when the excitation beam is placed on the membrane surface. In two previous reports, confocal microscopy was used to monitor small particles and single molecules moving freely in solution.8,9 Analysis of the time interval between fluorescent events indicated a substantial diffusion bias acting on both the particles and small molecules. Comparing analysis results to theoretical prediction revealed a discrepancy that the authors of both works attributed to an optical trap. In other work, BarZiv et al. demonstrated that direct optical trapping and manipulation of unlabeled lipid bilayers is possible when a tightly focused (diffraction-limited) laser beam is placed on a membrane surface.10 Using the 514 nm line from an Ar+ laser (50-100 mW), the interaction energy between the optical field and the lipid bilayer exceeds kT11 and is believed to draw lipid material into the beam center, causing microscopic buckling and bending of the membrane within the illuminated region. Here, we report translational and photophysical measurements of single fluorescent molecules in lipid bilayers using confocal microscopy at reduced optical power (0.04-1.3 mW, 20-600 * Corresponding author. E-mail:
[email protected]. Phn: (301) 975-5951. Fax: (301) 330-3447.
10.1021/jp0008546
kW/cm2). Heating effects at these powers for both absorbing and nonabsorbing membrane bilayers using similar optical gradients have been estimated by others to be small (i.e., 20 ms and indicates the expected Poisson behavior for molecules that are photobleached shortly after arrival. A diffusion simulation run with parameters matched to experimental conditions (open circles) reveals that some deviation from Poisson behavior is expected when photobleaching is neglected, but not to the extent observed. (B) Deviation from Poisson behavior as a function of optical power applied to the membrane. Points are calculated by normalizing the difference between the number of observed intervals (Nobs) and the number of expected intervals (Npois) for ∆t < 20 ms. A Boltzmann model that excludes TRITC fluorescence saturation kinetics gives a poor fit to the data (Inset). Incorporation of the measured saturation kinetics produces an excellent match to the data, implying that the transition polarizability of the label plays a crucial role in enhancing the trapping potential (see text). Data are reported as the mean ( SEM of three 24 s recordings.
To estimate the trapping potential magnitude, we analyzed the elapsed time between successive arrivals of single molecules at the detection-circle periphery. If the illuminated region behaves as a perfect sink (i.e., all fluorophores are rapidly photobleached before exit), each fluorescence burst is independent and the resulting Markovian process should follow the Poisson equation
N(∆t) ) Re-β∆t
(3)
where R is constant and β is proportional to the fluorophore flux through the circle boundary. Alternatively, if no photodestruction occurs and a molecule is allowed to exit and re-enter
6106 J. Phys. Chem. B, Vol. 104, No. 26, 2000
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the detection circle multiple times, computer simulation shows that a positive deviation away from Poisson behavior at short time intervals is expected. As shown in Figure 3A, the measured time-interval distribution deviates markedly from both behavioral types for ∆t < 20 ms. Attraction toward the beam center can account for this result.20 If a molecule that diffuses in the vicinity of the detection circle is biased into the illuminated region by a weak trap, it will cross back-and-forth over the detection boundary with increased frequency. This causes an increased number of events spaced by short time intervals. The increase in deviation [(Nobs - Npois)/Nobs] with applied power produces a measure of the well depth, if the characteristic beam radius remains constant. Similar arguments have been offered to interpret laser-induced diffusion biases of fluorescent spheres and single R6G molecules in free solution.8,9 From the experimentally determined threshold intensities (3 standard deviations above background) and estimates for Imax, we determine that the threshold radius for defining fluorescent events grew from 1.52ω (≈40 µW) to 1.84ω (1.3mW). To test the effects of increasing radius on [(Nobs - Npois)/Nobs], we conducted simulations at both the minimum and maximum threshold radii. Under simulation conditions (i.e., no photobleaching), we found [(Nsim - Npois)/Nsim] to increase by ≈0.03. In the limit of rapid photobleaching, ∆[(Nobs - Npois)/Nobs] ) 0. Because photobleaching readily occurs under real experimental conditions, 0.03 is an upper limit for the expected ∆[(Nobs - Npois)/Nobs] due to an increase in the threshold radii. Over the range of powers in Figure 3B, the observed ∆[(Nobs - Npois)/Nobs] is relatively large; thus, artifacts due to an increase in radius can be ruled out. The escape of a trapped molecule from a shallow potential well can be modeled by a Boltzmann factor exp(-U/kT).7,9,21,22 Conversely, the probability of a molecule remaining in the well is [1 - exp(-U/kT)]. Assuming a constant polarizability, substitution of uP for U, where u is the trapping potential per unit power, allows the data in Figure 3B to be fit using a nonlinear least-squares routine. However, as indicated in the inset, a simple linear increase in power results in a poor match to the data. The best fit using this simple model can account for only the low power data points, with significant deviation beginning at ≈0.2 mW, a power that also corresponds to the saturation point in the fluorescence emission intensity curve (Figure 2). This correspondence suggests that the force generated on the labeled molecule arises from the enhanced transition polarizability. If this is true, the potential well depth should increase in proportion to the fluorescence cycling rate, kf, rather than as a linear function of power (P). Replacing the power parameter in the exponent with a normalized function of kf results in the equation
(
kf (Nobs - Npois)/Nobs ∝ 1 - A exp -u /kT kmax
)
(4)
where
kmax ) lim ) Φ(τ + knr-1)-1 Pf∞
(5)
is the normalization factor and A is a prefactor that describes the potential well geometry.21,22 Values for kf and kmax are acquired from the fit to the data in Figure 2. By allowing u and A to vary freely, eq 4 produces an excellent fit to the data in Figure 3B and gives u ) 0.031 ( 0.002 eV/mW, a value slightly larger than kT (0.025 eV) at 1 mW.
Conclusion Two factors can account for the apparent trapping potential. The energy gained by the bilayer portion illuminated with the laser (0.04-1.3 mW) gives a baseline potential that approaches kT.11 The energy required to exceed kT may be attributed to the resonant polarizability enhancement of the fluorescent label. Accurate polarizability values in electronic transition regions are difficult to obtain from both experiment and theory. However, a recent measurement of R6G, a TRITC structural analogue, indicates a transition polarizability that is increased by 30-100.23 To our knowledge, no data exist for the transition polarizability of TRITC itself. Assuming that the published R6G value is a reasonable estimate for TRITC-DHPE, the energy available to bias diffusion exceeds kT. The results reported here are significant for a variety of microscopies that employ large optical gradients. Confocal microscopy has been widely used to study ensembles of fluorescent molecules in cells and lipid membranes.24 The technique has only recently been applied to the study of membrane kinetics at the single-molecule level.25 To make accurate measurements in cells or model membranes, precautions must be taken to avoid the apparent perturbations caused by high optical fields. For a given measurement, the power density should be low enough to avoid diffusion bias, but high enough to generate a good signal-to-noise ratio. For the fluorescent labels of our study, this power level is between 10 and 50 µW. Acknowledgment. D.L.B. gratefully acknowledges the National Research Council and NIST for fellowship support. Commercial names of materials and apparatus are identified only to specify the experimental procedure. This does not imply a recommendation by NIST, nor does it imply that they are the best available for the purpose. References and Notes (1) Keller, R. A.; Ambrose, W. P.; Goodwin, P. M.; Jet, J. H.; Martin, J. C.; Wu, M. Appl. Spectrosc. 1996, 50 (7), A12-A32. (2) Nie, S.; Zare, R. N. Annu. ReV. Biophys. Biomol. Struct. 1997, 26, 567. (3) Xie, X. S.; Trautmann, J. K. Annu. ReV. Phys. Chem. 1998, 49, 441. (4) Schmidt, Th.; Schutz, G.; Baumgartner, W.; Gruber, H.; Schindler, H. J. Phys. Chem. 1995, 99, 17662. (5) Sonnleitner, A.; Schutz, G.; Schmidt, Th. Biophys. J. 1999, 77, 2638. (6) Ide, T.; Yanagida, T. Biochem. Biophys. Res. Commun. 1999, 265, 595. (7) Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Opt. Lett. 1986, 11, 288. (8) Chiu, D.; Zare, R. N. J. Am. Chem. Soc. 1996, 118, 6512. (9) Osborne, M.; Balasubramanian, S.; Furey, W.; Klenerman, D. J. Phys. Chem. B 1998, 102, 3160. (10) Bar-Ziv, R.; Menes, R.; et al. Phys. ReV. Lett., 1995, 75, 3356. (11) For lipids within a bilayer, the maximum energy gained when a molecule falls into the trap is given by 〈U〉δaol, [Nelson, P.; Powers, T. Phys. ReV. Lett. 1995, 74, 3384] where 〈U〉 is the optical energy density, δ is the dielectric contrast (≈0.19) between the lipid and the surrounding 1 M KCl solution, and ao is the area of a molecule’s head. Summing over the region illuminated by 50 mW gives an interaction energy of ≈0.65 eV, or ≈25kT. For the optical power range used in the present work (0.04-1.3 mW), an interaction energy of 0.02-0.65kT is calculated. (12) Bar-Ziv, R.; Moses, E.; Nelson, P. Biophys. J. 1998, 75, 294. (13) Schonle, A.; Hell, S. Opt. Lett. 1998, 23, 325. (14) Mueller, P.; Rudin, D.; Tien, H.; Wescott, W. C. Nature 1962, 194, 979. (15) Kasianowicz, J.; Bezrukov, S. Biophys. J. 1995, 69, 94. (16) Fluorescent bursts from R6G in dilute (500 pM) aqueous solution were recorded as individual molecules diffused into and out of the
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J. Phys. Chem. B, Vol. 104, No. 26, 2000 6107
three-dimensional confocal probe volume. Bursts were logged for 0.8 s intervals with a 100 µs bin width. The real-time record was autocorrelated and fit to the function
g(t) ) 1 +
(
)(
1 4Dt 1+ 2 〈N〉 ω
-1
1+
)
4Dt z2
-1/2
following [Rigler, R.; et al. Eur. Biophys. J. 1993, 22, 169] where 〈N〉 is the average number of molecules in the volume and ω is the characteristic radial dimension. By assuming a diffusion coefficient, D, of 2.8 × 10-6 cm2/s for R6G in water [Rigler, R.; et al. Eur. Biophys. J. 1993, 22, 169], the nonlinear least-squares fit produced an average value of ω ) 264 ( 14 nm. (17) Nie, S.; Chiu, D.; Zare, R. N. Anal. Chem. 1995, 67, 2849. (18) Fahey, P. F.; Koppel, D. E.; Barak, L. S.; Wolf, D. E.; Elson, E. L.; Webb, W. W. Science 1977, 195, 305. (19) Soper, S.; Nutter, H.; Keller, R.; Davis, L.; Shera, E. Photochem. Photobiol. 1993, 57, 972.
(20) It is possible that a light-induced single-molecule blinking phenomenon may also contribute to deviation away from expected behavior. Emission fluctuations on the time scale of milliseconds to seconds have been reported for a few immobilized fluorescent compounds and are thought to be the result of dynamic alterations in conformation [Weston, K.; Buratto, S. J. Phys. Chem A 1998, 102, 3635]. However, we observe similar interburst-interval curves for both headgroup labeled TRITC and C-12 labeled BODIPY lipids. Given the gross structural differences between the two molecules, it is unlikely that both exhibit comparable blinking characteristics. Furthermore, the simulation data of Figure 3A demonstrate that the onset of deviation away from Poisson prediction is consistent with the time scale of translational motion, as characterized by the measured D. (21) Kramers, H. A. Physica 1940, 7, 284. (22) Simon, A.; Libchaber, A. Phys. ReV. Lett. 1992, 68, 3375. (23) Xu, Z.; He, G.; Elking, M. J. Chem. Phys. 1997, 107 (10), 3947. (24) Pawley, J., Ed. Handbook of Biological Confocal Microscopy; Plenum Press: New York, 1990. (25) Schwille, P.; Korlach, J.; Webb, W. Cytometry 1999, 36, 176.
