Biased Diffusion, Optical Trapping, and Manipulation of Single Molecules in Solution

The detection of a single molecule in solution has recently aroused considerable interest, both for its analytical utility and for gaining insight into the chemistry and dynamics at the singlemolecule level.1-3 The ability to manipulate a single molecule in solution has even more exciting possibilities. In this communication, we present our investigation of the diffusional behavior of a single molecule near the focal volume of a confocal fluorescence microscope. We report the first direct optical trapping and manipulation of a single molecule in solution, in particular, a single λ DNA molecule (≈48 kb, isolated from the bacteriophage lambda and purchased from New England Biolabs) labeled with YOYO dye (≈1 YOYO per 20 bases) under conditions in which the λ DNA supercoils. Many studies have been made on DNA in which it is stretched or transported by attaching DNA to a polystyrene bead and using an optical tweezer to exert force on the bead.4-6 This report uses the same physical principles, but it describes the direct action of the radiation field on DNA. In confocal fluorescence microscopy, the entrance of a single molecule into the laser probe volume is generally assumed to follow Poissonian statistics which characterizes the time behavior of uncorrelated random events.7-9 At long timescales, we found complete agreement with the Poissonian model, in which the distribution of intervals of entry into the probe volume decreases exponentially with time. At short timescales, however, we found dramatic deviation from the behavior predicted by Poisson statistics. Figure 1 shows a representative signal from a 14 nm fluorescent polystyrene sphere containing roughly 15 fluorescein-like dye molecules per particle. When the sphere enters the probe volume, it emits a burst of photons that gives rise to a sharp peak in our spectrum. It can be seen from the inset of Figure 1 that several photon bursts are often buried within a larger burst when the timescale is expanded. These buried bursts are most likely caused by the same molecule recrossing into the probe volume. Figure 2 shows the Poissonian analysis of the resulting signal from the 14 nm particles after many spectra were accumulated.10 The straight line drawn is the least-squares fit to the Poissonian distribution. A large deviation from the fit begins at about 600 ms; the re-entry probability is 18.9 times higher than that expected between 6 and 60 ms where the deviation is most pronounced. Part of the deviation can be explained by the recrossings of the same molecule into the focal volume once it is already in the vicinity of the probe. This probability is approximately 35% for unbiased diffusion,9 which is insufficient to explain the actual deviation. In view of this discrepancy, we postulate that the increased recrossing frequencies is caused by an optical trapping potential that arises from the interaction between the electric field of the laser beam and the electric dipole moment induced by the laser beam in the molecule through its polarizability.11 To test this hypothesis, we superimposed the probe beam (488 nm at 0.5 mW from an argon ion laser) with a trapping beam (830 nm at variable power from a diode laser). This procedure allows us to vary the trapping potential independently without perturbing the signal generated by the probe beam. We find in a typical data set that whereas with no power in the trapping beam the number of recrossings between 6 and 60 ms is 5881, the recrossing number becomes 7407 at 10 mW, 8243 at 17 mW, 9244 at 24 mW, and 10 716 at 31 mW. As expected, the (1) Davis, L. M.; Fairfield, F. R.; Harger, C. A.; Jett, J. H.; Keller, R. A.; Hahn, J. H.; Krakowski, L. A.; Marrone, B. L.; Martin, J. C.; Nutter, H. L.; Ratliff, R. L.; Shera, E. B.; Simpson, D. J.; Soper, S. A. Genet. Anal. Tech. Appl. 1991, 8, 1-7. (2) Eigen, M.; Rigler, R. Proc. Natl. Acad. Sci. USA 1994, 91, 57405747. (3) Nie, S.; Chiu, D. T.; Zare, R. N. Science 1994, 266, 1018-1021. (4) Smith, S.; Cui, Y.; Bustamante, C. Science 1996, 271, 795-799. (5) Svoboda, K.; Block, S. Annu. ReV. Biophys. Biomol. Struct. 1994, 23, 247-285. (6) Chu, S. Science 1991, 253, 861-866. (7) Nie, S.; Chiu, D. T.; Zare, R. N. Anal. Chem. 1995, 67, 2849-2857. (8) Hungerford, J. M.; Christian, G. D. Anal. Chem. 1986, 58, 25672568. (9) Feller, W. An Introduction to Probability Theory and its Applications; John Wiley and Sons: New York, 1957; pp 327-330. (10) The distribution of photon burst intervals that satisfies Poisson statistics is given by F(∆t) ) â exp(-â∆t), where â is the characteristic appearance frequency of a photon burst, ∆t is the time interval between successive photon bursts, and F(∆t) is the number of photon bursts that occur with value ∆t. A plot of ln(F(∆t)) vs ∆t should result in a straight line for photon bursts satisfying the Poisson statistics. (11) Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Opt. Lett. 1986, 11, 288-290. Figure 1. Signal observed from a 10-11 M solution of fluorescent polystyrene spheres. Data acquisition speed is 167 points/s (6 ms integration), and the CW laser excitation has a wavelength of 488 nm at a power of 0.5 mW. The inset is an expanded view of the bracketed section of the data.