The dynamics of large biological molecules such as nucleic acids and proteins are intrinsically random. Brownian motion drives the translational and intramolecular motion of each molecule so, assuming they do not interact, each molecule in solution moves independently of each other. When many molecules are observed at once, the absence of correlations between molecules obscures this motion entirely. This so-called "ensemble averaging" has led to the development of single-molecule detection methods, because by looking at only one or a few molecules at a time this uncorrelated random motion can be resolved.

Fluorescence Correlation Spectroscopy (FCS) is a very popular method for studying single molecules in solution. A laser beam is focused tightly into a solution containing fluorescence-labelled molecules that emit bursts of fluorescence when they drift through the laser focus. FCS has very high time resolution and has been used to measure many properties of biological molecules (See References below); however, FCS still does rely on averaging: each molecule remains in focus only briefly, so data from many molecules must be combined to generate good statistics. Furthermore, building statistics on time-scales longer than the average molecular dwell time is difficult, requiring an exponentially increasing number of single-molecule transits.

Our group has pioneered the field of closed-loop fluorescence correlation spectroscopy, in which we sense the position of one moving molecule in real time and use feedback to move either the optics (in x and y) or the sample (in z) to keep the molecule in focus. We have resolved fluorescence and diffusion statistics over time-scales spanning over 9 orders of magnitude (photon anti-bunching on the nanosecond scale, blinking on the millisecond scale, and diffusion over tens of seconds) on a single quantum dot diffusing freely in water. Our focus has always been the simultaneous development of careful experimental methods and sound theory, and as a result we have developed the most advanced system for tracking molecules in three dimensions[6]; an apparatus for tracking in two dimensions that nearly reached the shot-noise localization limit[8]; and nearly complete theoretical descriptions of the stochastic dynamics of the tracking apparatus[7,11] and the noise statistics of our localization method[10].

We are currently shifting focus away from technique development in favor of applications. We first applied our technique to the study of quantum dots, on which we measured the first-ever photon anti-bunching statistics on a single freely-diffusing particle and studied fluorescence intermittency on time-scales that are longer than FCS time-scales but shorter than what can be resolved with intensified CCD cameras. We are now moving into more biologically-relevant applications, in which we hope to measure conformational fluctuations on freely-moving nucleic acids and proteins. Right now our technique offers an alternative to popular methods for immobilizing such molecules on surfaces or in vesicles. In the future, by comparing methods we may be able to say with confidence just how disruptive immobilization methods are to the molecule's native dynamics.

The most difficult part of a single-molecule tracking experiment is sensing the position of the molecule. Both the excitation laser beam and the detection optics are cylindrically symmetric, so it is impossible to determine the position of the molecule in the plane perpendicular to the laser beam. Furthermore, the optics and beam have reflection symmetry above and below the focal plane of the beam, so it is impossible to determine the molecule's position along that axis as well. In order to sense the particle's position, these symmetries must be broken.

On the left, we illustrate the method we use for symmetry breaking in the plane perpendicular to the optical axis of the microscope. The laser beam is translated rapidly in a circular orbit about the origin O, resulting in a fluorescence signal that is brightest when the beam is close to the particle and dimmest when it is far away (see the plot on the right). This method was first proposed by Jörg Enderlein in 2000[4], first implemented by Enrico Gratton in 2003[5], and adopted by our group a year later. Our group's final-generation two-dimensional tracking apparatus was able to achieve localization of 210nm fluorescent spheres limited almost entirely by photon-counting noise using this technique[7]; this is a testament to its robustness. By encoding position information on a high-frequency component of the fluorescence signal we avoid low-frequency sources of noise that plague other localization methods, and by using an off-the-shelf DSP lock-in amplifier to demodulate the fluorescence signal we achieve low-noise position estimates without complicated computer software or unnecessary digital hardware.

In the drawing on the left we illustrate the three-dimensional localization method developed in our group. We use two rotating lasers that are focused in two different planes within the sample. Localization along the x- and y-axes is done just as we described above, and localization along the z-axis uses the same principle: the fluorescence signal is brightest from the beam focused closest to the particle. We modulate the power of the two beams 180 degrees out-of-phase at a high frequency, so that we can measure which beam produces the brightest fluorescence. An illustration of the way this modulation affects the fluorescence intensity is shown in the plot on the right. Just as for x and y, we demodulate the fluorescence signal with a lock-in amplifier to extract information about the z-position of the molecule.

This schematic shows the design of our apparatus, with the beam path beginning in the upper left. We use acousto-optic modulators (AOM) for both the beam rotation and the power-switching between the two beams. The first AOM deflects the beam along the y-axis, after which the beam is split in two. The other two AOMs complete the rotation for the split beams by deflecting along the x-axis. These x-axis AOMs are also responsible for alternating the power between the two beams with a 180-degree phase difference. The beams are recombined and passed through a microscope objective that focuses them into the sample. The focusing depth is different for the two samples because we adjust the divergence of each beam using a pair of lenses located immediately after the x-axis AOMs. We collect fluorescence through the same microscope objective that focuses the beams, image it onto photon-counting APDs, demodulate the measured fluorescence signal and feed back to piezo stages to follow the molecule's motion.

Above are photos of our apparatus. Most of the optics you see on the left are responsible for the beam deflection and modulation described in the previous section. The apparatus lives inside a big black box to keep room light off the APDs. Cardboard and vinyl shrouds are used to further isolate the APDs; they might look low-tech, but they work very well. Visible in the reflections off the walls of the box is the last remaining NBA-player-name-sharing member of MabuchiLab. The photo on the right shows where all the action takes place. The microscope objective is mounted on a 2-axis piezo stage. The objective itself is moved to follow the molecules along the x- and y-axes. The sample is mounted above the objective on a single-axis piezo stage. Along the z-axis, we track molecules by moving the entire sample.

The first results of all our hard work: error signals. We immobilized a fluorescent bead on a glass surface and scanned it through the focus of our microscope. We recorded the output of the lock-in amplifiers that make the position estimates. As you can see, the error voltages near the origin are linearly dependent on the particle's position along all three axes. This means that we can translate these voltages into real position estimates just by scaling them by the appropriate conversion factor, and hence we can also use them for tracking. Of course, we can not compute position estimates when the laser beam is too far from the particle simply because the beam has a finite diameter. This is why the error voltages begin to fall back to zero as we move farther from the bead.

And finally, the big payoff: tracking! The plots on the left show data acquired from a freely-diffusing quantum dot in water. The top shows the fluorescence we collected, and the bottom shows the positions of the tracking stages. Over the course of this trajectory the particle explored a region roughly 20000 times bigger than the laser focal volume, but on average was tracked to within 350nm of the center of the focal volume. Its diffusion coefficient was about 20 um^2/s, implying it was about 20nm in diameter. In the absence of feedback, this particle would remain within the focus of our laser for approximately 26ms; we have extended this time scale by three orders of magnitude! We are able to resolve photon statistics at extremely short time-scales because we have collected so many photons from this one quantum dot. The plot on the right shows that this quantum dot exhibits photon anti-bunching at times near 10ns; this is the first documented measurement of anti-bunching on a single freely-moving particle.

Our ability to track quantum dots suggests that we are getting quite close to being able to track single protein molecules in three dimensions. This ability would free researchers of the need to study proteins by immobilizing them on glass surfaces and, at the very least, will allow us to determine whether such immobilization methods affect the dynamics of the molecules under study. It certainly is an exciting time here in MabuchiBioLab!

(last updated 9/2007)

References

Group publications