Tutorials - Optical Tweezers

General aspects

Measurement parameters
Microscopic objects in a viscous medium undergo Brownian motion. If the particles are also exposed to a harmonic potential - as in an optical trap - the Brownian motion will be confined to a specific volume, changing the diffusive behavior. This predictable behavior is used for the calibration of the trap. Furthermore, the measurement of thermal fluctuations of a particle provides information on the particle's interaction with its local environment. Any obstacle will have a pronounced influence on its displacement freedom. Quantitatively, these changes can be tracked by evaluating the fluctuation range of the movement, the shift of the particle's mean position or by looking at the autocorrelation time. The values give quantitative information on changes in viscosity or binding.
The flipside of the Brownian motion comes up when performing force spectroscopy or tracking experiments with an optical tweezers. The particle's movement introduces noise into the measurements, fundamentally limiting the spatial, temporal and the force resolution of the measurements. Fortunately, these effects can be calculated and the experimental parameters can be tuned to reduce these effects as long as the given experiment permits it. Parameters like the bead size, bandwidth and stiffness can be optimized to decrease the noise of the probe, which is defined as follows:

According to this equation, spatial resolution can be improved by decreasing the bandwidth B and the viscous drag γ, which itself is proportional to the viscosity of the medium and the diameter of the object. The stiffness κ of the system has the greatest impact on resolution, which includes both the intrinsic stiffness of the probe and the stiffness of the molecule attached to the probe. In the case of optical tweezers, this probe stiffness is mainly influenced by the trap stiffness. The stiffness of the tether linking molecule and probe may additionally play an important role in pulling experiments.
Force resolution is independent of the stiffness, and can thus only be improved by decreasing the drag or the bandwidth. Decreasing the bandwidth on the other hand will also decrease the temporal resolution. In the end, the proper selection of these parameters strongly depends on the individual experiment type.

Molecule attachment
Depending on the experimental assay, one or both ends of the molecule under study have to be attached to a bead or to the surface. Generally speaking, the binding of the molecule has to be stable under the experiment buffer conditions, sustain at least the load that will be exerted on the particle, and leave any biophysical properties of the molecule investigated unaffected. In case of a single-sided attachment, well-established methods of non-specific adsorption can be applied. However as these techniques are not applicable to all molecules, and as unambiguous binding is often crucial to dual-sided attachment, schemes for specific binding are to be used. In the first step, the molecules are specifically (often covalently) labeled with ligands or antibodies. The linkage is performed either chemically or enzymatically. Commonly used labels include the ligand-receptor pair biotin-avidin as well as the antigen-antibody pair digoxigenin and anti-digoxigenin. Using these common linker pairs highly facilitates the attachment of the molecules to the particles, as a broad range of functionalized polystyrene and silica beads are already commercially available. Regardless of the type of experiment, non-specific binding of the bead with other beads, the molecule of interest or the surface of the experiment chamber has to be excluded. Non-specific binding can introduce errors in the measured data or just lower the concentration of active beads such that no data can be recorded. To prevent such non-specific interactions, particles and surfaces are passivated with inert proteins such as bovine serum albumin (BSA) or casein and non-ionic surfactants. Also, tuning buffer conditions such as lowering of salt concentration or addition of mild detergents can be useful to minimize interactions.

Force spectroscopy mode

Force spectroscopy measurements performed with an optical tweezers setup give access to forces in the range of from 0.1 up to several hundred picoNewtons. By actively applying force to a molecule, measurements of the force-extension relationship (elasticity) can be performed. By quantifying rupture forces, information on bond energies can be obtained. Furthermore, energy landscapes of molecular bonding can be unraveled by analyzing binding or enzymatic kinetics at different forces and pulling rates (so-called dynamic force spectroscopy).

Depending on the optical tweezers setup at hand and the experiment to be performed, there are multiple assay configurations to perform force spectroscopy measurements. Analogous to an AFM experiment, the molecule of interest can be clamped between the glass surface of the chamber and the probe held by the trap. In this tethered assay, the molecule under investigation can then be stretched or unfolded by moving either the stage or the trap. Accordingly, the tethered assay can be performed with a simple setup where the trap is not mobile - a fine positioning of the sample by a piezo table is sufficient in this case. If a dual trap setup is available, the extension experiment can be performed in a dumbbell assay.

Instead of attaching the free end of the molecule to the surface, it is attached to a second bead, which is held in a second, independent optical trap. By moving one of the traps, a calibrated force can be applied to the clamped molecule.

A dumbbell experiment, in which both traps are simultaneously monitored, can significantly increase the signal-to-noise ratio as compared to an experiment where only the signal of one trap is registered. In a dumbbell configuration, the movement of both beads is correlated. By monitoring the movement of the beads in both traps, a differential measurement on the molecules can be performed, improving the overall resolution by cancelling drift effects in the system.

The experimental setup can not only be utilized to exert an increasing force onto a clamped molecule, but also to apply a constant force. By using a feedback algorithm, the trap can be steered such that the bead is always exposed to a constant force (force clamp). The force range of optical tweezers makes it a powerful tool to investigate single molecules: elasticity, rupture forces and forces associated with the activity of proteins, be it motor or DNA processing proteins. Areas of investigations further include the processive stepping of motor proteins such as kinesin and myosin. The force-extension relationship has been probed on several individual polymers, the most prominent being nucleic acids. Since the first single-molecule stretching experiments on DNA, many reports on its elasticity have appeared. Those fundamental investigations have paved the way for measurements including processive, DNA-binding proteins, such as DNA and RNA polymerase. Those experiments yielded data on the force and step size of the protein's DNA or RNA polymerisation. Optical tweezers do not only allow measurements on single molecules, but also investigations on cells. Measurements on single cells include the investigation of the strength of receptor binding and other adhesion forces.

Tracking mode

An optical tweezers setup including a fast detection system, a steerable trap and an appropriate feedback algorithm can be used for tracking experiments. If the particle is to be investigated with as little bias on its movement as possible, the trap should follow the movement of the particle. In this kind of experimental design, the particle only senses a very soft trapping force, still allowing it to probe its environment with minimal influence and respond freely to the internal and external forces exerted on it. If desired, it is also possible to apply a force other than zero to the particle and use feedback to maintain this force.

Crucial experimental parameters for fast and reliable tracking are a fast detection and a fast steering system. Accurate and fast position detection is provided in back-focal plane interferometry on quadrant photo diodes. If the displacement of the particle exceeds a certain threshold, the optical trap has to follow the particle’s movement. The key element to this detection scheme is that the measured signal is sensitive to displacements relative to the trap center, but not to movements of the trap itself. The trap is typically moved by the use of AODs or galvanometric mirrors. It is also possible to move the particle relatively to the trap by moving the sample stage just in the opposite direction of the particle’s movement. Piezo tables allow a sufficiently fast movement to perform tracking via the sample stage.

Tracking experiments are both useful when performing single molecule measurements and experiments with cells. During experiments with motor proteins or other processive proteins like the RNA polymerase, the enzymatic activity pulls the molecules out of the trap and thereby increases the restoring force acting on the particle. Tracking can be very useful in order to keep the force acting on the particle constant. Another useful application is the tracking of directed or random motion, be it lateral diffusion in a cell membrane. Moreover, tracking of active processes exerted by the cell can be performed, as well as measurements of local viscosities inside a cell or one of its compartments. The high bandwidth of this kind of tracking experiments, as compared to investigations with a camera, allows a precise reconstitution of a trajectory in time and space. The path taken by the particle can be described with nm precision and down to µs time resolution.