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Optical Tweezers

Optical tweezers are one the key tools biophysicists are using to unravel the energetics and kinetic pathways of single, biologically active molecules and proteins. This method has been used to study DNA mechanics, viral packaging mechanics and kinetics, RNA and DNA polymerization and a plethora of other topics. The short time the students have does not enable them to tackle a full, novel project using optical tweezers, especially considering most students have not worked with them before this course.

The aim of this project is three-fold: students become familiar with the necessary optical techniques and equipment to build the setup from scratch, they learn the theory necessary to understand why the particle is trapped and how thermal fluctuations will affect the particle, finally they write their own software to analyze the images and determine the 'stiffness' of the trap.

Ray optics gives us the simplest explanation as to why the particle remains in the trap despite random thermal fluctuations. The basic principle is that the light's momentum is conserved through the scattering process, or in other words, the total momentum is the same before the light sees the particle as after. The particle must have a different index of refraction from the surrounding medium in order to scatter the light and induce a momentum change. The trap itself is the source of a large optical gradient, which provides the directionality of the force - always towards the trap's center.

Diagram showing net momentum change during light scattering - the intensity gradient pulls the bead to the trap's center.

The students start with a simple diode laser (~30mW @ 632nm) and must convert this rather 'dirty' beam into a well colimated laser. The laser is then steered by a series of mirrors to a dichroic mirror whose reflectance is wavelength dependent. The laser is reflected by the dichroic through the objective (100X oil) and the trap forms at the focal point of the objective (working distance of roughly 250um). A bright field light source is on the other side of the objective allowing us to image the particle. The light 'pollution' from the laser is removed by a series of red light filters, and the final filtered image strikes a high-speed CCD camera for data collection. The total strength of the optical trap is regulated by a variable neutral density filter in the laser's path. This allows the students to measure the trap strength as a function of laser power. Finally, as before, the students must spatially calibrate the objective.

Diagram showing the basic components of the optical tweezers setup.

Trapping a particle is not a trivial task as it requires precise alignment of the laser into the objective, however once aligned data collection is fairly easy. Videos of the particle are taken a few minutes at a time in order to gather enough data to be statistically significant.

Real-time video of a trapped particle.

With data in hand, the students then venture into writing Matlab(c) code to analyze the particle's movement. The particle is sitting in an energy well created by the optical trap that is roughly Gaussian in shape, and hence approximately harmonic near the trap's center. Statistical mechanics tells us that all harmonic degrees of freedom contain the same amount of energy at equilibrium, hence we know:

where k is the trap stiffness and kT is the thermal energy unit. This means that a measure of the RMS movement of the particle directly tells us the stiffness of the trap. Measuring particle position requires a fair amount of image processing, the movies are read in as a series of image files; each file having a calculable x and y position for the particle.

A single intensity image showing the characteristic peak which indicates the particle's position.

After simple intensity adjustments (contrast, thresholding etc) the particle's x and y position is tracked using the centroid method, or in other words, tracking the position of the average intensity of the image over time. A histogram of the particle's position shows the probability with which the particle was found at any one position.

Histogram of particle's x and y position.

Finally, this histogram essentially maps out the energy surface felt by the particle in the trap via the partition function.

Representative plot of the energy surface.



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