Optical tweezers use highly focussed beams to trap microscopic particles in three dimensions. It is possible to carry out quantitative force measurements, on the order of piconewtons, if calibration of the system is done first. This requires finding the optical force for a given trapping power and position in the trap. Two tools commonly used for calibration are the camera and position-sensitive detector (PSD). Both are commonly used to track trapped particles, but they give complementary information. The camera gives the position of the particle. The PSD measures the defection of the beam, which is the force exerted on the particle. Since these data are obtained on different instruments, usually at vastly different rates, there is difficulty in synchronising the force and position data. Here we look at a force calibration method, without synchronising the data, by mapping force and position measurements. If the force-position relation is monotonic, then the median of the force distribution corresponds to the median of the position distribution; in general, the nth percentile of one corresponds to the (100-n)th percentile of the other. This intuitively works for traps whose force-position relations are monotonic, which includes Hookean traps like a single round symmetric trap. We discuss the limits at which this method can be applied to non-Hookean trapping arrangements, such as independent or coherent double-well traps.
We have estimated the mitotic forces exerted on individual isolated mammalian chromosomes using optical trapping. The chromosomes were trapped by an optical tweezers system created by a continuous wave ytterbium laser at 1064 nm. Individual chromosomes were trapped at different in situ powers in the range of ≈20-50 mW. The corresponding trapping forces were determined by a viscous drag method. In the range of laser powers used, the preliminary data show a linear relationship between the chromosome trapping forces and in situ powers. We have calculated the dimensionless trapping efficiency coefficient (Q) of the chromosomes at 1064 nm and the corresponding effects of trapping power on Q. The value of Q in our experiments was determined to be ≈0.01. The results of this study validate optical tweezers as a non-invasive and precise technique to determine intracellular forces in general, and specifically, the spindle forces exerted on the chromosomes during cell division.
With suitable calibration, optical tweezers can be used to measure forces. If the maximum force that can be exerted is of interest, calibration can be performed using viscous drag to remove a particle from the trap, typically by moving the stage. The stage velocity required to remove the particle then gives the escape force. However, the escape force can vary by up to 30% or more, depending on the particle trajectory. This can have significant quantitative impact on measurements. We describe the variation of escape force and escape trajectory, using both experimental measurements and simulations, and discuss implications for experimental measurement of forces.