Measurement Of The Non-conservative Force Generated By Optical Tweezers

Abstract

Optical tweezers have been widely used by biophysicists to measure forces in molecular processes on the single molecule level, such as the force generated by a motor molecular or the force required to unfold RNA. In these and similar force measurements, the usual assumption is that the force applied to a particle inside the tweezers is proportional to the displacement of the particle away from the trapping center, which would imply that the force field is conservative. However, the Gaussian beam model has indicated that the force field generated by optical tweezers is actually non-conservative, yet no experiments have measured or accounted for this effect. We introduce an experimental method that can measure the force field in optical tweezers with high precision without any assumptions about the functional form of the force field. The force field is determined by analyzing the Brownian motion of a trapped particle. We successfully measure the 3D force field with 10 nm resolution for a particle in the Rayleigh regime. The results can be well-approximated with the Gaussian beam model for small displacements, and the non-conservative effect becomes more prominent as the trapped particle is pulled farther away from the trapping center. The energy put into the system along different paths can be directly calculated using the force field. The assumption that Hooke's law applies to optical tweezers neglects the non-conservative component of the force field and can introduce a systematic error when measuring the force.