Beyond the Hookean Spring Model: Direct Measurement of Optical Forces Through Light Momentum Changes

The ability to measure forces in the range of 0.1-100 pN is a key feature of optical tweezers used for biophysical and cell biological studies. Analysis of the interactions between biomolecules and the forces that biomolecular motors generate at the single-molecule level has provided valuable insights in the molecular mechanisms that govern key cellular functions such as gene expression and the long-distance transport of organelles. Methods for determining the minute forces that biomolecular motors generate exhibit notable constraints that limit their application for studies other than the well-controlled in vitro experiments (although recent advances have been made that permit more quantitative optical tweezers studies insight living cells). One constraint comes from the linear approximation of the distance vs. force relationship used to extract the force from the position of the bead in the trap. This commonly employed "indirect" approach, although usually sufficiently precise, restricts the use of optical tweezers to a limited range of displacements (typically up to ±150 nm for small beads). Measurements based on the detection of the light-momentum changes, on the other hand, offer a "direct" and precise way to determine forces even when the generated displacements reach the escape point, thus covering the complete force range developed by the trap. In this chapter, we detail the requirements for the design of a force-sensor instrument based on light-momentum changes using a high-numerical-aperture objective lens and provide insights into its construction. We further discuss the calibration of the system and the main steps for its routine operation.