Optical Tweezers: Trap Stiffness for Calculating External Force

Question

I've been reading this article about calibrating optical tweezers (finding the trap stiffness $\kappa$). Around the end of section 2.2 it says

Once an optical tweezers is calibrated, a constant and homogeneous external force $F_{ext,x}$ shifts the equilibrium position of the trap. The value of the force can be obtained as $$F_{ext,x}=\kappa_{x}\Delta x_{eq}$$ where $\Delta x_{eq}$ is the average particle displacement from the original equilibrium position without the external force.

I'm confused why there is a constant external force that's shifting the equilibrium position of the trap. As I understood, the trapped particle should be in an equilibrium position where the force (or rather momentum) of the laser beam is equal to the force of gravity acting on the particle.

Answer 1

Once you have your optical trap calibrated and stable, you want to do something useful with it. Maybe you wish to measure flow-induced drag; this is an external force. Maybe you wish to measure the stiffness of a molecule that you'll stretch between the particle and a rigid substrate; this is an external force. Maybe you wish to measure the pulling force of a transmembrane receptor of a biological cell; this is an external force. Maybe you wish to weigh the particle by its Brownian motion; this depends on the effective stiffness of its equilibrium position, and temperature acts as a driving force for motion around that position. As you note, gravity has already been corrected for in the calibration process, but there are many other forces of interest!