Approximating Geometry of Unknown Particles from Coupled Brownian Motion in Optical Tweezers
DOI:
https://doi.org/10.33011/cuhj20264879Keywords:
Brownian motion, Optical tweezers, Optical trapping, Stochastic dynamicsAbstract
Abstract
Optical tweezers are widely used in biophysics to trap and manipulate microscopic particles and enable precise measurements of forces, diffusion, and mechanical properties at the single-particle level. In this project, we modeled the stochastic dynamics of asymmetric particles in optical tweezers using an overdamped Langevin equation that included a full translational-rotational (TR) diffusion tensor. We performed numerical simulations for particles of increasing geometric complexity and reconstructed diffusion tensors from simulated average trajectory data. We compared the reconstructed tensors to the true inputs and computed the resulting estimation error. The simulations showed that increasing particle asymmetry strengthened TR coupling and systematically increased diffusion tensor reconstruction error. These results suggest limitations of diffusion-based inference methods for complex particle geometries and motivate further study of how particle geometry influences stochastic dynamics in confined optical systems.
Lay Summary
At microscopic scales, particles in a fluid constantly undergo seemingly random movement, called Brownian motion, as they collide with surrounding molecules. Because shape influences drag, and drag determines diffusion, motion should carry geometric information. We therefore asked: Can motion alone be used to determine a particle’s geometry?
To investigate this, we built a computational model of a particle confined in an optical tweezer, which is a tightly focused laser beam used to trap microscopic objects. Optical tweezers were recognized with the 2018 Nobel Prize in Physics and are widely used in biophysics and medical research to manipulate cells, bacteria, and molecules. They are also widely used in research laboratories such as JILA. By assuming the restoring force increases linearly with distance from the trap center, we were able to isolate how shape influences motion.
For a sphere, which is symmetrical in every direction, movement along one axis does not affect movement along another. For more complex shapes, rotation and translation become linked: turning slightly can produce sideways motion. We implemented a model that accounts for both the restoring force and Brownian motion and can be applied to particles of any shape.
Using this framework, we simulated shapes based on real bacteria – a sphere, a rod, a comma-shaped form, and a spiral – and tracked motion inside the trap. From trajectories alone, we inferred the component of the particle’s motion determined by its shape and compared it to the values we had built into the model.
Our results showed that a particle’s movement contains information about its shape. For simple particles, recovery was accurate. As shapes became more irregular, estimates became less reliable. We also observed a tradeoff introduced by the optical trap: while it confines motion and enables experimental measurement, it also limits the natural motion that reveals geometric differences.
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11-August-2014
