Feedback Control of Brownian Motion for Single-Particle Fluorescence Spectroscopy

Citation

Berglund, Andrew John (2007) Feedback Control of Brownian Motion for Single-Particle Fluorescence Spectroscopy. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EBKX-BP40. https://resolver.caltech.edu/CaltechETD:etd-10092006-165831

Abstract

The stochastic Brownian motion of individual particles in solution constrains the utility of single-particle fluorescence microscopy both by limiting the dwell time of particles in the observation volume and by convolving their internal degrees of freedom with their random spatial trajectories. This thesis describes the use of active feedback control to eliminate these undesirable effects. We designed and implemented a feedback tracking system capable of locking the position of a fluorescent particle to the optic axis of our microscope, i.e., capable of tracking the two-dimensional, planar Brownian motion of a free particle in solution. A full theoretical description of the experiment is given in the language of linear stochastic control theory. The model describes both the statistics of the tracking system and provides a generalization of the theory of open-loop Fluorescence Correlation Spectroscopy (FCS) that accounts for fluctuations in fluorescence arising from competition between diffusion and damping. We find excellent agreement between theory and experiment. Using fluorescent polymer microspheres as test particles, we find that the observation time for these particles can be increased by 2-3 orders of magnitude over the open-loop scenario. The system achieves nearly optimal performance for moderately fast-moving particles at very low fluorescent count rates, comparable to those of a single fluorescent protein molecule. The system can classify particles in a binary mixture based on a real-time estimate of their diffusion coefficients (differing by a factor of ~4), achieving 90% success using fewer than 600 photons detected over 120 ms. Future directions for both the experimental and theoretical techniques are briefly discussed.

Thesis Files