Monte Carlo Simulation of Brownian Motion using a Piezo-Actuated Microscope Stage.

Single particle tracking is a powerful tool for studying and understanding the motions of biological macromolecules integral to cellular processes. In the past three decades there has been continuous and rapid development of these techniques in both optical microscope design and in algorithms to estimate the statistics and positions of the molecule's trajectory. Although there has been great progress, comparison between different microscope configurations and estimation algorithms has been difficult beyond simulated data. In this paper we explore using a piezo actuated microscope stage to reproduce Brownian motion. Our goal is to use this as a tool to test performance of single particle tracking optical microscopes and estimation algorithms. In this study, Monte Carlo simulations were used to assess the ability of piezo actuated microscope stages for reproducing Brownian motion. Surprisingly, the dynamics of the stage together with configuration of the system allow for preservation of the Brownian motion statistics. Further, feed forward model inverse control allows for low error tracking of Brownian motion trajectories over a wide range of diffusion constants, varying stage response times, and trajectory discrete time steps. These results show great promise in using a piezo actuated microscope stage for testing single particle tracking experimental setups.