Transactions on Control Systems Technology

Transactions on Control Systems Technology Optimal tracking of a Brownian particle Optical tracking of a fluorescent particle in solution faces fundamental constraints due to Brownian motion, diffraction, and photon shot noise. Background photons and imperfect tracking apparatus further degrade tracking precision. Here we use a model of particle motion to combine information from multiple time-points to improve the localization precision. We derive successive approximations that enable realtime particle tracking with well controlled tradeoffs between precision and computational cost. We present the theory in the context of feedback electrokinetic trapping, though the results apply to optical tracking of any particle subject to diffusion and drift. We use numerical simulations and experimental data to validate the algorithm’s performance. Mechatronics Single-molecule study of molecular mobility in the cytoplasm of Escherichia coli The cytoplasm of bacterial cells is filled with individual molecules and molecular complexes that rely on diffusion to bring them together for interaction. The mobility of molecules in the cytoplasm has been characterized by several techniques mainly using fluorescent probes and ensemble methods. In order to probe the microenvrionment inside the cytoplasm as viewed by an individual molecule, we have studied single green fluorescent proteins (GFPs) diffusing in the cytoplasm of Escherichia coli cells at observation at rates ranging from 60 to 1000 Hz. Over long times the diffusion shows confinement due to the geometry of the cells themselves. A simulation in model cells using the actual distribution of cell sizes found in the experiments describes accurately the experimental results as well as reveals a short time diffusion coefficient that agrees well with that determined by ensemble methods. Higher short time diffusion coefficients can be obtained by filling the simulated cell with small spheres modeling cytoplasmic molecules and, depending on the density of particles included in the modeled cytoplasm, can approach the diffusion coefficient of GFPs found in water. Thus, single-molecule tracking combined with analysis using simple simulation of Brownian motion is able to reveal the main contributors to the GFP mobility in the cytoplasm of E. coli. Stochastic noise in atomic force microscopy Having reached the quantum and thermodynamic limits of detection, atomic force microscopy (AFM) experiments are routinely being performed at the fundamental limit of signal to noise. A critical understanding of the statistical properties of noise leads to more accu-rate interpretation of data, optimization of experimental protocols, advancements in instrumentation, and new measurement techniques. Furthermore, accurate simulation of cantilever dynamics requires knowledge of stochastic behavior of the system, as stochastic noise may exceed the deterministic signals of interest, and even dominate the outcome of an experiment. In this article, the power spectral density (PSD), used to quantify stationary stochastic processes, is introduced in the context of a thorough noise analysis of the light source used to detect cantilever deflections. The statistical properties of PSDs are then outlined for various stationary, nonstationary, and deterministic noise sources in the context of AFM experiments. Following these developments, a method for integrating PSDs to provide an accurate standard deviation of linear measurements is described. Lastly, a method for simulating stochastic Gaussian noise from any arbitrary power spectral density is presented. The result demonstrates that mechanical vibrations of the AFM can cause a logarithmic velocity dependence of friction and induce multiple slip events in the atomic stick slip process, as well as predicts an artifactual temperature dependence of friction measured by AFM.