Auto- and cross-power spectral analysis of dual trap optical tweezer experiments using Bayesian inference

Review of Scientific Instruments - Tập 83 Số 9 - 2012
Yann von Hansen1,2, Alexander Mehlich2, Benjamin Pelz2, Matthias Rief2, Roland R. Netz1,2
1Freie Universität Berlin 1 Department of Physics, , 14195 Berlin, Germany
2Technische Universität München 2 Physics Department, , 85748 Garching, Germany

Tóm tắt

The thermal fluctuations of micron-sized beads in dual trap optical tweezer experiments contain complete dynamic information about the viscoelastic properties of the embedding medium and—if present—macromolecular constructs connecting the two beads. To quantitatively interpret the spectral properties of the measured signals, a detailed understanding of the instrumental characteristics is required. To this end, we present a theoretical description of the signal processing in a typical dual trap optical tweezer experiment accounting for polarization crosstalk and instrumental noise and discuss the effect of finite statistics. To infer the unknown parameters from experimental data, a maximum likelihood method based on the statistical properties of the stochastic signals is derived. In a first step, the method can be used for calibration purposes: We propose a scheme involving three consecutive measurements (both traps empty, first one occupied and second empty, and vice versa), by which all instrumental and physical parameters of the setup are determined. We test our approach for a simple model system, namely a pair of unconnected, but hydrodynamically interacting spheres. The comparison to theoretical predictions based on instantaneous as well as retarded hydrodynamics emphasizes the importance of hydrodynamic retardation effects due to vorticity diffusion in the fluid. For more complex experimental scenarios, where macromolecular constructs are tethered between the two beads, the same maximum likelihood method in conjunction with dynamic deconvolution theory will in a second step allow one to determine the viscoelastic properties of the tethered element connecting the two beads.

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Review of Scientific Instruments

Tập 83 Số 9

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