Feedback Trap

Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

Feedback traps can create arbitrary virtual potentials for exploring the dynamics of small Brownian particles. In a feedback trap, the particle position is measured periodically and, after each measurement, one applies the force that would be produced by the gradient of the “virtual potential,” at the particle location. Virtual potentials differ from real ones in that the feedback loop introduces dynamical effects not present in ordinary potentials. These dynamical effects are caused by small time scales associated with the feedback, including the delay between the measurement of a particle’s position and the feedback response, the feedback response that is applied for a finite update time, and the finite camera exposure from integrating motion. Here, we characterize the relevant experimental parameters and compare to theory the observed power spectra and variance for a particle in a virtual harmonic potential. We show that deviations from the dynamics expected of a continuous potential are measured by the ratio of these small time scales to the relaxation time scale of the virtual potential.

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References

  1. 1.
    A.E. Cohen, W.E. Moerner, Method for trapping and manipulating nanoscale objects in solution. App. Phys. Lett. 86, 093109 (2005)ADSCrossRefGoogle Scholar
  2. 2.
    A.E. Cohen, W.E. Moerner, Suppressing Brownian motion of individual biomolecules in solution. PNAS 103, 4362–4365 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    A.E. Cohen, Control of nanoparticles with arbitrary two-dimensional force fields. Phys. Rev. Lett. 94, 118102 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    Q. Wang, W.E. Moerner, Single-molecule motions enable direct visualization of biomolecular interactions in solution. Nat. Methods 11(5), 556–558 (2014)CrossRefGoogle Scholar
  5. 5.
    A.E. Cohen, W.E. Moerner, Principal-components analysis of shape fluctuations of single DNA molecules. PNAS 104, 12622–12627 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    R.H. Goldsmith, W.E. Moerner, Watching conformational- and photodynamics of single fluorescent proteins in solution. Nature Chem. 2(179–186) (2010)Google Scholar
  7. 7.
    A.P. Fields, A.E. Cohen, Electrokinetic trapping at the one nanometer limit. PNAS 108, 8937–8942 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    J.A. Germann, L.M. Davis, Three-dimensional tracking of a single fluorescent nanoparticle using four-focus excitation in a confocal microscope. Opt. Express 22, 5641–5650 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    M. Kayci, H.-C. Chang, A. Radenovic, Electron spin resonance of nitrogen-vacancy defects embedded in single nanodiamonds in an ABEL trap. Nano Lett. 14, 5335–5341 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Jun, J. Bechhoefer, Virtual potentials for feedback traps. Phys. Rev. E 86, 061106 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    M. Gavrilov, Y. Jun, J. Bechhoefer, Particle dynamics in a virtual harmonic potential. Proc. SPIE. 8810 (2013)Google Scholar
  12. 12.
    Y. Jun, M. Gavrilov, J. Bechhoefer, High-precision test of Landauer’s principle in a feedback trap. Phys. Rev. Lett. 113, 190601 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    D.Y. Lee, C. Kwon, H.K. Pak, Nonequilibrium fluctuations for a single-particle analog of gas in a soft wall. Phys. Rev. Lett. 114, 060603 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    M. Gavrilov, J. Koloczek, and J. Bechhoefer. Feedback trap with scattering-based illumination. In Novel Techniques in Microscopy, page JT3A. 4. Opt. Soc. Am., 2015Google Scholar
  15. 15.
    M. Gavrilov, J. Bechhoefer, Arbitrarily slow, non-quasistatic, isothermal transformations. EPL (Europhys. Lett.) 114(5), 50002 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    Momčilo Gavrilov, John Bechhoefer, Erasure without work in an asymmetric, double-well potential. Phys. Rev. Lett. 117, 200601 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    Karel Proesmans, Yannik Dreher, Momčilo Gavrilov, John Bechhoefer, Christian Van den Broeck, Brownian duet: a novel tale of thermodynamic efficiency. Phys. Rev. X 6, 041010 (2016)Google Scholar
  18. 18.
    R. Landauer, Irreversibility and heat generation in the computing process. IBM J. Res. Develop. 5, 183–191 (1961)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–190 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Charlie Gosse, Vincent Croquette, Magnetic tweezers: micromanipulation and force measurement at the molecular level. Biophys. J. 82, 3314–3329 (2002)CrossRefGoogle Scholar
  21. 21.
    A.E. Cohen, Trapping and manipulating single molecules in solution. Ph.D. thesis, Stanford University, 2006Google Scholar
  22. 22.
    Q. Wang, W.E. Moerner, Optimal strategy for trapping single fluorescent molecules in solution using the ABEL trap. Appl. Phys. B 99, 23–30 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    A.P. Fields, A.E. Cohen, Optimal tracking of a Brownian particle. Opt. Express 20, 22585–22601 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    A.J. Berglund, M.D. McMahon, J.J. McClelland, J.A. Liddle, Fast, bias-free algorithm for tracking single particles with variable size and shape. Opt. Express 16, 14064–14075 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    A.E. Cohen, W.E. Moerner, An all-glass microfluidic cell for the ABEL trap: Fabrication and modeling. Proc. SPIE 5930, 191–198 (2005)ADSGoogle Scholar
  26. 26.
    A.E. Cohen, W.E. Moerner, The anti-brownian electrophoretic trap (ABEL trap): fabrication and software. Proc. SPIE 5699, 296–305 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    S.G. Serra, A. Schneider, K.Malecki, S.E. Huq, W. Brenner, A simple bonding process of SU-8 to glass to seal a microfluidic device, 4M 2007 - Third international Conference on Multi-material Micro Manufacture-Proceedings, (2007), pp. 43–46Google Scholar
  28. 28.
    G.H. Hardy, E.M. Wright. An Introduction to the Theory of Numbers, 6th edn. (Oxford University Press, 2008)Google Scholar
  29. 29.
    Kevin McHale, Hideo Mabuchi, Precise characterization of the conformation fluctuations of freely diffusing DNA: beyond Rouse and Zimm. J. Am. Chem. Soc. 131, 17901–17907 (2009)CrossRefGoogle Scholar
  30. 30.
    M. Gavrilov, Y. Jun, J. Bechhoefer. Real-time calibration of a feedback trap. Rev. Sci. Instrum. 85(9), (2014)Google Scholar
  31. 31.
    A. Weigel, A. Sebesta, P. Kukura, Dark field microspectroscopy with single molecule fluorescence sensitivity. ACS Photonics 1, 848–856 (2014)CrossRefGoogle Scholar
  32. 32.
    Maksymilian. Pluta. Advanced Light Microscopy: Special Methods, vol. 2 (Elsevier, 1989)Google Scholar
  33. 33.
    P. Lebel, A. Basu, F.C Oberstrass, E.M. Tretter, Z. Bryant, Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension. Nat. Methods 11, 456–462 (2014)Google Scholar
  34. 34.
    J. Koloczek, Non-Fluorescent Particle Imaging For A Feedback Trap, Bachelor Thesis. University Konstanz, 2014Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Biophysics and Biophysical ChemistryJohns Hopkins UniversityBaltimoreUSA

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