Abstract
We consider fundamental bounds on the performance of single-particle tracking schemes based on non-imaging, fluorescence modulation methods. We calculate the noise density of a linearized position estimate arising from photon-counting statistics and find the optimal estimate of a freely diffusing particle’s position in the presence of this noise. For the experimentally relevant case of a Gaussian laser rapidly translated in a circular pattern, explicit expressions are derived for the noise density. Tracking performance limits are obtained by considering the variance in the estimated position of a Brownian particle with diffusion coefficient D in the presence of a noise density nm, which we find scales generically as (Dnm 2)1/2. For reasonable experimental parameters, a particle with diffusion coefficient D=1 μm2/s cannot be tracked with accuracy better than approximately 100 nm in three dimensions or 80 nm in two dimensions. Using a combination of exact results and numerical simulation, we construct a ‘phase diagram’ for determining parameter regimes in which a particle can be tracked in the presence of measurement noise.
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References
Ha T, Chemla DS, Enderle T, Weiss S (1997) Appl. Phys. Lett. 70:782
Enderlein J (2000) Appl. Phys. B 71:773
Enderlein J (2000) Single Mol. 1:225
Decca RS, Lee C-W, Wassall SR (2002) Rev. Sci. Instrum. 73:2675
Berglund AJ, Mabuchi H (2004) Appl. Phys. B 78:653
Andersson SB (2005) Appl. Phys. B 80:809
Levi V, Ruan Q, Kis-Petikova K, Gratton E (2003) Biochem. Soc. Trans. 31:997
Levi V, Ruan Q, Gratton E (2005) Biophys. J. 88:2919
Digman MA, Brown CM, Sengupta P, Wiseman PW, Horwitz AR, Gratton E (2005) Biophys. J. 90:1317
Berglund AJ, Mabuchi H (2005) Opt. Express 13:8069
Yildiz A, Forkey JN, McKinney SA, Ha T, Goodman YE, Selvin PR (2003) Science 300:2061
van Kampen NG (2001) Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam
Gardiner CW (1985) Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, Berlin
Jacobs OLR (1996) Introduction to Control Theory, 2nd edn. Oxford University Press, Oxford
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87.64.Tt; 87.64.Ni; 87.15.Vv
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Berglund, A., Mabuchi, H. Performance bounds on single-particle tracking by fluorescence modulation. Appl. Phys. B 83, 127–133 (2006). https://doi.org/10.1007/s00340-005-2111-z
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DOI: https://doi.org/10.1007/s00340-005-2111-z