Abstract

We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of the ABEL trap is limited by the latency of the feedback loop. In previous versions of the trap, this latency was set by the finite frame rate of the camera used for video-tracking. In the present system, the motion of the particle is tracked entirely in hardware (without a camera or image-processing software) using a rapidly rotating laser focus and lock-in detection. The feedback latency is set by the finite rate of arrival of photons. We demonstrate trapping of individual molecules of the protein GroEL in buffer, and we show confinement of single fluorophores of the dye Cy3 in water.

© 2008 Optical Society of America

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  1. R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
    [CrossRef] [PubMed]
  2. M. B. Comisarow and A. G. Marshall, "Frequency-sweep Fourier transform ion cyclotron resonance spectroscopy," Chem. Phys. Lett. 26, 489-490 (1974).
    [CrossRef]
  3. J. Enderlein, "Tracking of fluorescent molecules diffusing within membranes," Appl. Phys. B 71, 773-777 (2000).
    [CrossRef]
  4. A. J. Berglund and H. Mabuchi, "Feedback controller design for tracking a single fluorescent molecule," Appl. Phys. B 78, 653-659 (2004).
    [CrossRef]
  5. A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005).
    [CrossRef] [PubMed]
  6. A. J. Berglund and H. Mabuchi, "Performance bounds on single-particle tracking by fluorescence modulation," Appl. Phys. B 83, 127-133 (2006).
    [CrossRef]
  7. A. J. Berglund, K. McHale, and H. Mabuchi, "Fluctuations in closed-loop fluorescent particle tracking," Opt. Express 15, 7752-7773 (2007).
    [CrossRef] [PubMed]
  8. D. Montiel, H. Cang, and H. Yang, "Quantitative characterization of changes in dynamical behavior for singleparticle tracking studies," J. Phys. Chem. B (2006).
    [CrossRef] [PubMed]
  9. H. Cang, C. M. Wong, C. S. Xu, A. H. Rizvi, and H. Yang, "Confocal three dimensional tracking of a single nanoparticle with concurrent spectroscopic readouts," Appl. Phys. Lett. 88, 223,901 (2006).
    [CrossRef]
  10. C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
    [CrossRef]
  11. S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology 14, 669-680 (2005).
  12. M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).
  13. A. E. Cohen and W. E. Moerner, "Method for trapping and manipulating nanoscale objects in solution," Appl. Phys. Lett. 86, 093,109 (2005).
    [CrossRef]
  14. A. E. Cohen and W. E. Moerner, "Suppressing Brownian motion of individual biomolecules in solution," Proc. Natl. Acad. Sci. USA 103, 4362-4365 (2006).
    [CrossRef] [PubMed]
  15. A. E. Cohen and W. E. Moerner, "Internal mechanical response of a polymer in solution," Phys. Rev. Lett. 98, 116,001 (2007).
    [CrossRef]
  16. A. E. Cohen and W. E. Moerner, "Principal Components Analysis of shape fluctuations of single DNA molecules," Proc. Natl. Acad. Sci. USA 104, 12,622-12,627 (2007).
    [CrossRef]
  17. A. E. Cohen, "Control of nanoparticles with arbitrary two-dimensional force fields," Phys. Rev. Lett. 94, 118,102 (2005).
    [CrossRef]
  18. A. E. Cohen, "Trapping and manipulating single molecules in solution," Ph.D. thesis, Stanford University (2007). Https://www2.lsdiv.harvard.edu/labs/cohen/Publications/AEC Thesis2 OneSided.pdf.
  19. A. E. Cohen and W. E. Moerner, "An all-glass microfluidic cell for the ABEL trap: fabrication and modeling," Proc. SPIE 5930, 191-198 (2005).
  20. H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
    [CrossRef]
  21. Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
    [CrossRef]
  22. S. S. Sommer and J. E. Cohen, "The size distributions of proteins, mRNA, and nuclear RNA," J. Molec. Evol. 15, 37-57 (1980).
    [CrossRef] [PubMed]
  23. S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
    [CrossRef] [PubMed]

2007 (3)

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

A. E. Cohen and W. E. Moerner, "Principal Components Analysis of shape fluctuations of single DNA molecules," Proc. Natl. Acad. Sci. USA 104, 12,622-12,627 (2007).
[CrossRef]

A. J. Berglund, K. McHale, and H. Mabuchi, "Fluctuations in closed-loop fluorescent particle tracking," Opt. Express 15, 7752-7773 (2007).
[CrossRef] [PubMed]

2006 (2)

A. E. Cohen and W. E. Moerner, "Suppressing Brownian motion of individual biomolecules in solution," Proc. Natl. Acad. Sci. USA 103, 4362-4365 (2006).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, "Performance bounds on single-particle tracking by fluorescence modulation," Appl. Phys. B 83, 127-133 (2006).
[CrossRef]

2005 (3)

A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005).
[CrossRef] [PubMed]

A. E. Cohen and W. E. Moerner, "An all-glass microfluidic cell for the ABEL trap: fabrication and modeling," Proc. SPIE 5930, 191-198 (2005).

S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology 14, 669-680 (2005).

2004 (1)

A. J. Berglund and H. Mabuchi, "Feedback controller design for tracking a single fluorescent molecule," Appl. Phys. B 78, 653-659 (2004).
[CrossRef]

2003 (1)

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

2000 (2)

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

J. Enderlein, "Tracking of fluorescent molecules diffusing within membranes," Appl. Phys. B 71, 773-777 (2000).
[CrossRef]

1997 (1)

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

1987 (1)

R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
[CrossRef] [PubMed]

1980 (1)

S. S. Sommer and J. E. Cohen, "The size distributions of proteins, mRNA, and nuclear RNA," J. Molec. Evol. 15, 37-57 (1980).
[CrossRef] [PubMed]

1974 (1)

M. B. Comisarow and A. G. Marshall, "Frequency-sweep Fourier transform ion cyclotron resonance spectroscopy," Chem. Phys. Lett. 26, 489-490 (1974).
[CrossRef]

Armani, M.

M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).

Belle, A.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Berglund, A. J.

A. J. Berglund, K. McHale, and H. Mabuchi, "Fluctuations in closed-loop fluorescent particle tracking," Opt. Express 15, 7752-7773 (2007).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, "Performance bounds on single-particle tracking by fluorescence modulation," Appl. Phys. B 83, 127-133 (2006).
[CrossRef]

A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, "Feedback controller design for tracking a single fluorescent molecule," Appl. Phys. B 78, 653-659 (2004).
[CrossRef]

Bower, K.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Cang, H.

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

Chaudhary, S.

S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology 14, 669-680 (2005).

M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).

Cohen, A. E.

A. E. Cohen and W. E. Moerner, "Principal Components Analysis of shape fluctuations of single DNA molecules," Proc. Natl. Acad. Sci. USA 104, 12,622-12,627 (2007).
[CrossRef]

A. E. Cohen and W. E. Moerner, "Suppressing Brownian motion of individual biomolecules in solution," Proc. Natl. Acad. Sci. USA 103, 4362-4365 (2006).
[CrossRef] [PubMed]

A. E. Cohen and W. E. Moerner, "An all-glass microfluidic cell for the ABEL trap: fabrication and modeling," Proc. SPIE 5930, 191-198 (2005).

Cohen, J. E.

S. S. Sommer and J. E. Cohen, "The size distributions of proteins, mRNA, and nuclear RNA," J. Molec. Evol. 15, 37-57 (1980).
[CrossRef] [PubMed]

Comisarow, M. B.

M. B. Comisarow and A. G. Marshall, "Frequency-sweep Fourier transform ion cyclotron resonance spectroscopy," Chem. Phys. Lett. 26, 489-490 (1974).
[CrossRef]

Dehmelt, H. G.

R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
[CrossRef] [PubMed]

Dephoure, N.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Ding, Z.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Enderlein, J.

J. Enderlein, "Tracking of fluorescent molecules diffusing within membranes," Appl. Phys. B 71, 773-777 (2000).
[CrossRef]

Foote, R. S.

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Ghaemmaghami, S.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Howson, R.W.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Huh, W.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Jacobson, S. C.

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Lai, G.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Mabuchi, H.

A. J. Berglund, K. McHale, and H. Mabuchi, "Fluctuations in closed-loop fluorescent particle tracking," Opt. Express 15, 7752-7773 (2007).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, "Performance bounds on single-particle tracking by fluorescence modulation," Appl. Phys. B 83, 127-133 (2006).
[CrossRef]

A. J. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles," Opt. Express 13, 8069-8082 (2005).
[CrossRef] [PubMed]

A. J. Berglund and H. Mabuchi, "Feedback controller design for tracking a single fluorescent molecule," Appl. Phys. B 78, 653-659 (2004).
[CrossRef]

Marshall, A. G.

M. B. Comisarow and A. G. Marshall, "Frequency-sweep Fourier transform ion cyclotron resonance spectroscopy," Chem. Phys. Lett. 26, 489-490 (1974).
[CrossRef]

McHale, K.

Moerner, W. E.

A. E. Cohen and W. E. Moerner, "Principal Components Analysis of shape fluctuations of single DNA molecules," Proc. Natl. Acad. Sci. USA 104, 12,622-12,627 (2007).
[CrossRef]

A. E. Cohen and W. E. Moerner, "Suppressing Brownian motion of individual biomolecules in solution," Proc. Natl. Acad. Sci. USA 103, 4362-4365 (2006).
[CrossRef] [PubMed]

A. E. Cohen and W. E. Moerner, "An all-glass microfluidic cell for the ABEL trap: fabrication and modeling," Proc. SPIE 5930, 191-198 (2005).

Montiel, D.

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

O???Shea, E. K.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Probst, R.

M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).

Ramsey, J. M.

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Sakakibara, T.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Schneibel, J. H.

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Schwinberg, P. B.

R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
[CrossRef] [PubMed]

Shapiro, B.

S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology 14, 669-680 (2005).

M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).

Shinohara, S.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Sommer, S. S.

S. S. Sommer and J. E. Cohen, "The size distributions of proteins, mRNA, and nuclear RNA," J. Molec. Evol. 15, 37-57 (1980).
[CrossRef] [PubMed]

Van Dyck, R. S.

R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
[CrossRef] [PubMed]

Wang, H. Y.

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Weissman, J. S.

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Xu, C. S.

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

Yang, H.

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

Appl. Phys. B (3)

J. Enderlein, "Tracking of fluorescent molecules diffusing within membranes," Appl. Phys. B 71, 773-777 (2000).
[CrossRef]

A. J. Berglund and H. Mabuchi, "Feedback controller design for tracking a single fluorescent molecule," Appl. Phys. B 78, 653-659 (2004).
[CrossRef]

A. J. Berglund and H. Mabuchi, "Performance bounds on single-particle tracking by fluorescence modulation," Appl. Phys. B 83, 127-133 (2006).
[CrossRef]

Chem. Phys. Lett. (1)

M. B. Comisarow and A. G. Marshall, "Frequency-sweep Fourier transform ion cyclotron resonance spectroscopy," Chem. Phys. Lett. 26, 489-490 (1974).
[CrossRef]

IEEE Transactions on Control Systems Technology (1)

S. Chaudhary and B. Shapiro, "Arbitrary steering of multiple particles independently in an electro-osmotically driven microfluidic system," IEEE Transactions on Control Systems Technology 14, 669-680 (2005).

J. Appl. Phys. (1)

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, "Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection," J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

J. Molec. Evol. (1)

S. S. Sommer and J. E. Cohen, "The size distributions of proteins, mRNA, and nuclear RNA," J. Molec. Evol. 15, 37-57 (1980).
[CrossRef] [PubMed]

J. Phys. Chem. C (1)

C. S. Xu, H. Cang, D. Montiel, and H. Yang, "Rapid and quantitative sizing of nanoparticles using three-dimensional single-particle tracking," J. Phys. Chem. C 111, 32-35 (2007).
[CrossRef]

Journal of Microelectromechanical Systems (1)

M. Armani, S. Chaudhary, R. Probst, and B. Shapiro, "Using feedback control and micro-fluidics to steer individual particles," Journal of Microelectromechanical Systems(JMEMS) 15, 945-956 (2006).

Nature (1)

S. Ghaemmaghami,W. Huh, K. Bower, R.W. Howson, A. Belle, N. Dephoure, E. K. O�??Shea, and J. S. Weissman, "Global analysis of protein expression in yeast," Nature 425, 737-741 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. Lett. (1)

R. S. Van Dyck, P. B. Schwinberg, and H. G. Dehmelt, "New high-precision comparison of electron and positron g factors," Phys. Rev. Lett. 59, 26-29 (1987).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

A. E. Cohen and W. E. Moerner, "Suppressing Brownian motion of individual biomolecules in solution," Proc. Natl. Acad. Sci. USA 103, 4362-4365 (2006).
[CrossRef] [PubMed]

A. E. Cohen and W. E. Moerner, "Principal Components Analysis of shape fluctuations of single DNA molecules," Proc. Natl. Acad. Sci. USA 104, 12,622-12,627 (2007).
[CrossRef]

Proc. SPIE (1)

A. E. Cohen and W. E. Moerner, "An all-glass microfluidic cell for the ABEL trap: fabrication and modeling," Proc. SPIE 5930, 191-198 (2005).

Sens. Actuators B (1)

H. Y. Wang, R. S. Foote, S. C. Jacobson, J. H. Schneibel, and J. M. Ramsey, "Low temperature bonding for microfabrication of chemical analysis devices," Sens. Actuators B 45, 199-207 (1997).
[CrossRef]

Other (6)

A. E. Cohen, "Control of nanoparticles with arbitrary two-dimensional force fields," Phys. Rev. Lett. 94, 118,102 (2005).
[CrossRef]

A. E. Cohen, "Trapping and manipulating single molecules in solution," Ph.D. thesis, Stanford University (2007). Https://www2.lsdiv.harvard.edu/labs/cohen/Publications/AEC Thesis2 OneSided.pdf.

A. E. Cohen and W. E. Moerner, "Internal mechanical response of a polymer in solution," Phys. Rev. Lett. 98, 116,001 (2007).
[CrossRef]

A. E. Cohen and W. E. Moerner, "Method for trapping and manipulating nanoscale objects in solution," Appl. Phys. Lett. 86, 093,109 (2005).
[CrossRef]

D. Montiel, H. Cang, and H. Yang, "Quantitative characterization of changes in dynamical behavior for singleparticle tracking studies," J. Phys. Chem. B (2006).
[CrossRef] [PubMed]

H. Cang, C. M. Wong, C. S. Xu, A. H. Rizvi, and H. Yang, "Confocal three dimensional tracking of a single nanoparticle with concurrent spectroscopic readouts," Appl. Phys. Lett. 88, 223,901 (2006).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the hardware-feedback ABEL trap. A two-dimensional acousto-optic beam deflector (AOBD) deflects a laser beam in a small circle at 40 kHz. The excitation light reflects of dichroic mirror DC and illuminates a particle in the trap. A bandpass filter BP blocks scattered excitation light while passing fluorescence. The tube lens TL focuses the fluorescence onto a pinhole PH, and the fluorescence photons are then detected by an avalanche photodiode (APD). Phase-sensitive detection of individual photons provides a sensitive indicator of the offset between the location of the particle and the center of the trap. A time-correlated single-photon counting module (PH 300) records the arrival time of each photon, and a beamsplitter BS diverts a small fraction of the fluorescence light toward a camera.

Fig. 2.
Fig. 2.

Excitation path for the hardware-feedback ABEL trap. a) Geometry of the excitation beam in the trapping region. We want the beam to propagate perpendicular to the trapping plane, and to have a confocal depth much greater than the depth of the trapping region. b) Optical setup to create the beam pictured in (a). Lens L1 has a focal length of f 1=40 cm and lens L2 has a focal length of f 2=18 cm.

Fig. 3.
Fig. 3.

Detection path for the hardware-feedback ABEL trap.

Fig. 4.
Fig. 4.

Fused silica microfluidic cell for the hardware-feedback ABEL trap. a) Macroscopic layout of the deep channels. The annular channel equalizes the hydrostatic pressure in the four arms of the trap, eliminating pressure-driven flows through the trapping region. b) Trapping region. The ends of the deep channels extend from the edges of the image. The wedges jutting from the corners are raised ~400 nm above the trapping region and set the depth of the trapping region. These wedges also act to focus the electric field into the center of the trapping region.

Fig. 5.
Fig. 5.

Calibration of the ABEL trap performed by scanning a fixed 100 nm fluorescent bead through the trapping region. a) Scan in the x-y plane. The x and y feedback voltages are proportional to the respective offsets of the particle, and the total photon count rate is independent of the offset. b) Scan in the x-z plane. The x feedback voltage is proportional to the offset, with a gain that does not vary strongly with z. Within a large region, the photon count rate is independent of position.

Fig. 6.
Fig. 6.

Feedback voltages as a 100 nm fluorescent bead is scanned through the trapping region. Blue: feedback voltage along the scan axis; green: voltage perpendicular to the scan axis. The sensitivity in this case is 0.76 V/µm and the noise is 1.4 µm√N.

Fig. 7.
Fig. 7.

Trapping of a 100 nm bead in the hardware-feedback ABEL trap. a) Image of a trapped bead obtained by averaging 11 video frames (corresponding to 1 s of data). b) Histogram of voltages applied along the x-axis to keep the bead trapped. c) Impulse response function of the feedback electronics. The latency is dominated by the cruddy SR844 lockin amplifier. d) Power spectrum of the voltage oscillations (blue), and fits based on Eq. 5 including the effect of measurement noise (red), and without measurement noise (black).

Fig. 8.
Fig. 8.

Measurement of the mobility of a trapped 100 nm bead. a) The position of the trap center was modulated with a square wave of increasing amplitude and the cycle-average voltage was recorded. b) The area under the voltage vs. time curve is proportional to the mobility.

Fig. 9.
Fig. 9.

Trapping of a single chaperonin in buffer. a) Time-lapse image of a single trapped molecule of GroEL (held for ~1:7 s). b) Histogram of the displacements of the molecule, extracted from the trajectory of video images. c) Photobleaching time-trace of trapped single molecules of the fluorescently labeled archeal chaperonin MmCpn. Discrete photobleaching steps are clearly visible.

Fig. 10.
Fig. 10.

Trapping of Cy3. a) Molecular structure of Cy3. The molecular weight is 507 g/mol. b) Histogram of count-rates in the trapping region, with no feedback, feedback, and anti-feedback. c) Representative time-traces with and without feedback. d) Autocorrelation of the intensity with no feedback, feedback, and anti-feedback.

Equations (6)

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b = 2 π w b 2 λ ,
θ b = λ π w b ,
dx dt = μ E ( t ) + ξ ( t )
E ( t ) = 0 d τ A G ( τ ) [ x ( t τ ) + χ ( t τ ) ] ,
E ~ ( ω ) 2 = A G ~ 2 ( ξ ~ 2 + ω 2 χ ~ 2 ) ω 2 1 + A μ G ~ i ω 2 .
x ~ ( ω ) 2 = ξ ~ 2 + A μ G ~ χ ~ 2 ω 2 ( 1 + A μ G ~ i ω ) 2 .

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