Abstract

We consider the problem of optimizing superresolution microscopy with photoswitchable molecules that irreversibly photobleach. Using variational methods, we show that the number of single-molecule images is maximized in a simple scheme with a constant number of activated fluorophores per cycle. For high-speed acquisition, deviations from the optimal scheme do reduce the information collected but fortuitously also reduce certain types of errors, making the scheme very robust. Finally, we calculate the amount of information lost due to bleaching and noise.

© 2011 Optical Society of America

Full Article  |  PDF Article

Corrections

Edward Shore and Alex Small, "Optimal acquisition scheme for subwavelength localization microscopy of bleachable fluorophores: erratum," Opt. Lett. 36, 3057-3057 (2011)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-36-16-3057

References

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M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

A. Small, Biophys. J. 96, L16 (2009).
[CrossRef] [PubMed]

2008 (2)

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef] [PubMed]

2005 (1)

Amberger, R.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
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M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
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Betzig, E.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
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H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Chachuat, B.

B. Chachuat, Nonlinear and Dynamic Optimization: From Theory to Practice (Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne, 2007).

Cremer, C.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Crooks, G. E.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Erdel, F.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Forthmann, C.

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

Galbraith, C. G.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

Galbraith, J. A.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef] [PubMed]

Greenfield, D.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Gunkel, M.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Heintzmann, R.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef] [PubMed]

Hrmann, C.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Jovin, T.

Kaufmann, R.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Lemmer, P.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Lidke, K.

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Liphardt, J.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef] [PubMed]

McEvoy, A. L.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Rieger, B.

Rippe, K.

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Shroff, H.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

Small, A.

A. Small, Biophys. J. 96, L16 (2009).
[CrossRef] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Steinhauer, C.

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

Tinnefeld, P.

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

Vogelsang, J.

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

Wingreen, N. S.

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Biophys. J. (2)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, Biophys. J. 91, 4258 (2006).
[CrossRef] [PubMed]

A. Small, Biophys. J. 96, L16 (2009).
[CrossRef] [PubMed]

Biotechnol. J. (1)

M. Gunkel, F. Erdel, K. Rippe, P. Lemmer, R. Kaufmann, C. Hrmann, R. Amberger, and C. Cremer, Biotechnol. J. 4, 927 (2009).
[CrossRef] [PubMed]

J. Am. Chem. Soc. (1)

C. Steinhauer, C. Forthmann, J. Vogelsang, and P. Tinnefeld, J. Am. Chem. Soc. 130, 16840 (2008).
[CrossRef] [PubMed]

Nat. Meth. (2)

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, Nat. Meth. 5, 417 (2008).
[CrossRef]

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Opt. Express (1)

PLoS Biology (1)

D. Greenfield, A. L. McEvoy, H. Shroff, G. E. Crooks, N. S. Wingreen, E. Betzig, and J. Liphardt, PLoS Biology 7, e1000137 (2009).
[CrossRef] [PubMed]

Science (1)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).
[CrossRef] [PubMed]

Other (1)

B. Chachuat, Nonlinear and Dynamic Optimization: From Theory to Practice (Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne, 2007).

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Figures (2)

Fig. 1
Fig. 1

n ( t ) (solid) and p ( t ) (dashed) for constant E 2 .

Fig. 2
Fig. 2

p γ versus E 2 for different b and f 1 values. E 2 ranges with different qualitative features are noted.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

p = 2 f 1 E 2 / f 2 n + 2 f 1 E 2 / f 2 1 2 f 1 E 2 / f 2 n ,
n ˙ = β n ( t ) p ( t ) ,
t m = 0 t f p m ( t ) d t = 0 t f n ( n 1 ) ... ( n m + 1 ) m ! p m ( 1 p ) n m d t ,
t m = 0 t f ( n ˙ / β ) m m ! e n ˙ / β d t .
p 0 = ( 1 p ) n 1 = ( 1 2 f 1 E 2 f 2 ( n 1 ) ) n 1 e 2 f 1 E 2 / f 2 ,
p γ = j = 1 b ( 1 b ) j 1 ( 1 f 1 e 2 f 1 E 2 / f 2 ) j
= b e 2 f 1 E 2 / f 2 f 1 f 1 + b * ( e 2 f 1 E 2 / f 2 f 1 ) .

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