Ultrafast, accurate, and robust localization of anisotropic dipoles

Abstract

The resolution of single molecule localization imaging techniques largely depends on the precision of localization algorithms. However, the commonly used Gaussian function is not appropriate for anisotropic dipoles because it is not the true point spread function. We derived the theoretical point spread function of tilted dipoles with restricted mobility and developed an algorithm based on an artificial neural network for estimating the localization, orientation and mobility of individual dipoles. Compared with fitting-based methods, our algorithm demonstrated ultrafast speed and higher accuracy, reduced sensitivity to defocusing, strong robustness and adaptability, making it an optimal choice for both two-dimensional and threedimensional super-resolution imaging analysis.

Key words： point spread function; restricted mobility; artificial neural network; super-resolution imaging

References

[1] Aquino, D., Schonle, A., Geisler, C., Middendorff, C.V., Wurm, C.A., Okamura, Y., Lang, T., Hell, S.W., and Egner, A. (2011). Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched f1uorophores. Nat Methods 8, 353-359 .10.1038/nmeth.1583
[2] Backlund, M.P., Lew, M.D., Backer, A.S., Sahl, S.J., Grover, G., Agrawal, A., Piestun, R., and Moerner, W.E. (2012). Simultaneous, accurate measurement of the 3D position and orientation of single molecules. Proc Natl Acad Sci U S A 109, 19087-19092 .10.1073/pnas.1216687109
[3] Betzig, E., Patterson, G.H., Sougrat, R., Lindwasser, O.W., Olenych, S., Bonifacino, J.S., Davidson, M.W., Lippincott-Schwartz, J., and Hess, H.F. (2006). Imaging intracellular f1uorescent proteins at nanometer resolution. Science 313, 1642-1645 .10.1126/science.1127344
[4] Born, M., and Wolf, E. (1999). Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th expanded edn (Cambridge; New York, Cambridge University Press) . 10.1017/CBO9781139644181
[5] Cartwright, H.M. (2008). Artificial neural networks in biology and chemistry: the evolution of a new analytical tool. Methods Mol Biol 458, 1-13 .10.1007/978-1-60327-101-1_1
[6] Chang, H., Zhang, M., Ji, W., Chen, J., Zhang, Y., Liu, B., Lu, J., Zhang, J., Xu, P., and Xu, T. (2012). A unique series of reversibly switchable f1uorescent proteins with beneficial properties for various applications. Proc Natl Acad Sci U S A 109, 4455-4460 .10.1073/pnas.1113770109
[7] Dale, R.E., Hopkins, S.C., an der Heide, U.A., Marszalek, T., Irving, M., and Goldman, Y.E. (1999). Model-independent analysis of the orientation of f1uorescent probes with restricted mobility in muscle fibers. Biophys J 76, 1606-1618 .10.1016/S0006-3495(99)77320-0
[8] Enderlein, J., Toprak, E., and Selvin, P.R. (2006). Polarization effect on position accuracy of f1uorophore localization. Opt Express 14, 8111-8120 .10.1364/OE.14.008111
[9] Engelhardt, J., Keller, J., Hoyer, P., Reuss, M., Staudt, T., and Hell, S.W. (2011). Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy. Nano Lett 11, 209-213 .10.1021/nl103472b
[10] Ha, T., Laurence, T.A., Chemla, D.S., and Weiss, S. (1999). Polarization spectroscopy of single f1uorescent molecules. Phy Chem 103, 6839-6850 .
[11] Hess, S.T., Girirajan, T.P., and Mason, M.D. (2006). Ultra-high resolution imaging by f1uorescence photoactivation localization microscopy. Biophys J 91, 4258-4272 .10.1529/biophysj.106.091116
[12] Irving, M. (1996). Steady-state polarization from cylindrically symmetric f1uorophores undergoing rapid restricted motion. Biophys J 70, 1830-1835 .10.1016/S0006-3495(96)79748-5
[13] Juette, M.F., Gould, T.J., Lessard, M.D., Mlodzianoski, M.J., Nagpure, B.S., Bennett, B.T., Hess, S.T., and Bewersdorf, J. (2008). Threedimensional sub-100 nm resolution fluorescence microscopy of thick samples. Nat Methods 5, 527-529 .10.1038/nmeth.1211
[14] McKinney, S.A., Murphy, C.S., Hazelwood, K.L., Davidson, M.W., and Looger, L.L. (2009). A bright and photostable photoconvertible fluorescent protein. Nat Methods 6, 131-133 .10.1038/nmeth.1296
[15] Mortensen, K.I., Churchman, L.S., Spudich, J.A., and Flyvbjerg, H. (2010). Optimized localization analysis for single-molecule tracking and super-resolution microscopy. Nat Methods 7, 377-381 .10.1038/nmeth.1447
[16] Ober, R.J., Ram, S., and Ward, E.S. (2004). Localization accuracy in single-molecule microscopy. Biophys J 86, 1185-1200 .10.1016/S0006-3495(04)74193-4
[17] Ohmachi, M., Komori, Y., Iwane, A.H., Fujii, F., Jin, T., and Yanagida, T. (2012). Fluorescence microscopy for simultaneous observation of 3D orientation and movement and its application to quantum rodtagged myosin V. Proc Natl Acad Sci U S A 109, 5294-5298 .10.1073/pnas.1118472109
[18] Quirin, S., Pavani, S.R., and Piestun, R. (2012). Optimal 3D singlemolecule localization for superresolution microscopy with aberrations and engineered point spread functions. Proc Natl Acad Sci USA 109, 675-679 .10.1073/pnas.1109011108
[19] Riedl, J., Crevenna, A.H., Kessenbrock, K., Yu, J.H., Neukirchen, D., Bista, M., Bradke, F., Jenne, D., Holak, T.A., Werb, Z., . (2008). Lifeact: a versatile marker to visualize F-actin. Nat Methods 5, 605-607 .10.1038/nmeth.1220
[20] Rust, M.J., Bates, M., and Zhuang, X. (2006). Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat Methods 3, 793-795 .10.1038/nmeth929
[21] Schoen, I., Ries, J., Klotzsch, E., Ewers, H., and Vogel, V. (2011). Binding-activated localization microscopy of DNA structures. Nano Lett 11, 4008-4011 .10.1021/nl2025954
[22] Shtengel, G., Galbraith, J.A., Galbraith, C.G., Lippincott-Schwartz, J., Gillette, J.M., Manley, S., Sougrat, R., Waterman, C.M., Kanchanait wong, P., Davidson, M.W., . (2009). Interferometric f1uorescent super-resolution microscopy resolves 3D cellular ultrastructure. Proc Natl Acad Sci U S A 106, 3125-3130 .10.1073/pnas.0813131106
[23] Smith, C.S., Joseph, N., Rieger, B., and Lidke, K.A. (2010). Fast, single-molecule localization that achieves theoretically minimum uncertainty. Nat Methods 7, 373-375 .10.1038/nmeth.1449
[24] Stallinga, S., and Rieger, B. (2010). Accuracy of the Gaussian Point Spread Function model in 2D localization microscopy. Opt Express 18, 24461-24476 .10.1364/OE.18.024461
[25] Testa, I., Schonle, A., von Middendorff, C., Geisler, C., Medda, R., Wurm, C.A., Stiel, A.C., Jakobs, S., Bossi, M., Eggeling, C., . (2008). Nanoscale separation of molecular species based on their rotational mobility. Opt Express 16, 21093-21104 .10.1364/OE.16.021093
[26] Thompson, R.E., Larson, D.R., and Webb, W.W. (2002). Precise nanometer localization analysis for individual f1uorescent probes. Biophys J 82, 2775-2783 .10.1016/S0006-3495(02)75618-X
[27] Zhang, M., Chang, H., Zhang, Y., Yu, J., Wu, L., Ji, W., Chen, J., Liu, B., Lu, J., Liu, Y., . (2012). Rational design of true monomeric and bright photoactivatable f1uorescent proteins. Nat Methods 9, 727-729 .10.1038/nmeth.2021