Abstract
The classical three-point method for obtaining a diffusion coefficient of probes from the fluorescence recovery function in the Fluorescence Recovery After Photobleaching (FRAP) technique, when Gaussian or uniform spot-photobleaching profiles are used, leads to an expression that is not suitable for linear fittings. Therefore, determination of the diffusion coefficient is complex and very dependent on the recovery time. In this work we propose a new solution for the fluorescence recovery function after spot-bleaching using a Gaussian beam, which is a better alternative method than the three-point method for the data analysis of the FRAP kinetics. The new method can be applied for shorter recovery times thereby minimizing errors due to convective effects. It leads to a linear relationship between the recovery function and the diffusion coefficient and, as shown in the analysis of a model case, allows a more accurate determination of the diffusion coefficient of fluorescent probes.
Similar content being viewed by others
References
Peters, R., Peters, J., Tews, K.H., Bähr, W.: A microfluorimetric study of translational diffusion in erythrocyte membranes. Biochim. Biophys. Acta Biomembr. 367, 282–294 (1974)
Jacobson, K., Wu, E., Poste, G.: Measurement of the translational mobility of concanavalin A in glycerol-saline solution and on the cell surface by fluorescence recovery after photobleaching. Biochim. Biophys. Acta Biomembr. 433, 215–222 (1976)
Schlessinger, J., Koppel, D.E., Axelrod, D., Jacobson, K., Webb, W.W., Elson, E.L.: Lateral transport on cell membranes: mobility of concanavalin A receptors on myoblasts. Proc. Natl. Acad. Sci. USA 73, 2409–2413 (1976). doi:10.1073/pnas.73.7.2409
Edidin, M., Zagyansky, Y., Lardner, T.J.: Measurement of membrane protein lateral diffusion in single cells. Science 191, 466–468 (1976). doi:10.1126/science.1246629
Axelrod, D., Koppel, D.E., Schlessinger, J., Elson, E., Webb, W.W.: Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys. J. 16, 1055–1069 (1976)
Koppel, D.E., Axelrod, D., Schlessinger, J., Elson, E., Webb, W.W.: Dynamics of fluorescence marker concentration as a probe of mobility. Biophys. J. 16, 1315–1329 (1976)
Kovaleski, J.M., Wirth, M.J.: Applications of fluorescence recovery after photobleaching. Anal. Chem. News Features (October 1), 601A–605A (1997)
Mustafa, M.B., Tipton, D.L., Barkely, M.D., Russo, P.S.: Dye diffusion in isotropic and liquid crystalline aqueous (hydroxypropyl)cellulose. Macromolecules 26, 370–378 (1993). doi:10.1021/ma00054a017
Champion, D., Hevert, H., Blond, G., Simatos, D.: Comparison between two methods to measure translational diffusion of a small molecule at subzero temperature. J. Agric. Food Chem. 43, 2887–2891 (1995). doi:10.1021/jf00059a022
Blackburn, F.R., Wang, C., Ediger, M.D.: Translational and rotational motion of probes in supercooled 1,3,5-tris(naphthyl)benzene. J. Phys. Chem. 100, 18249–18257 (1996). doi:10.1021/jp9622041
Champion, D., Hevert, H., Blond, G., Le Meste, M., Simatos, D.: Translational diffusion in sucrose solutions in the vicinity of their glass transition temperature. J. Phys. Chem. B 101, 10674–10679 (1997). doi:10.1021/jp971899i
Rampp, M., Buttersack, C., Lüdemann, H.-D.: c,T-dependence of the viscosity and the self-diffusion coefficients in some aqueous carbohydrate solutions. Carbohydr. Res. 328, 561–572 (2000). doi:10.1016/S0008-6215(00)00141-5
Longinotti, M.P., Corti, H.R.: Diffusion of ferrocene methanol in supercooled aqueous solutions using cylindrical microelectrodes. Electrochem. Commun. 9, 1444–1450 (2006). doi:10.1016/j.elecom.2007.02.003
Magazù, S., Maisano, G., Migliardo, P., Villari, V.: Experimental simulation of macromolecules in trehalose aqueous solutions: a photon correlation spectroscopy study. J. Chem. Phys. 111, 9086–9092 (1999). doi:10.1063/1.480250
Eggeling, C., Widengren, J., Rigler, R., Seidel, C.A.M.: Photobleaching of fluorescent dyes under conditions used for single-molecule detection: evidence of two-step photolysis. Anal. Chem. 70, 2651–2659 (1998). doi:10.1021/ac980027p
Pringsheim, P.: Fluorescence and Phosphorescence. Interscience Publishers Inc., London (1949)
Wells, S.: Fundamentals of Fluorescence. In: O’Brien Workshop. Optical Microscopy in Renal Research, Indiana University-School of Medicine (2003)
Song, L., Hennink, E.J., Young, I.T., Tanke, H.J.: Photobleaching kinetics of fluorescein in quantitative fluorescence microscopy. Biophys. J. 68, 2588–2600 (1995)
Davis, P.J.: Gamma function and related functions. In: Abramowitz, M., Stegun, I.A. (eds.) Handbook of Mathematical Functions, 4th edn. Dover, New York (1965)
Box, M.J.: Bias in nonlinear estimation. J. R. Stat. Soc. B 33, 171–201 (1971)
Olver, F.W.J.: Bessel functions of integer order. In: Abramowitz, M., Stegun, I.A. (eds.) Handbook of Mathematical Functions, 4th edn. Dover, New York (1965)
Luke, Y.L.: Integrals of Bessel functions. In: Abramowitz, M., Stegun, I.A. (eds.) Handbook of Mathematical Functions, 4th edn. Dover, New York (1965)
Wrench, J.W.: Concerning two series for the gamma function. Math. Comput. 22, 617–626 (1968). doi:10.2307/2004538
Mathews, J.H., Fink, K.D.: Métodos Numéricos con Matlab, 3rd edn., p. 393. Pearson Educación S.A., Madrid (2005)
Barreto, H., Maharry, D.: Least median of squares and regression through the origin. Comput. Stat. Data Anal. 50, 1391–1397 (2006). doi:10.1016/j.csda.2005.01.005
Saxton, M.J.: Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study. Biophys. J. 81, 2226–2240 (2001)
Hubert, M., Rousseeuw, P.J.: Robust regression with both continuous and binary regressors. J. Stat. Plann. Inf. 57, 153–163 (1997). doi:10.1016/S0378-3758(96)00041-9
Corti, H.R., Frank, G.A., Marconi, M.C.: An alternative solution of the fluorescence recovery kinetics after spot-bleaching for measuring diffusion coefficients. 2. Diffusion of fluorescein in sucrose aqueous solutions. J. Solution Chem. 37 (2008). doi:10.1007/s10953-008-9329-4
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Frank, G.A., Marconi, M.C. & Corti, H.R. An Alternate Solution of the Fluorescence Recovery Kinetics after Spot-Bleaching for Measuring Diffusion Coefficients. 1. Theory and Numerical Analysis. J Solution Chem 37, 1575–1591 (2008). https://doi.org/10.1007/s10953-008-9330-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10953-008-9330-y