AbstractLaser scanning fluorescence confocal microscope (LSFCM) imaging is an

extensively used modality in biological research [1]. However, these images present low signal to noise ratio and a time intensity decay effect due to the so called photoblinking/photobleaching (PBPB) phenomenon that corresponds to an intensity fading of a fluorescent probe along the time, as shown in Figure. This effect is caused by quantum phenomena associated with the electronic excitation and photochemical reactions among the fluorescent and the surrounding molecules induced by the incident radiation that temporarily or irreversibly destroy their ability to fluoresce. Since illumination is needed to excite and observe the tagging fluorescent proteins in the specimen and all the fluorophores will eventually photobleach upon extended excitation, the acquisition of this type of images becomes a hard task for long exposures.

There are in the literature several proposals [2] to model this fading effects and among them the single and double exponential are the most used. However, simple and tractable theoretical models based on the physics of the observation process to support these empirical laws are not available.

From a fluorescence point of view, tagging molecules can be in three main states [3] (see Jablonski state diagram), i) ON-state, where they are able to fluoresce and be observed, ii) OFF-state, where they are temporarily not able to fluoresce and therefore are not visible and finally at the iii) BLEACHED-state where they become permanently OFF. Here, a continuous time differential equation dynamic model is proposed to describe the number of molecules at the ON- state and OFF-state along the time. The model is based on the underlying quantum mechanic physics theory of the observation process associated with this type of images and the common empirical weighted sum of two decaying exponentials (DExp), usually used in the literature, is derived from the model.

J.Miguel Sanches and Isabel RodriguesInstitute for Systems and Robotics

Department of Bioengineering, Instituto Superior Técnico, Technical University of LisbonPortugal

Photobleaching/Photoblinking model

Three main states of the fluorescence molecules:

1. ON-state - able to fluoresce and be observed2. OFF-state - not able to fluoresce and not visible3. Permanently-OFF-state - permanently OFF.

Number of molecules dynamics at the ON-state, (directly related with the Intensity of the image)

Experimental Results

In this work an a differential equation model to describe the photoblinking/photobleaching fading effects observed in fluorescence images of microscopy is presented. The model is derived form the quantum physics underlying the acquisition process and the obtained intensity decreasing law fits the observations. The two decaying exponential provided by the model is, since long time, used in several experimental works described in the literature, without theorectical reasoning . In this work, a theoretical model is derived to validate the justify the usual empriacl and experimental based approach

Conclusions

A Photobleaching/Photoblinking analytical model for LSFCM imaging

where

References1. J. W. Lichtman and J.-A. Conchello, “Fluorescence microscopy,” Nature Methods, vol. 2, pp. 910–919, November 2005.2. N. B. Vicente, J. E. D. Zamboni, J. F. Adur, E. V. Paravani, and V. H. Casco, “Photobleaching correction in fluorescence

microscopy images,” Journal of Physics: Conference Series, vol. 90, no. 012068, pp. 1 – 8, 2007.3. J. Schuster, J. Brabandt, and C. von Borczyskowski, “Discrimination of photoblinking and photobleaching on the single

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Phys. Rev. Lett., vol. 95, no. 9, p. 090602, Aug 2005.7. R. Zondervan, F. Kulzer, M. A. Kol’chenko, and M. Orrit, “Photobleaching of rhodamine 6g in poly(vinyl alcohol) at the

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Standardized average intensity per image as a function of the experiment time, for two LSFCM real data sequences, one without using FLIP nor any other technique (dark circles in A) and the other using the FLIP technique (dark stars in B). Red and orange curves stand for the fits of the data with two exponentials models. Blue and cyan curves stand for the fits of the data with one-exponential models. The root mean square error (RMSE) is displayed in the plot legend. (Data provided by the Instituto de Medicina Molecular (UL) Lisbon).

Synthetic Data