Trapped Brownian Motion in Single- and Two-Photon Excitation Fluorescence Correlation Experiments Giuseppe Chirico,* Carlo Fumagalli, and Giancarlo Baldini Dipartimento di Fisica, Istituto Nazionale per la Fisica della Materia, udr Milano-Bicocca, Piazza delle Scienze 3, I20126 Milano, Italy ReceiVed: August 10, 2001; In Final Form: NoVember 27, 2001 We investigate possible trapping effects induced by the infrared radiation employed for two-photon fluorescence spectroscopy and microscopy on the diffusion of small fluorophores and draw a comparison to single-photon excitation. A first-order treatment of the effect of an optical trapping potential on the diffusion time and the number of molecules per excitation volume is also derived. By analyzing the fluorescence fluctuations arising from solutions of small dyes versus the excitation power and comparing them to the results with microspheres, we show that the bias on the molecular diffusion of small dyes is negligible when two-photon excitation is employed. In single-photon excitation, close to the resonance absorption of the dye, a small but detectable bias effect on the diffusion is found, in agreement with the study by Osborne et al. [Osborne, M. A.; Balasubramanian, S.; Furey, W. S.; Klenerman, D. J. Phys. Chem. B 1998, 102 (17), 3160]. 1. Introduction Two-photon excitation (TPE) fluorescence microscopy and spectroscopy was conceived more than 20 years ago 1,2 but has largely been developed in its modern form in the past decade. 3 It can be considered a comparatively young technique that takes advantage of both wide-field and confocal laser scanning microscopy (CLSM) 4,5 for the study of the three-dimensional (3-D) and dynamic properties of biological systems in vitro and in vivo. 6,7 A new type of spectroscopy related to the use of tiny excitation volumes has grown together with the development of confocal and two-photon excitation microscopy. The use of two-photon excitation microscopes has fostered the application of techniques such as fluorescence correlation spectroscopy (FCS) 8-11 or fluorescence lifetime (FL) to single biological molecules 12,13 and to the characterization of cellular environ- ment 14,15 and tissues. 16 These applications have also been made possible by the development of mode-locked infrared (IR) lasers, which provide moderate average powers at high repetition rates with ultrafast pulses. 17 The use of infrared radiation in mul- tiphoton experiments might affect the Brownian motion of the observed chromophores, and on the other hand, laser tweezers have been reported to induce two-photon excitation. 18 The main aim of the present report is to ascertain the extent to which the diffusion properties of small molecules of the size of simple dyes or small proteins (such as the green fluorescent protein) are affected by the use of pulsed IR radiation. This issue is particularly relevant for the investigation of dim fluorophores for which high excitation intensities should be used in two- photon experiments. In fact, optical trapping is currently a valuable technique for the manipulation of microscopic objects ranging from a few tens of nanometers to a few micrometers in size. It is known 19 that electromagnetic radiation can apply a force on dielectric particles when strongly focused by a high-numerical-aperture objective. 20,21 Two types of forces act on the particles in this case: a gradient force that acts in the plane perpendicular to the light beam and is related the strength of the focalization of the laser beam and a scattering force that acts in the direction of the impinging light and is related to the scattering of the photons by the dielectric particle. The ratio of the two forces, which determines the stability of the trap, depends strongly on the wavelength (∼λ 0 5 ), and the most stable traps have been developed in the infrared part of the light spectrum. 19 For molecules whose diameter 2a is less than the light wavelength (Rayleigh regime), the scattering force depends on the light intensity I(r) ) I 0 i(r) [with i(0) ) 1], the refractive index of the medium n m , and the particle polarizability R as 22 where ǫ 0 , λ 0 , and c are the vacuum dielectric constant, light wavelength, and speed of light, respectively. The gradient force depends on the gradient of the light intensity and the particle polarizability as 22,23 where ǫ r is the medium dielectric permittivity. The stability condition of the trap for a particle far from the absorption resonance is determined by the ratio of the gradient force to the scattering force that scales as 22 where w 0 is the waist of the laser beam. It is therefore easier to trap particles with infrared than with ultraviolet (UV) radiation, and the trapping of a dielectric particles depends on their size. Moreover, the trapping of small molecules might occur close * Corresponding author: Giuseppe Chirico, Dipartimento di Fisica, Piazza delle Scienze 3, I20126 Milano, Italy. Tel.: 39-0264482872. Fax: 39-0264482894. E-mail: giuseppe.chirico@mib.infn.it. |F h scat | ) 8π 3 n m 3ǫ 0 cλ 0 4 R 2 I 0 (1) F h grad ) n m 2 2cǫ r ǫ 0 R∇I h(r) (2) | F grad F scat | ∝ λ 0 5 Rw 0 2 g 1 (3) 2508 J. Phys. Chem. B 2002, 106, 2508-2519 10.1021/jp013087z CCC: $22.00 © 2002 American Chemical Society Published on Web 02/16/2002