Remote temperature measurements in femto-liter ... - Joerg Enderlein

approach with temperature measurements based on fluorescencelifetime changes of Rhodamine B and with measurements basedon diffusion changes of thermosensitive particles. In contrast tothe last two methods, 2fFCS is generally applicable and does notdepend on the availability of specific materials.Temperature dependent measurements require a precisetemperature control in the sample environment. The technicalimplementations of such a sample environment e.g. in a microfluidicchamber 22 or a sealed microscope sample cell is far beyondthe scope of this contribution. Recently, we have reported ona temperature controlled and sealed sample cell for fluorescencemicroscopes. 23 As already mentioned above, the opticalrequirements of the 2fFCS technique are comparable to otheroptical techniques and thus 2fFCS is well suited for LOC devices.Methods and materialsTheoretical backgroundHere, we briefly recall the theoretical background of 2fFCS. 24 In2fFCS, two overlapping detection volumes are generated, whichare identical in shape but shifted to each other perpendicular tothe optical axis. This is achieved by using one (or two) pulsedlasers in such a way that the polarization of each laser pulse isturned by 90 with respect to the preceding pulse. When sendingthis excitation light through a Nomarski prism as used inconventional differential interference contrast (DIC) microscopy,each laser pulse is slightly deflected according to itspolarization. After focusing the light through a water-immersionobjective with high numerical aperture, this generates two fociwith small lateral shift between them. To distinguish whichfluorescence photon was generated by which laser pulse (i.e. inwhich focus), one measures the photon detection times withpicosecond accuracy using time-correlated single-photon counting(TCSPC) and associates each detected photon with the latestpreceding excitation pulse. This allows for calculating the autocorrelationfunction (ACF) for each focus as well as the crosscorrelationfunction (CCF) between both foci. Because thelateral shift between both foci is precisely known (it only dependson the properties of the Nomarksi prism), a global analysis ofboth the ACFs and CCF allows for determining an absolutevalue of the diffusion coefficient of fluorescent molecules orparticles in solution.As was shown in detail in ref. 24, adequate model functions forthe diffusion-related part of the ACF or CCF (neglecting fora moment any photophysics-related fluorescence fluctuations)are given by eqn (1):~gðt; d; vÞ ¼ c rffiffiffiffiffið ðpkðz 1 Þkðz 2 Þdz 1 dz 24 Dt 8Dt þ w 2 ðz 1 Þþw 2 ðz 2 Þ" # (1)ðz 2 z 1 Þ 22d 2exp4Dt 8Dt þ w 2 ðz 1 Þþw 2 ðz 2 Þwhere t is the lag-time of correlation, d is the lateral distancebetween the detection volumes, 3 1 and 3 2 are factors proportionalto overall excitation intensity and detection efficiency in eachfocus, c is the concentration of fluorescent molecules or particles,and D their diffusion coefficient. Here, the functions k(z) andw(z) are given by eqn (2)–(4):andwithð a drrkðzÞ ¼2R 2 ðzÞ exp0" # 2 1=2lex zwðzÞ ¼ w 0 1 þpw 2 0 n (2)2r 2¼ 1R 2 ðzÞexp2a 2R 2 ðzÞ(3)" #21=2lem zRðzÞ ¼R 0 1 þpR 2 0 n (4)where l ex and l em are excitation and centre emission wavelengths,n is the sample refractive index, a is the confocal pinholeradius, and w 0 and R 0 are fit parameters. For calculating theACF of each focus, one has to set, in eqn (1), d to zero, and toreplace 3 1,2 by either 3 12 or 3 22 , respectively. The integration ineqn (1) has to be performed numerically. Fitting of experimentaldata is done globally for both the ACFs and the CCF, where onehas fit parameters 3 1 $c 1/2 , 3 2 $c 1/2 , w 0 , R 0 , and D.As was recently shown in ref. 25, the absolute fitted values ofw 0 and R 0 can become rather arbitrary when working underoptical conditions with strong aberration. However, as was alsoshown in ref. 25, the fitted value of diffusion coefficient is stillremarkably exact. In other words, the absolute values of w 0 andR 0 , are not significant for the calculation of the diffusion coefficientand therefore they are not reported.The distance d between detection volumes is a setup constantand has to be determined only once for a given measurementsystem. This can be done for example by determining the diffusioncoefficient of fluorescently labelled polymer particles withknown size. This calibration procedure has been described indetail in ref. 26.More technical details concerning the setup can be found inref. 24.ExperimentsDynamic light scattering (DLS) measurements were performedon a standard ALV 5000 system, equipped with a laser of 633 nmwavelength. Scattering intensity was detected at angles of 60 ,90 , and 120 , respectively, and the hydrodynamic radius wascalculated with a second order cumulant fit using the Stokes–Einstein relation. The measurement system was equipped witha temperature controlled water bath giving a precision in sampletemperature stabilization of 0.2 K.The 2fFCS measurement system was based on a Micro-Time200 Fluorescence Spectroscopy and Microscopy System(MT200, PicoQuant GmbH, Berlin, Germany) as described inref. 26 and 27 with a dual-focus modification as presented in ref.24 and Fig. 1. The setup is equipped with two identical 470 nmlasers (LDH-P-C-470B), two identical 635 nm lasers (LDH-P-635), as well as one 532 nm laser (PicoTA530N), whose beam issplit into two mutually time-delayed pulse trains. All lasers arelinearly polarized in such a way that, after combining the light ofall lasers, one obtains for each wavelength pulse trains withalternately switching polarization. Pulse width is 50 ps, andThis journal is ª The Royal Society of Chemistry 2009 Lab Chip, 2009, 9, 1248–1253 | 1249