A new FRAP/FRAPa method for three-dimensional diffusion measurements based on multiphoton excitation microscopy

Abstract

We present a new convenient method for quantitative three-dimensionally resolved diffusion measurements based on the photobleaching (FRAP) or photoactivation (FRAPa) of a disk-shaped area by the scanning laser beam of a multiphoton microscope. Contrary to previously reported spot-photobleaching protocols, this method has the advantage of full scalability of the size of the photobleached area and thus the range of diffusion coefficients, which can be measured conveniently. The method is compatible with low as well as high numerical aperture objective lenses, allowing us to perform quantitative diffusion measurements in three-dimensional extended samples as well as in very small volumes, such as cell nuclei. Furthermore, by photobleaching/photoactivating a large area, diffusion along the optical axis can be measured separately, which is convenient when studying anisotropic diffusion. First, we show the rigorous mathematical derivation of the model, leading to a closed-form formula describing the fluorescence recovery/redistribution phase. Next, the ability of the multiphoton FRAP method to correctly measure absolute diffusion coefficients is tested thoroughly on many test solutions of FITC-dextrans covering a wide range of diffusion coefficients. The same is done for the FRAPa method on a series of photoactivatable green fluorescent protein solutions with different viscosities. Finally, we apply the method to photoactivatable green fluorescent protein diffusing freely in the nucleus of living NIH-3T3 mouse embryo fibroblasts.

FIGURE 1

Schematic representation of the bleaching phase of a two-photon FRAP measurement. The bleaching illumination distribution I_b(x,y,z) scans line by line the selected circular region of radius w. A high laser power is delivered on the sample when the system is scanning the inner part of the circle (dashed lines), inducing the photobleaching/photoactivation of the fluorescent molecules. An x,z view of the scanning process is also shown, where r_e and z_e are the axial and radial 1/e² extensions of the Gaussian bleaching illumination distribution.

FIGURE 2

Schematic representation of the optical system. The light emitted by an argon laser is delivered by an optical fiber to the confocal head. The power delivered to the sample can be tuned via an acousto-optic tunable filter. An infrared Ti:sapphire laser is also coupled to the confocal head for two-photon experiments. In this case, the power is controlled by an electro-optic modulator. A short-pass dichroic mirror (715 nm, SP715) prevents reflected infrared light to reach the detector. Scanning is accomplished either with conventional scanning mirrors SM1 and SM2, or with a couple of resonant scanning mirrors to acquire images at a fast rate (not shown). The fluorescent light coming from the sample is discriminated from the excitation light by the acousto-optic beam splitter and brought to the detector after passing through the pinhole (in the case of confocal imaging) and through a diffractive element which allows selecting the detected wavelength range.

FIGURE 3

(A) An example is shown of a two-photon disk FRAP experiment on FD500 in an 85% (w/w) glycerol solution. Images of the sample are acquired at a regular time interval of 0.36 s. The first image shows the sample before photobleaching. The white disk (3 μm radius) in the second image comes from the photobleaching step at t = 0. Within the (user-defined) disk, the laser intensity is switched to a high value to quickly induce local photobleaching. From the third image on, the laser is switched back to a low intensity and a series of images is acquired of the recovery process at regular time intervals. The outlined circle in the first frame represents the selected reference region to account for bleaching during imaging and laser intensity fluctuations. (B) Custom image processing software is used to extract the normalized recovery curve from the images, as explained in the main text (solid dots). The diffusion coefficient D, the mobile fraction k, and the bleaching parameter K_0n are calculated from a best fit of the model to the recovery data (solid line). (C and D) A corresponding two-photon FRAPa experiment is shown on paGFP in a 51% (w/w) sucrose solution. The solid dots are the experimental data and the solid line is the best fit of the model. The outlined circle in the first frame of panel C indicates the selected reference region.

FIGURE 4

(A) Two-photon FRAP experiments were performed on FD500 in an 85% (w/w) glycerol solution by bleaching a disk of 3 μm in radius with different laser powers to evaluate the axial extension z_e of the effective photobleaching PSF. The axial bleaching resolution was determined by fitting of the two-photon disk FRAP model to the experimental recovery curves. Every data point is the average of 10 measurements. The error bars are the corresponding standard deviations (SDs). (B) The corresponding K₀ values are shown as a function of the bleaching laser power in a log-log plot. The slope of the linear fit is 2.7. (C) The same measurement was performed on paGFP in a solution containing 56% (w/w) of sucrose. The horizontal solid line represents the average of the z_e values corresponding to a laser power ≤25 mW. The dashed lines indicate the corresponding SD. (D) A log-log plot of K₀ as a function of the photoactivation laser power is shown. The solid line is a linear fit to the data at the left of the vertical dashed line, having a slope of 1.8.

FIGURE 5

The capability of the model to provide correct estimates of D depending on the size of the bleached region has been tested by performing FRAP experiments for different radii of the disk between 0.75 μm and 3 μm. The experiments have been performed on FD150 in 90% w/w glycerol (A) and on FD500 in 85% w/w glycerol (B). Each value is the average of 10 measurements and the error bars are the corresponding SDs. The horizontal solid line represents the value of the diffusion coefficient as measured by conventional confocal FRAP.

FIGURE 6

(A–C) The diffusion coefficients of three different FITC-dextrans probes in solutions of different viscosities are measured with the multiphoton FRAP method (10 measurements for each sample) and with the conventional confocal FRAP method (five measurements for each sample): (A) FD150, (B) FD250, and (C) FD500. Within the experimental error a good correspondence is found between both measurements. (D) The diffusion coefficients of paGFP solutions of different viscosities are measured with the two-photon FRAPa method (10 measurements for each sample) and with the confocal FRAPa method (five measurement for each sample). Again, a good correspondence is found between both measurements.

FIGURE 7

(A and B) Two-photon FRAP experiment on paGFP diffusing in the nucleus of a mouse embryo fibroblast. The first image shows the sample before photoactivation in the selected region (2.5 μm in radius). The subsequent images show the fluorescence redistribution after photoactivation of the selected region. The scale bar in (A) is 5 μm. (C) The redistribution curve is the average of seven experiments in different cells to obtain a smoother curve. The thickness of the nuclei was h = 8 μm on average. This value was used to fit Eq. 15 to the experimental data, from which a diffusion coefficient was obtained of (19 ± 4) μm²/s. As expected, all molecules were found to be mobile (k = 1.002 ± 0.007).