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. 2011;6(8):e22962.
doi: 10.1371/journal.pone.0022962. Epub 2011 Aug 19.

Protein diffusion in mammalian cell cytoplasm

Thomas Kühn  1 , Teemu O Ihalainen, Jari Hyväluoma, Nicolas Dross, Sami F Willman, Jörg Langowski, Maija Vihinen-Ranta, Jussi Timonen
Affiliations

Protein diffusion in mammalian cell cytoplasm

Thomas Kühn et al. PLoS One. 2011.

Abstract

We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. FRAP experiment in an NLFK cell stably expressing EYFP.
(a) The average (n = 10) bleach profile measured on fixed cells expressing EYFP. Scale bar 2 formula imagem. (b) Fluorescence distribution before the bleach pulse and the position of the circular bleach area (diameter 20 pixels, FWHM 3.7 formula imagem). Subsequent images show the fluorescence distribution immediately (t = 0 ms), and 250 ms and 1 s after the bleach pulse. Scale bar 10 formula imagem. (c) The measured recovery curve (Axelrod normalization) and a fit by the free-diffusion model of Soumpasis.
Figure 2
Figure 2. Duration of the bleaching phase in FRAP experiments for two confocal microscope setups.
(a) Schematic representation of the confocal imaging combined with bleaching phase. (b) Bleach phase duration as a function of the number of bleaching iterations for the two confocal microscope setups used in the study, red is the results for a Zeiss LSM510 and blue for an Olympus FV1000 confocal microscope.
Figure 3
Figure 3. 2D cross-section of a digital model cell.
The different regions of the cell are displayed in different colors (cytoplasm in cyan, nucleus in yellow, and nuclear envelope in red). The color intensity at each pixel refers to the effective porosity (volume fraction available for protein motion) at that point in the cell. Scale bar 10 µm.
Figure 4
Figure 4. Visualization of the cross-correlation fitting of corresponding frames.
For a given experimental image formula image, the cross-correlation coefficients formula image (red) each have a global maximum formula image (blue crosses). By tuning the parameters formula image and formula image, formula image becomes a linear function of formula image (black crosses and curve), whose slope determines the simulation time step formula image. The deterioration of the maximum in formula image as a function of the experiment frame number stems from the broadening of the bleach profile, which inevitably decreases the relative difference between adjacent frames. Ultimately, this relative difference limits the amount of analyzable experimental frames, which may limit the applicability of the method to slow enough diffusion processes.
Figure 5
Figure 5. Simulated Virtual Cell data for FRAP experiments with a particle diffusion coefficient of D = 25 m/s.
Simulations are for two different bleach locations, different bleach phase durations, and different bleach-laser profiles. (a) A bleached region in the middle of an isotropic environment immediately after a 1 ms bleach pulse with either a cylindrical (diameter 3.7 formula imagem) or Gaussian bleach-laser profile (FWHM 3.7 formula imagem). (b) A cross section of the cell with the bleached region far away from the cell boundaries and the nucleus. The blow-up images show the bleached region after 1 ms and 75 ms bleach pulses for the cylindrical bleach profile, and after a 75 ms bleach pulse for the Gaussian profile. (c) A bleached region near the cell boundary and immediately after a 75 ms bleach pulse for the Gaussian bleach profile. (d) The recovery curves for an isotropic environment and 1 ms bleach time with a cylindrical (purple) or Gaussian (dark green) bleach profile, for a real cell geometry with a cylindrical bleach profile and 1 ms (blue) or 75 ms (black) bleach time, with a Gaussian bleach profile and 75 ms (dark gray) bleach time, and for a bleached region near the cell boundary with a Gaussian bleach profile and 75 ms bleach time (light gray). Scale bars 10 formula imagem.
Figure 6
Figure 6. Virtual Cell simulation results for different FRAP experiments (blue) and their fits by the free diffusion model of Soumpasis (green).
In the upper panels the bleach duration is very short, 1 ms, while the simulation geometry and bleach profile are varied. In the lower panels the bleach duration is much longer, 75 ms, and bleaching is done in a 2D outline derived from a real cell, either in the middle of the cell or near the plasma membrane.
Figure 7
Figure 7. Results of FRAP analysis by the new method.
(a) Correlation between experiment and simulation. Data points correspond to the function formula image and the lines of the same color show the linear fit through the data. (b) Measured (data points) and simulated curves (continuous curves) of fluorescence recovery at the bleached ROI. The data were normalized by the maximum pixel value of the provided image data. Curves of the same color in (a) and (b) are taken from the same measurement. (c) Map of the local cytoplasm and nucleoplasm diffusion coefficients in a cross section of an NLFK cell. Scale bar 10 formula imagem.
Figure 8
Figure 8. FFM results for NLFK cells.
(a) An image of a cell taken before the fluorescence fluctuation measurements. The marked dots denote the points measured. Scale bar 5 m. (b) Autocorrelation curves of the measurements. The colors of the lines correspond to those of the measured point. (c) Distribution of the measured diffusion coefficients of the fast component (44 cells and 138 points).
Figure 9
Figure 9. A cross section of an artificial porous medium that is homogeneous in the third dimension.
Its porosity is 68%. The liquid phase is marked blue and the impermeable solid phase is brown.
See this image and copyright information in PMC

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