Analysis of diffusion and binding in cells using the RICS approach

Abstract

The movement of macromolecules in cells is assumed to occur either through active transport or by diffusion. However, the determination of the diffusion coefficients in cells using fluctuation methods or FRAP frequently give diffusion coefficient that are orders of magnitude smaller than the diffusion coefficients measured for the same macromolecule in solution. It is assumed that the cell internal viscosity is partially responsible for this decrease in the apparent diffusion. When the apparent diffusion is too slow to be due to cytoplasm viscosity, it is assumed that weak binding of the macromolecules to immobile or quasi immobile structures is taking place. In this article, we derive equations for fitting of the RICS (Raster-scan Image Correlations Spectroscopy) data in cells to a model that includes transient binding to immobile structures, and we show that under some conditions, the spatio-temporal correlation provided by the RICS approach can distinguish the process of diffusion and weak binding. We apply the method to determine the diffusion in the cytoplasm and binding of Focal Adhesion Kinase-EGFP to adhesions in MEF cells.

Figure 1

A) Schematic representation of the multiplying-shifting operation used in the 2-dimensional correlation function calculation. B) In the random-locations model, particles diffuse and stop at specific locations (red circles). In the ordered-locations model, particles diffuse and then stop ad specific structures in the cell (yellow circles).

Figure 2

A) One frame showing the streaks due to the fast diffusing molecules and the round shapes due to the transiently immobile molecules. B) RICS autocorrelation function. C), D) and E are the fit (lower surface) and the residues (upper surface) using the diffusion, binding and diffusion + binding models (respectively). The binding + diffusion model gives the best fit.

Figure 3

Frames A), B) C) and RICS function D), E), F) obtained using the binding model showing the effect of the narrowing of the RICS function as the binding time decreases from 0.5s to 0.005s, respectively.

Figure 4

Effect of the immobile subtraction algorithm. A) Molecules are diffusing and binding to fixed locations. B) The RICS function is the sum of the diffusion and the binding. When the molecules are bound they give a contribution to the RICS function which is due to the shape of the PSF. C) Since the location of binding are fixed, this contribution can be subtracted using the immobile subtraction algorithm.

Figure 5

A) and B) Horizontal and C) and D) vertical sections of the RICS surface for different values of the diffusion coefficient and binding time. A) The diffusion coefficient varied from D=400 to 2µm²/s). B) The binding time varied from 0.00001 to 0.01s. C) The diffusion coefficient varied from D=200 to 0.02µm²/s). D) The binding time varied from 0.0001 to 0.1s

Figure 6

RICS analysis of a MEF cell1 expressing FAK-EGFP. This cell has regions with few adhesions (A) and regions with many adhesions (B). The corresponding RICS function (C) and (D) and the fits according to the diffusion model (E) and (F) and binding model (G) and (H) are reported in table 3.

Figure 7

A) MEF cell2 expressing FAK-EGFP. Cell 2 has high concentration of adhesions everywhere. B) The RICS function has the characteristics shape of “binding”. C) and E) correspond to the horizontal and vertical fits using the binding + diffusion model after immobile subtraction using 10 frames for the moving average. ”. D) and F) correspond to the horizontal and vertical fits using the binding + diffusion model after immobile subtraction using 40 frames for the moving average.