A quantitative approach to analyze binding diffusion kinetics by confocal FRAP

Abstract

Most of the important types of interactions that occur in cells can be characterized as binding-diffusion type processes, and can be quantified by kinetic rate constants such as diffusion coefficients (D) and binding rate constants (k(on) and k(off)). Confocal FRAP is a potentially important tool for the quantitative analysis of intracellular binding-diffusion kinetics, but how to dependably extract accurate kinetic constants from such analyses is still an open question. To this end, in this study, we developed what we believe is a new analytical model for confocal FRAP-based measurements of intracellular binding-diffusion processes, based on a closed-form equation of the FRAP formula for a spot photobleach geometry. This approach incorporates a binding diffusion model that allows for diffusion of both the unbound and bound species, and also compensates for binding diffusion that occurs during photobleaching, a critical consideration in confocal FRAP analysis. In addition, to address the problem of parametric multiplicity, we propose a scheme to reduce the number of fitting parameters in the effective diffusion subregime when D's for the bound and unbound species are known. We validate this method by measuring kinetic rate constants for the CAAX-mediated binding of Ras to membranes of the endoplasmic reticulum, obtaining binding constants of k(on) ∼ 255/s and k(off) ∼ 31/s.

Figure 1

Experimentally determined postbleach fluorescence intensity profiles and recovery curves for EGFP-HRas C181S C184S in the ER. (A) A representative image of EGFP-HRas C181S C184S in a COS7 cell. The two white boxes represent 40 × 40- and 60 × 60-pixel square observation ROIs in the ER area. (B) Time points from a representative FRAP experiment for EGFP-HRas C181S C184S in the ER area of COS7 cells for $r_{\text{n}}=0.6\mu \text{m}$ and $r_{\text{n}}=1.1\mu \text{m}$ (dashed white circles) in 40 × 40- and 60 × 60-pixel squares (4.4 × 4.4 $\mu {\text{m}}^2$ and 6.6 × 6.6 $\mu {\text{m}}^2$). (C) Representative averaged initial postbleach profiles of EGFP-HRas C181S C184S from the ER area of COS7 cells (n = 10) for r_n = 0.6 μm and r_n = 1.1 μm after 10 or 20 photobleaching scans. Profiles were fitted by exponentials of Gaussians (Eq. 4) to obtain effective radii. (D) The effective radii (r_e) found for different FRAP-setup data were compared with the nominal radii (r_n) and bleaching-depth parameter (K). (E) Representative averaged FRAP curves (n = 10) for r_n = 0.6 μm and r_n = 1.1 μm after 10 or 20 photobleaching scans. Error bars show standard errors. Solid black lines are fit by the effective-diffusion model. (F) Comparison of $D_{\text{eff}}$ values for FRAP data obtained for the above experimental r_n conditions.

Figure 2

Fitting the FRAP data with an effective-diffusion model and determination of the approximate order of binding rate constants. (A) A representative averaged FRAP data set (solid circles) for EGFP-HRas C181S C184S in the ER area of COS7 cells ($r_{\text{n}}$ = 1.1 $\mu \text{m}$, 10 bleach scan iterations) was fitted by the effective-diffusion submodel with $D_{\text{eff}}=7.3\mu \text{m}/{\text{s}}^2$ (solid black line). (B) To obtain approximate orders of the rate constants, theoretical FRAP curves were plotted using Eqs. 6 and 7 for different $k_{\text{on}}$ (1, 10, 50, 100, 200, and 400 (${\text{s}}^{-1}$)) for k_off = k_on/K_p, where K_p = 8.0. (C) The residuals between the averaged FRAP data and theoretical FRAP curves in B are plotted. The binding rate constants, k_on > 150/s, produce residuals similar to the effective-diffusion model (solid black line). Stars represent the minimal residual points and squares the residuals at $k_{\text{on}}=$1, 10, 50, 100, 200, and 400 (${\text{s}}^{-1}$).(Insets) Zooms of the boxed areas not shown to scale to emphasize the differences.

Figure 3

Binding rate constants from one-parameter fitting. (A) $k_{\text{on}}$ found from one-parameter fitting for different FRAP setups. (B) $k_{\text{off}}$ determined from $k_{\text{off}}=k_{\text{on}}/K_{\text{P}}$ for $K_{\text{P}}$ determined using Eq. 9. Error bars show standard deviations. (C) The best-fitting curve from one-parameter fitting (solid black line, $k_{\text{on}}=214.8/\text{s}$, $k_{\text{off}}=24.8/\text{s}$, and $K_{\text{P}}=8.4$) was compared with a representative FRAP data set ($r_{\text{n}}$ = 1.1 $\mu \text{m}$, 10 bleach scan iterations) and an FRAP curve generated by the effective-diffusion submodel (solid gray line, $D_{\text{eff}}=7.3\mu \text{m}/{\text{s}}^2$).