Figure 1.
A schematic illustration on using FE analysis to compute the kinase activity map from apparent FRET video images.
(A) An image showing the original location of activated FRET biosensors. (B) A possible apparent FRET signals at the next time step, where newly activated biosensors (hence actions of kinase) are mixed with those translocated from (A) due to diffusion. (C) The simulated FRET distribution map of the biosensor due to diffusion from (A). (D) The actions of kinase activity detected by subtracting (C) from (B). Yellow or red dots represent the FRET biosensors activated by the target kinase at different time steps. Green dots represent the activated biosensors translocated from other locations due to diffusion.
Figure 2.
The flow chart representing the application of FE method to discretize the cell geometry and calculate diffusion coefficient using Fick's Law and linear regression based on two consecutive concentration images and the time interval (dt).
Step (A) shows the computation of stiffness matrix K and the mass matrix M based on the FE discretization on the cell geometry. In step (B), the concentration vectors (un and un+1) are obtained by collecting the concentration values at the nodes of FE discretization in the images. In step (C), the least-square linear fitting is used to estimate the diffusion coefficient based on all the information from the previous steps: M, K, un, un+1 and dt.
Figure 3.
The computational procedure used to simulate FRAP experiment and calculate diffusion coefficient to evaluate the accuracy of the FE-analysis.
With an assigned cell geometry, an initial concentration, and a diffusion coefficient, a series of concentration images at later time steps were generated using the finite element method and diffusion model. The simulated concentration maps were then used as the input to calculate diffusion coefficients using FE analysis and linear regression. This calculated diffusion coefficient was compared with the assigned diffusion coefficient to examine the accuracy of the method. The main output of this procedure is the simulated concentration images and the estimated diffusion coefficient as outlined in the dashed boxes. The data connected by dashed line arrows were shared between different layers.
Figure 4.
The validation of the FE-based method using computer simulation.
(A) The initial concentration map of a diffusive fluorescence molecule in a single cell; (B) the concentration map at 0.0313 s produced by computer simulation with an assigned diffusion coefficient of 29 µm2/sec; (C) the simulated fluorescence recovery curve for 9 sec after photobleaching; (D) the scattered plot of the WDLC, −dt·K·0.5(un+un+1), vs. the WCCT, M(un+1−un), on each mesh node. Linear fitting is represented by the solid line.
Figure 5.
The characterization of the Src biosensors.
(A) The Lyn-Src biosensor is anchored to the lipid rafts of the plasma membrane via N-terminal acylation sequences derived from the N-termini of Lyn kinase; the KRas-Src biosensor is connected to the non-lipid-rafts region through C-terminal prenylation sequences derived from KRas. Panel (B) shows the expression level of HeLa cells transfected with Cytosolic-Src, Lyn-Src, or KRas-Src biosensors, from left to right, respectively.
Figure 6.
The FE analysis procedures for assessing and simulating diffusion based on experimental FRAP images are illustrated.
With two consecutive experimental concentration maps and the time interval (dt), the apparent diffusion coefficient and boundary conditions were estimated by using our FE-based diffusion analysis. Subsequently, the diffusion coefficient and the boundary conditions were used to simulate and predict the concentration image at the next time step (est_un+1), which was produced by allowing linear diffusion from the current image (un). The main outputs of the described procedure are the apparent diffusion coefficient and the simulated concentration maps, as outlined in the dashed boxes.
Figure 7.
The experimental FRAP images of Lyn-Src biosensor are compared with those predicted by simulation.
(A) Left: the fluorescence intensity image of a cell before photobleaching, with the red-colored outline defining the cell edge in simulation and blue-colored outline defining the region of interest monitored for fluorescence recovery. Middle and right: the fluorescence intensity images at 0 and 1 min after photobleaching, respectively. The complete time course of this FRAP experiment is shown in Movie S1. (B) The time course of fluorescence recovery in the photobleached area as marked in (A). (C) Left: the concentration map after photobleaching (0 min), computed by normalizing the fluorescence intensity with the image before photobleaching. Middle and right: the experimental and simulated concentration maps at 1 min after photobleaching. (D) The scattered plot of WDLC vs. WCCT on each mesh node, with the linear fitting indicated by the solid line.
Figure 8.
The experimental recovery images after photobleaching of Src biosensor targeted to plasma membrane outside of lipid rafts (KRas-Src biosensor) are compared with those predicted by simulation.
(A) Left: the fluorescence intensity image of a cell before photobleaching, with the red-colored outline defining the cell edge in simulation and blue-colored outline defining the region of interest monitored for fluorescence recovery. Middle and right: the fluorescence intensity images at 0 and 1 min after photobleaching, respectively. (B) The time course of fluorescence recovery in the photobleached area as marked in (A). (C) Left: the concentration map after photobleaching (0 min), computed by normalizing the fluorescence intensity with the reference image before photobleaching. Middle and right: at 1 min after photobleaching, the experimental concentration map is similar to the simulation. (D) The scattered plot of the weighted Laplacian of the concentration vs. the weighted change of concentration in time on each mesh node, with the linear fitting indicated by the solid line.
Figure 9.
The experimental FRAP images for the cytosolic Src biosensor are compared with those predicted by simulation.
(A) Left: the fluorescence intensity image of a cell before photobleaching, with the red-colored outline defining the cell edge in simulation and blue-colored outline defining the region of interest monitored for fluorescence recovery. Middle and right: the fluorescence intensity images at 0 and 1 min after photobleaching, respectively. (B) The time course of fluorescence recovery in the photobleached area as marked in (A). (C) Left: the concentration map after photobleaching (0 sec), computed by normalizing the fluorescence intensity with the image before photobleaching. Middle and right: the experimental and simulated concentration maps at 6 seconds after photobleaching, with the difference between experiment and simulate indicated by two arrows. (D) The scattered plot of the weighted Laplacian of the concentration vs. the weighted change of concentration in time on each mesh node, with the linear fitting indicated by the solid line.
Figure 10.
The assessment of the accuracy of the diffusion model for the Lyn-Src, KRas-Src, and Cytosolic-Src biosensors.
(A) the difference (absolute value) of fluorescence intensity between simulated and experimental images for (i) Lyn-Src biosensor at 10 sec after photobleaching, (ii) KRas-Src biosensor at 10 sec after photobleaching, (iii) Cytosolic-Src biosensor at 1 sec after photobleaching because of its fast recovery rate; (B, i–iii) the scattered plots of smoothed WDLC vs. smoothed WCCT for the corresponding cells shown in (A, i–iii).
Figure 11.
The assessment of the diffusion model accuracy and the subtraction of biosensor diffusion effects from the apparent FRET images.
(A) The bar graph shows the apparent diffusion coefficients (mean±S.E.M.) of Lyn-Src and KRas-Src biosensors in control cells [0.11±0.01 µm2/sec (n = 43) and 0.18±0.02 µm2/sec (n = 17), respectively], and in cells treated with MβCD [0.17±0.01 µm2/sec (n = 20) and 0.20±0.01 µm2/sec (n = 22), respectively]. (B) The bar graph shows the coefficients of determination (mean±S.E.M.) of the diffusion models for Lyn-Src and KRas-Src biosensors in control cells [0.79±0.033 (n = 50) and 0.56±0.06 (n = 15), respectively], and in cells treated with MβCD [0.68±0.07 (n = 11) and 0.47±0.06 (n = 16), respectively]. Asterisks in (A) and (B) denote significant differences (p<0.05) between different groups as indicated. (C) The FRET signals before and after the subtraction of the effect of Lyn-Src biosensor diffusion from the apparent FRET ratio images. Top panels show the apparent FRET images and lower panels show the corresponding diffusion-subtracted FRET images of the Lyn-Src biosensor, at 0.7, 3.1, 6.1 min after EGF stimulation as indicated. The spatial-temporal dynamics of FRET signals before and after subtracting diffusion is also shown in Movie S2.