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  • In order t http www apexbt

    2021-09-15

    In order to validate the correctness of our interpretation of the gap-FRAP data and the analysis of GJC in astrocytes, we used a mathematical model based on morphological and experimental data. This mathematical model is based on SR101 diffusion in an elementary network. In agreement with the morphologies shown in Fig. 1, the photo-bleached cell (Cell 1 in Fig. 5A) was modeled as an object of 50 μm total length, which included a 10 μm-large Phenformin flanked by two 20 μm long processes on each side. These parameters were deduced from morphological analysis of stained astrocytes as illustrated in Figs. 1C1 and C2. Since we do not expect significant signal variation in the Z-axis during the experiments, we considered cells as two-dimensional objects. To emulate diffusion into the bleached astrocyte of SR101 molecules coming from nearby coupled astrocytes, we also position two “reservoir” cells (Cell 2 and Cell 2′ in Fig. 5A) that are coupled to the extremities of Cell 1 processes via gap junctions. Note that the overall shape of Cells 2 and Cell 2′ was kept as simple as possible to limit computation times. As a starting point, we used the experimental data obtained in the presence of CBX (Fig. 4C), i.e. without GJC, to estimate the SR101 diffusion coefficient Dcbx and the soma surface area of the bleached cell (Cell 1), vS. Fig. 4F shows that in the presence of CBX the fluorescence level in astrocytes around the bleached cell is not altered by the photo-bleaching process, even for those that are found close to the bleached cell. Therefore we considered that in the presence of CBX, GJC between astrocytes is totally abolished, in agreement with the well-documented effect of CBX on GJC in acute slices (Wallraff et al., 2004; Rouach et al., 2008). We thus fixed the coupling strength G in the mathematical model to G = 0 and used nonlinear optimization to estimate the values of Dcbx and vS based on the experimental data of Fig. 4C. We estimated Dcbx = 1.35 μm2/s and vS = 70 μm2. As illustrated in Fig. 5B1, the initial reduction of fluorescence in the ROI after photo-bleaching progressively recovered due to Phenformin fluorescent SR101 molecules coming from the processes of the photo-bleached cell itself but not from the reservoir cells, as expected. Note that in this case the resulting quality of the fit between the curve obtained from the model and the experimental data was excellent (Fig. 5B2). When applied to the gap-FRAP data in the Double KO mice (Fig. 4D), we obtained similar results (DdoubleKO = 1.00 μm2/s and vS = 50 μm2), with, again an excellent fit to the data (Fig. 5B2). We then used the experimental gap-FRAP data obtained in control condition (Fig. 4C) to estimate the SR101 diffusion coefficient in control condition Dctrl; the surface area of each reservoir cells vR and the coupling strength G. In this case, we fixed the soma surface area of the bleached cell to the value estimated with CBX condition indicated above, i.e. vS = 70 μm2. Our estimations yielded: Dctrl = 3.04 μm2/s, G = 1.0 and vR = 105 μm2, with excellent fit to the experimental data (Fig. 5C2). Unlike the CBX case, the initial reduction of fluorescence in the ROI after photobleaching now recovered both by fluorescence coming from the processes of the photo-bleached cell and from the reservoir cells. This is evidenced in Fig. 5C1 where the color intensity of both the processes of Cell 1 and that of Cell 2 and Cell 2' decreased during fluorescence recovery while intensity in the ROI increased. The estimated apparent diffusion coefficient D is therefore reduced by a factor of 2.2 with CBX, (Dctrl = 3.04 vs Dcbx = 1.35 μm2/s). We note that such a difference between the apparent diffusion coefficients (ctrl vs CBX) was consistently obtained in our fits to the experimental data. For instance, we could not get good fitting quality when the two diffusion coefficients (ctrl and CBX) were constrained to adopt identical values. Hence, our study indicates that CBX reduces the apparent diffusion coefficient of SR101 within the processes of the photo-bleached cell.