Supplementary Figure 3: Simulated FCS-calibrated imaging

(a) Illustration of a homogeneous fluorophore distribution. (b) The slope of the fluorophore concentration as function of pixel fluorescence intensity gives the calibration coefficient. Simulated PSF is a 3D Gaussian (Eq. S1). The size of the PSF is characterized by its e² decay w₀ and z₀ in XY and Z direction, respectively. Here and in all subsequent panels background and detector noise are not simulated. (c) Simulated Z-stack of a point source (50 fluorophores). (d) Using the calibration coefficient and Eqs. S15, S16, and S19 the total number of proteins in each plane is calculated. Several planes along the Z-direction are summed (circles). The expected protein number is obtained when a large region along Z is considered (>2*z0). Simulated images have a pixel-size of 0.4, 0.6, 0.8, 1 times w₀ in all directions (different colors). Triangles give the result when all pixels are considered (Eq. S19). Squares give the approximation using the integral of the PSF along Z (Eq. S21). Diamonds give the approximation when the integral of the whole PSF and the pixel with the highest intensity is used (Eq. S23). (e) Simulated fluorophores distributed in a XZ plane (density of 100 fluorophores/μm²). Scale bar 10 μm. (f) Protein density is computed using Eqs. S15 and S24. The expected density is obtained for a region width along the X direction of > 2*w₀. Triangles give the result when all pixels are considered. Squares give the approximation when the integral of the PSF along X is used (Eq. S26). (g) Simulated fluorophores distributed in a XY plane (density of 100 fluorophores/μm²). (h) The average protein density is summed for planes along Z (Eqs. S15 and S17). The expected density is obtained for a region width > 2*z₀. Triangles give the result when all pixels are considered. Squares give the approximation when the integral of the PSF along Z is used (Eq. S29). Each fluorophore has a simulated intensity of 1000 (a.u.), the simulated PSF is characterized by w₀ = 250 nm, z₀ = 1500 nm. The black lines give the theoretically expected result after integration of the Gaussian function where N e is the expected protein number/density (50 in d, and 100 in f and h) and Rs is the region size in unit of the PSF characteristic size.