FRAP Diffusion Coefficient Calculator
Calculate diffusion coefficients from Fluorescence Recovery After Photobleaching data.
Results
Recovery curve
Model
F(t) = F(0) + M (F_i − F(0)) f(t), τ_D = w²/(4D), D = γ w²/(4τ½)
Disk: f(t) = e^(−2τ_D/t) [I₀(2τ_D/t) + I₁(2τ_D/t)], γ = 0.8946
Gaussian: F(t)/F_i = Σ (−K)ⁿ/n! / (1 + n(1 + 2t/τ_D)), F(0)/F_i = (1 − e^(−K))/K
Free 2D diffusion after an instantaneous bleach, with an immobile fraction 1 − M that stays bleached. The fluorescence is collected over the bleached disk (Soumpasis) or through the same Gaussian beam (Axelrod). Soumpasis (1983) solved the uniformly bleached disk exactly (his D = 0.224 w²/τ½); Axelrod et al. (1976) the Gaussian beam, where γ grows with the bleach depth K. Bleaching during the bleach pulse, flow, binding reactions and loss of fluorescence during the recovery imaging are not included; the bleached area must be small next to the cell.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Free 2D diffusion after an instantaneous bleach, with an immobile fraction. Bleaching during the pulse, flow, binding and the finite size of the cell are not included.
- Soumpasis D. M. (1983). Theoretical analysis of fluorescence photobleaching recovery experiments. Biophys. J. 41, 95–97. Closed-form recovery of a uniformly bleached disk, D = 0.224 w²/τ½. doi:10.1016/S0006-3495(83)84410-5
- Axelrod D., Koppel D. E., Schlessinger J., Elson E., Webb W. W. (1976). Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys. J. 16, 1055–1069. Gaussian-beam series in the bleach depth K and the mobile fraction. doi:10.1016/S0006-3495(76)85755-4