Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy

Abstract

Fluorescence recovery after photobleaching (FRAP) is a widely used technique for studying diffusion in biological tissues. Most of the existing approaches for the analysis of FRAP experiments assume isotropic diffusion, while only a few account for anisotropic diffusion. In fibrous tissues, such as articular cartilage, tendons and ligaments, diffusion, the main mechanism for molecular transport, is anisotropic and depends on the fibre alignment. In this work, we solve the general diffusion equation governing a FRAP test, assuming an anisotropic diffusivity tensor and using a general initial condition for the case of an elliptical (thereby including the case of a circular) bleaching profile. We introduce a closed-form solution in the spatial coordinates, which can be applied directly to FRAP tests to extract the diffusivity tensor. We validate the approach by measuring the diffusivity tensor of \(3~\mathrm {kDa}\) FITC-Dextran in porcine medial collateral ligaments. The measured diffusion anisotropy was \(1.42 \pm 0.015\) (SE), which is in agreement with that reported in the literature. The limitations of the approach, such as the size of the bleached region and the intensity of the bleaching, are studied using COMSOL simulations.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

References

  1. Axelrod D, Koppel D, Schlessinger J, Elson E, Webb WW (1976) Mobility measurement by analysis of fluorescence photobleaching recovery kinetics. Biophys J 16(9):1055–1069

    Article  Google Scholar 

  2. Brezis H (2010) Functional analysis. Sobolev spaces and partial differential equations. Springer, New York

    Google Scholar 

  3. Brinkman H (1949) A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl Sci Res 1(1):27–34

    Article  Google Scholar 

  4. Burton-Wurster N, Lust G (1990) Fibronectin and proteoglycan synthesis in long term cultures of cartilage explants in Ham’s F12 supplemented with insulin and calcium: effects of the addition of TGF-\(\beta\). Arch Biochem Biophys 283(1):27–33

    Article  Google Scholar 

  5. Curnier A, He Q-C, Zysset P (1995) Conewise linear elastic materials. J Elast 37:1–38

    MathSciNet  Article  Google Scholar 

  6. DiDomenico CD, Lintz M, Bonassar LJ (2018) Molecular transport in articular cartilage—what have we learned from the past 50 years? Nat Rev Rheumatol 14(7):393–403

    Article  Google Scholar 

  7. Greene GW, Zappone B, Zhao B, Söderman O, Topgaard D, Rata G, Israelachvili JN (2008) Changes in pore morphology and fluid transport in compressed articular cartilage and the implications for joint lubrication. Biomaterials 29(33):4455–4462

    Article  Google Scholar 

  8. Jönsson P, Jonsson MP, Tegenfeldt JO, Höök F (2008) A method improving the accuracy of fluorescence recovery after photobleaching analysis. Biophys J 95(11):5334–5348

    Article  Google Scholar 

  9. Kang M, Day CA, DiBenedetto E, Kenworthy AK (2010) A quantitative approach to analyze binding diffusion kinetics by confocal frap. Biophys J 99(9):2737–2747

    Article  Google Scholar 

  10. Kang M, Day CA, Kenworthy AK, DiBenedetto E (2012) Simplified equation to extract diffusion coefficients from confocal frap data. Traffic 13(12):1589–1600

    Article  Google Scholar 

  11. Le Bihan D, Mangin J-F, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H (2001) Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging 13(4):534–546

    Article  Google Scholar 

  12. Leddy HA, Guilak F (2003) Site-specific molecular diffusion in articular cartilage measured using fluorescence recovery after photobleaching. Ann Biomed Eng 31(7):753–760

    Article  Google Scholar 

  13. Leddy HA, Haider MA, Guilak F (2006) Diffusional anisotropy in collagenous tissues: fluorescence imaging of continuous point photobleaching. Biophys J 91(1):311–316

    Article  Google Scholar 

  14. Lee JI, Sato M, Ushida K, Mochida J (2011) Measurement of diffusion in articular cartilage using fluorescence correlation spectroscopy. BMC Biotechnol 11(1):19

    Article  Google Scholar 

  15. Lori N, Akbudak E, Shimony J, Cull T, Snyder A, Guillory R, Conturo T (2002) Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results. NMR Biomed 15(7–8):494–515

    Article  Google Scholar 

  16. Maroudas A (1968) Physicochemical properties of cartilage in the light of ion exchange theory. Biophys J 8(5):575–595

    Article  Google Scholar 

  17. Mazza D, Braeckmans K, Cella F, Testa I, Vercauteren D, Demeester J, De Smedt SS, Diaspro A (2008) A new FRAP/FRAPa method for three-dimensional diffusion measurements based on multiphoton excitation microscopy. Biophys J 95(7):3457–3469

    Article  Google Scholar 

  18. Qian H, Sheetz MP, Elson EL (1991) Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys J 60(40):910–921

    Article  Google Scholar 

  19. Shi C, Cisewski SE, Bell PD, Yao H (2014) Measurement of three-dimensional anisotropic diffusion by multiphoton fluorescence recovery after photobleaching. Ann Biomed Eng 42(3):555

    Article  Google Scholar 

  20. Shi C, Kuo J, Bell PD, Yao H (2010) Anisotropic solute diffusion tensor in porcine TMJ discs measured by frap with spatial fourier analysis. Ann Biomed Eng 38(11):3398–3408

    Article  Google Scholar 

  21. Sprague BL, Pego RL, Stavreva DA, McNally JG (2004) Analysis of binding reactions by fluorescence recovery after photobleaching. Biophys J 86(6):3473–3495

    Article  Google Scholar 

  22. Verkman AS (2002) Solute and macromolecule diffusion in cellular aqueous compartments. Trends Biochem Sci 27(1):27–33

    Article  Google Scholar 

  23. Xia Y, Farquhar T, Burton-Wurster N, Ray E, Jelinski LW (1994) Diffusion and relaxation mapping of cartilage-bone plugs and excised disks using microscopic magnetic resonance imaging. Magn Reson Med 31(3):273–282

    Article  Google Scholar 

  24. Xia Y, Farquhar T, Burton-Wurster N, Vernier-Singer M, Lust G, Jelinski L (1995) Self-diffusion monitors degraded cartilage. Arch Biochem Biophys 323(2):323–328

    Article  Google Scholar 

Download references

Acknowledgements

The Authors gratefully acknowledge the help of Ruth Seerattan for the help with sample preparation and of Elyar Asl Sabbaghian Hokm Abadi for useful discussions. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme [SF, WH], the Canadian Institutes of Health Research (CIHR) [WH], the Canada Research Chair Programme [WH], the Killam Foundation [WH], Dipartimento di Eccellenza 2018–2022, Politecnico di Torino, Project No. E11G18000350001 [AG, ART], the Biomedical Engineering Graduate Programme of the University of Calgary (Canada), through the BME GP Academic Award [KH] and the BME Research Scholarship Award [KH], the University of Calgary Eyes High Doctoral Programme [KH] and the Canadian Society for Biomechanics, through the CSB PhD Student Travel Grant [KH]. Part of this work was conducted during the visit of KH at the Department of Mathematical Sciences (DISMA) “G.L. Lagrange”, Politecnico di Torino, under the supervision of AG and with the support of the CSB PhD Student Travel Award.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Salvatore Federico.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hashlamoun, K., Abusara, Z., Ramírez-Torres, A. et al. Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy. Biomech Model Mechanobiol (2020). https://doi.org/10.1007/s10237-020-01346-z

Download citation

Keywords

  • FRAP
  • Anisotropic diffusion
  • Fibrous tissues
  • Ligaments
  • Direct measure