The Journal of Membrane Biology

, Volume 251, Issue 4, pp 601–608 | Cite as

Statistical Analysis of Bending Rigidity Coefficient Determined Using Fluorescence-Based Flicker-Noise Spectroscopy

  • Joanna DoskoczEmail author
  • Dominik Drabik
  • Grzegorz Chodaczek
  • Magdalena Przybyło
  • Marek Langner


Bending rigidity coefficient describes propensity of a lipid bilayer to deform. In order to measure the parameter experimentally using flickering noise spectroscopy, the microscopic imaging is required, which necessitates the application of giant unilamellar vesicles (GUV) lipid bilayer model. The major difficulty associated with the application of the model is the statistical character of GUV population with respect to their size and the homogeneity of lipid bilayer composition, if a mixture of lipids is used. In the paper, the bending rigidity coefficient was measured using the fluorescence-enhanced flicker-noise spectroscopy. In the paper, the bending rigidity coefficient was determined for large populations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 1,2-dioleoyl-sn-glycero-3-phosphocholine vesicles. The quantity of obtained experimental data allows to perform statistical analysis aiming at the identification of the distribution, which is the most appropriate for the calculation of the value of the membrane bending rigidity coefficient. It has been demonstrated that the bending rigidity coefficient is characterized by an asymmetrical distribution, which is well approximated with the gamma distribution. Since there are no biophysical reasons for that we propose to use the difference between normal and gamma fits as a measure of the homogeneity of vesicle population. In addition, the effect of a fluorescent label and types of instrumental setups on determined values has been tested. Obtained results show that the value of the bending rigidity coefficient does not depend on the type of a fluorescent label nor on the type of microscope used.


Membrane mechanics Vesicle fluctuation analysis Lipid bilayer 



This work was supported by the statutory found of Department of Biomedical Engineering, Wrocław University of Science and Technology, a Grant POIR.04.01.04-00-0050/15 to MP and ML by the National Centre for Research and Development (NCBiR) and Grant 2016/21/N/NZ1/02767 to DD by the National Science Centre. We would like to acknowledge the great contribution of reviewers to the final version of the manuscript.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Supplementary material

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Supplementary material 1 (DOCX 1268 KB)


  1. Angelova M, Dimitrov DS (1988) A mechanism of liposome electroformation. Trends in colloid and interface science II. Steinkopff, Darmstadt, pp 59–67CrossRefGoogle Scholar
  2. Behera GB, Mishra BK, Behera PK, Panda M (1999) Fluorescent probes for structural and distance effect studies in micelles, reversed micelles and microemulsions. Adv Colloid Interface Sci 82(1):1–42CrossRefGoogle Scholar
  3. Bouvrais H (2012) Bending rigidities of lipid bilayers: their determination and main inputs in biophysical studies. In: Iglic A (ed) Advances in planar lipid bilayers and liposomes, 15th edn. Elsevier Inc, Oxford, UK, pp 2–7Google Scholar
  4. Bouvrais H, Holmstrup M, Westh P, Ipsen JH (2013) Analysis of the shape fluctuations of reconstituted membranes using GUVs made from lipid extracts of invertebrates. Biol Open 2(4):373–378CrossRefPubMedPubMedCentralGoogle Scholar
  5. Bradski G (2000) The OpenCV library. Dr Dobb’s J: Softw Tools Prof Program 25(11):120–123Google Scholar
  6. Brochard F, Lennon JF (1975) Frequency spectrum of the flicker phenomenon in erythrocytes. J Phys 36(11):1035–1047CrossRefGoogle Scholar
  7. Bustamante C, Chemla YR, Forde NR, Izhaky D (2004) Mechanical processes in biochemistry. Annu Rev Biochem 73(1):705–748CrossRefPubMedGoogle Scholar
  8. De Vequi-Suplicy CC, Benatti CR, Lamy MT (2006) Laurdan in fluid bilayers: position and structural sensitivity. J Fluoresc 16(3):431–439CrossRefPubMedGoogle Scholar
  9. Dimova R (2014) Recent developments in the field of bending rigidity measurements on membranes. Adv Colloid Interface Sci 208:225–234CrossRefPubMedGoogle Scholar
  10. Drabik D, Przybyło M, Chodaczek G, Iglič A, Langner M (2016) The modified fluorescence based vesicle fluctuation spectroscopy technique for determination of lipid bilayer bending properties. Biochim Biophys Acta (BBA)-Biomembr 1858(2):244–252CrossRefGoogle Scholar
  11. Duwe HD, Sackmann E (1990) Bending elasticity and thermal excitations of lipid bilayer vesicles: modulation by solutes. Phys A 163(1):410–428CrossRefGoogle Scholar
  12. Faucon JF, Mitov MD, Méléard P, Bivas I, Bothorel P (1989) Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements. J Phys 50(17):2389–2414CrossRefGoogle Scholar
  13. Henriksen J, Rowat AC, Brief E, Hsueh YW, Thewalt JL, Zuckermann MJ, Ipsen JH (2006) Universal behavior of membranes with sterols. Biophys J 90(5):1639–1649CrossRefPubMedGoogle Scholar
  14. Huster D, Müller P, Arnold K, Herrmann A (2001) Dynamics of membrane penetration of the fluorescent 7-nitrobenz-2-oxa-1, 3-diazol-4-yl (NBD) group attached to an acyl chain of phosphatidylcholine. Biophys J 80(2):822–831CrossRefPubMedPubMedCentralGoogle Scholar
  15. Kocun M, Janshoff A (2012) Pulling tethers from pore-spanning bilayers: towards simultaneous determination of local bending modulus and lateral tension of membranes. Small 8(6):847–851CrossRefPubMedGoogle Scholar
  16. Kozlov MM, Campelo F, Liska N, Chernomordik LV, Marrink SJ, McMahon HT (2014) Mechanisms shaping cell membranes. Curr Opin Cell Biol 29:53–60CrossRefPubMedPubMedCentralGoogle Scholar
  17. Kyrychenko A (2010) A molecular dynamics model of rhodamine-labeled phospholipid incorporated into a lipid bilayer. Chem Phys Lett 485(1):95–99CrossRefGoogle Scholar
  18. Levine ZA, Venable RM, Watson MC, Lerner MG, Shea JE, Pastor RW, Brown FL (2014) Determination of biomembrane bending moduli in fully atomistic simulations. J Am Chem Soc 136(39):13582–13585CrossRefPubMedPubMedCentralGoogle Scholar
  19. Loftus AF, Noreng S, Hsieh VL, Parthasarathy R (2013) Robust measurement of membrane bending moduli using light sheet fluorescence imaging of vesicle fluctuations. Langmuir 29(47):14588–14594CrossRefPubMedGoogle Scholar
  20. Massey FJ Jr (1951) The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 46(253):68–78CrossRefGoogle Scholar
  21. Méléard P, Pott T, Bouvrais H, Ipsen JH (2011) Advantages of statistical analysis of giant vesicle flickering for bending elasticity measurements. Eur Phys J E: Soft Matter Biol Phys 34(10):1–14CrossRefGoogle Scholar
  22. Nagle JF (2017) Experimentally determined tilt and bending moduli of single-component lipid bilayers. Chem Phys Lipids 205: 18–24CrossRefPubMedGoogle Scholar
  23. Niggemann G, Kummrow M, Helfrich W (1995) The bending rigidity of phosphatidylcholine bilayers: dependences on experimental method, sample cell sealing and temperature. J Phys II 5(3):413–425Google Scholar
  24. Šachl R, Boldyrev I, Johansson LB (2010) Localisation of BODIPY-labelled phosphatidylcholines in lipid bilayers. Phys Chem Chem Phys 12(23):6027–6034CrossRefPubMedGoogle Scholar
  25. Shitamichi Y, Ichikawa M, Kimura Y (2009) Mechanical properties of a giant liposome studied using optical tweezers. Chem Phys Lett 479(4):274–278CrossRefGoogle Scholar
  26. Solmaz ME, Biswas R, Sankhagowit S, Thompson JR, Mejia CA, Malmstadt N, Povinelli ML (2012) Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap. Biomed Opt Express 3(10):2419–2427CrossRefPubMedPubMedCentralGoogle Scholar
  27. Tabarin T, Martin A, Forster RJ, Keyes TE (2012) Poly-ethylene glycol induced super-diffusivity in lipid bilayer membranes. Soft Matter 8(33):8743–8751CrossRefGoogle Scholar
  28. Taubin G (1991) Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans Pattern Anal Mach Intell 11:1115–1138CrossRefGoogle Scholar
  29. Wang J, Lü D, Mao D, Long M (2014) Mechanomics: an emerging field between biology and biomechanics. Protein Cell 5(7):518–531CrossRefPubMedPubMedCentralGoogle Scholar
  30. Venable RM, Brown FLH, Pastor RW (2015) Mechanical properties of lipid bilayers from molecular dynamics simulation. Chem Phys Lipids 192:60–74CrossRefPubMedPubMedCentralGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Biomedical Engineering, Faculty of Fundamental Problems of TechnologyWrocław University of Science and TechnologyWrocławPoland
  2. 2.Wroclaw Research Centre EIT+WrocławPoland
  3. 3.Lipid Systems sp. z o.o.WrocławPoland

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