Abstract
Studies of thermal fluctuations in discocytes, echinocytes, and spherocytes suggest that the coupling between lipid bilayer and cytoskeleton can affect viscoelastic behavior of single erythrocyte membranes. To test this hypothesis, we developed a 3D constitutive model describing viscoelastic behavior of erythrocyte membranes, at long relaxation times \(t \in [0.20\,\mathrm {s}, 1.05\,\mathrm {s}]\) and short relaxation times \(t \in [0.03\,\mathrm {s}, 0.20\,\mathrm {s}]\). The model was constructed using combination of spring and spring pot rheological elements arranged in parallel. The rearrangement of cytoskeleton induced by changing the bending state of lipid bilayer was described by a modified Eyring model. The model predictions point to an anomalous nature of energy dissipation and an ordered harmonic nature of the coupling mechanism described by a series of fractional derivatives of the order n \(\alpha \) (where \( n \in [- 1, 2]\)). As a result, the stress generated within the lipid bilayer is related to the rate of change of the irreversible stress within the cytoskeleton.
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Acknowledgments
The authors gratefully acknowledge funding support of the Ministry of Education, Science and Technological Development of the Republic Serbia (Grants III 46001, and III 46010). The authors thank Professor Gordana Vunjak-Novakovic (Columbia University) for useful suggestions which improved this work.
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Pajic-Lijakovic, I., Milivojevic, M. Modeling analysis of the lipid bilayer–cytoskeleton coupling in erythrocyte membrane. Biomech Model Mechanobiol 13, 1097–1104 (2014). https://doi.org/10.1007/s10237-014-0559-7
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DOI: https://doi.org/10.1007/s10237-014-0559-7