Skip to main content
SpringerLink
Log in

Mesoscopic modeling of membranes at cellular scale

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Cellular membranes span a wide range of spatio-temporal scales from sub-microsecond dynamics of lipid molecules and intra-membrane proteins to multi-minute deformations of the whole cell. Since no single simulation method would cover all these scales, there exists a variety of membrane modeling techniques, each presenting unique advantages for addressing a diverse range of scientific questions. This review focuses on current advances in mesoscopic models that represent membranes as two-dimensional surfaces with selected mechanical properties. Two categories of approaches are considered, including fluid membrane (e.g., lipid bilayer) and polymerized membrane (e.g., red blood cell) models. Both particle-based and continuum models for these two classes of membranes are discussed. To illustrate the potential of these models, several examples from recent simulation studies are presented, including equilibrium and non-equilibrium membrane structures, membrane remodeling, and deformation in fluid flow. Finally, we briefly discuss further developments related to these membrane models.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability statement

No data are associated with this manuscript.

References

  1. P. Bassereau, P. Sens, editors. Physics of Biological Membranes. Springer, Cham, first edition, (2018)

  2. J.T. Groves, J. Kuriyan, Molecular mechanisms in signal transduction at the membrane. Nat. Struct. Mol. Biol. 17, 659–665 (2010)

    Article  Google Scholar 

  3. M. Doktorova, J.L. Symons, I. Levental, Structural and functional consequences of reversible lipid asymmetry in living membranes. Nat. Chem. Biol. 16, 1321–1330 (2020)

    Article  Google Scholar 

  4. H.T. McMahon, J.L. Gallop, Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 438, 590–596 (2005)

    Article  ADS  Google Scholar 

  5. J.G. Carlton, H. Jones, U.S. Eggert, Membrane and organelle dynamics during cell division. Nat. Rev. Mol. Cell Biol. 21, 151–166 (2020)

    Article  Google Scholar 

  6. A. Diz-Muñoz, D.A. Fletcher, O.D. Weiner, Use the force: membrane tension as an organizer of cell shape and motility. Trends Cell Biol. 23, 47–53 (2013)

    Article  Google Scholar 

  7. K.M. Yamada, M. Sixt, Mechanisms of 3D cell migration. Nat. Rev. Mol. Cell Biol. 20, 738–752 (2019)

    Article  Google Scholar 

  8. G. van Meer, D.R. Voelker, G.W. Feigenson, Membrane lipids: where they are and how they behave. Nat. Rev. Mol. Cell Biol. 9, 112–124 (2008)

    Article  Google Scholar 

  9. R. Phillips, J. Kondev, J. Theriot, H. Garcia, Physical Biology of the Cell (New York, second edition, Garland Science, 2012)

    Book  Google Scholar 

  10. B.M. Discher, Y.-Y. Won, D.S. Ege, J.C.-M. Lee, F.S. Bates, D.E. Discher, D.A. Hammer, Polymersomes: tough vesicles made from diblock copolymers. Science 284, 1143–1146 (1999)

    Article  ADS  Google Scholar 

  11. V. Percec, D.A. Wilson, P. Leowanawat, C.J. Wilson, A.D. Hughes, M.S. Kaucher, D.A. Hammer, D.H. Levine, A.J. Kim, F.S. Bates, K.P. Davis, T.P. Lodge, M.L. Klein, R.H. DeVane, E. Aqad, B.M. Rosen, A.O. Argintaru, M.J. Sienkowska, K. Rissanen, S. Nummelin, J. Ropponen, Self-assembly of Janus dendrimers into uniform dendrimersomes and other complex architectures. Science 328, 1009–1014 (2010)

    Article  ADS  Google Scholar 

  12. A. M. Wagner, J. Quandt, D. Söder, M. Garay-Sarmiento, A. Joseph, V. S. Petrovskii, L. Witzdam, T. Hammoor, P. Steitz, Haraszti T., Potemkin I. I., Kostina N. Y., A. Herrman, C. Rodriguez-Emmenegger, Ionic combisomes: a new class of biomimetic vesicles to fuse with life. Adv. Sci., 9:2200617, (2022)

  13. D.A. Fedosov, H. Noguchi, G. Gompper, Multiscale modeling of blood flow: from single cells to blood rheology. Biomech. Model. Mechanobiol. 13, 239–258 (2014)

    Article  Google Scholar 

  14. J.B. Freund, Numerical simulation of flowing blood cells. Annu. Rev. Fluid Mech. 46, 67–95 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  15. S.J. Marrink, V. Corradi, P.C.T. Souza, H.I. Ingólfsson, D.P. Tieleman, M.S.P. Sansom, Computational modeling of realistic cell membranes. Chem. Rev. 119, 6184–6226 (2019)

    Article  Google Scholar 

  16. T. Auth, D. A. Fedosov, G. Gompper. Simulating membranes, vesicles, cells. In R. Dimova and C. Marques, editors, The giant vesicle book. CRC Press, 2019

  17. G. Kumar, S.C. Duggisetty, A. Srivastava, A review of mechanics-based mesoscopic membrane remodeling methods: capturing both the physics and the chemical diversity. J. Mem. Biol. 255, 757–777 (2022)

    Article  Google Scholar 

  18. G. Gompper, D.A. Fedosov, Modeling microcirculatory blood flow: current state and future perspectives. WIREs Syst. Biol. Med. 8, 157–168 (2016)

    Article  Google Scholar 

  19. A.L. Duncan, W. Pezeshkian, Mesoscale simulations: an indispensable approach to understand biomembranes. Biophys. J. 122, 1883–1889 (2023)

    Article  ADS  Google Scholar 

  20. H. Noguchi, Membrane simulation models from nanometer to micrometer scale. J. Phys. Soc. Jpn. 78, 041007 (2009)

    Article  ADS  Google Scholar 

  21. D.P. Tieleman, S.J. Marrink, H.J.C. Berendsen, A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems. Biochim. Biophys. Acta 1331, 235–270 (1997)

    Article  Google Scholar 

  22. E.H. Lee, J. Hsin, M. Sotomayor, G. Comellas, K. Schulten, Discovery through the computational microscope. Structure 17, 1295–1306 (2009)

    Article  Google Scholar 

  23. A.A. Skjevik, B.D. Madej, C.J. Dickson, C. Lin, K. Teigen, R.C. Walker, I.R. Gould, Simulation of lipid bilayer self-assembly using all-atom lipid force fields. Phys. Chem. Chem. Phys. 18, 10573–10584 (2016)

    Article  Google Scholar 

  24. A.P. Lyubartsev, A.L. Rabinovich, Recent development in computer simulations of lipid bilayers. Soft Matter 7, 25–39 (2011)

    Article  ADS  Google Scholar 

  25. C.J. Dickson, B.D. Madej, A.A. Skjevik, R.M. Betz, K. Teigen, I.R. Gould, R.C. Walker, Lipid14: the amber lipid force field. J. Chem. Theory Comput. 10, 865–879 (2014)

    Article  Google Scholar 

  26. P.M. Kasson, E. Lindahl, V.S. Pande, Atomic-resolution simulations predict a transition state for vesicle fusion defined by contact of a few lipid tails. PLoS Comput. Biol. 6, e1000829 (2010)

    Article  ADS  Google Scholar 

  27. R. Goetz, G. Gompper, R. Lipowsky, Mobility and elasticity of self-assembled membranes. Phys. Rev. Lett. 82, 221–224 (1999)

    Article  ADS  Google Scholar 

  28. J.C. Shillcock, R. Lipowsky, Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics simulations. J. Chem. Phys. 117, 5048–5061 (2002)

    Article  ADS  Google Scholar 

  29. S.J. Marrink, A.E. Mark, Molecular dynamics simulation of the formation, structure, dynamics of small phospholipid vesicles. J. Am. Chem. Soc. 125, 15233–15242 (2003)

    Article  Google Scholar 

  30. M. Laradji, P.B.S. Kumar, Dynamics of domain growth in self-assembled fluid vesicles. Phys. Rev. Lett. 93, 198105 (2004)

    Article  ADS  Google Scholar 

  31. I.R. Cooke, K. Kremer, M. Deserno, Tunable generic model for fluid bilayer membranes. Phys. Rev. E 72, 011506 (2005)

    Article  ADS  Google Scholar 

  32. M. Deserno, Mesoscopic membrane physics: concepts, simulations, selected applications. Macromol. Rapid Commun. 30, 752–771 (2009)

    Article  Google Scholar 

  33. W.K. den Otter, W.J. Briels, The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics. J. Chem. Phys. 118, 4712–4720 (2003)

    Article  ADS  Google Scholar 

  34. J.M. Drouffe, A.C. Maggs, S. Leibler, Computer simulations of self-assembled membranes. Science 254, 1353–1356 (1991)

    Article  ADS  Google Scholar 

  35. G. Gompper, D. M. Kroll, Network models of fluid, hexatic and polymerized membranes. J. Phys.: Condens. Matter, 9:8795–8834, (1997)

  36. H. Noguchi, G. Gompper, Meshless membrane model based on the moving least-squares method. Phys. Rev. E 73, 021903 (2006)

    Article  ADS  Google Scholar 

  37. I.V. Pivkin, G.E. Karniadakis, Accurate coarse-grained modeling of red blood cells. Phys. Rev. Lett. 101, 118105 (2008)

    Article  ADS  Google Scholar 

  38. S.K. Doddi, P. Bagchi, Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys. Rev. E 79, 046318 (2009)

    Article  ADS  Google Scholar 

  39. H. Zhao, A.H.G. Isfahani, L.N. Olson, J.B. Freund, A spectral boundary integral method for flowing blood cells. J. Comput. Phys. 229, 3726–3744 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  40. R.M. MacMeccan, J.R. Clausen, G.P. Neitzel, C.K. Aidun, Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method. J. Fluid Mech. 618, 13–39 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  41. D.A. Fedosov, B. Caswell, G.E. Karniadakis, A multiscale red blood cell model with accurate mechanics, rheology, dynamics. Biophys. J. 98, 2215–2225 (2010)

    Article  ADS  Google Scholar 

  42. G. Brannigan, F.L.H. Brown, Solvent-free simulations of fluid membrane bilayers. J. Chem. Phys. 120, 1059–1071 (2004)

    Article  ADS  Google Scholar 

  43. P. Ballone, M.G. Del Pópolo, Simple models of complex aggregation: vesicle formation by soft repulsive spheres with dipolelike interactions. Phys. Rev. E 73, 031404 (2006)

    Article  ADS  Google Scholar 

  44. T. Kohyama, Simulations of flexible membranes using a coarse-grained particle-based model with spontaneous curvature variables. Phys. A 388, 3334–3344 (2009)

    Article  Google Scholar 

  45. H. Yuan, C. Huang, J. Li, G. Lykotrafitis, S. Zhang, One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes. Phys. Rev. E 82, 011905 (2010)

    Article  ADS  Google Scholar 

  46. G. Gompper, D. M. Kroll, Triangulated-surface models of fluctuating membranes. In D. R. Nelson, T. Piran, S. Weinberg, editors, Statistical mechanics of membranes and surfaces, pages 359–426. World Scientific, Singapore, 2nd edition, (2004)

  47. S.K. Boey, D.H. Boal, D.E. Discher, Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models. Biophys. J. 75, 1573–1583 (1998)

    Google Scholar 

  48. J. Li, G. Lykotrafitis, M. Dao, S. Suresh, Cytoskeletal dynamics of human erythrocyte. Proc. Natl. Acad. Sci. USA 104, 4937–4942 (2007)

    Article  ADS  Google Scholar 

  49. E. Atilgan, S.X. Sun, Shape transitions in lipid membranes and protein mediated vesicle fusion and fission. J. Chem. Phys. 126, 095102 (2007)

    Article  ADS  Google Scholar 

  50. J. Li, M. Dao, C.T. Lim, S. Suresh, Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys. J. 88, 3707–3719 (2005)

    Article  ADS  Google Scholar 

  51. T. Biben, K. Kassner, C. Misbah, Phase-field approach to three-dimensional vesicle dynamics. Phys. Rev. E 72, 041921 (2005)

    Article  ADS  Google Scholar 

  52. F. Feng, W.S. Klug, Finite element modeling of lipid bilayer membranes. J. Comput. Phys. 220, 394–408 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  53. Z. Peng, R.J. Asaro, Q. Zhu, Multiscale modelling of erythrocytes in Stokes flow. J. Fluid Mech. 686, 299–337 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  54. T. Krüger, F. Varnik, D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method. Comput. Math. Appl. 61, 3485–3505 (2011)

    Article  MathSciNet  Google Scholar 

  55. T. Omori, Y. Imai, K. Kikuchi, T. Ishikawa, T. Yamaguchi, Hemodynamics in the microcirculation and in microfluidics. Ann. Biomed. Eng. 43, 238–257 (2015)

    Article  Google Scholar 

  56. D.A. Fedosov, M. Dao, G.E. Karniadakis, S. Suresh, Computational biorheology of human blood flow in health and disease. Ann. Biomed. Eng. 42, 368–387 (2014)

    Article  Google Scholar 

  57. X. Li, P.M. Vlahovska, G.E. Karniadakis, Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter 9, 28–37 (2013)

    Article  ADS  Google Scholar 

  58. M. Ju, S.S. Ye, B. Namgung, S. Cho, H.T. Low, H.L. Leo, S. Kim, A review of numerical methods for red blood cell flow simulation. Computer Meth. Biomech. Biomed. Eng. 18, 130–140 (2015)

    Article  Google Scholar 

  59. F.J. Alenghat, D.E. Golan, Membrane protein dynamics and functional implications in mammalian cells. Curr. Top. Membr. 72, 89–120 (2013)

    Article  Google Scholar 

  60. A.-S. Smith, K. Sengupta, S. Goennenwein, U. Seifert, E. Sackmann, Force-induced growth of adhesion domains is controlled by receptor mobility. Proc. Natl. Acad. Sci. USA 105, 6906–6911 (2008)

    Article  ADS  Google Scholar 

  61. R. Lipowsky, The conformation of membranes. Nature 349, 475–481 (1991)

    Article  ADS  Google Scholar 

  62. E.A. Evans, R. Skalak, Mechanics and thermodynamics of biomembranes (CRC Press Inc, Boca Raton, 1980)

    Google Scholar 

  63. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28, 693–703 (1973)

    Article  Google Scholar 

  64. U.S. Schwarz, M.L. Gardel, United we stand - integrating the actin cytoskeleton and cell-matrix adhesions in cellular mechanotransduction. J. Cell Sci. 125, 3051–3060 (2012)

    Google Scholar 

  65. J. Plastino, L. Blanchoin, Dynamic stability of the actin ecosystem. J. Cell Sci. 132, 219832 (2019)

    Article  Google Scholar 

  66. K.S. Chang, W.L. Olbricht, Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech. 250, 609–633 (1993)

    Article  ADS  Google Scholar 

  67. P. Erni, P. Fisher, Windhab E. Deformation of single emulsion drops covered with a viscoelastic adsorbed protein layer in simple shear flow. Appl. Phys. Lett., 87:244104, 2005

  68. D. Barthés-Biesel, Modeling the motion of capsules in flow. Curr. Opin. Colloid Interface Sci. 16, 3–12 (2011)

    Article  Google Scholar 

  69. D. Barthés-Biesel, Mechanics of encapsulated droplets. Progr. Colloid. Polym. Sci. 111, 58–64 (1998)

    Article  Google Scholar 

  70. D.R. Nelson, T. Piran, S. Weinberg, Statistical mechanics of membranes and surfaces, 2nd edn. (World Scientific, Singapore, 2004)

    Book  Google Scholar 

  71. H.R. Vutukuri, M. Hoore, C. Abaurrea-Velasco, L. van Buren, A. Dutto, T. Auth, D.A. Fedosov, G. Gompper, J. Vermant, Active particles induce large shape deformations in giant lipid vesicles. Nature 586, 52–56 (2020)

    Article  ADS  Google Scholar 

  72. S.C. Takatori, A. Sahu, Active contact forces drive nonequilibrium fluctuations in membrane vesicles. Phys. Rev. Lett. 124, 158102 (2020)

    Article  ADS  Google Scholar 

  73. M. Paoluzzi, R. Di Leonardo, M.C. Marchetti, L. Angelani, Shape and displacement fluctuations in soft vesicles filled by active particles. Sci. Rep. 6, 34146 (2016)

    Article  ADS  Google Scholar 

  74. J. Chen, Y. Hua, Y. Jiang, X. Zhou, L. Zhang, Rotational diffusion of soft vesicles filled by chiral active particles. Sci. Rep. 7, 15006 (2017)

    Article  ADS  Google Scholar 

  75. Y. Li, P.R. ten Wolde, Shape transformations of vesicles induced by swim pressure. Phys. Rev. Lett. 123, 148003 (2019)

    Article  ADS  Google Scholar 

  76. C. Wang, Y. Guo, W. Tian, K. Chen, Shape transformation and manipulation of a vesicle by active particles. J. Chem. Phys. 150, 044907 (2019)

    Article  ADS  Google Scholar 

  77. M.S.E. Peterson, A. Baskaran, M.F. Hagan, Vesicle shape transformations driven by confined active filaments. Nat. Comm. 12, 7247 (2021)

    Article  ADS  Google Scholar 

  78. P. Iyer, G. Gompper, D.A. Fedosov, Non-equilibrium shapes and dynamics of active vesicles. Soft Matter 18, 6868–6881 (2022)

    Article  ADS  Google Scholar 

  79. P. Iyer, G. Gompper, D.A. Fedosov, Dynamic shapes of floppy vesicles enclosing active Brownian particles with membrane adhesion. Soft Matter 19, 3436–3449 (2023)

    Article  ADS  Google Scholar 

  80. L. Le Nagard, A.T. Brown, A. Dawson, V.A. Martinez, W.C.K. Poon, M. Staykova, Encapsulated bacteria deform lipid vesicles into flagellated swimmers. Proc. Natl. Acad. Sci. USA 119, e2206096119 (2022)

    Article  Google Scholar 

  81. T. Wollert, C. Wunder, J. Lippincott-Schwartz, J.H. Hurley, Membrane scission by the ESCRT-III complex. Nature 458, 172–177 (2009)

    Article  ADS  Google Scholar 

  82. L. Harker-Kirschneck, B. Baum, A. Šarić, Changes in ESCRT-III filament geometry drive membrane remodelling and fission in silico. BMC Biol. 17, 82 (2019)

    Article  Google Scholar 

  83. M. Lenz, D.J.G. Crow, J.-F. Joanny, Membrane buckling induced by curved filaments. Phys. Rev. Lett. 103, 038101 (2009)

    Article  ADS  Google Scholar 

  84. G. Fabrikant, S. Lata, J.D. Riches, J.A.G. Briggs, W. Weissenhorn, M.M. Kozlov, Computational model of membrane fission catalyzed by ESCRT-III. PLoS Comput. Biol. 5, e1000575 (2009)

    Article  ADS  Google Scholar 

  85. J. Agudo-Canalejo, R. Lipowsky, Domes and cones: adhesion-induced fission of membranes by ESCRT proteins. PLoS Comput. Biol. 14, e1006422 (2018)

    Article  ADS  Google Scholar 

  86. O. Daumke, A. Roux, V. Haucke, BAR domain scaffolds in dynamin-mediated membrane fission. Cell 156, 882–892 (2014)

    Article  Google Scholar 

  87. W. Römer, L. Berland, V. Chambon, K. Gaus, B. Windschiegl, D. Tenza, M.R.E. Aly, V. Fraisier, J.-C. Florent, D. Perrais, C. Lamaze, G. Raposo, C. Steinem, P. Sens, P. Bassereau, L. Johannes, Shiga toxin induces tubular membrane invaginations for its uptake into cells. Nature 450, 670–675 (2007)

    Article  ADS  Google Scholar 

  88. N. Ramakrishnan, P.B.S. Kumar, J.H. Ipsen, Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation. Biophys. J. 104, 1018–1028 (2013)

    Article  ADS  Google Scholar 

  89. P. Rangamani, K.K. Mandadap, G. Oster, Protein-induced membrane curvature alters local membrane tension. Biophys. J. 107, 751–762 (2014)

    Article  ADS  Google Scholar 

  90. N.S. Gov, Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces. Phil. Trans. R. Soc. B 373, 20170115 (2018)

    Article  Google Scholar 

  91. W. Pezeshkian, J.H. Ipsen, Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions. Soft Matter 15, 9974–9981 (2019)

    Article  ADS  Google Scholar 

  92. H. Noguchi, C. Tozzi, M. Arroyo, Binding of anisotropic curvature-inducing proteins onto membrane tubes. Soft Matter 18, 3384–3394 (2022)

    Article  ADS  Google Scholar 

  93. H. Noguchi, Vesicle budding induced by binding of curvature-inducing proteins. Phys. Rev. E 104, 014410 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  94. J. Steinkühler, R.L. Knorr, Z. Zhao, T. Bhatia, S.M. Bartelt, S. Wegner, R. Dimova, R. Lipowsky, Controlled division of cell-sized vesicles by low densities of membrane-bound proteins. Nat. Comm. 11, 905 (2020)

    Article  ADS  Google Scholar 

  95. T. Bhatia, S. Christ, J. Steinkühler, R. Dimova, R. Lipowsky, Simple sugars shape giant vesicles into multispheres with many membrane necks. Soft Matter 16, 1246–1258 (2020)

    Article  ADS  Google Scholar 

  96. R. Lipowsky, Multispherical shapes of vesicles highlight the curvature elasticity of biomembranes. Adv. Colloid Interface Sci. 301, 102613 (2022)

    Article  Google Scholar 

  97. F. Brochard, J.F. Lennon, Frequency spectrum of the flicker phenomenon in erythrocytes. J. Phys. 36, 1035–1047 (1975)

    Article  Google Scholar 

  98. H. Strey, M. Peterson, E. Sackmann, Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. Biophys. J. 69, 478–488 (1995)

    Article  ADS  Google Scholar 

  99. S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, S. Yedgar, Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force. Proc. Natl. Acad. Sci. USA 94, 5045–5049 (1997)

    Article  ADS  Google Scholar 

  100. N. Gov, S.A. Safran, Red blood cell shape and fluctuations: cytoskeleton confinement and ATP activity. J. Biol. Phys. 31, 453–464 (2005)

    Article  Google Scholar 

  101. G. Marcelli, K.H. Parker, C.P. Winlove, Thermal fluctuations of red blood cell membrane via a constant-area particle-dynamics model. Biophys. J. 89, 2473–2480 (2005)

    Article  ADS  Google Scholar 

  102. T. Betz, M. Lenz, J.-F. Joanny, C. Sykes, ATP-dependent mechanics of red blood cells. Proc. Natl. Acad. Sci. USA 106, 15320–15325 (2009)

    Article  ADS  Google Scholar 

  103. J.P. Hale, G. Marcelli, K.H. Parker, C.P. Winlove, P.G. Petrov, Red blood cell thermal fluctuations: comparison between experiment and molecular dynamics simulations. Soft Matter 5, 3603–3606 (2009)

    Article  ADS  Google Scholar 

  104. Y.-K. Park, C.A. Best, T. Auth, N.S. Gov, S.A. Safran, G. Popescu, S. Suresh, M.S. Feld, Metabolic remodeling of the human red blood cell membrane. Proc. Natl. Acad. Sci. USA 107, 1289–1294 (2010)

    Article  ADS  Google Scholar 

  105. E. Ben-Isaac, Y.-K. Park, G. Popescu, F.L.H. Brown, N.S. Gov, Y. Shokef, Effective temperature of red-blood-cell membrane fluctuations. Phys. Rev. Lett. 106, 238103 (2011)

    Article  ADS  Google Scholar 

  106. H. Turlier, D.A. Fedosov, B.A. Audoly, T. Auth, N.S. Gov, C. Sykes, J.-F. Joanny, G. Gompper, T. Betz, Equilibrium physics breakdown reveals the active nature of red blood cell membrane fluctuations. Nat. Phys. 12, 513–519 (2016)

    Article  Google Scholar 

  107. A.A. Evans, B. Bhaduri, G. Popescu, A.J. Levine, Geometric localization of thermal fluctuations in red blood cells. Proc. Natl. Acad. Sci. USA 114, 2865–2870 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  108. M. Abkarian, M. Faivre, R. Horton, K. Smistrup, C.A. Best-Popescu, H.A. Stone, Cellular-scale hydrodynamics. Biomed. Mater. 3, 034011 (2008)

    Article  ADS  Google Scholar 

  109. H. Noguchi, G. Gompper, Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc. Natl. Acad. Sci. USA 102, 14159–14164 (2005)

    Article  ADS  Google Scholar 

  110. J.L. McWhirter, H. Noguchi, G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries. Proc. Natl. Acad. Sci. USA 106, 6039–6043 (2009)

    Article  ADS  Google Scholar 

  111. G. Tomaiuolo, M. Simeone, V. Martinelli, B. Rotoli, S. Guido, Red blood cell deformation in microconfined flow. Soft Matter 5, 3736–3740 (2009)

    Article  ADS  Google Scholar 

  112. J.B. Freund, M.M. Orescanin, Cellular flow in a small blood vessel. J. Fluid Mech. 671, 466–490 (2011)

    Article  ADS  Google Scholar 

  113. H. Noguchi, Dynamic modes of red blood cells in oscillatory shear flow. Phys. Rev. E 81, 061920 (2010)

    Article  ADS  Google Scholar 

  114. H. Noguchi, Swinging and synchronized rotations of red blood cells in simple shear flow. Phys. Rev. E 80, 021902 (2009)

    Article  ADS  Google Scholar 

  115. D.A. Fedosov, M. Peltomäki, G. Gompper, Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft Matter 10, 4258–4267 (2014)

    Article  ADS  Google Scholar 

  116. L. Lanotte, J. Mauer, S. Mendez, D.A. Fedosov, J.-M. Fromental, V. Claveria, F. Nicoud, G. Gompper, M. Abkarian, Red cells’ dynamic morphologies govern blood shear thinning under microcirculatory flow conditions. Proc. Natl. Acad. Sci. USA 113, 13289–13294 (2016)

    Article  ADS  Google Scholar 

  117. A. Guckenberger, A. Kihm, T. John, C. Wagner, S. Gekle, Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel. Soft Matter 14, 2032–2043 (2018)

    Article  ADS  Google Scholar 

  118. F. Reichel, J. Mauer, A.A. Nawaz, G. Gompper, J. Guck, D.A. Fedosov, High-throughput microfluidic characterization of erythrocyte shapes and mechanical variability. Biophys. J. 117, 14–24 (2019)

    Article  ADS  Google Scholar 

  119. A.K. Dasanna, J. Mauer, G. Gompper, D.A. Fedosov, Importance of viscosity contrast for the motion of erythrocytes in microcapillaries. Front. Phys. 9, 666913 (2021)

    Article  Google Scholar 

  120. K. Sinha, M.D. Graham, Dynamics of a single red blood cell in simple shear flow. Phys. Rev. E 92, 042710 (2015)

    Article  ADS  Google Scholar 

  121. D. Cordasco, P. Bagchi, Orbital drift of capsules and red blood cells in shear flow. Phys. Fluids 25, 091902 (2013)

    Article  ADS  Google Scholar 

  122. D. Cordasco, A. Yazdani, P. Bagchi, Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys. Fluids 26, 041902 (2014)

    Article  ADS  Google Scholar 

  123. A.Z.K. Yazdani, P. Bagchi, Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow. Phys. Rev. E 84, 026314 (2011)

    Article  ADS  Google Scholar 

  124. A.Z.K. Yazdani, R.M. Kalluri, P. Bagchi, Tank-treading and tumbling frequencies of capsules and red blood cells. Phys. Rev. E 83, 046305 (2011)

    Article  ADS  Google Scholar 

  125. A.F. Cowman, B.S. Crabb, Invasion of red blood cells by malaria parasites. Cell 124, 755–766 (2006)

    Article  Google Scholar 

  126. S. Dasgupta, T. Auth, N. Gov, T.J. Satchwell, E. Hanssen, E.S. Zuccala, D.T. Riglar, A.M. Toye, T. Betz, J. Baum, G. Gompper, Membrane-wrapping contributions to malaria parasite invasion of the human erythrocyte. Biophys. J. 107, 43–54 (2014)

    Article  ADS  Google Scholar 

  127. A.J. Crick, M. Theron, T. Tiffert, V.L. Lew, P. Cicuta, J.C. Rayner, Quantitation of malaria parasite-erythrocyte cell-cell interactions using optical tweezers. Biophys. J. 107, 846–853 (2014)

    Article  ADS  Google Scholar 

  128. G.E. Weiss, P.R. Gilson, T. Taechalertpaisarn, W.-H. Tham, N.W.M. de Jong, K.L. Harvey, F.J.I. Fowkes, P.N. Barlow, J.C. Rayner, G.J. Wright, A.F. Cowman, B.S. Crabb, Revealing the sequence and resulting cellular morphology of receptor-ligand interactions during Plasmodium falciparum invasion of erythrocytes. PLoS Pathog. 11, e1004670 (2015)

    Article  Google Scholar 

  129. V. Introini, A. Carciati, G. Tomaiuolo, P. Cicuta, S. Guido, Endothelial glycocalyx regulates cytoadherence in Plasmodium falciparum malaria. J. R. Soc. Interface 15, 20180773 (2018)

    Article  Google Scholar 

  130. S. Hillringhaus, A.K. Dasanna, G. Gompper, D.A. Fedosov, Importance of erythrocyte deformability for the alignment of malaria parasite upon invasion. Biophys. J. 117, 1202–1214 (2019)

    Article  ADS  Google Scholar 

  131. S. Hillringhaus, A.K. Dasanna, G. Gompper, D.A. Fedosov, Stochastic bond dynamics facilitates alignment of malaria parasite at erythrocyte membrane upon invasion. eLife 9, e56500 (2020)

    Article  Google Scholar 

  132. A.K. Dasanna, S. Hillringhaus, G. Gompper, D.A. Fedosov, Effect of malaria parasite shape on its alignment at erythrocyte membrane. eLife 10, e68818 (2021)

    Article  Google Scholar 

  133. D.M. Kroll, G. Gompper, The conformation of fluid membranes: Monte Carlo simulations. Science 255, 968–971 (1992)

    Article  ADS  Google Scholar 

  134. D.H. Boal, M. Rao, Topology changes in fluid membranes. Phys. Rev. A 46, 3037–3045 (1992)

    Article  ADS  Google Scholar 

  135. S.-J. Zhao, J.T. Kindt, Monte Carlo calculations of the free-energy landscape of vesicle formation and growth. Europhys. Lett. 69, 839–845 (2005)

    Article  ADS  Google Scholar 

  136. J.-S. Ho, A. Baumgärtner, Simulations of fluid self-avoiding membranes. Europhys. Lett. 12, 295–300 (1990)

    Article  ADS  Google Scholar 

  137. H. Zhao, E.S.G. Shaqfeh, The dynamics of a vesicle in simple shear flow. J. Fluid Mech. 674, 578–604 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  138. S.K. Veerapaneni, A. Rahimian, G. Biros, D. Zorin, A fast algorithm for simulating vesicle flows in three dimensions. J. Comput. Phys. 230, 5610–5634 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  139. Q. Du, C. Liu, X. Wang, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 198, 450–468 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  140. R.A. Sauer, T.X. Duong, K.K. Mandadapu, D.J. Steigmann, A stabilized finite element formulation for liquid shells and its application to lipid bilayers. J. Comput. Phys. 330, 436–466 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  141. S. Aland, S. Egerer, J. Lowengrub, A. Voigt, Diffuse interface models of locally inextensible vesicles in a viscous fluid. J. Comput. Phys. 277, 32–47 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  142. H. Noguchi, G. Gompper, Dynamics of fluid vesicles in shear flow: effect of the membrane viscosity and thermal fluctuations. Phys. Rev. E 72, 011901 (2005)

    Article  ADS  Google Scholar 

  143. P.B. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theoret. Biol. 26, 61–81 (1970)

    Article  ADS  Google Scholar 

  144. M. Deserno, Fluid lipid membranes: from differential geometry to curvature stresses. Chem. Phys. Lipids 185, 11–45 (2015)

    Article  Google Scholar 

  145. G. Gompper, D.M. Kroll, Random surface discretizations and the renormalization of the bending rigidity. J. Phys. I France 6, 1305–1320 (1996)

    Article  Google Scholar 

  146. F. Jülicher, The morphology of vesicles of higher topological genus: conformal degeneracy and conformal modes. J. Phys. II France 6, 1797–1824 (1996)

    Google Scholar 

  147. K. Tsubota, Short note on the bending models for a membrane in capsule mechanics: comparison between continuum and discrete models. J. Comput. Phys. 277, 320–328 (2014)

    Article  ADS  Google Scholar 

  148. A. Guckenberger, M.P. Schraml, P.G. Chen, M. Leonetti, S. Gekle, On the bending algorithms for soft objects in flows. Comput. Phys. Commun. 207, 1–23 (2016)

    Article  ADS  Google Scholar 

  149. A. Guckenberger, S. Gekle, Theory and algorithms to compute Helfrich bending forces: a review. J. Phys.: Condens. Matter 29, 203001 (2017)

    ADS  Google Scholar 

  150. X. Bian, S. Litvinov, P. Koumoutsakos, Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity. Comput. Methods Appl. Mech. Eng. 359, 112758 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  151. C. Zhu, C.T. Lee, P. Rangamani, Mem3DG: modeling membrane mechanochemical dynamics in 3D using discrete differential geometry. Biophys. Rep. 2, 100062 (2022)

    Google Scholar 

  152. H. Noguchi, G. Gompper, Fluid vesicles with viscous membranes in shear flow. Phys. Rev. Lett. 93, 258102 (2004)

    Article  ADS  Google Scholar 

  153. M.P. Allen, D.J. Tildesley, Computer simulation of liquids (Clarendon Press, New York, 1991)

    Google Scholar 

  154. S. Succi, The Lattice Boltzmann equation for fluid dynamics and beyond (Oxford University Press, Oxford, 2001)

    Book  Google Scholar 

  155. J. F. Wendt, editor. Computational Fluid Dynamics. Springer, Berlin, 3rd edition, 2009

  156. I.V. Pivkin, B. Caswell, G.E. Karniadakis, Dissipative particle dynamics, in Reviews in Computational Chemistry, vol. 27, ed. by K.B. Lipkowitz (John Wiley & Sons Inc, Hoboken, 2011), pp.85–110

    Chapter  Google Scholar 

  157. M. Ellero, P. Español, Everything you always wanted to know about SDPD\(^*\) (\(^*\)but were afraid to ask). Appl. Math. Mech. 39, 103–124 (2018)

    Article  MathSciNet  Google Scholar 

  158. G. Gompper, T. Ihle, D.M. Kroll, R.G. Winkler, Multi-particle collision dynamics: a particle-based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv. Polym. Sci. 221, 1–87 (2009)

    Google Scholar 

  159. J.J. Monaghan, Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  160. C.S. Peskin, The immersed boundary method. Acta Numer. 11, 479–517 (2002)

    Article  MathSciNet  Google Scholar 

  161. Y. Liu, W.K. Liu, Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220, 139–154 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  162. P. Ahlrichs, B. Dünweg, Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics. J. Chem. Phys. 111, 8225–8239 (1999)

    Article  ADS  Google Scholar 

  163. T.R. Powers, Dynamics of filaments and membranes in a viscous fluid. Rev. Mod. Phys. 82, 1607–1631 (2010)

    Article  ADS  Google Scholar 

  164. D.J. Steigmann, Fluid films with curvature elasticity. Arch. Ration. Mech. Anal. 150, 127–152 (1999)

    Article  MathSciNet  Google Scholar 

  165. C. Pozrikidis, Interfacial dynamics for Stokes flow. J. Comput. Phys. 169, 250–301 (2001)

    Article  ADS  Google Scholar 

  166. P. Schwille, J. Spatz, K. Landfester, E. Bodenschatz, S. Herminghaus, V. Sourjik, T.J. Erb, P. Bastiaens, R. Lipowsky, A. Hyman, P. Dabrock, J.-C. Baret, T. Vidakovic-Koch, P. Bieling, R. Dimova, H. Mutschler, T. Robinson, T.-Y.D. Tang, S. Wegner, K. Sundmacher, MaxSynBio: avenues towards creating cells from the bottom up. Angew. Chem. Int. Ed. 57, 13382–13392 (2018)

    Article  Google Scholar 

  167. D. Needleman, Z. Dogic, Active matter at the interface between materials science and cell biology. Nat. Rev. Mater. 2, 17048 (2017)

    Article  ADS  Google Scholar 

  168. K. Weirich, K.L. Dasbiswas, T.A. Witten, S. Vaikuntanathan, M.L. Gardel, Self-organizing motors divide active liquid droplets. Proc. Natl. Acad. Sci. USA 116, 11125–11130 (2019)

    Article  ADS  Google Scholar 

  169. A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101, 038102 (2008)

    Article  ADS  Google Scholar 

  170. G. Li, J.X. Tang, Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Phys. Rev. Lett. 103, 078101 (2009)

    Article  ADS  Google Scholar 

  171. J. Elgeti, G. Gompper, Wall accumulation of self-propelled spheres. Europhys. Lett. 101, 48003 (2013)

    Article  ADS  Google Scholar 

  172. S. Dasgupta, T. Auth, G. Gompper, Shape and orientation matter for the cellular uptake of nonspherical particles. Nano Lett. 14, 687–693 (2014)

    Article  ADS  Google Scholar 

  173. A.H. Bahrami, M. Raatz, J. Agudo-Canalejo, R. Michel, E.M. Curtis, C.K. Hall, M. Gradzielski, R. Lipowsky, T.R. Weikl, Wrapping of nanoparticles by membranes. Adv. Colloid Interface Sci. 208, 214–224 (2014)

    Article  Google Scholar 

  174. A. Šarić, A. Cacciuto, Mechanism of membrane tube formation induced by adhesive nanocomponents. Phys. Rev. Lett. 109, 188101 (2012)

    Article  ADS  Google Scholar 

  175. M. Raatz, R. Lipowsky, T.R. Weikl, Cooperative wrapping of nanoparticles by membrane tubes. Soft Matter 10, 3570–3577 (2014)

    Article  ADS  Google Scholar 

  176. Q. Yu, S. Othman, S. Dasgupta, T. Auth, G. Gompper, Nanoparticle wrapping at small non-spherical vesicles: curvatures at play. Nanoscale 10, 6445–6458 (2018)

    Article  Google Scholar 

  177. A.H. Bahrami, R. Lipowsky, T.R. Weikl, The role of membrane curvature for the wrapping of nanoparticles. Soft Matter 12, 581–587 (2016)

    Article  ADS  Google Scholar 

  178. A. Šarić, A. Cacciuto, Fluid membranes can drive linear aggregation of adsorbed spherical nanoparticles. Phys. Rev. Lett. 108, 118101 (2012)

    Article  ADS  Google Scholar 

  179. S. Dasgupta, T. Auth, G. Gompper, Wrapping of ellipsoidal nano-particles by fluid membranes. Soft Matter 9, 5473–5482 (2013)

    Article  ADS  Google Scholar 

  180. J. McCullough, A.K. Clippinger, N. Talledge, M.L. Skowyra, M.G. Saunders, T.V. Naismith, L.A. Colf, P. Afonine, C. Arthur, W.I. Sundquist, P.I. Hanson, A. Frost, Structure and membrane remodeling activity of ESCRT-III helical polymers. Science 350, 1548–1551 (2015)

    Article  ADS  Google Scholar 

  181. J.G. Carlton, J. Martin-Serrano, Parallels between cytokinesis and retroviral budding: a role for the ESCRT machinery. Science 316, 1908–1912 (2007)

    Article  ADS  Google Scholar 

  182. M.A.Y. Adell, G.F. Vogel, M. Pakdel, M. Müller, H. Lindner, M.W. Hess, D. Teis, Coordinated binding of Vps4 to ESCRT-III drives membrane neck constriction during MVB vesicle formation. J. Cell Biol. 205, 33–49 (2014)

    Article  Google Scholar 

  183. P.D. Bieniasz, Late budding domains and host proteins in enveloped virus release. Virology 344, 55–63 (2006)

    Article  Google Scholar 

  184. W.M. Henne, N.J. Buchkovich, Y. Zhao, S.D. Emr, The endosomal sorting complex ESCRT-II mediates the assembly and architecture of ESCRT-III helices. Cell 151, 356–371 (2012)

    Article  Google Scholar 

  185. N. Chiaruttini, A. Roux, Dynamic and elastic shape transitions in curved ESCRT-III filaments. Curr. Opin. Cell Biol. 47, 126–135 (2017)

    Article  Google Scholar 

  186. W. Pezeshkian, J.H. Ipsen, Mesoscale simulation of biomembranes with FreeDTS. Nat. Comm. 15, 548 (2024)

    Article  ADS  Google Scholar 

  187. G. Kumar, N. Ramakrishnan, A. Sain, Tubulation pattern of membrane vesicles coated with biofilaments. Phys. Rev. E 99, 022414 (2019)

    Article  ADS  Google Scholar 

  188. R. Lipowsky, Spontaneous tubulation of membranes and vesicles reveals membrane tension generated by spontaneous curvature. Faraday Discuss. 161, 305–331 (2013)

    Article  ADS  Google Scholar 

  189. M. Goulian, R. Bruinsma, P. Pincus, Long-range forces in heterogeneous fluid membranes. Europhys. Lett. 22, 145–150 (1993)

    Article  ADS  Google Scholar 

  190. P.G. Dommersnes, J.-B. Fournier, N-body study of anisotropic membrane inclusions: membrane mediated interactions and ordered aggregation. Eur. Phys. J. B 12, 9–12 (1999)

    Article  ADS  Google Scholar 

  191. H.-K. Lin, R. Zandi, U. Mohideen, L.P. Pryadko, Fluctuation-induced forces between inclusions in a fluid membrane under tension. Phys. Rev. Lett 107, 228104 (2011)

    Article  ADS  Google Scholar 

  192. A.H. Bahrami, T.R. Weikl, Curvature-mediated assembly of Janus nanoparticles on membrane vesicles. Nano Lett. 18, 1259–1263 (2018)

    Article  ADS  Google Scholar 

  193. J. Midya, T. Auth, G. Gompper, Membrane-mediated interactions between nonspherical elastic particles. ACS Nano 17, 1935–1945 (2023)

    Article  Google Scholar 

  194. N. Ramakrishnan, P.B.S. Kumar, R. Radhakrishnan, Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins. Phys. Rep. 543, 1–60 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  195. G. Kumar, A. Srivastava, Membrane remodeling due to a mixture of multiple types of curvature proteins. J. Chem. Theory Comput. 18, 5659–5671 (2022)

    Article  Google Scholar 

  196. Y.-H. Tang, L. Lu, H. Li, C. Evangelinos, L. Grinberg, V. Sachdeva, G.E. Karniadakis, OpenRBC: a fast simulator of red blood cells at protein resolution. Biophys. J. 112, 2030–2037 (2017)

    Article  ADS  Google Scholar 

  197. D.A. Fedosov, B. Caswell, G.E. Karniadakis, Systematic coarse-graining of spectrin-level red blood cell models. Comput. Meth. Appl. Mech. Eng. 199, 1937–1948 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  198. C. Pozrikidis, Numerical simulation of cell motion in tube flow. Ann. Biomed. Eng. 33, 165–178 (2005)

    Article  Google Scholar 

  199. S. Mendez, E. Gibaud, F. Nicoud, An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers. J. Comput. Phys. 256, 465–483 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  200. J. Sigüenza, S. Mendez, D. Ambard, F. Dubois, F. Jourdan, R. Mozul, F. Nicoud, Validation of an immersed thick boundary method for simulating fluid-structure interactions of deformable membranes. J. Comput. Phys. 322, 723–746 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  201. T. Ye, N. Phan-Thien, B.C. Khoo, C.T. Lim, Dissipative particle dynamics simulations of deformation and aggregation of healthy and diseased red blood cells in a tube flow. Phys. Fluids 26, 111902 (2014)

    Article  Google Scholar 

  202. T. Ye, N. Phan-Thien, C.T. Lim, Y. Li, Red blood cell motion and deformation in a curved microvessel. J. Biomech. 65, 12–22 (2017)

    Article  Google Scholar 

  203. J. Mauer, S. Mendez, L. Lanotte, F. Nicoud, M. Abkarian, G. Gompper, D.A. Fedosov, Flow-induced transitions of red blood cell shapes under shear. Phys. Rev. Lett. 121, 118103 (2018)

    Article  ADS  Google Scholar 

  204. J.L. McWhirter, H. Noguchi, G. Gompper, Ordering and arrangement of deformed red blood cells in flow through microcapillaries. New J. Phys. 14, 085026 (2012)

    Article  Google Scholar 

  205. D.A. Fedosov, B. Caswell, A.S. Popel, G.E. Karniadakis, Blood flow and cell-free layer in microvessels. Microcirculation 17, 615–628 (2010)

    Article  Google Scholar 

  206. D.A. Fedosov, W. Pan, B. Caswell, G. Gompper, G.E. Karniadakis, Predicting human blood viscosity in silico. Proc. Natl. Acad. Sci. USA 108, 11772–11777 (2011)

    Article  ADS  Google Scholar 

  207. D. Katanov, G. Gompper, D.A. Fedosov, Microvascular blood flow resistance: role of red blood cell migration and dispersion. Microvasc. Res. 99, 57–66 (2015)

    Article  Google Scholar 

  208. W. Chien, G. Gompper, D.A. Fedosov, Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels. Microcirculation 28, e12668 (2021)

    Article  Google Scholar 

  209. R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264 (1973)

    Article  ADS  Google Scholar 

  210. D. Barthés-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251–267 (1981)

    Article  ADS  Google Scholar 

  211. C. Pozrikidis, Axisymmetric motion of a file of red blood cells through capillaries. Phys. Fluids 17, 031503 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  212. J.P. Mills, L. Qie, M. Dao, C.T. Lim, S. Suresh, Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech. Chem. Biosystems 1, 169–180 (2004)

    Google Scholar 

  213. D. Barthés-Biesel, A. Diaz, E. Dhenin, Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222 (2002)

    Article  ADS  Google Scholar 

  214. P. Bagchi, R.M. Kalluri, Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81, 056320 (2010)

    Article  ADS  Google Scholar 

  215. E. Foessel, J. Walter, A.-V. Salsac, D. Barthés-Biesel, Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672, 477–486 (2011)

    Article  ADS  Google Scholar 

  216. E. Lac, D. Barthés-Biesel, Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17, 072105 (2005)

    Article  ADS  Google Scholar 

  217. T. Omori, T. Ishikawa, D. Barthés-Biesel, A.-V. Salsac, Y. Imai, T. Yamaguchi, Tension of red blood cell membrane in simple shear flow. Phys. Rev. E 86, 056321 (2012)

    Article  ADS  Google Scholar 

  218. A. Yazdani, P. Bagchi, Influence of membrane viscosity on capsule dynamics in shear flow. J. Fluid Mech. 718, 569–595 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  219. Z. Wang, Y. Sui, P.D.M. Spelt, W. Wang, Three-dimensional dynamics of oblate and prolate capsules in shear flow. Phys. Rev. E 88, 053021 (2013)

    Article  ADS  Google Scholar 

  220. Y. Sui, Y.T. Chew, P. Roy, Y.P. Cheng, H.T. Low, Dynamic motion of red blood cells in simple shear flow. Phys. Fluids 20, 112106 (2008)

    Article  ADS  Google Scholar 

  221. S. Mendez, M. Abkarian, In-plane elasticity controls the full dynamics of red blood cells in shear flow. Phys. Rev. Fluids 3, 101101 (2018)

    Article  ADS  Google Scholar 

  222. S.K. Doddi, P. Bagchi, Lateral migration of a capsule in a plane Poiseuille flow in a channel. Int. J. Multiphase Flow 34, 966–986 (2008)

    Article  Google Scholar 

  223. C. Wang, J. Li, L. Zhao, P. Qian, Shape transformations of red blood cells in the capillary and their possible connections to oxygen transportation. J. Biol. Phys. 48, 79–92 (2022)

    Article  Google Scholar 

  224. M. Gross, T. Krüger, F. Varnik, Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects. Soft Matter 10, 4360–4372 (2014)

    Article  ADS  Google Scholar 

  225. M. Mehrabadi, D.N. Ku, C.K. Aidun, Effects of shear rate, confinement, particle parameters on margination in blood flow. Phys. Rev. E 93, 023109 (2016)

    Article  ADS  Google Scholar 

  226. K. Vahidkhah, P. Balogh, P. Bagchi, Flow of red blood cells in stenosed microvessels. Sci. Rep. 6, 28194 (2016)

    Article  ADS  Google Scholar 

  227. P. Balogh, P. Bagchi, A computational approach to modeling cellular-scale blood flow in complex geometry. J. Comput. Phys. 334, 280–307 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  228. P. Balogh, P. Bagchi, Direct numerical simulation of cellular-scale blood flow in 3D microvascular networks. Biophys. J. 113, 2815–2826 (2017)

    Article  ADS  Google Scholar 

  229. Q. Zhou, J. Fidalgo, M.O. Bernabeu, M.S.N. Oliveira, T. Krüger, Emergent cell-free layer asymmetry and biased haematocrit partition in a biomimetic vascular network of successive bifurcations. Soft Matter 17, 3619–3633 (2021)

    Article  ADS  Google Scholar 

  230. T. Browicz, Further observation of motion phenomena on red blood cells in pathological states. Zbl. Med. Wiss. 28, 625 (1890)

    Google Scholar 

  231. J. Evans, W. Gratzer, N. Mohandas, K. Parker, J. Sleep, Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence. Biophys. J. 94, 4134–4144 (2008)

    Article  ADS  Google Scholar 

  232. Y.Z. Yoon, J. Kotar, A.T. Brown, P. Cicuta, Red blood cell dynamics: from spontaneous fluctuations to non-linear response. Soft Matter 7, 2042–2051 (2011)

    Article  ADS  Google Scholar 

  233. R. Rodríguez-García, I. López-Montero, M. Mell, G. Egea, N.S. Gov, F. Monroy, Direct cytoskeleton forces cause membrane softening in red blood cells. Biophys. J. 108, 2794–2806 (2015)

    Article  ADS  Google Scholar 

  234. N.S. Gov, S.A. Safran, Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys. J. 88, 1859–1874 (2005)

    Article  Google Scholar 

  235. N.S. Gov, Active elastic network: cytoskeleton of the red blood cell. Phys. Rev. E 75, 011921 (2007)

    Article  ADS  Google Scholar 

  236. J.-B. Manneville, P. Bassereau, D. Lévy, J. Prost, Activity of transmembrane proteins induces magnification of shape fluctuations of lipid membranes. Phys. Rev. Lett. 82, 4356–4359 (1999)

    Article  ADS  Google Scholar 

  237. S. Ramaswamy, J. Toner, J. Prost, Nonequilibrium fluctuations, traveling waves, instabilities in active membranes. Phys. Rev. Lett. 84, 3494–3497 (2000)

    Article  ADS  Google Scholar 

  238. L.H. Miller, D.I. Baruch, K. Marsh, O.K. Doumbo, The pathogenic basis of malaria. Nature 415, 673–679 (2002)

    Article  Google Scholar 

  239. M. Koch, J. Baum, The mechanics of malaria parasite invasion of the human erythrocyte - towards a reassessment of the host cell contribution. Cell. Microbiol. 18, 319–329 (2016)

    Article  Google Scholar 

  240. K. Yahata, M. Treeck, R. Culleton, T.-W. Gilberger, O. Kaneko, Time-lapse imaging of red blood cell invasion by the rodent malaria parasite Plasmodium yoelii. PLoS ONE 7, e50780 (2012)

    Article  ADS  Google Scholar 

  241. G.A. Barabino, M.O. Platt, D.K. Kaul, Sickle cell biomechanics. Annu. Rev. Biomed. Eng. 12, 345–367 (2010)

    Article  Google Scholar 

  242. W. Pezeshkian, S.J. Marrink, Simulating realistic membrane shapes. Curr. Opin. Cell Biol. 71, 103–111 (2021)

    Article  Google Scholar 

  243. W. Pezeshkian, M. König, T.A. Wassenaar, S.J. Marrink, Backmapping triangulated surfaces to coarse-grained membrane models. Nat. Comm. 11, 2296 (2020)

    Article  ADS  Google Scholar 

  244. M. Sadeghi, F. Noé, Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models. Nat. Comm. 11, 2951 (2020)

    Article  ADS  Google Scholar 

  245. C.M. Elliott, B. Stinner, C. Venkataraman, Modelling cell motility and chemotaxis with evolving surface finite elements. J. R. Soc. Interface 9, 3027–3044 (2012)

    Article  Google Scholar 

  246. H. Berthoumieux, J.-L. Maître, C.-P. Heisenberg, E.K. Paluch, F. Jülicher, G. Salbreux, Active elastic thin shell theory for cellular deformations. New J. Phys. 16, 065005 (2014)

    Article  ADS  Google Scholar 

  247. A. Mietke, F. Jülicher, I.F. Sbalzarini, Self-organized shape dynamics of active surfaces. Proc. Natl. Acad. Sci. USA 116, 29–34 (2019)

    Article  ADS  Google Scholar 

  248. H. Li, G. Lykotrafitis, Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network. Biophys. J. 107, 642–653 (2014)

    Article  ADS  Google Scholar 

  249. Z. Peng, X. Li, I.V. Pivkin, M. Dao, G.E. Karniadakis, S. Suresh, Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc. Natl. Acad. Sci. USA 110, 13356–13361 (2013)

    Article  ADS  Google Scholar 

  250. H. Ni, G.A. Papoian, Membrane-MEDYAN: simulating deformable vesicles containing complex cytoskeletal networks. J. Phys. Chem. B 125, 10710–10719 (2021)

    Article  Google Scholar 

  251. N. Tamemoto, H. Noguchi, Reaction-diffusion waves coupled with membrane curvature. Soft Matter 17, 6589–6596 (2021)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Palakkad, 678623, India

    Anil K. Dasanna

  2. Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Knowledge City, Mohali, 140306, India

    Anil K. Dasanna

  3. Theoretical Physics of Living Matter, Institute for Advanced Simulation, Forschungszentrum Jülich, 52425, Jülich, Germany

    Dmitry A. Fedosov

Authors
  1. Anil K. Dasanna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitry A. Fedosov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anil K. Dasanna.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dasanna, A.K., Fedosov, D.A. Mesoscopic modeling of membranes at cellular scale. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01177-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjs/s11734-024-01177-4

Search

Navigation