Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 1, pp 191–203 | Cite as

Theoretical modeling of mechanical homeostasis of a mammalian cell under gravity-directed vector

  • Lüwen Zhou
  • Chen Zhang
  • Fan Zhang
  • Shouqin Lü
  • Shujin Sun
  • Dongyuan Lü
  • Mian LongEmail author
Original Paper


Translocation of dense nucleus along gravity vector initiates mechanical remodeling of a eukaryotic cell. In our previous experiments, we quantified the impact of gravity vector on cell remodeling by placing an MC3T3-E1 cell onto upward (U)-, downward (D)-, or edge-on (E)- orientated substrate. Our experimental data demonstrate that orientation dependence of nucleus longitudinal translocation is positively correlated with cytoskeletal (CSK) remodeling of their expressions and structures and also is associated with rearrangement of focal adhesion complex (FAC). However, the underlying mechanism how CSK network and FACs are reorganized in a mammalian cell remains unclear. In this paper, we developed a theoretical biomechanical model to integrate the mechanosensing of nucleus translocation with CSK remodeling and FAC reorganization induced by a gravity vector. The cell was simplified as a nucleated tensegrity structure in the model. The cell and CSK filaments were considered to be symmetrical. All elements of CSK filaments and cytomembrane that support the nucleus were simplified as springs. FACs were simplified as an adhesion cluster of parallel bonds with shared force. Our model proposed that gravity vector-directed translocation of the cell nucleus is mechanically balanced by CSK remodeling and FAC reorganization induced by a gravitational force. Under gravity, dense nucleus tends to translocate and exert additional compressive or stretching force on the cytoskeleton. Finally, changes of the tension force acting on talin by microfilament alter the size of FACs. Results from our model are in qualitative agreement with those from experiments.


Gravity directed Mechanosensing Nucleus translocation Cytoskeletal remodeling FAC reorganization 



This work was supported by Strategic Priority Research Program of Chinese Science Academy of Sciences grant XDA04020219, National Natural Science Foundation of China grant 31110103918, and National Key Basic Research Foundation of China grant 2011CB710904.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Balaban NQ, Schwarz US, Riveline D, Goichberg P, Tzur G, Sabanay I, Mahalu D, Safran S, Bershadsky A, Addadi L et al (2001) Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat Cell Biol 3(5):466CrossRefGoogle Scholar
  2. Bell GI (1978) Models for the specific adhesion of cells to cells. Science 200(4342):618CrossRefGoogle Scholar
  3. Clément G, Slenzka K (2006) Fundamentals of space biology: research on cells, animals, and plants in space, vol 18. Springer, New YorkCrossRefGoogle Scholar
  4. Cogoli A, Cogoli-Greuter M (1996) Activation and proliferation of lymphocytes and other mammalian cells in microgravity. Adv Space Biol Med 6:33CrossRefGoogle Scholar
  5. Feric M, Brangwynne CP (2013) A nuclear F-actin scaffold stabilizes RNP droplets against gravity in large cells. Nat Cell Biol 15(10):1253CrossRefGoogle Scholar
  6. Feric M, Broedersz CP, Brangwynne CP (2015) Scientific reports 5Google Scholar
  7. Fletcher DA, Mullins RD (2010) Cell mechanics and the cytoskeleton. Nature 463(7280):485CrossRefGoogle Scholar
  8. Geiger B, Spatz JP, Bershadsky AD (2009) Environmental sensing through focal adhesions. Nat Rev Mol Cell Biol 10(1):21CrossRefGoogle Scholar
  9. George TF, Jelski D, Letfullin RR, Zhang G (2011) Computational studies of new materials II: from ultrafast processes and nanostructures to optoelectronics, energy storage and nanomedicine. World Scientific, SingaporeCrossRefGoogle Scholar
  10. Grimm D, Wise P, Lebert M, Richter P, Baatout S (2011) How and why does the proteome respond to microgravity? Expert Rev Proteom 8(1):13CrossRefGoogle Scholar
  11. Herrmann H, Bär H, Kreplak L, Strelkov SV, Aebi U (2007) Intermediate filaments: from cell architecture to nanomechanics. Nat Rev Mol Cell Biol 8(7):562CrossRefGoogle Scholar
  12. Howard J et al (2001) Mechanics of motor proteins and the cytoskeleton. Sinauer Associates, SunderlandGoogle Scholar
  13. Ingber DE (1993) Cellular tensegrity: defining new rules of biological design that govern the cytoskeleton. J Cell Sci 104(3):613Google Scholar
  14. Kalwarczyk T, Ziebacz N, Bielejewska A, Zaboklicka E, Koynov K, Szymanski J, Wilk A, Patkowski A, Gapinski J, Butt HJ et al (2011) Comparative analysis of viscosity of complex liquids and cytoplasm of mammalian cells at the nanoscale. Nano Lett 11(5):2157CrossRefGoogle Scholar
  15. Kamei H (1994) Relationship of nuclear imaginations to perinuclear rings composed of intermediate filaments in MIA PaCa-2 and some other cells. Cell Struct Funct 19(3):123MathSciNetCrossRefGoogle Scholar
  16. Li H, Chen J, Zhang Y, Sun S, Tao Z, Long M (2010) Effects of oriented substrates on cell morphology, the cell cycle, and the cytoskeleton in Ros 17/2.8 cells. Sci China Life Sci 53(9):1085CrossRefGoogle Scholar
  17. Lim C, Zhou E, Quek S (2006) Mechanical models for living cells—a review. J Biomech 39(2):195CrossRefGoogle Scholar
  18. Milo R, Phillips R (2015) Cell biology by the numbers. Garland Science, New YorkGoogle Scholar
  19. Mofrad MR, Kamm MR (2006) Cytoskeletal mechanics: models and measurements in cell mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  20. Nava MM, Raimondi MT, Pietrabissa R (2014) Bio-chemo-mechanical models for nuclear deformation in adherent eukaryotic cells. Biomech Model Mechanobiol 13(5):929CrossRefGoogle Scholar
  21. Nichols HL, Zhang N, Wen X (2006) Proteomics and genomics of microgravity. Physiol Genom 26(3):163CrossRefGoogle Scholar
  22. Orr AW, Helmke BP, Blackman BR, Schwartz MA (2006) Mechanisms of mechanotransduction. Dev Cell 10(1):11CrossRefGoogle Scholar
  23. Pollard EC (1965) Theoretical studies on living systems in the absence of mechanical stress. J Theor Biol 8(1):113CrossRefGoogle Scholar
  24. Prescott D, Myerson D, Wallace J (1972) Enucleation of mammalian cells with cytochalasin B. Exp Cell Res 71(2):480CrossRefGoogle Scholar
  25. Satcher R, Dewey CF (1996) Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. Biophys J 71(1):109CrossRefGoogle Scholar
  26. Schwarz US, Safran SA (2013) Physics of adherent cells. Rev Mod Phys 85(3):1327CrossRefGoogle Scholar
  27. Schwarz US, Balaban NQ, Riveline D, Bershadsky A, Geiger B, Safran S (2002) Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization. Biophys J 83(3):1380CrossRefGoogle Scholar
  28. Stamenović D, Coughlin MF (1999) The role of prestress and architecture of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis. J Theor Biol 201(1):63CrossRefGoogle Scholar
  29. Tadokoro S, Shattil SJ, Eto K, Tai V, Liddington RC, de Pereda JM, Ginsberg MH, Calderwood DA (2003) Talin binding to integrin ß tails: a final common step in integrin activation. Science 302(5642):103CrossRefGoogle Scholar
  30. Vorselen D, Roos WH, MacKintosh FC, Wuite GJ, van Loon JJ (2014) The role of the cytoskeleton in sensing changes in gravity by nonspecialized cells. FASEB J 28(2):536CrossRefGoogle Scholar
  31. Wang N, Tytell JD, Ingber DE (2009) Mechanotransduction at a distance: mechanically coupling the extracellular matrix with the nucleus. Nat Rev Mol Cell Biol 10(1):75CrossRefGoogle Scholar
  32. Wegener J, Janshoff A, Galla HJ (1998) Cell adhesion monitoring using a quartz crystal microbalance: comparative analysis of different mammalian cell lines. Eur Biophys J 28(1):26CrossRefGoogle Scholar
  33. Wiseman PW, Brown CM, Webb DJ, Hebert B, Johnson NL, Squier JA, Ellisman MH, Horwitz A (2004) Spatial mapping of integrin interactions and dynamics during cell migration by image correlation microscopy. J Cell Sci 117(23):5521CrossRefGoogle Scholar
  34. Zhang C, Zhou L, Zhang F, Lü D, Li N, Zheng L, Xu Y, Li Z, Sun S, Long M (2017) Mechanical remodeling of normally sized mammalian cells under a gravity vector. FASEB J 31(2):802CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Center for Biomechanics and Bioengineering, Key Laboratory of Microgravity (National Microgravity Laboratory), and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations