Skip to main content
SpringerLink
Log in

Computational models of the primary cilium and endothelial mechanotransmission

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

In endothelial cells (ECs), the mechanotransduction of fluid shear stress is partially dependent on the transmission of force from the fluid into the cell (mechanotransmission). The role of the primary cilium in EC mechanotransmission is not yet known. To motivate a framework towards quantifying cilia contribution to EC mechanotransmission, we have reviewed mechanical models of both (1) the primary cilium (three-dimensional and lower-dimensional) and (2) whole ECs (finite element, non-finite element, and tensegrity). Both the primary cilia and whole EC models typically incorporate fluid-induced wall shear stress and spatial geometry based on experimentally acquired images of cells. This paper presents future modelling directions as well as the major goals towards integrating primary cilium models into a multi-component EC mechanical model. Finally, we outline how an integrated cilium-EC model can be used to better understand mechanotransduction in the endothelium.

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

Similar content being viewed by others

References

  • AbouAlaiwi WA, Takahashi M, Mell BR, Jones TJ, Ratnam S, Kolb RJ, Nauli SM (2009) Ciliary polycystin-2 is a mechanosensitive calcium channel involved in nitric oxide signaling cascades. Circ Res 104(7):860–869

  • Aird WC (2004) Endothelium as an organ system. Crit Care Med 32(5):S271–S279. doi:10.1097/01.CCM.0000129669.21649.40

    Article  Google Scholar 

  • Ando J, Yamamoto K (2009) Vascular mechanobiology endothelial cell responses to fluid shear stress. Circ J 73(11):1983–1992

    Article  Google Scholar 

  • Ando J, Yamamoto K (2013) Flow detection and calcium signaling in vascular endothelial cells. Cardiovasc Res 99(2):260–268

  • Barakat AI (2001) A model for shear stress-induced deformation of a flow sensor on the surface of vascular endothelial cells. J Theor Biol 210(2):221–236

    Article  Google Scholar 

  • Barreto S, Clausen CH, Perrault CM, Fletcher DA, Lacroix D (2013) A multi-structural single cell model of force-induced interactions of cytoskeletal components. Biomaterials 34(26):6119–6126

    Article  Google Scholar 

  • Besschetnova TY, Kolpakova-Hart E, Guan Y, Zhou J, Olsen BR, Shah JV (2010) Identification of signaling pathways regulating primary cilium length and flow-mediated adaptation. Curr Biol 20(2):182–187

    Article  Google Scholar 

  • Buck TE, Li J, Rohde GK, Murphy RF (2012) Toward the virtual cell: automated approaches to building models of subcellular organization “learned” from microscopy images. Bioessays 34(9):791–799

  • Caille N, Thoumine O, Tardy Y, Meister JJ (2002) Contribution of the nucleus to the mechanical properties of endothelial cells. J Biomech 35(2):177–187

    Article  Google Scholar 

  • Chouinard JA, Grenier G, Khalil A, Vermette P (2008) Oxidized-LDL induce morphological changes and increase stiffness of endothelial cells. Exp Cell Res 314(16):3007–3016

    Article  Google Scholar 

  • Costa KD, Yin FCP, Sim AJ (2005) Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy. J Biomech Eng 128(2):176–184

    Article  Google Scholar 

  • Dabagh M, Jalali P, Butler PJ, Trabell JM (2014) Shear-induced force transmission in a multicomponent, multicell model of the endothelium. J R Soc Interface 11(98):20140431. doi:10.1098/rsif.2014.0431

  • Dai G, Kaazempur-Mofrad MR, Natarajan S, Zhang Y, Vaughn S, Blackman BR, Kamm RD, Garca-Cardea G, Gimbrone MA (2004) Distinct endothelial phenotypes evoked by arterial waveforms derived from atherosclerosis-susceptible and -resistant regions of human vasculature. Proc Natl Acad Sci USA 101(41):14871–14876

    Article  Google Scholar 

  • Dangaria JH, Butler PJ (2007) Macrorheology and adaptive microrheology of endothelial cells subjected to fluid shear stress. Am J Physiol Cell Physiol 293(5):C1568–C1575

    Article  Google Scholar 

  • Davies PF (1995) Flow-mediated endothelial mechanotransduction. Physiol Rev 75(3):519–560

    Google Scholar 

  • Davies PF (2009) Hemodynamic shear stress and the endothelium in cardiovascular pathophysiology. Nat Clin Pract Cardiovasc Med 6(1):16–26

    Article  Google Scholar 

  • Davies PF, Shi C, DePaola N, Helmke BP, Polacek DC (2001) Hemodynamics and the focal origin of atherosclerosis. Ann N Y Acad Sci 947(1):7–17

    Article  Google Scholar 

  • Davies PF, Polacek DC, Shi C, Helmke BP (2002) The convergence of haemodynamics, genomics, and endothelial structure in studies of the focal origin of atherosclerosis. Biorheology 39(3):299–306

    Google Scholar 

  • Deguchi S, Fukamachi H, Hashimoto K, Iio K, Tsujioka K (2009) Measurement and finite element modeling of the force balance in the vertical section of adhering vascular endothelial cells. J Mech Behav Biomed Mater 2(2):173–185

    Article  Google Scholar 

  • Downs ME, Nguyen AM, Herzog FA, Hoey DA, Jacobs CR (2014) An experimental and computational analysis of primary cilia deflection under fluid flow. Comput Methods Biomech Biomed Eng 17(1):2–10

  • Egorova AD, van der Heiden K, Poelmann RE, Hierck BP (2012) Primary cilia as biomechanical sensors in regulating endothelial function. Differentiation 83(2):S56–S61

    Article  Google Scholar 

  • Espinha LC, Hoey DA, Fernandes PR, Rodrigues HC, Jacobs CR (2014) Oscillatory fluid flow influences primary cilia and microtubule mechanics. Cytoskeleton 71(7):435–445

    Article  Google Scholar 

  • Farnum CE, Wilsman NJ (2011) Axonemal positioning and orientation in three-dimensional space for primary cilia: What is known, what is assumed, and what needs clarification. Dev Dyn 240(11):2405–2431

    Article  Google Scholar 

  • Ferko M, Bhatnagar A, Garcia M, Butler P (2007) Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial cells. Ann Biomed Eng 35(2):208–223

    Article  Google Scholar 

  • Ferko MC, Patterson BW, Butler PJ (2006) High-resolution solid modeling of biological samples imaged with 3d fluorescence microscopy. Microsc Res Tech 69(8):648–655

    Article  Google Scholar 

  • Frisch-Fay R (1962) Flexible bars. Butterworths, London

    MATH  Google Scholar 

  • Fung YC, Liu SQ (1993) Elementary mechanics of the endothelium of blood vessels. J Biomech Eng 115(1):1–12

    Article  Google Scholar 

  • Grashoff C, Hoffman BD, Brenner MD, Zhou R, Parsons M, Yang MT, McLean MA, Sligar SG, Chen CS, Ha T, Schwartz MA (2010) Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics. Nature 466(7303):263–266

    Article  Google Scholar 

  • Guo P, Weinstein AM, Weinbaum S (2000) A hydrodynamic mechanosensory hypothesis for brush border microvilli. Am J Physiol Ren Physiol 279(4):F698–712

    Google Scholar 

  • Hagiwara H, Kano A, Aoki T, Ohwada N (2000) Immunocytochemistry of the striated rootlets associated with solitary cilia in human oviductal secretory cells. Histochem Cell Biol 114(3):205–212

    Google Scholar 

  • Hagiwara H, Ohwada N, Aoki T, Suzuki T, Takata K (2008) The primary cilia of secretory cells in the human oviduct mucosa. Med Mol Morphol 41(4):193–198

    Article  Google Scholar 

  • Haust MD (1987) Endothelial cilia in human aortic atherosclerotic lesions. Virchows Archiv 410(4):317–326

    Article  Google Scholar 

  • Helmke BP, Thakker DB, Goldman RD, Davies PF (2001) Spatiotemporal analysis of flow-induced intermediate filament displacement in living endothelial cells. Biophys J 80(1):184–194

    Article  Google Scholar 

  • Helmke BP, Rosen AB, Davies PF (2003) Mapping mechanical strain of an endogenous cytoskeletal network in living endothelial cells. Biophys J 84(4):2691–2699

    Article  Google Scholar 

  • Herzog F (2010) A mechanical approach to study the bending of the primary cilium in response to fluid flow. Masters

  • Hoey DA, Downs ME, Jacobs CR (2012) The mechanics of the primary cilium: an intricate structure with complex function. J Biomech 45(1):17–26

    Article  Google Scholar 

  • Ingber DE (1997) Tensegrity: the architectural basis of cellular mechanotransduction. Annu Rev Physiol 59(1):575–599

    Article  Google Scholar 

  • Ingber DE (2008) Tensegrity and mechanotransduction. J Bodyw Mov Ther 12(3):198–200

    Article  Google Scholar 

  • Iomini C, Tejada K, Mo W, Vaananen H, Piperno G (2004) Primary cilia of human endothelial cells disassemble under laminar shear stress. J Cell Biol 164(6):811–817

    Article  Google Scholar 

  • Jean RP, Chen CS, Spector AA (2005) Finite-element analysis of the adhesion–cytoskeleton–nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model. J Biomech Eng 127(4):594–600

    Article  Google Scholar 

  • Jensen CG, Poole CA, McGlashan SR, Marko M, Issa ZI, Vujcich KV, Bowser SS (2004) Ultrastructural, tomographic and confocal imaging of the chondrocyte primary cilium in situ. Cell Biol Int 28(2):101–110

    Article  Google Scholar 

  • Kumar S, Maxwell IZ, Heisterkamp A, Polte TR, Lele TP, Salanga M, Mazur E, Ingber DE (2006) Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. Biophys J 90(10):3762–3773

    Article  Google Scholar 

  • Kwon RY, Hoey DA, Jacobs CR (2011) Mechanobiology of primary cilia cellular and biomolecular mechanics and mechanobiology, studies in mechanobiology, tissue engineering and biomaterials, vol 4. Springer, Berlin

    Google Scholar 

  • Leiderman KM, Miller LA, Fogelson AL (2008) The effects of spatial inhomogeneities on flow through the endothelial surface layer. J Theor Biol 252:313–325

    Article  MathSciNet  Google Scholar 

  • Lim CT, Zhou EH, Quek ST (2006) Mechanical models for living cellsa review. J Biomech 39(2):195–216

    Article  Google Scholar 

  • Liu W, Xu S, Woda C, Kim P, Weinbaum S, Satlin LM (2003) Effect of flow and stretch on the \([\text{ Ca }^{2+}]_{i}\) response of principal and intercalated cells in cortical collecting duct. Am J Physiol Ren Physiol 285(5):F998–F1012

    Article  Google Scholar 

  • Masyuk AI, Masyuk TV, Splinter PL, Huang BQ, Stroope AJ, LaRusso NF (2006) Cholangiocyte cilia detect changes in luminal fluid flow and transmit them into intracellular ca\(^{2+}\) and camp signaling. Gastroenterology 131(3):911–920

    Article  Google Scholar 

  • Mathur AB, Truskey GA, Monty Reichert W (2000) Atomic force and total internal reflection fluorescence microscopy for the study of force transmission in endothelial cells. Biophys J 78(4):1725–1735

  • Mazzag B, Barakat A (2011) The effect of noisy flow on endothelial cell mechanotransduction: a computational study. Ann Biomed Eng 39(2):911–921

    Article  Google Scholar 

  • McMurray RJ, Wann AKT, Thompson CL, Connelly JT, Knight MM (2013) Surface topography regulates wnt signaling through control of primary cilia structure in mesenchymal stem cells. Scientific reports 3

  • Moser JJ, Fritzler MJ, Ou Y, Rattner JB (2010) The pcmbasal body/primary cilium coalition. Semin Cell Dev Biol 21(2):148–155

    Article  Google Scholar 

  • Nauli SM, Kawanabe Y, Kaminski JJ, Pearce WJ, Ingber DE, Zhou J (2008) Endothelial cilia are fluid shear sensors that regulate calcium signaling and nitric oxide production through polycystin-1. Circulation 117(9):1161–1171

    Article  Google Scholar 

  • Park CY, Tambe D, Alencar AM, Trepat X, Zhou EH, Millet E, Butler JP, Fredberg JJ (2010) Mapping the cytoskeletal prestress. Am J Physiol-Cell Physiol 298(5):C1245–C1252

    Article  Google Scholar 

  • Pitaval A, Tseng Q, Bornens M, Thery M (2010) Cell shape and contractility regulate ciliogenesis in cell cycle-arrested cells. J Cell Biol 191(2):303–312

    Article  Google Scholar 

  • Poole CA, Zhang ZJ, Ross JM (2001) The differential distribution of acetylated and detyrosinated alpha-tubulin in the microtubular cytoskeleton and primary cilia of hyaline cartilage chondrocytes. J Anat 199(4):393–405

    Article  Google Scholar 

  • Pozrikidis C (2010) Shear flow over cylindrical rods attached to a substrate. J Fluids Struct 26(3):393–405

    Article  MathSciNet  Google Scholar 

  • Pozrikidis C (2011) Shear flow past slender elastic rods attached to a plane. Int J Solids Struct 48(1):137–143

    Article  MATH  Google Scholar 

  • Radmacher M (2002) Measuring the elastic properties of living cells by the atomic force microscope. In: Jena BP, Heinrich Hrber JK (eds) Methods in cell biology, vol 68. Academic Press, New York, pp 67–90

    Google Scholar 

  • Rahimzadeh J, Meng F, Sachs F, Wang J, Verma D, Hua SZ (2011) Real-time observation of flow-induced cytoskeletal stress in living cells. Am J Physiol Cell Physiol 301(3):C646–C652

    Article  Google Scholar 

  • Rydholm S, Zwartz G, Kowalewski JM, Kamali-Zare P, Frisk T, Brismar H (2010) Mechanical properties of primary cilia regulate the response to fluid flow. Am J Physiol-Ren Physiol 298(5):F1096–F1102

    Article  Google Scholar 

  • Satcher JRL, Gimbrone JMA, Dewey JCF, Bussolari SR (1992) The distribution of fluid forces on model arterial endothelium using computational fluid dynamics. J Biomech Eng 114(3):309–316

    Article  Google Scholar 

  • Satcher RL Jr, Dewey CF Jr (1996) Theoretical estimates of mechanical properties of the endothelial cell cytoskeleton. Biophys J 71(1):109–118

    Article  Google Scholar 

  • Schwartz EA, Leonard ML, Bizios R, Bowser SS (1997) Analysis and modeling of the primary cilium bending response to fluid shear. Am J Physiol-Ren Physiol 272(1):F132–F138

    Google Scholar 

  • Slomka N, Gefen A (2010) Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics. J Biomech 43(9):1806–1816

    Article  Google Scholar 

  • Sugita S, Adachi T, Ueki Y, Sato M (2011) A novel method for measuring tension generated in stress fibers by applying external forces. Biophys J 101(1):53–60

    Article  Google Scholar 

  • Tritton DJ (1988) Physical fluid dynamics. Clarendon Press, Oxford

    Google Scholar 

  • Ueki Y, Sakamoto N, Ohashi T, Sato M (2009) Morphological responses of vascular endothelial cells induced by local stretch transmitted through intercellular junctions. Exp Mech 49(1):125–134

    Article  Google Scholar 

  • Ueki Y, Sakamoto N, Sato M (2010a) Cyclic force applied to fas induces actin recruitment depending on the dynamic loading pattern. Open Biomed Eng J 4:34–129

    Article  Google Scholar 

  • Ueki Y, Sakamoto N, Sato M (2010b) Direct measurement of shear strain in adherent vascular endothelial cells exposed to fluid shear stress. Biochem Biophys Res Commun 394(1):94–99

    Article  Google Scholar 

  • Ueki Y, Uda Y, Sakamoto N, Sato M (2010c) Measurements of strain on single stress fibers in living endothelial cells induced by fluid shear stress. Biochem Biophys Res Commun 395(3):441–446

    Article  Google Scholar 

  • Van der Heiden K, Hierck BP, Krams R, de Crom R, Cheng C, Baiker M, Pourquie MJBM, Alkemade FE, DeRuiter MC, Gittenberger-de Groot AC, Poelmann RE (2008) Endothelial primary cilia in areas of disturbed flow are at the base of atherosclerosis. Atherosclerosis 196(2):542–550

    Article  Google Scholar 

  • Vargas-Pinto R, Gong H, Vahabikashi A, Johnson M (2013) The effect of the endothelial cell cortex on atomic force microscopy measurements. Biophys J 105(2):300–309

    Article  Google Scholar 

  • Verma D, Ye N, Meng F, Sachs F, Rahimzadeh J, Hua SZ (2012) Interplay between cytoskeletal stresses and cell adaptation under chronic flow. PLoS One 7(9):e44–167

  • Vogel V, Sheetz M (2006) Local force and geometry sensing regulate cell functions. Nat Rev Mol Cell Biol 7(4):265–275

    Article  Google Scholar 

  • Wang N, Naruse K, Stamenovi D, Fredberg JJ, Mijailovich SM, Toli-Nrrelykke IM, Polte T, Mannix R, Ingber DE (2001) Mechanical behavior in living cells consistent with the tensegrity model. Proc Natl Acad Sci 98(14):7765–7770

    Article  Google Scholar 

  • Wang Y, Shyy JY, Chien S (2008) Fluorescence proteins, live-cell imaging, and mechanobiology: seeing is believing. Annu Rev Biomed Eng 10:1–38

    Article  MATH  Google Scholar 

  • Yamada H, Mouri N, Nobuhara S (2010) Three-dimensional morphometry of single endothelial cells with substrate stretching and image-based finite element modeling. EURASIP J Adv Signal Proc 2010(1):091–616

    Google Scholar 

  • Young YN, Downs M, Jacobs CR (2012) Dynamics of the primary cilium in shear flow. Biophys J 103(4):629–639

    Article  Google Scholar 

  • Zeng D, Juzkiw T, Read AT, Chan DH, Glucksberg M, Ethier CR, Johnson M (2010) Youngs modulus of elasticity of schlemms canal endothelial cells. Biomech Model Mechanobiol 9(1):19–33

    Article  Google Scholar 

Download references

Acknowledgments

Yi Chung Lim is supported by a University of Auckland Doctoral Scholarship. This work was supported by a Faculty Research Development Fund Grant (3702516, D.S.L.).

Author information

Authors and Affiliations

  1. Auckland Bioengineering Institute, University of Auckland, 70 Symonds St, Auckland, 1010, New Zealand

    Yi Chung Lim & Michael T. Cooling

  2. Department of Engineering Science, Auckland Bioengineering Institute, University of Auckland, 70 Symonds St, Auckland, 1010, New Zealand

    David S. Long

Authors
  1. Yi Chung Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael T. Cooling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David S. Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David S. Long.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lim, Y.C., Cooling, M.T. & Long, D.S. Computational models of the primary cilium and endothelial mechanotransmission. Biomech Model Mechanobiol 14, 665–678 (2015). https://doi.org/10.1007/s10237-014-0629-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-014-0629-x

Keywords

Search

Navigation