Abstract
Micro-indentation is a new experimental approach to assess physical cellular properties. Here we attempt to quantify the contribution of geometrical parameters to a cylindrical plant cell’s resistance to lateral deformation. This information is important to correctly interpret data obtained from experiments using the device, such as the local cellular stiffness in pollen tubes. We built a simple finite-element model of the micro-indentation interacting partners – micro-indenter, cell (pollen tube), and underlying substratum, that allowed us to manipulate geometric variables, such as geometry of the cell, cell radius, thickness of the cell wall and radius of the indenting stylus. Performing indentation experiments on this theoretical model demonstrates that all four parameters influence stiffness measurement and can therefore not be neglected in the interpretation of micro-indentation data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A-Hassan E, Heinz WF, Antonik MD, D’Costa NP, Nageswaran S, Schoenenberger C-A, Hoh JH (1998) Relative microelastic mapping of living cells by atomic force microscopy. Biophys J 74:1564–1578
Bao G, Suresh S (2003) Cell and molecular mechanics of biological materials. Nat Mater 2:715–725 DOI 10.1038/nature0110.1038/nmat1001
Bruce DM (2003) Mathematical modelling of the cellular mechanics of plants. Philos Trans R Soc Lond Biol Sci 358:1437–1444 DOI: 10.1098/rstb.2003.1337
Chanliaud E, Burrows KM, Jeronimidis G, Gidley MJ (2002) Mechanical properties of primary plant cell wall analogues. Planta 215:989–996 DOI 10.1007/s00425-002-0783-8
Cheng LY (1987a) Deformation analysis in cell and developmental biology Part I-Formal methodology. J Biomech Eng 109:10–17
Cheng LY (1987b) Deformation analysis in cell and developmental biology Part II-Mechanical experiments on cells. J Biomech Eng 109:18–24
Feng WW, Yang W-H (1973) On the contact problem of an inflated spherical nonlinear membrane. J Appl Mech 41:209–214
Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ (2001) Scaling the microrheology of living cells. Phys Rev Lett 87(14):148102 DOI 10.1103/PhysRevLett.87.148102
Geitmann A, Parre E (2004) The local cytomechanical properties of growing pollen tubes correspond to the axial distribution of structural cellular elements. Sex Plant Reprod 17:9–16 DOI 10.1007/s00497-004-0210-3
Geitmann A, McConnaughey WB, Lang-Pauluzzi I, Franklin-Tong VE, Emons AMC (2004) Cytomechanical properties of Papaver pollen tubes are altered after self-incompatibility challenge. Biophys J 86:3314–3323
Hettiaratchi DRP, O’Callaghan (1974) A membrane model of plant cell extension. J Theor Biol 45:459–465
Jones WR, Ting-Beall HP, Lee GM, Kelley SL, Hochmuth RM, Guilak F (1999) Alterations in the Young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J Biomech 32:119–127
Lardner TJ, Pujara P (1980) Compression of spherical cells. Mech Today 161-176
Lintilhac PM, Wei C, Tanguay JJ, Outwater JO (2000) Ball tonometry: a rapid, nondestructive method for measuring cell turgor pressure in thin-walled plant cells. J Plant Growth Regul 19:90–97 DOI 10.1007/s003440000009
Liu KK, Williams DR, Briscoe BJ (1996) Compressive deformation of a single microcapsule. Phys Rev E 54(6):6673–6680
Mitchison JM, Swann MM (1954) The mechanical properties of the cell surface. I. The cell elastimeter. J Exp Biol 31(3):443–460
Obataya I, Nakamura C, Han SW, Nakamura N, Miyake J (2005) Mechanical sensing of the penetration of various nanoneedles into a living cell using atomic force microscopy. Biosens Bioelectron 20:1652–1655
Parre E, Geitmann A (2005a) Pectin and the role of the physical properties of the cell wall in pollen tube growth of Solanum chacoense. Planta 220(4):582–592 DOI 10.1007/s00425-004-1368-5
Parre E, Geitmann A (2005b) More than a leak sealant: the mechanical properties of callose in growing plant cells. Plant Physiol 137:274–286 DOI 10.1104/pp.104.050773
Pitt RE, Davis DC (1984) Finite element analysis of fluid-filled cell response to external loading. Trans Am Soc Agric Eng 27:1976–1983
Petersen NO, McConnaughey WB, Elson EL (1982) Dependence of locally measured cellular deformability on position on the cell, temperature, and cytochalasin b. Proc Natl Acad Sci USA 79:5327–5331
Shin D, Athanasiou K (1999) Cytoindentation for obtaining cell biomechanical properties. J Orthop Res 17(6):880–890
Smith AE, Moxham KE, Middelberg APJ (1998) On uniquely determining cell-wall material properties with the compression experiment. Chem Eng Sci 53(23):3913–3922
Tomos D (2000) The plant cell pressure probe. Biotechnol Lett 42:437–442
Thomas CR, Zhang Z, Cowen C (2000) Micromanipulation measurements of biological materials. Biotechnol Lett 22:531–537
Wang CX, Wang L, Thomas CR (2004) Modelling the mechanical properties of single suspension-cultured tomato cells. Ann Bot 93:443–453 DOI 10.1093/aob/mch062
Wei C, Lintilhac PM, Tanguay JJ (2001) An insight into cell elasticity and load-bearing ability. Measurement and theory Plant Physiol 126:1129–1138
Zahalak GI, McConnaughey WB, Elson EL (1990) Determination of cellular mechanical properties by cell poking, with an application to leukocytes. J Biomech Eng 112:283–294
Zhao L, Schaefer D, Xu H, Modi SJ, LaCourse WR, Marten MR (2005) Elastic properties of the cell wall of Aspergillus nidulans studied with atomic force microscopy. Biotechnol Prog 21:292–299
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bolduc, JF., Lewis, L.J., Aubin, CÉ. et al. Finite-Element Analysis of Geometrical Factors in Micro-Indentation of Pollen Tubes. Biomech Model Mechanobiol 5, 227–236 (2006). https://doi.org/10.1007/s10237-005-0010-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-005-0010-1