Deformation of the cell nucleus under indentation: Mechanics and mechanisms

Abstract

Computational models of the cell nucleus, along with experimental observations, can help in understanding the biomechanics of force-induced nuclear deformation and mechanisms of stress transition throughout the nucleus. Here, we develop a computational model for an isolated nucleus undergoing indentation, which includes separate components representing the nucleoplasm and the nuclear envelope. The nuclear envelope itself is composed of three separate layers: two thin elastic layers representing the inner and outer nuclear membranes and one thicker layer representing the nuclear lamina. The proposed model is capable of separating the structural role of major nuclear components in the force-induced biological response of the nucleus (and ultimately the cell). A systematic analysis is carried out to explore the role of major individual nuclear elements, namely inner and outer membranes, nuclear lamina, and nucleoplasm, as well as the loading and experimental factors such as indentation rate and probe angle, on the biomechanical response of an isolated nucleus in atomic force microscopy indentation experiment.

Assessment of the mechanical properties of the nucleus inside a spherical endothelial cell based on microtensile testing

“…We used this model in the finite element analysis of the tensile test. We assumed both the cytoplasm and nucleus are almost incompressible, with Poisson's ratio of 0.48 [Vaziri et al 2006]. The entire cell and nucleus were both modeled as concentric spheres, with diameters of 21 µm and 10 µm, respectively.…”

“…To understand the physical pathway of intracellular force transmission, mechanical behaviors of individual cells [Dong et al 1991;Karcher et al 2003;Hashimoto et al 2004;Desprat et al 2005;Fernandez et al 2006;Kasza et al 2007] and subcellular structural components such as cytoskeletal filaments [Deguchi et al 2006] and the nucleus [Caille et al 1998;2002;Dahl et al 2004;2005;Tseng et al 2004;Deguchi et al 2005a;Rowat et al 2005;Vaziri et al 2006] have been investigated. The cytoskeletal filaments are thin protein fibers used for support of intracellular Keywords: cell biomechanics, microtensile test, mechanical properties, viscoelastic properties, nucleus, finite element method.…”

“…Detection of the cantilever's deflection by the use of an optical technique yields the relation between the indentation lengths and forces loaded onto the specimen surface, giving the stiffness of the specimen. This technique was applied to adherent cells [Haga et al 2000;Sato et al 2000] or isolated nuclei [Vaziri et al 2006]. Employment of analytical [Sato et al 1990;Haider and Guilak 2000] or computational models [Vaziri et al 2006] in interpretations of these experimental results can provide more accurate estimations of the mechanical properties.…”

“…This technique was applied to adherent cells [Haga et al 2000;Sato et al 2000] or isolated nuclei [Vaziri et al 2006]. Employment of analytical [Sato et al 1990;Haider and Guilak 2000] or computational models [Vaziri et al 2006] in interpretations of these experimental results can provide more accurate estimations of the mechanical properties. The optical tweezers, introduced by Ashkin et al [1986], enable a noncontact trapping as well as a manipulation of a specimen by laser radiation pressure.…”

A computational mechanics approach to assess the link between cell morphology and forces during confined migration

“…The nominal values of the Young moduli E cortex,0 of the cell cortex and E cytosol,0 of the cytosol have been chosen equal to 100 and 10 Pa (Crick and Hughes 1950). For the nucleus, assuming that its stiffness is mostly provided by the nuclear lamina, we have set E lamina,0 and E nucleoplasm,0 to 3,000 Pa (Caille et al 2002;Dahl et al 2008) and 25 Pa (Vaziri et al 2006), respectively. According to a simple spatial homogenization approach (Christensen 1991;Larson 1998), such moduli have then been recalculated according to the surface occupied by each component in the cell to obtain E cortex , E cytosol , E lamina and E nucleoplasm (Table 1).…”