## 2 Method  
### Geometry and Materials Properties  
In this study, a cell attached to the elastic substrate was modeled. For this purpose, the geometry of the adherent cell is needed. As reported by [PERSON] and [PERSON] [12], the dimensions of the fibroblast cell were recorded 5 min after the cell was attached to the substrate. The dimensions and geometry of the cell are shown in Figure 1.  
The cytoplasm was modeled as a sphere cut by a plane at its bottom to simulate the adherent cell geometry. An elliptical hole was created inside the cytoplasm to define the nucleus position. As shown in Figure 1, the ellipsoid center was located 5.1 \(\upmu\)m above the bottom of the cell. A 3D axisymmetric shell was utilized to model the membrane. Two different layers cover animal cells. The thinner plasma membrane is known as a phospholipid bilayer, and the thicker actin-gel layer is called the actin cortex. In this study, a single shell as the membrane was tangential to the cytoplasm's outer surface with a thickness of 0.2 \(\upmu\)m to represent the two abovementioned layers [13]. Similar to the membrane, the NE was modeled by the shell elements. The NE was tangential to the surface of the elliptical hole. The length of the large and small diameters of the NE were chosen to be 6.2 \(\upmu\)m and 5.2 \(\upmu\)m, respectively. The thickness of the NE was set to 40 nm [14]. The tensegrity structure was used here to model the CSK and NSK. Tensegrity is a structure that is capable of providing structural stability on any scale; thus, it is well suited to model the structure of the CSK. Studies indicate [15] that this structure can model the experimental data for measuring the Young modulus. A nonlinear increase in cell stiffness under AFM load was also modeled by tensegrity [16; 17; 18]. Spherical tensegrity is a type of tensegrity structure where all vertexes are located on a sphere. It has been shown [19] that all vertexes of any spherical tensegrity are coincident with the vertexes of a polyhedron. For example, the vertexes of a 6-strut spherical tensegrity are the vertexes of a regular icosahedron. Tensegrity has been successful in modeling cell's mechanical behavior with regard to a few compressive and tensile elements. The tension cables were included as the elements that provide stability. In the case of the CSK, the cables simulate the behavior of actin. On the other hand, compressive struts, which reach equilibrium with tensile forces generated on the cables were used to mimic microtubules [20]. [PERSON] [21] suggested the tensegrity structure for investigating the NSK in 1993. Even though the nucleus has its own actin and myosin, it is not clear whether nuclear activity causes tension in these fibers or not. The alteration in the shape of the nucleus has been investigated in cell spreading studies [22; 23]. Usually, the deformed nucleus retracts rapidly after the external load is removed. [24]. In NSK, chromatin is constructed by tightly wound coils of DNA that have sufficient stiffness to resist compression [25]. The geodesic nuclear lamina has been described as a prestress lattice [26]. Thus, one may use tensegrity to simulate nuclear stability. In this study, CSK and NSK were modeled by using a 12-strut tensegrity. Since these two structures are different sizes, CSK was surrounded by a sphere with the same radius as the cytoplasm, but the NSK was surrounded by a smaller sphere with a radius equal to the diameter of the nucleus. Any tensegrity structure may be constructed using several hypothetical planes passing through the center of the sphere [19]. The struts are located in these planes. For example, for the 6-strut tensegrity model, each pair of struts are located in a plane, and three planes are needed to create a structure (Figure 2). Figure 1: Geometry of a cell and its dimensions (\(\upmu\)m). Both ends of the strut are located on the surface of the sphere. [PERSON] et al. [7] modeled struts with a length of 12 \(\upmu\)m for simulating 12-strut tensegrity.