Abstract
Cytoskeleton plays important roles in intracellular force equilibrium and extracellular force transmission from/to attaching substrate through focal adhesions (FAs). Numerical simulations of intracellular force distribution to describe dynamic cell behaviors are still limited. The tensegrity structure comprises tension-supporting cables and compression-supporting struts that represent the actin filament and microtubule respectively, and has many features consistent with living cells. To simulate the dynamics of intracellular force distribution and total stored energy during cell spreading, the present study employed different complexities of the tensegrity structures by using octahedron tensegrity (OT) and cuboctahedron tensegrity (COT). The spreading was simulated by assigning specific connection nodes for radial displacement and attachment to substrate to form FAs. The traction force on each FA was estimated by summarizing the force carried in sounding cytoskeletal elements. The OT structure consisted of 24 cables and 6 struts and had limitations soon after the beginning of spreading by declining energy stored in struts indicating the abolishment of compression in microtubules. The COT structure, double the amount of cables and struts than the OT structure, provided sufficient spreading area and expressed similar features with documented cell behaviors. The traction force pointed inward on peripheral FAs in the spread out COT structure. The complex structure in COT provided further investigation of various FA number during different spreading stages. Before the middle phase of spreading (half of maximum spreading area), cell attachment with 8 FAs obtained minimized cytoskeletal energy. The maximum number of 12 FAs in the COT structure was required to achieve further spreading. The stored energy in actin filaments increased as cells spread out, while the energy stored in microtubules increased at initial spreading, peaked in middle phase, and then declined as cells reached maximum spreading. The dynamic flows of energy in struts imply that microtubules contribute to structure stabilization.
Highlights
The biological functions of cells, such as differentiation, growth, metastasis, and apoptosis are associated with cell shape, which is related to the mechanical forces in the cytoskeleton [1,2,3,4]
The dynamics of cytoskeletal spreading and energy arrangement in both actin filament and microtubule were demonstrated by simulating the tensegrity structures in present study
Among various stimulatory models related to actin filaments, the elastic modulus of cell was estimated based on the bending of actin element in the open-cell foam model [12]
Summary
The biological functions of cells, such as differentiation, growth, metastasis, and apoptosis are associated with cell shape, which is related to the mechanical forces in the cytoskeleton [1,2,3,4]. The cytoskeleton transmits mechanical stimulation for intracellular signal transduction [5,6,7]. Several cytoskeleton models investigated the mechanical properties of cells using computational stimulations [1,4,8,9,10,11,12]. The prestressed cable net [8,10] and semi-flexible chain net [11] are used to form actin cytoskeleton model for prediction of cell stiffness under mechanical perturbations in two-dimensions. The tensegrity [1,7] and granular model [9] comprise tensile elements and compressive elements (microtubules) that providing cell stability and intracellular force equilibrium [13,14]
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