Modeling microtubule cytoskeleton via an active liquid crystal elastomer model

In this work, a three-dimensional (3D) liquid crystal polymer model is developed to model the microtubule cytoskeleton aggregate and to study its interaction with the extracellular matrix. In the proposed microtubule cytoskeleton model, the cytoskeleton aggregate is treated as a homogenized liquid crystal elastomer medium, with an extra active stress term included to account for the effect of the active process of Guanosine Triphosphate (GTP) hydrolysis. The cell extracellular matrix (ECM) is modeled as a hyperelastic material. The specific and non-specific interactions between the cell and its ECM are modeled by a Coarse-Grained Contact Model. Surface tension effects are incorporated into the simulation, through a Multiscale Dynamic Wetting Model, to account for the interface conditions between the cell and its surrounding environment. The cell model is implemented in a Lagrange type Galerkin formulation. The numerical results show that the cell can sense and move under the gradient of matrix elasticity.