Modeling and simulation of cytoskeleton cortex in the studies of intracellular mechanics

Abstract

In the past decades, simulations and modeling are widely used in the study of cytoskeleton mechanics. Polymer-based model is well established to investigate actin networks reconstituted in vitro. On the other hand, continuum models are usually used in exploring global material properties by turning drown the effects of actin cortex microstructure. To bridge the gap between the continuum model and the polymer-based actin network, a whole cell cortex model is proposed in this thesis. We combine shell mechanics with semi-flexible polymer theories to explore the elasticity of cellular cortex. The cortex elastic modulus calculated by FEM simulations of normal indentation varies from tens of Pa to several kPa, which are consistent with experimental measurements for suspension and adherent cell types. The deformation behavior switches from bending dominated to stretching dominated as the cortex network transits from a low- to high-density regime. An analytical model is proposed to describe the linear relation of the high-density regime. Then this cortex model is adopted in the studies of cancer cell treatment with mechanical oscillations: to enhance gene or drug delivery into cells, and to induce cell-specific structure necrosis. The transfection of nanomaterials including siRNAs into suspended cells is found to be significantly enhanced after subjecting the cells to mechanical vibrations at frequencies of 100 Hz. Oscillating a cell by a low-power laser trap at specific frequencies of a few Hz is also found to result in increased death rate in different types of leukemia cells, while normal leukocytes showed little response to similar laser manipulations. Results of FEM simulations reveal severe distortion of the cortex at frequencies in the same range as the experiments for enhanced transfection or peaked cell death. The cortex distortion arises due to the combined inertial forces and viscoelastic forces from the intracellular medium, and the frequency at which this becomes significant is cell-type specific. The disruption of cell membrane leading to enhanced transfection and cell death is therefore due to the cortex distortion. In addition, the difference in stiffness in Hey A8 cells with different metastasis is found to associate with their F-actin rearrangement. Finite-element simulation of cell migration is conducted with a model of a typical portion of the actin cortex, and the result shows that a migrating cell would have its actin filaments bundled together to form stress fibers, which would exhibit lower indentation stiffness than the less aligned arrangement of filaments in a non-migrating cell. At last, indentation on a spherical lipid membrane with various speeds is studied with coarse-grained MD simulation. Results show that when the indentation velocity is lower than a critical value, the stiffness of the membrane is rarely affected by the loading rate. In such conditions, the indentation stiffness is proportional to the reciprocal of the sphere size. When the indentation speed is higher than the critical velocity, the viscoelastic feature becomes significant, and an exponential relation has been deduced between the indentation stiffness k_indent and speed v, that is, k_indent∝v^1.2. Moreover, the critical velocity is found to be the relaxation rate of the bending stress within the membrane. This thesis aims at searching for the relation between cellular structures and functions using modeling and simulations, to assist the development of biomedical engineering applications.