The mechanical behavior of cortical actin cytoskeleton, a network of cross-linked semiflexible actin filaments (F-actin), is of interest to biologists and engineers since it plays a key role in many fundamental cellular properties and processes, such ascell shape and motility. The dynamics of flexible filaments in low-Reynolds number viscous shear flow has also gained much interest in the last decades in a wide variety of applications involving biological systems like DNA, polymers and proteins. In this dissertation, two numerical algorithms based on the Immersed Boundary Method (IBM) are proposed and implemented for the study of the actin cortex and the dynamics of semiflexible filaments immersed in low-Reynolds flows.

A new, modified, and more computationally efficient version of the IBM that combines the Coarse-Graining Method (CGM) with IBM is developed for modeling of inextensible filaments in shear flow at low Reynolds numbers. The various two-dimensional orbit regimes of flexible filaments are studied and the results of the proposed method are validated with theoretical results and previous works, numerical and experimental, showing excellent agreement. They are subsequently used to develop a prediction model using Artificial Neural Networks (ANN) to effectively forecast the orbit regime of a filament in shear flow with different parameters.

An extension of the traditional IBM to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the cytoplasmic fluid surrounding the actin cortex. The theoretical values for time-averaged contraction for a single inextensible filament under hydrodynamic thermal fluctuations are verified through numerical simulation. The mechanical behavior of the actin cortex and its elasticity when subjected to shear flow is investigated, illustrating a stiffening of the cross-linked network with increasing strain under shear flow, as other experimental and numerical studies have shown. By implementing the proposed extension of the IBM, the behavior and interaction of passive F-actin under thermal fluctuations is also studied in the current work, where a trend of filaments to spread out is observed.