A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

Abstract

We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling.This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular fiber assemblies. We use the non-local slender body theory to compute the fluid-structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multiple method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by the nonlinear Euler-Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit HIs in the time-stepping to resolve large fiber deformations, and to allow time-steps not constrained by temporal stiffness or fiber-fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of fibers.

Dynamics of Flexible Fibers in Viscous Flows and Fluids

“…In a related, but very different, work [96] studied the rheology of centrosomal arrays of flexible microtubules in eukaryotic cells. Using nonlocal SBT, they simulated the dynamics of flexible fibers radially anchored to a sphere moving under an external oscillatory force, F = F 0 cos ωt (schematic inset in Fig.…”

Coarse graining the dynamics of immersed and driven fiber assemblies

“…A central aspect of all of these examples is that the relevant dynamics is collective and not well-described by the dynamics of a single fiber.Given the importance of fluid-fiber systems, specialized computational methods have been developed to treat them, most especially in the zero Reynolds limit where flows are governed by the Stokes equation. These approaches include the use of nonlocal slender body theory [28,39], the immersed boundary method [19,29,33,37], bead-spring or -rod models [9,13,22,38], the regularized Stokeslet method [3,7,32,35], and overlapping grid methods [23]. See [20] for a recent review.…”

Rotation of a low-Reynolds-number watermill: theory and simulations

“…Pak et al (2012) where the propulsion of two touching rotating spheres in viscoelastic fluids was investigated and the numerical results were in excellent agreement with the asymptotic analysis in the small Deborah number regime. It is worth noting that prior studies of interacting slender bodies in viscous flows have adopted other numerical implementations (Yamamoto & Matsuoka 1995;Ross & Klingenberg 1997;Saintillan & Shelley 2007;Nazockdast et al 2017).…”