TY - JOUR
T1 - A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics
AU - Nazockdast, Ehssan
AU - Rahimian, Abtin
AU - Zorin, Denis
AU - Shelley, Michael
N1 - Funding Information:
We extend our thanks to Aleksandar Donev, Sebastian Füerthauer, Tong Gao, Hassan Masoud, Daniel Needleman, Michael O'Neil, and Shravan Veerapaneni for stimulating conversations about various aspects of this work. We thank Dhairya Malhotra and George Biros for kindly supplying the kernel-independent FMM code. E.N. and M.S. acknowledge support from National Institutes of Health Grant 1R01GM104976-01 , and National Science Foundation Grants DMS-1463962 and DMS-1620331 . A.R. and D.Z. acknowledge the support of the US National Science Foundation (NSF) through Grant DMS-1320621 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/15
Y1 - 2017/1/15
N2 - We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. 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 assemblies of flexible fibers. We use 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 multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by 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 time-stepping to resolve large fiber deformations, and to allow time-steps not excessively 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 semi-flexible fibers.
AB - We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. 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 assemblies of flexible fibers. We use 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 multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by 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 time-stepping to resolve large fiber deformations, and to allow time-steps not excessively 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 semi-flexible fibers.
KW - Boundary integral methods
KW - Cytoskeleton
KW - Fiber suspensions
KW - Fluid–structure interactions
KW - Mitotic spindle
KW - Motor protein
KW - Semi-flexible fibers
KW - Slender-body theory
UR - http://www.scopus.com/inward/record.url?scp=84997821022&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84997821022&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.10.026
DO - 10.1016/j.jcp.2016.10.026
M3 - Article
AN - SCOPUS:84997821022
SN - 0021-9991
VL - 329
SP - 173
EP - 209
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -