Integral-based spectral method for inextensible slender fibers in Stokes flow

Maxian, Ondrej; Mogilner, Alex; Donev, Aleksandar

doi:10.1103/physrevfluids.6.014102

Cited by 30 publications

(168 citation statements)

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“…We then discuss the three approximations to the mobility (force-velocity) relationship: (non-isotropic) local drag, intra-fiber hydrodynamics, and full nonlocal hydrodynamics, as well as how we evaluate them. Most of the details of this can be found in [55]; here we only elaborate on the modifications we have made for efficient simulation of a bundled many-fiber gel. We conclude this section with our temporal integration (network evolution) strategy, which uses operator splitting to turn over the fiber positions, update the cross-linked network, and update the fiber positions in a sequential order.…”

Section: Methodsmentioning

confidence: 99%

“…In [55, Section 4.1.3], we discuss how to discretize the operator to spectral accuracy in a manner consistent with the boundary conditions (3) using a method called rectangular spectral collocation [6, 15].…”

Section: Methodsmentioning

confidence: 99%

“…Then, accounting for the constraint force, bending force, and any other external forces f (CL) (e.g., those coming from attached CLs), the evolution equation on the fiber is given by subject to the boundary conditions (3) and inextensibility constraint (1). In [55], we show how to obtain λ and enforce inextensibility via the principle of virtual work. We discuss different approximations to in Section 2.4.…”

Section: Methodsmentioning

confidence: 99%

“…We now specify a method to compute the external or cross-linking force density f (CL) in (4). Here we extend [55] to account for transient cross linking, where the links can come on and off through the course of a simulation. To model this, we assume that the density of cross-links is sufficiently high that CLs do not get locally depleted by binding, and that the links diffuse rapidly.…”

Section: Methodsmentioning

confidence: 99%

“…We use our previous work [55, Section 6.1] to define the cross-linking force density between two fibers X ( i ) and X ( j ) in a manner that can preserve the problem smoothness and therefore the spectral accuracy of our numerical method. Suppose that a CL connects two fibers by attaching to arclength coordinate on fiber i and on fiber j .…”

Section: Methodsmentioning

confidence: 99%

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Simulations of dynamically cross-linked actin networks: morphology, rheology, and hydrodynamic interactions

Maxian

Peláez

Mogilner

et al. 2021

Preprint

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Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and derive continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct continuum Maxwell-type models of the networks.

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Section: Methodsmentioning

confidence: 99%