Computational modeling of active deformable membranes embedded in three-dimensional flows

Abstract

Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a 3D flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an Immersed-Boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g. Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of [Berthoumieux et al. New J. Phys. 16, 065005 (2014)] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a so far unobserved non-axisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows. Published as: Phys. Rev. E 99(6), 062418 (2019)

Rayleigh–Plateau instability of anisotropic interfaces. Part 1. An analytical and numerical study of fluid interfaces

“…(2014) considered the Green's function for an elastic cell membrane subjected to active tension, which again leads to the prediction of a Rayleigh–Plateau instability. Bächer & Gekle (2019) confirmed the instability threshold predicted by Berthoumieux et al. (2014) and presented the shape of a membrane undergoing Rayleigh–Plateau instability in three-dimensional simulations of active membranes.…”

“…Neglecting inertial effects corresponds to and an Ohnesorge number . Membrane forces due to interfacial tension are calculated as detailed in Bächer & Gekle (2019). As the interfacial tension in the simulation we use , a typical tension expected for blood cells (Dmitrieff et al.…”

A hyperelastic model for simulating cells in flow

“…We use the Lattice Boltzmann implementation of the open source software package ESPResSo (Limbach et al 2006;Roehm and Arnold 2012). Coupling between fluid and cell is achieved via the immersedboundary algorithm (Devendran and Peskin 2012;Saadat et al 2018) which we implemented into ESPResSo (Bächer et al 2017;Bächer and Gekle 2019). We note here that, in contrast to Saadat et al (2018), we do not subtract the fluid stress within the particle interior.…”

Rayleigh–Plateau instability of anisotropic interfaces. Part 2. Limited instability of elastic interfaces

“…In contrast to Part 1, the elasticity of the interface now requires us to consider the total deformation of an interface point from its initial location, and not only the local curvature and velocity. For this we employ the differential geometry (Kreyszig 1968) of thin shells as detailed in Green & Zerna (1954), Deserno (2015), Salbreux & Jülicher (2017) and Bächer & Gekle (2019), whose notation we follow. In the following, we introduce all quantities used in the linear stability analysis.…”

“…If in addition interface viscosity is included, we would expect effects similar to those discussed in Part 1. In general, mechanical properties of the interface are described by the surface stress (Green & Zerna 1954; Barthès-Biesel 2016; Guckenberger & Gekle 2017; Salbreux & Jülicher 2017; Bächer & Gekle 2019), which can be expressed in vector notation as with its in-plane components and the normal component . As introduced above, we split the surface stress into an (i) anisotropic and an (ii) elastic contribution …”