Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes

Abstract

Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics of plain lipid membranes in experimental model systems are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, and the rearrangement of the lipid molecules. We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its midsurface and by a lipid density field for each monolayer. The viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the inter-monolayer friction and the membrane interfacial shear viscosity. While the bilayer equilibria are well understood theoretically, dynamical calculations have relied on simplified continuum approaches of uncertain transferability, or on molecular simulations reaching very limited length and time scales. Our approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We validate it with the well understood tether extension. We investigate the tubular lipid transport between cells, the dynamics of bud absorption by a planar membrane, and the fate of a localized lipid density asymmetry in vesicles. These axisymmetric examples bear biological relevance and highlight the diversity of dynamical regimes that bilayers can experience.

Onsager’s Variational Principle in Soft Matter: Introduction and Application to the Dynamics of Adsorption of Proteins onto Fluid Membranes

“…When it comes to the interaction of bilayers with proteins, the bilayer architecture is bound to play an important role since proteins can merely scaffold the membrane, shallowly insert into one monolayer, or pierce through the entire bilayer. Elasto-hydrodynamical models capturing the bilayer architecture have been developed under the assumption of linearized perturbations (Seifert and Langer, 1993;Fournier et al, 2009;CallanJones et al, 2016), or in a fully nonlinear albeit axisymmetric setting (Rahimi and Arroyo, 2012). In the present Chapter, we will not focus on this aspect.…”

“…Furthermore, we present some original applications of this principle to model nonlinear adsorption phenomena, and curvature sensing and generation by proteins. The interested reader may find recent applications of Onsager's principle to lipid membranes elsewhere (Arroyo and DeSimone, 2009;Rahimi and Arroyo, 2012;Fournier, 2015;Callan-Jones et al, 2016).…”

“…For instance, the classical bending model of Helfrich (Helfrich, 1973;Lipowsky, 1991;Jülicher and Lipowsky, 1993;Staykova et al, 2013) has been very successful in understanding equilibrium conformations (Steigmann, 1999;Capovilla and Guven, 2002;Tu and Ou-Yang, 2004;Feng and Klug, 2006;Rangarajan and Gao, 2015;Sauer et al, 2017), but is insufficient to understand the reconfigurations of membranes when subjected to transient stimuli. To address this challenge, models and simulations coupling membrane hydrodynamics and elasticity (Arroyo and DeSimone, 2009;Arroyo et al, 2010;Rahimi and Arroyo, 2012;Rangamani et al, 2013;Rodrigues et al, 2013;Barrett et al, 2016) or elasticity and the phaseseparation of chemical species (Embar et al, 2013;Elliott and Stinner, 2013) are emerging in recent years, but only provide initial steps towards a general dynamical framework. Capture the bilayer architecture.…”

Nonsingular isogeometric boundary element method for Stokes flows in 3D

“…We are planning applications of the method proposed in this paper to model full three dimensional flows induced by swimming bacteria and unicellular organisms, extending [1,4,3,2,6] and to model the relaxation dynamics and the flow around three dimensional lipid bilayer membranes, extending [5,38]. The flexibility and the accuracy of the nonsingular IGA BEM makes it also a good candidate to replace or complement more complex fluid structure interaction methods, such as the ones presented in [34,21,11].…”

“…The im proved performance obtained thanks to isogeometric analysis makes IGA BEM a very promising tool for the solution of com plex fluid structure interaction problems arising in biophysics and bio medical applications [15,12]. In fact, our choice of Stokes flows as a model problem is motivated by our interest in modeling the flows induced by swimming bacteria and uni cellular organisms [1,4,3,2,6] and lipid bilayer membranes [5,38].…”