Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

Abstract

The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager's formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.To quantitatively understand these phenomena, various biophysical studies have exposed artificial lipid membranes to purified proteins in controlled conditions [14]. At high concentration, curved proteins can induce severe membrane curvature when incubated with liposomes [15], can stabilize membrane tubes [10,16], and can dynamically trigger protein-rich tubular protrusions out of tense vesicles [17][18][19]. At lower concentrations, proteins sense curvature and preferentially adsorb or migrate to favorably curved membranes, as probed in assays involving polydisperse vesicle suspensions [20], vesicles with membrane tethers [18,21] or supported lipid bilayers on wavy substrates [22]. Since protein-rich curved domains sequester apparent membrane area from the adjacent planar membrane, their formation perform work against membrane tension, and thus can be hindered if tension is large enough. This kind of mechano-chemical coupling, tested in vitro by exposing aspirated vesicles to BAR proteins [19], has physiological implications during the mechano-protection of stressed cells by the release of membrane area through disassembly of caveolae [4], or in the regulation of clathrin-mediated endocytosis by membrane tension [23].A number of theoretical and computational studies at various scales have been developed to understand the interaction between curved proteins and membranes. At the nanoscale, all-atom molecular dynamics have described curvature generation by single domains [24] and curvature maintenance by multiple proteins [25]. Reaching a micron, coarse-grained molecular dynamics simulations, treating the membrane either molecularly or as a continuum object, hav...

Dynamic Mechanochemical feedback between curved membranes and BAR protein self-organization

“…Video 11 and 12). Previous results have shown the formation of pearled membrane tubes as a result of a sufficiently large isotropic and uniform spontaneous curvature 24,23,25 . Indeed, we hypothesized and our simulations show that, if initial tubes were large-enough, then at low coverage they should exhibit a largely uniform and isotropic arrangement of molecules, Fig.…”

“…To account for this and for the out-of-equilibrium nature of our experiments, we took the mean field energy density functional theory, as a foundation to develop a selfconsistent continuum chemo-mechanical model. This model predicts the interplay between protein behavior and membrane shape, and accounts for + , for the dynamics of protein adsorption from a bulk reservoir, for the diffusion of proteins on the surface, and for the membrane dissipation associated with shape changes 23 (see Methods, Theoretical Model, for a discussion of the model and its parameters). Starting from membrane protrusions in mechanical equilibrium (tubular or spherical, Fig.…”

“…All these equations are self-consistently coupled in this formalism. We refer to 23 for a full account of this formulation and of its computational axisymmetric implementation using a Galerkin finite element method based on B-Spline approximations. We model sorption with a modified Langmuir model given by 39…”

“…In previous work 23 , we presented a general continuum framework to study the dynamics of curved proteinmembrane interaction, highlighting the role of protein curvature and self-interaction on their curvaturesensing and generation capability. This theory accounted for protein diffusion and for membrane elasticity and hydrodynamics.…”

“…where k 0 is the bending stiffness of the membrane and H = (tr k)/2 is the mean curvature and dS is the area element of Γ. To model the dynamics and as described elsewhere 23,40,41 , we introduce a dissipation potential accounting for membrane viscosity D m [v], and obtain the governing equations of the system by minimizing the Rayleighian functional…”