Flexible Membrane Inclusions and Membrane Inclusions Induced by Rigid Globular Proteins

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

On the role of external force of actin filaments in the formation of tubular protrusions of closed membrane shapes with anisotropic membrane components

Biological membranes are composed of different components and there is no a priori reason to assume that all components are isotropic. It was previously shown that the anisotropic properties of membrane components may explain the stability of membrane tubular protrusions even without the application of external force. Our theoretical study focuses on the role of anisotropic membrane components in the stability of membrane tubular structures generated or stabilized by actin filaments. We show that the growth of the actin cytoskeleton inside the vesicle can induce the partial lateral segregation of different membrane components. The entropy of mixing of membrane components hinders the total lateral segregation of the anisotropic and isotropic membrane components. Self-assembled aggregates formed by anisotropic membrane components facilitate the growth of long membrane tubular protrusions. Protrusive force generated by actin filaments favors strong segregation of membrane components by diminishing the opposing effect of mixing entropy.

Closed membrane shapes with attached BAR domains subject to external force of actin filaments

Membrane deformations induced by attached BAR superfamily domains could trigger or facilitate the growth of plasma membrane protrusions. The BAR domain family consists of BAR, F-BAR and I-BAR domains, each enforcing a different local curvature when attached to the membrane surface. Our theoretical study mainly focuses on the role of I-BAR in the membrane tubular deformations generated or stabilised by actin filaments. The influence of the area density of membrane attached BAR domains and their intrinsic curvature on the closed membrane shapes (vesicles) was investigated numerically. We derived an analytical approximative expression for the critical relative area density of BARs at which the membrane tubular protrusions on vesicles are most prominent. We have shown that the BARs with a higher intrinsic curvature induce thinner and longer cylindrical protrusions. The average orientation of the membrane attached BARs is altered when the vesicle shape is subjected to external force of growing actin rod-like structure inside a vesicle. The average orientation angle of membrane attached BARs may indicate whether the actin filaments are just stabilising the protrusion or generating it by stretching the vesicle.