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

Abstract

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.

The Effect of the Osmotically Active Compound Concentration Difference on the Passive Water and Proton Fluxes across a Lipid Bilayer

“…The spontaneous lipid pore formation can be energetically feasible, even without any external stress [ 30 ], since the energy required for its opening is of the order of a few tenths 10 k B T [ 30 , 72 , 73 ]. The probability of the lipid pore opening would depend on spontaneous curvature of the lipid bilayer and its components [ 30 , 31 ] and the Gaussian elastic modulus according to the Helfrich representation of the membrane [ 26 , 74 , 75 ]. The membrane propensity for spontaneous lipid pore formation can be enhanced by system asymmetry, such as the difference in water activities in the adjacent aqueous phases [ 76 ].…”

“…Experimental data presented in the paper leads to the new coherent perception of the lipid bilayer, which addressed a number of unresolved issues important for understanding molecular mechanisms of passive transport of hydrophilic substances across a lipid bilayer. The lipid bilayer can be treated as a soft dynamic matter, which intrinsic properties are responsible for its continuity, mechanics and permeability of hydrophilic compounds [ 75 , 77 , 78 , 79 ]. All these properties can be quantitated using the Helfrich model [ 26 , 27 , 28 , 29 ].…”

Curvature Potential Unveiled Topological Defect Attractors

“…Here, we demonstrate the similarity between the extrinsic term used in our study and the deviatoric term used in the study of biological membranes. Phospholipid bilayers forming a closed surface of biological membranes are assumed to be covered with anisotropic components oriented at different directions [25,26,47,48]. The orientation of the inclusion can be described by θ, which in this case represents the rotation of the principal directions of the inclusion's intrinsic shape relative to the membrane principal directions.…”

“…The orientation of the inclusion can be described by θ, which in this case represents the rotation of the principal directions of the inclusion's intrinsic shape relative to the membrane principal directions. The energy of a single inclusion is proportional to the mismatch between the intrinsic shape of the inclusion and the local membrane shape [9,11,13,26,47,48]:…”

“…where K 1 and K 2 are constants, H is the local mean curvature of the membrane given by Equation (7a) and D = (σ 1 − σ 2 )/2 is the curvature deviator of the membrane. Inclusion's intrinsic shape is described by its intrinsic mean curvature H m and its intrinsic curvature deviator D m [25,26,47,48]. If D m = 0 the inclusion is isotropic while if D m = 0 it is anisotropic.…”