Biaxial Structures of Localized Deformations and Line-like Distortions in Effectively 2D Nematic Films.

We numerically studied localized elastic distortions in curved, effectively two-dimensional nematic shells. We used a mesoscopic Landau-de Gennes-type approach, in which the orientational order is theoretically considered by introducing the appropriate tensor nematic order parameter, while the three-dimensional shell shape is described by the curvature tensor. We limited our theoretical consideration to axially symmetric shapes of nematic shells. It was shown that in the surface regions of stomatocyte-class nematic shell shapes with large enough magnitudes of extrinsic (deviatoric) curvature, the direction of the in-plane orientational ordering can be mutually perpendicular above and below the narrow neck region. We demonstrate that such line-like nematic distortion configurations may run along the parallels (i.e., along the circular lines of constant latitude) located in the narrow neck regions of stomatocyte-like nematic shells. It was shown that nematic distortions are enabled by the order reconstruction mechanism. We propose that the regions of nematic shells that are strongly elastically deformed, i.e., topological defects and line-like distortions, may attract appropriately surface-decorated nanoparticles (NPs), which could potentially be useful for the controlled assembly of NPs.

Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells.

The impact of the intrinsic curvature of in-plane orientationally ordered curved flexible nematic molecules attached to closed 3D flexible shells was studied numerically. A Helfrich-Landau-de Gennes-type mesoscopic approach was adopted where the flexible shell's curvature field and in-plane nematic field are coupled and concomitantly determined in the process of free energy minimisation. We demonstrate that this coupling has the potential to generate a rich diversity of qualitatively new shapes of closed 3D nematic shells and the corresponding specific in-plane orientational ordering textures, which strongly depend on the shell's volume-to-surface area ratio, so far not predicted in mesoscopic-type numerical studies of 3D shapes of closed flexible nematic shells.

Stable Assemblies of Topological Defects in Nematic Orientational Order.

We considered general mechanisms enabling the stabilization of localized assemblies of topological defects (TDs). There is growing evidence that physical fields represent fundamental natural entities, and therefore these features are of interest to all branches of physics. In general, cores of TDs are energetically costly, and consequently, assemblies of TDs are unfavorable. Owing to the richness of universalities in the physics of TDs, it is of interest to identify systems where they are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, and cross-fertilizing knowledge in different areas of physics. In this respect, thermotropic nematic liquid crystals (NLCs) represent an ideal experiment testbed for such studies. In addition, TDs in NLCs could be exploited in several applications. We present examples that emphasize the importance of curvature imposed on the phase component of the relevant order parameter field. In NLCs, it is represented by the nematic tensor order parameter. Using a simple Landau-type approach, we show how the coupling between chirality and saddle splay elasticity, which can be expressed as a Gaussian curvature contribution, can stabilize Meron TDs. The latter have numerous analogs in other branches of physics. TDs in 2D curved manifolds reveal that the Gaussian curvature dominantly impacts the assembling and stabilization of TDs. Furthermore, a strong enough curvature that serves as an attractor for TDs is a respective field that could be imposed in a fast enough phase transition. Assemblies of created TDs created in such a disordered environment could be stabilized by appropriate impurities.

Spatial manipulation of topological defects in nematic shells.

It is well known that positions of topological defects (TDs) in liquid crystals can be manipulated experimentally by locally distorting the liquid crystalline (LC) order, as for example by melting induced by optical tweezers. In this work, we study numerically the nematic ordering profiles and the corresponding topological defect configurations in thin nematic liquid crystalline shells controlled by imposed local distortion of LC order. We demonstrate that within curved LC films such manipulations could be strongly affected by local Gaussian curvature if it exhibits strong spatial variations. We use mesoscopic approach in which the shell geometry and LC orientational order are described by curvature of the surface and nematic order parameter tensor. For illustration purposes, we consider LC shells exhibiting spherical topology. We show that on increasing prolateness of shells, which imposes spatially inhomogeneous Gaussian curvature, TDs are relatively strongly "glued" to a local Gaussian curvature.

On the Role of Electrostatic Repulsion in Topological Defect-Driven Membrane Fission.

Within a modified Langevin Poisson-Boltzmann model of electric double layers, we derived an analytical expression for osmotic pressure between two charged surfaces. The orientational ordering of the water dipoles as well as the space dependencies of electric potentials, electric fields, and osmotic pressure between two charged spheres were taken into account in the model. Thus, we were able to capture the interaction between the parent cell and connected daughter vesicle or the interactions between neighbouring beads in necklace-like membrane protrusions. The predicted repulsion between them can facilitate the topological antidefect-driven fission of membrane daughter vesicles and the fission of beads of undulated membrane protrusions.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces.

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson-Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces' nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO2 nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO2 nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

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.

Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types.

Tiny membrane-enclosed cellular fragments that can mediate interactions between cells and organisms have recently become a subject of increasing attention. In this work the mechanism of formation of cell membrane nanovesicles (CNVs) was studied experimentally and theoretically. CNVs were isolated by centrifugation and washing of blood cells and observed by optical microscopy and scanning electron microscopy. The shape of the biological membrane in the budding process, as observed in phospholipid vesicles, in erythrocytes and in CNVs, was described by an unifying model. Taking the mean curvature h and the curvature deviator d of the membrane surface as the relevant parameters, the shape and the distribution of membrane constituents were determined theoretically by minimization of membrane free energy. Considering these results and previous results on vesiculation of red blood cells it was interpreted that the budding processes may lead to formation of different types of CNVs as regards the compartment (exo/endovesicles), shape (spherical/tubular/torocytic) and composition (enriched/depleted in particular kinds of molecules). It was concluded that the specificity of pinched off nanovesicles derives from the shape of the membrane constituents and not primarily from their chemical identity, which explains evidences on great heterogeneity of isolated extracellular vesicles with respect to composition.

The effect of lipid phase on liposome stability upon exposure to the mechanical stress.

Mechanical properties of a lipid bilayer are parameters determined mainly for giant unilamellar vesicles (GUVs). It is not clear if values obtained on the GUV model can be directly translated to submicron large unilamellar vesicles (LUVs). This ambiguity is a major obstacle in exploring the effect of lipid bilayer mechanics on membrane associated processes and effectiveness of liposome-based targeted drug delivery systems. In presented work extrusion, which is a common method to prepare LUVs, was used to study liposomes preparation and stability upon exposure to mechanical stress. The effect of parameters of the extrusion process (temperature, membrane pore size, extrusion force and volumetric flux) on the properties of liposome suspension (average liposome size, polydispersity index and lipid recovery ratio) was determined for model liposomes composed of DPPC lipid. The state of the DPPC lipid bilayer depends on temperature, therefore, the effect of lipid bilayer mechanics on the extrusion process can be quantitated without altering membrane composition. The extrusion process was carried out with the automated extruder delivering quantitative data on the extrusion force and volumetric flux. Obtained results have been interpreted in terms of mechanical properties of the lipid bilayer. Determined mechanical properties of the lipid bilayer and its dependence on temperature are in good agreement with the literature results determined for GUVs. This shows that mechanical properties of the lipid bilayer does not depend on the liposome size in the range from 100 nm to hundreds of microns.

Active Forces of Myosin Motors May Control Endovesiculation of Red Blood Cells.

By using Monte Carlo (MC) simulations, we have shown that the active forces generated by (NMIIA) motor domains bound to F-actin may partially control the endovesiculation of the red blood cell (RBC) membrane. The myosin generated active forces favor pancake-like (torocyte) RBC endovesicles with a large flat central membrane region and a bulby periphery. We suggest that the myosin generated active forces acting on the RBC membrane in the direction perpendicular to the membrane surface towards the interior of the RBC may influence also other RBC shape transformations and the stability of different types of RBC shapes and should be therefore considered in the future theoretical studies of the RBC vesiculation and shape transformations.

Asymmetric Finite Size of Ions and Orientational Ordering of Water in Electric Double Layer Theory Within Lattice Model.

In the present review, a brief historical survey of the mean-field theoretical description of Electric Double Layer (EDL) is presented. Special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed.

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.

Effective Topological Charge Cancelation Mechanism.

Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.

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.