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Vesiculation of biological membrane driven by curvature induced frustrations in membrane orientational ordering
Dalija Povše Jesenek, Šárka Perutková, Wojciech Góźdź, Veronika Kralj-Iglič, Aleš Iglič, Samo Kralj, 2013, original scientific article

Abstract: Membrane budding often leads to the formation and release of microvesicles. The latter might play an important role in long distance cell-to-cell communication, owing to their ability to move with body fluids. Several mechanisms exist which might trigger the pinching off of globular buds from the parent membrane (vesiculation). In this paper, we consider the theoretical impacts of topological defects (frustrations) on this process in the membranes that exhibit global in-plane orientational order. A Landau–de Gennes theoretical approach is used in terms of tensor orientational order parameters. The impact of membrane shapes on position and the number of defects is analyzed. In studied cases, only defects with winding numbers m = ±1/2 appear, where we refer to the number of defects with m = 1/2 as defects, and with m = –1/2 as anti-defects. It is demonstrated that defects are attracted to regions with maximal positive Gaussian curvature, K. On the contrary, anti-defects are attracted to membrane regions exhibiting minimal negative values of K. We show on membrane structures exhibiting spherical topology that the coexistence of regions with K > 0 and K < 0 might trigger formation of defect–anti-defect pairs for strong enough local membrane curvatures. Critical conditions for triggering pairs are determined in several demonstrative cases. Then the additionally appeared anti-defects are assembled at the membrane neck, where K < 0. Consequent strong local fluctuations of membrane constituent anisotropic molecules might trigger membrane fission neck rupture, enabling a membrane fission process and the release of membrane daughter microvesicles (ie, vesiculation).
Keywords: structural transitions, topological defects, membrane microvesicles, membrane curvature, membrane fission, vesiculation
Published in DKUM: 03.08.2017; Views: 844; Downloads: 377
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Curvature-controlled topological defects
Luka Mesarec, Pavlo Kurioz, Aleš Iglič, Wojciech Góźdź, Samo Kralj, original scientific article

Abstract: Effectively, two-dimensional (2D) closed films exhibiting in-plane orientational ordering (ordered shells) might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs) within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers) which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.
Keywords: topological defects, Gaussian curvature, self-assembling, crystal growth nucleation
Published in DKUM: 20.07.2017; Views: 860; Downloads: 391
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Effective topological charge cancelation mechanism
Luka Mesarec, Wojciech Góźdź, Aleš Iglič, Samo Kralj, 2016, original scientific article

Abstract: 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.
Keywords: topological defects, topological charge, numerical studies, orientational ordering, nematic liquid crystals, liquid crystalline shells, biological membranes, nanoparticles, Gaussian curvature, electrostatic analogy, annihilation, topology
Published in DKUM: 23.06.2017; Views: 733; Downloads: 308
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Numerical study of membrane configurations
Luka Mesarec, Miha Fošnarič, Samo Penič, Veronika Kralj-Iglič, Samo Kralj, Wojciech Góźdź, Aleš Iglič, 2014, original scientific article

Abstract: We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit inplane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells).The topological defects are always present on the surfaces with the topology of a sphere.The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.
Keywords: biological membranes, vesicles, spontaneous curvature model, Monte Carlo simulations, nematic shells, orientational ordering, topological defects
Published in DKUM: 14.06.2017; Views: 792; Downloads: 324
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