1
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Mesarec L, Kralj S, Iglič A. Biaxial Structures of Localized Deformations and Line-like Distortions in Effectively 2D Nematic Films. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:246. [PMID: 38334517 PMCID: PMC10856884 DOI: 10.3390/nano14030246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Revised: 01/17/2024] [Accepted: 01/20/2024] [Indexed: 02/10/2024]
Abstract
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.
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Affiliation(s)
- Luka Mesarec
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia;
| | - Samo Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia;
- Condensed Matter Physics Department, Jožef Stefan Institute, 1000 Ljubljana, Slovenia
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia;
- Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, 1000 Ljubljana, Slovenia
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2
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Mesarec L, Góźdź W, Kralj-Iglič V, Kralj S, Iglič A. Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells. Sci Rep 2023; 13:10663. [PMID: 37393271 DOI: 10.1038/s41598-023-37664-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 06/25/2023] [Indexed: 07/03/2023] Open
Abstract
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.
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Affiliation(s)
- Luka Mesarec
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška Cesta 25, 1000, Ljubljana, Slovenia.
| | - Wojciech Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland
| | - Veronika Kralj-Iglič
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, Zdravstvena 5, 1000, Ljubljana, Slovenia
| | - Samo Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000, Maribor, Slovenia
- Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška Cesta 25, 1000, Ljubljana, Slovenia
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3
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Hölbl A, Mesarec L, Polanšek J, Iglič A, Kralj S. Stable Assemblies of Topological Defects in Nematic Orientational Order. ACS OMEGA 2023; 8:169-179. [PMID: 36643572 PMCID: PMC9835183 DOI: 10.1021/acsomega.2c07174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
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.
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Affiliation(s)
- Arbresha Hölbl
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
| | - Luka Mesarec
- Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia
| | - Juš Polanšek
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
| | - Aleš Iglič
- Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia
| | - Samo Kralj
- Faculty of Natural
Sciences and Mathematics, University of
Maribor, Koroška
160, 2000 Maribor, Slovenia
- Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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4
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Polanšek J, Holbl A, Starzonek S, Drozd-Rzoska A, Rzoska SJ, Kralj S. History-dependent phase transition character. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:70. [PMID: 35997865 PMCID: PMC9399213 DOI: 10.1140/epje/s10189-022-00221-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 07/26/2022] [Indexed: 06/15/2023]
Abstract
We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems' stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.
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Affiliation(s)
- Juš Polanšek
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000, Maribor, Slovenia
| | - Arbresha Holbl
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000, Maribor, Slovenia
| | - Szymon Starzonek
- Institute of High Pressure Physics Polish Academy of Sciences, ul. Sokołowska 29/37, 01-142, Warsaw, Poland.
| | - Aleksandra Drozd-Rzoska
- Institute of High Pressure Physics Polish Academy of Sciences, ul. Sokołowska 29/37, 01-142, Warsaw, Poland
| | - Sylwester J Rzoska
- Institute of High Pressure Physics Polish Academy of Sciences, ul. Sokołowska 29/37, 01-142, Warsaw, Poland
| | - Samo Kralj
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000, Maribor, Slovenia
- Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
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5
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Mesarec L, Iglič A, Kralj S. Spatial manipulation of topological defects in nematic shells. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:62. [PMID: 35876913 DOI: 10.1140/epje/s10189-022-00216-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 06/28/2022] [Indexed: 06/15/2023]
Abstract
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.
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Affiliation(s)
- Luka Mesarec
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia.
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
| | - Samo Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Condensed Matter Physics Department, Jožef Stefan Institute, Ljubljana, Slovenia
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6
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Klebes J, Clegg P, Evans RML. Effects of orientational order on modulated cylindrical interfaces. Phys Rev E 2022; 105:064802. [PMID: 35854580 DOI: 10.1103/physreve.105.064802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinderlike surfaces may host orientational order with n-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets 2n topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. By examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore, cylindrical systems can be divided into type I, without defects, and type II, which go through a spectrum of defect states with up to 4n excess defects. The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly.
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Affiliation(s)
- Jason Klebes
- School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tate Road, Edinburgh EH9 3FD, United Kingdom
| | - Paul Clegg
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tate Road, Edinburgh EH9 3FD, United Kingdom
| | - R M L Evans
- School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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7
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Kanyolo GM, Masese T. Cationic vacancies as defects in honeycomb lattices with modular symmetries. Sci Rep 2022; 12:6465. [PMID: 35440682 PMCID: PMC9018820 DOI: 10.1038/s41598-022-10226-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 04/05/2022] [Indexed: 11/27/2022] Open
Abstract
Layered materials tend to exhibit intriguing crystalline symmetries and topological characteristics based on their two dimensional (2D) geometries and defects. We consider the diffusion dynamics of positively charged ions (cations) localized in honeycomb lattices within layered materials when an external electric field, non-trivial topologies, curvatures and cationic vacancies are present. The unit (primitive) cell of the honeycomb lattice is characterized by two generators, [Formula: see text] of modular symmetries in the special linear group with integer entries, corresponding to discrete re-scaling and rotations respectively. Moreover, applying a 2D conformal metric in an idealized model, we can consistently treat cationic vacancies as topological defects in an emergent manifold. The framework can be utilized to elucidate the molecular dynamics of the cations in exemplar honeycomb layered frameworks and the role of quantum geometry and topological defects not only in the diffusion process such as prediction of conductance peaks during cationic (de-)intercalation process, but also pseudo-spin and pseudo-magnetic field degrees of freedom on the cationic honeycomb lattice responsible for bilayers.
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Affiliation(s)
- Godwill Mbiti Kanyolo
- Department of Engineering Science, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan.
| | - Titus Masese
- Research Institute of Electrochemical Energy (RIECEN), National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka, 563-8577, Japan.
- AIST-Kyoto University Chemical Energy Materials Open Innovation Laboratory (ChEM-OIL), Sakyo-ku, Kyoto, 606-8501, Japan.
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8
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Gongadze E, Mesarec L, Kralj S, Kralj-Iglič V, Iglič A. On the Role of Electrostatic Repulsion in Topological Defect-Driven Membrane Fission. MEMBRANES 2021; 11:membranes11110812. [PMID: 34832041 PMCID: PMC8619715 DOI: 10.3390/membranes11110812] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Revised: 10/16/2021] [Accepted: 10/21/2021] [Indexed: 12/29/2022]
Abstract
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.
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Affiliation(s)
- Ekaterina Gongadze
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (L.M.)
| | - Luka Mesarec
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (L.M.)
| | - Samo Kralj
- Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia;
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
| | - Veronika Kralj-Iglič
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, 1000 Ljubljana, Slovenia;
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (L.M.)
- Faculty of Medicine, University of Ljubljana, 1000 Ljubljana, Slovenia
- Correspondence: ; Tel.: +386-1-4768-825
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9
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Mesarec L, Drab M, Penič S, Kralj-Iglič V, Iglič A. On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding. Int J Mol Sci 2021; 22:2348. [PMID: 33652934 PMCID: PMC7956631 DOI: 10.3390/ijms22052348] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 02/18/2021] [Accepted: 02/20/2021] [Indexed: 02/03/2023] Open
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.
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Affiliation(s)
- Luka Mesarec
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (L.M.); (M.D.); (S.P.)
| | - Mitja Drab
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (L.M.); (M.D.); (S.P.)
| | - Samo Penič
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (L.M.); (M.D.); (S.P.)
| | - Veronika Kralj-Iglič
- Faculty of Health Sciences, University of Ljubljana, SI-1000 Ljubljana, Slovenia;
- Institute of Biosciences and Bioresources, National Research Council, 80131 Napoli, Italy
| | - Aleš Iglič
- Faculty of Electrical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (L.M.); (M.D.); (S.P.)
- Institute of Biosciences and Bioresources, National Research Council, 80131 Napoli, Italy
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10
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Kralj-Iglič V, Pocsfalvi G, Mesarec L, Šuštar V, Hägerstrand H, Iglič A. Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types. PLoS One 2020; 15:e0244796. [PMID: 33382808 PMCID: PMC7775103 DOI: 10.1371/journal.pone.0244796] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 12/16/2020] [Indexed: 12/25/2022] Open
Abstract
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. One of the amazing properties of a biological membrane is the ability to undergo dramatic changes of its shape. It may exhibit very high curvature and thereby enclose nano-sized compartments that pinch off from the mother membrane and become freely moving cellular nanovesicles (CNVs). CNVs externalize the pieces of the cell and make them available to other cells within the same organism or other organisms. Therefore they have been acknowledged as mediators of communication between microorganisms, plants, animals and human. Furthernore, they dwell on the border between living and non-living things. Recent findings report on heterogeneity of the size and composition of CNVs found in isolates from different biological samples. As communication between cells is involved in many physiological and patophysiological processes, it is of importance to understand the mechanisms of CNVs formation and recognize the natural laws that mainly govern them. We point to an unifying mechanism that explains stability of differently shaped and composed CNVs by taking into account that the biological membrane tends to attain the minimum of its relevant energy. Conveniently, the procedure can be described by a mathematical model which allows for transparent comparison between experimentally induced shapes of membrane-enclosed vesicular structures and numerical calculations.
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Affiliation(s)
- Veronika Kralj-Iglič
- Faculty of Health Sciences, Laboratory of Clinical Biophysics, University of Ljubljana, Ljubljana, Slovenia
- Extracellular Vesicles and Mass Spetrometry Group, Institute of Biosciences and Bioresources, National Research Council of Italy, Napoli, Italy
- * E-mail:
| | - Gabriella Pocsfalvi
- Extracellular Vesicles and Mass Spetrometry Group, Institute of Biosciences and Bioresources, National Research Council of Italy, Napoli, Italy
| | - Luka Mesarec
- Faculty of Electrical Engineering, Laboratory of Physics, University of Ljubljana, Ljubljana, Slovenia
| | - Vid Šuštar
- Faculty of Medicine, Lymphocyte Cytoskeleton Group, University of Turku, Turku, Finland
| | - Henry Hägerstrand
- Faculty of Science and Engineering, Cell Biology, Åbo Akademi University, Åbo/Turku, Finland
- Novia University of Applied Sciences, Ekenäs, Finland
| | - Aleš Iglič
- Extracellular Vesicles and Mass Spetrometry Group, Institute of Biosciences and Bioresources, National Research Council of Italy, Napoli, Italy
- Faculty of Electrical Engineering, Laboratory of Physics, University of Ljubljana, Ljubljana, Slovenia
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11
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Lieu UT, Yoshinaga N. Topological defects of dipole patchy particles on a spherical surface. SOFT MATTER 2020; 16:7667-7675. [PMID: 32804175 DOI: 10.1039/d0sm00103a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We investigate the assembly of dipole-like patchy particles confined to a spherical surface by Brownian dynamics simulations. The surface property of the spherical particle is described by the spherical harmonic Y10, and the orientation of the particle is defined as the uniaxial axis. On a flat space, we observe a defect-free square lattice with nematic order. On a spherical surface, defects appear due to the topological constraint. As for the director field, four defects of winding number +1/2 are observed, satisfying the Euler characteristic. We have found many configurations of the four defects lying near a great circle. Regarding the positional order for the square lattice, eight grain boundary scars proliferate linearly with the sphere size. The positions and orientations of the eight grain boundary scars are strongly related to the four +1/2 defect cores.
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Affiliation(s)
- Uyen Tu Lieu
- Mathematics for Advanced Materials-OIL, AIST, 2-1-1 Katahira, Aoba, 980-8577 Sendai, Japan.
| | - Natsuhiko Yoshinaga
- Mathematics for Advanced Materials-OIL, AIST, 2-1-1 Katahira, Aoba, 980-8577 Sendai, Japan. and WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba, 980-8577 Sendai, Japan.
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12
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Mesarec L, Góźdź W, Iglič A, Kralj-Iglič V, Virga EG, Kralj S. Normal red blood cells' shape stabilized by membrane's in-plane ordering. Sci Rep 2019; 9:19742. [PMID: 31875042 PMCID: PMC6930264 DOI: 10.1038/s41598-019-56128-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Accepted: 12/04/2019] [Indexed: 11/19/2022] Open
Abstract
Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.
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Affiliation(s)
- L Mesarec
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, 1000, Ljubljana, Slovenia
| | - W Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224, Warsaw, Poland
| | - A Iglič
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, 1000, Ljubljana, Slovenia
- Laboratory of Mass Spectrometry and Proteomics, Institute of Biosciences and BioResources, National Research Council of Italy, Napoli, 80132, Italy
| | - V Kralj-Iglič
- Laboratory of Mass Spectrometry and Proteomics, Institute of Biosciences and BioResources, National Research Council of Italy, Napoli, 80132, Italy
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, 1000, Ljubljana, Slovenia
- Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, 1000, Ljubljana, Slovenia
| | - E G Virga
- Department of Mathematics, University of Pavia, Via Ferrata 5, 27100, Pavia, Italy
| | - S Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, 2000, Maribor, Slovenia.
- Condensed Matter Physics Department, Jožef Stefan Institute, 1000, Ljubljana, Slovenia.
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Kumar G, Ramakrishnan N, Sain A. Tubulation pattern of membrane vesicles coated with biofilaments. Phys Rev E 2019; 99:022414. [PMID: 30934309 DOI: 10.1103/physreve.99.022414] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Indexed: 06/09/2023]
Abstract
Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.
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Affiliation(s)
- Gaurav Kumar
- Physics Department, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - N Ramakrishnan
- Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Anirban Sain
- Physics Department, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
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Sonnet AM, Virga EG. Bistable curvature potential at hyperbolic points of nematic shells. SOFT MATTER 2017; 13:6792-6802. [PMID: 28828443 DOI: 10.1039/c7sm01216k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.
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Affiliation(s)
- André M Sonnet
- Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK.
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Duan X, Yao Z. Curvature-driven stability of defects in nematic textures over spherical disks. Phys Rev E 2017; 95:062706. [PMID: 28709326 DOI: 10.1103/physreve.95.062706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 06/07/2023]
Abstract
Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature-driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defects are repelled to the boundary of the disk. Our calculations reveal that the movement of the equilibrium position of the +1 defect from the boundary to the center of the spherical disk occurs in a very narrow window of the disk area, exhibiting the first-order phase-transition-like behavior. For the pair of +1/2 defects by splitting a +1 defect, we find the curvature-driven alternating repulsive and attractive interactions between the two defects. With the growth of the spherical disk these two defects tend to approach and finally recombine towards a +1 defect texture. The sensitive response of defects to curvature and the curvature-driven stability mechanism demonstrated in this work in nematic disk systems may have implications towards versatile control and engineering of liquid-crystal textures in various applications.
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Affiliation(s)
- Xiuqing Duan
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Zhenwei Yao
- School of Physics and Astronomy, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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