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Waltmann C, Shrestha A, Olvera de la Cruz M. Patterning of multicomponent elastic shells by gaussian curvature. Phys Rev E 2024; 109:054409. [PMID: 38907410 DOI: 10.1103/physreve.109.054409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 04/19/2024] [Indexed: 06/24/2024]
Abstract
Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.
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Affiliation(s)
| | | | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
- Center for Computation and Theory of Soft Materials, Northwestern University, Evanston, Illinois 60208, USA
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
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2
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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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3
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Alimohamadi H, Rangamani P. Effective cell membrane tension protects red blood cells against malaria invasion. PLoS Comput Biol 2023; 19:e1011694. [PMID: 38048346 PMCID: PMC10721198 DOI: 10.1371/journal.pcbi.1011694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2023] [Revised: 12/14/2023] [Accepted: 11/16/2023] [Indexed: 12/06/2023] Open
Abstract
A critical step in how malaria parasites invade red blood cells (RBCs) is the wrapping of the membrane around the egg-shaped merozoites. Recent experiments have revealed that RBCs can be protected from malaria invasion by high membrane tension. While cellular and biochemical aspects of parasite actomyosin motor forces during the malaria invasion have been well studied, the important role of the biophysical forces induced by the RBC membrane-cytoskeleton composite has not yet been fully understood. In this study, we use a theoretical model for lipid bilayer mechanics, cytoskeleton deformation, and membrane-merozoite interactions to systematically investigate the influence of effective RBC membrane tension, which includes contributions from the lipid bilayer tension, spontaneous tension, interfacial tension, and the resistance of cytoskeleton against shear deformation on the progression of membrane wrapping during the process of malaria invasion. Our model reveals that this effective membrane tension creates a wrapping energy barrier for a complete merozoite entry. We calculate the tension threshold required to impede the malaria invasion. We find that the tension threshold is a nonmonotonic function of spontaneous tension and undergoes a sharp transition from large to small values as the magnitude of interfacial tension increases. We also predict that the physical properties of the RBC cytoskeleton layer-particularly the resting length of the cytoskeleton-play key roles in specifying the degree of the membrane wrapping. We also found that the shear energy of cytoskeleton deformation diverges at the full wrapping state, suggesting the local disassembly of the cytoskeleton is required to complete the merozoite entry. Additionally, using our theoretical framework, we predict the landscape of myosin-mediated forces and the physical properties of the RBC membrane in regulating successful malaria invasion. Our findings on the crucial role of RBC membrane tension in inhibiting malaria invasion can have implications for developing novel antimalarial therapeutic or vaccine-based strategies.
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Affiliation(s)
- Haleh Alimohamadi
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California, United States of America
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California, United States of America
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4
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Alas CD, Haselwandter CA. Dependence of protein-induced lipid bilayer deformations on protein shape. Phys Rev E 2023; 107:024403. [PMID: 36932542 DOI: 10.1103/physreve.107.024403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.
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Affiliation(s)
- Carlos D Alas
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
| | - Christoph A Haselwandter
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
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5
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Božič B, Svetina S. Membrane Localization of Piezo1 in the Context of Its Role in the Regulation of Red Blood Cell Volume. Front Physiol 2022; 13:879038. [PMID: 35669579 PMCID: PMC9163432 DOI: 10.3389/fphys.2022.879038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 04/29/2022] [Indexed: 11/29/2022] Open
Abstract
Piezo1 is a membrane nonspecific cation channel involved in red blood cells (RBCs) in the regulation of their volume. Recently, it was shown that it is distributed on the RBC membrane in a nonuniform manner. Here it is shown that it is possible to interpret the lateral distribution of Piezo1 molecules on RBC membrane by the curvature dependent Piezo1—bilayer interaction which is the consequence of the mismatch between the intrinsic principal curvatures of the Piezo1 trimer and the principal curvatures of the membrane at Piezo1′s location but without its presence. This result supports the previously proposed model for the role of Piezo1 in the regulation of RBC volume.
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Affiliation(s)
- Bojan Božič
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
| | - Saša Svetina
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
- Jožef Stefan Institute, Ljubljana, Slovenia
- *Correspondence: Saša Svetina,
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6
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Bashkirov PV, Kuzmin PI, Vera Lillo J, Frolov VA. Molecular Shape Solution for Mesoscopic Remodeling of Cellular Membranes. Annu Rev Biophys 2022; 51:473-497. [PMID: 35239417 PMCID: PMC10787580 DOI: 10.1146/annurev-biophys-011422-100054] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Cellular membranes self-assemble from and interact with various molecular species. Each molecule locally shapes the lipid bilayer, the soft elastic core of cellular membranes. The dynamic architecture of intracellular membrane systems is based on elastic transformations and lateral redistribution of these elementary shapes, driven by chemical and curvature stress gradients. The minimization of the total elastic stress by such redistribution composes the most basic, primordial mechanism of membrane curvature-composition coupling (CCC). Although CCC is generally considered in the context of dynamic compositional heterogeneity of cellular membrane systems, in this article we discuss a broader involvement of CCC in controlling membrane deformations. We focus specifically on the mesoscale membrane transformations in open, reservoir-governed systems, such as membrane budding, tubulation, and the emergence of highly curved sites of membrane fusion and fission. We reveal that the reshuffling of molecular shapes constitutes an independent deformation mode with complex rheological properties.This mode controls effective elasticity of local deformations as well as stationary elastic stress, thus emerging as a major regulator of intracellular membrane remodeling.
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Affiliation(s)
- Pavel V Bashkirov
- Federal Research and Clinical Center of Physical-Chemical Medicine, Moscow, Russia
- Department of Molecular and Biological Physics, Moscow Institute of Physics and Technology, Moscow, Russia
| | - Peter I Kuzmin
- A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia
| | - Javier Vera Lillo
- Biofisika Institute (CSIC, UPV/EHU) and Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain;
| | - Vadim A Frolov
- Biofisika Institute (CSIC, UPV/EHU) and Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain;
- Ikerbasque, Basque Foundation for Science, Bilbao, Spain
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7
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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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8
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Raval J, Gongadze E, Benčina M, Junkar I, Rawat N, Mesarec L, Kralj-Iglič V, Góźdź W, Iglič A. Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces. MEMBRANES 2021; 11:membranes11070533. [PMID: 34357183 PMCID: PMC8307671 DOI: 10.3390/membranes11070533] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Revised: 07/05/2021] [Accepted: 07/05/2021] [Indexed: 11/27/2022]
Abstract
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.
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Affiliation(s)
- Jeel Raval
- Group of Physical Chemistry of Complex Systems, Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland; (J.R.); (W.G.)
| | - Ekaterina Gongadze
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (N.R.); (L.M.)
| | - Metka Benčina
- Department of Surface Engineering and Optoelectronics, Jožef Stefan Institute, 1000 Ljubljana, Slovenia; (M.B.); (I.J.)
| | - Ita Junkar
- Department of Surface Engineering and Optoelectronics, Jožef Stefan Institute, 1000 Ljubljana, Slovenia; (M.B.); (I.J.)
| | - Niharika Rawat
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (N.R.); (L.M.)
| | - Luka Mesarec
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (N.R.); (L.M.)
| | - Veronika Kralj-Iglič
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, 1000 Ljubljana, Slovenia;
| | - Wojciech Góźdź
- Group of Physical Chemistry of Complex Systems, Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland; (J.R.); (W.G.)
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia; (E.G.); (N.R.); (L.M.)
- Laboratory of Clinical Biophysics, Chair of Orthopaedics, Faculty of Medicine, University of Ljubljana, 1000 Ljubljana, Slovenia
- Correspondence: ; Tel.: +386-1-4768-825
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9
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Alimohamadi H, Bell MK, Halpain S, Rangamani P. Mechanical Principles Governing the Shapes of Dendritic Spines. Front Physiol 2021; 12:657074. [PMID: 34220531 PMCID: PMC8242199 DOI: 10.3389/fphys.2021.657074] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 05/13/2021] [Indexed: 02/04/2023] Open
Abstract
Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.
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Affiliation(s)
- Haleh Alimohamadi
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, United States
| | - Miriam K. Bell
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, United States
| | - Shelley Halpain
- Sanford Consortium for Regenerative Medicine, La Jolla, CA, United States
- Section of Neurobiology, Division of Biological Sciences, University of California, San Diego, La Jolla, CA, United States
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, United States
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10
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Tsai FC, Simunovic M, Sorre B, Bertin A, Manzi J, Callan-Jones A, Bassereau P. Comparing physical mechanisms for membrane curvature-driven sorting of BAR-domain proteins. SOFT MATTER 2021; 17:4254-4265. [PMID: 33870384 DOI: 10.1039/d0sm01573c] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Protein enrichment at specific membrane locations in cells is crucial for many cellular functions. It is well-recognized that the ability of some proteins to sense membrane curvature contributes partly to their enrichment in highly curved cellular membranes. In the past, different theoretical models have been developed to reveal the physical mechanisms underlying curvature-driven protein sorting. This review aims to provide a detailed discussion of the two continuous models that are based on the Helfrich elasticity energy, (1) the spontaneous curvature model and (2) the curvature mismatch model. These two models are commonly applied to describe experimental observations of protein sorting. We discuss how they can be used to explain the curvature-induced sorting data of two BAR proteins, amphiphysin and centaurin. We further discuss how membrane rigidity, and consequently the membrane curvature generated by BAR proteins, could influence protein organization on the curved membranes. Finally, we address future directions in extending these models to describe some cellular phenomena involving protein sorting.
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Affiliation(s)
- Feng-Ching Tsai
- Institut Curie, Université PSL, CNRS UMR168, Sorbonne Université, Laboratoire Physico Chimie Curie, 75005 Paris, France.
| | - Mijo Simunovic
- Department of Chemical Engineering, Columbia University, New York, NY 10027, USA and Department of Genetics and Development, Columbia Stem Cell Initiative, Columbia University Irving Medical Center, NY 10032, USA
| | - Benoit Sorre
- Institut Curie, Université PSL, CNRS UMR168, Sorbonne Université, Laboratoire Physico Chimie Curie, 75005 Paris, France. and Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université de Paris, Paris, France.
| | - Aurélie Bertin
- Institut Curie, Université PSL, CNRS UMR168, Sorbonne Université, Laboratoire Physico Chimie Curie, 75005 Paris, France.
| | - John Manzi
- Institut Curie, Université PSL, CNRS UMR168, Sorbonne Université, Laboratoire Physico Chimie Curie, 75005 Paris, France.
| | - Andrew Callan-Jones
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université de Paris, Paris, France.
| | - Patricia Bassereau
- Institut Curie, Université PSL, CNRS UMR168, Sorbonne Université, Laboratoire Physico Chimie Curie, 75005 Paris, France.
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11
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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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12
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Diffusion on Membrane Domes, Tubes, and Pearling Structures. Biophys J 2020; 120:424-431. [PMID: 33359464 DOI: 10.1016/j.bpj.2020.12.014] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Revised: 11/19/2020] [Accepted: 12/08/2020] [Indexed: 02/06/2023] Open
Abstract
Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.
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13
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Goršak T, Drab M, Križaj D, Jeran M, Genova J, Kralj S, Lisjak D, Kralj-Iglič V, Iglič A, Makovec D. Magneto-mechanical actuation of barium-hexaferrite nanoplatelets for the disruption of phospholipid membranes. J Colloid Interface Sci 2020; 579:508-519. [PMID: 32623117 DOI: 10.1016/j.jcis.2020.06.079] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Revised: 06/01/2020] [Accepted: 06/18/2020] [Indexed: 01/09/2023]
Abstract
HYPOTHESIS The magneto-mechanical actuation (MMA) of magnetic nanoparticles with a low-frequency alternating magnetic field (AMF) can be used to destroy cancer cells. So far, MMA was tested on different cells using different nanoparticles and different field characteristics, which makes comparisons and any generalizations about the results of MMA difficult. In this paper we propose the use of giant unilamellar vesicles (GUVs) as a simple model system to study the effect of MMA on a closed lipid bilayer membrane, i.e., a basic building block of any cell. EXPERIMENTS The GUVs were exposed to barium-hexaferrite nanoplatelets (NPLs, ~50 nm wide and 3 nm thick) with unique magnetic properties dominated by a permanent magnetic moment that is perpendicular to the platelet, at different concentrations (1-50 µg/mL) and pH values (4.2-7.4) of the aqueous suspension. The GUVs were observed with an optical microscope while being exposed to a uniaxial AMF (3-100 Hz, 2.2-10.6 mT). FINDINGS When the NPLs were electrostatically attached to the GUV membranes, the MMA induced cyclic fluctuations of the GUVs' shape corresponding to the AMF frequency at the low NPL concentration (1 µm/mL), whereas the GUVs were bursting at the higher concentration (10 µg/mL). Theoretical considerations suggested that the bursting of the GUVs is a consequence of the local action of an assembly of several NPLs, rather than a collective effect of all the absorbed NPLs.
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Affiliation(s)
- Tanja Goršak
- Department for Materials Synthesis, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia; Jožef Stefan International Postgraduate School, Jamova 39, SI-1000 Ljubljana, Slovenia
| | - Mitja Drab
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Dejan Križaj
- Laboratory of Bioelectromagnetics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Marko Jeran
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia; Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, Zdravstvena pot 5, SI-1000 Ljubljana, Slovenia
| | - Julia Genova
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Tzarigradsko 72, 784 Sofia, Bulgaria
| | - Slavko Kralj
- Department for Materials Synthesis, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
| | - Darja Lisjak
- Department for Materials Synthesis, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia; Jožef Stefan International Postgraduate School, Jamova 39, SI-1000 Ljubljana, Slovenia
| | - Veronika Kralj-Iglič
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, Zdravstvena pot 5, SI-1000 Ljubljana, Slovenia
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Darko Makovec
- Department for Materials Synthesis, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia.
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14
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Svetina S. Theoretical Bases for the Role of Red Blood Cell Shape in the Regulation of Its Volume. Front Physiol 2020; 11:544. [PMID: 32581839 PMCID: PMC7297144 DOI: 10.3389/fphys.2020.00544] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 04/30/2020] [Indexed: 12/21/2022] Open
Abstract
The red blood cell (RBC) membrane contains a mechanosensitive cation channel Piezo1 that is involved in RBC volume homeostasis. In a recent model of the mechanism of its action it was proposed that Piezo1 cation permeability responds to changes of the RBC shape. The aim here is to review in a descriptive manner different previous studies of RBC behavior that formed the basis for this proposal. These studies include the interpretation of RBC and vesicle shapes based on the minimization of membrane bending energy, the analyses of various consequences of compositional and structural features of RBC membrane, in particular of its membrane skeleton and its integral membrane proteins, and the modeling of the establishment of RBC volume. The proposed model of Piezo1 action is critically evaluated, and a perspective presented for solving some remaining experimental and theoretical problems. Part of the discussion is devoted to the usefulness of theoretical modeling in studies of the behavior of cell systems in general.
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Affiliation(s)
- Saša Svetina
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia.,Jožef Stefan Institute, Ljubljana, Slovenia
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15
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Alimohamadi H, Smith AS, Nowak RB, Fowler VM, Rangamani P. Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation. PLoS Comput Biol 2020; 16:e1007890. [PMID: 32453720 PMCID: PMC7274484 DOI: 10.1371/journal.pcbi.1007890] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Revised: 06/05/2020] [Accepted: 04/21/2020] [Indexed: 12/11/2022] Open
Abstract
The biconcave disk shape of the mammalian red blood cell (RBC) is unique to the RBC and is vital for its circulatory function. Due to the absence of a transcellular cytoskeleton, RBC shape is determined by the membrane skeleton, a network of actin filaments cross-linked by spectrin and attached to membrane proteins. While the physical properties of a uniformly distributed actin network interacting with the lipid bilayer membrane have been assumed to control RBC shape, recent experiments reveal that RBC biconcave shape also depends on the contractile activity of nonmuscle myosin IIA (NMIIA) motor proteins. Here, we use the classical Helfrich-Canham model for the RBC membrane to test the role of heterogeneous force distributions along the membrane and mimic the contractile activity of sparsely distributed NMIIA filaments. By incorporating this additional contribution to the Helfrich-Canham energy, we find that the RBC biconcave shape depends on the ratio of forces per unit volume in the dimple and rim regions of the RBC. Experimental measurements of NMIIA densities at the dimple and rim validate our prediction that (a) membrane forces must be non-uniform along the RBC membrane and (b) the force density must be larger in the dimple than the rim to produce the observed membrane curvatures. Furthermore, we predict that RBC membrane tension and the orientation of the applied forces play important roles in regulating this force-shape landscape. Our findings of heterogeneous force distributions on the plasma membrane for RBC shape maintenance may also have implications for shape maintenance in different cell types. The spectrin-actin network of the membrane skeleton plays an important role in controlling specialized cell membrane morphology. In the paradigmatic red blood cell (RBC), where actin filaments are present exclusively in the membrane skeleton, recent experiments reveal that nonmuscle myosin IIA (NMIIA) motor contractility maintains the RBC biconcave disk shape. In this study, we have identified criteria for micron-scale distributions of NMIIA forces at the membrane required to maintain the biconcave disk shape of an RBC in the resting condition. Supported by experimental measurements of RBC NMIIA distribution, we showed that a heterogeneous force distribution with a larger force density at the dimple is able to capture the experimentally observed biconcave morphology of an RBC with better accuracy compared to previous models that did not consider the heterogeneity in the force distribution. Furthermore, we showed that the biconcave geometry of the RBC is closely regulated by the effective membrane tension and the direction of applied forces on the membrane. These findings can be generalized to any force-mediated membrane shape, providing insight into the role of actomyosin forces in prescribing and maintaining the morphology of different cell types.
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Affiliation(s)
- Haleh Alimohamadi
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California, United States of America
| | - Alyson S. Smith
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, California, United States of America
| | - Roberta B. Nowak
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, California, United States of America
| | - Velia M. Fowler
- Department of Molecular Medicine, The Scripps Research Institute, La Jolla, California, United States of America
- Department of Biological Sciences, University of Delaware, Newark, Delaware, United States of America
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California, United States of America
- * E-mail:
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16
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Jani VP, Lucas A, Jani VP, Munoz C, Williams AT, Ortiz D, Yalcin O, Cabrales P. Numerical Model for the Determination of Erythrocyte Mechanical Properties and Wall Shear Stress in vivo From Intravital Microscopy. Front Physiol 2020; 10:1562. [PMID: 32038273 PMCID: PMC6989587 DOI: 10.3389/fphys.2019.01562] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 12/12/2019] [Indexed: 12/30/2022] Open
Abstract
The mechanical properties and deformability of Red Blood Cells (RBCs) are important determinants of blood rheology and microvascular hemodynamics. The objective of this study is to quantify the mechanical properties and wall shear stress experienced by the RBC membrane during capillary plug flow in vivo utilizing high speed video recording from intravital microscopy, biomechanical modeling, and computational methods. Capillaries were imaged in the rat cremaster muscle pre- and post-RBC transfusion of stored RBCs for 2-weeks. RBC membrane contours were extracted utilizing image processing and parametrized. RBC parameterizations were used to determine updated deformation gradient and Lagrangian Green strain tensors for each point along the parametrization and for each frame during plug flow. The updated Lagrangian Green strain and Displacement Gradient tensors were numerically fit to the Navier-Lame equations along the parameterized boundary to determined Lame's constants. Mechanical properties and wall shear stress were determined before and transfusion, were grouped in three populations of erythrocytes: native cells (NC) or circulating cells before transfusion, and two distinct population of cells after transfusion with stored cells (SC1 and SC2). The distinction, between the heterogeneous populations of cells present after the transfusion, SC1 and SC2, was obtained through principle component analysis (PCA) of the mechanical properties along the membrane. Cells with the first two principle components within 3 standard deviations of the mean, were labeled as SC1, and those with the first two principle components greater than 3 standard deviations from the mean were labeled as SC2. The calculated shear modulus average was 1.1±0.2, 0.90±0.15, and 12 ± 8 MPa for NC, SC1, and SC2, respectively. The calculated young's modulus average was 3.3±0.6, 2.6±0.4, and 32±20 MPa for NC, SC1, and SC2, respectively. o our knowledge, the methods presented here are the first estimation of the erythrocyte mechanical properties and shear stress in vivo during capillary plug flow. In summary, the methods introduced in this study may provide a new avenue of investigation of erythrocyte mechanics in the context of hematologic conditions that adversely affect erythrocyte mechanical properties.
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Affiliation(s)
- Vivek P Jani
- School of Medicine, Johns Hopkins University, Baltimore, MD, United States
| | - Alfredo Lucas
- Functional Cardiovascular Engineering, Department of Bioengineering, University of California, San Diego, San Diego, CA, United States
| | - Vinay P Jani
- Functional Cardiovascular Engineering, Department of Bioengineering, University of California, San Diego, San Diego, CA, United States
| | - Carlos Munoz
- Functional Cardiovascular Engineering, Department of Bioengineering, University of California, San Diego, San Diego, CA, United States
| | - Alexander T Williams
- Functional Cardiovascular Engineering, Department of Bioengineering, University of California, San Diego, San Diego, CA, United States
| | - Daniel Ortiz
- Department of Biomedical Engineering, Universidad de los Andes, Bogota, Colombia
| | - Ozlem Yalcin
- Koc University School of Medicine, Istanbul, Turkey
| | - Pedro Cabrales
- Functional Cardiovascular Engineering, Department of Bioengineering, University of California, San Diego, San Diego, CA, United States
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17
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Reddy B, Bavi N, Lu A, Park Y, Perozo E. Molecular basis of force-from-lipids gating in the mechanosensitive channel MscS. eLife 2019; 8:50486. [PMID: 31880537 PMCID: PMC7299334 DOI: 10.7554/elife.50486] [Citation(s) in RCA: 69] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Accepted: 12/27/2019] [Indexed: 12/28/2022] Open
Abstract
Prokaryotic mechanosensitive (MS) channels open by sensing the physical state of the membrane. As such, lipid-protein interactions represent the defining molecular process underlying mechanotransduction. Here, we describe cryo-electron microscopy (cryo-EM) structures of the E. coli small-conductance mechanosensitive channel (MscS) in nanodiscs (ND). They reveal a novel membrane-anchoring fold that plays a significant role in channel activation and establish a new location for the lipid bilayer, shifted ~14 Å from previous consensus placements. Two types of lipid densities are explicitly observed. A phospholipid that ‘hooks’ the top of each TM2-TM3 hairpin and likely plays a role in force sensing, and a bundle of acyl chains occluding the permeation path above the L105 cuff. These observations reshape our understanding of force-from-lipids gating in MscS and highlight the key role of allosteric interactions between TM segments and phospholipids bound to key dynamic components of the channel.
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Affiliation(s)
- Bharat Reddy
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States
| | - Navid Bavi
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States
| | - Allen Lu
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States
| | - Yeonwoo Park
- Department of Ecology and Evolution, The University of Chicago, Chicago, United States
| | - Eduardo Perozo
- Department of Biochemistry and Molecular Biology, The University of Chicago, Chicago, United States.,Institute for Biophysical Dynamics, The University of Chicago, Chicago, United States
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18
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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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19
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Fošnarič M, Penič S, Iglič A, Kralj-Iglič V, Drab M, Gov NS. Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces. SOFT MATTER 2019; 15:5319-5330. [PMID: 31237259 DOI: 10.1039/c8sm02356e] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.
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Affiliation(s)
- Miha Fošnarič
- Faculty of Health Sciences, University of Ljubljana, Ljubljana, Slovenia
| | - Samo Penič
- Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
| | - Aleš Iglič
- Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
| | | | - Mitja Drab
- Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
| | - Nir S Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel.
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20
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Gov NS. Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces. Philos Trans R Soc Lond B Biol Sci 2019; 373:rstb.2017.0115. [PMID: 29632267 DOI: 10.1098/rstb.2017.0115] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/19/2017] [Indexed: 01/11/2023] Open
Abstract
Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.
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Affiliation(s)
- N S Gov
- Department of Chemical Physics, Weizmann Institute of Science, PO Box 26, Rehovot 76100, Israel
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21
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Svetina S, Švelc Kebe T, Božič B. A Model of Piezo1-Based Regulation of Red Blood Cell Volume. Biophys J 2018; 116:151-164. [PMID: 30580922 DOI: 10.1016/j.bpj.2018.11.3130] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Revised: 10/06/2018] [Accepted: 11/19/2018] [Indexed: 01/06/2023] Open
Abstract
A red blood cell (RBC) performs its function of adequately carrying respiratory gases in blood by its volume being ∼60% of that of a sphere with the same membrane area. For this purpose, human and most other vertebrate RBCs regulate their content of potassium (K+) and sodium (Na+) ions. The focus considered here is on K+ efflux through calcium-ion (Ca2+)-activated Gárdos channels. These channels open under conditions that allow Ca2+ to enter RBCs through Piezo1 mechanosensitive cation-permeable channels. It is postulated that the fraction of open Piezo1 channels depends on the RBC shape as a result of the curvature-dependent Piezo1-bilayer membrane interaction. The consequences of this postulate are studied by introducing a simple model of RBC osmotic behavior supplemented by the dependence of RBC membrane K+ permeability on the reduced volume (i.e., the ratio of cell volume to its maximal possible volume) of RBC discoid shapes. It is assumed that because of its intrinsic curvature and strong interaction with the surrounding membrane, Piezo1 tends to concentrate in the dimple regions of these shapes, and the fraction of open Piezo1 channels depends on the membrane curvature in that region. It is shown that the properties of the described model can provide the basis for the formation of the negative feedback loop that interrelates cell volume and its content of potassium ions. The model predicts the relation, valid for each cell in an RBC population, between RBC volume and membrane area, thus explaining the large value of the measured membrane area versus the volume correlation coefficient. The mechanism proposed here for RBC volume regulation is in accord with the loss of this correlation in RBCs of Piezo1 knockout mice.
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Affiliation(s)
- Saša Svetina
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia; Jožef Stefan Institute, Ljubljana, Slovenia.
| | | | - Bojan Božič
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia
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22
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Alimohamadi H, Rangamani P. Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions. Biomolecules 2018; 8:E120. [PMID: 30360496 PMCID: PMC6316661 DOI: 10.3390/biom8040120] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Revised: 10/15/2018] [Accepted: 10/16/2018] [Indexed: 01/03/2023] Open
Abstract
To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.
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Affiliation(s)
- Haleh Alimohamadi
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA.
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA.
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23
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Mesarec L, Góźdź W, Kralj S, Fošnarič M, Penič S, Kralj-Iglič V, Iglič A. On the role of external force of actin filaments in the formation of tubular protrusions of closed membrane shapes with anisotropic membrane components. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2017; 46:705-718. [PMID: 28488019 DOI: 10.1007/s00249-017-1212-z] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Revised: 04/06/2017] [Accepted: 04/13/2017] [Indexed: 02/08/2023]
Abstract
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.
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Affiliation(s)
- Luka Mesarec
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia.
| | - Wojciech Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland
| | - Samo Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia.,Jožef Stefan Institute, PO Box 3000, 1000, Ljubljana, Slovenia
| | - Miha Fošnarič
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia
| | - Samo Penič
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia
| | - Veronika Kralj-Iglič
- Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, Zdravstvena 5, 1000, Ljubljana, Slovenia.,Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, Zaloška 9, 1000, Ljubljana, Slovenia
| | - Aleš Iglič
- Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia.,Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, Zaloška 9, 1000, Ljubljana, Slovenia
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24
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Svetina S. Curvature-dependent protein–lipid bilayer interaction and cell mechanosensitivity. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2015; 44:513-9. [DOI: 10.1007/s00249-015-1046-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2015] [Revised: 05/13/2015] [Accepted: 05/14/2015] [Indexed: 05/28/2023]
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25
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Božič B, Das SL, Svetina S. Sorting of integral membrane proteins mediated by curvature-dependent protein-lipid bilayer interaction. SOFT MATTER 2015; 11:2479-2487. [PMID: 25675862 DOI: 10.1039/c4sm02289k] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Cell membrane proteins, both bound and integral, are known to preferentially accumulate at membrane locations with curvatures favorable to their shape. This is mainly due to the curvature dependent interaction between membrane proteins and their lipid environment. Here, we analyze the effects of the protein-lipid bilayer interaction energy due to mismatch between the protein shape and the principal curvatures of the surrounding bilayer. The role of different macroscopic parameters that define the interaction energy term is elucidated in relation to recent experiment in which the lateral distribution of a membrane embedded protein potassium channel KvAP is measured on a giant unilamellar lipid vesicle (reservoir) and a narrow tubular extension - a tether - kept at constant length. The dependence of the sorting ratio, defined as the ratio between the areal density of the protein on the tether and on the vesicle, on the inverse tether radius is influenced by the strength of the interaction, the intrinsic shape of the membrane embedded protein, and its abundance in the reservoir. It is described how the values of these constants can be extracted from experiments. The intrinsic principal curvatures of a protein are related to the tether radius at which the sorting ratio attains its maximum value. The estimate of the principal intrinsic curvature of the protein KvAP, obtained by comparing the experimental and theoretical sorting behavior, is consistent with the available information on its structure.
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Affiliation(s)
- Bojan Božič
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia.
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Bassereau P, Sorre B, Lévy A. Bending lipid membranes: experiments after W. Helfrich's model. Adv Colloid Interface Sci 2014; 208:47-57. [PMID: 24630341 DOI: 10.1016/j.cis.2014.02.002] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Revised: 02/02/2014] [Accepted: 02/03/2014] [Indexed: 10/25/2022]
Abstract
Current description of biomembrane mechanics originates for a large part from W. Helfrich's model. Based on his continuum theory, many experiments have been performed in the past four decades on simplified membranes in order to characterize the mechanical properties of lipid membranes and the contribution of polymers or proteins. The long-term goal was to develop a better understanding of the mechanical properties of cell membranes. In this paper, we will review representative experimental approaches that were developed during this period and the main results that were obtained.
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27
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Mrówczyńska L, Lindqvist C, Iglič A, Hägerstrand H. Spontaneous curvature of ganglioside GM1--effect of cross-linking. Biochem Biophys Res Commun 2012; 422:776-9. [PMID: 22634013 DOI: 10.1016/j.bbrc.2012.05.083] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2012] [Accepted: 05/16/2012] [Indexed: 11/28/2022]
Abstract
The membrane-curvature dependent lateral distribution of outer leaflet ganglioside GM1 (GM1) and the influence of GM1 cross-linking induced by fluorophore-tagged cholera toxin subunit B (CTB) plus anti-CTB was analysed in cell membranes by fluorescence microscopy. Data are presented indicating that cross-linked GM1-ligand patches accumulated at the tips of human erythrocyte echinocytic spiculae induced by Ca(2+)/ionophore A23187. However, when lipid fixative osmium tetroxide was added prior to the ligand no accumulation in spiculae occurred. GM1-staining remained here distributed over the spheroid cell body and in spiculae. Similarly, osmium tetroxide completely prohibited CTB plus anti-CTB-induced GM1 patching in representatives for flat membrane, i.e. discoid erythrocytes and K562 cells. Our results demonstrate that GM1 per se shows low membrane curvature dependent distribution and therefore holds flexible spontaneous curvature. In contrast, the cross-linked GM1-ligand complex has a strong preference for highly outward curved membrane and possesses overall positive spontaneous curvature. Osmium tetroxide efficiently immobilises GM1.
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Affiliation(s)
- Lucyna Mrówczyńska
- Department of Cell Biology, A. Mickiewicz University, Umultowska 89, PL-61614 Poznań, Poland.
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28
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Jesenek D, Perutková S, Kralj-Iglič V, Kralj S, Iglič A. Exocytotic fusion pore stability and topological defects in the membrane with orientational degree of ordering. Cell Calcium 2012; 52:277-82. [PMID: 22541648 DOI: 10.1016/j.ceca.2012.04.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2012] [Revised: 03/26/2012] [Accepted: 04/02/2012] [Indexed: 11/30/2022]
Abstract
Regulated exocytosis is a process that strongly depends on the formation and stability of the fusion pore. It was indicated experimentally and theoretically that narrow and highly curved fusion pore may be stabilized by accumulation of anisotropic membrane components possessing orientational ordering. On the other hand, narrow fusion pore may also undergo repetitive opening and closing, disruption in the so called kiss and run process or become completely opened in the process of full fusion of the vesicle with the membrane. In this paper we attempt to elucidate the subtle interplay between the stabilizing and destabilizing processes in the fusion neck. A possible physical mechanism which may lead to disruption of the stable fusion pore or complete fusion of the vesicle with the membrane is discussed. It is indicated that topologically driven defects of the in-plane orientational membrane ordering in the region of the fusion pore may disrupt the fusion. Alternatively, it may facilitate repetitive opening and closing of the fusion pore or induce full fusion of the vesicle with the target membrane.
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Affiliation(s)
- Dalija Jesenek
- Department of Condensed Matter Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
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29
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Red blood cell shape and deformability in the context of the functional evolution of its membrane structure. Cell Mol Biol Lett 2012; 17:171-81. [PMID: 22271334 PMCID: PMC6275855 DOI: 10.2478/s11658-012-0001-z] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Accepted: 01/12/2012] [Indexed: 11/20/2022] Open
Abstract
It is proposed that it is possible to identify some of the problems that had to be solved in the course of evolution for the red blood cell (RBC) to achieve its present day effectiveness, by studying the behavior of systems featuring different, partial characteristics of its membrane. The appropriateness of the RBC volume to membrane area ratio for its circulation in the blood is interpreted on the basis of an analysis of the shape behavior of phospholipid vesicles. The role of the membrane skeleton is associated with preventing an RBC from transforming into a budded shape, which could form in its absence due to curvature-dependent transmembrane protein-membrane interaction. It is shown that, by causing the formation of echinocytes, the skeleton also acts protectively when, in vesicles with a bilayer membrane, the budded shapes would form due to increasing difference between the areas of their outer and inner layers.
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30
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Nature of curvature coupling of amphiphysin with membranes depends on its bound density. Proc Natl Acad Sci U S A 2011; 109:173-8. [PMID: 22184226 DOI: 10.1073/pnas.1103594108] [Citation(s) in RCA: 215] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Cells are populated by a vast array of membrane-binding proteins that execute critical functions. Functions, like signaling and intracellular transport, require the abilities to bind to highly curved membranes and to trigger membrane deformation. Among these proteins is amphiphysin 1, implicated in clathrin-mediated endocytosis. It contains a Bin-Amphiphysin-Rvs membrane-binding domain with an N-terminal amphipathic helix that senses and generates membrane curvature. However, an understanding of the parameters distinguishing these two functions is missing. By pulling a highly curved nanotube of controlled radius from a giant vesicle in a solution containing amphiphysin, we observed that the action of the protein depends directly on its density on the membrane. At low densities of protein on the nearly flat vesicle, the distribution of proteins and the mechanical effects induced are described by a model based on spontaneous curvature induction. The tube radius and force are modified by protein binding but still depend on membrane tension. In the dilute limit, when practically no proteins were present on the vesicle, no mechanical effects were detected, but strong protein enrichment proportional to curvature was seen on the tube. At high densities, the radius is independent of tension and vesicle protein density, resulting from the formation of a scaffold around the tube. As a consequence, the scaling of the force with tension is modified. For the entire density range, protein was enriched on the tube as compared to the vesicle. Our approach shows that the strength of curvature sensing and mechanical effects on the tube depends on the protein density.
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Callan-Jones A, Sorre B, Bassereau P. Curvature-driven lipid sorting in biomembranes. Cold Spring Harb Perspect Biol 2011; 3:cshperspect.a004648. [PMID: 21421916 DOI: 10.1101/cshperspect.a004648] [Citation(s) in RCA: 97] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
It has often been suggested that the high curvature of transport intermediates in cells may be a sufficient means to segregate different lipid populations based on the relative energy costs of forming bent membranes. In this review, we present in vitro experiments that highlight the essential physics of lipid sorting at thermal equilibrium: It is driven by a trade-off between bending energy, mixing entropy, and interactions between species. We collect evidence that lipid sorting depends strongly on lipid-lipid and protein-lipid interactions, and hence on the underlying composition of the membrane and on the presence of bound proteins.
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Affiliation(s)
- Andrew Callan-Jones
- CNRS UMR 5207, Laboratoire de Physique Théorique et Astroparticules, Université Montpellier II, 34095 Montpellier Cedex 05, France
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32
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Góźdź WT. Shape transformation of lipid vesicles induced by diffusing macromolecules. J Chem Phys 2011; 134:024110. [DOI: 10.1063/1.3530069] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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33
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Inhomogeneities in sodium decylsulfate doped 1,2-dipalmitoylphosphatidylcholine bilayer. J Colloid Interface Sci 2010; 343:401-7. [DOI: 10.1016/j.jcis.2009.11.054] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2009] [Revised: 11/19/2009] [Accepted: 11/20/2009] [Indexed: 11/17/2022]
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Bohinc K, Lombardo D, Kraljiglič V, Fošnarič M, May S, Pernuš F, Hägerstrand H, Iglič A. Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions. Cell Mol Biol Lett 2009; 11:90-101. [PMID: 16847752 PMCID: PMC6275760 DOI: 10.2478/s11658-006-0009-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2005] [Accepted: 01/06/2006] [Indexed: 11/20/2022] Open
Abstract
A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.
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Affiliation(s)
- Klemen Bohinc
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
- University College for Health Studies, University of Ljubljana, Poljanska 26a, SI-1000 Ljubljana, Slovenia
| | - Darko Lombardo
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Veronika Kraljiglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, 1000 Ljubljana, Slovenia
| | - Miha Fošnarič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Sylvio May
- Department of Physics, North Dakota State University, Fargo, ND 58105-5566 USA
| | - Franjo Pernuš
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
| | - Henry Hägerstrand
- Department of Biology, Åbo Akademi University, Abo/Turku, FIN-20520 Finland
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
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35
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Encapsulation of small spherical liposome into larger flaccid liposome induced by human plasma proteins. Comput Methods Biomech Biomed Engin 2009. [DOI: 10.1080/10255840802560326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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36
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Chapter 3 Membrane Nanotubes in Urothelial Cell Line T24. ACTA ACUST UNITED AC 2009. [DOI: 10.1016/s1554-4516(09)10003-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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37
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Fošnarič M, Iglič A, Kroll DM, May S. Monte Carlo simulations of complex formation between a mixed fluid vesicle and a charged colloid. J Chem Phys 2009. [DOI: 10.1063/1.3191782] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Fošnarič M, Iglič A, Slivnik T, Kralj-Iglič V. Flexible Membrane Inclusions and Membrane Inclusions Induced by Rigid Globular Proteins. ADVANCES IN PLANAR LIPID BILAYERS AND LIPOSOMES 2008. [DOI: 10.1016/s1554-4516(08)00006-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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39
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Iglic A, Slivnik T, Kralj-Iglic V. Elastic properties of biological membranes influenced by attached proteins. J Biomech 2007; 40:2492-500. [PMID: 17198707 DOI: 10.1016/j.jbiomech.2006.11.005] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2006] [Accepted: 11/08/2006] [Indexed: 11/23/2022]
Abstract
Positively charged proteins can attach themselves to the negatively charged outer surface of biological cell membranes and liposomes. In this work, the influence of the intrinsic shape of the membrane-attached proteins on the elastic properties of the membrane is considered theoretically. It is shown that attachment of anisotropic proteins to the outer surface of biological membranes may induce tubulation of the membrane. The attachment of semi-flexible rod-like proteins increases the local bending constant, while the attachment of semi-flexible plate-like anisotropic proteins may also reduce the local bending constant of the membrane. The role of the hydrophobic protrusion of the attached protein which is embedded in the outer membrane layer is also discussed.
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Affiliation(s)
- Ales Iglic
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia.
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40
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Fosnaric M, Iglic A, May S. Influence of rigid inclusions on the bending elasticity of a lipid membrane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:051503. [PMID: 17279913 DOI: 10.1103/physreve.74.051503] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2006] [Indexed: 05/13/2023]
Abstract
We model the influence of rigid inclusions on the curvature elasticity of a lipid membrane. Our focus is on conelike transmembrane inclusions that are able to induce long-range deformations in the host bilayer membrane. The elastic properties of the membrane are described in terms of curvature and tilt elasticity. The latter adds an additional degree of freedom that allows the membrane to accommodate an inclusion not only through a curvature deformation but also via changes in lipid tilt. Using a (mean-field level) cell model for homogeneously distributed inclusions in a small membrane segment of prescribed (mesoscopic-scale) spherical shape, we calculate the optimal microscopic-scale deviation of the membrane shape around the intercalated inclusions and the corresponding free energy, analytically. We show that the lipid tilt degree of freedom can lead to local softening of the inclusion-containing lipid bilayer segment. The predicted softening requires a sufficiently small value of the tilt modulus; its origin lies in the reduction of the excess membrane-inclusion interaction energy. We compare our results to the case of suppressed microscopic shape relaxation. Here, too, local softening of the membrane is possible.
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Affiliation(s)
- Miha Fosnaric
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Trzaska 25, SI-1000 Ljubljana, Slovenia.
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41
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Abstract
Despite continual membrane reorganization in the Golgi complex, the number of cisternae in a Golgi stack is a stable parameter. The cisternal number is conserved within any given cell line and also after Golgi reassembly, e.g. following brefeldin-A-induced disruption. However, the factors that determine the cisternal number in a single Golgi stack remain to be fully determined. We propose a simple mechanical model of the Golgi stack and present a theoretical analysis of different physical factors that may affect the number of cisternae in a Golgi stack. The model takes into account the Golgi membrane bending elasticity, which is related to the membrane curvature, and the adhesion, which holds the cisternae together. The analysis shows that the equilibrium configuration of the Golgi stack can be regarded as a balance between these two effects - the adhesion, which tends to increase the number of cisternae, is opposed by the membrane resistance to bending, which does not favor highly curved cisternal rims. The adhesion strength that is needed to hold together a typical stack is calculated. In addition, the model is used to analyze changes in the cisternal numbers as a controlled traffic wave enters a Golgi stack and increases the amount of the membrane in that stack.
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Affiliation(s)
- Jure Derganc
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Slovenia.
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42
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Bozic B, Kralj-Iglic V, Svetina S. Coupling between vesicle shape and lateral distribution of mobile membrane inclusions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:041915. [PMID: 16711844 DOI: 10.1103/physreve.73.041915] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2005] [Revised: 02/06/2006] [Indexed: 05/09/2023]
Abstract
Membrane inclusions such as membrane-embedded peptides or proteins exhibit a curvature-dependent interaction with the surrounding lipid matrix due to the mismatch between their intrinsic curvature and the local membrane curvature. This interaction causes an inhomogeneous lateral distribution of the inclusions and a corresponding adjustment of the vesicle shape. We have studied theoretically the axisymmetric equilibrium shapes of lipid vesicles with mobile inclusions, taking into account that the membrane free energy includes the elastic energy of the lipid bilayer and a contribution due to an inclusion-membrane interaction. Equations describing the shape are derived by minimizing the total free energy at fixed membrane area, enclosed volume, and number of inclusions and are then solved numerically. It is shown that vesicle shape may assume a symmetry that differs from that of the vesicle with no inclusions. If the inclusion-membrane interaction exceeds a certain value, there is no axisymmetric solution of the equations with a continuous and derivable lateral density of inclusions over the whole area of the vesicle. When approaching the critical vesicle shape, the shapes obtained differ qualitatively from those described by the area difference elasticity model of the elastic properties of lipid membranes. In general, vesicle shapes adjust to the presence of inclusions by increasing regions with favorable curvature and decreasing regions of unfavorable curvature in a way such that the lateral distribution of inclusions becomes inhomogeneous.
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Affiliation(s)
- Bojan Bozic
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipiceva 2, SI-1000 Ljubljana, Slovenia.
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43
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Iglic A, Hägerstrand H, Veranic P, Plemenitas A, Kralj-Iglic V. Curvature-induced accumulation of anisotropic membrane components and raft formation in cylindrical membrane protrusions. J Theor Biol 2005; 240:368-73. [PMID: 16277995 DOI: 10.1016/j.jtbi.2005.09.020] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2005] [Revised: 08/02/2005] [Accepted: 09/27/2005] [Indexed: 10/25/2022]
Abstract
Coupling between the area density of anisotropic membrane inclusions and local membrane curvature is considered theoretically for a simple case of nearly flat bilayer membrane with thin tubular membrane protrusions. Lateral phase separation, i.e. accumulation of membrane inclusions in tubular membrane protrusions was obtained for strongly anisotropic inclusions if the radius of tubular protrusions is small enough. In accordance with these theoretical predictions we observed persistence of long tubular membrane protrusions devoid of internal rod-like microtubular structure in cells. We suggest that the stability of the tubular membrane protrusions without the inner supporting rod-like cytoskeleton is a consequence of the accumulation of anisotropic membrane components in the bilayer membrane of these protrusions. Based on the presented theoretical and experimental results it is suggested that previously reported concentration of prominin rafts in thin tubular membrane protrusions may be caused by a curvature-induced accumulation of small prominin-lipid complexes (inclusions) in protrusions and their coalescence into larger rafts.
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Affiliation(s)
- Ales Iglic
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Trzaska 25, SI-1000 Ljubljana, Slovenia.
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44
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Vitkova V, Méléard P, Pott T, Bivas I. Alamethicin influence on the membrane bending elasticity. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2005; 35:281-6. [PMID: 16211403 DOI: 10.1007/s00249-005-0019-5] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2005] [Revised: 08/22/2005] [Accepted: 08/25/2005] [Indexed: 11/25/2022]
Abstract
We investigate the bending elasticity of lipid membranes with the increase of the alamethicin concentrations in the membrane via analysis of the thermally induced shape fluctuations of quasi-spherical giant vesicles. Our experimental results prove the strong influence of alamethicin molecules on the bending elasticity of diphytanoyl phosphatidylcholine and dilauroyl phosphatidylcholine membranes even in the range of very low peptide concentrations (less than 10(-3) mol/mol in the membrane). The results presented in this work, testify to the peripheral orientation of alamethicin molecules at low peptide concentrations in the membrane for both types of lipid bilayers. An upper limit of the concentration of the peptide in the membrane is determined below which the system behaves as an ideal two-dimensional solution and the peptide molecules have a planar orientation in the membrane.
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Affiliation(s)
- Victoria Vitkova
- Liquid Crystal Laboratory, Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria
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45
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Kralj-Iglic V, Hägerstrand H, Veranic P, Jezernik K, Babnik B, Gauger DR, Iglic A. Amphiphile-induced tubular budding of the bilayer membrane. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2005; 34:1066-70. [PMID: 15997398 DOI: 10.1007/s00249-005-0481-0] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2005] [Accepted: 02/28/2005] [Indexed: 11/26/2022]
Abstract
Amphiphile-induced tubular budding of the erythrocyte membrane was studied using transmission electron microscopy. No chiral patterns of the intramembraneous particles were found, either on the cylindrical buds, or on the tubular nanoexovesicles. In agreement with these observations, the tubular budding may be explained by in-plane ordering of anisotropic membrane inclusions in the buds where the difference between the principal membrane curvatures is very large. In contrast to previously reported theories, no direct external mechanical force is needed to explain tubular budding of the bilayer membrane.
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Affiliation(s)
- Veronika Kralj-Iglic
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipiceva 2, 1000 Ljubljana, Slovenia
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46
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Hägerstrand H, Kralj-Iglic V, Fosnaric M, Bobrowska-Hägerstrand M, Wróbel A, Mrówczyńska L, Söderström T, Iglic A. Endovesicle formation and membrane perturbation induced by polyoxyethyleneglycolalkylethers in human erythrocytes. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2004; 1665:191-200. [PMID: 15471585 DOI: 10.1016/j.bbamem.2004.08.010] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2003] [Revised: 08/19/2004] [Accepted: 08/26/2004] [Indexed: 11/20/2022]
Abstract
Polyoxyethyleneglycolalkylether (CmEn, m=12, n=8) can induce a large torocyte-like endovesicle in human erythrocytes. The present study aimed to examine how variations in the molecular structure of CmEn (m=10,12,14,16,18; n=1-10,23) affect the occurrence of torocyte endovesicles. Our results show that torocytes occur most frequently when m=12,14 and n=8,9. At this molecular configuration the detergents induce inward membrane bending (stomatocytic S1-S2 shapes) resulting in the formation of a large membrane invagination. These detergents have a strong membrane perturbing, i.e., haemolytic, effect. Theoretical calculations indicate that a torocyte-shaped inside-out membrane vesicle can be created from a large membrane invagination due to the impact of laterally mobile anisotropic membrane inclusions. Such inclusions may be detergent-membrane component complexes or unanchored integral membrane proteins. It is shown that a nonhomogeneous lateral distribution of anisotropic membrane inclusions may stabilise the torocyte endovesicle shape, characterised by having opposite membranes in the thin central region of the vesicles separated by a certain distance. Tubular, conical or inverted conical isotropic inclusions cannot do so.
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Affiliation(s)
- Henry Hägerstrand
- Department of Biology, Abo Akademi University, Biocity, FIN-20520, Abo/Turku, Finland.
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47
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Bozic B, Svetina S. A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2004; 33:565-71. [PMID: 15095026 DOI: 10.1007/s00249-004-0404-5] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2003] [Revised: 02/27/2004] [Accepted: 03/16/2004] [Indexed: 10/26/2022]
Abstract
Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.
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Affiliation(s)
- B Bozic
- Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipiceva 2, 1000 Ljubljana, Slovenia
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48
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Fošnarič M, Kralj-Iglič V, Bohinc K, Iglič A, May S. Stabilization of Pores in Lipid Bilayers by Anisotropic Inclusions. J Phys Chem B 2003. [DOI: 10.1021/jp035035a] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Miha Fošnarič
- Laboratory of Applied Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia, Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, SI-1000 Ljubljana, Slovenia, and Institute of Molecular Biology, Friedrich-Schiller-University, Winzerlaer Strasse 10, Jena 07745, Germany
| | - Veronika Kralj-Iglič
- Laboratory of Applied Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia, Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, SI-1000 Ljubljana, Slovenia, and Institute of Molecular Biology, Friedrich-Schiller-University, Winzerlaer Strasse 10, Jena 07745, Germany
| | - Klemen Bohinc
- Laboratory of Applied Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia, Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, SI-1000 Ljubljana, Slovenia, and Institute of Molecular Biology, Friedrich-Schiller-University, Winzerlaer Strasse 10, Jena 07745, Germany
| | - Aleš Iglič
- Laboratory of Applied Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia, Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, SI-1000 Ljubljana, Slovenia, and Institute of Molecular Biology, Friedrich-Schiller-University, Winzerlaer Strasse 10, Jena 07745, Germany
| | - Sylvio May
- Laboratory of Applied Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia, Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Lipičeva 2, SI-1000 Ljubljana, Slovenia, and Institute of Molecular Biology, Friedrich-Schiller-University, Winzerlaer Strasse 10, Jena 07745, Germany
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49
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Babnik B, Miklavcic D, Kanduser M, Hägerstrand H, Kralj-Iglic V, Iglic A. Shape transformation and burst of giant POPC unilamellar liposomes modulated by non-ionic detergent C12E8. Chem Phys Lipids 2003; 125:123-38. [PMID: 14499471 DOI: 10.1016/s0009-3084(03)00084-7] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We studied spontaneous shape transformations and burst of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) vesicles with exogeneously added non-ionic detergent octaethylene-glycol dodecylether C(12)E(8). The addition of C(12)E(8) increased the speed of the vesicle shape transformation, so that we were able to study for the first time the complete sequence of POPC vesicle shapes starting from initial spherical vesicle with long thin tubular protrusion to final shape with invagination(s). The average mean curvature of the vesicle membrane continuously decreases during this process. The shape of the invaginations is usually spherical, however also non-spherical shapes of invaginations were observed. C(12)E(8) increases amplitudes of the fluctuations of the vesicle membrane. At higher concentrations in the membrane, C(12)E(8) induces the membrane leakage and burst of the vesicles.
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Affiliation(s)
- Blaz Babnik
- Faculty of Electrical Engineering, University of Ljubljana, Trzaska 25, SI-1000, Ljubljana, Slovenia
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50
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Kandušer M, Fošnarič M, Šentjurc M, Kralj-Iglič V, Hägerstrand H, Iglič A, Miklavčič D. Effect of surfactant polyoxyethylene glycol (C12E8) on electroporation of cell line DC3F. Colloids Surf A Physicochem Eng Asp 2003. [DOI: 10.1016/s0927-7757(02)00410-7] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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