1
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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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2
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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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3
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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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4
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Lipowsky R, Dimova R. Introduction to remodeling of biomembranes. SOFT MATTER 2021; 17:214-221. [PMID: 33406179 DOI: 10.1039/d0sm90234a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In general, biomembranes and giant vesicles can respond to cues in their aqueous environment by remodeling their molecular composition, shape, or topology. This themed collection focuses on remodeling of membrane shape which is intimately related to membrane curvature. In this introductory contribution, we clarify the different notions of curvature and describe the general nanoscopic mechanisms for curvature generation and membrane scaffolding. At the end, we give a brief outlook on membrane tension.
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Affiliation(s)
- Reinhard Lipowsky
- Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany.
| | - Rumiana Dimova
- Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany.
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5
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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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6
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Goychuk A, Frey E. Protein Recruitment through Indirect Mechanochemical Interactions. PHYSICAL REVIEW LETTERS 2019; 123:178101. [PMID: 31702232 DOI: 10.1103/physrevlett.123.178101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Indexed: 06/10/2023]
Abstract
Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.
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Affiliation(s)
- Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
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7
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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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8
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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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9
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Campelo F, van Galen J, Turacchio G, Parashuraman S, Kozlov MM, García-Parajo MF, Malhotra V. Sphingomyelin metabolism controls the shape and function of the Golgi cisternae. eLife 2017; 6. [PMID: 28500756 PMCID: PMC5462544 DOI: 10.7554/elife.24603] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Accepted: 05/04/2017] [Indexed: 12/11/2022] Open
Abstract
The flat Golgi cisterna is a highly conserved feature of eukaryotic cells, but how is this morphology achieved and is it related to its function in cargo sorting and export? A physical model of cisterna morphology led us to propose that sphingomyelin (SM) metabolism at the trans-Golgi membranes in mammalian cells essentially controls the structural features of a Golgi cisterna by regulating its association to curvature-generating proteins. An experimental test of this hypothesis revealed that affecting SM homeostasis converted flat cisternae into highly curled membranes with a concomitant dissociation of membrane curvature-generating proteins. These data lend support to our hypothesis that SM metabolism controls the structural organization of a Golgi cisterna. Together with our previously presented role of SM in controlling the location of proteins involved in glycosylation and vesicle formation, our data reveal the significance of SM metabolism in the structural organization and function of Golgi cisternae. DOI:http://dx.doi.org/10.7554/eLife.24603.001 The Golgi complex is a hub inside cells that transports many proteins to various parts of the cell. It also receives freshly made proteins and modifies them to help them mature into their final active forms. The complex is made up of a stack of disc-like membrane structures called cisternae. Are the shapes of the cisternae important for the Golgi complex to work properly? Membranes are made of mixtures of molecules known as lipids and proteins. Previous experiments show that when the mixture of lipids in the Golgi membranes changes in a specific manner, the cisternae curl into an onion-like shape and the Golgi cannot process or send out proteins anymore. Campelo et al. used mathematics and experimental approaches to investigate what causes the Golgi to change shape when the lipid mixture of the cisternae changes. A mathematical description of the shape of the Golgi predicted that some proteins keep the cisternae flat by holding the membrane rim that connects the two faces of a cisterna. To test this prediction, Campelo et al. performed experiments in human cells, which showed that when the mixture of lipids in the Golgi membranes changes, certain proteins jump from the rim, causing the cisternae to curl. These same proteins are also needed to transport cargo proteins out of the Golgi, meaning that there is a connection between the shape of the Golgi and the tasks it carries out. The shape of the Golgi complex is altered in Alzheimer’s disease and many other neurodegenerative diseases. The next challenges are to understand how these shape changes happen, how this affects cells, and if it could be possible to develop drugs that prevent these changes from occurring in patients. DOI:http://dx.doi.org/10.7554/eLife.24603.002
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Affiliation(s)
- Felix Campelo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - Josse van Galen
- Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain.,Universitat Pompeu Fabra, Barcelona, Spain
| | - Gabriele Turacchio
- Institute of Protein Biochemistry, National Research Council of Italy, Naples, Italy
| | | | - Michael M Kozlov
- Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - María F García-Parajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain.,Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
| | - Vivek Malhotra
- Centre for Genomic Regulation, The Barcelona Institute of Science and Technology, Barcelona, Spain.,Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain.,Universitat Pompeu Fabra, Barcelona, Spain
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10
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Rosholm KR, Leijnse N, Mantsiou A, Tkach V, Pedersen SL, Wirth VF, Oddershede LB, Jensen KJ, Martinez KL, Hatzakis NS, Bendix PM, Callan-Jones A, Stamou D. Membrane curvature regulates ligand-specific membrane sorting of GPCRs in living cells. Nat Chem Biol 2017; 13:724-729. [DOI: 10.1038/nchembio.2372] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Accepted: 02/02/2017] [Indexed: 11/09/2022]
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11
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Mally M, Božič B, Hartman SV, Klančnik U, Mur M, Svetina S, Derganc J. Controlled shaping of lipid vesicles in a microfluidic diffusion chamber. RSC Adv 2017. [DOI: 10.1039/c7ra05584f] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
The chemical environment around flaccid lipid vesicles, i.e., the osmotic conditions and the concentration of membrane-shaping molecules, is regulated only by diffusion without any hydrodynamic flow.
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Affiliation(s)
- M. Mally
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - B. Božič
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - S. Vrhovec Hartman
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - U. Klančnik
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - M. Mur
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - S. Svetina
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
| | - J. Derganc
- Institute of Biophysics
- Faculty of Medicine
- University of Ljubljana
- Ljubljana
- Slovenia
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12
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Bernardino de la Serna J, Schütz GJ, Eggeling C, Cebecauer M. There Is No Simple Model of the Plasma Membrane Organization. Front Cell Dev Biol 2016; 4:106. [PMID: 27747212 PMCID: PMC5040727 DOI: 10.3389/fcell.2016.00106] [Citation(s) in RCA: 97] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2016] [Accepted: 09/14/2016] [Indexed: 12/29/2022] Open
Abstract
Ever since technologies enabled the characterization of eukaryotic plasma membranes, heterogeneities in the distributions of its constituents were observed. Over the years this led to the proposal of various models describing the plasma membrane organization such as lipid shells, picket-and-fences, lipid rafts, or protein islands, as addressed in numerous publications and reviews. Instead of emphasizing on one model we in this review give a brief overview over current models and highlight how current experimental work in one or the other way do not support the existence of a single overarching model. Instead, we highlight the vast variety of membrane properties and components, their influences and impacts. We believe that highlighting such controversial discoveries will stimulate unbiased research on plasma membrane organization and functionality, leading to a better understanding of this essential cellular structure.
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Affiliation(s)
- Jorge Bernardino de la Serna
- Science and Technology Facilities Council, Rutherford Appleton Laboratory, Central Laser Facility, Research Complex at Harwell Harwell, UK
| | - Gerhard J Schütz
- Institute of Applied Physics, Technische Universität Wien Wien, Austria
| | - Christian Eggeling
- MRC Human Immunology Unit, Weatherall Institute of Molecular Medicine, University of Oxford Headley Way, UK
| | - Marek Cebecauer
- Department of Biophysical Chemistry, J.Heyrovsky Institute of Physical Chemistry, Czech Academy of Sciences Prague, Czech Republic
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13
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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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14
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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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15
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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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16
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Aimon S, Callan-Jones A, Berthaud A, Pinot M, Toombes GES, Bassereau P. Membrane shape modulates transmembrane protein distribution. Dev Cell 2014; 28:212-8. [PMID: 24480645 DOI: 10.1016/j.devcel.2013.12.012] [Citation(s) in RCA: 158] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2013] [Revised: 07/22/2013] [Accepted: 12/19/2013] [Indexed: 01/01/2023]
Abstract
Although membrane shape varies greatly throughout the cell, the contribution of membrane curvature to transmembrane protein targeting is unknown because of the numerous sorting mechanisms that take place concurrently in cells. To isolate the effect of membrane shape, we used cell-sized giant unilamellar vesicles (GUVs) containing either the potassium channel KvAP or the water channel AQP0 to form membrane nanotubes with controlled radii. Whereas the AQP0 concentrations in flat and curved membranes were indistinguishable, KvAP was enriched in the tubes, with greater enrichment in more highly curved membranes. Fluorescence recovery after photobleaching measurements showed that both proteins could freely diffuse through the neck between the tube and GUV, and the effect of each protein on membrane shape and stiffness was characterized using a thermodynamic sorting model. This study establishes the importance of membrane shape for targeting transmembrane proteins and provides a method for determining the effective shape and flexibility of membrane proteins.
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Affiliation(s)
- Sophie Aimon
- Centre de Recherche, Institut Curie, Paris F-75248, France; CNRS, PhysicoChimie Curie, UMR168, Paris F-75248, France; Université Pierre et Marie Curie, Paris F-75252, France; Kavli Institute for Brain and Mind, UCSD, La Jolla, CA 92093, USA
| | - Andrew Callan-Jones
- Laboratoire Matière et Systèmes Complexes, CNRS/Université Paris-Diderot, UMR 7057, 75205 Paris Cedex 13, France
| | - Alice Berthaud
- Centre de Recherche, Institut Curie, Paris F-75248, France; CNRS, PhysicoChimie Curie, UMR168, Paris F-75248, France; Université Pierre et Marie Curie, Paris F-75252, France; CelTisPhyBio Labex, Paris Sciences et Lettres, 75005 Paris, France
| | - Mathieu Pinot
- Centre de Recherche, Institut Curie, Paris F-75248, France; CelTisPhyBio Labex, Paris Sciences et Lettres, 75005 Paris, France; CNRS, Subcellular Structure and Cellular Dynamics, UMR144, Paris F-75248, France
| | - Gilman E S Toombes
- Molecular Physiology and Biophysics Section, Porter Neuroscience Research Center, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892-3017, USA.
| | - Patricia Bassereau
- Centre de Recherche, Institut Curie, Paris F-75248, France; CNRS, PhysicoChimie Curie, UMR168, Paris F-75248, France; Université Pierre et Marie Curie, Paris F-75252, France; CelTisPhyBio Labex, Paris Sciences et Lettres, 75005 Paris, France
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17
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Mercker M, Ptashnyk M, Kühnle J, Hartmann D, Weiss M, Jäger W. A multiscale approach to curvature modulated sorting in biological membranes. J Theor Biol 2012; 301:67-82. [DOI: 10.1016/j.jtbi.2012.01.039] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2011] [Revised: 01/26/2012] [Accepted: 01/27/2012] [Indexed: 11/29/2022]
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18
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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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19
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Kabaso D, Gongadze E, Jorgačevski J, Kreft M, Van Rienen U, Zorec R, Iglič A. Exploring the binding dynamics of BAR proteins. Cell Mol Biol Lett 2011; 16:398-411. [PMID: 21614490 PMCID: PMC6275656 DOI: 10.2478/s11658-011-0013-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2010] [Accepted: 05/11/2011] [Indexed: 11/20/2022] Open
Abstract
We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.
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Affiliation(s)
- Doron Kabaso
- Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000, Ljubljana, Slovenia.
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20
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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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21
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Tian A, Capraro BR, Esposito C, Baumgart T. Bending stiffness depends on curvature of ternary lipid mixture tubular membranes. Biophys J 2009; 97:1636-46. [PMID: 19751668 DOI: 10.1016/j.bpj.2009.07.012] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2009] [Revised: 07/01/2009] [Accepted: 07/13/2009] [Indexed: 12/14/2022] Open
Abstract
Lipid and protein sorting and trafficking in intracellular pathways maintain cellular function and contribute to organelle homeostasis. Biophysical aspects of membrane shape coupled to sorting have recently received increasing attention. Here we determine membrane tube bending stiffness through measurements of tube radii, and demonstrate that the stiffness of ternary lipid mixtures depends on membrane curvature for a large range of lipid compositions. This observation indicates amplification by curvature of cooperative lipid demixing. We show that curvature-induced demixing increases upon approaching the critical region of a ternary lipid mixture, with qualitative differences along two roughly orthogonal compositional trajectories. Adapting a thermodynamic theory earlier developed by M. Kozlov, we derive an expression that shows the renormalized bending stiffness of an amphiphile mixture membrane tube in contact with a flat reservoir to be a quadratic function of curvature. In this analytical model, the degree of sorting is determined by the ratio of two thermodynamic derivatives. These derivatives are individually interpreted as a driving force and a resistance to curvature sorting. We experimentally show this ratio to vary with composition, and compare the model to sorting by spontaneous curvature. Our results are likely to be relevant to the molecular sorting of membrane components in vivo.
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Affiliation(s)
- Aiwei Tian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania, USA
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22
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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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23
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Balazs AC, Kuksenok O, Alexeev A. Modeling the Interactions between Membranes and Inclusions: Designing Self-Cleaning Films and Resealing Pores. MACROMOL THEOR SIMUL 2009. [DOI: 10.1002/mats.200800057] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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24
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Nowak SA, Chou T. Membrane lipid segregation in endocytosis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021908. [PMID: 18850866 DOI: 10.1103/physreve.78.021908] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2008] [Indexed: 05/26/2023]
Abstract
We explore the equilibrium mechanics of a binary lipid membrane that wraps around a spherical or cylindrical particle. One of the lipid membrane components induces a positive spontaneous curvature, while the other induces a negative local curvature. Using a Hamiltonian approach, we derive the equations governing the membrane shape and lipid concentrations near the wrapped object. Asymptotic expressions and numerical solutions for membrane shapes are presented. We determine the regimes of bending rigidity, surface tension, intrinsic lipid curvature, and effective receptor binding energies that lead to efficient wrapping and endocytosis. Our model is directly applicable to the study of invagination of clathrin-coated pits and receptor-induced wrapping of colloids such as spherical virus particles.
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Affiliation(s)
- Sarah A Nowak
- Department of Biomathematics, David Geffen School of Medicine, UCLA, Los Angeles, California 90095-1766, USA
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25
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Alexeev A, Uspal WE, Balazs AC. Harnessing janus nanoparticles to create controllable pores in membranes. ACS NANO 2008; 2:1117-1122. [PMID: 19206328 DOI: 10.1021/nn8000998] [Citation(s) in RCA: 138] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We use a coarse-grained numerical simulation to design a synthetic membrane with stable pores that can be controllably opened and closed. Specifically, we use dissipative particle dynamics to probe the interactions between lipid bilayer membranes and nanoparticles. The particles are nanoscopic Janus beads that comprise both hydrophobic and hydrophilic portions. We demonstrate that when the membrane rips and forms a hole due to an external stress, these nanoparticles diffuse to the edge of the hole and form a stable pore, which persists after the stress is released. Once the particle-lined pore is formed, a small increase in membrane tension readily reopens the pore, allowing transport through the membrane. Besides the application of an external force, the membrane tension can be altered by varying, for example, temperature or pH. Thus, the findings provide guidelines for designing nanoparticle-bilayer assemblies for targeted delivery, where the pores open and the cargo is released only when the local environmental conditions reach a critical value.
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Affiliation(s)
- Alexander Alexeev
- George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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26
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Cocquyt J, Soenen SJH, Saveyn P, Van der Meeren P, De Cuyper M. Partitioning of propranolol in the phospholipid bilayer coat of anionic magnetoliposomes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:204102. [PMID: 21694232 DOI: 10.1088/0953-8984/20/20/204102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This work deals with the partitioning of the cationic amphiphilic drug, propranolol, in the coating of so-called magnetoliposomes (MLs), which consist of nanometre-sized, magnetizable iron oxide cores covered with a phospholipid bilayer. MLs of two types were used: either the ML coat consisted entirely of anionic dimyristoylphosphatidylglycerol, or it was mixed with zwitterionic dimyristoylphosphatidylcholine in a 5/95 molar ratio. To separate sorbed from non-sorbed propranolol, high-gradient magnetophoresis was used. The sorption profiles clearly show that electrostatic interactions play a key role in the sorption process as drug incorporation in the ML coat was favoured by increasing the anionic character of the ML envelope and by reducing the salt concentration of the medium. Also, upon drug binding some phospholipid molecules were expelled from the ML coat. The observations may be of relevance in the biomedical field, i.e. in the development of ML-based, intracellular theranostics.
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Affiliation(s)
- J Cocquyt
- Particle and Interfacial Technology Group, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium
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27
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Attachment of beta 2-glycoprotein I to negatively charged liposomes may prevent the release of daughter vesicles from the parent membrane. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2008; 37:1085-95. [PMID: 18188552 DOI: 10.1007/s00249-007-0252-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2007] [Revised: 11/27/2007] [Accepted: 12/13/2007] [Indexed: 12/16/2022]
Abstract
The temperature-induced budding of POPC-cardiolipin-cholesterol, POPC-POPS-cholesterol and POPC-POPG-cholesterol giant lipid vesicles in the presence of beta 2-glycoprotein I (beta 2-GPI) in the outer solution was studied experimentally and theoretically. The observed budding transition of vesicles was continuous which can be explained by taking into account the orientational ordering and direct interactions between oriented lipids. The attachment of positively charged beta 2-GPI to the negatively charged outer surface of POPC-cardiolipin-cholesterol, POPC-POPS-cholesterol and POPC-POPG-cholesterol giant vesicles caused coalescence of the spheroidal membrane bud with the parent vesicle before the bud could detach from the parent vesicle, i.e. vesiculate. Theoretically, the protein-mediated attraction between the membrane of a bud and the parent membrane was described as an interaction between two electric double layers. It was shown that the specific spatial distribution of charge within beta 2-GPI molecules attached to the negatively charged membrane surface may explain the observed attraction between like-charged membrane surfaces.
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28
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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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29
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Derganc J. Curvature-driven lateral segregation of membrane constituents in Golgi cisternae. Phys Biol 2007; 4:317-24. [DOI: 10.1088/1478-3975/4/4/008] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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30
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Abstract
Formation of protrusions and protein segregation on the membrane is of a great importance for the functioning of the living cell. This is most evident in recent experiments that show the effects of the mechanical properties of the surrounding substrate on cell morphology. We propose a mechanism for the formation of membrane protrusions and protein phase separation, which may lay behind this effect. In our model, the fluid cell membrane has a mobile but constant population of proteins with a convex spontaneous curvature. Our basic assumption is that these membrane proteins represent small adhesion complexes, and also include proteins that activate actin polymerization. Such a continuum model couples the membrane and protein dynamics, including cell-substrate adhesion and protrusive actin force. Linear stability analysis shows that sufficiently strong adhesion energy and actin polymerization force can bring about phase separation of the membrane protein and the appearance of protrusions. Specifically, this occurs when the spontaneous curvature and aggregation potential alone (passive system) do not cause phase separation. Finite-size patterns may appear in the regime where the spontaneous curvature energy is a strong factor. Different instability characteristics are calculated for the various regimes, and are compared to various types of observed protrusions and phase separations, both in living cells and in artificial model systems. A number of testable predictions are proposed.
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Affiliation(s)
- Alex Veksler
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, Israel.
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31
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Iglic A, Lokar M, Babnik B, Slivnik T, Veranic P, Hägerstrand H, Kralj-Iglic V. Possible role of flexible red blood cell membrane nanodomains in the growth and stability of membrane nanotubes. Blood Cells Mol Dis 2007; 39:14-23. [PMID: 17475520 DOI: 10.1016/j.bcmd.2007.02.013] [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: 02/03/2007] [Accepted: 02/03/2007] [Indexed: 11/26/2022]
Abstract
Tubular budding of the erythrocyte membrane may be induced by exogenously added substances. It is shown that tubular budding may be explained by self-assembly of anisotropic membrane nanodomains into larger domains forming nanotubular membrane protrusions. In contrast to some previously reported theories, no direct external mechanical force is needed to explain the observed tubular budding of the bilayer membrane. The mechanism that explains tubular budding may also be responsible for stabilization of the thin tubes that connect cells or cell organelles and which might be important for the transport of matter and information in cellular systems. It is shown that small carrier vesicles (gondolas), transporting enclosed material or the molecules composing their membrane, may travel over long distances along the nanotubes connecting two cells.
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Affiliation(s)
- Ales Iglic
- Laboratory of Physics, University of Ljubljana, Ljubljana, Slovenia.
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32
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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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33
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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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