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Janssen M, Liese S, Al-Izzi SC, Carlson A. Stability of a biomembrane tube covered with proteins. Phys Rev E 2024; 109:044403. [PMID: 38755805 DOI: 10.1103/physreve.109.044403] [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: 09/28/2022] [Accepted: 02/29/2024] [Indexed: 05/18/2024]
Abstract
Membrane tubes are essential structural features in cells that facilitate biomaterial transport and inter- and intracellular signaling. The shape of these tubes can be regulated by the proteins that surround and adhere to them. We study the stability of a biomembrane tube coated with proteins by combining linear stability analysis, out-of-equilibrium hydrodynamic calculations, and numerical solutions of a Helfrich-like membrane model. Our analysis demonstrates that both long- and short-wavelength perturbations can destabilize the tubes. Numerical simulations confirm the derived linear stability criteria and yield the nonlinearly perturbed vesicle shapes. Our study highlights the interplay between membrane shape and protein density, where the shape instability concurs with a redistribution of proteins into a banded pattern.
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Affiliation(s)
- Mathijs Janssen
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
- Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, N-0379 Oslo, Norway
- Norwegian University of Life Sciences, Faculty of Science and Technology, 1433 Ås, Norway
| | - Susanne Liese
- Institute of Physics, University of Augsburg, 86159 Augsburg, Germany
| | - Sami C Al-Izzi
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
| | - Andreas Carlson
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, 0315 Oslo, Norway
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Tchoufag J, Sahu A, Mandadapu KK. Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes. PHYSICAL REVIEW LETTERS 2022; 128:068101. [PMID: 35213207 DOI: 10.1103/physrevlett.128.068101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 09/01/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl-von Kármán number Γ and the recently introduced Scriven-Love number SL, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions-reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher-Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.
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Affiliation(s)
- Joël Tchoufag
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Amaresh Sahu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Zhang X, Kang R, Liu Y, Yan Z, Xu Y, Yue T. From reversible to irreversible: When the membrane nanotube pearling is coupled with phase separation. Colloids Surf B Biointerfaces 2021; 209:112160. [PMID: 34736219 DOI: 10.1016/j.colsurfb.2021.112160] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Revised: 09/17/2021] [Accepted: 10/07/2021] [Indexed: 12/11/2022]
Abstract
Membrane nanotubes, which are ubiquitous in biology and act as channels maintaining transport between different cells and organelles, readily undergo pearling in response to external stimuli. Membrane nanotube pearling involves generation of heterogeneous curvature coupled with redistribution of membrane components that may interfere with the shape recovery of pearled nanotubes. However, the mechanism underlying such delicate process remains unclear and difficult to study at the molecular scale in vivo. By means of molecular dynamics simulation, here we investigate pearling of multi-component membrane nanotubes and reversibility through manipulating system temperature and osmotic pressure. With the equilibrium shape of membrane nanotubes controlled by the osmotic pressure, our results demonstrate that the process of membrane nanotube pearling can be reversible or irreversible, depending on the phase segregation state. For the pearled nanotube releasing high surface energy, different lipid components redistribute along the tube axial direction. Lipids with unsaturated tails prefer gathering at the high-curvature shrinking region, whereas the swelling region is constituted by saturated lipids forming the liquid-ordered phase of a higher bending rigidity. Such curvature sensitive phase segregation minimizes the system free energy by reducing both the membrane bending energy and line tension at the phase boundary. As such, the pearled nanotube fails to recover its shape upon retracting stimuli, suggesting irreversibility of the membrane nanotube pearling coupled with phase separation. Given importance of membrane nanotube pearling in various cellular activities, these results provide a new mechanism of controlling equilibrium shapes of membrane nanotubes in complex cellular environment.
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Affiliation(s)
- Xiaoyang Zhang
- College of Chemical Engineering, China University of Petroleum (East China), Qingdao 266580, China
| | - Runshan Kang
- College of Chemical Engineering, China University of Petroleum (East China), Qingdao 266580, China
| | - Yingjie Liu
- Institute of Coastal Environmental Pollution Control, Key Laboratory of Marine Environment and Ecology, Ministry of Education, Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao 266100, China
| | - Zengshuai Yan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan Xu
- College of Electronic Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
| | - Tongtao Yue
- Institute of Coastal Environmental Pollution Control, Key Laboratory of Marine Environment and Ecology, Ministry of Education, Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao 266100, China; Laboratory for Marine Ecology and Environmental Science, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China.
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Patil N, Bonneau S, Joubert F, Bitbol AF, Berthoumieux H. Mitochondrial cristae modeled as an out-of-equilibrium membrane driven by a proton field. Phys Rev E 2021; 102:022401. [PMID: 32942462 DOI: 10.1103/physreve.102.022401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 06/27/2020] [Indexed: 01/27/2023]
Abstract
As the places where most of the fuel of the cell, namely, ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as a crista, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the crista shape remains unclear. In this work, we investigate the crista membrane deformations using a pH-dependent Helfrich model, maintained out of equilibrium by a diffusive flux of protons. This model gives rise to shape changes of a cylindrical invagination, in particular to the formation of necks between wider zones under variable, and especially oscillating, proton flux.
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Affiliation(s)
- Nirbhay Patil
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), Sorbonne Université, CNRS, F-75005 Paris, France.,Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Stéphanie Bonneau
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Fréderic Joubert
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France
| | - Anne-Florence Bitbol
- Laboratoire Jean Perrin (UMR 8237), Institut de Biologie Paris-Seine, Sorbonne Université, CNRS, F-75005 Paris, France.,School of Life Sciences, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Hélène Berthoumieux
- Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), Sorbonne Université, CNRS, F-75005 Paris, France
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Al-Izzi SC, Sens P, Turner MS, Komura S. Dynamics of passive and active membrane tubes. SOFT MATTER 2020; 16:9319-9330. [PMID: 32935733 DOI: 10.1039/d0sm01290d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) m-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.
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Affiliation(s)
- Sami C Al-Izzi
- School of Physics & EMBL-Australia node in Single Molecule Science, University of New South Wales, Sydney, Australia and Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK and Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France and Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Pierre Sens
- Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France and Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Matthew S Turner
- Department of Physics & Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, UK and Department of Chemical Engineering, University of Kyoto, Kyoto 615-8510, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
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Sahu A, Glisman A, Tchoufag J, Mandadapu KK. Geometry and dynamics of lipid membranes: The Scriven-Love number. Phys Rev E 2020; 101:052401. [PMID: 32575240 DOI: 10.1103/physreve.101.052401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 04/07/2020] [Indexed: 06/11/2023]
Abstract
The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven-Love number, and the well-known Föppl-von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl-von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl-von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces-with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.
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Affiliation(s)
- Amaresh Sahu
- Department of Chemical & Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Alec Glisman
- Department of Chemical & Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Joël Tchoufag
- Department of Chemical & Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Kranthi K Mandadapu
- Department of Chemical & Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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