1
|
Chen K, Wang Q, Yu X, Wang C, Gao J, Zhang S, Cheng S, You S, Zheng H, Lu J, Zhu X, Lei D, Jian A, He X, Yu H, Chen Y, Zhou M, Li K, He L, Tian Y, Liu X, Liu S, Jiang L, Bao Y, Wang H, Zhao Z, Wan J. OsSRF8 interacts with OsINP1 and OsDAF1 to regulate pollen aperture formation in rice. Nat Commun 2024; 15:4512. [PMID: 38802369 PMCID: PMC11130342 DOI: 10.1038/s41467-024-48813-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 05/14/2024] [Indexed: 05/29/2024] Open
Abstract
In higher plants, mature male gametophytes have distinct apertures. After pollination, pollen grains germinate, and a pollen tube grows from the aperture to deliver sperm cells to the embryo sac, completing fertilization. In rice, the pollen aperture has a single-pore structure with a collar-like annulus and a plug-like operculum. A crucial step in aperture development is the formation of aperture plasma membrane protrusion (APMP) at the distal polar region of the microspore during the late tetrad stage. Previous studies identified OsINP1 and OsDAF1 as essential regulators of APMP and pollen aperture formation in rice, but their precise molecular mechanisms remain unclear. We demonstrate that the Poaceae-specific OsSRF8 gene, encoding a STRUBBELIG-receptor family 8 protein, is essential for pollen aperture formation in Oryza sativa. Mutants lacking functional OsSRF8 exhibit defects in APMP and pollen aperture formation, like loss-of-function OsINP1 mutants. OsSRF8 is specifically expressed during early anther development and initially diffusely distributed in the microsporocytes. At the tetrad stage, OsSRF8 is recruited by OsINP1 to the pre-aperture region through direct protein-protein interaction, promoting APMP formation. The OsSRF8-OsINP1 complex then recruits OsDAF1 to the APMP site to co-regulate annulus formation. Our findings provide insights into the mechanisms controlling pollen aperture formation in cereal species.
Collapse
Affiliation(s)
- Keyi Chen
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Qiming Wang
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Xiaowen Yu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Chaolong Wang
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Junwen Gao
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Shihao Zhang
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Siqi Cheng
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Shimin You
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Hai Zheng
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Jiayu Lu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Xufei Zhu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Dekun Lei
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Anqi Jian
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Xiaodong He
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Hao Yu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Yun Chen
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Mingli Zhou
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Kai Li
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Ling He
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Yunlu Tian
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Xi Liu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Shijia Liu
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Ling Jiang
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China
| | - Yiqun Bao
- School of Life Sciences, Nanjing Agricultural University, Nanjing, 210095, China
| | - Haiyang Wang
- National Key Facility for Crop Gene Resources and Genetic Improvement, Institute of Crop Science, Chinese Academy of Agricultural Sciences, Beijing, 100081, China
| | - Zhigang Zhao
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China.
| | - Jianmin Wan
- State Key Laboratory for Crop Genetics & Germplasm Enhancement and Utilization, Nanjing Agricultural University, Zhongshan Biological Breeding Laboratory, Nanjing, 210095, China.
- National Key Facility for Crop Gene Resources and Genetic Improvement, Institute of Crop Science, Chinese Academy of Agricultural Sciences, Beijing, 100081, China.
| |
Collapse
|
2
|
Omar YAD, Lipel ZG, Mandadapu KK. (2+δ)-dimensional theory of the electromechanics of lipid membranes: Electrostatics. Phys Rev E 2024; 109:054401. [PMID: 38907464 DOI: 10.1103/physreve.109.054401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 02/13/2024] [Indexed: 06/24/2024]
Abstract
The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the (2+δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the (2+δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. This model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.
Collapse
Affiliation(s)
- Yannick A D Omar
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zachary G Lipel
- 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, California 94720, USA
| |
Collapse
|
3
|
Sadeghi M, Rosenberger D. Dynamic framework for large-scale modeling of membranes and peripheral proteins. Methods Enzymol 2024; 701:457-514. [PMID: 39025579 DOI: 10.1016/bs.mie.2024.03.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.
Collapse
Affiliation(s)
- Mohsen Sadeghi
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany.
| | | |
Collapse
|
4
|
Liu L, Duan C, Wang R. Kinetic pathway and micromechanics of fusion/fission for polyelectrolyte vesicles. J Chem Phys 2024; 160:024908. [PMID: 38214388 DOI: 10.1063/5.0185934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 12/26/2023] [Indexed: 01/13/2024] Open
Abstract
Despite the wide existence of vesicles in living cells as well as their important applications like drug delivery, the underlying mechanism of vesicle fusion/fission remains under debate. Classical models cannot fully explain recent observations in experiments and simulations. Here, we develop a constrained self-consistent field theory that allows tracking the shape evolution and free energy as a function of center-of-mass separation distance. Fusion and fission are described in a unified framework. Both the kinetic pathway and the mechanical response can be simultaneously captured. By taking vesicles formed by polyelectrolytes as a model system, we predict discontinuous transitions between the three morphologies: parent vesicle with a single cavity, hemifission/hemifusion, and two separated child vesicles, as a result of breaking topological isomorphism. With the increase in inter-vesicle repulsion, we observe a great reduction in the cleavage energy, indicating that vesicle fission can be achieved without hemifission, in good agreement with simulation results. The force-extension relationship elucidates typical plasticity for separating two vesicles. The super extensibility in the mechanical response of vesicle is in stark contrast to soft particles with other morphologies, such as cylinder and sphere. Our work elucidates the fundamental physical chemistry based on intrinsic topological features of vesicle fusion/fission, which provides insights into various phenomena observed in experiments and simulations.
Collapse
Affiliation(s)
- Luofu Liu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Chao Duan
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| | - Rui Wang
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley, California 94720, USA
| |
Collapse
|
5
|
Bhatnagar A, Nestler M, Gross P, Kramar M, Leaver M, Voigt A, Grill SW. Axis convergence in C. elegans embryos. Curr Biol 2023; 33:5096-5108.e15. [PMID: 37979577 DOI: 10.1016/j.cub.2023.10.050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 08/31/2023] [Accepted: 10/25/2023] [Indexed: 11/20/2023]
Abstract
Embryos develop in a surrounding that guides key aspects of their development. For example, the anteroposterior (AP) body axis is always aligned with the geometric long axis of the surrounding eggshell in fruit flies and worms. The mechanisms that ensure convergence of the AP axis with the long axis of the eggshell remain unresolved. We investigate axis convergence in early C. elegans development, where the nascent AP axis, when misaligned, actively re-aligns to converge with the long axis of the egg. We identify two physical mechanisms that underlie axis convergence. First, bulk cytoplasmic flows, driven by actomyosin cortical flows, can directly reposition the AP axis. Second, active forces generated within the pseudocleavage furrow, a transient actomyosin structure similar to a contractile ring, can drive a mechanical re-orientation such that it becomes positioned perpendicular to the long axis of the egg. This in turn ensures AP axis convergence. Numerical simulations, together with experiments that either abolish the pseudocleavage furrow or change the shape of the egg, demonstrate that the pseudocleavage-furrow-dependent mechanism is a major driver of axis convergence. We conclude that active force generation within the actomyosin cortical layer drives axis convergence in the early nematode.
Collapse
Affiliation(s)
- Archit Bhatnagar
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrase 108, Dresden 01037, Germany
| | - Michael Nestler
- Institute of Scientific Computing, Technische Universitӓt Dresden, Zellescher Weg 25, Dresden 01217, Germany
| | - Peter Gross
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrase 108, Dresden 01037, Germany; Biotechnology Center (BIOTEC), Technische Universitӓt Dresden, Tatzberg 47/49, Dresden 01307, Germany
| | - Mirna Kramar
- Biotechnology Center (BIOTEC), Technische Universitӓt Dresden, Tatzberg 47/49, Dresden 01307, Germany
| | - Mark Leaver
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrase 108, Dresden 01037, Germany
| | - Axel Voigt
- Institute of Scientific Computing, Technische Universitӓt Dresden, Zellescher Weg 25, Dresden 01217, Germany; Cluster of Excellence Physics of Life, Technische Universitӓt Dresden, Arnoldstrase 18, Dresden 01307, Germany; Center for Systems Biology Dresden, Pfotenhauerstrase 108, Dresden 01037, Germany.
| | - Stephan W Grill
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrase 108, Dresden 01037, Germany; Cluster of Excellence Physics of Life, Technische Universitӓt Dresden, Arnoldstrase 18, Dresden 01307, Germany; Center for Systems Biology Dresden, Pfotenhauerstrase 108, Dresden 01037, Germany.
| |
Collapse
|
6
|
Wang Z, Servio P, Rey AD. Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution. SOFT MATTER 2023. [PMID: 38031449 DOI: 10.1039/d3sm01164j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
We review our recent contributions to anisotropic soft matter models for liquid crystal interfaces, drops and membranes, emphasizing validations with experimental and biological data, and with related theory and simulation literature. The presentation aims to illustrate and characterize the rich output and future opportunities of using a methodology based on the liquid crystal-membrane shape equation applied to static and dynamic pattern formation phenomena. The geometry of static and kinetic shapes is usually described with dimensional curvatures that co-mingle shape and curvedness. In this review, we systematically show how the application of a novel decoupled shape-curvedness framework to practical and ubiquitous soft matter phenomena, such as the shape of drops and tactoids and bending of evolving membranes, leads to deeper quantitative insights than when using traditional dimensional mean and Gaussian curvatures. The review focuses only on (1) statics of wrinkling and shape selection in liquid crystal interfaces and membranes; (2) kinetics and dissipative dynamics of shape evolution in membranes; and (3) computational methods for shape selection and shape evolution; due to various limitations other important topics are excluded. Finally, the outlook follows a similar structure. The main results include: (1) single and multiple wavelength corrugations in liquid crystal interfaces appear naturally in the presence of surface splay and bend orientation distortions with scaling laws governed by ratios of anchoring-to-isotropic tension energy; adding membrane elasticity to liquid crystal anchoring generates multiple scales wrinkling as in tulips; drops of liquid crystals encapsulates in membranes can adopt, according to the ratios of anchoring/tension/bending, families of shapes as multilobal, tactoidal, and serrated as observed in biological cells. (2) Mapping the liquid crystal director to a membrane unit normal. The dissipative shape evolution model with irreversible thermodynamics for flows dominated by bending rates, yields new insights. The model explains the kinetic stability of cylinders, while spheres and saddles are attractors. The model also adds to the evolving understanding of outer hair cells in the inner ear. (3) Computational soft matter geometry includes solving shape equations, trajectories on energy and orientation landscapes, and shape-curvedness evolutions on entropy production landscape with efficient numerical methods and adaptive approaches.
Collapse
Affiliation(s)
- Ziheng Wang
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
| | - Phillip Servio
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
| | - Alejandro D Rey
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, H3A 2B2, Canada.
| |
Collapse
|
7
|
Quiroga X, Walani N, Disanza A, Chavero A, Mittens A, Tebar F, Trepat X, Parton RG, Geli MI, Scita G, Arroyo M, Le Roux AL, Roca-Cusachs P. A mechanosensing mechanism controls plasma membrane shape homeostasis at the nanoscale. eLife 2023; 12:e72316. [PMID: 37747150 PMCID: PMC10569792 DOI: 10.7554/elife.72316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 09/24/2023] [Indexed: 09/26/2023] Open
Abstract
As cells migrate and experience forces from their surroundings, they constantly undergo mechanical deformations which reshape their plasma membrane (PM). To maintain homeostasis, cells need to detect and restore such changes, not only in terms of overall PM area and tension as previously described, but also in terms of local, nanoscale topography. Here, we describe a novel phenomenon, by which cells sense and restore mechanically induced PM nanoscale deformations. We show that cell stretch and subsequent compression reshape the PM in a way that generates local membrane evaginations in the 100 nm scale. These evaginations are recognized by I-BAR proteins, which triggers a burst of actin polymerization mediated by Rac1 and Arp2/3. The actin polymerization burst subsequently re-flattens the evagination, completing the mechanochemical feedback loop. Our results demonstrate a new mechanosensing mechanism for PM shape homeostasis, with potential applicability in different physiological scenarios.
Collapse
Affiliation(s)
- Xarxa Quiroga
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
- Departament de Biomedicina, Unitat de Biofísica i Bioenginyeria, Facultat de Medicina i Ciències de la Salut, Universitat de BarcelonaBarcelonaSpain
| | - Nikhil Walani
- Department of Applied Mechanics, IIT DelhiNew DelhiIndia
| | - Andrea Disanza
- IFOM ETS - The AIRC Institute of Molecular OncologyMilanItaly
| | - Albert Chavero
- Departament de Biomedicina, Unitat de Biologia Cel·lular, Facultat de Medicina i Ciències de la Salut, Centre de Recerca Biomèdica CELLEX, Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Universitat de BarcelonaBarcelonaSpain
| | - Alexandra Mittens
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
| | - Francesc Tebar
- Departament de Biomedicina, Unitat de Biologia Cel·lular, Facultat de Medicina i Ciències de la Salut, Centre de Recerca Biomèdica CELLEX, Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), Universitat de BarcelonaBarcelonaSpain
| | - Xavier Trepat
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
| | - Robert G Parton
- Institute for Molecular Bioscience and Centre for Microscopy and Microanalysis, University of QueenslandBrisbaneAustralia
| | | | - Giorgio Scita
- IFOM ETS - The AIRC Institute of Molecular OncologyMilanItaly
- Department of Oncology and Haemato-Oncology, University of MilanMilanItaly
| | - Marino Arroyo
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
- Universitat Politècnica de Catalunya (UPC), Campus Nord, Carrer de Jordi GironaBarcelonaSpain
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)BarcelonaSpain
| | - Anabel-Lise Le Roux
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
| | - Pere Roca-Cusachs
- Institute for Bioengineering of Catalonia, the Barcelona Institute of Technology (BIST)BarcelonaSpain
- Departament de Biomedicina, Unitat de Biofísica i Bioenginyeria, Facultat de Medicina i Ciències de la Salut, Universitat de BarcelonaBarcelonaSpain
| |
Collapse
|
8
|
Santiago JA, Monroy F. Inhomogeneous Canham-Helfrich Abscission in Catenoid Necks under Critical Membrane Mosaicity. MEMBRANES 2023; 13:796. [PMID: 37755218 PMCID: PMC10534449 DOI: 10.3390/membranes13090796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Revised: 09/12/2023] [Accepted: 09/12/2023] [Indexed: 09/28/2023]
Abstract
The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous to neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution of necking forces is determined by the equilibrium mechanical equations and the boundary conditions as considered in the axisymmetric setting compatible with the necking process. To establish the role played by mechanical inhomogeneity, we focus on the catenoid, a surface of zero mean curvature. Analytic solutions are shown to exist for the spontaneous curvature and the constrictive forces in terms of the border radii. Our theoretical analysis shows that the inhomogeneous distribution of spontaneous curvature in a mosaic-like neck constrictional forces potentially contributes to the membrane scission under minimized work in living cells.
Collapse
Affiliation(s)
- José Antonio Santiago
- Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, Vasco de Quiroga 4871, Ciudad de México 05384, Mexico
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense s/n, 28040 Madrid, Spain;
- Translational Biophysics, Institute for Biomedical Research, Hospital Doce de Octubre (imas12), Av. Andalucía s/n, 28041 Madrid, Spain
| | - Francisco Monroy
- Departamento de Química Física, Universidad Complutense de Madrid, Av. Complutense s/n, 28040 Madrid, Spain;
- Translational Biophysics, Institute for Biomedical Research, Hospital Doce de Octubre (imas12), Av. Andalucía s/n, 28041 Madrid, Spain
| |
Collapse
|
9
|
Zhao Y, Feng X. Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1338. [PMID: 37420358 DOI: 10.3390/e24101338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Revised: 09/14/2022] [Accepted: 09/19/2022] [Indexed: 07/09/2023]
Abstract
In this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangential condition. The first-order backward Euler scheme and second-order BDF scheme are used to discretize the time separately, and the stability of the two schemes is analyzed. The mixed finite element pair (P2,P1) is applied to discretization of space. Finally, numerical examples are given to verify the accuracy and effectiveness of the proposed method.
Collapse
Affiliation(s)
- Yanzi Zhao
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Xinlong Feng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| |
Collapse
|
10
|
Frey F, Idema T. Membrane area gain and loss during cytokinesis. Phys Rev E 2022; 106:024401. [PMID: 36110005 DOI: 10.1103/physreve.106.024401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell's volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.
Collapse
Affiliation(s)
- Felix Frey
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, The Netherlands
| | - Timon Idema
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, The Netherlands
| |
Collapse
|
11
|
Mitchell NP, Cislo DJ, Shankar S, Lin Y, Shraiman BI, Streichan SJ. Visceral organ morphogenesis via calcium-patterned muscle constrictions. eLife 2022; 11:77355. [PMID: 35593701 PMCID: PMC9275821 DOI: 10.7554/elife.77355] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 05/08/2022] [Indexed: 11/24/2022] Open
Abstract
Organ architecture is often composed of multiple laminar tissues arranged in concentric layers. During morphogenesis, the initial geometry of visceral organs undergoes a sequence of folding, adopting a complex shape that is vital for function. Genetic signals are known to impact form, yet the dynamic and mechanical interplay of tissue layers giving rise to organs' complex shapes remains elusive. Here, we trace the dynamics and mechanical interactions of a developing visceral organ across tissue layers, from subcellular to organ scale in vivo. Combining deep tissue light-sheet microscopy for in toto live visualization with a novel computational framework for multilayer analysis of evolving complex shapes, we find a dynamic mechanism for organ folding using the embryonic midgut of Drosophila as a model visceral organ. Hox genes, known regulators of organ shape, control the emergence of high-frequency calcium pulses. Spatiotemporally patterned calcium pulses trigger muscle contractions via myosin light chain kinase. Muscle contractions, in turn, induce cell shape change in the adjacent tissue layer. This cell shape change collectively drives a convergent extension pattern. Through tissue incompressibility and initial organ geometry, this in-plane shape change is linked to out-of-plane organ folding. Our analysis follows tissue dynamics during organ shape change in vivo, tracing organ-scale folding to a high-frequency molecular mechanism. These findings offer a mechanical route for gene expression to induce organ shape change: genetic patterning in one layer triggers a physical process in the adjacent layer – revealing post-translational mechanisms that govern shape change.
Collapse
Affiliation(s)
- Noah P Mitchell
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, United States
| | - Dillon J Cislo
- Department of Physics, University of California, Santa Barbara, Santa Barbara, United States
| | - Suraj Shankar
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, United States
| | - Yuzheng Lin
- Department of Physics, University of California, Santa Barbara, Santa Barbara, United States
| | - Boris I Shraiman
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, United States
| | - Sebastian J Streichan
- Department of Physics, University of California, Santa Barbara, Santa Barbara, United States
| |
Collapse
|
12
|
Agostinelli D, Elfring GJ, Bacca M. The morphological role of ligand inhibitors in blocking receptor- and clathrin-mediated endocytosis. SOFT MATTER 2022; 18:3531-3545. [PMID: 35445221 DOI: 10.1039/d1sm01710a] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Cells often internalize particles through endocytic pathways that involve the binding between cell receptors and particle ligands, which drives the cell membrane to wrap the particle into a delivery vesicle. Previous findings showed that receptor-mediated endocytosis is impossible for spherical particles smaller than a minimum size because of the energy barrier created by membrane bending. In this study, we investigate the morphological role of ligand inhibitors in blocking endocytosis, inspired by antibodies that inhibit virus ligands to prevent infection. While ligand inhibitors have the obvious effect of reducing the driving force due to adhesion, they also have a nontrivial (morphological) impact on the entropic and elastic energy of the system. We determine the necessary conditions for endocytosis by considering the additional energy barrier due to the membrane bending to wrap the inhibiting protrusions. We find that inhibitors increase the minimum radius previously reported, depending on their density and size. In addition, we extend this result to the case of clathrin-mediated endocytosis, which is the most common pathway for virus entry. The assembly of a clathrin coat with a spontaneous curvature increases the energy barrier and sets a maximum particle size (in agreement with experimental observations on spherical particles). Our investigation suggests that morphological considerations can inform the optimal design of neutralizing viral antibodies and new strategies for targeted nanomedicine.
Collapse
Affiliation(s)
- Daniele Agostinelli
- Mechanical Engineering Department, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Institute of Applied Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
| | - Gwynn J Elfring
- Mechanical Engineering Department, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Institute of Applied Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
| | - Mattia Bacca
- Mechanical Engineering Department, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Institute of Applied Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
- School of Biomedical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| |
Collapse
|
13
|
Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology. MEMBRANES 2022; 12:membranes12020217. [PMID: 35207138 PMCID: PMC8878405 DOI: 10.3390/membranes12020217] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Revised: 01/14/2022] [Accepted: 01/18/2022] [Indexed: 02/06/2023]
Abstract
In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.
Collapse
|
14
|
Dynamic mechanochemical feedback between curved membranes and BAR protein self-organization. Nat Commun 2021; 12:6550. [PMID: 34772909 PMCID: PMC8589976 DOI: 10.1038/s41467-021-26591-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 10/11/2021] [Indexed: 12/23/2022] Open
Abstract
In many physiological situations, BAR proteins reshape membranes with pre-existing curvature (templates), contributing to essential cellular processes. However, the mechanism and the biological implications of this reshaping process remain unclear. Here we show, both experimentally and through modelling, that BAR proteins reshape low curvature membrane templates through a mechanochemical phase transition. This phenomenon depends on initial template shape and involves the co-existence and progressive transition between distinct local states in terms of molecular organization (protein arrangement and density) and membrane shape (template size and spherical versus cylindrical curvature). Further, we demonstrate in cells that this phenomenon enables a mechanotransduction mode, in which cellular stretch leads to the mechanical formation of membrane templates, which are then reshaped into tubules by BAR proteins. Our results demonstrate the interplay between membrane mechanics and BAR protein molecular organization, integrating curvature sensing and generation in a comprehensive framework with implications for cell mechanical responses.
Collapse
|
15
|
Auddya D, Zhang X, Gulati R, Vasan R, Garikipati K, Rangamani P, Rudraraju S. Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework. Proc Math Phys Eng Sci 2021; 477:20210246. [PMID: 35153593 PMCID: PMC8580429 DOI: 10.1098/rspa.2021.0246] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 10/11/2021] [Indexed: 01/10/2023] Open
Abstract
Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.
Collapse
Affiliation(s)
- Debabrata Auddya
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Xiaoxuan Zhang
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Rahul Gulati
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Ritvik Vasan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Krishna Garikipati
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.,Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.,Michigan Institute for Computational Discovery and Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA
| | - Shiva Rudraraju
- Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| |
Collapse
|
16
|
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.
Collapse
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
| |
Collapse
|
17
|
Mahapatra A, Uysalel C, Rangamani P. The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes. J Membr Biol 2021; 254:273-291. [PMID: 33462667 PMCID: PMC8184589 DOI: 10.1007/s00232-020-00164-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 12/11/2020] [Indexed: 02/07/2023]
Abstract
Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.
Collapse
Affiliation(s)
- Arijit Mahapatra
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA, 92093, USA
| | - Can Uysalel
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA, 92093, USA
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Dr, La Jolla, CA, 92093, USA.
| |
Collapse
|
18
|
Fu M, Franquelim HG, Kretschmer S, Schwille P. Non‐Equilibrium Large‐Scale Membrane Transformations Driven by MinDE Biochemical Reaction Cycles. Angew Chem Int Ed Engl 2021. [DOI: 10.1002/ange.202015184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Meifang Fu
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
| | - Henri G. Franquelim
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
| | - Simon Kretschmer
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
- Department of Bioengineering and Therapeutic Science University of California San Francisco San Francisco CA USA
| | - Petra Schwille
- Dept. Cellular and Molecular Biophysics Max Planck Institute of Biochemistry Am Klopferspitz 18 82152 Martinsried Germany
| |
Collapse
|
19
|
Fu M, Franquelim HG, Kretschmer S, Schwille P. Non-Equilibrium Large-Scale Membrane Transformations Driven by MinDE Biochemical Reaction Cycles. Angew Chem Int Ed Engl 2021; 60:6496-6502. [PMID: 33285025 PMCID: PMC7986748 DOI: 10.1002/anie.202015184] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Indexed: 12/11/2022]
Abstract
The MinDE proteins from E. coli have received great attention as a paradigmatic biological pattern-forming system. Recently, it has surfaced that these proteins do not only generate oscillating concentration gradients driven by ATP hydrolysis, but that they can reversibly deform giant vesicles. In order to explore the potential of Min proteins to actually perform mechanical work, we introduce a new model membrane system, flat vesicle stacks on top of a supported lipid bilayer. MinDE oscillations can repeatedly deform these flat vesicles into tubules and promote progressive membrane spreading through membrane adhesion. Dependent on membrane and buffer compositions, Min oscillations further induce robust bud formation. Altogether, we demonstrate that under specific conditions, MinDE self-organization can result in work performed on biomimetic systems and achieve a straightforward mechanochemical coupling between the MinDE biochemical reaction cycle and membrane transformation.
Collapse
Affiliation(s)
- Meifang Fu
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
| | - Henri G. Franquelim
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
| | - Simon Kretschmer
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
- Department of Bioengineering and Therapeutic ScienceUniversity of California San FranciscoSan FranciscoCAUSA
| | - Petra Schwille
- Dept. Cellular and Molecular BiophysicsMax Planck Institute of BiochemistryAm Klopferspitz 1882152MartinsriedGermany
| |
Collapse
|
20
|
Raote I, Chabanon M, Walani N, Arroyo M, Garcia-Parajo MF, Malhotra V, Campelo F. A physical mechanism of TANGO1-mediated bulky cargo export. eLife 2020; 9:e59426. [PMID: 33169667 PMCID: PMC7704110 DOI: 10.7554/elife.59426] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 11/09/2020] [Indexed: 01/08/2023] Open
Abstract
The endoplasmic reticulum (ER)-resident protein TANGO1 assembles into a ring around ER exit sites (ERES), and links procollagens in the ER lumen to COPII machinery, tethers, and ER-Golgi intermediate compartment (ERGIC) in the cytoplasm (Raote et al., 2018). Here, we present a theoretical approach to investigate the physical mechanisms of TANGO1 ring assembly and how COPII polymerization, membrane tension, and force facilitate the formation of a transport intermediate for procollagen export. Our results indicate that a TANGO1 ring, by acting as a linactant, stabilizes the open neck of a nascent COPII bud. Elongation of such a bud into a transport intermediate commensurate with bulky procollagens is then facilitated by two complementary mechanisms: (i) by relieving membrane tension, possibly by TANGO1-mediated fusion of retrograde ERGIC membranes and (ii) by force application. Altogether, our theoretical approach identifies key biophysical events in TANGO1-driven procollagen export.
Collapse
Affiliation(s)
- Ishier Raote
- Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and TechnologyBarcelonaSpain
| | - Morgan Chabanon
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and TechnologyBarcelonaSpain
- Universitat Politècnica de Catalunya-BarcelonaTechBarcelonaSpain
| | - Nikhil Walani
- Universitat Politècnica de Catalunya-BarcelonaTechBarcelonaSpain
| | - Marino Arroyo
- Universitat Politècnica de Catalunya-BarcelonaTechBarcelonaSpain
- Institute for Bioengineering of Catalonia, The Barcelona Institute of Science and TechnologyBarcelonaSpain
- Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)BarcelonaSpain
| | - Maria F Garcia-Parajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and TechnologyBarcelonaSpain
- ICREABarcelonaSpain
| | - Vivek Malhotra
- Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and TechnologyBarcelonaSpain
- ICREABarcelonaSpain
- Universitat Pompeu Fabra (UPF)BarcelonaSpain
| | - Felix Campelo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and TechnologyBarcelonaSpain
| |
Collapse
|
21
|
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.
Collapse
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.
| |
Collapse
|
22
|
Omar YAD, Sahu A, Sauer RA, Mandadapu KK. Nonaxisymmetric Shapes of Biological Membranes from Locally Induced Curvature. Biophys J 2020; 119:1065-1077. [PMID: 32860742 DOI: 10.1016/j.bpj.2020.07.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Revised: 07/07/2020] [Accepted: 07/15/2020] [Indexed: 01/24/2023] Open
Abstract
In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes-an indeed unphysical constraint. Past studies predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane's ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.
Collapse
Affiliation(s)
- Yannick A D Omar
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California.
| | - Amaresh Sahu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California.
| | - Roger A Sauer
- Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, Aachen, Germany.
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California.
| |
Collapse
|
23
|
Al-Izzi SC, Sens P, Turner MS. Shear-Driven Instabilities of Membrane Tubes and Dynamin-Induced Scission. PHYSICAL REVIEW LETTERS 2020; 125:018101. [PMID: 32678660 DOI: 10.1103/physrevlett.125.018101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Revised: 10/21/2019] [Accepted: 06/08/2020] [Indexed: 06/11/2023]
Abstract
Motivated by the mechanics of dynamin-mediated membrane tube fission, we analyze the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a nonequilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in vitro experiments on membrane nanotubes, e.g., using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission.
Collapse
Affiliation(s)
- Sami C Al-Izzi
- Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France
- Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Pierre Sens
- Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France
- Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France
| | - Matthew S Turner
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
24
|
Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models. Nat Commun 2020; 11:2951. [PMID: 32528158 PMCID: PMC7289815 DOI: 10.1038/s41467-020-16424-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 04/28/2020] [Indexed: 12/12/2022] Open
Abstract
Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.
Collapse
|
25
|
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.
Collapse
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
| |
Collapse
|
26
|
Vasan R, Rudraraju S, Akamatsu M, Garikipati K, Rangamani P. A mechanical model reveals that non-axisymmetric buckling lowers the energy barrier associated with membrane neck constriction. SOFT MATTER 2020; 16:784-797. [PMID: 31830191 DOI: 10.1039/c9sm01494b] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Membrane neck formation is essential for scission, which, as recent experiments on tubules have demonstrated, can be location dependent. The diversity of biological machinery that can constrict a neck such as dynamin, actin, ESCRTs and BAR proteins, and the range of forces and deflection over which they operate, suggest that the constriction process is functionally mechanical and robust to changes in biological environment. In this study, we used a mechanical model of the lipid bilayer to systematically investigate the influence of location, symmetry constraints, and helical forces on membrane neck constriction. Simulations from our model demonstrated that the energy barriers associated with constriction of a membrane neck are location-dependent. Importantly, if symmetry restrictions are relaxed, then the energy barrier for constriction is dramatically lowered and the membrane buckles at lower values of forcing parameters. Our simulations also show that constriction due to helical proteins further reduces the energy barrier for neck formation when compared to cylindrical proteins. These studies establish that despite different molecular mechanisms of neck formation in cells, the mechanics of constriction naturally leads to a loss of symmetry that can lower the energy barrier to constriction.
Collapse
Affiliation(s)
- R Vasan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA.
| | | | | | | | | |
Collapse
|
27
|
Digumarti KM, Trimmer B, Conn AT, Rossiter J. Quantifying Dynamic Shapes in Soft Morphologies. Soft Robot 2019; 6:733-744. [DOI: 10.1089/soro.2018.0105] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
| | - Barry Trimmer
- Department of Biology, Tufts University, Medford, Massachusetts
| | - Andrew T. Conn
- Bristol Robotics Laboratory, University of Bristol, Bristol, United Kingdom
- Department of Mechanical Engineering and University of Bristol, Bristol, United Kingdom
| | - Jonathan Rossiter
- Bristol Robotics Laboratory, University of Bristol, Bristol, United Kingdom
- Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom
| |
Collapse
|
28
|
Abstract
Cellular nuclei are bound by two uniformly separated lipid membranes that are fused with each other at numerous donut-shaped pores. These membranes are structurally supported by an array of distinct proteins with distinct mechanical functions. As a result, the nuclear envelope possesses unique mechanical properties, which enables it to resist cytoskeletal forces. Here, we review studies that are beginning to provide quantitative insights into nuclear membrane mechanics. We discuss how the mechanical properties of the fused nuclear membranes mediate their response to mechanical forces exerted on the nucleus and how structural reinforcement by different nuclear proteins protects the nuclear membranes against rupture. We also highlight some open questions in nuclear envelope mechanics, and discuss their relevance in the context of health and disease.
Collapse
Affiliation(s)
- Ashutosh Agrawal
- Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
| | - Tanmay P Lele
- Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
| |
Collapse
|
29
|
Benet E, Zhu H, Vernerey FJ. Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes. Phys Rev E 2019; 99:042502. [PMID: 31108606 DOI: 10.1103/physreve.99.042502] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Indexed: 11/07/2022]
Abstract
Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.
Collapse
Affiliation(s)
- Eduard Benet
- Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Hongtian Zhu
- Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Franck J Vernerey
- Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| |
Collapse
|
30
|
The Effects of Intra-membrane Viscosity on Lipid Membrane Morphology: Complete Analytical Solution. Sci Rep 2018; 8:12845. [PMID: 30150612 PMCID: PMC6110749 DOI: 10.1038/s41598-018-31251-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Accepted: 08/03/2018] [Indexed: 02/06/2023] Open
Abstract
We present a linear theory of lipid membranes which accommodates the effects of intra-membrane viscosity into the model of deformations. Within the Monge parameterization, a linearized version of the shape equation describing membrane morphology is derived. Admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. We obtain a complete analytical expression illustrating the deformations of lipid membrane subjected to the influences of intra-membrane viscosity. The result predicts wrinkle phenomena in the event of membrane-substrate interactions. Finally, we mention that the obtained solutions reduce to those from the classical shape equation when the viscosity effects are removed.
Collapse
|
31
|
Angelova MI, Bitbol AF, Seigneuret M, Staneva G, Kodama A, Sakuma Y, Kawakatsu T, Imai M, Puff N. pH sensing by lipids in membranes: The fundamentals of pH-driven migration, polarization and deformations of lipid bilayer assemblies. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2018; 1860:2042-2063. [PMID: 29501601 DOI: 10.1016/j.bbamem.2018.02.026] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2018] [Revised: 02/22/2018] [Accepted: 02/24/2018] [Indexed: 01/27/2023]
Abstract
Most biological molecules contain acido-basic groups that modulate their structure and interactions. A consequence is that pH gradients, local heterogeneities and dynamic variations are used by cells and organisms to drive or regulate specific biological functions including energetic metabolism, vesicular traffic, migration and spatial patterning of tissues in development. While the direct or regulatory role of pH in protein function is well documented, the role of hydrogen and hydroxyl ions in modulating the properties of lipid assemblies such as bilayer membranes is only beginning to be understood. Here, we review approaches using artificial lipid vesicles that have been instrumental in providing an understanding of the influence of pH gradients and local variations on membrane vectorial motional processes: migration, membrane curvature effects promoting global or local deformations, crowding generation by segregative polarization processes. In the case of pH induced local deformations, an extensive theoretical framework is given and an application to a specific biological issue, namely the structure and stability of mitochondrial cristae, is described. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.
Collapse
Affiliation(s)
- Miglena I Angelova
- Sorbonne University, Faculty of Science and Engineering, UFR 925 Physics, Paris F-75005, France; University Paris Diderot - Paris 7, Sorbonne Paris Cité, Laboratory Matière et Systèmes Complexes (MSC) UMR 7057 CNRS, Paris F-75013, France.
| | - Anne-Florence Bitbol
- Sorbonne University, Faculty of Science and Engineering, Laboratory Jean Perrin, UMR 8237 CNRS, Paris F-75005, France
| | - Michel Seigneuret
- University Paris Diderot - Paris 7, Sorbonne Paris Cité, Laboratory Matière et Systèmes Complexes (MSC) UMR 7057 CNRS, Paris F-75013, France
| | - Galya Staneva
- Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria
| | - Atsuji Kodama
- Department of Physics, Tohoku University, Aoba, Sendai 980-8578, Japan
| | - Yuka Sakuma
- Department of Physics, Tohoku University, Aoba, Sendai 980-8578, Japan
| | | | - Masayuki Imai
- Department of Physics, Tohoku University, Aoba, Sendai 980-8578, Japan
| | - Nicolas Puff
- Sorbonne University, Faculty of Science and Engineering, UFR 925 Physics, Paris F-75005, France; University Paris Diderot - Paris 7, Sorbonne Paris Cité, Laboratory Matière et Systèmes Complexes (MSC) UMR 7057 CNRS, Paris F-75013, France
| |
Collapse
|
32
|
Onsager’s Variational Principle in Soft Matter: Introduction and Application to the Dynamics of Adsorption of Proteins onto Fluid Membranes. THE ROLE OF MECHANICS IN THE STUDY OF LIPID BILAYERS 2018. [DOI: 10.1007/978-3-319-56348-0_6] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
|
33
|
Sahu A, Sauer RA, Mandadapu KK. Irreversible thermodynamics of curved lipid membranes. Phys Rev E 2017; 96:042409. [PMID: 29347561 DOI: 10.1103/physreve.96.042409] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 01/15/2023]
Abstract
The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intramembrane lipid flow, intramembrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.
Collapse
Affiliation(s)
- Amaresh Sahu
- Department of Chemical & Biomolecular Engineering, University of California at Berkeley, Berkeley, California 94720, USA
| | - Roger A Sauer
- Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
| | - Kranthi K Mandadapu
- Department of Chemical & Biomolecular Engineering, University of California at Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
34
|
Nagao M, Kelley EG, Ashkar R, Bradbury R, Butler PD. Probing Elastic and Viscous Properties of Phospholipid Bilayers Using Neutron Spin Echo Spectroscopy. J Phys Chem Lett 2017; 8:4679-4684. [PMID: 28892394 DOI: 10.1021/acs.jpclett.7b01830] [Citation(s) in RCA: 77] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
The elastic and viscous properties of self-assembled amphiphilic membranes dictate the intricate hierarchy of their structure and dynamics ranging from the diffusion of individual molecules to the large-scale deformation of the membrane. We previously demonstrated that neutron spin echo spectroscopy measurements of model amphiphilic membranes can access the naturally occurring submicrosecond membrane motions, such as bending and thickness fluctuations. Here we show how the experimentally measured fluctuation parameters can be used to determine the inherent membrane properties and demonstrate how membrane viscosity and compressibility modulus are influenced by lipid composition in a series of simple phosphatidylcholine bilayers with different tail lengths as a function of temperature. This approach highlights the interdependence of the bilayer elastic and viscous properties and the collective membrane dynamics and opens new avenues to investigating the mechanical properties of more complex and biologically inspired systems.
Collapse
Affiliation(s)
- Michihiro Nagao
- NIST Center for Neutron Research, National Institute of Standards and Technology , Gaithersburg, Maryland 20899, United States
- Center for Exploration of Energy and Matter, Department of Physics, Indiana University , Bloomington, Indiana 47408, United States
| | - Elizabeth G Kelley
- NIST Center for Neutron Research, National Institute of Standards and Technology , Gaithersburg, Maryland 20899, United States
| | - Rana Ashkar
- Biology and Soft Matter Division, Oak Ridge National Laboratory , Oak Ridge, Tennessee 37831, United States
| | - Robert Bradbury
- NIST Center for Neutron Research, National Institute of Standards and Technology , Gaithersburg, Maryland 20899, United States
- Center for Exploration of Energy and Matter, Department of Physics, Indiana University , Bloomington, Indiana 47408, United States
| | - Paul D Butler
- NIST Center for Neutron Research, National Institute of Standards and Technology , Gaithersburg, Maryland 20899, United States
- Department of Chemical & Biomolecular Engineering, University of Delaware , Newark, Delaware 19716, United States
| |
Collapse
|
35
|
Aguilar Gutierrez OF, Herrera Valencia EE, Rey AD. Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes. J Colloid Interface Sci 2017; 503:103-114. [PMID: 28505495 DOI: 10.1016/j.jcis.2017.05.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Revised: 04/28/2017] [Accepted: 05/04/2017] [Indexed: 10/19/2022]
Abstract
Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces.
Collapse
Affiliation(s)
- Oscar F Aguilar Gutierrez
- Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec H3A 0C5, Canada
| | - Edtson E Herrera Valencia
- Departamento de Ingeniería Química, FES Zaragoza UNAM, Av. Guelatao No. 66 Col. Ejército de Oriente, Iztapalapa CP 09230, Mexico
| | - Alejandro D Rey
- Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec H3A 0C5, Canada.
| |
Collapse
|
36
|
Abstract
We derive a fully covariant theory of the mechanics of active surfaces. This theory provides a framework for the study of active biological or chemical processes at surfaces, such as the cell cortex, the mechanics of epithelial tissues, or reconstituted active systems on surfaces. We introduce forces and torques acting on a surface, and derive the associated force balance conditions. We show that surfaces with in-plane rotational symmetry can have broken up-down, chiral, or planar-chiral symmetry. We discuss the rate of entropy production in the surface and write linear constitutive relations that satisfy the Onsager relations. We show that the bending modulus, the spontaneous curvature, and the surface tension of a passive surface are renormalized by active terms. Finally, we identify active terms which are not found in a passive theory and discuss examples of shape instabilities that are related to active processes in the surface.
Collapse
Affiliation(s)
- Guillaume Salbreux
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
- The Francis Crick Institute, 1 Midland Road, London NW1 1AT, United Kingdom
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
| |
Collapse
|
37
|
Tsang KY, Lai YC, Chiang YW, Chen YF. Coupling of lipid membrane elasticity and in-plane dynamics. Phys Rev E 2017; 96:012410. [PMID: 29347274 DOI: 10.1103/physreve.96.012410] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Indexed: 11/07/2022]
Abstract
Biomembranes exhibit liquid and solid features concomitantly with their in-plane fluidity and elasticity tightly regulated by cells. Here, we present experimental evidence supporting the existence of the dynamics-elasticity correlations for lipid membranes and propose a mechanism involving molecular packing densities to explain them. This paper thereby unifies, at the molecular level, the aspects of the continuum mechanics long used to model the two membrane features. This ultimately may elucidate the universal physical principles governing the cellular phenomena involving biomembranes.
Collapse
Affiliation(s)
- Kuan-Yu Tsang
- Department of Chemical and Materials Engineering, National Central University, Taoyuan 32001, Taiwan
| | - Yei-Chen Lai
- Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Yun-Wei Chiang
- Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Yi-Fan Chen
- Department of Chemical and Materials Engineering, National Central University, Taoyuan 32001, Taiwan
| |
Collapse
|
38
|
Morris RG. Signatures of Mechanosensitive Gating. Biophys J 2017; 112:3-9. [PMID: 28076813 DOI: 10.1016/j.bpj.2016.12.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Revised: 12/05/2016] [Accepted: 12/07/2016] [Indexed: 01/10/2023] Open
Abstract
The question of how mechanically gated membrane channels open and close is notoriously difficult to address, especially if the protein structure is not available. This perspective highlights the relevance of micropipette-aspirated single-particle tracking-used to obtain a channel's diffusion coefficient, D, as a function of applied membrane tension, σ-as an indirect assay for determining functional behavior in mechanosensitive channels. While ensuring that the protein remains integral to the membrane, such methods can be used to identify not only the gating mechanism of a protein, but also associated physical moduli, such as torsional and dilational rigidity, which correspond to the protein's effective shape change. As an example, three distinct D-versus-σ "signatures" are calculated, corresponding to gating by dilation, gating by tilt, and gating by a combination of both dilation and tilt. Both advantages and disadvantages of the approach are discussed.
Collapse
Affiliation(s)
- Richard G Morris
- National Centre for Biological Sciences, Tata Institute for Fundamental Research, GKVK, Bangalore, India.
| |
Collapse
|
39
|
Guckenberger A, Gekle S. Theory and algorithms to compute Helfrich bending forces: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:203001. [PMID: 28240220 DOI: 10.1088/1361-648x/aa6313] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.
Collapse
Affiliation(s)
- Achim Guckenberger
- Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, Germany
| | | |
Collapse
|
40
|
Abstract
Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved spaces: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature- induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.
Collapse
|
41
|
Sachin Krishnan TV, Okamoto R, Komura S. Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid. Phys Rev E 2017; 94:062414. [PMID: 28085330 DOI: 10.1103/physreve.94.062414] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Indexed: 11/07/2022]
Abstract
We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.
Collapse
Affiliation(s)
- T V Sachin Krishnan
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan.,Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ryuichi Okamoto
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| |
Collapse
|
42
|
Sigurdsson JK, Atzberger PJ. Hydrodynamic coupling of particle inclusions embedded in curved lipid bilayer membranes. SOFT MATTER 2016; 12:6685-6707. [PMID: 27373277 DOI: 10.1039/c6sm00194g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets of the bilayer. We investigate relative to flat membranes how the membrane curvature and topology augment hydrodynamic responses. We show how both the translational and rotational mobility of protein inclusions are effected by the membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and intermonolayer slip. For general investigations of many-particle dynamics, we also discuss how our approaches can be used to treat the collective diffusion and hydrodynamic coupling within spherical bilayers.
Collapse
Affiliation(s)
| | - Paul J Atzberger
- Department of Mathematics, University of California, Santa Barbara, USA.
| |
Collapse
|
43
|
Debus JD, Mendoza M, Succi S, Herrmann HJ. Poiseuille flow in curved spaces. Phys Rev E 2016; 93:043316. [PMID: 27176437 DOI: 10.1103/physreve.93.043316] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Indexed: 11/07/2022]
Abstract
We investigate Poiseuille channel flow through intrinsically curved media, equipped with localized metric perturbations. To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the parameters of the metric perturbations (amplitude, range, and density). We find that the flux depends only on a specific combination of parameters, which we identify as the average metric perturbation, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently developed lattice Boltzmann model in curved space by considerably reducing discrete lattice effects.
Collapse
Affiliation(s)
- J-D Debus
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - S Succi
- Instituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185, Rome, Italy
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| |
Collapse
|
44
|
Okamoto R, Kanemori Y, Komura S, Fournier JB. Relaxation dynamics of two-component fluid bilayer membranes. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:52. [PMID: 27145960 DOI: 10.1140/epje/i2016-16052-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2015] [Revised: 03/08/2016] [Accepted: 03/09/2016] [Indexed: 06/05/2023]
Abstract
We theoretically investigate the relaxation dynamics of a nearly flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion. Mutual diffusion is the collective irreversible process that leads to homogenization of the density difference between the two lipid species. We find that two relaxation modes associated with the mutual diffusion appear in addition to the three previously discussed relaxation modes reflecting the bending and compression of the membrane. Because of the symmetry, only one of the two diffusive modes is coupled to the bending mode. The two diffusive modes are much slower than the bending and compression modes in the entire realistic wave number range. This means that the long time relaxation behavior is dominated by the mutual diffusion in binary membranes. The two diffusive modes become even slower in the vicinity of the unstable region towards phase separation, while the other modes are almost unchanged. In short time scales, on the other hand, the lipid composition heterogeneity induces in-plane compression and bending of the bilayer.
Collapse
Affiliation(s)
- Ryuichi Okamoto
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 192-0397, Tokyo, Japan.
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France.
| | - Yuichi Kanemori
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 192-0397, Tokyo, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 192-0397, Tokyo, Japan
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France
| | - Jean-Baptiste Fournier
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France
| |
Collapse
|
45
|
Barrett JW, Garcke H, Nürnberg R. A stable numerical method for the dynamics of fluidic membranes. NUMERISCHE MATHEMATIK 2016; 134:783-822. [PMID: 28603298 PMCID: PMC5444514 DOI: 10.1007/s00211-015-0787-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Revised: 10/12/2015] [Indexed: 06/06/2023]
Abstract
We develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in Navier-Stokes flow. Local inextensibility of the membrane is ensured by solving a tangential Navier-Stokes equation, taking surface viscosity effects of Boussinesq-Scriven type into account. In our approach the bulk and surface degrees of freedom are discretized independently, which leads to an unfitted finite element approximation of the underlying free boundary problem. Bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by Dziuk (Numer Math 111:55-80, 2008). The obtained numerical scheme can be shown to be stable and to have good mesh properties. Finally, the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions. The numerical results demonstrate the robustness of the method, and it is observed that the conservation properties are fulfilled to a high precision.
Collapse
Affiliation(s)
- John W. Barrett
- Department of Mathematics, Imperial College London, London, SW7 2AZ UK
| | - Harald Garcke
- Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
| | - Robert Nürnberg
- Department of Mathematics, Imperial College London, London, SW7 2AZ UK
| |
Collapse
|
46
|
Callan-Jones A, Durand M, Fournier JB. Hydrodynamics of bilayer membranes with diffusing transmembrane proteins. SOFT MATTER 2016; 12:1791-1800. [PMID: 26725841 DOI: 10.1039/c5sm02507a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We consider the hydrodynamics of lipid bilayers containing transmembrane proteins of arbitrary shape. This biologically-motivated problem is relevant to the cell membrane, whose fluctuating dynamics play a key role in phenomena ranging from cell migration, intercellular transport, and cell communication. Using Onsager's variational principle, we derive the equations that govern the relaxation dynamics of the membrane shape, of the mass densities of the bilayer leaflets, and of the diffusing proteins' concentration. With our generic formalism, we obtain several results on membrane dynamics. We find that proteins that span the bilayer increase the intermonolayer friction coefficient. The renormalization, which can be significant, is in inverse proportion to the protein's mobility. Second, we find that asymmetric proteins couple to the membrane curvature and to the difference in monolayer densities. For practically all accessible membrane tensions (σ > 10(-8) N m(-1)) we show that the protein density is the slowest relaxing variable. Furthermore, its relaxation rate decreases at small wavelengths due to the coupling to curvature. We apply our formalism to the large-scale diffusion of a concentrated protein patch. We find that the diffusion profile is not self-similar, owing to the wavevector dependence of the effective diffusion coefficient.
Collapse
Affiliation(s)
- Andrew Callan-Jones
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | | | | |
Collapse
|
47
|
Morris RG, Turner MS. Mobility Measurements Probe Conformational Changes in Membrane Proteins due to Tension. PHYSICAL REVIEW LETTERS 2015; 115:198101. [PMID: 26588417 DOI: 10.1103/physrevlett.115.198101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Indexed: 05/27/2023]
Abstract
The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations, and hence the drag, measurements of diffusivity can be used to infer-via an elastic model of the protein-how conformation is changed by tension. Motivated by recent experimental results [Quemeneur et al., Proc. Natl. Acad. Sci. U.S.A. 111, 5083 (2014)], we focus on KvAP, a voltage-gated potassium channel from Aeropyrum pernix. The conformation of KvAP is found to change considerably due to tension, with its "walls," where the protein meets the membrane, undergoing significant angular strains. The torsional stiffness is determined to be 26.8k(B)T per radian at room temperature. This has implications for both the structure and the function of such proteins in the environment of a tension-bearing membrane.
Collapse
Affiliation(s)
- Richard G Morris
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Matthew S Turner
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
48
|
Barrett JW, Garcke H, Nürnberg R. Numerical computations of the dynamics of fluidic membranes and vesicles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052704. [PMID: 26651720 DOI: 10.1103/physreve.92.052704] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Indexed: 06/05/2023]
Abstract
Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.
Collapse
Affiliation(s)
- John W Barrett
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Harald Garcke
- Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
| | - Robert Nürnberg
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
49
|
Rangamani P, Mandadap KK, Oster G. Protein-induced membrane curvature alters local membrane tension. Biophys J 2015; 107:751-762. [PMID: 25099814 DOI: 10.1016/j.bpj.2014.06.010] [Citation(s) in RCA: 62] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2014] [Revised: 06/01/2014] [Accepted: 06/09/2014] [Indexed: 10/24/2022] Open
Abstract
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.
Collapse
Affiliation(s)
- Padmini Rangamani
- Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, California
| | - Kranthi K Mandadap
- Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, California; Department of Chemistry, University of California at Berkeley, Berkeley, California
| | - George Oster
- Department of Molecular and Cell Biology, University of California at Berkeley, Berkeley, California.
| |
Collapse
|
50
|
Khalifat N, Rahimi M, Bitbol AF, Seigneuret M, Fournier JB, Puff N, Arroyo M, Angelova MI. Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant. Biophys J 2015; 107:879-90. [PMID: 25140423 DOI: 10.1016/j.bpj.2014.07.015] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2014] [Revised: 06/28/2014] [Accepted: 07/09/2014] [Indexed: 10/24/2022] Open
Abstract
In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin headgroups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.
Collapse
Affiliation(s)
- Nada Khalifat
- UPMC Université Paris 06, UMR 168, Institut Curie, Paris, France; CNRS, UMR 168, Institut Curie, Paris, France
| | - Mohammad Rahimi
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey
| | - Anne-Florence Bitbol
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey; Department of Physics, Princeton University, Princeton, New Jersey
| | - Michel Seigneuret
- Université Paris Diderot-Paris 7, Matière et Systèmes Complexes CNRS UMR 7057, Paris, France.
| | - Jean-Baptiste Fournier
- Université Paris Diderot-Paris 7, Matière et Systèmes Complexes CNRS UMR 7057, Paris, France
| | - Nicolas Puff
- Université Paris Diderot-Paris 7, Matière et Systèmes Complexes CNRS UMR 7057, Paris, France; Department of Physics-UFR 925, Université Pierre et Marie Curie, Paris, France
| | - Marino Arroyo
- Departament de Matemàtica Aplicada III, LaCàN, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Miglena I Angelova
- Université Paris Diderot-Paris 7, Matière et Systèmes Complexes CNRS UMR 7057, Paris, France; Department of Physics-UFR 925, Université Pierre et Marie Curie, Paris, France.
| |
Collapse
|