1
|
Takatori SC, Sahu A. Active Contact Forces Drive Nonequilibrium Fluctuations in Membrane Vesicles. PHYSICAL REVIEW LETTERS 2020; 124:158102. [PMID: 32357050 DOI: 10.1103/physrevlett.124.158102] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 03/20/2020] [Indexed: 05/24/2023]
Abstract
We analyze the nonequilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria-membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria-membrane contact forces. Taking advantage of the lengthscale and timescale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with nonequilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation-dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.
Collapse
Affiliation(s)
- Sho C Takatori
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Amaresh Sahu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
| |
Collapse
|
2
|
Komura S, Yasuda K, Okamoto R. Dynamics of two-component membranes surrounded by viscoelastic media. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:432001. [PMID: 26448393 DOI: 10.1088/0953-8984/27/43/432001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We discuss the dynamics of two-component fluid membranes which are surrounded by viscoelastic media. We assume that membrane-embedded proteins can diffuse laterally and induce a local membrane curvature. The mean squared displacement of a tagged membrane segment is obtained as a generalized Einstein relation. When the elasticity of the surrounding media obeys a power-law behavior in frequency, an anomalous diffusion of the membrane segment is predicted. We also consider the situation where the proteins generate active non-equilibrium forces. The generalized Einstein relation is further modified by an effective temperature that depends on the force dipole energy. The obtained generalized Einstein relations are useful for membrane microrheology experiments.
Collapse
Affiliation(s)
- Shigeyuki Komura
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | | | | |
Collapse
|
3
|
Guedda M. Membrane compression in tumbling and vacillating-breathing regimes for quasispherical vesicles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012703. [PMID: 24580253 DOI: 10.1103/physreve.89.012703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2013] [Indexed: 06/03/2023]
Abstract
We derive some analytical results of a well-known model for quasispherical vesicles in a linear shear flow at low deformability. Attention is focussed on the oscillatory regimes: the tumbling (TB) mode, vacillating-breathing (VB) mode, and the transition from vacillating-breathing to tumbling, depending on a control parameter Γ. It is shown that, during the VB-to-TB transition (Γ=1), the vesicle momentarily attains its maximal extension in the vorticity direction and transits through a circular profile in the shear plane for which the radius is exactly determined. In addition, we provide an explicit analytical expression for the effective membrane tension for different types of motions. We find a critical bending number below which the membrane undergoes compression at each instant and show that, during the VB-to-TB transition, a fourth-order membrane deformation is possible.
Collapse
Affiliation(s)
- M Guedda
- LAMFA, CNRS UMR 7352, Département de Mathématiques, Université de Picardie Jules Verne, Amiens, France
| |
Collapse
|
4
|
Loubet B, Seifert U, Lomholt MA. Effective tension and fluctuations in active membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031913. [PMID: 22587129 DOI: 10.1103/physreve.85.031913] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Indexed: 05/31/2023]
Abstract
We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular, we take constraints on the membrane area and the volume of fluid that it encapsulates into account when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the nonthermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane, a curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active transport of fluid through the membrane. For the direct force and curvature force cases, we compare our results to existing experiments on active membranes.
Collapse
Affiliation(s)
- Bastien Loubet
- Department of Physics, MEMPHYS-Center for Biomembrane Physics, Chemistry and Pharmacy, University of Southern Denmark, Odense M, Denmark
| | | | | |
Collapse
|
5
|
Abstract
Ever since it was discovered that biological membranes have a core of a bimolecular sheet of lipid molecules, lipid bilayers have been a model laboratory for investigating physicochemical and functional properties of biological membranes. Experimental and theoretical models help the experimental scientist to plan experiments and interpret data. Theoretical models are the theoretical scientist's preferred toys to make contact between membrane theory and experiments. Most importantly, models serve to shape our intuition about which membrane questions are the more fundamental and relevant ones to pursue. Here we review some membrane models for lipid self-assembly, monolayers, bilayers, liposomes, and lipid-protein interactions and illustrate how such models can help answering questions in modern lipid cell biology.
Collapse
Affiliation(s)
- Ole G Mouritsen
- MEMPHYS-Center for Biomembrane Physics, Department of Physics and Chemistry, University of Southern Denmark, DK-5230 Odense M, Denmark.
| |
Collapse
|
6
|
Mouritsen OG. Lipids, curvature, and nano-medicine. EUR J LIPID SCI TECH 2011; 113:1174-1187. [PMID: 22164124 PMCID: PMC3229985 DOI: 10.1002/ejlt.201100050] [Citation(s) in RCA: 78] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2011] [Revised: 06/30/2011] [Accepted: 06/30/2011] [Indexed: 12/29/2022]
Abstract
The physical properties of the lamellar lipid-bilayer component of biological membranes are controlled by a host of thermodynamic forces leading to overall tensionless bilayers with a conspicuous lateral pressure profile and build-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes. In particular, the average molecular shape and the propensity of the different lipid and protein species for forming non-lamellar and curved structures are a source of structural transitions and control of biological function. The effects of different lipids, sterols, and proteins on membrane structure are discussed and it is shown how one can take advantage of the curvature-stress modulations brought about by specific molecular agents, such as fatty acids, lysolipids, and other amphiphilic solutes, to construct intelligent drug-delivery systems that function by enzymatic triggering via curvature.Practical applications: The simple concept of lipid molecular shape and how it impacts on the structure of lipid aggregates, in particular the curvature and curvature stress in lipid bilayers and liposomes, can be exploited to construct liposome-based drug-delivery systems, e.g., for use as nano-medicine in cancer therapy. Non-lamellar-forming lysolipids and fatty acids, some of which may be designed to be prodrugs, can be created by phospholipase action in diseased tissues thereby providing for targeted drug release and proliferation of molecular entities with conical shape that break down the permeability barrier of the target cells and may hence enhance efficacy.
Collapse
Affiliation(s)
- Ole G Mouritsen
- MEMPHYS - Center for Biomembrane Physics, Department of Physics and Chemistry, University of Southern Denmark Campusvej, Odense M, Denmark
| |
Collapse
|
7
|
Mouritsen OG. Lipidology and lipidomics––quo vadis? A new era for the physical chemistry of lipids. Phys Chem Chem Phys 2011; 13:19195-205. [DOI: 10.1039/c1cp22484k] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
8
|
Lomholt MA, Loubet B, Ipsen JH. Elastic moderation of intrinsically applied tension in lipid membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011913. [PMID: 21405719 DOI: 10.1103/physreve.83.011913] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2010] [Indexed: 05/30/2023]
Abstract
Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membrane's electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory that demonstrates how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low-tension floppy state.
Collapse
Affiliation(s)
- Michael A Lomholt
- MEMPHYS-Center for Biomembrane Physics, Department of Physics and Chemistry, University of Southern Denmark, Odense M, Denmark
| | | | | |
Collapse
|
9
|
Ziebert F, Bazant MZ, Lacoste D. Effective zero-thickness model for a conductive membrane driven by an electric field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031912. [PMID: 20365775 DOI: 10.1103/physreve.81.031912] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2009] [Revised: 01/11/2010] [Indexed: 05/29/2023]
Abstract
The behavior of a conductive membrane in a static (dc) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Nonequilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.
Collapse
Affiliation(s)
- Falko Ziebert
- Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
| | | | | |
Collapse
|
10
|
El Alaoui Faris MD, Lacoste D, Pécréaux J, Joanny JF, Prost J, Bassereau P. Membrane tension lowering induced by protein activity. PHYSICAL REVIEW LETTERS 2009; 102:038102. [PMID: 19257398 DOI: 10.1103/physrevlett.102.038102] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Indexed: 05/27/2023]
Abstract
Using videomicroscopy we present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin pumps. When the pumps are activated, we observe a significant increase of the fluctuations in the low wave vector region, which we interpret as due to a lowering of the effective tension of the membrane.
Collapse
Affiliation(s)
- M D El Alaoui Faris
- Institut Curie, Centre de Recherche; CNRS, UMR 168; Université Pierre et Marie Curie, Paris, F-75248 France
| | | | | | | | | | | |
Collapse
|
11
|
Lomholt MA, Miao L. Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/33/005] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
12
|
Lomholt MA. Mechanics of nonplanar membranes with force-dipole activity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061913. [PMID: 16906870 DOI: 10.1103/physreve.73.061913] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2005] [Revised: 03/15/2006] [Indexed: 05/11/2023]
Abstract
A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through nonlocal force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for nonplanar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.
Collapse
Affiliation(s)
- Michael A Lomholt
- NORDITA--Nordic Institute for Theoretical Physics, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
| |
Collapse
|