1
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Ledesma-Durán A, Juárez-Valencia LH. Diffusion coefficients and MSD measurements on curved membranes and porous media. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:70. [PMID: 37578670 DOI: 10.1140/epje/s10189-023-00329-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 07/28/2023] [Indexed: 08/15/2023]
Abstract
We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.
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Affiliation(s)
- Aldo Ledesma-Durán
- Departmento de Matemáticas, Universidad Autónoma Metropolitana, CDMX, Mexico
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2
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Sapp K, Aleksanyan M, Kerr K, Dimova R, Sodt A. Kinetic relaxation of giant vesicles validates diffusional softening in a binary lipid mixture. Phys Rev E 2023; 107:054403. [PMID: 37329029 PMCID: PMC10548837 DOI: 10.1103/physreve.107.054403] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 03/15/2023] [Indexed: 06/18/2023]
Abstract
The stiffness of biological membranes determines the work required by cellular machinery to form and dismantle vesicles and other lipidic shapes. Model membrane stiffness can be determined from the equilibrium distribution of giant unilamellar vesicle surface undulations observable by phase contrast microscopy. With two or more components, lateral fluctuations of composition will couple to surface undulations depending on the curvature sensitivity of the constituent lipids. The result is a broader distribution of undulations whose complete relaxation is partially determined by lipid diffusion. In this work, kinetic analysis of the undulations of giant unilamellar vesicles made of phosphatidylcholine-phosphatidylethanolamine mixtures validates the molecular mechanism by which the membrane is made 25% softer than a single-component one. The mechanism is relevant to biological membranes, which have diverse and curvature-sensitive lipids.
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Affiliation(s)
- Kayla Sapp
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, 20892 Maryland, USA
| | - Mina Aleksanyan
- Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany
- Institute for Chemistry and Biochemistry, Freie Universität Berlin, 14195 Berlin, Germany
| | - Kaitlyn Kerr
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, 20892 Maryland, USA
| | - Rumiana Dimova
- Max Planck Institute of Colloids and Interfaces, 14476 Potsdam, Germany
| | - Alexander Sodt
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, 20892 Maryland, USA
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3
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Lee WS, Enomoto T, Akimoto AM, Yoshida R. Capsule self-oscillating gels showing cell-like nonthermal membrane/shape fluctuations. MATERIALS HORIZONS 2023; 10:1332-1341. [PMID: 36722870 DOI: 10.1039/d2mh01490d] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
A primary interest in cell membrane and shape fluctuations is establishing experimental models reflecting only nonthermal active contributions. Here we report a millimeter-scaled capsule self-oscillating gel model mirroring the active contribution effect on cell fluctuations. In the capsule self-oscillating gels, the propagating chemical signals during a Belousov-Zhabotinsky (BZ) reaction induce simultaneous local deformations in the various regions, showing cell-like shape fluctuations. The capsule self-oscillating gels do not fluctuate without the BZ reaction, implying that only the active chemical parameter induces the gel fluctuations. The period and amplitude depend on the gel layer thickness and the concentration of the chemical substrate for the BZ reaction. Our results allow for a solid experimental platform showing actively driven cell-like fluctuations, which can potentially contribute to investigating the active parameter effect on cell fluctuations.
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Affiliation(s)
- Won Seok Lee
- Department of Materials Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
| | - Takafumi Enomoto
- Department of Materials Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
| | - Aya Mizutani Akimoto
- Department of Materials Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
| | - Ryo Yoshida
- Department of Materials Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
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4
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Defaveri L, Barkai E, Kessler DA. Brownian particles in periodic potentials: Coarse-graining versus fine structure. Phys Rev E 2023; 107:024122. [PMID: 36932490 DOI: 10.1103/physreve.107.024122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as 2D^{*}t, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor e^{-V(x)/k_{B}T}, the latter being nonnormalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula F=TS-E is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.
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Affiliation(s)
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 52900, Israel
| | - David A Kessler
- Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
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5
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Tran PD, Blanpied TA, Atzberger PJ. Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods. Phys Rev E 2022; 106:044402. [PMID: 36397472 DOI: 10.1103/physreve.106.044402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.
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Affiliation(s)
- Patrick D Tran
- Physics, College of Creative Studies, University of California, Santa Barbara, Santa Barbara, California 93106-3080, USA
| | - Thomas A Blanpied
- Department of Physiology, University of Maryland, Baltimore, Maryland 21201, USA
| | - Paul J Atzberger
- Department of Mathematics and Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106-3080, USA
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6
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Arricca M, Salvadori A, Bonanno C, Serpelloni M. Modeling Receptor Motility along Advecting Lipid Membranes. MEMBRANES 2022; 12:membranes12070652. [PMID: 35877855 PMCID: PMC9317916 DOI: 10.3390/membranes12070652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 06/21/2022] [Accepted: 06/21/2022] [Indexed: 11/24/2022]
Abstract
This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.
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Affiliation(s)
- Matteo Arricca
- The Mechanobiology Research Center, University of Brescia (UNIBS), 25123 Brescia, Italy; (M.A.); (C.B.); (M.S.)
- Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123 Brescia, Italy
| | - Alberto Salvadori
- The Mechanobiology Research Center, University of Brescia (UNIBS), 25123 Brescia, Italy; (M.A.); (C.B.); (M.S.)
- Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123 Brescia, Italy
- Correspondence:
| | - Claudia Bonanno
- The Mechanobiology Research Center, University of Brescia (UNIBS), 25123 Brescia, Italy; (M.A.); (C.B.); (M.S.)
- Department of Civil, Environmental, Architectural Engineering and Mathematics, Università degli Studi di Brescia, via Branze 43, 25123 Brescia, Italy
| | - Mattia Serpelloni
- The Mechanobiology Research Center, University of Brescia (UNIBS), 25123 Brescia, Italy; (M.A.); (C.B.); (M.S.)
- Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123 Brescia, Italy
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7
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Chung HT, Yu HY. Binding of a Brownian nanoparticle to a thermally fluctuating membrane surface. Phys Rev E 2020; 101:032604. [PMID: 32289911 DOI: 10.1103/physreve.101.032604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 02/21/2020] [Indexed: 06/11/2023]
Abstract
We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.
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Affiliation(s)
- Hsueh-Te Chung
- Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan
| | - Hsiu-Yu Yu
- Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan
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8
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Menny A, Serna M, Boyd CM, Gardner S, Joseph AP, Morgan BP, Topf M, Brooks NJ, Bubeck D. CryoEM reveals how the complement membrane attack complex ruptures lipid bilayers. Nat Commun 2018; 9:5316. [PMID: 30552328 PMCID: PMC6294249 DOI: 10.1038/s41467-018-07653-5] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Accepted: 11/12/2018] [Indexed: 01/08/2023] Open
Abstract
The membrane attack complex (MAC) is one of the immune system's first responders. Complement proteins assemble on target membranes to form pores that lyse pathogens and impact tissue homeostasis of self-cells. How MAC disrupts the membrane barrier remains unclear. Here we use electron cryo-microscopy and flicker spectroscopy to show that MAC interacts with lipid bilayers in two distinct ways. Whereas C6 and C7 associate with the outer leaflet and reduce the energy for membrane bending, C8 and C9 traverse the bilayer increasing membrane rigidity. CryoEM reconstructions reveal plasticity of the MAC pore and demonstrate how C5b6 acts as a platform, directing assembly of a giant β-barrel whose structure is supported by a glycan scaffold. Our work provides a structural basis for understanding how β-pore forming proteins breach the membrane and reveals a mechanism for how MAC kills pathogens and regulates cell functions.
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Affiliation(s)
- Anaïs Menny
- Department of Life Sciences, Sir Ernst Chain Building, Imperial College London, London, SW7 2AZ, UK
| | - Marina Serna
- Department of Life Sciences, Sir Ernst Chain Building, Imperial College London, London, SW7 2AZ, UK
- Spanish National Cancer Research Centre, CNIO, Melchor Fernández Almagro, 3.28029, Madrid, Spain
| | - Courtney M Boyd
- Department of Life Sciences, Sir Ernst Chain Building, Imperial College London, London, SW7 2AZ, UK
| | - Scott Gardner
- Department of Life Sciences, Sir Ernst Chain Building, Imperial College London, London, SW7 2AZ, UK
| | - Agnel Praveen Joseph
- Institute of Structural and Molecular Biology, Department of Biological Sciences, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK
- Scientific Computing Department, Science and Technology Facilities Council, Research Complex at Harwell, Didcot, OX11 0FA, UK
| | - B Paul Morgan
- Division of Infection and Immunity, School of Medicine, Cardiff University, Heath Park, Cardiff, CF14 4XN, UK
| | - Maya Topf
- Institute of Structural and Molecular Biology, Department of Biological Sciences, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK
| | - Nicholas J Brooks
- Department of Chemistry, Imperial College London, London, SW7 2AZ, UK
| | - Doryen Bubeck
- Department of Life Sciences, Sir Ernst Chain Building, Imperial College London, London, SW7 2AZ, UK.
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9
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Chen P, Huang Z, Liang J, Cui T, Zhang X, Miao B, Yan LT. Diffusion and Directionality of Charged Nanoparticles on Lipid Bilayer Membrane. ACS NANO 2016; 10:11541-11547. [PMID: 27936576 DOI: 10.1021/acsnano.6b07563] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Diffusion dynamics of charged nanoparticles on the lipid membrane is of essential importance to cellular functioning. Yet a fundamental insight into electrostatics-mediated diffusion dynamics of charged nanoparticles on the membrane is lacking and remains to be an urgent issue. Here we present the computational investigation to uncover the pivotal role of electrostatics in the diffusion dynamics of charged nanoparticles on the lipid membrane. Our results demonstrate diffusive behaviors and directional transport of a charged nanoparticle, significantly depending on the sign and spatial distribution of charges on its surface. In contrast to the Fickian diffusion of neutral nanoparticles, randomly charged nanoparticles undergo superdiffusive transport with directionality. However, the dynamics of uniformly charged nanoparticles favors Fickian diffusion that is significantly enhanced. Such observations can be explained in term of electrostatics-induced surface reconstruction and fluctuation of lipid membrane. We finally present an analytical model connecting surface reconstruction and local deformation of the membrane. Our findings bear wide implications for the understanding and control of the transport of charged nanoparticles on the cell membrane.
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Affiliation(s)
- Pengyu Chen
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University , Beijing 100084, China
| | - Zihan Huang
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University , Beijing 100084, China
| | - Junshi Liang
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University , Beijing 100084, China
| | - Tianqi Cui
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University , Beijing 100084, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University , Beijing 100044, China
| | - Bing Miao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences , Beijing 100049, China
| | - Li-Tang Yan
- Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University , Beijing 100084, China
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10
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Sapp K, Maibaum L. Suppressing membrane height fluctuations leads to a membrane-mediated interaction among proteins. Phys Rev E 2016; 94:052414. [PMID: 27967200 PMCID: PMC5376292 DOI: 10.1103/physreve.94.052414] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 01/27/2023]
Abstract
Membrane-induced interactions can play a significant role in the spatial distribution of membrane-bound proteins. We develop a model that combines a continuum description of lipid bilayers with a discrete particle model of proteins to probe the emerging structure of the combined membrane-protein system. Our model takes into account the membrane's elastic behavior, the steric repulsion between proteins, and the quenching of membrane shape fluctuations due to the presence of the proteins. We employ coupled Langevin equations to describe the dynamics of the system. We show that coupling to the membrane induces an attractive interaction among proteins, which may contribute to the clustering of proteins in biological membranes. We investigate the lateral protein diffusion and find that it is reduced due to transient fluctuations in membrane shape.
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Affiliation(s)
- Kayla Sapp
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Lutz Maibaum
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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11
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Daniels DR. Curvature correction to the mobility of fluid membrane inclusions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:96. [PMID: 27771858 DOI: 10.1140/epje/i2016-16096-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Accepted: 09/28/2016] [Indexed: 06/06/2023]
Abstract
Using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces, we provide, via a Stokeslet-type approach, a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions.
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Affiliation(s)
- D R Daniels
- College of Engineering, Swansea University, Bay Campus, Fabian Way, SA1 8EN, Swansea, UK.
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12
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Fowler PW, Hélie J, Duncan A, Chavent M, Koldsø H, Sansom MSP. Membrane stiffness is modified by integral membrane proteins. SOFT MATTER 2016; 12:7792-7803. [PMID: 27722554 PMCID: PMC5314686 DOI: 10.1039/c6sm01186a] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2016] [Accepted: 08/25/2016] [Indexed: 05/12/2023]
Abstract
The ease with which a cell membrane can bend and deform is important for a wide range of biological functions. Peripheral proteins that induce curvature in membranes (e.g. BAR domains) have been studied for a number of years. Little is known, however, about the effect of integral membrane proteins on the stiffness of a membrane (characterised by the bending rigidity, Kc). We demonstrate by computer simulation that adding integral membrane proteins at physiological densities alters the stiffness of the membrane. First we establish that the coarse-grained MARTINI forcefield is able to accurately reproduce the bending rigidity of a small patch of 1500 phosphatidyl choline lipids by comparing the calculated value to both experiment and an atomistic simulation of the same system. This enables us to simulate the dynamics of large (ca. 50 000 lipids) patches of membrane using the MARTINI coarse-grained description. We find that altering the lipid composition changes the bending rigidity. Adding integral membrane proteins to lipid bilayers also changes the bending rigidity, whilst adding a simple peripheral membrane protein has no effect. Our results suggest that integral membrane proteins can have different effects, and in the case of the bacterial outer membrane protein, BtuB, the greater the density of protein, the larger the reduction in stiffness.
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Affiliation(s)
- Philip W Fowler
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
| | - Jean Hélie
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
| | - Anna Duncan
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
| | - Matthieu Chavent
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
| | - Heidi Koldsø
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
| | - Mark S P Sansom
- Department of Biochemistry, University of Oxford, South Parks Rd, Oxford, OX1 3QU, UK.
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13
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Ackerman ML, Kumar P, Neek-Amal M, Thibado PM, Peeters FM, Singh S. Anomalous Dynamical Behavior of Freestanding Graphene Membranes. PHYSICAL REVIEW LETTERS 2016; 117:126801. [PMID: 27689288 DOI: 10.1103/physrevlett.117.126801] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Indexed: 06/06/2023]
Abstract
We report subnanometer, high-bandwidth measurements of the out-of-plane (vertical) motion of atoms in freestanding graphene using scanning tunneling microscopy. By tracking the vertical position over a long time period, a 1000-fold increase in the ability to measure space-time dynamics of atomically thin membranes is achieved over the current state-of-the-art imaging technologies. We observe that the vertical motion of a graphene membrane exhibits rare long-scale excursions characterized by both anomalous mean-squared displacements and Cauchy-Lorentz power law jump distributions.
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Affiliation(s)
- M L Ackerman
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - P Kumar
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - M Neek-Amal
- Department of Physics, Shahid Rajaee Teacher Training University, 16875-163 Lavizan, Tehran, Iran
| | - P M Thibado
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - F M Peeters
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
| | - Surendra Singh
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
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14
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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.
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Affiliation(s)
| | - Paul J Atzberger
- Department of Mathematics, University of California, Santa Barbara, USA.
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15
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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.
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Affiliation(s)
- Andrew Callan-Jones
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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16
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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.
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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
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Sapp K, Shlomovitz R, Maibaum L. Seeing the Forest in Lieu of the Trees: Continuum Simulations of Cell Membranes at Large Length Scales. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2014; 10:47-76. [PMID: 26366141 PMCID: PMC4567254 DOI: 10.1016/b978-0-444-63378-1.00003-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
Biological membranes exhibit long-range spatial structure in both chemical composition and geometric shape, which gives rise to remarkable physical phenomena and important biological functions. Continuum models that describe these effects play an important role in our understanding of membrane biophysics at large length scales. We review the mathematical framework used to describe both composition and shape degrees of freedom, and present best practices to implement such models in a computer simulation. We discuss in detail two applications of continuum models of cell membranes: the formation of microemulsion and modulated phases, and the effect of membrane-mediated interactions on the assembly of membrane proteins.
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Affiliation(s)
- Kayla Sapp
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA
| | - Roie Shlomovitz
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA
- Department of Physics, University of Washington, Seattle, WA 98195, USA
| | - Lutz Maibaum
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA
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18
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Castro-Villarreal P, Villada-Balbuena A, Méndez-Alcaraz JM, Castañeda-Priego R, Estrada-Jiménez S. A Brownian dynamics algorithm for colloids in curved manifolds. J Chem Phys 2014; 140:214115. [DOI: 10.1063/1.4881060] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavel Castro-Villarreal
- Centro de Estudios en Física y Matemáticas Básicas y Aplicadas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, C. P. 29050, Tuxtla Gutiérrez, Chiapas, México
| | | | | | - Ramón Castañeda-Priego
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Guanajuato, México
| | - Sendic Estrada-Jiménez
- Centro de Estudios en Física y Matemáticas Básicas y Aplicadas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, C. P. 29050, Tuxtla Gutiérrez, Chiapas, México
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Abstract
The lateral mobility of proteins within cell membranes is usually thought to be dependent on their size and modulated by local heterogeneities of the membrane. Experiments using single-particle tracking on reconstituted membranes demonstrate that protein diffusion is significantly influenced by the interplay of membrane curvature, membrane tension, and protein shape. We find that the curvature-coupled voltage-gated potassium channel (KvAP) undergoes a significant increase in protein mobility under tension, whereas the mobility of the curvature-neutral water channel aquaporin 0 (AQP0) is insensitive to it. Such observations are well explained in terms of an effective friction coefficient of the protein induced by the local membrane deformation.
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20
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Démery V. Diffusion of a particle quadratically coupled to a thermally fluctuating field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052105. [PMID: 23767485 DOI: 10.1103/physreve.87.052105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Revised: 04/02/2013] [Indexed: 06/02/2023]
Abstract
We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak-coupling limit, a path-integral formulation allows us to compute the effective diffusion coefficient in the cases of an active particle, which tends to suppress field fluctuations, and of a passive particle, which only undergoes field fluctuations. We show that the behavior is similar to what was previously found for a linear coupling: an active particle is always slowed down, whereas a passive particle is slowed down in a slow field and accelerated in a fast field. Numerical simulations show a good agreement with the analytical calculations. The examples of a membrane protein coupled to the curvature or composition of the membrane are discussed, with a focus on the room for anomalous diffusion.
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Affiliation(s)
- Vincent Démery
- Institut Jean Le Rond d'Alembert, CNRS and UPMC, Université Paris 6, UMR 7190, F-75005 Paris, France.
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21
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Sarkar N, Basu A. Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2012; 35:115. [PMID: 23149567 DOI: 10.1140/epje/i2012-12115-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2011] [Accepted: 09/19/2012] [Indexed: 06/01/2023]
Abstract
We construct a coarse-grained effective two-dimensional (2d hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy (Phys. Rev. Lett., 102, 118107 (2009)) to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.
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Affiliation(s)
- N Sarkar
- Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta, India.
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22
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Wang B, Kuo J, Bae SC, Granick S. When Brownian diffusion is not Gaussian. NATURE MATERIALS 2012; 11:481-5. [PMID: 22614505 DOI: 10.1038/nmat3308] [Citation(s) in RCA: 273] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Affiliation(s)
- Bo Wang
- Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA
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23
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Effect of hydroperoxides on red blood cell membrane mechanical properties. Biophys J 2012; 101:1921-9. [PMID: 22004746 DOI: 10.1016/j.bpj.2011.08.053] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2011] [Revised: 08/08/2011] [Accepted: 08/31/2011] [Indexed: 02/07/2023] Open
Abstract
We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.
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Oppenheimer N, Diamant H. In-plane dynamics of membranes with immobile inclusions. PHYSICAL REVIEW LETTERS 2011; 107:258102. [PMID: 22243117 DOI: 10.1103/physrevlett.107.258102] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
Cell membranes are anchored to the cytoskeleton via immobile inclusions. We investigate the effect of such anchors on the in-plane dynamics of a fluid membrane and mobile inclusions (proteins) embedded in it. The immobile particles lead to a decreased diffusion coefficient of mobile ones and suppress the correlated diffusion of particle pairs. Because of the long-range, quasi-two-dimensional nature of membrane flows, these effects become significant at a low area fraction (below 1%) of immobile inclusions.
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Affiliation(s)
- Naomi Oppenheimer
- Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel.
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25
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Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects. Q Rev Biophys 2011; 44:391-432. [PMID: 21729348 DOI: 10.1017/s0033583511000047] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.
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Démery V, Dean DS. Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011148. [PMID: 21867153 DOI: 10.1103/physreve.84.011148] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Indexed: 05/31/2023]
Abstract
We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.
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Affiliation(s)
- Vincent Démery
- Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 4, France
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27
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Sens P, Turner MS. Microphase separation in nonequilibrium biomembranes. PHYSICAL REVIEW LETTERS 2011; 106:238101. [PMID: 21770544 DOI: 10.1103/physrevlett.106.238101] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2010] [Indexed: 05/25/2023]
Abstract
Compositional heterogeneities of cell membranes are thought to play an important role in many physiological processes. We study how variations in the membrane composition can be driven by nonthermal fluctuating forces and therefore show how these can occur relatively far from any critical point for the membrane. We show that the membrane steady state is not only controlled by the strength of the forces and how they couple to the membrane, but also by their dynamics: In a simple class of models this is captured by a single force correlation time. We conclude that the coupling of membrane composition to normal mechanical forces, such as might be exerted by polymerizing cytoskeleton filaments, could play an important role in controlling the steady state of a cell membrane that exhibits transient lateral modulations of its composition on length scales in the 10-100 nm regime.
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Affiliation(s)
- Pierre Sens
- Laboratoire Gulliver, UMR 7083 CNRS-ESPCI, Paris, France
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28
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Ramachandran S, Komura S. Hydrodynamic coupling between two fluid membranes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:072205. [PMID: 21411875 DOI: 10.1088/0953-8984/23/7/072205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The coupled in-plane diffusion dynamics between point-particles embedded in stacked fluid membranes is investigated. We calculate the contributions to the coupling longitudinal and transverse diffusion coefficients due to particle motion within the different as well as the same membranes. The stacked geometry leads to a hydrodynamic coupling between the two membranes.
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Affiliation(s)
- Sanoop Ramachandran
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan
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29
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Oppenheimer N, Diamant H. Correlated dynamics of inclusions in a supported membrane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041912. [PMID: 21230318 DOI: 10.1103/physreve.82.041912] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2010] [Indexed: 05/30/2023]
Abstract
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as 1/r(2) with interparticle distance r. For the common case, where the distance to the substrate is of submicrometer scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.
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Affiliation(s)
- Naomi Oppenheimer
- Beverly and Raymond Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
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