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Hosaka Y, Komura S, Andelman D. Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity. Phys Rev E 2021; 104:064613. [PMID: 35030884 DOI: 10.1103/physreve.104.064613] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 11/12/2021] [Indexed: 11/07/2022]
Abstract
We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the passive case without odd viscosity, the lateral lift arises in the active case only when the in and out odd viscosities are different. The in-out contrast in the odd viscosity leads to nonreciprocal hydrodynamic responses of an active liquid domain.
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Affiliation(s)
- Yuto Hosaka
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan.,Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China.,Oujiang Laboratory, Wenzhou, Zhejiang 325000, China
| | - David Andelman
- School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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Hakobyan D, Heuer A. 2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration. J Chem Phys 2017; 146:064305. [DOI: 10.1063/1.4975163] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Davit Hakobyan
- Institute of Physical Chemistry, WWU Münster, Corrensstr. 28/30, 48149 Münster, Germany and Center for Multiscale Theory and Computation (CMTC), WWU Münster, 48149 Münster, Germany
| | - Andreas Heuer
- Institute of Physical Chemistry, WWU Münster, Corrensstr. 28/30, 48149 Münster, Germany and Center for Multiscale Theory and Computation (CMTC), WWU Münster, 48149 Münster, Germany
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Palmieri B, Yamamoto T, Brewster RC, Safran SA. Line active molecules promote inhomogeneous structures in membranes: theory, simulations and experiments. Adv Colloid Interface Sci 2014; 208:58-65. [PMID: 24630340 DOI: 10.1016/j.cis.2014.02.007] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Revised: 02/05/2014] [Accepted: 02/06/2014] [Indexed: 12/16/2022]
Abstract
We review recent theoretical efforts that predict how line-active molecules can promote lateral heterogeneities (or domains) in model membranes. This fundamental understanding may be relevant to membrane composition in living cells, where it is thought that small domains, called lipid rafts, are necessary for the cells to be functional. The theoretical work reviewed here ranges in scale from coarse grained continuum models to nearly atomistic models. The effect of line active molecules on domain sizes and shapes in the phase separated regime or on fluctuation length scales and lifetimes in the single phase, mixed regime, of the membrane is discussed. Recent experimental studies on model membranes that include line active molecules are also presented together with some comparisons with the theoretical predictions.
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Komura S, Andelman D. Physical aspects of heterogeneities in multi-component lipid membranes. Adv Colloid Interface Sci 2014; 208:34-46. [PMID: 24439258 DOI: 10.1016/j.cis.2013.12.003] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2013] [Accepted: 12/07/2013] [Indexed: 01/08/2023]
Abstract
Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an essential role. Focusing on the lateral phase separation of biomembranes and vesicles, we review some of the most relevant research conducted over the last decade. We mainly refer to those experimental works that are based on physical chemistry approach, and to theoretical explanations given in terms of soft matter physics. In the first part, we describe the phase behavior and the conformation of multi-component lipid bilayers. After formulating the hydrodynamics of fluid membranes in the presence of the surrounding solvent, we discuss the domain growth-law and decay rate of concentration fluctuations. Finally, we review several attempts to describe membrane rafts as two-dimensional microemulsion.
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Abstract
Time-dependent single molecule diffusion coefficients are discussed for a fluorescent probe molecule in lipid mixtures near a miscibility critical point. The calculations take advantage of the theoretical wave vector dependent composition diffusion coefficients obtained by Inaura and Fujitani [J. Phys. Soc. Jpn. 77, 114603 (2008)]. It is suggested that the diffusion of the probe molecule reflects in part the time-dependent composition diffusion near a critical point. The calculations show a striking biphasic time-dependent diffusion that switches from a faster diffusion at short times to a slower diffusion at a time approximately equal to πξ(2)/D where ξ is the correlation length and D is the composition diffusion coefficient at the switch time. This biphasic diffusion should be readily detectable experimentally.
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Affiliation(s)
- Harden McConnell
- Department of Chemistry, Stanford University, Stanford, California 94305, USA.
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Seki K, Ramachandran S, Komura S. Diffusion coefficient of an inclusion in a liquid membrane supported by a solvent of arbitrary thickness. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021905. [PMID: 21929018 DOI: 10.1103/physreve.84.021905] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2011] [Revised: 07/12/2011] [Indexed: 05/31/2023]
Abstract
The diffusion coefficient of an inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion coefficients of two types of inclusions, a circular domain composed of fluid with the same viscosity as the host membrane and that of a polymer chain embedded in the membrane, are studied. The diffusion coefficients are expressed in terms of the hydrodynamic screening lengths, which vary according to the solvent thickness. When the membrane fluid is dragged by the solvent of finite thickness, via stick boundary conditions, multiple hydrodynamic screening lengths together with the weight factors to the diffusion coefficients are obtained from the characteristic equation. The conditions for which the diffusion coefficients can be approximated by the expression including only a single hydrodynamic screening length are also shown.
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Affiliation(s)
- Kazuhiko Seki
- National Institute of Advanced Industrial Science and Technology AIST Tsukuba Central 5, Higashi 1-1-1, Tsukuba 305-8565, Japan
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Taniguchi T, Yanagisawa M, Imai M. Numerical investigations of the dynamics of two-component vesicles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:284103. [PMID: 21709319 DOI: 10.1088/0953-8984/23/28/284103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We examined the dynamics of the deformation and phase separation of two-component vesicles. First, we numerically investigated the effects of (i) thermal noise, (ii) hydrodynamic flow induced by the line tension of the domain boundary and (iii) composition-dependent bending rigidity on the coarsening dynamics of a phase-separated pattern on the surfaces of vesicles with fixed shapes. The dynamical exponent z (N(DB) ∼ t(-z), the total length of the domain boundaries) of the coarsening of the phase-separated pattern was found to decrease from z = 1/3 under no thermal noise to 1/5 < z < 1/4 when including the effects of thermal noise. We also found that the hydrodynamic effect enhances the coarsening in a bicontinuous phase separation for a spherical vesicle. In phase separations of a shape-fixed tubular vesicle, a band-like phase separation with periodicity along the longer axis of the tube occurs because of the composition-dependent bending rigidity and the higher curvatures at the tube end-caps. Second, we also explored the dynamics of shape deformation coupled with phase separation through the bending rigidity of the membrane which depends on the local composition in lipids and found that the composition-dependent bending rigidity crucially influences the phase separation and deformation of the vesicle. The results of simulations are in good agreement with experimentally observed behavior known as 'shape convergence' (Yanagisawa et al 2008 Phys. Rev. Lett. 100 148102).
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Ramachandran S, Komura S, Seki K, Gompper G. Dynamics of a polymer chain confined in a membrane. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:46. [PMID: 21562968 DOI: 10.1140/epje/i2011-11046-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2010] [Revised: 12/18/2010] [Accepted: 03/30/2011] [Indexed: 05/30/2023]
Abstract
We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.
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Affiliation(s)
- S Ramachandran
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Japan
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McConnell H. Communication: Critical dynamics and nuclear relaxation in lipid
bilayers. J Chem Phys 2011; 134:011102. [DOI: 10.1063/1.3529955] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Harden McConnell
- Department of Chemistry, Stanford University, Stanford,
California 94305, USA
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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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Ramachandran S, Komura S, Imai M, Seki K. Drag coefficient of a liquid domain in a two-dimensional membrane. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 31:303-310. [PMID: 20306216 DOI: 10.1140/epje/i2010-10577-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2009] [Revised: 01/28/2010] [Accepted: 02/19/2010] [Indexed: 05/29/2023]
Abstract
Using a hydrodynamic theory that incorporates a momentum decay mechanism, we calculate the drag coefficient of a circular liquid domain of finite viscosity moving in a two-dimensional membrane. We derive an analytical expression for the drag coefficient which covers the whole range of domain sizes. Several limiting expressions are discussed. The obtained drag coefficient decreases as the domain viscosity becomes smaller with respect to the outer membrane viscosity. This is because the flow induced in the domain acts to transport the fluid in the surrounding matrix more efficiently.
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Affiliation(s)
- S Ramachandran
- Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 192-0397, Tokyo, Japan
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Oppenheimer N, Diamant H. Correlated diffusion of membrane proteins and their effect on membrane viscosity. Biophys J 2009; 96:3041-9. [PMID: 19383450 DOI: 10.1016/j.bpj.2009.01.020] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2008] [Revised: 12/24/2008] [Accepted: 01/02/2009] [Indexed: 10/20/2022] Open
Abstract
We extend the Saffman theory of membrane hydrodynamics to account for the correlated motion of membrane proteins, along with the effect of protein concentration on that correlation and on the response of the membrane to stresses. Expressions for the coupling diffusion coefficients of protein pairs and their concentration dependence are derived in the limit of small protein size relative to the interprotein separation. The additional role of membrane viscosity as determining the characteristic length scale for membrane response leads to unusual concentration effects at large separation-the transverse coupling increases with protein concentration, whereas the longitudinal one becomes concentration-independent.
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Affiliation(s)
- Naomi Oppenheimer
- School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
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An introduction to critical points for biophysicists; observations of compositional heterogeneity in lipid membranes. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2008; 1788:53-63. [PMID: 18930706 DOI: 10.1016/j.bbamem.2008.09.010] [Citation(s) in RCA: 199] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2008] [Revised: 09/12/2008] [Accepted: 09/15/2008] [Indexed: 01/12/2023]
Abstract
Scaling laws associated with critical points have the power to greatly simplify our description of complex biophysical systems. We first review basic concepts and equations associated with critical phenomena for the general reader. We then apply these concepts to the specific biophysical system of lipid membranes. We recently reported that lipid membranes can contain composition fluctuations that behave in a manner consistent with the two-dimensional Ising universality class. Near the membrane's critical point, these fluctuations are micron-sized, clearly observable by fluorescence microscopy. At higher temperatures, above the critical point, we expect to find submicron fluctuations. In separate work, we have reported that plasma membranes isolated directly from cells exhibit the same Ising behavior as model membranes do. We review other models describing submicron lateral inhomogeneity in membranes, including microemulsions, nanodomains, and mean field critical fluctuations, and we describe experimental tests that may distinguish these models.
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