Curvature-Induced Spatial Ordering of Composition in Lipid Membranes

Katz, Shimrit; Givli, Sefi

doi:10.1155/2017/7275131

Cited by 9 publications

(10 citation statements)

References 55 publications

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“…In Equation (6), the first term is the conventional Helfrich bending energy with induced spontaneous curvature [118]. The second term represents the entropic contribution due to the thermal motion of proteins in the membrane [175,179]. The third term gives the aggregation energy, and the last term describes the energetic penalty for the spatial membrane composition gradient [175,178,179].…”

Section: Continuum Elastic Energy Models Of Membrane–protein Intermentioning

confidence: 99%

Modeling Membrane Curvature Generation due to Membrane–Protein Interactions

Alimohamadi

Rangamani

2018

Biomolecules

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To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

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Section: Continuum Elastic Energy Models Of Membrane–protein Intermentioning

confidence: 99%

Modeling Membrane Curvature Generation due to Membrane–Protein Interactions

Alimohamadi

Rangamani

2018

Biomolecules

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“…In this equation, k T B is the thermal energy, a p is the area on the membrane of a single protein so that f/a p is the number density, the term involving f m (a saturation area fraction) accounts for the entropy of uncovered spaces, χ determines the strength and sign (attractive or repulsive) of protein-protein interactions, and μ 0 is a reference chemical potential. Variants of this model have been used to understand the linear stability of fully mixed states [42,43] or to examine protein sorting by curvature at fixed shape [18,44,47].…”

Section: Energeticsmentioning

confidence: 99%

“…These models suggest that, rather than two different mechanisms, curvature sensing and generation are two manifestations of the same mechanochemical coupling. They have provided a background to understand the emergence of heterogeneous proteinrich curved domains using linear stability analysis [42,43], or curvature sorting of proteins in equilibrium and at fixed shape between tubes and vesicles [18,[44][45][46] or on wavy surfaces [47]. Also in equilibrium, proteinmembrane interactions allowing for shape changes were studied in [48].With a few exceptions under rather restrictive conditions [49,50], previous theories of the interaction between curved proteins and membranes have focused on equilibrium.…”

mentioning

confidence: 99%

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

2019

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The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager's formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.To quantitatively understand these phenomena, various biophysical studies have exposed artificial lipid membranes to purified proteins in controlled conditions [14]. At high concentration, curved proteins can induce severe membrane curvature when incubated with liposomes [15], can stabilize membrane tubes [10,16], and can dynamically trigger protein-rich tubular protrusions out of tense vesicles [17][18][19]. At lower concentrations, proteins sense curvature and preferentially adsorb or migrate to favorably curved membranes, as probed in assays involving polydisperse vesicle suspensions [20], vesicles with membrane tethers [18,21] or supported lipid bilayers on wavy substrates [22]. Since protein-rich curved domains sequester apparent membrane area from the adjacent planar membrane, their formation perform work against membrane tension, and thus can be hindered if tension is large enough. This kind of mechano-chemical coupling, tested in vitro by exposing aspirated vesicles to BAR proteins [19], has physiological implications during the mechano-protection of stressed cells by the release of membrane area through disassembly of caveolae [4], or in the regulation of clathrin-mediated endocytosis by membrane tension [23].A number of theoretical and computational studies at various scales have been developed to understand the interaction between curved proteins and membranes. At the nanoscale, all-atom molecular dynamics have described curvature generation by single domains [24] and curvature maintenance by multiple proteins [25]. Reaching a micron, coarse-grained molecular dynamics simulations, treating the membrane either molecularly or as a continuum object, hav...

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“…6, the first term is the conventional Helfrich bending energy with induced spontaneous curvature [102]. The second term represents the entropic contribution due to the thermal motion of proteins in the membrane [160,164]. The third term gives the aggregation energy, and the last term describes the energetic penalty for the spatial membrane composition gradient [160,163,164].…”

Section: Protein Aggregation Modelmentioning

confidence: 99%

“…The second term represents the entropic contribution due to the thermal motion of proteins in the membrane [160,164]. The third term gives the aggregation energy, and the last term describes the energetic penalty for the spatial membrane composition gradient [160,163,164]. The suggested protein aggregation model mainly used for theoretical analysis of dynamic phase transitions of coupled membrane-proteins-cytoskeleton systems in membrane protrusions such as microvilli and filopodia [160,[165][166][167].…”

Section: Protein Aggregation Modelmentioning

confidence: 99%

Modeling Membrane-Protein Interactions

Alimohamadi¹,

Rangamani²

2018

Preprint

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In order to alter and adjust the shape of the membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. One of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy that includes protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome in order to push the boundaries of current model applications.

show abstract

Curvature-Induced Spatial Ordering of Composition in Lipid Membranes

Cited by 9 publications

References 55 publications

Modeling Membrane Curvature Generation due to Membrane–Protein Interactions

Modeling Membrane Curvature Generation due to Membrane–Protein Interactions

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

Modeling Membrane-Protein Interactions

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