Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Agrawal, Neeraj J.; Weinstein, Joshua; Radhakrishnan, Ravi

doi:10.1080/00268970802365990

Cited by 14 publications

(43 citation statements)

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“…In [274], Aranda-Espinoza et al employed a combination of integral equation theory to describe the spatial distribution of the membrane-bound proteins and the linearized elastic free-energy model and reported that the interaction (in the absence of thermal undulations) between two membrane-bound curvature-inducing proteins is dominated by a repulsive interaction. Consistent with these published reports, the calculated binding energy (again without thermal undulations) between two membrane-bound proteins interacting through the curvature fields show dominant repulsive interactions governed by the range of the curvature field [268]. Thus, purely based on energetic grounds, the previous analyses have suggested that membrane-deformation-mediated energies tend to be repulsive and should prevent, rather than promote, the formation of protein dimers or clusters.…”

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldssupporting

confidence: 79%

“…In such models, there is only a one-way coupling between the membrane dynamics and the protein dynamics—i.e., a change in membrane morphology affects the diffusion of the proteins and not the reverse. These studies have been extended to simultaneous protein diffusion and membrane motion models to treat the case of curvature-inducing proteins diffusing on the membrane [92, 267, 268]. The new aspect introduced in these latter models is the two-way coupling between the protein and membrane motion.…”

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

“…The protein diffusion in turn affects membrane dynamics because the spatial location of the proteins determine the intrinsic curvature functions and hence the elastic energy of the membrane [267]. This methodology has been utilized in exploring the equilibrium behavior of bilayer membranes under the influence of cooperative effects induced by the diffusion of curvature-inducing proteins [268]. …”

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

“…Neighboring proteins collaborate in restricting the membrane undulations and reduce the total free-energy costs, yielding an effective (membrane-mediated) protein-protein attraction. Indeed, for the linearized free-energy model, computing the second variation of energy (note that at equilibrium, the first variation is zero, whereas the second variation governs the stiffness of the system against fluctuations), we see that the presence of a protein (or equivalently a curvature inducing function) leads to a localized suppression of membrane fluctuations [268, 283]. As will be discussed later in section 6, this calculation has been further verified by using a free-energy method to compute the change in Helmholtz free energy upon the introduction of a curvature field [283].…”

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

“…The outcome of the interplay between the attractive entropic forces and the repulsive energetic forces is context specific because both have the same dependence on the protein-protein distance and their absolute values differ only by coefficients with similar values. This has been demonstrated by examining the protein-protein pair correlation (spatial and bond-orientational) and through the effect on membrane morphology [268]. Indeed, the model predicts that the cooperative effects of membrane-mediated interactions between multiple proteins can drive different morphological transitions in membranes [166, 268, 274, 282].…”

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

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Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

2014

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Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular set...

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Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldssupporting

confidence: 79%

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

Section: Modeling Membrane Proteins As Spontaneous Curvature Fieldsmentioning

confidence: 99%

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Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

2014

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Phenomenology Based Multiscale Models as Tools to Understand Cell Membrane and Organelle Morphologies

Ramakrishnan

Radhakrishnan

2015

Advances in Planar Lipid Bilayers and Liposomes

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An intriguing question in cell biology is “how do cells regulate their shape?” It is commonly believed that the observed cellular morphologies are a result of the complex interaction among the lipid molecules (constituting the cell membrane), and with a number of other macromolecules, such as proteins. It is also believed that the common biophysical processes essential for the functioning of a cell also play an important role in cellular morphogenesis. At the cellular scale—where typical dimensions are in the order of micrometers—the effects arising from the molecular scale can either be modeled as equilibrium or non-equilibrium processes. In this chapter, we discuss the dynamically triangulated Monte Carlo technique to model and simulate membrane morphologies at the cellular scale, which in turn can be used to investigate several questions related to shape regulation in cells. In particular, we focus on two specific problems within the framework of isotropic and anisotropic elasticity theories: namely, (i) the origin of complex, physiologically relevant, membrane shapes due to the interaction of the membrane with curvature remodeling proteins, and (ii) the genesis of steady state cellular shapes due to the action of non-equilibrium forces that are generated by the fission and fusion of transport vesicles and by the binding and unbinding of proteins from the parent membrane.

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Top-down Mesoscale Models and Free Energy Calculations of Multivalent Protein-Protein and Protein-Membrane Interactions in Nanocarrier Adhesion and Receptor Trafficking

Liu

Agrawal

Eckmann

et al. 2012

Innovations in Biomolecular Modeling and Simulations

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In this chapter we present a summary of recent applications of top-down mesoscale modeling to two biologically relevant problems: (1) adhesion of nanocarriers to cells mediated by multivalent receptor-ligand interactions in targeted drug delivery; (2) internalization of cell surface receptors in cells via the biological process of endocytosis. In particular, we focus on methods for computing absolute/relative free energies using these mesoscale models in order to facilitate direct comparison with experimental data.

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Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Cited by 14 publications

References 48 publications

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Phenomenology Based Multiscale Models as Tools to Understand Cell Membrane and Organelle Morphologies

Top-down Mesoscale Models and Free Energy Calculations of Multivalent Protein-Protein and Protein-Membrane Interactions in Nanocarrier Adhesion and Receptor Trafficking

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