Endocytic proteins drive vesicle growth via instability in high membrane tension environment

Walani, Nikhil; Torres, Jennifer; Agrawal, Ashutosh

doi:10.1073/pnas.1418491112

Cited by 103 publications

(167 citation statements)

References 60 publications

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“…The requirement for two distinct mechanisms in two regions of neck radii could be related to the energy barrier that we found as the neck radius of the catenoid decreases. Other evidence of switch-like behaviors are found in endocytosis where multiple studies have reported the existence of a snap-through instability 35,[64][65][66] . Furthermore, soap films, with no bending rigidity, also exhibit a structural instability when held as catenoids 45,67 .…”

Section: Discussionmentioning

confidence: 95%

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks

Chabanon

Rangamani

2018

Soft Matter

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Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is the relationship between protein-induced spontaneous mean curvature and the Gaussian curvature at a membrane neck? Using an augmented Helfrich model for lipid bilayers to include membrane-protein interaction, we solve the shape equation on catenoids to find the field of spontaneous curvature that satisfies mechanical equilibrium of membrane necks. In this case, the shape equation reduces to a variable coefficient Helmholtz equation for spontaneous curvature, where the source term is proportional to the Gaussian curvature. We show how this latter quantity is responsible for non-uniform distribution of spontaneous curvature in minimal surfaces. We then explore the energetics of catenoids with different spontaneous curvature boundary conditions and geometric asymmetries to show how heterogeneities in spontaneous curvature distribution can couple with Gaussian curvature to result in membrane necks of different geometries.

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Section: Discussionmentioning

confidence: 95%

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks

Chabanon

Rangamani

2018

Soft Matter

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“…We use a modified version of the Helfrich energy that includes spatially varying spontaneous curvature C (θ α ) bending modulus κ(θ α ) and Gaussian modulus κG (θ α ) (42,48,50,52),…”

Section: Membrane Tensionmentioning

confidence: 99%

“…where ∆ is the surface Laplacian, p is the pressure difference across the membrane, λ is interpreted to be the membrane ten- sion, b αβ are components of the curvature tensor, f is a force per unit area applied to the membrane surface, and n is the unit normal to the surface (42,50). In this model, f represents the applied force exerted by the actin cytoskeleton; this force need not necessarily be normal to the membrane.…”

Section: Membrane Tensionmentioning

confidence: 99%

Design principles for robust vesiculation in clathrin-mediated endocytosis

Hassinger

Oster

Drubin

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

163

137

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A critical step in cellular-trafficking pathways is the budding of membranes by protein coats, which recent experiments have demonstrated can be inhibited by elevated membrane tension. The robustness of processes like clathrin-mediated endocytosis (CME) across a diverse range of organisms and mechanical environments suggests that the protein machinery in this process has evolved to take advantage of some set of physical design principles to ensure robust vesiculation against opposing forces like membrane tension. Using a theoretical model for membrane mechanics and membrane protein interaction, we have systematically investigated the influence of membrane rigidity, curvature induced by the protein coat, area covered by the protein coat, membrane tension, and force from actin polymerization on bud formation. Under low tension, the membrane smoothly evolves from a flat to budded morphology as the coat area or spontaneous curvature increases, whereas the membrane remains essentially flat at high tensions. At intermediate, physiologically relevant, tensions, the membrane undergoes a "snap-through instability" in which small changes in the coat area, spontaneous curvature or membrane tension cause the membrane to "snap" from an open, U-shape to a closed bud. This instability can be smoothed out by increasing the bending rigidity of the coat, allowing for successful budding at higher membrane tensions. Additionally, applied force from actin polymerization can bypass the instability by inducing a smooth transition from an open to a closed bud. Finally, a combination of increased coat rigidity and force from actin polymerization enables robust vesiculation even at high membrane tensions. membrane tension | clathrin-mediated endocytosis | membrane modeling C lathrin-mediated endocytosis (CME), an essential cellular process in eukaryotes, is an archetypal example of a membrane-deformation process that takes as input multiple variables, such as membrane bending, tension, protein-induced spontaneous curvature, and actin-mediated forces, and generates vesicular morphologies as its output (1). Although more than 60 different protein species act in a coordinated manner during CME (2), we can distill this process into a series of mechanochemical events where a feedback between the biochemistry of the protein machinery and the mechanics of the plasma membrane and the actin cytoskeleton control endocytic patch topology and morphology (3, 4).In Fig. 1, we outline the main steps that lead to bud formation. Despite the complexity of CME, a variety of experimental approaches have served to identify the governing principles of bud formation in CME. We have identified a few key features from recent experiments that govern bud formation and have summarized the main results below.i) Protein-induced spontaneous curvature: a critical step in CME is the assembly of a multicomponent protein coat that clusters cargo and bends the membrane into a budded morphology. Clathrin assembles into a lattice-like cage on the membrane with the assistance...

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“…The shape transitions occur as a result of lateral loading on the membranes from cytoskeletal filaments, such as actin, from osmotic pressure gradients across the membrane, or from reference configuration of finite element e membrane-protein interactions. For example, in endocytosis -a primary mode of transport of cargo between the exterior of the cell and its interior -proteins bind to the flat membrane and induce invaginations or bud shapes, followed by a tube formation by actin-mediated pulling forces [35,64].…”

Section: Introductionmentioning

confidence: 99%

A stabilized finite element formulation for liquid shells and its application to lipid bilayers

Sauer

Duong

Mandadapu

et al. 2017

Journal of Computational Physics

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This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using C 1 -continuous finite elements constructed from NURBS interpolation. Both displacement-based and mixed displacement/pressure FE formulations are proposed. The latter is needed for area-incompressible material behavior, where penalty-type regularizations can lead to misleading results. In order to obtain quasi-static solutions for liquid shells devoid of shear stiffness, several numerical stabilization schemes are proposed based on adding stiffness, adding viscosity or using projection. Several numerical examples are considered in order to illustrate the accuracy and the capabilities of the proposed formulation, and to compare the different stabilization schemes. The presented formulation is capable of simulating non-trivial surface shapes associated with tube formation and protein-induced budding of lipid bilayers. In the latter case, the presented formulation yields non-axisymmetric solutions, which have not been observed in previous simulations. It is shown that those non-axisymmetric shapes are preferred over axisymmetric ones.

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Endocytic proteins drive vesicle growth via instability in high membrane tension environment

Cited by 103 publications

References 60 publications

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks

Design principles for robust vesiculation in clathrin-mediated endocytosis

A stabilized finite element formulation for liquid shells and its application to lipid bilayers

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