Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Zhu, Cuncheng; Lee, Christopher T.; Rangamani, Padmini

doi:10.1016/j.bpr.2022.100062

Cited by 16 publications

(16 citation statements)

References 133 publications

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“…Simulations using general coordinates reveal that the early modes of deformation are axisymmetric (65). However, relaxation of the assumption of axisymmetry in tubulation would be necessary to investigate how forces and proteins may interact (65)(66)(67). In summary, we expect that the findings from our work will motivate the development of these future efforts and gain a deeper understanding of how membrane tubes form under different biophysical conditions.…”

Section: Discussionmentioning

confidence: 79%

“…We also anticipate that the interactions between protein-mediated tubulation and force-mediated tubulation would be necessary to capture cellular processes where both membrane-bound proteins and actin-mediated forces are involved (54). Finally, relaxation of the assumption of axisymmetry in tubulation could be necesary to investigate how forces and proteins may interact (55)(56)(57). In summary, we expect that the findings from our work will motivate the development of these future efforts and gain a deeper understanding of how membrane tubes form.…”

Section: Discussionmentioning

confidence: 99%

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Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Mahapatra

Rangamani

2022

Preprint

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Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. The formation of plasma membrane tubes can be due to localized forces acting on the membrane or by curvature-induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.1Significance StatementCylindrical tubes are ubiquitous on cellular membranes and many studies have focused on how forces can give rise to tubes. How do curvature-inducing proteins, in the absence of forces, form cylindrical tubes on lipid bilayers? The answer to this question relies on minimizing the bending energy of the membrane to accommodate two different principal curvatures such that a cylindrical shape is an energy minimizer. Here, we build on previous works to develop such a model and show that the formation of an elongated cylindrical tube is accompanied by a snapthrough transition in the bending energy. Furthermore, we identify how this transition depends on different membrane properties, providing a landscape for comparing with different experimental observations. These findings have implications for our understanding how tubes forms in different cellular processes including trafficking, mitochondrial inner membrane cristae formation, and T-tubule formation in myocytes.

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Section: Discussionmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 99%

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Mahapatra

Rangamani

2022

Preprint

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“…To demonstrate inward and outward tube formation, we used Mem3DG ( 28 ) to build a model of the membrane surface in three dimensions. Mem3DG is a framework and simulation engine that enables us to solve the governing equations of membrane bending using principles of discrete differential geometry.…”

Section: Resultsmentioning

confidence: 99%

The ins and outs of membrane bending by intrinsically disordered proteins

et al. 2023

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Membrane curvature is essential to diverse cellular functions. While classically attributed to structured domains, recent work illustrates that intrinsically disordered proteins are also potent drivers of membrane bending. Specifically, repulsive interactions among disordered domains drive convex bending, while attractive interactions drive concave bending, creating membrane-bound, liquid-like condensates. How might disordered domains that contain both repulsive and attractive domains affect curvature? Here, we examined chimeras that combined attractive and repulsive interactions. When the attractive domain was closer to the membrane, its condensation amplified steric pressure among repulsive domains, leading to convex curvature. In contrast, when the repulsive domain was closer to the membrane, attractive interactions dominated, resulting in concave curvature. Further, a transition from convex to concave curvature occurred with increasing ionic strength, which reduced repulsion while enhancing condensation. In agreement with a simple mechanical model, these results illustrate a set of design rules for membrane bending by disordered proteins.

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“…Given the limitations of our datasets, it is not reasonable to expect either model’s predictions to capture actual membrane shape. Further, the absence of data in these regions hints at the possibility that energy-minimizing shapes for these parameter combinations may not exist or different computational schemes may be needed to solve these equations [7,56,57]. A second more subtle difference between the predictions of the models is the edges in the phase maps which do not precisely align.…”

Section: Resultsmentioning

confidence: 99%

Modelling membrane curvature generation using mechanics and machine learning

Malingen

Rangamani

2022

J. R. Soc. Interface.

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The deformation of cellular membranes regulates trafficking processes, such as exocytosis and endocytosis. Classically, the Helfrich continuum model is used to characterize the forces and mechanical parameters that cells tune to accomplish membrane shape changes. While this classical model effectively captures curvature generation, one of the core challenges in using it to approximate a biological process is selecting a set of mechanical parameters (including bending modulus and membrane tension) from a large set of reasonable values. We used the Helfrich model to generate a large synthetic dataset from a random sampling of realistic mechanical parameters and used this dataset to train machine-learning models. These models produced promising results, accurately classifying model behaviour and predicting membrane shape from mechanical parameters. We also note emerging methods in machine learning that can leverage the physical insight of the Helfrich model to improve performance and draw greater insight into how cells control membrane shape change.

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Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Cited by 16 publications

References 133 publications

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

The ins and outs of membrane bending by intrinsically disordered proteins

Modelling membrane curvature generation using mechanics and machine learning

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