Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework

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

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. These tubes can be formed due to localized forces acting on the membrane or by the 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.

Generation of nanoscopic membrane curvature for membrane trafficking

Curved membranes are key features of intracellular organelles, and their generation involves dynamic protein complexes. Here we describe the fundamental mechanisms such as the hydrophobic insertion, scaffolding and crowding mechanisms these proteins use to produce membrane curvatures and complex shapes required to form intracellular organelles and vesicular structures involved in endocytosis and secretion. For each mechanism, we discuss its cellular functions as well as the underlying physical principles and the specific membrane properties required for the mechanism to be feasible. We propose that the integration of individual mechanisms into a highly controlled, robust process of curvature generation often relies on the assembly of proteins into coats. How cells unify and organize the curvature-generating factors at the nanoscale is presented for three ubiquitous coats central for membrane trafficking in eukaryotes: clathrin-coated pits, caveolae, and COPI and COPII coats. The emerging theme is that these coats arrange and coordinate curvature-generating factors in time and space to dynamically shape membranes to accomplish membrane trafficking within cells.

Modelling membrane curvature generation using mechanics and machine learning

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.