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During closed mitosis in fission yeast, growing microtubules push onto the nuclear envelope to deform it, which results in fission into two daughter nuclei. The resistance of the envelope to bending, quantified by the flexural stiffness, helps determine the microtubule-dependent nuclear shape transformations. Computational models of envelope mechanics have assumed values of the flexural stiffness of the envelope based on simple scaling arguments. The validity of these estimates is in doubt, however, owing to the complex structure of the nuclear envelope. Here, we performed computational analysis of the bending of the nuclear envelope under applied force using a model that accounts for envelope geometry. Our calculations show that the effective bending modulus of the nuclear envelope is an order of magnitude larger than a single membrane and approximately five times greater than the nuclear lamina. This large bending modulus is in part due to the 45 nm separation between the two membranes, which supports larger bending moments in the structure. Further, the effective bending modulus is highly sensitive to the geometry of the nuclear envelope, ranging from twofold to an order magnitude larger than the corresponding single membrane. These results suggest that spatial variations in geometry and mechanical environment of the envelope may cause a spatial distribution of flexural stiffness in the same nucleus. Overall, our calculations support the possibility that the nuclear envelope may balance significant mechanical stresses in yeast and in cells from higher organisms. 

The mitochondrial membrane undergoes extreme remodeling during fission. While a few membrane-squeezing proteins are recognized as the key drivers of fission, there is a growing body of evidence that strongly suggests that conical lipids play a critical role in regulating mitochondrial morphology and fission. However, the mechanisms by which proteins and lipids cooperate to execute fission have not been quantitatively investigated. Here, we computationally model the squeezing of the largely tubular mitochondrion and show that proteins and conical lipids can act synergistically to trigger buckling instability and achieve extreme constriction. More remarkably, the study reveals that the conical lipids can act with different fission proteins to induce hierarchical instabilities and create increasingly narrow and stable constrictions. We reason that this geometric plasticity imparts significant robustness to the fission reaction by arresting the elastic tendency of the membrane to rebound during protein polymerization and depolymerization cycles. Our in vitro study validates protein–lipid cooperativity in constricting membrane tubules. Overall, our work presents a general mechanism for achieving drastic topological remodeling in cellular membranes.