Complex mechanical response of stomatocyte morphology: Implications for the nuclear envelope

Among the fascinating shapes that biomembranes exhibit are stomatocytes, found for example in nuclear membranes and open autophagosomes. These morphologies, characterised by a high topological genus, can be visualised as spherical double membranes connected by neck-like structures. The necks are often occupied by specific biomolecular complexes, such as the nuclear pore complex, which divide the space into three distinct compartments. Understanding how the size of these necks responds to pressure gradients is fundamentally important for unravelling the influence of mechanical stimuli on traffic control through the necks, for example, in nuclear mechanosensing. In this work, we use computer simulations and theoretical analysis to investigate how neck size responds to variations in pressure or tension. Our findings reveal a two-phase behaviour: below a certain threshold, necks constrict as the pressure gradient increases, while above that threshold, they dilate. This response stems from the pure membrane’s mechanics and depends on the magnitude of the pressure gradient, the initial diameter of the neck and the membrane bending rigidity. We also provide a simple equation that links the threshold tension, the neck diameter and the bending rigidity, offering a useful tool to quickly assess different scenarios. Our results furthermore show that protein complexes in the neck partially counteract both constriction and dilation, stabilising neck size while preserving the same two-phase response to membrane tension. These findings uncover a novel, previously overlooked membrane property with implications for organelle shape and function.