# Bimodal Mechanical Response of Membrane Necks: Implications for the Nuclear Envelope

## TL;DR

This paper explores how membrane necks in structures like the nuclear envelope respond to mechanical forces, revealing a two-phase behavior that could impact cellular function and synthetic membrane design.

## Contribution

The study identifies a bimodal mechanical response in membrane necks and provides a simple equation to predict their behavior under tension.

## Key findings

- Membrane necks constrict under low pressure gradients but dilate above a threshold tension.
- Neck behavior depends on pressure gradient, initial diameter, and membrane bending rigidity.
- Protein complexes in the neck stabilize size while maintaining the two-phase response to tension.

## Abstract

Among the fascinating shapes that biomembranes exhibit
are stomatocytes
with multiple membrane necks, found for example in nuclear membranes
and open autophagosomes. These morphologies, characterized by a high
topological genus, can be visualized 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 deducing 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 demonstrate a two-phase behavior: 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, stabilizing neck size while preserving
the same two-phase response to membrane tension. These findings highlight
a promising, little-noticed membrane property with implications for
organelle shape and function, as well as for synthetic membrane design.