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This theoretical study demonstrates that membrane tension plays a critical role in determining whether cells engulf or expel nanoparticles during processes like endocytosis. The researchers show that the energy required to deform membrane regions not in direct contact with particles becomes dominant at finite tension levels, creating a competition between particle adhesion, membrane tension, and particle size that governs whether wrapping proceeds, stalls, or reverses. They developed a mathematical framework and simplified approximation to predict these wrapping-unwrapping transitions across different conditions.
Why it matters
This framework could improve the design of therapeutic nanoparticles for drug delivery by predicting which particle properties enable successful cellular uptake. The findings also advance understanding of fundamental biological processes including endocytosis, viral entry, and membrane fusion events.
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arXiv:2604.13415v2 Announce Type: replace
Abstract: Membrane wrapping controls nanoparticle uptake during endocytosis, whereas the reverse process of membrane unwrapping accompanies particle expulsion and membrane fusion events. Existing theoretical descriptions typically focus on adhesion and bending energies within the particle membrane contact region and often neglect the deformation energy of the membrane outside the contact zone. This approximation is valid only in the limit of vanishing membrane tension, where the non contact membrane assumes a catenoid like configuration with negligible bending energy. However, at finite tension the deformation of the non contact membrane becomes a dominant energetic contribution. Here we show that this tension dependent non contact energy governs the progression of particle wrapping. By analysing the variation of the total membrane energy with wrapping degree, we uncover a competition between particle adhesion, membrane tension and particle size that determines whether wrapping proceeds, stalls, or reverses into spontaneous unwrapping. This framework reveals a stalling boundary separating regimes of particle uptake and expulsion. To capture the non contact deformation efficiently, we derive a compact phenomenological approximation that accurately reproduces the full numerical solution of the membrane shape. The resulting energetic map provides a unified physical description of particle wrapping and unwrapping, with implications for endocytosis, membrane fusion, and nanoparticle design.
Source: Membrane Tension Governs Particle Wrapping-Unwrapping Transitions and Stalling