Patterns of Flexible Nanotubes Formed by Liquid-Ordered and Liquid-Disordered Membranes

Significance Statement

From an engineering point of view, biological and biomimetic membranes have rather unusual mechanical properties. Indeed, these membranes are very thin sheets of lipids and proteins, with the lipids forming molecular bilayers that have a thickness of 4 – 5 nm. These lipid bilayers are in a fluid state and their mechanical properties are primarily governed by two fluid-elastic parameters, the bending rigidity and the spontaneous curvature. The bending rigidity describes the resistance of the membrane against bending. This quantity can be measured by a variety of experimental methods and has a typical value of the order of 10-19 J. The spontaneous curvature, on the other hand, describes the preferred curvature of the membrane and provides a quantitative measure for the asymmetry between the two leaflets of the bilayer. In contrast to the bending rigidity, the spontaneous curvature can vary over several orders of magnitude, from 1/(20 nm) arising from molecular adsorption or protein scaffolding to 1/(50 μm) corresponding to the inverse size of giant vesicles.

So far, our ability to actually measure the spontaneous curvature has been rather limited. In fact, prior to the recent ACS Nano publication, we had essentially no reliable method to determine this curvature as soon as its magnitude became large compared to the inverse size of giant vesicles. The new publication now provides such a method, which is based on the spontaneous formation of membrane nanotubes and on the theoretical analysis of the resulting vesicle morphologies. We demonstrate the utility of our new method by applying it to liquid-ordered and liquid-disordered membranes exposed to aqueous two-phase systems, i.e., to aqueous solutions of two polymers, PEG and dextran, that undergo aqueous phase separation for relatively small weight fractions of the polymers. In addition to introducing a reliable method for measuring the spontaneous curvature, the publication provides three important insights. First, it elucidates the kinetics of tube formation and shows that the tubulation starts with the nucleation of small membrane buds which then grow into necklace-like tubes. When the length of a necklace-like tube reaches a certain critical value, the tube changes its morphology and transforms into a cylindrical one. Second, depending on the phase behavior of the aqueous solution and the wetting properties of the membranes, different tube patterns have been observed as illustrated in Fig. 1. Panel a of this figure displays a disordered tube pattern, corresponding to a vesicle membrane that is completely wetted by the PEG-rich phase. In this case, the nanotubes explore the whole PEG-rich droplet but stay away from the dextran rich phase. In Fig. 1b, on the other hand, we see a layer of densely packed tubes corresponding to a membrane that is partially wetted by both aqueous phases. The nanotubes now adhere to the interface between the two aqueous droplets and form a thin layer in which crowding leads to short-range orientational order of the tubes. Finally, the paper reveals the molecular mechanism for the curvature generation observed in the optical microscope. This mechanism is provided by the adsorption of PEG molecules from the aqueous solutions. The adsorption is relatively weak, with a binding affinity of about 4 kJ/mol or 1.6KBT  per chain. Nevertheless, the asymmetric adsorption layers that build up on the two sides of the membranes generate a substantial spontaneous curvature with a magnitude of about 1/(125 nm) and 1/(600 nm) for the liquid-disordered and the liquid-ordered membranes, respectively.

Membrane nanotubes represent highly curved membrane structures and have a large area-to-volume ratio, thereby providing reservoirs of membrane area that can be easily retracted back by applying relatively low mechanical tensions to the membrane. The tubes also enhance membrane-dependent processes and stably enclose thin water channels which are well-separated and shielded from their surroundings. The diameter of these tubes directly reflects the spontaneous curvature of the membranes. As shown in the publication, this curvature can be generated by asymmetric adsorption of solute molecules onto the two leaflets of the membranes.

The next challenge is to control the spatial location of the tubes. One promising approach is to use membranes with two different lipid domains, only one of which leads to the strong adsorption of curvature-generating molecules. The tubes will then primarily nucleate from these intramembrane domains which should allow us to control both the number and the length of the tubes. Biological membranes form both intra- and intercellular nanotubes that are used for molecular sorting within single cells and for long-distance connections between different cells. Intracellular tubes connect distant parts of the same cell and are used for molecular sorting, signaling, and transport. Intercellular nanotubes between two or more cells provide long-distance connections for cell-cell communication, intercellular transport, and virus infections. Some of the tubular networks found in the living cell, such as the plasmic reticulum, have a rather complex architecture and it will certainly take some time before we will be able to construct membrane architectures of comparable complexity.

For more information, see


Figure 1 Legend: Patterns of flexible nanotubes formed by liquid-disordered membranes after the interior aqueous compartment separated into a PEG-rich and dextran-rich phase: (a) Disordered pattern corresponding to a vesicle membrane that is completely wetted by the PEG-rich phase; and (b) Layer of densely packed tubes corresponding to a membrane that is partially wetted by both aqueous phases. All tubes are connected to the outer vesicle membranes (red circles). In both images, the diameter of the tubes is below the diffraction limit of the light microscope but the tubes are theoretically predicted to be necklace-like and cylindrical in (a) and (b), respectively.

Patterns of Flexible Nanotubes Formed by Liquid-Ordered and Liquid-Disordered Membranes.. Advances in Engineering

Figure 2 Legend : Authors (from left to right): Yonggang Liu, associate professor; Jaime Agudo-Canalejo, postdoctoral researcher; Andrea Grafmuller, group leader; Rumiana Dimova, group leader; and Reinhard Lipowsky, department head. All authors work at the Max Planck Institute of Colloids and Interfaces, Potsdam, Germany, apart from Yonggang Liu who is affiliated with the Changchun Institute of Applied Chemistry, Changchun, China.

Patterns of Flexible Nanotubes Formed by Liquid-Ordered and Liquid-Disordered Membranes.. Advances in Engineering

 Journal Reference

ACS Nano. 2016;10(1):463-74.

Liu Y1,2, Agudo-Canalejo J1, Grafmüller A1, Dimova R1, Lipowsky R1.

[expand title=”Show Affiliations”]
  1. Theory & Biosystems, Max Planck Institute of Colloids and Interfaces , 14424 Potsdam, Germany.
  2. State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences , 130022 Changchun, China.


Biological membranes form both intra- and intercellular nanotubes that are used for molecular sorting within single cells and for long-distance connections between different cells. Such nanotubes can also develop from synthetic lipid bilayers in their fluid state. Each nanotube has a large area-to-volume ratio and stably encloses a water channel that is thereby shielded from its surroundings. The tubes are rather flexible and can easily change both their length and their conformation. Here, we study nanotubes formed by liquid-ordered (Lo) and liquid-disordered (Ld) membranes with three lipid components exposed to aqueous mixtures of two polymers, polyethylene glycol (PEG) and dextran. Both types of membranes form striking patterns of nanotubes when we reduce the volume of giant vesicles by osmotic deflation, thereby exposing the two bilayer leaflets of the membranes to polymer solutions of different composition. With decreasing volume, three different patterns are observed corresponding to three distinct vesicle morphologies that reflect the interplay of spontaneous curvature and aqueous phase separation. We show that tube nucleation and growth is governed by two kinetic pathways and that the tubes undergo a novel shape transformation from necklace-like to cylindrical tubes at a certain critical tube length. We deduce the spontaneous curvature generated by the membrane-polymer interactions from the observed vesicle morphologies using three different and independent methods of image analysis. The spontaneous curvature of the Ld membranes is found to be 4.7 times larger than that of the Lo membranes. We also show that these curvatures are generated by weak PEG adsorption onto the membranes, with a binding affinity of about 1.6 kBT per chain. In this way, our study provides a direct connection between nanoscopic membrane shapes and molecular interactions. Our approach is rather general and can be applied to many other systems of interest such as polymersomes or membrane-bound proteins and peptides.

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