Topology and Dynamics of Active Nematic Vesicles

Cells are complex objects with a sophisticated metabolic system. Their evolutionary ancestors, the primordial cells, were merely composed of a membrane and a few molecules. These were minimalistic yet perfectly functioning systems. Our in vitro approach aims for this reduction of complexity to investigate specific cellular functions separately or to create new characteristics from bio-molecular building blocks.

In this study, together with our international collaborators, we created a minimalistic cell model that exhibits continuous active shape changes. (Video1: Various morphologies of active nematic vesicles.)

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Fig.1: Spherical vesicle. The microtubules form a cortex on the membrane that moves continuously.

The system basically encapsulates two kinds of biomolecules –microtubules and kinesins-  into a membrane shell. Analogously to living cells this envelope consists of a flexible lipid double-layer and is called a vesicle. Inside, microtubules –tube-like components of the cytoskeleton- align parallel to a liquid crystal film on the membrane. The kinesins are located in between of the microtubules. While in nature kinesins are walking on microtubules to transport cargo, here they are arranged in couples and exert forces that slide the microtubules alongside each other. Thus an active cortex layer is formed that drives deformations of the vesicle (Fig.1).

 

Decisive for this deformation is that the liquid crystal must always contain some so called “defects”, discontinuities where the parallel order of the tubes cannot be sustained. Mathematicians explain these kinds of phenomena by way of the Poincaré-Hopf theorem, figuratively also referred to as the “hairy ball problem.” Just as one can't comb a hairy ball flat without creating a cowlick, there will always be some microtubules that cannot lay flat against the membrane surface in a regular pattern. At certain locations the tubules will be oriented somewhat orthogonally to each other – in a very specific geometry.

Since the microtubules are in constant motion alongside each other due to the activity of the kinesin molecules, the defects  also migrate. Amazingly, they do this in a very uniform and periodic manner, oscillating between two fixed orientations.

As long as the vesicle has a spherical shape, the defect movement has no significant influence on the external shape of the membrane. However, as soon as some excess membrane is provided (which can be done by osmosis) the vesicle starts to change in shape due to the movement within the membrane. As even more water is pulled out by osmosis, slack in the membrane forms into spiked extensions resembling those used by single cells for locomotion.

The morphology of the vesicles is also affected by their size. While big vesicles with a radius above 18 µm always exhibit four defects, smaller ones also show only two defects. This results either in a temporary ring arrangement of the microtubules (Fig.2) or in a structure with two poles that resembles the spindle of a dividing cell (Fig.3).

Fig.2: Ring arrangement of the microtubules in a vesicle. Actively driven, the ring elongates and bends in its spherical confinement.
Fig.3: Spidle-like conformation. Two poles emerge, where the microtubules form asters. The system shows characteristic repetitive phases of elongation and collapse.