Professor Matthew Turner, Leverhulme Trust Research Fellowship
Active Sheets
Materials can be divided into two classes: passive and active. Passive materials are at, or very near, equilibrium. Nearly all man-made objects are passive. These can be deformed or forced to flow by external forces but do not spontaneously flow or move by themselves.
Some of the examples of active materials so-far studied include:
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Suspensions of active "swimmers" such as catalytic colloids or swimming micro-organisms,
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Mobile cells and tissues
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Active liquid crystals, made up of ordered molecules that exert forces on one another using chemical fuel.
Orientational-dependent stresses result that drive flows. The cortical cytoskeleton found just below the plasma membrane in cells is often cited as such an example. Here a meshwork of membrane-associated filaments are moved by molecular motors, see Figure. Similar systems have been reconstituted in quasi two dimensions (2D) at an oil-water interface and on the surface of a membrane vesicle. While these systems (swimmers, cell tissue and active liquid crystals) can all be rather different at the level of their constituent chemistry, they require a substantially similar physical description. This makes the development of a general physical theory for active sheets extremely attractive.
The aim of Professor Matthew Turner's Fellowship is to analyse theoretically quasi-2D sheets of active matter in order to explore how the activity of the force-generating process couples to the shape and motion of the surface itself. There are direct applications in biology (understanding the cytoskeletal cortex) but also for physicists (understanding the behaviour of such active materials), chemists (synthesising artificial analogues) and engineers (future applications of novel adaptive materials).
Pictured left: An "active sheet".
- (a) A cartoon of a phospholipid bilayer, ubiquitous in cell biology
- (b) Fibres (black lines) and motors (red), forming the cortical cytoskeleton, attach to this sheet (by yellow linkers); the motors generate forces (red arrows) depending on the ordering of the meshwork
- (c) On larger scales this active membrane can be treated as a continuous, actively deformable surface
- (d) The local geometry of this surface is specified by two local curvatures, the inverse of the radii of orthogonal tangent circles (shown)
- (e) Flows driven on this surface can drive shape changes, e.g. counter rotating flows imposed at the end of a membrane tube can lead to a growing helical instability with outward/inward pointing forces (shown).
These forces result from the coupling between viscous stresses, arising from the tangential flow of the membrane material, and the membrane shape, controlled by its mechanical properties. In active sheets there would also be a distributed, active stress.