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  • Mid-Term Report Summary - MICROMOTILITY (Multiscale modeling and simulation of biological and artificiallocomotion at the micron scale: from metastatic tumor cells and unicellular swimmers to bioinspired microrobots)


Project ID: 340685
Funded under: FP7-IDEAS-ERC
Country: Italy

Mid-Term Report Summary - MICROMOTILITY (Multiscale modeling and simulation of biological and artificiallocomotion at the micron scale: from metastatic tumor cells and unicellular swimmers to bioinspired microrobots)

Our goal is to use mathematical modelling as a tool to discover mechanisms used by Nature in motility at microscopic scales, and implement them into conceptual or physical prototypes that may be interesting for new applications, for example in the field of bio-inspired Soft Robotics. It may be interesting to give some concrete examples of how this can work, taken form the results of our project.
Euglenids are unicellular algae (protists). They have flagella but, besides classical flagellar locomotion (the one used by sperm cells, based on the beating of a flexible tail), they also move by executing dramatic shape changes of the whole body. This is called metaboly, and very little is actually known about function and mechanisms governing this amoeboid motion. It turns out that only those euglenids exhibiting under the plasma membrane a structure made of many interlocking and flexible pellicle strips show metaboly, and that the shape changes are due to the relative sliding of these pellicle strips, suitably coordinated. How does this work?
By sliding their pellicle strips, euglenids change and regulate distances among points of their bounding surface: they control the metric of that surface. The connection between a surface metric and its shape (its Gaussian curvature) is provided by a celebrated result of Differential Geometry: Theorema Egregium discovered by Gauss in the 19th century. In a sense, euglenids know Differential Geometry, and they use Theorema Egregium to control their shape.
The mechanisms by which microscopic components (microtubules and molecular motors) produce coordinated sliding of pellicle strips are similar to muscular contraction, but still unclear. But this question introduces our second example: how internal microscopic forces (active stresses) produced by biological agents (molecular motors) drive shape changes? Elasticity theory, suitably modified to account for active stresses, can predict how overall shape is controlled by active stresses.
In the presence of active stresses, a three-dimensional object will deform. In a two- or one-dimensional geometry (a surface or a rod), this will result in a spontaneously curved object, whose curvature can be adjusted by tuning the active stresses. The mathematical description of elastic systems with active stresses is common to a large variety of systems: elastic solids exhibiting distortions due to phase transformations (such as Liquid Crystal Elastomers, LCEs), hydrogels swollen by absorption of a solvent, purely elastic systems made of simple desk-top components which are first (differentially) pre-stretched and then assembled. Irrespectively of the origin of the active stresses, the governing equations and the functional relation between active stresses and resulting shapes is the same. The problem of controlling shape through the action of active stresses (molecular motors in the biological case) can be studied using a hierarchy of model systems. At one end of the hierarchy, the shape programming problem can be studied at a proof-of-principle stage using simple desk-top experiments. Later, more sophisticated and demanding fabrication techniques, based on hydrogels or LCEs, can be applied, which are however more suitable for miniaturisation.
A final example comes from undulatory locomotion in snakes and snake-like robots. We model these systems as flexible rods which, thanks to muscular contraction (in snakes) or internal motors (in robots), are able to control their curvature, and interact with the environment with frictional forces. Our governing equations can be solved if exactly three boundary conditions (two at the leading edge -the head- and one at the trailing edge - the tail) are prescribed. The extra boundary condition at the leading edge is related to the selection of the path ahead, i.e., to steering. This has led to discovering a new principle in snake-like locomotion: control of curvature along the body provides the propulsive force, curvature at the leading edge provides the steering.

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