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Multiscale modeling and simulation of biological and artificial
locomotion at the micron scale: from metastatic tumor cells and unicellular swimmers to bioinspired microrobots

Final 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)

The central idea of the project is the use of mathematical modelling as a working tool to discover mechanisms used by nature in motility at microscopic scales, and then to implement them into conceptual or physical prototypes that may be interesting for new applications, for example in the field of bio-inspired robotics.

This idea is best illustrated with a concrete example, taken form the results of our project. Euglenids are unicellular algae (protists) and 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, similar to peristaltic waves. This is called metaboly, and very little is actually known about function and mechanisms governing this amoeboid motion. We have proved with experiments and models that this gait switch from flagellar swimming to crawling locomotion occurring through the propagation of peristaltic waves is triggered by confinement. Remarkably, all the sensing and decision making involved in this behavioural switch take place in a unicellular organism without a brain or a central nervous system. This finding may inspire the design of new robots where part of the control is achieved thanks to elastic compliance, and intelligence is embodied in the architecture of the body.
It turns out that metaboly is only seen in those euglenids exhibiting under the plasma membrane a structure made of many interlocking and flexible pellicle strips. 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: the theorema egregium due to Gauss. In a sense, euglenids know Differential Geometry, and they use theorema egregium to control their shape. We have proved with experiments and models that this is indeed true for the biological organisms, and that this new concept for shape morphing by sliding of pellicle strips can be implemented in 3D-printed engineered structures.

While each biological system is governed by its own specific (and often exquisite) details, the mathematical structure of the problem of controlling shape is general, and can be used to transfer the ideas described above to other material systems, to understand locomotion of other biological organisms, to discover different general principles. The question of how to actively control local distances between material points has led us to the study of stimulus-responsive engineering materials (e.g. Liquid Crystal Elastomers where temperature changes produce active strains) and of the active stresses produced by molecular motors in biological structures. Replacing shape control of surfaces with shape control of curves (three-dimensional rods, whose shape is controlled by spontaneous curvature and twist) has led us to the study of biological or artificial beating flagella, and to realize that some of the same principles can be exported to the undulatory locomotion of snakes or to the motion of growing shoots in plants. Also the crawling motion of cells on patterned substrates follows similar principles.

Among other things, we have discovered in this way that propagation of peristaltic waves along the body provides an optimal actuation strategy for locomotion of slender (one-dimensional) objects (at least in the regime of small lateral oscillations);
that in snake-like locomotion the spontaneous curvature along the body provides the propulsive force, while the preferred curvature at the leading edge provides the steering; and that cells are guided along adhesive lines by forces of entropic origin arising from their shape fluctuations. These and similar ideas are finding applications in the vibrant current research for a new generation of bio-inspired robots.