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MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

1 SISSA–International School for Advanced Studies, 34136 Trieste, Italy
2 Dip. Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, 20090 Segrate (MI), Italy
3 Mechanical and Aerospace Engineering Dept., University of California San Diego, 9500 Gilman Drive, La Jolla CA, USA
4 The BioRobotics Institute, Scuola Superiore Sant’Anna, 56127 Pisa, Italy
5 DAMTP, University of Cambridge, UK
6 The Racah Institute of Physics, The Hebrew University of Jerusalem, Israel
7 The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, UK

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.
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