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.

10aactive matter10aadhesive locomotion10acell motility10acell sheet folding10aknotted DNA10atopological defects10aunicellular swimmers10aunjamming transition1 aAgostinelli, Daniele1 aCerbino, Roberto1 aDel Alamo, Juan, C1 aDeSimone, Antonio1 aHöhn, Stephanie1 aMicheletti, Cristian1 aNoselli, Giovanni1 aSharon, Eran1 aYeomans, Julia uhttp://dx.doi.org/10.3934/mine.202001102176nas a2200133 4500008004100000245010700041210006900148260003400217520165100251100002501902700002201927700002201949856007101971 2020 eng d00aNutations in plant shoots: endogenous and exogenous factors in the presence of mechanical deformations0 aNutations in plant shoots endogenous and exogenous factors in th bCold Spring Harbor Laboratory3 aWe present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots, as driven by differential growth at the tip. We discuss the evolution laws for endogenous oscillators, straightening mechanisms and reorientations to directional cues, such as phototropic responses to a far light source and gravitropic reactions governed by the statoliths avalanche dynamics. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of a Hopf bifurcation reminiscent of flutter instabilities exhibited by structural systems under nonconservative loads. When also oscillations due to endogenous cues are present, their weight relative to those associated with the Hopf instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the flutter induced oscillations becomes dominant. Our findings suggest that the relative importance of the two mechanisms is an emergent property of the system that is affected by the amplitude of elastic deformations, and highlight the crucial role of elasticity in the analysis of circumnutations.Competing Interest StatementThe authors have declared no competing interest.

1 aAgostinelli, Daniele1 aDeSimone, Antonio1 aNoselli, Giovanni uhttps://www.biorxiv.org/content/early/2020/07/06/2020.07.06.18898702026nas a2200205 4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773 2019 eng d a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio a1037023 aThe effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1016/j.jmps.2019.10370202205nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856004501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.