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.

VL - 2 UR - http://dx.doi.org/10.3934/mine.2020011 ER - TY - RPRT T1 - Nutations in plant shoots: endogenous and exogenous factors in the presence of mechanical deformations Y1 - 2020 A1 - Daniele Agostinelli A1 - Antonio DeSimone A1 - Giovanni Noselli AB -We 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.

JF - bioRxiv PB - Cold Spring Harbor Laboratory UR - https://www.biorxiv.org/content/early/2020/07/06/2020.07.06.188987 ER - TY - JOUR T1 - Nutations in growing plant shoots: The role of elastic deformations due to gravity loading JF - Journal of the Mechanics and Physics of Solids Y1 - 2019 A1 - Daniele Agostinelli A1 - Alessandro Lucantonio A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Circumnutations KW - Flutter instability KW - Gravitropism KW - Hopf bifurcation AB -The 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.

UR - https://doi.org/10.1016/j.jmps.2019.103702 ER - TY - JOUR T1 - Liquid crystal elastomer strips as soft crawlers JF - Journal of the Mechanics and Physics of Solids Y1 - 2015 A1 - Antonio DeSimone A1 - Paolo Gidoni A1 - Giovanni Noselli KW - Crawling motility KW - Directional surfaces KW - Frictional interactions KW - Liquid crystal elastomers KW - Soft biomimetic robots AB -In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

VL - 84 UR - http://www.sciencedirect.com/science/article/pii/S0022509615300430 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - JOUR T1 - A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model JF - Proceedings of the Royal Society A 470, 20140333 (2014) Y1 - 2014 A1 - Giovanni Noselli A1 - Antonio DeSimone AB - We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. PB - Royal Society Publishing U1 - 34594 U2 - Mathematics ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. PB - Elsevier U1 - 34590 U2 - Mathematics ER -