Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of deformable vesicles or soft tissue like cell walls, chorions, and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements - perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.
During morphogenesis, a featureless convex cerebellum develops folds. As it does so, the cortex thickness is thinnest at the crest (gyri) and thickest at the trough (sulci) of the folds. This observation cannot be simply explained by elastic theories of buckling. A recent minimal model explained this phenomenon by modeling the developing cortex as a growing fluid under the constraints of radially spanning elastic fibers, a plia membrane and a nongrowing sub-cortex (Engstrom, et. al., PRX 2019). In this minimal buckling without bending morphogenesis (BWBM) model, the elastic fibers were assumed…
We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics simulations. Compliant, DNA-like filaments are found to undergo a continuous crossover from two distinct surface-ordered quadrupolar states, both characterized by tetrahedral patterns of topological defects, to either longitudinal or latitudinal bipolar structures with increasing polymer concentrations. These transitions, along with the intermediary arrangements that…
School of Engineering and Applied Sciences, Harvard University（哈佛大学生物工程与应用科学学院）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Organismic and Evolutionary Biology, Harvard University（哈佛大学生物演化生物学系）
Confinement of filamentary objects is ubiquitous in numerous biological, medical, and engineering scenarios. Quantitatively determining the mechanical interaction between flexible filaments and surface confinement is particularly challenging due to the unknown contact force induced by elasticity interacting with geometric constraints. Here, we consider a simplified model of confined filamentary object: an elastic curve under surface confinement. Local force and moment balance equation incorporating the role of contact is utilized to derive the contact force exerted by surface on the confined e…
Motivated by bacterial transport through porous media, here we study the swimming of an actuated, flexible helical filament in both three-dimensional free space and within a cylindrical tube whose diameter is much smaller than the length of the helix. The filament, at rest, has a native helical shape modeled after the geometry of a typical bacterial flagellar bundle. The finite length filament is a free swimmer, and is driven by an applied torque as well as a counter-torque (of equal strength and opposite direction) that represents a virtual cell body. We use a regularized Stokeslet framework …
Optimal Translocation of Living \& Active Filaments in Confinement
University of Padova（帕多瓦大学）；ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista（国际理论物理中心南美基础研究所，理论物理研究所，圣保罗州立大学）；van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam（范德瓦耳斯-泽曼研究所，物理研究所，阿姆斯特丹大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；GISC - Grupo Interdisciplinar de Sistemas Complejos, Universidad Complutense de Madrid（跨学科复杂系统小组，马德里康普顿斯大学）；INFN, Sezione di Padova（意大利国家核物理研究所，帕多瓦分部）
One of the most celebrated contributions to the study of the mechanical behavior of materials is due to J.D. Eshelby, who in the late 50s revolutionized our understanding of the elastic stress and strain fields due to an ellipsoidal inclusion/inhomogeneity that undergoes a transformation of shape and size. While Eshelby's work laid the foundation for significant advancements in various fields, including fracture mechanics, theory of phase transitions, and homogenization methods, its extension into the range of large deformations, and to situations in which the material can actively reorganize …
In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses and perform work on the external environment. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligne…
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how …
