1
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Erisis S, Hörning M. Self-organization of PIP3 waves is controlled by the topology and curvature of cell membranes. Biophys J 2024; 123:1058-1068. [PMID: 38515298 PMCID: PMC11079865 DOI: 10.1016/j.bpj.2024.03.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2024] [Revised: 03/13/2024] [Accepted: 03/18/2024] [Indexed: 03/23/2024] Open
Abstract
Phosphatidylinositol (3,4,5)-trisphosphate (PIP3) is a signaling lipid on the plasma membrane that plays a fundamental role in cell signaling with a strong impact on cell physiology and diseases. It is responsible for the protruding edge formation, cell polarization, macropinocytosis, and other membrane remodeling dynamics in cells. It has been shown that the membrane confinement and curvature affects the wave formation of PIP3 and F-actin. But, even in the absence of F-actin, a complex self-organization of the spatiotemporal PIP3 waves is observed. In recent findings, we have shown that these waves can be guided and pinned on strongly bended Dictyostelium membranes caused by molecular crowding and curvature-limited diffusion. Based on these experimental findings, we investigate the spatiotemporal PIP3 wave dynamics on realistic three-dimensional cell-like membranes to explore the effect of curvature-limited diffusion, as observed experimentally. We use an established stochastic reaction-diffusion model with enzymatic Michaelis-Menten-type reactions that mimics the dynamics of Dictyostelium cells. As these cells mimic the three-dimensional shape and size observed experimentally, we found that the PIP3 wave directionality can be explained by a Hopf-like and a reverse periodic-doubling bifurcation for uniform diffusion and curvature-limited diffusion properties. Finally, we compare the results with recent experimental findings and discuss the discrepancy between the biological and numerical results.
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Affiliation(s)
- Sema Erisis
- Institute of Biomaterials and Biomolecular Systems, University of Stuttgart, Stuttgart, Germany
| | - Marcel Hörning
- Institute of Biomaterials and Biomolecular Systems, University of Stuttgart, Stuttgart, Germany.
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2
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Fossati M, Scheibner C, Fruchart M, Vitelli V. Odd elasticity and topological waves in active surfaces. Phys Rev E 2024; 109:024608. [PMID: 38491602 DOI: 10.1103/physreve.109.024608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 01/12/2024] [Indexed: 03/18/2024]
Abstract
Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.
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Affiliation(s)
- Michele Fossati
- SISSA, Trieste 34136, Italy
- INFN Sezione di Trieste, Trieste 34127, Italy
| | - Colin Scheibner
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Michel Fruchart
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Vincenzo Vitelli
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA
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3
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Maji A, Dasbiswas K, Rabin Y. Shape transitions in a network model of active elastic shells. SOFT MATTER 2023; 19:7216-7226. [PMID: 37724013 DOI: 10.1039/d3sm01041d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/20/2023]
Abstract
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.
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Affiliation(s)
- Ajoy Maji
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
| | - Yitzhak Rabin
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.
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4
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Würthner L, Goychuk A, Frey E. Geometry-induced patterns through mechanochemical coupling. Phys Rev E 2023; 108:014404. [PMID: 37583206 DOI: 10.1103/physreve.108.014404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 05/15/2023] [Indexed: 08/17/2023]
Abstract
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction-diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction-diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction-diffusion system. The feedback loop between membrane shape deformations and reaction-diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.
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Affiliation(s)
- Laeschkir Würthner
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Andriy Goychuk
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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5
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Chen X, Xu Y, Lou K, Peng Y, Zhou C, Zhang HP, Wang W. Programmable, Spatiotemporal Control of Colloidal Motion Waves via Structured Light. ACS NANO 2022; 16:12755-12766. [PMID: 35857820 DOI: 10.1021/acsnano.2c04596] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Traveling waves in a reaction-diffusion system are essential for long-range communication in living organisms and inspire biomimetic materials of similar capabilities. One recent example is the traveling motion waves among photochemically oscillating, silver (Ag)-containing colloids. Being able to manipulate these colloidal waves holds the key for potential applications. Here, we have discovered that these motion waves can be confined by light patterns and that the chemical clocks of silver particles are moved forward by reducing local light intensity. Using these discoveries as design principles, we have applied structured light technology for the precise and programmable control of colloidal motion waves, including their origins, propagation directions, paths, shapes, annihilation, frequency, and speeds. We have also used the controlled propagation of colloidal waves to guide chemical messages along a predefined path to activate a population of micromotors located far from the signal. Our demonstrated capabilities in manipulating colloidal waves in space and time offer physical insights on their operation and expand their usefulness in the fundamental study of reaction-diffusion processes. Moreover, our findings inspire biomimetic strategies for the directional transport of mass, energy, and information at micro- or even nanoscales.
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Affiliation(s)
- Xi Chen
- Sauvage Laboratory for Smart Materials, School of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Yankai Xu
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Kai Lou
- Guangzhou Kayja-Optics Technology Co., Ltd., Guangzhou 511458, China
| | - Yixin Peng
- Sauvage Laboratory for Smart Materials, School of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Chao Zhou
- Sauvage Laboratory for Smart Materials, School of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
- Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - H P Zhang
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Wei Wang
- Sauvage Laboratory for Smart Materials, School of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
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6
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Miller PW, Fortunato D, Muratov C, Greengard L, Shvartsman S. Forced and spontaneous symmetry breaking in cell polarization. NATURE COMPUTATIONAL SCIENCE 2022; 2:504-511. [PMID: 37309402 PMCID: PMC10260237 DOI: 10.1038/s43588-022-00295-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 07/12/2022] [Indexed: 06/14/2023]
Abstract
How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.
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Affiliation(s)
- Pearson W. Miller
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- These authors contributed equally: Pearson W. Miller, Daniel Fortunato
| | - Daniel Fortunato
- Center for Computational Mathematics, Flatiron Institute, New York, NY, USA
- These authors contributed equally: Pearson W. Miller, Daniel Fortunato
| | - Cyrill Muratov
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, USA
- Dipartimento di Matematica, Università di Pisa, Pisa, Italy
| | - Leslie Greengard
- Center for Computational Mathematics, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
| | - Stanislav Shvartsman
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
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7
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Nishide R, Ishihara S. Pattern Propagation Driven by Surface Curvature. PHYSICAL REVIEW LETTERS 2022; 128:224101. [PMID: 35714259 DOI: 10.1103/physrevlett.128.224101] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 04/15/2022] [Indexed: 06/15/2023]
Abstract
Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces has been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first time that a static Turing pattern on a flat surface can propagate on a curved surface, as opposed to previous studies, where the pattern is presupposed to be static irrespective of the surface geometry. To understand such significant changes on curved surfaces, we investigate reaction-diffusion systems on axisymmetric curved surfaces. Numerical and theoretical analyses reveal that both the symmetries of the surface and pattern participate in the initiation of pattern propagation. This study provides a novel and generic mechanism of pattern propagation that is caused by surface curvature, as well as insights into the general role of surface geometry.
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Affiliation(s)
- Ryosuke Nishide
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
| | - Shuji Ishihara
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
- Universal Biology Institute, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
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8
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Binysh J, Wilks TR, Souslov A. Active elastocapillarity in soft solids with negative surface tension. SCIENCE ADVANCES 2022; 8:eabk3079. [PMID: 35275714 PMCID: PMC8916726 DOI: 10.1126/sciadv.abk3079] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. Whereas active interfaces have been realized across many experimental systems, control of three-dimensional (3D) bulk materials remains a challenge. Here, we develop continuum theory and microscopic simulations that describe a 3D soft solid whose boundary experiences active surface stresses. The competition between active boundary and elastic bulk yields a broad range of previously unexplored phenomena, which are demonstrations of so-called active elastocapillarity. In contrast to thin shells and vesicles, we discover that bulk 3D elasticity controls snap-through transitions between different anisotropic shapes. These transitions meet at a critical point, allowing a universal classification via Landau theory. In addition, the active surface modifies elastic wave propagation to allow zero, or even negative, group velocities. These phenomena offer robust principles for programming shape change and functionality into active solids, from robotic metamaterials down to shape-shifting nanoparticles.
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Affiliation(s)
- Jack Binysh
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
| | - Thomas R. Wilks
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
- Exact Sciences Innovation, Sherard Building, Edmund Halley Road, Oxford OX4 4DQ, UK
| | - Anton Souslov
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
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9
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Peterson MSE, Baskaran A, Hagan MF. Vesicle shape transformations driven by confined active filaments. Nat Commun 2021; 12:7247. [PMID: 34903731 PMCID: PMC8668962 DOI: 10.1038/s41467-021-27310-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 11/12/2021] [Indexed: 12/02/2022] Open
Abstract
In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. 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-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.
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Affiliation(s)
- Matthew S E Peterson
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA, 02453, United States
| | - Aparna Baskaran
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA, 02453, United States.
| | - Michael F Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA, 02453, United States.
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10
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Chemically controlled pattern formation in self-oscillating elastic shells. Proc Natl Acad Sci U S A 2021; 118:2025717118. [PMID: 33649242 DOI: 10.1073/pnas.2025717118] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.
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11
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Mourran A, Jung O, Vinokur R, Möller M. Microgel that swims to the beat of light. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:79. [PMID: 34129113 PMCID: PMC8206062 DOI: 10.1140/epje/s10189-021-00084-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/27/2021] [Indexed: 05/04/2023]
Abstract
Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.
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Affiliation(s)
- Ahmed Mourran
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany.
| | - Oliver Jung
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany
| | - Rostislav Vinokur
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany
| | - Martin Möller
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany.
- Institut of Technical and Macromolecular Chemistry der RWTH Aachen, Forckenbeckstr. 50, D-52056, Aachen, Germany.
- 3 Max-Planck School Matter to life, D-69120, Heidelbergy, Germany.
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12
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Haas PA, Goldstein RE. Morphoelasticity of large bending deformations of cell sheets during development. Phys Rev E 2021; 103:022411. [PMID: 33736073 DOI: 10.1103/physreve.103.022411] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 01/07/2021] [Indexed: 11/07/2022]
Abstract
Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination.
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Affiliation(s)
- Pierre A Haas
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.,Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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13
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Levin I, Deegan R, Sharon E. Self-Oscillating Membranes: Chemomechanical Sheets Show Autonomous Periodic Shape Transformation. PHYSICAL REVIEW LETTERS 2020; 125:178001. [PMID: 33156660 DOI: 10.1103/physrevlett.125.178001] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Revised: 06/24/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
While living organisms have mastered the dynamic control of residual stresses within sheets to induce shape transformation and locomotion, man-made implementations are rudimentary. We present the first autonomously shape-shifting sheets made of a gel that shrinks and swells in response to the phase of an oscillatory chemical (Belousov-Zhabotinsky) reaction. Propagating reaction-diffusion fronts induce localized deformation of the gel. We show that these localized deformations prescribe a spatiotemporal pattern of Gaussian curvature, leading to time-periodic global shape changes. We present the computational tools and experimental protocols needed to control this system, principally the relationship between the Gaussian curvature and the reaction phase, and optical imprinting of the wave pattern. Together, our results demonstrate a route for developing fully autonomous soft machines mimicking some of the locomotive capabilities of living organisms.
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Affiliation(s)
- Ido Levin
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Robert Deegan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eran Sharon
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
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14
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Miller PW, Dunkel J. Gait-optimized locomotion of wave-driven soft sheets. SOFT MATTER 2020; 16:3991-3999. [PMID: 32255142 DOI: 10.1039/c9sm02103e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Inspired by the robust locomotion of limbless animals in a range of environments, the development of soft robots capable of moving by localized swelling, bending, and other forms of differential growth has become a target for soft matter research over the last decade. Engineered soft robots exhibit a wide range of morphologies, but theoretical investigations of soft robot locomotion have largely been limited to slender bodied or one-dimensional examples. Here, we demonstrate design principles regarding the locomotion of two-dimensional soft materials driven by morphoelastic waves along a dry substrate. Focusing on the essential common aspects of many natural and man-made soft actuators, a continuum model is developed which links the deformation of a thin elastic sheet to surface-bound excitation waves. Through a combination of analytic and numerical methods, we investigate the relationship between induced active stress and self-propulsion performance of self-propelling sheets driven by FitzHugh-Nagumo type chemical waves. Examining the role of both sheet geometry and terrain geography on locomotion, our results can provide guidance for the design of more efficient soft crawling devices.
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Affiliation(s)
- Pearson W Miller
- Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA, USA.
| | - Jörn Dunkel
- Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA, USA.
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15
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Metselaar L, Yeomans JM, Doostmohammadi A. Topology and Morphology of Self-Deforming Active Shells. PHYSICAL REVIEW LETTERS 2019; 123:208001. [PMID: 31809098 DOI: 10.1103/physrevlett.123.208001] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Indexed: 06/10/2023]
Abstract
We present a generic framework for modeling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding environment. We find that the cross talk between the self-induced flows of active particles and dynamic reshaping of the shell can result in conformations that are tunable by varying the form and magnitude of active stresses. We further demonstrate and explain how self-induced topological defects in the active layer can direct the morphodynamics of the shell. These findings are relevant to understanding morphological changes during organ development and the design of bioinspired materials that are capable of self-organization.
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Affiliation(s)
- Luuk Metselaar
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Amin Doostmohammadi
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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16
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Frank JR, Guven J, Kardar M, Shackleton H. Pinning of diffusional patterns by non-uniform curvature. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/127/48001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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