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Nicolaou ZG, Case DJ, Wee EBVD, Driscoll MM, Motter AE. Heterogeneity-stabilized homogeneous states in driven media. Nat Commun 2021; 12:4486. [PMID: 34301925 PMCID: PMC8302733 DOI: 10.1038/s41467-021-24459-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 06/17/2021] [Indexed: 11/09/2022] Open
Abstract
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.
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Affiliation(s)
- Zachary G Nicolaou
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA
| | - Daniel J Case
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA
| | | | - Michelle M Driscoll
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA
| | - Adilson E Motter
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA. .,Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, USA.
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2
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Reichl L, Heide D, Löwel S, Crowley JC, Kaschube M, Wolf F. Coordinated optimization of visual cortical maps (II) numerical studies. PLoS Comput Biol 2012; 8:e1002756. [PMID: 23144602 PMCID: PMC3493502 DOI: 10.1371/journal.pcbi.1002756] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2011] [Accepted: 08/17/2012] [Indexed: 11/18/2022] Open
Abstract
In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations. Neurons in the visual cortex of carnivores, primates and their close relatives form spatial representations or maps of multiple stimulus features. In part (I) of this study we theoretically predicted maps that are optima of a variety of optimization principles. When analyzing the joint optimization of two interacting maps we showed that for different optimization principles the resulting optima show a stereotyped, spatially perfectly periodic layout. Experimental maps, however, are much more irregular. In particular, in case of orientation columns it was found that different species show apparently species invariant statistics of point defects, so-called pinwheels. In this paper, we numerically investigate whether the spatial features of the stereotyped optima described in part (I) are expressed on biologically relevant timescales and whether other, spatially irregular, long-living states emerge that better reproduce the experimentally observed statistical properties of orientation maps. Moreover, we explore whether the coordinated optimization of more than two maps can lead to spatially irregular optima.
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Affiliation(s)
- Lars Reichl
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus Neurotechnology, Göttingen, Germany
- Faculty of Physics, Georg-August University, Göttingen, Germany
- * E-mail: (LR); (FW)
| | - Dominik Heide
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Frankfurt Institute of Advanced Studies, Frankfurt, Germany
| | - Siegrid Löwel
- Bernstein Focus Neurotechnology, Göttingen, Germany
- School of Biology, Georg-August University, Göttingen, Germany
| | - Justin C. Crowley
- Carnegie Mellon University, Department of Biological Sciences, Pittsburgh, Pennsylvania, United States of America
| | - Matthias Kaschube
- Frankfurt Institute of Advanced Studies, Frankfurt, Germany
- Physics Department and Lewis-Sigler Institute, Princeton University, Princeton, New Jersey, United States of America
| | - Fred Wolf
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Bernstein Focus Neurotechnology, Göttingen, Germany
- Faculty of Physics, Georg-August University, Göttingen, Germany
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California, United States of America
- * E-mail: (LR); (FW)
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Smith D, Ziebert F, Humphrey D, Duggan C, Steinbeck M, Zimmermann W, Käs J. Molecular motor-induced instabilities and cross linkers determine biopolymer organization. Biophys J 2007; 93:4445-52. [PMID: 17604319 PMCID: PMC2098725 DOI: 10.1529/biophysj.106.095919] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
All eukaryotic cells rely on the active self-organization of protein filaments to form a responsive intracellular cytoskeleton. The necessity of motility and reaction to stimuli additionally requires pathways that quickly and reversibly change cytoskeletal organization. While thermally driven order-disorder transitions are, from the viewpoint of physics, the most obvious method for controlling states of organization, the timescales necessary for effective cellular dynamics would require temperatures exceeding the physiologically viable temperature range. We report a mechanism whereby the molecular motor myosin II can cause near-instantaneous order-disorder transitions in reconstituted cytoskeletal actin solutions. When motor-induced filament sliding diminishes, the actin network structure rapidly and reversibly self-organizes into various assemblies. Addition of stable cross linkers was found to alter the architectures of ordered assemblies. These isothermal transitions between dynamic disorder and self-assembled ordered states illustrate that the interplay between passive crosslinking and molecular motor activity plays a substantial role in dynamic cellular organization.
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Affiliation(s)
- D Smith
- Institute for Soft Matter Physics, University of Leipzig, Germany
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Abarzhi SI, Desjardins O, Nepomnyashchy A, Pitsch H. Influence of parametric forcing on the nonequilibrium dynamics of wave patterns. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:046208. [PMID: 17500979 DOI: 10.1103/physreve.75.046208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2006] [Revised: 12/01/2006] [Indexed: 05/15/2023]
Abstract
We investigate analytically and numerically the effect of inhomogeneities on the nonequilibrium dynamics of wave patterns in the framework of a complex Ginzburg-Landau equation (CGLE) with parametric, nonresonant forcing periodic in space and time. It is found that the forcing results in occurrence of traveling waves with different dispersion properties. In the limiting case of forcing with very large wavelength, the waves have essentially anharmonic spatial structure. We consider the influence of modulations on the development of an intermittent chaos and show that the parametric forcing may completely suppress the appearance of chaotic patterns. The relations between this and other pattern-forming systems are discussed. The results obtained are applied to describe the dynamics of thermal Rossby waves influenced by surface topography.
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Affiliation(s)
- S I Abarzhi
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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Hilt M, Zimmermann W. Hexagonal, square, and stripe patterns of the ion channel density in biomembranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:016202. [PMID: 17358230 DOI: 10.1103/physreve.75.016202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2006] [Indexed: 05/14/2023]
Abstract
Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the channel density and the voltage drop across the membrane (cable equation) coupled to a binding-release reaction with the cell skeleton [P. Fromherz and W. Zimmerman, Phys. Rev. E 51, R1659 (1995)] is analyzed in one and two spatial dimensions. Due to the binding release reaction spatially periodic modulations of the channel density with a finite wave number are favored at the onset of pattern formation, whereby the wave number decreases with the kinetic rate of the binding-release reaction. In a two-dimensional extended membrane hexagonal modulations of the ion channel density are preferred in a large range of parameters. The stability diagrams of the periodic patterns near threshold are calculated and in addition the equations of motion in the limit of a slow binding-release kinetics are derived.
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Affiliation(s)
- Markus Hilt
- Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
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Kayodé S, Khayat RE. Spatially modulated thermal convection of viscoelastic fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:066319. [PMID: 15244738 DOI: 10.1103/physreve.69.066319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2003] [Indexed: 05/24/2023]
Abstract
The thermal convection of modulated viscoelastic flow is examined in this study. The modulation is assumed to be weak enough for a regular perturbation solution to be implemented. In addition to being more accurate, the second-order perturbation results reveal new physical phenomena that could not be predicted by the first-order analysis. Inertia was found to enhance globally the discrepancies between the first- and the second-order perturbation solution. A comparison between the Newtonian and the non-Newtonian solution is carried out and the influences of inertia, modulation amplitude, and wave number are emphasized. The present results show that elasticity has a marked effect on fluid patterns, especially regarding the roll structure and symmetry. The influence of elasticity is greater for larger Rayleigh number and aspect ratio.
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Affiliation(s)
- Séliatou Kayodé
- Laboratoire de Mécanique et Matériaux 1, Ecole Centrale de Nantes, rue de la Noë, Boîte Postale 62116, 44321 Nantes Cedex 03, France
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Schmitz R, Zimmermann W. Spatially periodic modulated Rayleigh-Bénard convection. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:5993-6011. [PMID: 9964956 DOI: 10.1103/physreve.53.5993] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Shattuck MD, Behringer RP, Johnson GA, Georgiadis JG. Onset and Stability of Convection in Porous Media: Visualization by Magnetic Resonance Imaging. PHYSICAL REVIEW LETTERS 1995; 75:1934-1937. [PMID: 10059166 DOI: 10.1103/physrevlett.75.1934] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Fromherz P, Zimmermann W. Stable spatially periodic patterns of ion channels in biomembranes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:R1659-R1662. [PMID: 9962950 DOI: 10.1103/physreve.51.r1659] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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