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Kuze M, Kitahata H, Nakata S. Traveling waves propagating through coupled microbeads in the Belousov-Zhabotinsky reaction. Phys Chem Chem Phys 2021; 23:24175-24179. [PMID: 34673865 DOI: 10.1039/d1cp03916d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Spatio-temporal patterns, namely global oscillations (GO) and traveling waves (TW), were investigated in spherical microbeads loaded with a catalyst for the Belousov-Zhabotinsky (BZ) reaction onto the surface (2D-loaded) or the entire volume of the bead (3D-loaded). GO and TW selectively appeared in the 2D- and 3D-loaded beads, respectively, placed on a polyethylene terephthalate (PET) sheet in the catalyst-free BZ solution. We examined two types of coupling of the two beads: 2D-3D and 3D-3D couplings. In both cases, synchronization occurred when the minimum distance between the two beads, l, was shorter than the threshold. Herein, we reported not only temporal information, that is, phase difference, but also spatial information, that is, the directions of the TW propagating through the coupled BZ beads. In the synchronization for the 2D-3D coupling, TW in the 3D-loaded bead were initiated from the point near the 2D-loaded bead as a pacemaker and propagated in the opposite direction. By contrast, the directions of the TW in the 3D-loaded bead changed depending on l in the synchronization for the 3D-3D coupling. These experimental results can be quantitatively reproduced by numerical calculations based on the diffusion dynamics of an activator of the BZ reaction. Our results suggest that the features of spatio-temporal wave propagation are indicative of the configuration of the oscillators.
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Affiliation(s)
- Masakazu Kuze
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan.
| | - Hiroyuki Kitahata
- Graduate School of Science, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba 263-8522, Japan
| | - Satoshi Nakata
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan.
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2
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Kuze M, Horisaka M, Suematsu NJ, Amemiya T, Steinbock O, Nakata S. Switching between Two Oscillatory States Depending on the Electrical Potential. J Phys Chem B 2021; 125:3638-3643. [PMID: 33797905 DOI: 10.1021/acs.jpcb.0c11019] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Various spatiotemporal patterns were created on the surface or in the body of cation-exchange resin beads which were loaded with the catalyst of the Belousov-Zhabotinsky (BZ) reaction. Either global oscillations (GO) or traveling waves (TW) and the switching between them were observed in the previous papers, but it was not clear how chemicals contribute to the reaction inside/around the BZ bead. In this paper, we scanned the electrical potential, E, from +1 to -1 V (negative scan) and then turned from -1 to +1 V (positive scan) to control the switching between GO and TW. We found that the electrical switching potential from TW to GO, ETG, and from GO to TW, EGT, depended on the scanning direction of E and the diameter of the bead, d. The present study suggests that the electrode-induced increase of the inhibitor, Br-, and the activator, HBrO2, around the BZ bead plays an important role in determining ETG and EGT.
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Affiliation(s)
- Masakazu Kuze
- Graduate School of Integrated Sciences for Life, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Mari Horisaka
- Graduate School of Integrated Sciences for Life, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | | | - Takashi Amemiya
- Graduate School of Environment and Information Sciences, Yokohama National University (YNU), 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
| | - Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Satoshi Nakata
- Graduate School of Integrated Sciences for Life, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
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3
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Nolet FE, Rombouts J, Gelens L. Synchronization in reaction-diffusion systems with multiple pacemakers. CHAOS (WOODBURY, N.Y.) 2020; 30:053139. [PMID: 32491903 DOI: 10.1063/5.0002251] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 05/06/2020] [Indexed: 06/11/2023]
Abstract
Spatially extended oscillatory systems can be entrained by pacemakers, regions that oscillate with a higher frequency than the rest of the medium. Entrainment happens through waves originating at a pacemaker. Typically, biological and chemical media can contain multiple pacemaker regions, which compete with each other. In this paper, we perform a detailed numerical analysis of how wave propagation and synchronization of the medium depend on the properties of these pacemakers. We discuss the influence of the size and intrinsic frequency of pacemakers on the synchronization properties. We also study a system in which the pacemakers are embedded in a medium without any local dynamics. In this case, synchronization occurs if the coupling determined by the distance and diffusion is strong enough. The transition to synchronization is reminiscent of systems of discrete coupled oscillators.
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Affiliation(s)
- F E Nolet
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, 3000 Leuven, Belgium
| | - J Rombouts
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, 3000 Leuven, Belgium
| | - L Gelens
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, 3000 Leuven, Belgium
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4
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Kuze M, Horisaka M, Suematsu NJ, Amemiya T, Steinbock O, Nakata S. Chemical Wave Propagation in the Belousov–Zhabotinsky Reaction Controlled by Electrical Potential. J Phys Chem A 2019; 123:4853-4857. [DOI: 10.1021/acs.jpca.9b02636] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Masakazu Kuze
- Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan
| | - Mari Horisaka
- Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan
| | | | - Takashi Amemiya
- Graduate School of Environment and Information Sciences, Yokohama National University (YNU), 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
| | - Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Satoshi Nakata
- Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan
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5
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González Ochoa HO, Perales GS, Epstein IR, Femat R. Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator. Phys Rev E 2018; 97:052214. [PMID: 29906855 DOI: 10.1103/physreve.97.052214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Indexed: 06/08/2023]
Abstract
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
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Affiliation(s)
- Héctor O González Ochoa
- Departamento de Electrónica, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, México
| | - Gualberto Solís Perales
- Departamento de Electrónica, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, México
| | - Irving R Epstein
- Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454-9110, USA
| | - Ricardo Femat
- Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, México
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6
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Kuze M, Kitahata H, Steinbock O, Nakata S. Distinguishing the Dynamic Fingerprints of Two- and Three-Dimensional Chemical Waves in Microbeads. J Phys Chem A 2018; 122:1967-1971. [DOI: 10.1021/acs.jpca.7b12210] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Masakazu Kuze
- Graduate
School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan
| | | | - Oliver Steinbock
- Department
of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Satoshi Nakata
- Graduate
School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan
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7
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Torbensen K, Rossi F, Ristori S, Abou-Hassan A. Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics. LAB ON A CHIP 2017; 17:1179-1189. [PMID: 28239705 DOI: 10.1039/c6lc01583b] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Chemical communication leading to synchronization and collective behaviour of dynamic elements, such as cell colonies, is a widespread phenomenon with biological, physical and chemical importance. Such synchronization between elements proceeds via chemical communication by emmision, interdiffusion and reception of specific messenger molecules. On a lab scale, these phenomena can be modeled by encapsulating an oscillating chemical reaction, which serves as a signal (information) sender/receiver element, inside microcompartments such as droplet emulsions, liposomes and polymersomes. Droplets can thus be regarded as single units, able to generate chemical messengers that diffuse in the environment and hence can interact with other compartments. The Belousov-Zhabotinsky (BZ) reaction is a well-known chemical oscillator largely used as a model for complex nonlinear phenomena, including chemical, physical and biological examples. When the BZ-reaction is encapsulated inside microcompartments, its chemical intermediates can serve as messengers by diffusing among different microcompartments, to trigger specific reactions leading to a collective behavior between the elements. The geometry and constitution of the diffusion pathways play an important role in governing the collective behaviour of the system. In this context, microfluidics is not only a versatile tool for mastering the encapsulation process of the BZ-reaction in monodisperse microcompartments, but also for creating geometries and networks with well defined boundaries. The individual compartments can be engineered with selected properties using different surfactants in the case of simple emulsions, or with specific membrane properties in the case of liposomes. Furthermore, it enables the arrangement of these microcompartments in various geometric configurations, where the diffusive coupling pathways between individual compartments are both spatially and chemically well-defined. In this tutorial paper, we review a number of articles reporting various approaches to generate networks of compartmentalized Belousov-Zhabotinsky (BZ) chemical oscillators using microfluidics. In contrast to biological cellular networks, the dynamical characteristics of the BZ-reaction is well-known and, when confined in microcompartments arranged in different configurations with a pure interdiffusive coupling, these communicative microreactors can serve to mimic various types of bio-physical networks, aiding to comprehend the concept of chemical communication.
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Affiliation(s)
- Kristian Torbensen
- UMR 8234, Laboratoire Physico-chimie des Electrolytes, Nanosystèmes InterfaciauX (PHENIX), UPMC Univ Paris 06, Sorbonne Universités, 4 place Jussieu - case 51, 75252 Paris cedex 05, France.
| | - Federico Rossi
- Department of Chemistry and Biology, University of Salerno, Via Giovanni Paolo II 132, Fisciano (SA), Italy
| | - Sandra Ristori
- Department of Earth Sciences & CSGI, University of Florence, Via della Lastruccia 3, 50019 Sesto Fiorentino, Firenze, Italy
| | - Ali Abou-Hassan
- UMR 8234, Laboratoire Physico-chimie des Electrolytes, Nanosystèmes InterfaciauX (PHENIX), UPMC Univ Paris 06, Sorbonne Universités, 4 place Jussieu - case 51, 75252 Paris cedex 05, France.
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8
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Guo D, Fu YQ, Zheng B. Synchronization of Coupled Oscillators on a Two-Dimensional Plane. Chemphyschem 2016; 17:2355-9. [PMID: 27124217 DOI: 10.1002/cphc.201600293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2016] [Indexed: 01/11/2023]
Abstract
The effect of the transfer rate of signal molecules on coupled chemical oscillators arranged on a two-dimensional plane was systematically investigated in this paper. A microreactor equipped with a surface acoustic wave (SAW) mixer was applied to adjust the transfer rate of the signal molecules in the microreactor. The SAW mixer with adjustable input powers provided a simple means to generate different mixing rates in the microreactor. A robust synchronization of the oscillators was found at an input radio frequency power of 20 dBm, with which the chemical waves were initiated at a fixed site of the oscillator system. With increasing input power, the frequency of the chemical waves was increased, which agreed well with the prediction given by the time-delayed phase oscillator model. Results from the finite element simulation agreed well with the experimental results.
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Affiliation(s)
- Dameng Guo
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Yong Qing Fu
- Department of Physics & Electrical Engineering, Faculty of Engineering and Environment, Northumbria University, Newcastle Upon Tyne, NE1 8ST, UK
| | - Bo Zheng
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.
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9
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English LQ, Zeng Z, Mertens D. Experimental study of synchronization of coupled electrical self-oscillators and comparison to the Sakaguchi-Kuramoto model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052912. [PMID: 26651767 DOI: 10.1103/physreve.92.052912] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Indexed: 06/05/2023]
Abstract
We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we show that the coupling can be quantitatively described by Sakaguchi's modification to the Kuramoto model. We also examine an ensemble of oscillators whose frequencies are taken from a flat distribution within a fixed frequency interval. We characterize in detail the synchronized cluster, its initial formation, as well as its effect on unsynchronized oscillators, all as a function of a global coupling strength.
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Affiliation(s)
- L Q English
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
| | - Zhuwei Zeng
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
| | - David Mertens
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
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10
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Totz JF, Snari R, Yengi D, Tinsley MR, Engel H, Showalter K. Phase-lag synchronization in networks of coupled chemical oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022819. [PMID: 26382466 DOI: 10.1103/physreve.92.022819] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Indexed: 06/05/2023]
Abstract
Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.
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Affiliation(s)
- Jan F Totz
- Institut für Theoretische Physik, EW 7-1, TU Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Razan Snari
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA
| | - Desmond Yengi
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA
| | - Mark R Tinsley
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA
| | - Harald Engel
- Institut für Theoretische Physik, EW 7-1, TU Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA
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11
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Li N, Delgado J, González-Ochoa HO, Epstein IR, Fraden S. Combined excitatory and inhibitory coupling in a 1-D array of Belousov–Zhabotinsky droplets. Phys Chem Chem Phys 2014; 16:10965-78. [DOI: 10.1039/c4cp00957f] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Experimental and theoretical studies of the coupling between Belousov–Zhabotinsky droplets in oil as a function of malonic acid, drop size, drop spacing, and time.
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Affiliation(s)
- Ning Li
- Department of Physics
- Brandeis University
- Waltham, USA
| | - Jorge Delgado
- Department of Chemistry
- Brandeis University
- Waltham, USA
- División de Ciencias e Ingenierías
- Universidad de Guanajuato
| | - Hector O. González-Ochoa
- Department of Physics
- Brandeis University
- Waltham, USA
- División de Matemáticas Aplicadas
- Instituto Potosino de Investigación Científica y Tecnológica (IPICyT)
| | | | - Seth Fraden
- Department of Physics
- Brandeis University
- Waltham, USA
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12
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Guo D, Li Y, Zheng B. A Microreactor and Imaging Platform for Studying Chemical Oscillators. J Phys Chem A 2013; 117:6402-8. [DOI: 10.1021/jp4030014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dameng Guo
- Department
of Chemistry, The Chinese University of Hong Kong, Hong Kong
| | - Yuefang Li
- Department
of Chemistry, The Chinese University of Hong Kong, Hong Kong
| | - Bo Zheng
- Department
of Chemistry, The Chinese University of Hong Kong, Hong Kong
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13
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Magnetic field induced hopping among Arnold entrainment tongues of coupled iron electrochemical oscillators. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2012.10.074] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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14
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Fukuda H, Ukai K, Oyama T. Self-arrangement of cellular circadian rhythms through phase-resetting in plant roots. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041917. [PMID: 23214625 DOI: 10.1103/physreve.86.041917] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2011] [Indexed: 05/08/2023]
Abstract
We discovered a striped pattern of gene expression with circadian rhythms in growing plant roots using bioluminescent imaging of gene expression. Our experimental analysis revealed that the stripe wave in the bioluminescent image originated at the root tip and was caused by a continuous phase resetting of circadian oscillations. Some complex stripe waves containing arrhythmic regions were also observed. We succeeded in describing the formation mechanisms of these patterns using a growing phase oscillator network with a phase-resetting boundary condition.
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Affiliation(s)
- Hirokazu Fukuda
- Department of Mechanical Engineering, Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan.
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15
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Tinsley MR, Taylor AF, Huang Z, Showalter K. Complex organizing centers in groups of oscillatory particles. Phys Chem Chem Phys 2011; 13:17802-8. [DOI: 10.1039/c1cp22109d] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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Nakabayashi S. ELECTROCHEMISTRY 2010; 78:773-778. [DOI: 10.5796/electrochemistry.78.773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
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17
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Yashin VV, Balazs AC. Chemomechanical synchronization in heterogeneous self-oscillating gels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:046210. [PMID: 18517713 DOI: 10.1103/physreve.77.046210] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2007] [Revised: 12/03/2007] [Indexed: 05/26/2023]
Abstract
Using computational modeling, we introduce patches of self-oscillating gels undergoing the Belousov-Zhabotinsky (BZ) reaction into a nonreactive polymer network and thereby demonstrate how these BZ gels can be harnessed to impart remarkable functionality to the entire system. By first focusing on two adjacent patches of BZ gels, we show that the patches' oscillations can become synchronized in phase or out of phase, with the oscillation frequency depending on the synchronization mode and the spatial separation between these domains. We then apply these results to an array of five adjacent BZ patches and by varying the distance between these pieces, we dramatically alter the dynamical behavior of the patterned gel. For example, the sample can be made to exhibit a unidirectional traveling wave or display a concerted expansion and contraction, properties that are valuable for creating gel-based devices, such as micropumps and microactuators. The findings point to a "modular" design approach, which can impart different functionality simply by arranging identical pieces of BZ gels into distinct spatial arrangements within a polymer matrix.
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Affiliation(s)
- Victor V Yashin
- Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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18
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Kiss IZ, Zhai Y, Hudson JL. Resonance clustering in globally coupled electrochemical oscillators with external forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:046204. [PMID: 18517707 DOI: 10.1103/physreve.77.046204] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2008] [Indexed: 05/26/2023]
Abstract
Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency omega1) states; periodic forcing produces forced-entrained (omegaF) states. As a result of the interaction of mutual and forced entrainment, resonant cluster states occur with equal spacing of frequencies that have discretized frequencies following a resonance rule omegan congruent with nomega1-(n-1)omegaF. Resonance clustering requires an optimal, intermediate global coupling strength; at weak coupling the clusters have smaller sizes and do not strictly follow the resonance rule, while at strong coupling the population behaves similar to a single, giant oscillator.
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Affiliation(s)
- István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclade Avenue, St. Louis, Missouri 63103, USA
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Fukuda H, Nakamichi N, Hisatsune M, Murase H, Mizuno T. Synchronization of plant circadian oscillators with a phase delay effect of the vein network. PHYSICAL REVIEW LETTERS 2007; 99:098102. [PMID: 17931039 DOI: 10.1103/physrevlett.99.098102] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2007] [Indexed: 05/25/2023]
Abstract
Synchronization phenomena in coupled circadian oscillators of plant leaves were investigated experimentally using bioluminescence technology for a clock gene. Analyzing the phase of circadian oscillation, the phase-wave propagations and the phase delay caused by the vein network were observed. We describe these phase dynamics using a two-layer model with coupled Stuart-Landau equations. Global synchronization of circadian oscillators in the leaf is also investigated.
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Affiliation(s)
- Hirokazu Fukuda
- Department of Applied Life Sciences, Graduate School of Life and Environmental Sciences, Osaka Prefecture University, Sakai 599-8531, Japan.
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20
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Toth R, Taylor AF. Loss of coherence in a population of diffusively coupled oscillators. J Chem Phys 2007; 125:224708. [PMID: 17176155 DOI: 10.1063/1.2404655] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The authors investigate the relationship between the natural frequency distribution of diffusively coupled chemical oscillators and their entrainment by pacemakers. The system consists of micrometer-sized catalyst beads which are coupled to their neighbors by diffusion of the activator/inhibitor species through the catalyst-free Belousov-Zhabotinsky (BZ) reaction solution. The frequency distribution is measured as a function of the beads' number of neighbors. With the maximum number of neighbors, either target waves or disordered patterns are observed in the reaction domain and there is a shift to higher frequencies than those observed in the natural frequency distribution. The loss of coherence between neighbor oscillators is quantified by a decrease in the phase synchronization index. The experimental results are reproduced in simulations which demonstrate that the decrease in the degree of synchronization is correlated with the appearance of a small fraction of permanently excited beads in BZ populations of high mean frequency and/or large width.
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Affiliation(s)
- Rita Toth
- Department of Chemistry, University of Leeds, Leeds LS2 9JT, UK
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