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Wigbers MC, Brauns F, Hermann T, Frey E. Pattern localization to a domain edge. Phys Rev E 2020; 101:022414. [PMID: 32168714 DOI: 10.1103/physreve.101.022414] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Accepted: 12/03/2019] [Indexed: 06/10/2023]
Abstract
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g., membrane-bound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud site in budding yeast and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can "sense" the edge of the template. A mechanism for how this edge sensing may work remains elusive. Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a two-component mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems and for the design of synthetic pattern forming systems.
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Affiliation(s)
- Manon C Wigbers
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Tobias Hermann
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, 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 München, Germany
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2
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Zykov VS. Spiral wave initiation in excitable media. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2017.0379. [PMID: 30420544 PMCID: PMC6232601 DOI: 10.1098/rsta.2017.0379] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/08/2018] [Indexed: 05/15/2023]
Abstract
Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.
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Affiliation(s)
- V S Zykov
- Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany
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3
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Zykov VS. Spiral wave initiation in excitable media. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2017.0385. [PMID: 30420544 DOI: 10.1098/rsta.2017.0385] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/19/2018] [Indexed: 05/20/2023]
Abstract
Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.
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Affiliation(s)
- V S Zykov
- Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany
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4
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Larkin JW, Zhai X, Kikuchi K, Redford SE, Prindle A, Liu J, Greenfield S, Walczak AM, Garcia-Ojalvo J, Mugler A, Süel GM. Signal Percolation within a Bacterial Community. Cell Syst 2018; 7:137-145.e3. [PMID: 30056004 DOI: 10.1016/j.cels.2018.06.005] [Citation(s) in RCA: 58] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Revised: 05/08/2018] [Accepted: 06/07/2018] [Indexed: 12/29/2022]
Abstract
Signal transmission among cells enables long-range coordination in biological systems. However, the scarcity of quantitative measurements hinders the development of theories that relate signal propagation to cellular heterogeneity and spatial organization. We address this problem in a bacterial community that employs electrochemical cell-to-cell communication. We developed a model based on percolation theory, which describes how signals propagate through a heterogeneous medium. Our model predicts that signal transmission becomes possible when the community is organized near a critical phase transition between a disconnected and a fully connected conduit of signaling cells. By measuring population-level signal transmission with single-cell resolution in wild-type and genetically modified communities, we confirm that the spatial distribution of signaling cells is organized at the predicted phase transition. Our findings suggest that at this critical point, the population-level benefit of signal transmission outweighs the single-cell level cost. The bacterial community thus appears to be organized according to a theoretically predicted spatial heterogeneity that promotes efficient signal transmission.
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Affiliation(s)
- Joseph W Larkin
- Division of Biological Sciences, University of California San Diego, Pacific Hall Room 2225B, Mail Code 0347, 9500 Gilman Drive, La Jolla, CA 92093, USA
| | - Xiaoling Zhai
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
| | - Kaito Kikuchi
- Division of Biological Sciences, University of California San Diego, Pacific Hall Room 2225B, Mail Code 0347, 9500 Gilman Drive, La Jolla, CA 92093, USA
| | - Samuel E Redford
- Division of Biological Sciences, University of California San Diego, Pacific Hall Room 2225B, Mail Code 0347, 9500 Gilman Drive, La Jolla, CA 92093, USA
| | - Arthur Prindle
- Department of Biochemistry and Molecular Genetics, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA; Center for Synthetic Biology, Northwestern University, Evanston, IL 60208, USA
| | - Jintao Liu
- Center for Infectious Diseases Research and Tsinghua-Peking Center for Life Sciences, School of Medicine, Tsinghua University, 100084 Beijing, China
| | - Sacha Greenfield
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA; Department of Physics and Astronomy, Carleton College, Northfield, MN 55057, USA
| | - Aleksandra M Walczak
- Laboratoire de Physique Théorique, CNRS, PSL, Université Pierre et Marie Curie and École Normale Supérieure, Paris 75231, France
| | - Jordi Garcia-Ojalvo
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona 08003, Spain
| | - Andrew Mugler
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA
| | - Gürol M Süel
- Division of Biological Sciences, University of California San Diego, Pacific Hall Room 2225B, Mail Code 0347, 9500 Gilman Drive, La Jolla, CA 92093, USA; San Diego Center for Systems Biology, University of California San Diego, La Jolla, CA 92093, USA.
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5
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Nishi K, Suzuki S, Kayahara K, Kuze M, Kitahata H, Nakata S, Nishiura Y. Achilles' heel of a traveling pulse subject to a local external stimulus. Phys Rev E 2017; 95:062209. [PMID: 28709255 DOI: 10.1103/physreve.95.062209] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Indexed: 11/07/2022]
Abstract
The response of a traveling pulse to a local external stimulus is considered numerically for a modified three-component Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant. We are interested in the minimal strength of the spatially localized stimulus in order to eliminate the pulse. The use of a stimulus of small width allows us to detect the point in the pulse most sensitive to the external stimulus, referred to as the "Achilles' heel" of the traveling pulse, at which minimal strength of stimulus causes a collapse of the pulse. Our findings are demonstrated experimentally as well with the photosensitive BZ reaction.
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Affiliation(s)
- Kei Nishi
- Department of Mathematics, Graduate School of Science, Kyoto Sangyo University, Kyoto 603-8555, Japan
| | - Shogo Suzuki
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
| | - Katsuhiko Kayahara
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
| | - Masakazu Kuze
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
| | | | - Satoshi Nakata
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
| | - Yasumasa Nishiura
- Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan
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6
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Alonso S, Bär M, Echebarria B. Nonlinear physics of electrical wave propagation in the heart: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:096601. [PMID: 27517161 DOI: 10.1088/0034-4885/79/9/096601] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.
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Affiliation(s)
- Sergio Alonso
- Physikalisch-Technische Bundesanstalt, Abbestr. 2-12 10587, Berlin, Germany. Department of Physics, Universitat Politècnica de Catalunya, Av. Dr. Marañón 44, E-08028 Barcelona, Spain
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7
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Alonso S, Bär M, Kapral R. Effective medium approach for heterogeneous reaction-diffusion media. J Chem Phys 2009; 131:214102. [DOI: 10.1063/1.3265987] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Alonso S, Kapral R, Bär M. Effective medium theory for reaction rates and diffusion coefficients of heterogeneous systems. PHYSICAL REVIEW LETTERS 2009; 102:238302. [PMID: 19658977 DOI: 10.1103/physrevlett.102.238302] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2009] [Indexed: 05/28/2023]
Abstract
A simple effective medium theory is derived for spatially heterogeneous nonlinear reaction-diffusion media. Its validity is tested through comparisons with simulations of front and pulse propagation in systems with spatially varying diffusion coefficients and reaction rates. The theory is able to predict wave speeds if the characteristic front width is much larger than the length scale of the heterogeneities. This condition is violated in media with isolated or weakly connected sites. However, the theory nevertheless provides good results in cases where it correctly predicts the percolation threshold of the medium.
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Affiliation(s)
- Sergio Alonso
- Physikalisch-Technische Bundesanstalt, 10587 Berlin, Germany
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9
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Li BW, Zhang H, Ying HP, Hu G. Coherent wave patterns sustained by a localized inhomogeneity in an excitable medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026220. [PMID: 19391833 DOI: 10.1103/physreve.79.026220] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2008] [Revised: 12/19/2008] [Indexed: 05/27/2023]
Abstract
The influence of a localized inhomogeneity (oscillatory or stationary) on spatiotemporal chaotic state in an excitable reaction-diffusion system is investigated. We find that various coherent wave patterns, such as spiral waves (including multiarmed) and target wave patterns are able to be created by the inhomogeneity from the chaotic state. Due to the growth of these coherent wave patterns, the previously existing turbulent waves in the absence of inhomogeneity are suppressed. At last, the whole system is entrained by the coherent wave patterns. Closer investigations indicate that the possible mechanisms underlying the inhomogeneity sustained coherent wave patterns seem quite different for oscillatory and stationary inhomogeneities.
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Affiliation(s)
- Bing-Wei Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
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10
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Chapter 9 Non-linear Dynamics in Catalytic Reactions. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/s1573-4331(08)00009-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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11
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Liu JJ, Hua DY, Jiang LL. Effect of Surface Impurities on Oscillation in NO+CO/Pt(100) Reaction System. CHINESE J CHEM PHYS 2007. [DOI: 10.1088/1674-0068/20/03/279-284] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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12
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Qiao L, Kevrekidis IG, Punckt C, Rotermund HH. Guiding chemical pulses through geometry: Y junctions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:036219. [PMID: 16605643 DOI: 10.1103/physreve.73.036219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2005] [Indexed: 05/08/2023]
Abstract
We study computationally and experimentally the propagation of chemical pulses in complex geometries. The reaction of interest, CO oxidation, takes place on single crystal Pt(110) surfaces that are microlithographically patterned; they are also addressable through a focused laser beam, manipulated through galvanometer mirrors, capable of locally altering the crystal temperature and thus affecting pulse propagation. We focus on sudden changes in the domain shape (corners in a Y-junction geometry) that can affect the pulse dynamics; we also show how brief, localized temperature perturbations can be used to control reactive pulse propagation. The computational results are corroborated through experimental studies in which the pulses are visualized using reflection anisotropy microscopy.
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Affiliation(s)
- L Qiao
- Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
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13
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Qiao L, Kevrekidis IG, Punckt C, Rotermund HH. Geometry-induced pulse instability in microdesigned catalysts: the effect of boundary curvature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:036217. [PMID: 16605641 DOI: 10.1103/physreve.73.036217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2005] [Indexed: 05/08/2023]
Abstract
We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and we trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.
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Affiliation(s)
- L Qiao
- Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
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14
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Neubecker R, Jakoby O. Spatial synchronization of regular optical patterns. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 67:066221. [PMID: 16241340 DOI: 10.1103/physreve.67.066221] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2002] [Revised: 03/13/2003] [Indexed: 11/07/2022]
Abstract
We investigate an extended, nonlinear optical experiment, exhibiting the spontaneous formation of hexagonal patterns out of a stationary bifurcation. The system is exposed to a two-dimensional spatially periodic forcing, namely, static hexagonal patterns, under variation of their spatial periodicity. Parameters are the strength of the forcing and the distance to pattern forming threshold. The system response is quantitatively characterized with different methods. We observe several locking regimes, where the system is entrained by the forcing. Most of the locking regimes can be related to resonances between the different critical wave numbers and the forcing wave number or its spatial harmonics. One particular locking appears to result from two of these simple resonances in a kind of generalized order m:n synchronization. The width of the locking regimes increases with forcing strength, apparently representing a spatial analog of Arnold tongues.
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Affiliation(s)
- R Neubecker
- Institute of Applied Physics, Darmstadt University of Technology, Darmstadt, Germany.
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15
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Bub G, Shrier A, Glass L. Global organization of dynamics in oscillatory heterogeneous excitable media. PHYSICAL REVIEW LETTERS 2005; 94:028105. [PMID: 15698236 DOI: 10.1103/physrevlett.94.028105] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2004] [Indexed: 05/24/2023]
Abstract
An oscillatory heterogeneous excitable medium undergoes a transition from periodic target patterns to a bursting rhythm driven by the spontaneous initiation and termination of spiral waves as coupling or density is reduced. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium-sensitive fluorescent dyes. These results are modeled in a heterogeneous cellular automaton in which the neighborhood of interaction and cell density is modified. Parameters that give rise to bursting rhythms are organized in distinct zones in parameter space, leading to a global organization that should be applicable to the dynamics in a large class of excitable media.
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Affiliation(s)
- Gil Bub
- Department of Physiology and Pharmacology, State University of New York Downstate Medical Center, Brooklyn, New York 11203, USA
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16
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Hua DY, Liu JJ. Damped oscillation in the NO+CO/Pt(100) reaction system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016213. [PMID: 15697704 DOI: 10.1103/physreve.71.016213] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2004] [Revised: 09/07/2004] [Indexed: 05/24/2023]
Abstract
Considering the influence of the surface defects formed in the surface restructuring phase transition in the CO+NO/Pt(100) reaction system, we propose a lattice gas model to investigate the damped oscillation in the high-temperature oscillatory regime by means of a Monte Carlo simulation. The simulation results show that the persistent oscillation can change into a damped one when the fraction of the defects increases. The production rate of CO2 is near to the maximum value when the oscillation is damped to the end. Furthermore, it is found, in the early stage of the oscillation, that the NO decomposition mainly occurs in the 1 x 1 phase and the hex phase is inactive for the reaction. However, as the reaction proceeds, defects are gradually formed in the 1 x 1 <==> hex phase transition, the hex phase becomes active and dominative for the NO decomposition, and then the oscillation becomes damping. The simulation results give an explanation for some previous experimental phenomena.
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Affiliation(s)
- Da-Yin Hua
- Physics Department, Ningbo University, Ningbo 315211, China
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17
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Krishnan J, Runborg O, Kevrekidis I. Bifurcation analysis of nonlinear reaction–diffusion problems using wavelet-based reduction techniques. Comput Chem Eng 2004. [DOI: 10.1016/j.compchemeng.2003.08.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Bub G, Shrier A. Propagation through heterogeneous substrates in simple excitable media models. CHAOS (WOODBURY, N.Y.) 2002; 12:747-753. [PMID: 12779603 DOI: 10.1063/1.1502481] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The interaction of waves and obstacles is simulated by adding heterogeneities to a FitzHugh-Nagumo model and a cellular automata model. The cellular automata model is formulated to account for heterogeneities by modelling the interaction between current sources and current sinks. In both models, wave fronts propagate if the size of the heterogeneities is small, and block if the size of the heterogeneities is large. For intermediate values, wave fronts break up into numerous spiral waves. The theoretical models give insights concerning spiral wave formation in heterogeneous excitable media. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Gil Bub
- Center for Nonlinear Dynamics in Physiology and Medicine, Department of Physiology, McIntyer Medical Sciences Building, McGill University, Montreal, Quebec, Canada H3G 1Y6
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19
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Bar M, Meron E, Utzny C. Pattern formation on anisotropic and heterogeneous catalytic surfaces. CHAOS (WOODBURY, N.Y.) 2002; 12:204-214. [PMID: 12779548 DOI: 10.1063/1.1450565] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We review experimental and theoretical work addressing pattern formation on anisotropic and heterogeneous catalytic surfaces. These systems are typically modeled by reaction-diffusion equations reflecting the kinetics and transport of the involved chemical species. Here, we demonstrate the influence of anisotropy and heterogeneity in a simplified model, the FitzHugh-Nagumo equations. Anisotropy causes stratification of labyrinthine patterns and spiral defect chaos in bistable media. For heterogeneous media, we study the situation where the heterogeneity appears on a length scale shorter than the typical pattern length scale. Homogenization, i.e., computation of effective medium properties, is applied to an example and illustrated with simulations in one (fronts) and two dimensions (spirals). We conclude with a discussion of open questions and promising directions that comprise the coupling of the microscopic structure of the surface to the macroscopic concentration patterns and the fabrication of nanostructures with heterogeneous surfaces as templates. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Markus Bar
- Max-Planck-Institut fur Physik Komplexer Systeme, Nothnitzer Strasse 38, 01187 Dresden, Germany
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20
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Imbihl R. Catalysis on microstructured bimetallic surfaces. CHAOS (WOODBURY, N.Y.) 2002; 12:182-189. [PMID: 12779546 DOI: 10.1063/1.1450564] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Microstructured bimetallic Pt/Rh and Pt/Ti surfaces have been employed to study the dynamics of catalytic NO reduction and the O(2)+H(2) reaction at low pressure (p<10(-3) mbar). Photoelectron emission microscopy and scanning photoelectron microscopy were used as spatially resolved in situ methods to image the local work function changes and to identify chemical changes in the substrate and in the adsorbate layer. It is shown that diffusional coupling leads to dynamic effects which are dependent on the macroscopic size (&mgr;m range). With alkali metals on the surface, stationary patterns form whose mechanism of formation has been studied in detail. (c) 2002 American Institute of Physics.
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Affiliation(s)
- R. Imbihl
- Institut fur Physikalische Chemie und Elektrochemie, Universitat Hannover, Callinstrasse 3-3a, D-30167 Hannover, Germany
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21
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Li X, Kevrekidis IG, Pollmann M, Papathanasiou AG, Rotermund HH. Front initiation on microdesigned composite catalysts. CHAOS (WOODBURY, N.Y.) 2002; 12:190-203. [PMID: 12779547 DOI: 10.1063/1.1452739] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We first briefly review the subject of spatiotemporal pattern formation on microdesigned composite catalysts. One of the most significant interaction mechanisms between different reacting domains (consisting of different metal catalysts such as Pt and Rh, coupled through surface diffusion) is the initiation of reaction fronts at the interface between them. We then explore in some detail the effect of two-dimensional composite geometry on this basic building block of composite catalyst dynamics. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Xiujiang Li
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
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22
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Pollmann M, Rotermund HH, Ertl G, Li X, Kevrekidis IG. Formation of two-dimensional concentration pulses on microdesigned composite catalyst surfaces. PHYSICAL REVIEW LETTERS 2001; 86:6038-6041. [PMID: 11415423 DOI: 10.1103/physrevlett.86.6038] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2000] [Indexed: 05/23/2023]
Abstract
We study the effect of microdesigned composite geometries on pattern formation during the catalytic oxidation of CO on Pt-Ti, Pt-Rh, and Pt-Pd composite catalysts. In particular, we find experimentally (and rationalize through modeling) that adsorbate surface transport through the second (active) component drastically affects the shapes and interactions of concentration patterns (traveling pulses) observed on pure Pt.
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Affiliation(s)
- M Pollmann
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
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Bar M, Hagberg A, Meron E, Thiele U. Front propagation and pattern formation in anisotropic bistable media. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:366-374. [PMID: 11088470 DOI: 10.1103/physreve.62.366] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/1999] [Indexed: 05/23/2023]
Abstract
The effects of diffusion anisotropy on pattern formation in bistable media are studied using a FitzHugh-Nagumo reaction-diffusion model. A relation between the normal velocity of a front and its curvature is derived and used to identify distinct spatiotemporal patterns induced by the diffusion anisotropy. In a wide parameter range anisotropy is found to have an ordering effect: initial patterns evolve into stationary or breathing periodic stripes parallel to one of the principal axes. In a different parameter range, anisotropy is found to induce spatiotemporal chaos confined to one space dimension, a state we term "stratified chaos."
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Affiliation(s)
- M Bar
- Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, 01187 Dresden, Germany and The Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990, Israel
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von Oertzen A, Rotermund HH, Mikhailov AS, Ertl G. Standing Wave Patterns in the CO Oxidation Reaction on a Pt(110) Surface: Experiments and Modeling. J Phys Chem B 2000. [DOI: 10.1021/jp9927799] [Citation(s) in RCA: 84] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Alexander von Oertzen
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Harm H. Rotermund
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Alexander S. Mikhailov
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Gerhard Ertl
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
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Berdau M, Yelenin GG, Karpowicz A, Ehsasi M, Christmann K, Block JH. Macroscopic and mesoscopic characterization of a bistable reaction system: CO oxidation on Pt(111) surface. J Chem Phys 1999. [DOI: 10.1063/1.479097] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yamaguchi Y. X-ray photoemission electron microscopy (XPEEM) as a new promising tool for the real-time chemical imaging of active surfaces. ACTA ACUST UNITED AC 1999. [DOI: 10.1016/s1381-1169(98)00256-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Chávez F, Vicente L, Perera A, Moreau M. Dynamics of front propagation in the catalytic CO oxidation on Pt(100). J Chem Phys 1999. [DOI: 10.1063/1.478715] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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28
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CHÁVEZ FRANCISCO, VICENTE LUIS. Cellular automata approach to dissociative adsorption of diatomic molecules on a substrate with reconstruction. Mol Phys 1999. [DOI: 10.1080/00268979909483036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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29
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Chávez F, Vicente L, Perera A, Moreau M. Effect of inert sites on the kinetic oscillations in the catalytic CO oxidation on Pt(100). J Chem Phys 1998. [DOI: 10.1063/1.477528] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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von Oertzen A, Mikhailov AS, Rotermund HH, Ertl G. Subsurface Oxygen in the CO Oxidation Reaction on Pt(110): Experiments and Modeling of Pattern Formation. J Phys Chem B 1998. [DOI: 10.1021/jp981285t] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexander von Oertzen
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Alexander S. Mikhailov
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Harm H. Rotermund
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
| | - Gerhard Ertl
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft,
Faradayweg 4-6, D-14195 Berlin, Germany
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31
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Xu A, Guevara MR. Two forms of spiral-wave reentry in an ionic model of ischemic ventricular myocardium. CHAOS (WOODBURY, N.Y.) 1998; 8:157-174. [PMID: 12779719 DOI: 10.1063/1.166286] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
It is well known that there is considerable spatial inhomogeneity in the electrical properties of heart muscle, and that the many interventions that increase this initial degree of inhomogeneity all make it easier to induce certain cardiac arrhythmias. We consider here the specific example of myocardial ischemia, which greatly increases the electrical heterogeneity of ventricular tissue, and often triggers life-threatening cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. There is growing evidence that spiral-wave activity underlies these reentrant arrhythmias. We thus investigate whether spiral waves might be induced in a realistic model of inhomogeneous ventricular myocardium. We first modify the Luo and Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model of cardiac ventricular muscle so as to obtain maintained spiral-wave activity in a two-dimensional homogeneous sheet of ventricular muscle. Regional ischemia is simulated by raising the external potassium concentration ([K(+)](o)) from its nominal value of 5.4 mM in a subsection of the sheet, thus creating a localized inhomogeneity. Spiral-wave activity is induced using a pacing protocol in which the pacing frequency is gradually increased. When [K(+)](o) is sufficiently high in the abnormal area (e.g., 20 mM), there is complete block of propagation of the action potential into that area, resulting in a free end or wave break as the activation wave front encounters the abnormal area. As pacing continues, the free end of the activation wave front traveling in the normal area increasingly separates or detaches from the border between normal and abnormal tissue, eventually resulting in the formation of a maintained spiral wave, whose core lies entirely within an area of normal tissue lying outside of the abnormal area ("type I" spiral wave). At lower [K(+)](o) (e.g., 10.5 mM) in the abnormal area, there is no longer complete block of propagation into the abnormal area; instead, there is partial entrance block into the abnormal area, as well as exit block out of that area. In this case, a different kind of spiral wave (transient "type II" spiral wave) can be evoked, whose induction involves retrograde propagation of the action potential through the abnormal area. The number of turns made by the type II spiral wave depends on several factors, including the level of [K(+)](o) within the abnormal area and its physical size. If the pacing protocol is changed by adding two additional stimuli, a type I spiral wave is instead produced at [K(+)](o)=10.5 mM. When pacing is continued beyond this point, apparently aperiodic multiple spiral-wave activity is seen during pacing. We discuss the relevance of our results for arrythmogenesis in both the ischemic and nonischemic heart. (c) 1998 American Institute of Physics.
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Affiliation(s)
- Aoxiang Xu
- Department of Physiology and Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, 3655 Drummond Street, Montreal, Quebec, H3G 1Y6 Canada
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Annamalai J, Ballandis C, Somani M, Liauw MA, Luss D. Effects of reactant composition and nonuniformities on temperature fronts. J Chem Phys 1997. [DOI: 10.1063/1.474540] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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