1
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Hunter I, Norton MM, Chen B, Simonetti C, Moustaka ME, Touboul J, Fraden S. Pattern formation in a four-ring reaction-diffusion network with heterogeneity. Phys Rev E 2022; 105:024310. [PMID: 35291089 DOI: 10.1103/physreve.105.024310] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 01/28/2022] [Indexed: 11/07/2022]
Abstract
In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.
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Affiliation(s)
- Ian Hunter
- Brandeis University Physics, Waltham, Massachusetts 02453, USA
| | - Michael M Norton
- Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Bolun Chen
- Volen National Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA.,Department of Physics, Boston University, Boston Massachusetts 02215, USA
| | - Chris Simonetti
- Brandeis University Physics, Waltham, Massachusetts 02453, USA
| | | | - Jonathan Touboul
- Volen National Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA.,Brandeis University Mathematics Department, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Brandeis University Physics, Waltham, Massachusetts 02453, USA
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2
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Budroni MA, Pagano G, Conte D, Paternoster B, D'ambrosio R, Ristori S, Abou-Hassan A, Rossi F. Synchronization scenarios induced by delayed communication in arrays of diffusively coupled autonomous chemical oscillators. Phys Chem Chem Phys 2021; 23:17606-17615. [PMID: 34369507 DOI: 10.1039/d1cp02221k] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We study the impact of delayed feedbacks in the collective synchronization of ensembles of identical and autonomous micro-oscillators. To this aim, we consider linear arrays of Belousov-Zhabotinsky (BZ) oscillators confined in micro-compartmentalised systems, where the delayed feedback mimics natural lags that can arise due to the confinement properties and mechanisms driving the inter-oscillator communication. The micro-oscillator array is modeled as a set of Oregonator-like kinetics coupled via mass exchange of the chemical messengers. Changes in the synchronization patterns are explored by varying the delayed feedback introduced in the messenger species Br2. A direct transition from anti-phase to in-phase synchronization and back to the initial anti-phase scheme is observed by progressively increasing the time delay from zero to the value T0, which is the oscillation period characterising the system without any delayed coupling. The route from anti- to in-phase oscillations (and back) consists of regimes where windows of in-phase oscillations are periodically broken by anti-phase beats. Similarities between these phase transition dynamics and synchronization scenarios characterising the coordination of oscillatory limb movements are finally discussed.
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Affiliation(s)
- Marcello A Budroni
- Department of Chemistry and Pharmacy, University of Sassari, Via Vienna 2, 07100 Sassari, Italy.
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3
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Mallphanov IL, Vanag VK. Distance dependent types of coupling of chemical micro-oscillators immersed in a water-in-oil microemulsion. Phys Chem Chem Phys 2021; 23:9130-9138. [DOI: 10.1039/d1cp00758k] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally.
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Affiliation(s)
- Ilya L. Mallphanov
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad 236016
- Russia
| | - Vladimir K. Vanag
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad 236016
- Russia
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4
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Sheehy J, Hunter I, Moustaka ME, Aghvami SA, Fahmy Y, Fraden S. Impact of PDMS-Based Microfluidics on Belousov-Zhabotinsky Chemical Oscillators. J Phys Chem B 2020; 124:11690-11698. [PMID: 33315410 DOI: 10.1021/acs.jpcb.0c08422] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Sub-nanoliter volumes of the Belousov-Zhabotinsky (BZ) reaction are sealed in microfluidic devices made from polydimethylsiloxane (PDMS). Bromine, which is a BZ reaction intermediate that participates in the inhibitory pathway of the reaction, is known to permeate into PDMS, and it has been suggested that PDMS and bromine can react ( J. Phys. Chem. A. 108, 2004, 1325-1332). We characterize the extent to which PDMS affects BZ oscillations by varying the volume of the PDMS surrounding the BZ reactors. We measure how the oscillation period varies with PDMS volume and compare with a theoretical reaction-diffusion model, concluding that bromine reacts with PDMS. We demonstrate that minimizing the amount of PDMS by making the samples as thin as possible maximizes the number of oscillations before the BZ reaction reaches equilibrium and ceases to oscillate. We also demonstrate that the deleterious effects of the PDMS-BZ interactions are somewhat mitigated by imposing constant chemical boundary conditions through using a light-sensitive catalyst, ruthenium, in combination with patterned illumination. Furthermore, we show that light can modulate the frequency and phase of the BZ oscillators contained in a PDMS matrix by 20-30%.
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Affiliation(s)
- James Sheehy
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Ian Hunter
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Maria Eleni Moustaka
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - S Ali Aghvami
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Youssef Fahmy
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
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5
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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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6
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Budroni MA, Torbensen K, Ristori S, Abou-Hassan A, Rossi F. Membrane Structure Drives Synchronization Patterns in Arrays of Diffusively Coupled Self-Oscillating Droplets. J Phys Chem Lett 2020; 11:2014-2020. [PMID: 32078774 DOI: 10.1021/acs.jpclett.0c00072] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Networks of diffusively coupled inorganic oscillators, confined in nano- and microcompartments, are effective for predicting and understanding the global dynamics of those systems where the diffusion of activatory or inhibitory signals regulates the communication among different individuals. By taking advantage of a microfluidic device, we study the dynamics of arrays of diffusively coupled Belousov-Zhabotinsky (BZ) oscillators encapsulated in water-in-oil single emulsions. New synchronization patterns are induced and controlled by modulating the structural and chemical properties of the phospholipid-based biomimetic membranes via the introduction of specific dopants. Doping molecules do not alter the membrane basic backbone, but modify the lamellarity (and, in turn, the permeability) or interact chemically with the reaction intermediates. A transition from two-period clusters showing 1:2 period-locking to one-period antiphase synchronization is observed by decreasing the membrane lamellarity. An unsynchronized scenario is found when the dopant is able to interfere with chemical communication by reacting with the chemical messengers.
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Affiliation(s)
- Marcello A Budroni
- Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - Kristian Torbensen
- Sorbonne Université, CNRS, PHysico-chimie des Electrolytes et Nanosystèmes InterfaciauX (PHENIX), F-75005 Paris, France
| | - Sandra Ristori
- Department of Chemistry & CSGI, University of Florence, Via della Lastruccia 3, 50019 Sesto Fiorentino, Firenze, Italy
| | - Ali Abou-Hassan
- Sorbonne Université, CNRS, PHysico-chimie des Electrolytes et Nanosystèmes InterfaciauX (PHENIX), F-75005 Paris, France
| | - Federico Rossi
- Department of Physical Science, Earth and Environment, University of Siena, Pian dei Mantellini, 44 53100 Siena (SI), Italy
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7
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Budroni MA, Torbensen K, Pantani OL, Ristori S, Rossi F, Abou-Hassan A. Microfluidic compartmentalization of diffusively coupled oscillators in multisomes induces a novel synchronization scenario. Chem Commun (Camb) 2020; 56:11771-11774. [DOI: 10.1039/d0cc05046f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Multisome compartments encapsulating the Belousov–Zhabotinsky reaction produced by microfluidics arranged in 1D arrays showed a novel type of global synchronization.
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Affiliation(s)
| | - Kristian Torbensen
- Sorbonne Université
- CNRS UMR 8234
- PHysico-chimie des Electrolytes et Nanosystèmes InterfaciauX (PHENIX)
- Paris F-75005
- France
| | - Ottorino L. Pantani
- Department of Agrifood Production and Environmental Sciences
- University of Florence P.le delle Cascine 28
- Firenze 50144
- Italy
| | - Sandra Ristori
- Department of Chemistry & CSGI
- University of Florence
- Sesto Fiorentino 50019
- Italy
| | - Federico Rossi
- Department of Earth
- Environmental and Physical Sciences – DEEP Sciences – University of Siena
- Siena 53100
- Italy
| | - Ali Abou-Hassan
- Sorbonne Université
- CNRS UMR 8234
- PHysico-chimie des Electrolytes et Nanosystèmes InterfaciauX (PHENIX)
- Paris F-75005
- France
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8
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Norton MM, Tompkins N, Blanc B, Cambria MC, Held J, Fraden S. Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters. PHYSICAL REVIEW LETTERS 2019; 123:148301. [PMID: 31702219 DOI: 10.1103/physrevlett.123.148301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Revised: 09/09/2019] [Indexed: 06/10/2023]
Abstract
We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100 μm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength: (i) unlocked, uncorrelated phase shifts between all oscillators; (ii) locked, arm hubs synchronized in phase with a k-dependent phase shift between the arm and central hub; and (iii) center silent, a central hub stopped oscillating and the arm hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.
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Affiliation(s)
- Michael M Norton
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Nathan Tompkins
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
- Physics Department, Wabash College, Crawfordsville, Indiana 47933, USA
| | - Baptiste Blanc
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | | | - Jesse Held
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
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9
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Kitagaki BT, Pinto MR, Queiroz AC, Breitkreitz MC, Rossi F, Nagao R. Multivariate statistical analysis of chemical and electrochemical oscillators for an accurate frequency selection. Phys Chem Chem Phys 2019; 21:16423-16434. [PMID: 31144704 DOI: 10.1039/c9cp01998g] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
The effect of experimental parameters on the frequency of chemical oscillators has been systematically studied since the first observations of clock reactions. The approach is mainly based on univariate changes in one specific parameter while others are kept constant. The frequency is then monitored and the effect of each parameter is discussed separately. This type of analysis, however, does not take into account the multiple interactions among the controllable parameters and the synergic responses on the oscillation frequency. We have carried out a multivariate statistical analysis of chemical (BZ-ferroin catalyzed reaction) and electrochemical (Cu/Cu2O cathodic deposition) oscillators and identified the contributions of the experimental parameters on frequency variations. The BZ reaction presented a strong dependence on the initial concentration of sodium bromate and temperature, resulting in a frequency increase. The concentration of malonic acid, the organic substrate, affects the system but with lower intensity compared with the combination of sodium bromate and temperature. On the other hand, the Cu/Cu2O electrochemical oscillator was shown to be less sensitive to changes in the temperature. The applied current density and pH were the two parameters which most perturbed the system. Interestingly, the frequency behaved nonmonotonically with a quadratic dependence. The multivariate analysis of both oscillators exhibited significant differences - while the homogenous oscillator displayed a linear dependence with the factors, the heterogeneous one revealed a more complex dependence with quadratic terms. Our results may contribute, for instance, in the synthesis of self-organized materials in which an accurate frequency selection is required and, depending on its value, different physicochemical properties are obtained.
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Affiliation(s)
- Bianca T Kitagaki
- Institute of Chemistry, University of Campinas, CEP 13083-970, Campinas, SP, Brazil.
| | - Maria R Pinto
- Institute of Chemistry, University of Campinas, CEP 13083-970, Campinas, SP, Brazil.
| | - Adriana C Queiroz
- Institute of Chemistry, University of Campinas, CEP 13083-970, Campinas, SP, Brazil. and Center for Innovation on New Energies, University of Campinas, CEP 13083-841, Campinas, SP, Brazil
| | - Márcia C Breitkreitz
- Institute of Chemistry, University of Campinas, CEP 13083-970, Campinas, SP, Brazil.
| | - Federico Rossi
- Department of Earth, Environmental and Physical Sciences - DEEP Sciences, University of Siena, Pian dei Mantellini 44, 53100, Siena, Italy
| | - Raphael Nagao
- Institute of Chemistry, University of Campinas, CEP 13083-970, Campinas, SP, Brazil. and Center for Innovation on New Energies, University of Campinas, CEP 13083-841, Campinas, SP, Brazil
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10
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11
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Chang KM, de Planque MRR, Zauner KP. Towards Functional Droplet Architectures: a Belousov-Zhabotinsky Medium for Networks. Sci Rep 2018; 8:12656. [PMID: 30140015 PMCID: PMC6107623 DOI: 10.1038/s41598-018-30819-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2018] [Accepted: 07/31/2018] [Indexed: 02/04/2023] Open
Abstract
The confluence of droplet-compartmentalised chemical systems and architectures composed of interacting droplets points towards a novel technology mimicking core features of the cellular architecture that dominates biology. A key challenge to achieve such a droplet technology is long-term stability in conjunction with interdroplet communication. Here, we probed the parameter space of the Belousov-Zhabotinsky (BZ) medium, an extensively studied model for non-equilibrium chemical reactions, pipetted as 2.5 mm droplets in hexadecane oil. The presence of asolectin lipids enabled the formation of arrays of contacted BZ droplets, of which the wave patterns were characterised over time. We utilised laser-cut acrylic templates with over 40 linear oil-filled slots in which arrays are formed by pipetting droplets of the desired BZ composition, enabling parallel experiments and automated image analysis. Using variations of conventional malonic acid BZ medium, wave propagation over droplet-droplet interfaces was not observed. However, a BZ medium containing both malonic acid and 1,4-cyclohexanedione was found to enable inter-droplet wave propagation. We anticipate that the chemical excitation properties of this mixed-substrate BZ medium, in combination with the droplet stability of the networks demonstrated here for nearly 400 droplets in a template-defined topology, will facilitate the development of scalable functional droplet networks.
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Affiliation(s)
- Kai Ming Chang
- Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, United Kingdom
| | - Maurits R R de Planque
- Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, United Kingdom
| | - Klaus-Peter Zauner
- Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, United Kingdom.
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12
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Litschel T, Norton MM, Tserunyan V, Fraden S. Engineering reaction-diffusion networks with properties of neural tissue. LAB ON A CHIP 2018; 18:714-722. [PMID: 29297916 DOI: 10.1039/c7lc01187c] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale reactors containing the Belousov-Zhabotinsky (BZ) reaction. Microfluidic fabrication techniques are developed that provide the ability to vary the network topology and the reactor coupling strength and offer the freedom to choose whether an arbitrary reactor is inhibitory or excitatory coupled to its neighbor. This versatile experimental and theoretical framework can be used to create a wide variety of chemical networks. Here we design, construct and characterize chemical networks that achieve the complexity of central pattern generators (CPGs), which are found in the autonomic nervous system of a variety of organisms.
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Affiliation(s)
- Thomas Litschel
- Department of Physics, Brandeis University, Waltham, MA 02453, USA.
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13
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Proskurkin IS, Vanag VK. Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback. Phys Chem Chem Phys 2018; 20:16126-16137. [DOI: 10.1039/c8cp02283f] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov–Zhabotinsky (BZ) reaction.
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Affiliation(s)
- Ivan S. Proskurkin
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad
- Russia
| | - Vladimir K. Vanag
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad
- Russia
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14
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Voorsluijs V, Kevrekidis IG, De Decker Y. Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction. Phys Chem Chem Phys 2017; 19:22528-22537. [PMID: 28809962 DOI: 10.1039/c7cp03260a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10-21 L) or droplets (V ≈ [10-8-10-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.
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Affiliation(s)
- Valérie Voorsluijs
- Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.
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15
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Gentili PL, Giubila MS, Germani R, Romani A, Nicoziani A, Spalletti A, Heron BM. Optical Communication among Oscillatory Reactions and Photo-Excitable Systems: UV and Visible Radiation Can Synchronize Artificial Neuron Models. Angew Chem Int Ed Engl 2017. [DOI: 10.1002/ange.201702289] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Pier Luigi Gentili
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - Maria Sole Giubila
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - Raimondo Germani
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - Aldo Romani
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - Andrea Nicoziani
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - Anna Spalletti
- Department of Chemistry, Biology and Biotechnology; University of Perugia; Via Elce di sotto 8 06123 Perugia Italy
| | - B. Mark Heron
- Department of Chemical Sciences; School of Applied Science; University of Huddersfield, Queensgate; Huddersfield HD1 3DH UK
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16
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Gentili PL, Giubila MS, Germani R, Romani A, Nicoziani A, Spalletti A, Heron BM. Optical Communication among Oscillatory Reactions and Photo-Excitable Systems: UV and Visible Radiation Can Synchronize Artificial Neuron Models. Angew Chem Int Ed Engl 2017; 56:7535-7540. [PMID: 28560808 DOI: 10.1002/anie.201702289] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Revised: 04/27/2017] [Indexed: 11/08/2022]
Abstract
Neuromorphic engineering promises to have a revolutionary impact in our societies. A strategy to develop artificial neurons (ANs) is to use oscillatory and excitable chemical systems. Herein, we use UV and visible radiation as both excitatory and inhibitory signals for the communication among oscillatory reactions, such as the Belousov-Zhabotinsky and the chemiluminescent Orban transformations, and photo-excitable photochromic and fluorescent species. We present the experimental results and the simulations regarding pairs of ANs communicating by either one or two optical signals, and triads of ANs arranged in both feed-forward and recurrent networks. We find that the ANs, powered chemically and/or by the energy of electromagnetic radiation, can give rise to the emergent properties of in-phase, out-of-phase, anti-phase synchronizations and phase-locking, dynamically mimicking the communication among real neurons.
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Affiliation(s)
- Pier Luigi Gentili
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - Maria Sole Giubila
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - Raimondo Germani
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - Aldo Romani
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - Andrea Nicoziani
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - Anna Spalletti
- Department of Chemistry, Biology and Biotechnology, University of Perugia, Via Elce di sotto 8, 06123, Perugia, Italy
| | - B Mark Heron
- Department of Chemical Sciences, School of Applied Science, University of Huddersfield, Queensgate, Huddersfield, HD1 3DH, UK
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17
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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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Wang AL, Gold JM, Tompkins N, Heymann M, Harrington KI, Fraden S. Configurable NOR gate arrays from Belousov-Zhabotinsky micro-droplets. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2016; 225:211-227. [PMID: 27168916 PMCID: PMC4860281 DOI: 10.1140/epjst/e2016-02622-y] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
We investigate the Belousov-Zhabotinsky (BZ) reaction in an attempt to establish a basis for computation using chemical oscillators coupled via inhibition. The system consists of BZ droplets suspended in oil. Interdrop coupling is governed by the non-polar communicator of inhibition, Br2. We consider a linear arrangement of three droplets to be a NOR gate, where the center droplet is the output and the other two are inputs. Oxidation spikes in the inputs, which we define to be TRUE, cause a delay in the next spike of the output, which we read to be FALSE. Conversely, when the inputs do not spike (FALSE) there is no delay in the output (TRUE), thus producing the behavior of a NOR gate. We are able to reliably produce NOR gates with this behavior in microfluidic experiment.
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Affiliation(s)
- A L Wang
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - J M Gold
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - N Tompkins
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
| | - M Heymann
- Center for Free Electron Laser Science, Deutsches Elektronen Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - K I Harrington
- Center for Vascular Biology Research, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215, USA
| | - S Fraden
- Department of Physics, Brandeis University, Waltham, MA 02453, USA
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19
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González-Ochoa HO, Flores-Moreno R, Reyes LM, Femat R. Extended source model for diffusive coupling. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:4. [PMID: 26802012 DOI: 10.1140/epje/i2016-16004-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Accepted: 12/23/2015] [Indexed: 06/05/2023]
Abstract
Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.
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Affiliation(s)
- Héctor O González-Ochoa
- Departamento de Electrónica, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, Mexico.
| | - Roberto Flores-Moreno
- Departamento de Quımica, Universidad de Guadalajara. Blvd. Marcelino García Barragan 1421, 44430, Guadalajara Jal, Mexico
| | - Luz M Reyes
- Departamento de Ciencias Computacionales, Universidad de Guadalajara. Av. Revolución 1500, 44430, Guadalajara Jal, Mexico
| | - Ricardo Femat
- División de Matemáticas Aplicadas, IPICyT, Camino a la Presa San José 2055, 78216, San Luis Potosı, SLP, Mexico
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20
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Laing CR. Chimeras in networks with purely local coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:050904. [PMID: 26651635 DOI: 10.1103/physreve.92.050904] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Indexed: 05/26/2023]
Abstract
Chimera states in spatially extended networks of oscillators have some oscillators synchronized while the remainder are asynchronous. These states have primarily been studied in networks with nonlocal coupling, and more recently in networks with global coupling. Here, we present three networks with only local coupling (diffusive, to nearest neighbors) which are numerically found to support chimera states. One of the networks is analyzed using a self-consistency argument in the continuum limit, and this is used to find the boundaries of existence of a chimera state in parameter space.
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Affiliation(s)
- Carlo R Laing
- Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand
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Tompkins N, Cambria MC, Wang AL, Heymann M, Fraden S. Creation and perturbation of planar networks of chemical oscillators. CHAOS (WOODBURY, N.Y.) 2015; 25:064611. [PMID: 26117136 PMCID: PMC4457659 DOI: 10.1063/1.4922056] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2015] [Accepted: 05/14/2015] [Indexed: 05/17/2023]
Abstract
Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay.
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Affiliation(s)
- Nathan Tompkins
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | | | - Adam L Wang
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael Heymann
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
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Li N, Tompkins N, Gonzalez-Ochoa H, Fraden S. Tunable diffusive lateral inhibition in chemical cells. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:18. [PMID: 25795263 PMCID: PMC4403736 DOI: 10.1140/epje/i2015-15018-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Revised: 02/07/2015] [Accepted: 02/09/2015] [Indexed: 05/17/2023]
Abstract
The Belousov-Zhabotinsky (BZ) reaction has become the prototype of nonlinear chemical dynamics. Microfluidic techniques provide a convenient method for emulsifying BZ solutions into monodispersed drops with diameters of tens to hundreds of microns, providing a unique system in which reaction-diffusion theory can be quantitatively tested. In this work, we investigate monolayers of microfluidically generated BZ drops confined in close-packed two-dimensional (2D) arrays through experiments and finite element simulations. We describe the transition from oscillatory to stationary chemical states with increasing coupling strength, controlled by independently varying the reaction chemistry within a drop and diffusive flux between drops. For stationary drops, we studied how the ratio of stationary oxidized to stationary reduced drops varies with coupling strength. In addition, using simulation, we quantified the chemical heterogeneity sufficient to induce mixed stationary and oscillatory patterns.
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Affiliation(s)
- Ning Li
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Nathan Tompkins
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Hector Gonzalez-Ochoa
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
- Department of Applied Mathematics, IPICYT, San Luis Potosi, Mexico
| | - Seth Fraden
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
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Martinez A, Smalyukh II. Light-driven dynamic Archimedes spirals and periodic oscillatory patterns of topological solitons in anisotropic soft matter. OPTICS EXPRESS 2015; 23:4591-4604. [PMID: 25836496 DOI: 10.1364/oe.23.004591] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Oscillatory and excitable systems commonly exhibit formation of dynamic non-equilibrium patterns. For example, rotating spiral patterns are observed in biological, chemical, and physical systems ranging from organization of slime mold cells to Belousov-Zhabotinsky reactions, and to crystal growth from nuclei with screw dislocations. Here we describe spontaneous formation of spiral waves and a large variety of other dynamic patterns in anisotropic soft matter driven by low-intensity light. The unstructured ambient or microscope light illumination of thin liquid crystal films in contact with a self-assembled azobenzene monolayer causes spontaneous formation, rich spatial organization, and dynamics of twisted domains and topological solitons accompanied by the dynamic patterning of azobenzene group orientations within the monolayer. Linearly polarized incident light interacts with the twisted liquid crystalline domains, mimicking their dynamics and yielding patterns in the polarization state of transmitted light, which can be transformed to similar dynamic patterns in its intensity and interference color. This shows that the delicate light-soft-matter interaction can yield complex self-patterning of both. We uncover underpinning physical mechanisms and discuss potential uses.
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