1
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Ishii H, Kori H. Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements. Sci Rep 2024; 14:11019. [PMID: 38744886 PMCID: PMC11094171 DOI: 10.1038/s41598-024-61058-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 04/30/2024] [Indexed: 05/16/2024] Open
Abstract
Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from an attracting state driven by a fluctuation in the system's state. We consider a system of interacting bistable elements and investigate the effect of diffusive coupling among elements on the process of noise-induced escape. We focus on the influence of the coupling strength over the escape time, which is the time it takes for noise-induced escape to occur. We performed numerical simulations and observed that weak coupling reduced the mean escape time, whereas strong coupling impeded escape. We argue that, although diffusive coupling both facilitates and impedes escape, the facilitating effect is dominant when coupling is weak. For weak coupling cases, we develop an approximate theory that can predict the mean and variance of escape times. In contrast, strong coupling reduces the effective noise intensity to impede escape. Our results suggest that diffusive coupling among multistable elements contributes to regulating the rate of transitions among attracting states.
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Affiliation(s)
- Hidemasa Ishii
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan.
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan
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2
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Smart M, Shvartsman SY, Nunley H. A model of replicating coupled oscillators generates naturally occurring cell networks. Development 2023; 150:dev202187. [PMID: 37823332 PMCID: PMC10690053 DOI: 10.1242/dev.202187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 10/02/2023] [Indexed: 10/13/2023]
Abstract
When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Such networks are required for gamete production in many animals, and different species have evolved diverse final network topologies. Although mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devised a mathematical model for generating cell networks, in which each node is an oscillator and, after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations are transient and coupled via diffusion over the edges of the network. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of intra-species variation. Because cell networks outside of the ovary often form less deterministically, we propose model generalizations to account for sources of stochasticity.
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Affiliation(s)
- Matthew Smart
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
| | - Stanislav Y. Shvartsman
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
- Department of Molecular Biology and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08540, USA
| | - Hayden Nunley
- Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
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3
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Battogtokh D, Tyson JJ. Nucleation of stem cell domains in a bistable activator-inhibitor model of the shoot apical meristem. CHAOS (WOODBURY, N.Y.) 2022; 32:093117. [PMID: 36182391 DOI: 10.1063/5.0093841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/03/2022] [Indexed: 06/16/2023]
Abstract
Shoot apical meristems (SAMs) give rise to all above-ground tissues of a plant. Expansion of meristematic tissue is derived from the growth and division of stem cells that reside in a central zone of the SAM. This reservoir of stem cells is maintained by expression of a transcription factor WUSCHEL that is responsible for the development of stem cells in the central zone. WUSCHEL expression is self-activating and downregulated by a signaling pathway initiated by CLAVATA proteins, which are upregulated by WUSCHEL. This classic activator-inhibitor network can generate localized patterns of WUSCHEL activity by a Turing instability provided certain constraints on reaction rates and diffusion constants of WUSCHEL and CLAVATA are satisfied, and most existing mathematical models of nucleation and confinement of stem cells in the SAM rely on Turing's mechanism. However, Turing patterns have certain properties that are inconsistent with observed patterns of stem cell differentiation in the SAM. As an alternative mechanism, we propose a model for stem cell confinement based on a bistable-switch in WUSCHEL-CLAVATA interactions. We study the bistable-switch mechanism for pattern formation in a spatially continuous domain and in a discrete cellularized tissue in the presence of a non-uniform field of a rapidly diffusing hormone. By comparing domain formation by Turing and bistable-switch mechanisms in these contexts, we show that bistable switching provides a superior account of nucleation and confinement of the stem cell domain under reasonable assumptions on reaction rates and diffusion constants.
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Affiliation(s)
- Dorjsuren Battogtokh
- Department of Biological Sciences, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, USA
| | - John J Tyson
- Department of Biological Sciences, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, USA
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4
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Diegmiller R, Nunley H, Shvartsman SY, Imran Alsous J. Quantitative models for building and growing fated small cell networks. Interface Focus 2022; 12:20210082. [PMID: 35865502 PMCID: PMC9184967 DOI: 10.1098/rsfs.2021.0082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 03/31/2022] [Indexed: 02/07/2023] Open
Abstract
Small cell clusters exhibit numerous phenomena typically associated with complex systems, such as division of labour and programmed cell death. A conserved class of such clusters occurs during oogenesis in the form of germline cysts that give rise to oocytes. Germline cysts form through cell divisions with incomplete cytokinesis, leaving cells intimately connected through intercellular bridges that facilitate cyst generation, cell fate determination and collective growth dynamics. Using the well-characterized Drosophila melanogaster female germline cyst as a foundation, we present mathematical models rooted in the dynamics of cell cycle proteins and their interactions to explain the generation of germline cell lineage trees (CLTs) and highlight the diversity of observed CLT sizes and topologies across species. We analyse competing models of symmetry breaking in CLTs to rationalize the observed dynamics and robustness of oocyte fate specification, and highlight remaining gaps in knowledge. We also explore how CLT topology affects cell cycle dynamics and synchronization and highlight mechanisms of intercellular coupling that underlie the observed collective growth patterns during oogenesis. Throughout, we point to similarities across organisms that warrant further investigation and comment on the extent to which experimental and theoretical findings made in model systems extend to other species.
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Affiliation(s)
- Rocky Diegmiller
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ, USA,Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Hayden Nunley
- Flatiron Institute, Simons Foundation, New York, NY, USA
| | - Stanislav Y. Shvartsman
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA,Department of Molecular Biology, Princeton University, Princeton, NJ, USA,Flatiron Institute, Simons Foundation, New York, NY, USA
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5
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Kundu P, MacLaren NG, Kori H, Masuda N. Mean-field theory for double-well systems on degree-heterogeneous networks. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems.
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Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Neil G. MacLaren
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, The University of Tokyo, Chiba 277-8561, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, NY 14260-5030, USA
- Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
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6
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Kundu P, Kori H, Masuda N. Accuracy of a one-dimensional reduction of dynamical systems on networks. Phys Rev E 2022; 105:024305. [PMID: 35291116 DOI: 10.1103/physreve.105.024305] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)0028-083610.1038/nature16948] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.
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Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260-2900, USA
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, The University of Tokyo, Chiba 277-8561, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, New York 14260-5030, USA
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7
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Liu DJ, Wang CJ, Evans JW. Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice. Phys Rev E 2021; 104:014135. [PMID: 34412225 DOI: 10.1103/physreve.104.014135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/24/2021] [Indexed: 11/07/2022]
Abstract
Schloegl's second model (also known as the quadratic contact process) on a lattice involves spontaneous particle annihilation at rate p and autocatalytic particle creation at empty sites with n≥2 occupied neighbors. The particle creation rate for exactly n occupied neighbors is selected here as n(n-1)/[z(z-1)] for lattice coordination number z. We analyze this model on a Bethe lattice. Precise behavior for stochastic models on regular periodic infinite lattices is usually surmised from kinetic Monte Carlo simulation on a finite lattice with periodic boundary conditions. However, the persistence of boundary effects for a Bethe lattice complicates this process, e.g., by inducing spatially heterogenous states. This motivates the exploration of various boundary conditions and unconventional simulation ensembles on the Bethe lattice to predict behavior for infinite size. We focus on z=3, and predict a discontinuous transition to the vacuum state on the infinite lattice when p exceeds a threshold value of around 0.053.
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Affiliation(s)
- Da-Jiang Liu
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
| | - Chi-Jen Wang
- Department of Mathematics, National Chung Cheng University, Chiayi 62102, Taiwan
| | - James W Evans
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA.,Department of Physics & Astronomy and Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
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8
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Fortin D, Brooke CF, Lamirande P, Fritz H, McLoughlin PD, Pays O. Quantitative Spatial Ecology to Promote Human-Wildlife Coexistence: A Tool for Integrated Landscape Management. FRONTIERS IN SUSTAINABLE FOOD SYSTEMS 2020. [DOI: 10.3389/fsufs.2020.600363] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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9
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Wang CJ, Liu DJ, Evans JW. Extended families of critical and stationary droplets for nonequilibrium phase transitions in spatially discrete bistable systems. Phys Rev E 2020; 101:022803. [PMID: 32168646 DOI: 10.1103/physreve.101.022803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/03/2020] [Indexed: 06/10/2023]
Abstract
Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, p_{eq}, of a control parameter, p, with metastability and hysteresis around p_{eq}. For each p, there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p→p_{eq}. Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. We show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.
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Affiliation(s)
- Chi-Jen Wang
- Department of Mathematics, National Chung Cheng University, Chiayi 62102, Taiwan
| | - Da-Jiang Liu
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
| | - James W Evans
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
- Department of Mathematics and Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011, USA
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10
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Putra PS, Susanto H, Nuraini N. Turing Patterns of Non-linear S-I Model on Random and Real-Structure Networks with Diarrhea Data. Sci Rep 2019; 9:8892. [PMID: 31221999 PMCID: PMC6586790 DOI: 10.1038/s41598-019-45069-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Accepted: 05/28/2019] [Indexed: 11/26/2022] Open
Abstract
Most developed models for solving problems in epidemiology use deterministic approach. To cover the lack of spatial sense in the method, one uses statistical modeling, reaction-diffusion in continuous medium, or multi-patch model to depict epidemic activities in several connected locations. Here, we show that an epidemic model that is set as an organized system on networks can yield Turing patterns and other interesting behaviors that are sensitive to the initial conditions. The formed patterns can be used to determine the epidemic arrival time, its first peak occurrence and the peak duration. These epidemic quantities are beneficial to identify contribution of a disease source node to the others. Using a real structure network, the system also exhibits a comparable disease spread pattern of Diarrhea in Jakarta.
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Affiliation(s)
- Prama Setia Putra
- Industrial and Financial Mathematics Research Group, Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung, 40132, Indonesia.
| | - Hadi Susanto
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom
| | - Nuning Nuraini
- Industrial and Financial Mathematics Research Group, Department of Mathematics, Institut Teknologi Bandung, Ganesha 10, Bandung, 40132, Indonesia
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11
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Patchy spread patterns in three-species bistable systems with facultative mutualism. Biosystems 2019; 177:24-33. [PMID: 30659865 DOI: 10.1016/j.biosystems.2019.01.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2018] [Revised: 01/08/2019] [Accepted: 01/15/2019] [Indexed: 11/21/2022]
Abstract
A three-species population system under a facultative mutualistic relationship of one of the species is studied. The considered interactions are as follows: facultative between the first species and the second species, obligatory mutualism between the second species and the first one, and the third species is a predator of the first species. For this purpose, we extend the model proposed by Morozov et al., originally used to describe obligatory mutualism, to consider obligatory and facultative mutualism and prove that under adequately selected parameters this system produces a spatial patchy spread of populations or continuous wave fronts. Since the analytical treatment of a three-species model is often prohibitive, we first analyze the interaction between two mutualist species without diffusion and without the presence of the predator. Some parameters are fixed in the bistable regime of the mutualistic species to further consider the influence of the third species. The remaining parameters are then selected to produce patchy patterns under different mortality rates. Finally, the equations of the final three-species system are numerically solved to test the influence of different initial conditions in the formation of patchy populations. It is confirmed that the velocity and the profile of a traveling front are independent on the initial conditions. Our approach opens the way to study more general biological situations.
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12
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Rospendowiski J, Pinto MR, Hessel C, Sitta E, Nagao R. Tuning Electrochemical Bistability by Surface Area Blocking in the Cathodic Deposition of Copper. ACS OMEGA 2018; 3:13636-13646. [PMID: 31458069 PMCID: PMC6644789 DOI: 10.1021/acsomega.8b02353] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Accepted: 10/01/2018] [Indexed: 05/09/2023]
Abstract
We report herein a precise control of the electrochemical bistability induced by surface area changes during the cathodic deposition of copper. Small additions of 1,10-phenanthroline (Phen) in the reaction media present an inhibiting effect on the global rate mainly due to the adsorption of protonated Phen. The increase of its concentration favors a shrinkage of the bifurcation (saddle-node) diagram and shifts it to less negative potentials. The dynamic instability is verified by impedance measurements, and a negative impedance is clearly found. We calculated the apparent molar mass of the adsorbents using in situ gravimetric monitoring in the electrochemical experiments, and the results indicate that mass changes occur mainly due to the reduction of copper from bivalent ions dissolved in the reaction media. Importantly, the adsorption of protonated Phen molecules does not show a considerable contribution in mass variations but prevents the formation of a copper course grained morphology over the surface. Imaging analysis indicates finer nodulations at the lower branch compared to the upper branch in the bistability domain. On the basis of these observations, a kinetic mechanism is proposed and a good agreement is obtained between the apparent molar mass extracted from experiments and the theoretical values. Altogether, our results contribute to a detailed physical chemical description of the nonlinear behavior, bringing new insights about this reaction and pointing out the possibility to design switchable surface electrodes by taking advantage of the bistable behavior.
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Affiliation(s)
- Júlia Rospendowiski
- Institute
of Chemistry, University of Campinas, CEP 13083-970 Campinas, Sao Paulo, Brazil
| | - Maria R. Pinto
- Institute
of Chemistry, University of Campinas, CEP 13083-970 Campinas, Sao Paulo, Brazil
| | - Cristian Hessel
- Department
of Chemistry, Federal University of Sao Carlos, CEP 13565-905 Sao Carlos, Sao Paulo, Brazil
| | - Elton Sitta
- Department
of Chemistry, Federal University of Sao Carlos, CEP 13565-905 Sao Carlos, Sao Paulo, Brazil
- Center
for Innovation on New Energies, University
of Campinas, CEP 13083-841 Campinas, Sao Paulo, Brazil
| | - Raphael Nagao
- Institute
of Chemistry, University of Campinas, CEP 13083-970 Campinas, Sao Paulo, Brazil
- Center
for Innovation on New Energies, University
of Campinas, CEP 13083-841 Campinas, Sao Paulo, Brazil
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13
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Bozdech S, Biecher Y, Savinova ER, Schuster R, Krischer K, Bonnefont A. Oscillations in an array of bistable microelectrodes coupled through a globally conserved quantity. CHAOS (WOODBURY, N.Y.) 2018; 28:045113. [PMID: 31906625 DOI: 10.1063/1.5022475] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The dynamical behavior of an array of microelectrodes is investigated under controlled current conditions during CO electrooxidation, a bistable electrochemical reaction with an S-shaped negative differential resistance (S-NDR) current-potential curve. Under these conditions, the total current constitutes a globally conserved quantity, thus coupling all microelectrodes globally. Upon increasing the total current, the microelectrodes activate one by one, with a single microelectrode being on its intermediate S-NDR current branch and the other ones being either on their passive or their active branches. When a few coupled microelectrodes are activated, the electrochemical system exhibits spontaneous potential oscillations. Mathematical analysis shows that oscillations arise already in a two group approximation of the dynamics, the two groups consisting of 1 electrode and n - 1 electrodes with n ≥ 3, respectively, with each group being described by a single evolution equation. In this minimal representation, oscillations occur when the single electrode is on the intermediate branch and the larger group is on the active branch.
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Affiliation(s)
- S Bozdech
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - Y Biecher
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - E R Savinova
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - R Schuster
- Institut für Physikalische Chemie, Karlsruher Institute of Technology, Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - K Krischer
- Physik Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany
| | - A Bonnefont
- Institut de Chimie de Strasbourg, UMR7177, CNRS-Université de Strasbourg, 4 rue Blaise Pascal, 67070 Strasbourg, France
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14
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Prima M, Duchesne T, Fortin A, Rivest L, Fortin D. Combining network theory and reaction–advection–diffusion modelling for predicting animal distribution in dynamic environments. Methods Ecol Evol 2018. [DOI: 10.1111/2041-210x.12997] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Thierry Duchesne
- Department of Mathematics and StatisticsLaval University Quebec City QC Canada
| | - André Fortin
- Department of Mathematics and StatisticsLaval University Quebec City QC Canada
| | - Louis‐Paul Rivest
- Department of Mathematics and StatisticsLaval University Quebec City QC Canada
| | - Daniel Fortin
- Department of BiologyLaval University Quebec City QC Canada
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15
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Zankoc C, Fanelli D, Ginelli F, Livi R. Intertangled stochastic motifs in networks of excitatory-inhibitory units. Phys Rev E 2017; 96:022308. [PMID: 28950520 DOI: 10.1103/physreve.96.022308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 06/07/2023]
Abstract
A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust internode correlations that persist at large distances. Antiphase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns that invade the network as a whole. These patterns are lacking under the idealized deterministic scenario, and could provide hints on how living systems implement and handle a large gallery of delicate computational tasks.
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Affiliation(s)
- Clement Zankoc
- Dipartimento di Fisica e Astronomia and CSDC, Università degli Studi di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
- INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
| | - Duccio Fanelli
- Dipartimento di Fisica e Astronomia and CSDC, Università degli Studi di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
- INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
| | - Francesco Ginelli
- SUPA, Institute for Complex Systems and Mathematical Biology, Kings College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Roberto Livi
- Dipartimento di Fisica e Astronomia and CSDC, Università degli Studi di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
- INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italia
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16
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Abstract
In large random networks, each eigenvector of the Laplacian matrix tends to localize on a subset of network nodes having similar numbers of edges, namely, the components of each Laplacian eigenvector take relatively large values only on a particular subset of nodes whose degrees are close. Although this localization property has significant consequences for dynamical processes on random networks, a clear theoretical explanation has not yet been established. Here we analyze the origin of localization of Laplacian eigenvectors on random networks by using a perturbation theory. We clarify how heterogeneity in the node degrees leads to the eigenvector localization and that there exists a clear degree-eigenvalue correspondence, that is, the characteristic degrees of the localized nodes essentially determine the eigenvalues. We show that this theory can account for the localization properties of Laplacian eigenvectors on several classes of random networks, and argue that this localization should occur generally in networks with degree heterogeneity.
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17
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Hernandez-Hernandez G, Myers J, Alvarez-Lacalle E, Shiferaw Y. Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering. Phys Rev E 2017; 95:032313. [PMID: 28415301 DOI: 10.1103/physreve.95.032313] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2016] [Indexed: 11/07/2022]
Abstract
Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological function.
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Affiliation(s)
| | - Jesse Myers
- Department of Physics & Astronomy, California State University, Northridge, California 91330, USA
| | - Enrique Alvarez-Lacalle
- Departament de Física, Universitat Politècnica de Catalunya, BarcelonaTech, Castelldefels 08860, Spain
| | - Yohannes Shiferaw
- Department of Physics & Astronomy, California State University, Northridge, California 91330, USA
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Kouvaris NE, Sebek M, Iribarne A, Díaz-Guilera A, Kiss IZ. Stationary patterns in star networks of bistable units: Theory and application to chemical reactions. Phys Rev E 2017; 95:042203. [PMID: 28505836 DOI: 10.1103/physreve.95.042203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Indexed: 06/07/2023]
Abstract
We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).
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Affiliation(s)
- Nikos E Kouvaris
- Center for Brain and Cognition, Universitat Pompeu Fabra, E-08005 Barcelona, Spain
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, E-08005 Barcelona, Spain
| | - Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Albert Iribarne
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
| | - Albert Díaz-Guilera
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, E-08007 Barcelona, Spain
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Kouvaris NE, Sebek M, Mikhailov AS, Kiss IZ. Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions. Angew Chem Int Ed Engl 2016; 55:13267-13270. [DOI: 10.1002/anie.201607030] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Indexed: 12/12/2022]
Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics; University of Barcelona; Martí i Franquès 1 08028 Barcelona Spain
| | - Michael Sebek
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
| | - Alexander S. Mikhailov
- Department of Physical Chemistry; Fritz Haber Institute of the Max Planck Society; Faradayweg 4-6 14195 Berlin Germany
| | - István Z. Kiss
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
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20
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Kouvaris NE, Sebek M, Mikhailov AS, Kiss IZ. Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions. Angew Chem Int Ed Engl 2016. [DOI: 10.1002/ange.201607030] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics; University of Barcelona; Martí i Franquès 1 08028 Barcelona Spain
| | - Michael Sebek
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
| | - Alexander S. Mikhailov
- Department of Physical Chemistry; Fritz Haber Institute of the Max Planck Society; Faradayweg 4-6 14195 Berlin Germany
| | - István Z. Kiss
- Department of Chemistry; Saint Louis University; 3501 Laclede Avenue St. Louis Missouri 63103 USA
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21
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Kouvaris NE, Hata S, Guilera AD. Pattern formation in multiplex networks. Sci Rep 2015; 5:10840. [PMID: 26042606 PMCID: PMC4455352 DOI: 10.1038/srep10840] [Citation(s) in RCA: 79] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 04/17/2015] [Indexed: 11/24/2022] Open
Abstract
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.
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Affiliation(s)
- Nikos E. Kouvaris
- Department of Physics, University of Barcelona, Martí i Franqués 1, E-08028, Barcelona, Spain
| | - Shigefumi Hata
- Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, 236-0001 Kanagawa, Japan
| | - Albert Díaz- Guilera
- Department of Physics, University of Barcelona, Martí i Franqués 1, E-08028, Barcelona, Spain
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22
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Hata S, Nakao H, Mikhailov AS. Advection of passive particles over flow networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:020801. [PMID: 25353407 DOI: 10.1103/physreve.89.020801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2013] [Indexed: 06/04/2023]
Abstract
The problem of stochastic advection of passive particles by circulating conserved flows on networks is formulated and investigated. The particles undergo transitions between the nodes, with the transition rates determined by the flows passing through the links. Such stochastic advection processes lead to mixing of particles in the network and, in the final equilibrium state, concentration of particles in all nodes becomes equal. As we find, equilibration begins in the subset of nodes, representing flow hubs, and extends to the periphery nodes with weak flows. This behavior is related to the effect of localization of the eigenvectors of the advection matrix for considered networks. Applications of the results to problems involving spreading of infections or pollutants by traffic networks are discussed.
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Affiliation(s)
- Shigefumi Hata
- Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - Hiroya Nakao
- Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Ookayama 2-12-1, 152-8552 Tokyo, Japan
| | - Alexander S Mikhailov
- Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
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23
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Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks. Sci Rep 2014; 4:3585. [PMID: 24394959 PMCID: PMC3882759 DOI: 10.1038/srep03585] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Accepted: 12/02/2013] [Indexed: 11/16/2022] Open
Abstract
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.
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Atsumi Y, Hata S, Nakao H. Phase ordering in coupled noisy bistable systems on scale-free networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052806. [PMID: 24329317 DOI: 10.1103/physreve.88.052806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2013] [Indexed: 06/03/2023]
Abstract
We study a system consisting of diffusively coupled noisy bistable elements on a scale-free random network. This system exhibits an order-disorder phase transition as the noise intensity is varied. The phase ordering process takes place consecutively and in order of the degrees, reflecting strong degree heterogeneity of the scale-free network. A nonlinear Fokker-Planck equation describing the network dynamics is derived under mean-field approximation of the network, and is used to explain the phase ordering dynamics of the system.
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Affiliation(s)
- Yu Atsumi
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Shigefumi Hata
- Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - Hiroya Nakao
- Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
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25
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Shen C, Chen H, Ye M, Hou Z. Nucleation pathways on complex networks. CHAOS (WOODBURY, N.Y.) 2013; 23:013112. [PMID: 23556949 DOI: 10.1063/1.4790832] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks using the forward flux sampling method, and find that the nucleation processes represent distinct features along pathways for different network topologies. For homogeneous networks, there always exists a dominant nucleating cluster to which relatively small clusters are attached gradually to form the critical nucleus. For heterogeneous ones, many small isolated nucleating clusters emerge at the early stage of the nucleation process, until suddenly they form the critical nucleus through a sharp merging process. Moreover, we also compare the nucleation pathways for different degree-mixing networks. By analyzing the properties of the nucleating clusters along the pathway, we show that the main reason behind the different routes is the heterogeneous character of the underlying networks.
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Affiliation(s)
- Chuansheng Shen
- Hefei National Laboratory for Physical Sciences at Microscales, and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
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