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Mulholland HN, Kaschube M, Smith GB. Self-organization of modular activity in immature cortical networks. Nat Commun 2024; 15:4145. [PMID: 38773083 PMCID: PMC11109213 DOI: 10.1038/s41467-024-48341-x] [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: 07/28/2023] [Accepted: 04/26/2024] [Indexed: 05/23/2024] Open
Abstract
During development, cortical activity is organized into distributed modular patterns that are a precursor of the mature columnar functional architecture. Theoretically, such structured neural activity can emerge dynamically from local synaptic interactions through a recurrent network with effective local excitation with lateral inhibition (LE/LI) connectivity. Utilizing simultaneous widefield calcium imaging and optogenetics in juvenile ferret cortex prior to eye opening, we directly test several critical predictions of an LE/LI mechanism. We show that cortical networks transform uniform stimulations into diverse modular patterns exhibiting a characteristic spatial wavelength. Moreover, patterned optogenetic stimulation matching this wavelength selectively biases evoked activity patterns, while stimulation with varying wavelengths transforms activity towards this characteristic wavelength, revealing a dynamic compromise between input drive and the network's intrinsic tendency to organize activity. Furthermore, the structure of early spontaneous cortical activity - which is reflected in the developing representations of visual orientation - strongly overlaps that of uniform opto-evoked activity, suggesting a common underlying mechanism as a basis for the formation of orderly columnar maps underlying sensory representations in the brain.
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Affiliation(s)
- Haleigh N Mulholland
- Department of Neuroscience, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Matthias Kaschube
- Frankfurt Institute for Advanced Studies, 60438, Frankfurt am Main, Germany
- Department of Computer Science and Mathematics, Goethe University, 60054, Frankfurt am Main, Germany
| | - Gordon B Smith
- Department of Neuroscience, University of Minnesota, Minneapolis, MN, 55455, USA.
- Optical Imaging and Brain Sciences Medical Discovery Team, University of Minnesota, Minneapolis, MN, 55455, USA.
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Mulholland HN, Kaschube M, Smith GB. Self-organization of modular activity in immature cortical networks. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.03.02.583133. [PMID: 38464130 PMCID: PMC10925298 DOI: 10.1101/2024.03.02.583133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2024]
Abstract
During development, cortical activity is organized into distributed modular patterns that are a precursor of the mature columnar functional architecture. Theoretically, such structured neural activity can emerge dynamically from local synaptic interactions through a recurrent network with effective local excitation with lateral inhibition (LE/LI) connectivity. Utilizing simultaneous widefield calcium imaging and optogenetics in juvenile ferret cortex prior to eye opening, we directly test several critical predictions of an LE/LI mechanism. We show that cortical networks transform uniform stimulations into diverse modular patterns exhibiting a characteristic spatial wavelength. Moreover, patterned optogenetic stimulation matching this wavelength selectively biases evoked activity patterns, while stimulation with varying wavelengths transforms activity towards this characteristic wavelength, revealing a dynamic compromise between input drive and the network's intrinsic tendency to organize activity. Furthermore, the structure of early spontaneous cortical activity - which is reflected in the developing representations of visual orientation - strongly overlaps that of uniform opto-evoked activity, suggesting a common underlying mechanism as a basis for the formation of orderly columnar maps underlying sensory representations in the brain.
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Affiliation(s)
| | - Matthias Kaschube
- Frankfurt Institute for Advanced Studies, Frankfurt am Main, 60438, Germany
| | - Gordon B. Smith
- Department of Neuroscience, University of Minnesota, Minneapolis, MN, 55455, USA
- Optical Imaging and Brain Sciences Medical Discovery Team, University of Minnesota, Minneapolis, MN, 55455, USA
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Jin M, Wang L, Ge F, Yan J. Detecting the interaction between urban elements evolution with population dynamics model. Sci Rep 2023; 13:12367. [PMID: 37524780 PMCID: PMC10390572 DOI: 10.1038/s41598-023-38979-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 07/18/2023] [Indexed: 08/02/2023] Open
Abstract
Exploring the evolution of urban elements can improve understanding of the developmental process of city and drive such development into a better direction. However, the non-linearity and complexity of changes in urban elements have brought great challenges to understanding this process. In this paper, we propose a cross-diffusion partial differential equation based on ecological dynamics to simulate the evolutionary process of urban elements from the microscopic viewpoint. The interaction between urban elements is simulated by constructing a non-linear and spatiotemporal change equation, and the main influence between elements is evaluated by the key parameters in the discussed equation. Our model is first experimented to time-series data on population density and housing prices to analyzes the interaction of these two elements in the evolution process. We then extend the model to label data, land cover data, to obtain a quantitative expression of the interaction between different land types in the process of urban land cover change.
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Affiliation(s)
- Min Jin
- School of Computer Science, China University of Geosciences, Wuhan, 430074, China
- Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, 430074, China
| | - Lizhe Wang
- School of Computer Science, China University of Geosciences, Wuhan, 430074, China.
- Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, 430074, China.
| | - Fudong Ge
- School of Computer Science, China University of Geosciences, Wuhan, 430074, China
| | - Jining Yan
- School of Computer Science, China University of Geosciences, Wuhan, 430074, China
- Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, 430074, China
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Turing patterns, 70 years later. NATURE COMPUTATIONAL SCIENCE 2022; 2:463-464. [PMID: 38177795 DOI: 10.1038/s43588-022-00306-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
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Escárcega-Bobadilla MV, Maldonado-Domínguez M, Romero-Ávila M, Zelada-Guillén GA. Turing patterns by supramolecular self-assembly of a single salphen building block. iScience 2022; 25:104545. [PMID: 35747384 PMCID: PMC9209723 DOI: 10.1016/j.isci.2022.104545] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 05/15/2022] [Accepted: 06/02/2022] [Indexed: 11/02/2022] Open
Abstract
In the 1950s, Alan Turing showed that concerted reactions and diffusion of activating and inhibiting chemical species can autonomously generate patterns without previous positional information, thus providing a chemical basis for morphogenesis in Nature. However, access to these patterns from only one molecular component that contained all the necessary information to execute agonistic and antagonistic signaling is so far an elusive goal, since two or more participants with different diffusivities are a must. Here, we report on a single-molecule system that generates Turing patterns arrested in the solid state, where supramolecular interactions are used instead of chemical reactions, whereas diffusional differences arise from heterogeneously populated self-assembled products. We employ a family of hydroxylated organic salphen building blocks based on a bis-Schiff-base scaffold with portions responsible for either activation or inhibition of assemblies at different hierarchies through purely supramolecular reactions, only depending upon the solvent dielectric constant and evaporation as fuel.
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Affiliation(s)
- Martha V Escárcega-Bobadilla
- School of Chemistry, National Autonomous University of Mexico (UNAM), Circuito Escolar s/n, Ciudad Universitaria, 04510 Mexico City, Mexico
| | - Mauricio Maldonado-Domínguez
- School of Chemistry, National Autonomous University of Mexico (UNAM), Circuito Escolar s/n, Ciudad Universitaria, 04510 Mexico City, Mexico.,Department of Computational Chemistry, J. Heyrovský Institute of Physical Chemistry, The Czech Academy of Sciences, Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Margarita Romero-Ávila
- School of Chemistry, National Autonomous University of Mexico (UNAM), Circuito Escolar s/n, Ciudad Universitaria, 04510 Mexico City, Mexico
| | - Gustavo A Zelada-Guillén
- School of Chemistry, National Autonomous University of Mexico (UNAM), Circuito Escolar s/n, Ciudad Universitaria, 04510 Mexico City, Mexico
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Whiteley TD, Avitabile D, Siebers PO, Robinson D, Owen MR. Modelling the emergence of cities and urban patterning using coupled integro-differential equations. J R Soc Interface 2022; 19:20220176. [PMID: 35506210 PMCID: PMC9065963 DOI: 10.1098/rsif.2022.0176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Human residential population distributions show patterns of higher density clustering around local services such as shops and places of employment, displaying characteristic length scales; Fourier transforms and spatial autocorrelation show the length scale between UK cities is around 45 km. We use integro-differential equations to model the spatio-temporal dynamics of population and service density under the assumption that they benefit from spatial proximity, captured via spatial weight kernels. The system tends towards a well-mixed homogeneous state or a spatial pattern. Linear stability analysis around the homogeneous steady state predicts a modelled length-scale consistent with that observed in the data. Moreover, we show that spatial instability occurs only for perturbations with a sufficiently long wavelength and only where there is a sufficiently strong dependence of service potential on population density. Within urban centres, competition for space may cause services and population to be out of phase with one another, occupying separate parcels of land. By introducing competition, along with a preference for population to be located near, but not too near, to high service density areas, secondary out-of-phase patterns occur within the model, at a higher density and with a shorter length scale than in phase patterning. Thus, we show that a small set of core behavioural ingredients can generate aggregations of populations and services, and pattern formation within cities, with length scales consistent with real-world data. The analysis and results are valid across a wide range of parameter values and functional forms in the model.
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Affiliation(s)
- Timothy D Whiteley
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Daniele Avitabile
- Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Peer-Olaf Siebers
- School of Computer Science, University of Nottingham, Nottingham, UK
| | - Darren Robinson
- School of Architecture, University of Sheffield, Sheffield, UK
| | - Markus R Owen
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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Kuznetsov M. Robust controlled formation of Turing patterns in three-component systems. Phys Rev E 2022; 105:014209. [PMID: 35193238 DOI: 10.1103/physreve.105.014209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
Over the past few decades, formation of Turing patterns in reaction-diffusion systems has been shown to be the underlying process in several examples of biological morphogenesis, confirming Alan Turing's hypothesis, put forward in 1952. However, theoretical studies suggest that Turing patterns formation via classical "short-range activation and long-range inhibition" concept in general can happen within only narrow parameter ranges. This feature seemingly contradicts the accuracy and reproducibility of biological morphogenesis given the stochasticity of biochemical processes and the influence of environmental perturbations. Moreover, it represents a major hurdle to synthetic engineering of Turing patterns. In this work it is shown that this problem can be overcome in some systems under certain sets of interactions between their elements, one of which is immobile and therefore corresponding to a cell-autonomous factor. In such systems Turing patterns formation can be guaranteed by a simple universal control under any values of kinetic parameters and diffusion coefficients of mobile elements. This concept is illustrated by analysis and simulations of a specific three-component system, characterized in absence of diffusion by a presence of codimension two pitchfork-Hopf bifurcation.
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Affiliation(s)
- Maxim Kuznetsov
- Division of Theoretical Physics, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia and Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), Moscow 117198, Russia
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Morozov A. Towards creating a mechanistic predictive theory of self-organized vegetation patterns: Comment on "Belowground feedbacks as drivers of spatial self-organization and community assembly" by Inderjit, Callaway and Meron. Phys Life Rev 2021; 40:54-56. [PMID: 34838506 DOI: 10.1016/j.plrev.2021.11.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Accepted: 11/09/2021] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew Morozov
- Institute of Ecology and Evolution, Russian Academy of Sciences, Moscow, Russia; School of Computing and Mathematical Sciences, University of Leicester, UK.
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