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Sampaio Filho CIN, de Arcangelis L, Herrmann HJ, Plenz D, Kells P, Ribeiro TL, Andrade JS. Ising-like model replicating time-averaged spiking behaviour of in vitro neuronal networks. Sci Rep 2024; 14:7002. [PMID: 38523136 DOI: 10.1038/s41598-024-55922-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 02/28/2024] [Indexed: 03/26/2024] Open
Abstract
We analyze time-averaged experimental data from in vitro activities of neuronal networks. Through a Pairwise Maximum-Entropy method, we identify through an inverse binary Ising-like model the local fields and interaction couplings which best reproduce the average activities of each neuron as well as the statistical correlations between the activities of each pair of neurons in the system. The specific information about the type of neurons is mainly stored in the local fields, while a symmetric distribution of interaction constants seems generic. Our findings demonstrate that, despite not being directly incorporated into the inference approach, the experimentally observed correlations among groups of three neurons are accurately captured by the derived Ising-like model. Within the context of the thermodynamic analogy inherent to the Ising-like models developed in this study, our findings additionally indicate that these models demonstrate characteristics of second-order phase transitions between ferromagnetic and paramagnetic states at temperatures above, but close to, unity. Considering that the operating temperature utilized in the Maximum-Entropy method isT o = 1 , this observation further expands the thermodynamic conceptual parallelism postulated in this work for the manifestation of criticality in neuronal network behavior.
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Affiliation(s)
| | - Lucilla de Arcangelis
- Department of Mathematics and Physics, University of Campania "Luigi Vanvitelli", 81100, Caserta, Italy
| | - Hans J Herrmann
- Departamento de Física, Universidade Federal do Ceará, Fortaleza, 60451-970, Brazil
- PMMH, ESPCI, CNRS UMR 7636, 7 Quai St. Bernard, 75005, Paris, France
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, NIMH, Bethesda, MD, 20892, USA
| | - Patrick Kells
- Section on Critical Brain Dynamics, NIMH, Bethesda, MD, 20892, USA
| | | | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará, Fortaleza, 60451-970, Brazil
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Habibollahi F, Kagan BJ, Burkitt AN, French C. Critical dynamics arise during structured information presentation within embodied in vitro neuronal networks. Nat Commun 2023; 14:5287. [PMID: 37648737 PMCID: PMC10469171 DOI: 10.1038/s41467-023-41020-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2022] [Accepted: 08/17/2023] [Indexed: 09/01/2023] Open
Abstract
Understanding how brains process information is an incredibly difficult task. Amongst the metrics characterising information processing in the brain, observations of dynamic near-critical states have generated significant interest. However, theoretical and experimental limitations associated with human and animal models have precluded a definite answer about when and why neural criticality arises with links from attention, to cognition, and even to consciousness. To explore this topic, we used an in vitro neural network of cortical neurons that was trained to play a simplified game of 'Pong' to demonstrate Synthetic Biological Intelligence (SBI). We demonstrate that critical dynamics emerge when neural networks receive task-related structured sensory input, reorganizing the system to a near-critical state. Additionally, better task performance correlated with proximity to critical dynamics. However, criticality alone is insufficient for a neuronal network to demonstrate learning in the absence of additional information regarding the consequences of previous actions. These findings offer compelling support that neural criticality arises as a base feature of incoming structured information processing without the need for higher order cognition.
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Affiliation(s)
- Forough Habibollahi
- Cortical Labs Pty Ltd, Melbourne, 3056, VIC, Australia
- Biomedical Engineering Department, University of Melbourne, Parkville, 3010, VIC, Australia
- Neural Dynamics Laboratory, Department of Medicine, University of Melbourne, Parkville, 3010, VIC, Australia
| | - Brett J Kagan
- Cortical Labs Pty Ltd, Melbourne, 3056, VIC, Australia.
| | - Anthony N Burkitt
- Biomedical Engineering Department, University of Melbourne, Parkville, 3010, VIC, Australia
| | - Chris French
- Neural Dynamics Laboratory, Department of Medicine, University of Melbourne, Parkville, 3010, VIC, Australia
- Neurology Department, Royal Melbourne Hospital, Melbourne, Australia
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3
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Baravalle R, Montani F. Heterogeneity across neural populations: Its significance for the dynamics and functions of neural circuits. Phys Rev E 2021; 103:042308. [PMID: 34005927 DOI: 10.1103/physreve.103.042308] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2020] [Accepted: 03/18/2021] [Indexed: 11/07/2022]
Abstract
Neural populations show patterns of synchronous activity, as they share common correlated inputs. Neurons in the cortex that are connected by strong synapses cause rapid firing explosions. In addition, areas that are connected by weaker synapses have a slower dynamics and they can contribute to asymmetries in the input distributions. The aim of this work is to develop a neural model to investigate how the heterogeneities in the synaptic input distributions affect different levels of organizational activity in the brain dynamics. We analytically show how small changes in the correlation inputs can cause large changes in the interactions of the outputs that lead to a phase transition, demonstrating that a simple variation in the direction of a biased skewed distribution in the neuronal inputs can generate a transition of states in the firing rate, passing from spontaneous silence ("down state") to an absolute spiking activity ("up state"). We present an exact quantification of the dynamics of the output variables, showing that when considering a biased skewed distribution in the inputs of neuronal population, the critical point is not in an asynchronous or synchronous state but rather at an intermediate value.
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Affiliation(s)
- Roman Baravalle
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata (1900) La Plata, Argentina
| | - Fernando Montani
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata (1900) La Plata, Argentina
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Lotfi N, Feliciano T, Aguiar LAA, Silva TPL, Carvalho TTA, Rosso OA, Copelli M, Matias FS, Carelli PV. Statistical complexity is maximized close to criticality in cortical dynamics. Phys Rev E 2021; 103:012415. [PMID: 33601583 DOI: 10.1103/physreve.103.012415] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 01/04/2021] [Indexed: 11/07/2022]
Abstract
Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a nonequilibrium phase transition.
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Affiliation(s)
- Nastaran Lotfi
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Leandro A A Aguiar
- Departamento de Ciências Fundamentais e Sociais, Universidade Federal da Paraíba, Areia PB 58397-000, Brazil
| | | | - Tawan T A Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Osvaldo A Rosso
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Fernanda S Matias
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
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Carvalho TTA, Fontenele AJ, Girardi-Schappo M, Feliciano T, Aguiar LAA, Silva TPL, de Vasconcelos NAP, Carelli PV, Copelli M. Subsampled Directed-Percolation Models Explain Scaling Relations Experimentally Observed in the Brain. Front Neural Circuits 2021; 14:576727. [PMID: 33519388 PMCID: PMC7843423 DOI: 10.3389/fncir.2020.576727] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 11/30/2002] [Indexed: 12/14/2022] Open
Abstract
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.
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Affiliation(s)
- Tawan T A Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | | | - Mauricio Girardi-Schappo
- Department of Physics, University of Ottawa, Ottawa, ON, Canada.,Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Leandro A A Aguiar
- Departamento de Ciências Fundamentais e Sociais, Universidade Federal da Paraíba, Areia, Brazil
| | - Thais P L Silva
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Nivaldo A P de Vasconcelos
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, Portugal.,Life and Health Sciences Research Institute/Biomaterials, Biodegradables and Biomimetics, Braga, Portugal
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
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