1
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Rhamidda SL, Girardi-Schappo M, Kinouchi O. Optimal input reverberation and homeostatic self-organization toward the edge of synchronization. CHAOS (WOODBURY, N.Y.) 2024; 34:053127. [PMID: 38767461 DOI: 10.1063/5.0202743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Accepted: 04/25/2024] [Indexed: 05/22/2024]
Abstract
Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.
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Affiliation(s)
- Sue L Rhamidda
- Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP 14040-901, Brazil
| | - Mauricio Girardi-Schappo
- Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, SC 88040-900, Brazil
| | - Osame Kinouchi
- Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP 14040-901, Brazil
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2
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Lombardi F, Herrmann HJ, Parrino L, Plenz D, Scarpetta S, Vaudano AE, de Arcangelis L, Shriki O. Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state. Cell Rep 2023; 42:113162. [PMID: 37777965 PMCID: PMC10842118 DOI: 10.1016/j.celrep.2023.113162] [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: 05/16/2022] [Revised: 06/07/2023] [Accepted: 09/07/2023] [Indexed: 10/03/2023] Open
Abstract
Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations-the "waxing and waning" phenomenon-are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the "waning" phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition).
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Affiliation(s)
- Fabrizio Lombardi
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria; Department of Biomedical Sciences, University of Padova, Via Ugo Bassi 58B, 35131 Padova, Italy.
| | - Hans J Herrmann
- Departamento de Fisica, Universitade Federal do Ceara, Fortaleza 60451-970, Ceara, Brazil; PMMH, ESPCI, 7 quai St. Bernard, 75005 Paris, France
| | - Liborio Parrino
- Sleep Disorders Center, Department of Neurosciences, University of Parma, 43121 Parma, Italy
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, NIH, Bethesda, MD 20892, USA
| | - Silvia Scarpetta
- Department of Physics, University of Salerno, 84084 Fisciano, Italy; INFN sez, Napoli Gr. Coll, 84084 Fisciano, Italy
| | - Anna Elisabetta Vaudano
- Neurology Unit, Azienda Ospedaliero-Universitaria of Modena, OCB Hospital, 41125 Modena, Italy; Department of Biomedical, Metabolic, and Neural Sciences, University of Modena and Reggio Emilia, 41125 Modena, Italy
| | - Lucilla de Arcangelis
- Department of Mathematics and Physics, University of Campania "Luigi Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy.
| | - Oren Shriki
- Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer-sheva, Israel.
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3
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Scarpetta S, Morrisi N, Mutti C, Azzi N, Trippi I, Ciliento R, Apicella I, Messuti G, Angiolelli M, Lombardi F, Parrino L, Vaudano AE. Criticality of neuronal avalanches in human sleep and their relationship with sleep macro- and micro-architecture. iScience 2023; 26:107840. [PMID: 37766992 PMCID: PMC10520337 DOI: 10.1016/j.isci.2023.107840] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Revised: 06/30/2023] [Accepted: 09/03/2023] [Indexed: 09/29/2023] Open
Abstract
Sleep plays a key role in preserving brain function, keeping brain networks in a state that ensures optimal computation. Empirical evidence indicates that this state is consistent with criticality, where scale-free neuronal avalanches emerge. However, the connection between sleep architecture and brain tuning to criticality remains poorly understood. Here, we characterize the critical behavior of avalanches and study their relationship with sleep macro- and micro-architectures, in particular, the cyclic alternating pattern (CAP). We show that avalanches exhibit robust scaling behaviors, with exponents obeying scaling relations consistent with the mean-field directed percolation universality class. We demonstrate that avalanche dynamics is modulated by the NREM-REM cycles and that, within NREM sleep, avalanche occurrence correlates with CAP activation phases-indicating a potential link between CAP and brain tuning to criticality. The results open new perspectives on the collective dynamics underlying CAP function, and on the relationship between sleep architecture, avalanches, and self-organization to criticality.
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Affiliation(s)
- Silvia Scarpetta
- Department of Physics, University of Salerno, 84084 Fisciano, Italy
- INFN sez. Napoli Gr. Coll. Salerno, 84084 Fisciano, Italy
| | - Niccolò Morrisi
- Nephrology, Dialysis and Transplant Unit, University Hospital of Modena, 41121 Modena, Italy
| | - Carlotta Mutti
- Sleep Disorders Center, Department of Medicine and Surgery, University of Parma, 43121 Parma, Italy
| | - Nicoletta Azzi
- Sleep Disorders Center, Department of Medicine and Surgery, University of Parma, 43121 Parma, Italy
| | - Irene Trippi
- Sleep Disorders Center, Department of Medicine and Surgery, University of Parma, 43121 Parma, Italy
| | - Rosario Ciliento
- Department of Neurology, University of Wisconsin, Madison, WI 53705, USA
| | - Ilenia Apicella
- INFN sez. Napoli Gr. Coll. Salerno, 84084 Fisciano, Italy
- Department of Physics, University of Naples “Federico II”, 80126 Napoli, Italy
| | - Giovanni Messuti
- Department of Physics, University of Salerno, 84084 Fisciano, Italy
- INFN sez. Napoli Gr. Coll. Salerno, 84084 Fisciano, Italy
| | - Marianna Angiolelli
- Department of Physics, University of Salerno, 84084 Fisciano, Italy
- INFN sez. Napoli Gr. Coll. Salerno, 84084 Fisciano, Italy
- Engineering Department, University Campus Bio-Medico of Rome, 00128 Roma, Italy
| | - Fabrizio Lombardi
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
- Department of Biomedical Sciences, University of Padova, Via Ugo Bassi 58B, 35131 Padova, Italy
| | - Liborio Parrino
- Sleep Disorders Center, Department of Medicine and Surgery, University of Parma, 43121 Parma, Italy
| | - Anna Elisabetta Vaudano
- Neurology Unit, Azienda Ospedaliero-Universitaria of Modena, OCB Hospital, 41125 Modena, Italy
- Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, 41125 Modena, Italy
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4
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Nattagh-Najafi M, Nabil M, Mridha RH, Nabavizadeh SA. Anomalous Self-Organization in Active Piles. ENTROPY (BASEL, SWITZERLAND) 2023; 25:861. [PMID: 37372205 DOI: 10.3390/e25060861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 05/16/2023] [Accepted: 05/17/2023] [Indexed: 06/29/2023]
Abstract
Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.
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Affiliation(s)
| | - Mohammad Nabil
- Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA
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5
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Lombardi F, Pepić S, Shriki O, Tkačik G, De Martino D. Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain. NATURE COMPUTATIONAL SCIENCE 2023; 3:254-263. [PMID: 38177880 PMCID: PMC10766559 DOI: 10.1038/s43588-023-00410-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 02/02/2023] [Indexed: 01/06/2024]
Abstract
Neurons in the brain are wired into adaptive networks that exhibit collective dynamics as diverse as scale-specific oscillations and scale-free neuronal avalanches. Although existing models account for oscillations and avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically or intractable to infer from data rigorously. Here we propose a feedback-driven Ising-like class of neural networks that captures avalanches and oscillations simultaneously and quantitatively. In the simplest yet fully microscopic model version, we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations to collective behaviors of extreme events and neuronal avalanches. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.
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Affiliation(s)
- Fabrizio Lombardi
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
| | - Selver Pepić
- Institute of Science and Technology Austria, Klosterneuburg, Austria
| | - Oren Shriki
- Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
| | - Daniele De Martino
- Biofisika Institute (CSIC, UPV-EHU) and Ikerbasque Foundation, Bilbao, Spain.
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6
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Juanico DEO. Neuronal Population Transitions Across a Quiescent-to-Active Frontier and Bifurcation. Front Physiol 2022; 13:840546. [PMID: 35222095 PMCID: PMC8867020 DOI: 10.3389/fphys.2022.840546] [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: 12/21/2021] [Accepted: 01/12/2022] [Indexed: 11/13/2022] Open
Abstract
The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity.
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Affiliation(s)
- Drandreb Earl O. Juanico
- DataSc/ense TechnoCoRe, Technological Institute of the Philippines, Quezon City, Philippines
- NICER Program, Center for Advanced Batteries, Quezon City, Philippines
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7
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Pazzini R, Kinouchi O, Costa AA. Neuronal avalanches in Watts-Strogatz networks of stochastic spiking neurons. Phys Rev E 2021; 104:014137. [PMID: 34412363 DOI: 10.1103/physreve.104.014137] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 06/08/2021] [Indexed: 01/03/2023]
Abstract
Networks of stochastic leaky integrate-and-fire neurons, both at the mean-field level and in square lattices, present a continuous absorbing phase transition with power-law neuronal avalanches at the critical point. Here we complement these results showing that small-world Watts-Strogatz networks have mean-field critical exponents for any rewiring probability p>0. For the ring (p=0), the exponents are the same from the dimension d=1 of the directed-percolation class. In the model, firings are stochastic and occur in discrete time steps, based on a sigmoidal firing probability function. Each neuron has a membrane potential that integrates the signals received from its neighbors. The membrane potentials are subject to a leakage parameter. We study topologies with a varied number of neuron connections and different values of the leakage parameter. Results indicate that the dynamic range is larger for p=0. We also study a homeostatic synaptic depression mechanism to self-organize the network towards the critical region. These stochastic oscillations are characteristic of the so-called self-organized quasicriticality.
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Affiliation(s)
- Renata Pazzini
- Universidade de São Paulo, FFCLRP, Departamento de Física, Ribeirão Preto, São Paulo 14040-901, Brazil
| | - Osame Kinouchi
- Universidade de São Paulo, FFCLRP, Departamento de Física, Ribeirão Preto, São Paulo 14040-901, Brazil
| | - Ariadne A Costa
- Grupo de Redes Complexas Aplicadas de Jataí, Universidade Federal de Jataí, Jataí, GO 75801-615, Brazil
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8
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Valderhaug VD, Heiney K, Ramstad OH, Bråthen G, Kuan WL, Nichele S, Sandvig A, Sandvig I. Early functional changes associated with alpha-synuclein proteinopathy in engineered human neural networks. Am J Physiol Cell Physiol 2021; 320:C1141-C1152. [PMID: 33950697 DOI: 10.1152/ajpcell.00413.2020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
A patterned spread of proteinopathy represents a common characteristic of many neurodegenerative diseases. In Parkinson's disease (PD), misfolded forms of α-synuclein proteins accumulate in hallmark pathological inclusions termed Lewy bodies and Lewy neurites. Such protein aggregates seem to affect selectively vulnerable neuronal populations in the substantia nigra and to propagate within interconnected neuronal networks. Research findings suggest that these proteinopathic inclusions are present at very early time points in disease development, even before clear behavioral symptoms of dysfunction arise. In this study, we investigate the early pathophysiology developing after induced formation of such PD-related α-synuclein inclusions in a physiologically relevant in vitro setup using engineered human neural networks. We monitor the neural network activity using multielectrode arrays (MEAs) for a period of 3 wk following proteinopathy induction to identify associated changes in network function, with a special emphasis on the measure of network criticality. Self-organized criticality represents the critical point between resilience against perturbation and adaptational flexibility, which appears to be a functional trait in self-organizing neural networks, both in vitro and in vivo. We show that although developing pathology at early onset is not clearly manifest in standard measurements of network function, it may be discerned by investigating differences in network criticality states.
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Affiliation(s)
- Vibeke D Valderhaug
- Department of Neuromedicine and Movement Science, Faculty of Medicine, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Kristine Heiney
- Department of Computer Science, Faculty of Technology, Art and Design, Oslo Metropolitan University (OsloMet), Oslo, Norway
| | - Ola Huse Ramstad
- Department of Neuromedicine and Movement Science, Faculty of Medicine, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Geir Bråthen
- Department of Neuromedicine and Movement Science, Faculty of Medicine, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Wei-Li Kuan
- John van Geest Centre for Brain Repair, Department of Clinical Neurosciences, University of Cambridge, Cambridge, United Kingdom
| | - Stefano Nichele
- Department of Computer Science, Faculty of Technology, Art and Design, Oslo Metropolitan University (OsloMet), Oslo, Norway
| | - Axel Sandvig
- Department of Neuromedicine and Movement Science, Faculty of Medicine, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.,Department of Neurology and Clinical Neurophysiology, St Olav's Hospital, Trondheim, Norway.,Department of Clinical Neurosciences, Umeå University Hospital, Umeå, Sweden.,Department of Rehabilitation Medicine, Umeå University Hospital, Umeå, Sweden.,Department of Community Medicine and Rehabilitation, Umeå University, Umeå, Sweden.,Clinical Sciences, Umeå University, Umeå, Sweden
| | - Ioanna Sandvig
- Department of Neuromedicine and Movement Science, Faculty of Medicine, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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9
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Heiney K, Huse Ramstad O, Fiskum V, Christiansen N, Sandvig A, Nichele S, Sandvig I. Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation. Front Comput Neurosci 2021; 15:611183. [PMID: 33643017 PMCID: PMC7902700 DOI: 10.3389/fncom.2021.611183] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 01/18/2021] [Indexed: 01/03/2023] Open
Abstract
It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.
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Affiliation(s)
- Kristine Heiney
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Computer Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Ola Huse Ramstad
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Vegard Fiskum
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Nicholas Christiansen
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Axel Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
- Department of Clinical Neuroscience, Umeå University Hospital, Umeå, Sweden
- Department of Neurology, St. Olav's Hospital, Trondheim, Norway
| | - Stefano Nichele
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Holistic Systems, Simula Metropolitan, Oslo, Norway
| | - Ioanna Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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10
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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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11
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Hints from statistical physics and graph theory to build synthetic connectomes: Comment on "What would a synthetic connectome look like?" by I. Rabinowitch. Phys Life Rev 2020; 33:19-21. [PMID: 32224044 DOI: 10.1016/j.plrev.2020.03.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Accepted: 03/17/2020] [Indexed: 12/28/2022]
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12
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Virkar YS, Restrepo JG, Shew WL, Ott E. Dynamic regulation of resource transport induces criticality in interdependent networks of excitable units. Phys Rev E 2020; 101:022303. [PMID: 32168577 DOI: 10.1103/physreve.101.022303] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Accepted: 12/24/2019] [Indexed: 11/06/2022]
Abstract
Various functions of a network of excitable units can be enhanced if the network is in the "critical regime," where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to operate in the critical regime. Previously, it was shown that regulation via resource transport on a secondary network can robustly maintain the primary network dynamics in a balanced state where activity doesn't grow or decay. Here we show that this internetwork regulation process robustly produces a power-law distribution of activity avalanches, as observed in experiments, over ranges of model parameters spanning orders of magnitude. We also show that the resource transport over the secondary network protects the system against the destabilizing effect of local variations in parameters and heterogeneity in network structure. For homogeneous networks, we derive a reduced three-dimensional map which reproduces the behavior of the full system.
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Affiliation(s)
- Yogesh S Virkar
- Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Woodrow L Shew
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Edward Ott
- Departments of Electrical and Computer Engineering and of Physics, University of Maryland, College Park, Maryland 20742, USA
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13
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Marhl U, Gosak M. Proper spatial heterogeneities expand the regime of scale-free behavior in a lattice of excitable elements. Phys Rev E 2019; 100:062203. [PMID: 31962506 DOI: 10.1103/physreve.100.062203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Indexed: 06/10/2023]
Abstract
Signatures of criticality, such as power law scaling of observables, have been empirically found in a plethora of real-life settings, including biological systems. The presence of critical states is believed to have many functional advantages and is associated with optimal operational abilities. Typically, critical dynamics arises in the proximity of phase transition points between absorbing disordered states (subcriticality) and ordered active regimes (supercriticality) and requires a high degree of fine tuning to emerge, which is unlikely to occur in real biological systems. In the present study we propose a rather simple, and biologically relevant mechanism that profoundly expands the critical-like region. In particular, by means of numerical simulation we show that incorporating spatial heterogeneities into the square lattice of map-based excitable oscillators broadens the parameter space in which the distribution of excitation wave sizes follows closely a power law. Most importantly, this behavior is only observed if the spatial profile exhibits intermediate-sized patches with similar excitability levels, whereas for large and small spatial clusters only marginal widening of the critical state is detected. Furthermore, it turned out that the presence of spatial disorder in general amplifies the size of excitation waves, whereby the relatively highest contributions are observed in the proximity of the critical point. We argue that the reported mechanism is of particular importance for excitable systems with local interactions between individual elements.
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Affiliation(s)
- Urban Marhl
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
| | - Marko Gosak
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- Institute of Physiology, Faculty of Medicine, University of Maribor, Taborska ulica 8, SI-2000 Maribor, Slovenia
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Dalla Porta L, Copelli M. Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic M/EEG results. PLoS Comput Biol 2019; 15:e1006924. [PMID: 30951525 PMCID: PMC6469813 DOI: 10.1371/journal.pcbi.1006924] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2018] [Revised: 04/17/2019] [Accepted: 03/06/2019] [Indexed: 01/17/2023] Open
Abstract
We revisit the CROS ("CRitical OScillations") model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.
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Affiliation(s)
- Leonardo Dalla Porta
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Recife, PE, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Recife, PE, Brazil
- * E-mail:
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