1
|
Kramer MA, Chu CJ. A General, Noise-Driven Mechanism for the 1/f-Like Behavior of Neural Field Spectra. Neural Comput 2024; 36:1643-1668. [PMID: 39028955 DOI: 10.1162/neco_a_01682] [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: 11/07/2023] [Accepted: 03/25/2024] [Indexed: 07/21/2024]
Abstract
Consistent observations across recording modalities, experiments, and neural systems find neural field spectra with 1/f-like scaling, eliciting many alternative theories to explain this universal phenomenon. We show that a general dynamical system with stochastic drive and minimal assumptions generates 1/f-like spectra consistent with the range of values observed in vivo without requiring a specific biological mechanism or collective critical behavior.
Collapse
Affiliation(s)
- Mark A Kramer
- Department of Mathematics and Statistics, and Center for Systems Neuroscience, Boston University, Boston, MA 02214, U.S.A.
| | - Catherine J Chu
- Department of Neurology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, U.S.A.
| |
Collapse
|
2
|
Morrell MC, Nemenman I, Sederberg A. Neural criticality from effective latent variables. eLife 2024; 12:RP89337. [PMID: 38470471 PMCID: PMC10957169 DOI: 10.7554/elife.89337] [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] [Indexed: 03/13/2024] Open
Abstract
Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is 'avalanche criticality', which has been observed in various systems, including cultured neurons, zebrafish, rodent cortex, and human EEG. More recently, power laws were also observed in neural populations in the mouse under an activity coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which latent dynamical variables give rise to avalanche criticality. We find that populations coupled to multiple latent variables produce critical behavior across a broader parameter range than those coupled to a single, quasi-static latent variable, but in both cases, avalanche criticality is observed without fine-tuning of model parameters. We identify two regimes of avalanches, both critical but differing in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which activity is effectively modeled as a population driven by a few dynamical variables and these variables can be inferred from the population activity.
Collapse
Affiliation(s)
- Mia C Morrell
- Department of Physics, New York UniversityNew YorkUnited States
| | - Ilya Nemenman
- Department of Physics, Department of Biology, Initiative in Theory and Modeling of Living Systems, Emory UniversityAtlantaUnited States
| | - Audrey Sederberg
- Department of Neuroscience, University of Minnesota Medical SchoolMinneapolisUnited States
| |
Collapse
|
3
|
Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
Collapse
Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
| |
Collapse
|
4
|
Pan W, Zhao F, Han B, Dong Y, Zeng Y. Emergence of brain-inspired small-world spiking neural network through neuroevolution. iScience 2024; 27:108845. [PMID: 38327781 PMCID: PMC10847652 DOI: 10.1016/j.isci.2024.108845] [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: 05/08/2023] [Revised: 08/23/2023] [Accepted: 01/03/2024] [Indexed: 02/09/2024] Open
Abstract
Studies suggest that the brain's high efficiency and low energy consumption may be closely related to its small-world topology and critical dynamics. However, existing efforts on the performance-oriented structural evolution of spiking neural networks (SNNs) are time-consuming and ignore the core structural properties of the brain. Here, we introduce a multi-objective Evolutionary Liquid State Machine (ELSM), which blends the small-world coefficient and criticality to evolve models and guide the emergence of brain-inspired, efficient structures. Experiments reveal ELSM's consistent and comparable performance, achieving 97.23% on NMNIST and outperforming LSM models on MNIST and Fashion-MNIST with 98.12% and 88.81% accuracies, respectively. Further analysis shows its versatility and spontaneous evolution of topologies such as hub nodes, short paths, long-tailed degree distributions, and numerous communities. This study evolves recurrent spiking neural networks into brain-inspired energy-efficient structures, showcasing versatility in multiple tasks and potential for adaptive general artificial intelligence.
Collapse
Affiliation(s)
- Wenxuan Pan
- Brain-inspired Cognitive Intelligence Lab, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Feifei Zhao
- Brain-inspired Cognitive Intelligence Lab, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
| | - Bing Han
- Brain-inspired Cognitive Intelligence Lab, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Yiting Dong
- Brain-inspired Cognitive Intelligence Lab, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Yi Zeng
- Brain-inspired Cognitive Intelligence Lab, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
- School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
- School of Future Technology, University of Chinese Academy of Sciences, Beijing 101408, China
- Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, China
| |
Collapse
|
5
|
Liang J, Yang Z, Zhou C. Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits. Neuroscientist 2024:10738584231221766. [PMID: 38291889 DOI: 10.1177/10738584231221766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2024]
Abstract
Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.
Collapse
Affiliation(s)
- Junhao Liang
- Eberhard Karls University of Tübingen and Max Planck Institute for Biological Cybernetics, Tübingen, Germany
| | - Zhuda Yang
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Changsong Zhou
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Life Science Imaging Centre, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Research Centre, Hong Kong Baptist University Institute of Research and Continuing Education, Shenzhen, China
| |
Collapse
|
6
|
Morrell M, Nemenman I, Sederberg AJ. Neural criticality from effective latent variables. ARXIV 2023:arXiv:2301.00759v3. [PMID: 36713239 PMCID: PMC9882570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is "avalanche criticality," which has been observed in various systems, including cultured neurons, zebrafish, rodent cortex, and human EEG. More recently, power laws were also observed in neural populations in the mouse under an activity coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which latent dynamical variables give rise to avalanche criticality. We find that populations coupled to multiple latent variables produce critical behavior across a broader parameter range than those coupled to a single, quasi-static latent variable, but in both cases, avalanche criticality is observed without fine-tuning of model parameters. We identify two regimes of avalanches, both critical but differing in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which activity is effectively modeled as a population driven by a few dynamical variables and these variables can be inferred from the population activity.
Collapse
Affiliation(s)
| | - Ilya Nemenman
- Department of Physics, Department of Biology, Initiative in Theory and Modeling of Living Systems, Emory University
| | - Audrey J. Sederberg
- Department of Neuroscience, University of Minnesota Medical School
- School of Psychology and School of Physics, Georgia Institute of Technology (current)
| |
Collapse
|
7
|
Lei X, Xiang Y, Duan M, Peng X. Exploring the criticality hypothesis using programmable swarm robots with Vicsek-like interactions. J R Soc Interface 2023; 20:20230176. [PMID: 37464802 PMCID: PMC10354469 DOI: 10.1098/rsif.2023.0176] [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: 03/27/2023] [Accepted: 06/28/2023] [Indexed: 07/20/2023] Open
Abstract
A widely mentioned but not experimentally confirmed view (known as the 'criticality hypothesis') argues that biological swarm systems gain optimal responsiveness to perturbations and information processing capabilities by operating near the critical state where an ordered-to-disordered state transition occurs. However, various factors can induce the ordered-disordered transition, and the explicit relationship between these factors and the criticality is still unclear. Here, we present an experimental validation for the criticality hypothesis by employing real programmable swarm-robotic systems (up to 50 robots) governed by Vicsek-like interactions, subject to time-varying stimulus-response and hazard avoidance. We find that (i) not all ordered-disordered motion transitions correspond to the functional advantages for groups; (ii) collective response of groups is maximized near the critical state induced by alignment weight or scale rather than noise and other non-alignment factors; and (iii) those non-alignment factors act to highlight the functional advantages of alignment-induced criticality. These results suggest that the adjustability of velocity or directional coupling between individuals plays an essential role in the acquisition of maximizing collective response by criticality. Our results contribute to understanding the adjustment strategies of animal interactions from a perspective of criticality and provide insights into the design and control of swarm robotics.
Collapse
Affiliation(s)
- Xiaokang Lei
- College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, People’s Republic of China
| | - Yalun Xiang
- College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, People’s Republic of China
| | - Mengyuan Duan
- College of Information and Control Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, People’s Republic of China
| | - Xingguang Peng
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China
| |
Collapse
|
8
|
Grosu GF, Hopp AV, Moca VV, Bârzan H, Ciuparu A, Ercsey-Ravasz M, Winkel M, Linde H, Mureșan RC. The fractal brain: scale-invariance in structure and dynamics. Cereb Cortex 2023; 33:4574-4605. [PMID: 36156074 PMCID: PMC10110456 DOI: 10.1093/cercor/bhac363] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Revised: 08/09/2022] [Accepted: 08/10/2022] [Indexed: 11/12/2022] Open
Abstract
The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.
Collapse
Affiliation(s)
- George F Grosu
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | | | - Vasile V Moca
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
| | - Harald Bârzan
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | - Andrei Ciuparu
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Electronics, Telecommunications and Information Technology, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania
| | - Maria Ercsey-Ravasz
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Faculty of Physics, Babes-Bolyai University, Str. Mihail Kogalniceanu 1, 400084 Cluj-Napoca, Romania
| | - Mathias Winkel
- Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Helmut Linde
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
- Merck KGaA, Frankfurter Straße 250, 64293 Darmstadt, Germany
| | - Raul C Mureșan
- Department of Experimental and Theoretical Neuroscience, Transylvanian Institute of Neuroscience, Str. Ploiesti 33, 400157 Cluj-Napoca, Romania
| |
Collapse
|
9
|
Neto JP, Spitzner FP, Priesemann V. Sampling effects and measurement overlap can bias the inference of neuronal avalanches. PLoS Comput Biol 2022; 18:e1010678. [PMID: 36445932 PMCID: PMC9733887 DOI: 10.1371/journal.pcbi.1010678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 12/09/2022] [Accepted: 10/24/2022] [Indexed: 12/02/2022] Open
Abstract
To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a simple spiking model to quantify how they alter observed correlations and signatures of criticality. We describe a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increases the correlation between the signals. For coarse-sampled activity, this can produce power-law distributions even for non-critical systems. In contrast, spike recordings do not suffer this particular bias and underlying dynamics can be identified. This may resolve why coarse measures and spikes have produced contradicting results in the past.
Collapse
Affiliation(s)
- Joao Pinheiro Neto
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - F. Paul Spitzner
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Viola Priesemann
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Georg-August University Göttingen, Göttingen, Germany
- * E-mail:
| |
Collapse
|
10
|
Beggs JM. Addressing skepticism of the critical brain hypothesis. Front Comput Neurosci 2022; 16:703865. [PMID: 36185712 PMCID: PMC9520604 DOI: 10.3389/fncom.2022.703865] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 08/08/2022] [Indexed: 11/16/2022] Open
Abstract
The hypothesis that living neural networks operate near a critical phase transition point has received substantial discussion. This “criticality hypothesis” is potentially important because experiments and theory show that optimal information processing and health are associated with operating near the critical point. Despite the promise of this idea, there have been several objections to it. While earlier objections have been addressed already, the more recent critiques of Touboul and Destexhe have not yet been fully met. The purpose of this paper is to describe their objections and offer responses. Their first objection is that the well-known Brunel model for cortical networks does not display a peak in mutual information near its phase transition, in apparent contradiction to the criticality hypothesis. In response I show that it does have such a peak near the phase transition point, provided it is not strongly driven by random inputs. Their second objection is that even simple models like a coin flip can satisfy multiple criteria of criticality. This suggests that the emergent criticality claimed to exist in cortical networks is just the consequence of a random walk put through a threshold. In response I show that while such processes can produce many signatures criticality, these signatures (1) do not emerge from collective interactions, (2) do not support information processing, and (3) do not have long-range temporal correlations. Because experiments show these three features are consistently present in living neural networks, such random walk models are inadequate. Nevertheless, I conclude that these objections have been valuable for refining research questions and should always be welcomed as a part of the scientific process.
Collapse
Affiliation(s)
- John M. Beggs
- Department of Physics, Indiana University Bloomington, Bloomington, IN, United States
- Program in Neuroscience, Indiana University Bloomington, Bloomington, IN, United States
- *Correspondence: John M. Beggs,
| |
Collapse
|
11
|
O'Byrne J, Jerbi K. How critical is brain criticality? Trends Neurosci 2022; 45:820-837. [PMID: 36096888 DOI: 10.1016/j.tins.2022.08.007] [Citation(s) in RCA: 49] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 07/27/2022] [Accepted: 08/10/2022] [Indexed: 10/31/2022]
Abstract
Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.
Collapse
Affiliation(s)
- Jordan O'Byrne
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada
| | - Karim Jerbi
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada; MILA (Quebec Artificial Intelligence Institute), Montreal, Quebec, Canada; UNIQUE Center (Quebec Neuro-AI Research Center), Montreal, Quebec, Canada.
| |
Collapse
|
12
|
Mariani B, Nicoletti G, Bisio M, Maschietto M, Vassanelli S, Suweis S. Disentangling the critical signatures of neural activity. Sci Rep 2022; 12:10770. [PMID: 35750684 PMCID: PMC9232560 DOI: 10.1038/s41598-022-13686-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 05/26/2022] [Indexed: 11/09/2022] Open
Abstract
The critical brain hypothesis has emerged as an attractive framework to understand neuronal activity, but it is still widely debated. In this work, we analyze data from a multi-electrodes array in the rat’s cortex and we find that power-law neuronal avalanches satisfying the crackling-noise relation coexist with spatial correlations that display typical features of critical systems. In order to shed a light on the underlying mechanisms at the origin of these signatures of criticality, we introduce a paradigmatic framework with a common stochastic modulation and pairwise linear interactions inferred from our data. We show that in such models power-law avalanches that satisfy the crackling-noise relation emerge as a consequence of the extrinsic modulation, whereas scale-free correlations are solely determined by internal interactions. Moreover, this disentangling is fully captured by the mutual information in the system. Finally, we show that analogous power-law avalanches are found in more realistic models of neural activity as well, suggesting that extrinsic modulation might be a broad mechanism for their generation.
Collapse
Affiliation(s)
| | - Giorgio Nicoletti
- Department of Physics and Astronomy "G. Galilei", INFN, University of Padova, Padua, Italy
| | - Marta Bisio
- Department of Biomedical Sciences, University of Padova, Padua, Italy
| | - Marta Maschietto
- Department of Biomedical Sciences, University of Padova, Padua, Italy
| | - Stefano Vassanelli
- Padova Neuroscience Center, University of Padova, Padua, Italy. .,Department of Biomedical Sciences, University of Padova, Padua, Italy.
| | - Samir Suweis
- Department of Physics and Astronomy "G. Galilei", INFN, University of Padova, Padua, Italy. .,Padova Neuroscience Center, University of Padova, Padua, Italy.
| |
Collapse
|
13
|
Mikaberidze G, D'Souza RM. Sandpile cascades on oscillator networks: The BTW model meets Kuramoto. CHAOS (WOODBURY, N.Y.) 2022; 32:053121. [PMID: 35649989 DOI: 10.1063/5.0095094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
Cascading failures abound in complex systems and the Bak-Tang-Weisenfeld (BTW) sandpile model provides a theoretical underpinning for their analysis. Yet, it does not account for the possibility of nodes having oscillatory dynamics, such as in power grids and brain networks. Here, we consider a network of Kuramoto oscillators upon which the BTW model is unfolding, enabling us to study how the feedback between the oscillatory and cascading dynamics can lead to new emergent behaviors. We assume that the more out-of-sync a node is with its neighbors, the more vulnerable it is and lower its load-carrying capacity accordingly. Also, when a node topples and sheds load, its oscillatory phase is reset at random. This leads to novel cyclic behavior at an emergent, long timescale. The system spends the bulk of its time in a synchronized state where load builds up with minimal cascades. Yet, eventually, the system reaches a tipping point where a large cascade triggers a "cascade of larger cascades," which can be classified as a dragon king event. The system then undergoes a short transient back to the synchronous, buildup phase. The coupling between capacity and synchronization gives rise to endogenous cascade seeds in addition to the standard exogenous ones, and we show their respective roles. We establish the phenomena from numerical studies and develop the accompanying mean-field theory to locate the tipping point, calculate the load in the system, determine the frequency of the long-time oscillations, and find the distribution of cascade sizes during the buildup phase.
Collapse
Affiliation(s)
- Guram Mikaberidze
- Department of Mathematics, University of California, Davis, Davis, California 95616, USA
| | - Raissa M D'Souza
- Department of Computer Science and Department of Mechanical and Aerospace Engineering, University of California, Davis, Davis, California 95616, USA
| |
Collapse
|
14
|
Toker D, Pappas I, Lendner JD, Frohlich J, Mateos DM, Muthukumaraswamy S, Carhart-Harris R, Paff M, Vespa PM, Monti MM, Sommer FT, Knight RT, D'Esposito M. Consciousness is supported by near-critical slow cortical electrodynamics. Proc Natl Acad Sci U S A 2022; 119:e2024455119. [PMID: 35145021 PMCID: PMC8851554 DOI: 10.1073/pnas.2024455119] [Citation(s) in RCA: 42] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 12/20/2021] [Indexed: 12/21/2022] Open
Abstract
Mounting evidence suggests that during conscious states, the electrodynamics of the cortex are poised near a critical point or phase transition and that this near-critical behavior supports the vast flow of information through cortical networks during conscious states. Here, we empirically identify a mathematically specific critical point near which waking cortical oscillatory dynamics operate, which is known as the edge-of-chaos critical point, or the boundary between stability and chaos. We do so by applying the recently developed modified 0-1 chaos test to electrocorticography (ECoG) and magnetoencephalography (MEG) recordings from the cortices of humans and macaques across normal waking, generalized seizure, anesthesia, and psychedelic states. Our evidence suggests that cortical information processing is disrupted during unconscious states because of a transition of low-frequency cortical electric oscillations away from this critical point; conversely, we show that psychedelics may increase the information richness of cortical activity by tuning low-frequency cortical oscillations closer to this critical point. Finally, we analyze clinical electroencephalography (EEG) recordings from patients with disorders of consciousness (DOC) and show that assessing the proximity of slow cortical oscillatory electrodynamics to the edge-of-chaos critical point may be useful as an index of consciousness in the clinical setting.
Collapse
Affiliation(s)
- Daniel Toker
- Department of Psychology, University of California, Los Angeles, CA 90095;
| | - Ioannis Pappas
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
- Laboratory of Neuro Imaging, Stevens Institute for Neuroimaging and Informatics, Keck School of Medicine, University of Southern California, Los Angeles, CA 90033
| | - Janna D Lendner
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Anesthesiology and Intensive Care, University Medical Center, 72076 Tübingen, Germany
| | - Joel Frohlich
- Department of Psychology, University of California, Los Angeles, CA 90095
| | - Diego M Mateos
- Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina, C1425 Buenos Aires, Argentina
- Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos, E3202 Paraná, Entre Ríos, Argentina
- Grupo de Análisis de Neuroimágenes, Instituo de Matemática Aplicada del Litoral, S3000 Santa Fe, Argentina
| | - Suresh Muthukumaraswamy
- School of Pharmacy, Faculty of Medical and Health Sciences, The University of Auckland, 1010 Auckland, New Zealand
| | - Robin Carhart-Harris
- Neuropsychopharmacology Unit, Centre for Psychiatry, Imperial College London, London SW7 2AZ, United Kingdom
- Centre for Psychedelic Research, Department of Psychiatry, Imperial College London, London SW7 2AZ, United Kingdom
| | - Michelle Paff
- Department of Neurological Surgery, University of California, Irvine, CA 92697
| | - Paul M Vespa
- Brain Injury Research Center, Department of Neurosurgery, University of California, Los Angeles, CA 90095
| | - Martin M Monti
- Department of Psychology, University of California, Los Angeles, CA 90095
- Brain Injury Research Center, Department of Neurosurgery, University of California, Los Angeles, CA 90095
| | - Friedrich T Sommer
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94704
| | - Robert T Knight
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
| | - Mark D'Esposito
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
| |
Collapse
|
15
|
Lombardi F, Shriki O, Herrmann HJ, de Arcangelis L. Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.05.126] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
16
|
de Heuvel J, Wilting J, Becker M, Priesemann V, Zierenberg J. Characterizing spreading dynamics of subsampled systems with nonstationary external input. Phys Rev E 2021; 102:040301. [PMID: 33212575 DOI: 10.1103/physreve.102.040301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 09/21/2020] [Indexed: 11/07/2022]
Abstract
Many systems with propagation dynamics, such as spike propagation in neural networks and spreading of infectious diseases, can be approximated by autoregressive models. The estimation of model parameters can be complicated by the experimental limitation that one observes only a fraction of the system (subsampling) and potentially time-dependent parameters, leading to incorrect estimates. We show analytically how to overcome the subsampling bias when estimating the propagation rate for systems with certain nonstationary external input. This approach is readily applicable to trial-based experimental setups and seasonal fluctuations as demonstrated on spike recordings from monkey prefrontal cortex and spreading of norovirus and measles.
Collapse
Affiliation(s)
- Jorge de Heuvel
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Jens Wilting
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Moritz Becker
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.,Department of Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, 37077 Göttingen, Germany
| | - Viola Priesemann
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Johannes Zierenberg
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| |
Collapse
|
17
|
Bansal K, Garcia JO, Lauharatanahirun N, Muldoon SF, Sajda P, Vettel JM. Scale-specific dynamics of high-amplitude bursts in EEG capture behaviorally meaningful variability. Neuroimage 2021; 241:118425. [PMID: 34303795 DOI: 10.1016/j.neuroimage.2021.118425] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Revised: 06/25/2021] [Accepted: 07/21/2021] [Indexed: 10/20/2022] Open
Abstract
Cascading high-amplitude bursts in neural activity, termed avalanches, are thought to provide insight into the complex spatially distributed interactions in neural systems. In human neuroimaging, for example, avalanches occurring during resting-state show scale-invariant dynamics, supporting the hypothesis that the brain operates near a critical point that enables long range spatial communication. In fact, it has been suggested that such scale-invariant dynamics, characterized by a power-law distribution in these avalanches, are universal in neural systems and emerge through a common mechanism. While the analysis of avalanches and subsequent criticality is increasingly seen as a framework for using complex systems theory to understand brain function, it is unclear how the framework would account for the omnipresent cognitive variability, whether across individuals or tasks. To address this, we analyzed avalanches in the EEG activity of healthy humans during rest as well as two distinct task conditions that varied in cognitive demands and produced behavioral measures unique to each individual. In both rest and task conditions we observed that avalanche dynamics demonstrate scale-invariant characteristics, but differ in their specific features, demonstrating individual variability. Using a new metric we call normalized engagement, which estimates the likelihood for a brain region to produce high-amplitude bursts, we also investigated regional features of avalanche dynamics. Normalized engagement showed not only the expected individual and task dependent variability, but also scale-specificity that correlated with individual behavior. Our results suggest that the study of avalanches in human brain activity provides a tool to assess cognitive variability. Our findings expand our understanding of avalanche features and are supportive of the emerging theoretical idea that the dynamics of an active human brain operate close to a critical-like region and not a singular critical-state.
Collapse
Affiliation(s)
- Kanika Bansal
- Human Research and Engineering Directorate, US DEVCOM Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA; Department of Biomedical Engineering, Columbia University, New York, NY 10027, USA.
| | - Javier O Garcia
- Human Research and Engineering Directorate, US DEVCOM Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
| | - Nina Lauharatanahirun
- Department of Biomedical Engineering and Department of Biobehavioral Health, Pennsylvania State University, State College, PA 16802, USA
| | - Sarah F Muldoon
- Mathematics Department, CDSE Program, and Neuroscience Program, University at Buffalo, SUNY, Buffalo, NY 14260, USA
| | - Paul Sajda
- Department of Biomedical Engineering, Columbia University, New York, NY 10027, USA; Data Science Institute, Columbia University, New York, NY 10027, USA
| | - Jean M Vettel
- Human Research and Engineering Directorate, US DEVCOM Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA; Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA; Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA 93106, USA
| |
Collapse
|
18
|
Fosque LJ, Williams-García RV, Beggs JM, Ortiz G. Evidence for Quasicritical Brain Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:098101. [PMID: 33750159 DOI: 10.1103/physrevlett.126.098101] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Revised: 11/20/2020] [Accepted: 12/23/2020] [Indexed: 05/24/2023]
Abstract
Much evidence seems to suggest the cortex operates near a critical point, yet a single set of exponents defining its universality class has not been found. In fact, when critical exponents are estimated from data, they widely differ across species, individuals of the same species, and even over time, or depending on stimulus. Interestingly, these exponents still approximately hold to a dynamical scaling relation. Here we show that the theory of quasicriticality, an organizing principle for brain dynamics, can account for this paradoxical situation. As external stimuli drive the cortex, quasicriticality predicts a departure from criticality along a Widom line with exponents that decrease in absolute value, while still holding approximately to a dynamical scaling relation. We use simulations and experimental data to confirm these predictions and describe new ones that could be tested soon.
Collapse
Affiliation(s)
- Leandro J Fosque
- Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
| | - Rashid V Williams-García
- Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, Indiana 46202, USA
| | - John M Beggs
- Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
| | - Gerardo Ortiz
- Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
| |
Collapse
|
19
|
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.
Collapse
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
| |
Collapse
|
20
|
Wilting J, Priesemann V. Between Perfectly Critical and Fully Irregular: A Reverberating Model Captures and Predicts Cortical Spike Propagation. Cereb Cortex 2020; 29:2759-2770. [PMID: 31008508 PMCID: PMC6519697 DOI: 10.1093/cercor/bhz049] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Revised: 01/20/2019] [Indexed: 12/11/2022] Open
Abstract
Knowledge about the collective dynamics of cortical spiking is very informative about the underlying coding principles. However, even most basic properties are not known with certainty, because their assessment is hampered by spatial subsampling, i.e., the limitation that only a tiny fraction of all neurons can be recorded simultaneously with millisecond precision. Building on a novel, subsampling-invariant estimator, we fit and carefully validate a minimal model for cortical spike propagation. The model interpolates between two prominent states: asynchronous and critical. We find neither of them in cortical spike recordings across various species, but instead identify a narrow "reverberating" regime. This approach enables us to predict yet unknown properties from very short recordings and for every circuit individually, including responses to minimal perturbations, intrinsic network timescales, and the strength of external input compared to recurrent activation "thereby informing about the underlying coding principles for each circuit, area, state and task.
Collapse
Affiliation(s)
- J Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faß berg 17, Göttingen, Germany
| | - V Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faß berg 17, Göttingen, Germany.,Bernstein-Center for Computational Neuroscience, Göttingen, Germany
| |
Collapse
|
21
|
Cramer B, Stöckel D, Kreft M, Wibral M, Schemmel J, Meier K, Priesemann V. Control of criticality and computation in spiking neuromorphic networks with plasticity. Nat Commun 2020; 11:2853. [PMID: 32503982 PMCID: PMC7275091 DOI: 10.1038/s41467-020-16548-3] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 04/23/2020] [Indexed: 11/08/2022] Open
Abstract
The critical state is assumed to be optimal for any computation in recurrent neural networks, because criticality maximizes a number of abstract computational properties. We challenge this assumption by evaluating the performance of a spiking recurrent neural network on a set of tasks of varying complexity at - and away from critical network dynamics. To that end, we developed a plastic spiking network on a neuromorphic chip. We show that the distance to criticality can be easily adapted by changing the input strength, and then demonstrate a clear relation between criticality, task-performance and information-theoretic fingerprint. Whereas the information-theoretic measures all show that network capacity is maximal at criticality, only the complex tasks profit from criticality, whereas simple tasks suffer. Thereby, we challenge the general assumption that criticality would be beneficial for any task, and provide instead an understanding of how the collective network state should be tuned to task requirement.
Collapse
Affiliation(s)
- Benjamin Cramer
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120, Heidelberg, Germany.
| | - David Stöckel
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120, Heidelberg, Germany
| | - Markus Kreft
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120, Heidelberg, Germany
| | - Michael Wibral
- Campus Institute for Dynamics of Biological Networks, Georg-August University, Hermann-Rein-Straße 3, 37075, Göttingen, Germany
| | - Johannes Schemmel
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120, Heidelberg, Germany
| | - Karlheinz Meier
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120, Heidelberg, Germany
| | - Viola Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany.
- Bernstein Center for Computational Neuroscience, Georg-August University, Am Faßberg 17, 37077, Göttingen, Germany.
- Department of Physics, Georg-August University, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany.
| |
Collapse
|
22
|
Faqeeh A, Osat S, Radicchi F, Gleeson JP. Emergence of power laws in noncritical neuronal systems. Phys Rev E 2020; 100:010401. [PMID: 31499795 PMCID: PMC7217540 DOI: 10.1103/physreve.100.010401] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 11/07/2022]
Abstract
Experimental and computational studies provide compelling evidence that neuronal systems are characterized by power-law distributions of neuronal avalanche sizes. This fact is interpreted as an indication that these systems are operating near criticality, and, in turn, typical properties of critical dynamical processes, such as optimal information transmission and stability, are attributed to neuronal systems. The purpose of this Rapid Communication is to show that the presence of power-law distributions for the size of neuronal avalanches is not a sufficient condition for the system to operate near criticality. Specifically, we consider a simplistic model of neuronal dynamics on networks and show that the degree distribution of the underlying neuronal network may trigger power-law distributions for neuronal avalanches even when the system is not in its critical regime. To certify and explain our findings we develop an analytical approach based on percolation theory and branching processes techniques.
Collapse
Affiliation(s)
- Ali Faqeeh
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland.,Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Saeed Osat
- Deep Quantum Labs, Skolkovo Institute of Science and Technology, Moscow 143026, Russia
| | - Filippo Radicchi
- Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - James P Gleeson
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| |
Collapse
|
23
|
Bocaccio H, Pallavicini C, Castro MN, Sánchez SM, De Pino G, Laufs H, Villarreal MF, Tagliazucchi E. The avalanche-like behaviour of large-scale haemodynamic activity from wakefulness to deep sleep. J R Soc Interface 2019; 16:20190262. [PMID: 31506046 PMCID: PMC6769314 DOI: 10.1098/rsif.2019.0262] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 08/08/2019] [Indexed: 02/02/2023] Open
Abstract
Increasing evidence suggests that responsiveness is associated with critical or near-critical cortical dynamics, which exhibit scale-free cascades of spatio-temporal activity. These cascades, or 'avalanches', have been detected at multiple scales, from in vitro and in vivo microcircuits to voltage imaging and brain-wide functional magnetic resonance imaging (fMRI) recordings. Criticality endows the cortex with certain information-processing capacities postulated as necessary for conscious wakefulness, yet it remains unknown how unresponsiveness impacts on the avalanche-like behaviour of large-scale human haemodynamic activity. We observed a scale-free hierarchy of co-activated connected clusters by applying a point-process transformation to fMRI data recorded during wakefulness and non-rapid eye movement (NREM) sleep. Maximum-likelihood estimates revealed a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests showed that differences were maximal between wakefulness and N2 sleep. These results were robust against spatial coarse graining, fitting alternative statistical models and different point-process thresholds, and disappeared upon phase shuffling the fMRI time series. Evoked neural bistabilities preventing arousals during N2 sleep do not suffice to explain these differences, which point towards changes in the intrinsic dynamics of the brain that could be necessary to consolidate a state of deep unresponsiveness.
Collapse
Affiliation(s)
- H. Bocaccio
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - C. Pallavicini
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - M. N. Castro
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Fisiología, Facultad de Medicina, UBA, Buenos Aires, Argentina
- Departamento Salud Mental, Unidad Docente FLENI, Facultad de Medicina, UBA, Buenos Aires, Argentina
| | - S. M. Sánchez
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - G. De Pino
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- Laboratorio de Neuroimágenes, Departamento de Imágenes, FLENI, Buenos Aires, Argentina
- Escuela de Ciencia y Tecnología (ECyT), Universidad Nacional de San Martín, Argentina
| | - H. Laufs
- Department of Neurology, Christian-Albrechts-University, Kiel, Germany
| | - M. F. Villarreal
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - E. Tagliazucchi
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| |
Collapse
|
24
|
Wilting J, Priesemann V. 25 years of criticality in neuroscience - established results, open controversies, novel concepts. Curr Opin Neurobiol 2019; 58:105-111. [PMID: 31546053 DOI: 10.1016/j.conb.2019.08.002] [Citation(s) in RCA: 61] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 08/25/2019] [Indexed: 12/19/2022]
Abstract
Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.
Collapse
Affiliation(s)
- J Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - V Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany; Bernstein-Center for Computational Neuroscience, Göttingen, Germany
| |
Collapse
|
25
|
Villegas P, di Santo S, Burioni R, Muñoz MA. Time-series thresholding and the definition of avalanche size. Phys Rev E 2019; 100:012133. [PMID: 31499802 DOI: 10.1103/physreve.100.012133] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Indexed: 11/07/2022]
Abstract
Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here we show that there is a hidden peril in thresholding continuous times series-from either empirical or synthetic data-for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used, e.g., in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) if-as sometimes done in the literature-avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem-that we have detected in some recent works-leads to misinterpretations of the resulting scaling regimes.
Collapse
Affiliation(s)
- Pablo Villegas
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain
| | - Serena di Santo
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.,Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.,Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
| |
Collapse
|
26
|
Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality. J Neurosci 2019; 39:4738-4759. [PMID: 30952810 DOI: 10.1523/jneurosci.3163-18.2019] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 03/01/2019] [Accepted: 03/25/2019] [Indexed: 11/21/2022] Open
Abstract
What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V m fluctuations.
Collapse
|