1
|
Fan L, Li Y, Zhao X, Huang ZG, Liu T, Wang J. Dynamic nonreversibility view of intrinsic brain organization and brain dynamic analysis of repetitive transcranial magnitude stimulation. Cereb Cortex 2024; 34:bhae098. [PMID: 38494890 DOI: 10.1093/cercor/bhae098] [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: 01/14/2024] [Revised: 02/20/2024] [Accepted: 02/21/2024] [Indexed: 03/19/2024] Open
Abstract
Intrinsic neural activities are characterized as endless spontaneous fluctuation over multiple time scales. However, how the intrinsic brain organization changes over time under local perturbation remains an open question. By means of statistical physics, we proposed an approach to capture whole-brain dynamics based on estimating time-varying nonreversibility and k-means clustering of dynamic varying nonreversibility patterns. We first used synthetic fMRI to investigate the effects of window parameters on the temporal variability of varying nonreversibility. Second, using real test-retest fMRI data, we examined the reproducibility, reliability, biological, and physiological correlation of the varying nonreversibility substates. Finally, using repetitive transcranial magnetic stimulation-fMRI data, we investigated the modulation effects of repetitive transcranial magnetic stimulation on varying nonreversibility substate dynamics. The results show that: (i) as window length increased, the varying nonreversibility variance decreased, while the sliding step almost did not alter it; (ii) the global high varying nonreversibility states and low varying nonreversibility states were reproducible across multiple datasets and different window lengths; and (iii) there were increased low varying nonreversibility states and decreased high varying nonreversibility states when the left frontal lobe was stimulated, but not the occipital lobe. Taken together, these results provide a thermodynamic equilibrium perspective of intrinsic brain organization and reorganization under local perturbation.
Collapse
Affiliation(s)
- Liming Fan
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
| | - Youjun Li
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
| | - Xingjian Zhao
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
| | - Zi-Gang Huang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
| | - Tian Liu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
| | - Jue Wang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
- National Engineering Research Center of Health Care and Medical Devices, Guangzhou, Guangdong 510500, China
- The Key Laboratory of Neuro-informatics & Rehabilitation Engineering of Ministry of Civil Affairs, Xi'an, Shaanxi 710049, China
| |
Collapse
|
2
|
Munn BR, Müller EJ, Aru J, Whyte CJ, Gidon A, Larkum ME, Shine JM. A thalamocortical substrate for integrated information via critical synchronous bursting. Proc Natl Acad Sci U S A 2023; 120:e2308670120. [PMID: 37939085 PMCID: PMC10655573 DOI: 10.1073/pnas.2308670120] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 09/21/2023] [Indexed: 11/10/2023] Open
Abstract
Understanding the neurobiological mechanisms underlying consciousness remains a significant challenge. Recent evidence suggests that the coupling between distal-apical and basal-somatic dendrites in thick-tufted layer 5 pyramidal neurons (L5PN), regulated by the nonspecific-projecting thalamus, is crucial for consciousness. Yet, it is uncertain whether this thalamocortical mechanism can support emergent signatures of consciousness, such as integrated information. To address this question, we constructed a biophysical network of dual-compartment thick-tufted L5PN, with dendrosomatic coupling controlled by thalamic inputs. Our findings demonstrate that integrated information is maximized when nonspecific thalamic inputs drive the system into a regime of time-varying synchronous bursting. Here, the system exhibits variable spiking dynamics with broad pairwise correlations, supporting the enhanced integrated information. Further, the observed peak in integrated information aligns with criticality signatures and empirically observed layer 5 pyramidal bursting rates. These results suggest that the thalamocortical core of the mammalian brain may be evolutionarily configured to optimize effective information processing, providing a potential neuronal mechanism that integrates microscale theories with macroscale signatures of consciousness.
Collapse
Affiliation(s)
- Brandon R. Munn
- Brain and Mind Centre, School of Medical Sciences, Faculty of Medicine and Health, University of Sydney, Sydney2050, Australia
- Complex Systems, School of Physics, Faculty of Science, University of Sydney, Sydney2050, Australia
| | - Eli J. Müller
- Brain and Mind Centre, School of Medical Sciences, Faculty of Medicine and Health, University of Sydney, Sydney2050, Australia
- Complex Systems, School of Physics, Faculty of Science, University of Sydney, Sydney2050, Australia
| | - Jaan Aru
- Institute of Computer Science, University of Tartu, Tartu51009, Estonia
| | - Christopher J. Whyte
- Brain and Mind Centre, School of Medical Sciences, Faculty of Medicine and Health, University of Sydney, Sydney2050, Australia
- Complex Systems, School of Physics, Faculty of Science, University of Sydney, Sydney2050, Australia
| | - Albert Gidon
- Institute of Biology, Humboldt University of Berlin, Berlin10099, Germany
- NeuroCure Center of Excellence, Charité Universitätsmedizin Berlin, Berlin10099, Germany
| | - Matthew E. Larkum
- Institute of Biology, Humboldt University of Berlin, Berlin10099, Germany
- NeuroCure Center of Excellence, Charité Universitätsmedizin Berlin, Berlin10099, Germany
| | - James M. Shine
- Brain and Mind Centre, School of Medical Sciences, Faculty of Medicine and Health, University of Sydney, Sydney2050, Australia
- Complex Systems, School of Physics, Faculty of Science, University of Sydney, Sydney2050, Australia
| |
Collapse
|
3
|
Liu S, Li F, Wan F. Distance to Criticality Undergoes Critical Transition Before Epileptic Seizure Attacks. Brain Res Bull 2023:110684. [PMID: 37353038 DOI: 10.1016/j.brainresbull.2023.110684] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 06/03/2023] [Accepted: 06/10/2023] [Indexed: 06/25/2023]
Abstract
Epilepsy is a common neurological disorder characterized by recurring seizures, but its underlying mechanisms remain poorly understood. Despite extensive research, there are still gaps in our knowledge about the relationship between brain dynamics and seizures. In this study, our aim is to address these gaps by proposing a novel approach to assess the role of brain network dynamics in the onset of seizures. Specifically, we investigate the relationship between brain dynamics and seizures by tracking the distance to criticality. Our hypothesis is that this distance plays a crucial role in brain state changes and that seizures may be related to critical transitions of this distance. To test this hypothesis, we develop a method to measure the evolution of the brain network's distance to the critical dynamic systems (i.e., the distance to the tipping point, DTP) using dynamic network biomarker theory and random matrix theory. The results show that the DTP of the brain decreases significantly immediately after onset of an epileptic seizure, suggesting that the brain loses its well-defined quasi-critical state during seizures. We refer to this phenomenon as the "criticality of the criticality" (COC). Furthermore, we observe that DTP exhibits a shape transition before and after the onset of the seizures. This phenomenon suggests the possibility of early warning signal (EWS) identification in the dynamic sequence of DTP, which could be utilized for seizure prediction. Our results show that the Hurst exponent, skewness, kurtosis, autocorrelation, and variance of the DTP sequence are potential EWS features. This study advances our understanding of the relationship between brain dynamics and seizures and highlights the potential for using criticality-based measures to predict and prevent seizures.
Collapse
Affiliation(s)
- Shun Liu
- The Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau; The Centre for Cognitive and Brain Sciences, Institute of Collaborative Innovation, University of Macau, Macau; The Centre for Artificial Intelligence and Robotics, Institute of Collaborative Innovation, University of Macau, Macau
| | - Fali Li
- The Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau; The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuro-information, University of Electronic Science and Technology of China, Chengdu, China; School of Life Science and Technology, the Center for Information in Bio-Medicine, University of Electronic Science and Technology of China, Chengdu, China
| | - Feng Wan
- The Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau; The Centre for Cognitive and Brain Sciences, Institute of Collaborative Innovation, University of Macau, Macau; The Centre for Artificial Intelligence and Robotics, Institute of Collaborative Innovation, University of Macau, Macau.
| |
Collapse
|
4
|
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
|
5
|
Fosque LJ, Alipour A, Zare M, Williams-García RV, Beggs JM, Ortiz G. Quasicriticality explains variability of human neural dynamics across life span. Front Comput Neurosci 2022; 16:1037550. [PMID: 36532868 PMCID: PMC9747757 DOI: 10.3389/fncom.2022.1037550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 10/27/2022] [Indexed: 08/26/2023] Open
Abstract
Aging impacts the brain's structural and functional organization and over time leads to various disorders, such as Alzheimer's disease and cognitive impairment. The process also impacts sensory function, bringing about a general slowing in various perceptual and cognitive functions. Here, we analyze the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) resting-state magnetoencephalography (MEG) dataset-the largest aging cohort available-in light of the quasicriticality framework, a novel organizing principle for brain functionality which relates information processing and scaling properties of brain activity to brain connectivity and stimulus. Examination of the data using this framework reveals interesting correlations with age and gender of test subjects. Using simulated data as verification, our results suggest a link between changes to brain connectivity due to aging and increased dynamical fluctuations of neuronal firing rates. Our findings suggest a platform to develop biomarkers of neurological health.
Collapse
Affiliation(s)
- Leandro J. Fosque
- Department of Physics, Indiana University, Bloomington, IN, United States
| | - Abolfazl Alipour
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, United States
| | | | | | - John M. Beggs
- Department of Physics, Indiana University, Bloomington, IN, United States
| | - Gerardo Ortiz
- Department of Physics, Indiana University, Bloomington, IN, United States
| |
Collapse
|
6
|
Tian Y, Tan Z, Hou H, Li G, Cheng A, Qiu Y, Weng K, Chen C, Sun P. Theoretical foundations of studying criticality in the brain. Netw Neurosci 2022; 6:1148-1185. [PMID: 38800464 PMCID: PMC11117095 DOI: 10.1162/netn_a_00269] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/12/2022] [Indexed: 05/29/2024] Open
Abstract
Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information-processing capacities in the brain. While considerable evidence generally supports this hypothesis, nonnegligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the nontriviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, that is, ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistical techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.
Collapse
Affiliation(s)
- Yang Tian
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
- Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China
| | - Zeren Tan
- Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, China
| | - Hedong Hou
- UFR de Mathématiques, Université de Paris, Paris, France
| | - Guoqi Li
- Institute of Automation, Chinese Academy of Science, Beijing, China
- University of Chinese Academy of Science, Beijing, China
| | - Aohua Cheng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Yike Qiu
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Kangyu Weng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Chun Chen
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| | - Pei Sun
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| |
Collapse
|
7
|
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
|
8
|
Heiney K, Huse Ramstad O, Fiskum V, Sandvig A, Sandvig I, Nichele S. Neuronal avalanche dynamics and functional connectivity elucidate information propagation in vitro. Front Neural Circuits 2022; 16:980631. [PMID: 36188125 PMCID: PMC9520060 DOI: 10.3389/fncir.2022.980631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 08/30/2022] [Indexed: 11/13/2022] Open
Abstract
Cascading activity is commonly observed in complex dynamical systems, including networks of biological neurons, and how these cascades spread through the system is reliant on how the elements of the system are connected and organized. In this work, we studied networks of neurons as they matured over 50 days in vitro and evaluated both their dynamics and their functional connectivity structures by observing their electrophysiological activity using microelectrode array recordings. Correlations were obtained between features of their activity propagation and functional connectivity characteristics to elucidate the interplay between dynamics and structure. The results indicate that in vitro networks maintain a slightly subcritical state by striking a balance between integration and segregation. Our work demonstrates the complementarity of these two approaches—functional connectivity and avalanche dynamics—in studying information propagation in neurons in vitro, which can in turn inform the design and optimization of engineered computational substrates.
Collapse
Affiliation(s)
- Kristine Heiney
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway
- *Correspondence: Kristine Heiney
| | - Ola Huse Ramstad
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, Trondheim, Norway
| | - Vegard Fiskum
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, Trondheim, Norway
| | - Axel Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, Trondheim, Norway
- Department of Neurology, St. Olav's Hospital, Trondheim, Norway
- Department of Community Medicine and Rehabilitation, St. Olav's Hospital, Trondheim, Norway
- Department of Clinical Neuroscience, Umeå University Hospital, Umeå, Sweden
| | - Ioanna Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology, Trondheim, Norway
- Department of Neurology, St. Olav's Hospital, Trondheim, Norway
| | - Stefano Nichele
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Computer Science and Communication, Østfold University College, Halden, Norway
| |
Collapse
|
9
|
Kelty-Stephen DG, Mangalam M. Turing's cascade instability supports the coordination of the mind, brain, and behavior. Neurosci Biobehav Rev 2022; 141:104810. [PMID: 35932950 DOI: 10.1016/j.neubiorev.2022.104810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 06/09/2022] [Accepted: 08/01/2022] [Indexed: 10/16/2022]
Abstract
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.
Collapse
Affiliation(s)
- Damian G Kelty-Stephen
- Department of Psychology, State University of New York at New Paltz, New Paltz, NY, USA.
| | - Madhur Mangalam
- Department of Physical Therapy, Movement and Rehabilitation Sciences, Northeastern University, Boston, MA, USA.
| |
Collapse
|
10
|
Tian Y, Sun P. Percolation may explain efficiency, robustness, and economy of the brain. Netw Neurosci 2022; 6:765-790. [PMID: 36605416 PMCID: PMC9810365 DOI: 10.1162/netn_a_00246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 03/11/2022] [Indexed: 01/09/2023] Open
Abstract
The brain consists of billions of neurons connected by ultra-dense synapses, showing remarkable efficiency, robust flexibility, and economy in information processing. It is generally believed that these advantageous properties are rooted in brain connectivity; however, direct evidence remains absent owing to technical limitations or theoretical vacancy. This research explores the origins of these properties in the largest yet brain connectome of the fruit fly. We reveal that functional connectivity formation in the brain can be explained by a percolation process controlled by synaptic excitation-inhibition (E/I) balance. By increasing the E/I balance gradually, we discover the emergence of these properties as byproducts of percolation transition when the E/I balance arrives at 3:7. As the E/I balance keeps increase, an optimal E/I balance 1:1 is unveiled to ensure these three properties simultaneously, consistent with previous in vitro experimental predictions. Once the E/I balance reaches over 3:2, an intrinsic limitation of these properties determined by static (anatomical) brain connectivity can be observed. Our work demonstrates that percolation, a universal characterization of critical phenomena and phase transitions, may serve as a window toward understanding the emergence of various brain properties.
Collapse
Affiliation(s)
- Yang Tian
- Department of Psychology and Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China,Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China,* Corresponding Author: ;
| | - Pei Sun
- Department of Psychology and Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China,* Corresponding Author: ;
| |
Collapse
|
11
|
Yu C. Toward a Unified Analysis of the Brain Criticality Hypothesis: Reviewing Several Available Tools. Front Neural Circuits 2022; 16:911245. [PMID: 35669452 PMCID: PMC9164306 DOI: 10.3389/fncir.2022.911245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 04/19/2022] [Indexed: 11/13/2022] Open
Abstract
The study of the brain criticality hypothesis has been going on for about 20 years, various models and methods have been developed for probing this field, together with large amounts of controversial experimental findings. However, no standardized protocol of analysis has been established so far. Therefore, hoping to make some contributions to standardization of such analysis, we review several available tools used for estimating the criticality of the brain in this paper.
Collapse
|
12
|
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
|
13
|
Gu L, Wu R. Robust cortical criticality and diverse dynamics resulting from functional specification. Phys Rev E 2021; 103:042407. [PMID: 34005915 DOI: 10.1103/physreve.103.042407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 03/23/2021] [Indexed: 11/07/2022]
Abstract
Despite the recognition of the layered structure and evident criticality in the cortex, how the specification of input, output, and computational layers affects the self-organized criticality has not been much explored. By constructing heterogeneous structures with a well-accepted model of leaky neurons, we find that the specification can lead to robust criticality rather insensitive to the strength of external stimuli. This naturally unifies the adaptation to strong inputs without extra synaptic plasticity mechanisms. Low degree of recurrence constitutes an alternative explanation to subcriticality other than the high-frequency inputs. Unlike fully recurrent networks where external stimuli always render subcriticality, the dynamics of networks with sufficient feedforward connections can be driven to criticality and supercriticality. These findings indicate that functional and structural specification and their interplay with external stimuli are of crucial importance for the network dynamics. The robust criticality puts forward networks of the leaky neurons as promising platforms for realizing artificial neural networks that work in the vicinity of critical points.
Collapse
Affiliation(s)
- Lei Gu
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Ruqian Wu
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| |
Collapse
|
14
|
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
|
15
|
Lotfi N, Feliciano T, Aguiar LAA, Silva TPL, Carvalho TTA, Rosso OA, Copelli M, Matias FS, Carelli PV. Statistical complexity is maximized close to criticality in cortical dynamics. Phys Rev E 2021; 103:012415. [PMID: 33601583 DOI: 10.1103/physreve.103.012415] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 01/04/2021] [Indexed: 11/07/2022]
Abstract
Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a nonequilibrium phase transition.
Collapse
Affiliation(s)
- Nastaran Lotfi
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Leandro A A Aguiar
- Departamento de Ciências Fundamentais e Sociais, Universidade Federal da Paraíba, Areia PB 58397-000, Brazil
| | | | - Tawan T A Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Osvaldo A Rosso
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| | - Fernanda S Matias
- Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil
| |
Collapse
|
16
|
Diffuse neural coupling mediates complex network dynamics through the formation of quasi-critical brain states. Nat Commun 2020; 11:6337. [PMID: 33303766 PMCID: PMC7729877 DOI: 10.1038/s41467-020-19716-7] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 10/28/2020] [Indexed: 01/17/2023] Open
Abstract
The biological mechanisms that allow the brain to balance flexibility and integration remain poorly understood. A potential solution may lie in a unique aspect of neurobiology, which is that numerous brain systems contain diffuse synaptic connectivity. Here, we demonstrate that increasing diffuse cortical coupling within a validated biophysical corticothalamic model traverses the system through a quasi-critical regime in which spatial heterogeneities in input noise support transient critical dynamics in distributed subregions. The presence of quasi-critical states coincides with known signatures of complex, adaptive brain network dynamics. Finally, we demonstrate the presence of similar dynamic signatures in empirical whole-brain human neuroimaging data. Together, our results establish that modulating the balance between local and diffuse synaptic coupling in a thalamocortical model subtends the emergence of quasi-critical brain states that act to flexibly transition the brain between unique modes of information processing.
Collapse
|
17
|
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: 35] [Impact Index Per Article: 8.8] [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
|
18
|
Time-dependent branching processes: a model of oscillating neuronal avalanches. Sci Rep 2020; 10:13678. [PMID: 32792658 PMCID: PMC7426838 DOI: 10.1038/s41598-020-69705-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 07/15/2020] [Indexed: 11/08/2022] Open
Abstract
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results.
Collapse
|
19
|
Antiepileptic drugs induce subcritical dynamics in human cortical networks. Proc Natl Acad Sci U S A 2020; 117:11118-11125. [PMID: 32358198 DOI: 10.1073/pnas.1911461117] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Cortical network functioning critically depends on finely tuned interactions to afford neuronal activity propagation over long distances while avoiding runaway excitation. This importance is highlighted by the pathological consequences and impaired performance resulting from aberrant network excitability in psychiatric and neurological diseases, such as epilepsy. Theory and experiment suggest that the control of activity propagation by network interactions can be adequately described by a branching process. This hypothesis is partially supported by strong evidence for balanced spatiotemporal dynamics observed in the cerebral cortex; however, evidence of a causal relationship between network interactions and cortex activity, as predicted by a branching process, is missing in humans. Here this cause-effect relationship is tested by monitoring cortex activity under systematic pharmacological reduction of cortical network interactions with antiepileptic drugs. This study reports that cortical activity cascades, presented by the propagating patterns of epileptic spikes, as well as temporal correlations decline precisely as predicted for a branching process. The results provide a missing link to the branching process theory of cortical network function with implications for understanding the foundations of cortical excitability and its monitoring in conditions like epilepsy.
Collapse
|
20
|
Zierenberg J, Wilting J, Priesemann V, Levina A. Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence. Phys Rev E 2020; 101:022301. [PMID: 32168601 DOI: 10.1103/physreve.101.022301] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2019] [Accepted: 12/17/2019] [Indexed: 06/10/2023]
Abstract
Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal nonlinear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established estimates of the macroscopic branching parameter. To overcome this difference, we propose a nonlinear estimator that correctly infers the microscopic model parameter for all system sizes.
Collapse
Affiliation(s)
- Johannes Zierenberg
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Am Fassberg 17, 37077 Göttingen, Germany
| | - Jens Wilting
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
| | - Viola Priesemann
- Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Am Fassberg 17, 37077 Göttingen, Germany
| | - Anna Levina
- University of Tübingen, Max Planck Ring 8, 72076 Tübingen, Germany
- Max Planck Institute for Biological Cybernetics, Max Planck Ring 8, 72076 Tübingen, Germany
| |
Collapse
|
21
|
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: 66] [Impact Index Per Article: 13.2] [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
|
22
|
Guo X, Yu H, Kodama NX, Wang J, Galán RF. Fluctuation Scaling of Neuronal Firing and Bursting in Spontaneously Active Brain Circuits. Int J Neural Syst 2019; 30:1950017. [PMID: 31390911 DOI: 10.1142/s0129065719500175] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency - regularly firing neurons (RNs) - from 1 to 8Hz while 8% fired in burst with two dominant frequencies - bursting neurons (BNs) - corresponding to the inter-burst (2-6Hz) and intra-burst intervals (20-160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.
Collapse
Affiliation(s)
- Xinmeng Guo
- School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, P. R. China
| | - Haitao Yu
- School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, P. R. China
| | - Nathan X Kodama
- Department of Electrical Engineering and Computer Science, School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA
| | - Jiang Wang
- School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, P. R. China
| | - Roberto F Galán
- Department of Electrical Engineering and Computer Science, School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA
| |
Collapse
|
23
|
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
|
24
|
Agrawal V, Chakraborty S, Knöpfel T, Shew WL. Scale-Change Symmetry in the Rules Governing Neural Systems. iScience 2019; 12:121-131. [PMID: 30682624 PMCID: PMC6352707 DOI: 10.1016/j.isci.2019.01.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Revised: 12/05/2018] [Accepted: 01/04/2019] [Indexed: 11/16/2022] Open
Abstract
Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems. Experiments suggest that the cerebral cortex can also operate near a critical phase transition. Thus we hypothesize that the laws governing cortical dynamics may obey scale-change symmetry. Here we develop a practical approach to test this hypothesis. We confirm, using two different computational models, that neural dynamical laws exhibit scale-change symmetry near a dynamical phase transition. Moreover, we show that as a mouse awakens from anesthesia, scale-change symmetry emerges. Scale-change symmetry of the rules governing cortical dynamics may explain observations of similar critical phenomena across diverse neural systems.
Collapse
Affiliation(s)
- Vidit Agrawal
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA
| | - Srimoy Chakraborty
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA
| | - Thomas Knöpfel
- Laboratory for Neuronal Circuit Dynamics, Faculty of Medicine Imperial College London, London W12 0NN, UK; Centre for Neurotechnology, Institute of Biomedical Engineering, Imperial College London, London SW7 2AZ, UK
| | - Woodrow L Shew
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA.
| |
Collapse
|
25
|
Girardi-Schappo M, Tragtenberg MHR. Measuring neuronal avalanches in disordered systems with absorbing states. Phys Rev E 2018; 97:042415. [PMID: 29758702 DOI: 10.1103/physreve.97.042415] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2017] [Indexed: 11/07/2022]
Abstract
Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.
Collapse
Affiliation(s)
- M Girardi-Schappo
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, McGill University, Montreal Neurological Institute and Hospital, H3A 2B4, Montreal, Quebec, Canada.,Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - M H R Tragtenberg
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| |
Collapse
|
26
|
Agrawal V, Cowley AB, Alfaori Q, Larremore DB, Restrepo JG, Shew WL. Robust entropy requires strong and balanced excitatory and inhibitory synapses. CHAOS (WOODBURY, N.Y.) 2018; 28:103115. [PMID: 30384653 DOI: 10.1063/1.5043429] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Accepted: 10/01/2018] [Indexed: 06/08/2023]
Abstract
It is widely appreciated that balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, balance could be achieved by many possible configurations of excitatory and inhibitory synaptic strengths and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses or a few inhibitory neurons with strong synapses. Among the continuum of different but balanced configurations, why should any particular configuration be favored? Here, we address this question in the context of the entropy of network dynamics by studying an analytically tractable network of binary neurons. We find that entropy is highest at the boundary between excitation-dominant and inhibition-dominant regimes. Entropy also varies along this boundary with a trade-off between high and robust entropy: weak synapse strengths yield high network entropy which is fragile to parameter variations, while strong synapse strengths yield a lower, but more robust, network entropy. In the case where inhibitory and excitatory synapses are constrained to have similar strength, we find that a small, but non-zero fraction of inhibitory neurons, like that seen in mammalian cortex, results in robust and relatively high entropy.
Collapse
Affiliation(s)
- Vidit Agrawal
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Andrew B Cowley
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Qusay Alfaori
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Daniel B Larremore
- Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Woodrow L Shew
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| |
Collapse
|
27
|
Inferring collective dynamical states from widely unobserved systems. Nat Commun 2018; 9:2325. [PMID: 29899335 PMCID: PMC5998151 DOI: 10.1038/s41467-018-04725-4] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Accepted: 05/09/2018] [Indexed: 12/02/2022] Open
Abstract
When assessing spatially extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events. We derive a subsampling-invariant estimator, and demonstrate that it correctly infers the infectiousness of various diseases under subsampling, making it particularly useful in countries with unreliable case reports. In neuroscience, recordings are strongly limited by subsampling. Here, the subsampling-invariant estimator allows to revisit two prominent hypotheses about the brain’s collective spiking dynamics: asynchronous-irregular or critical. We identify consistently for rat, cat, and monkey a state that combines features of both and allows input to reverberate in the network for hundreds of milliseconds. Overall, owing to its ready applicability, the novel estimator paves the way to novel insight for the study of spatially extended dynamical systems. From infectious diseases to brain activity, complex systems can be approximated using autoregressive models. Here, the authors show that incomplete sampling can bias estimates of the stability of such systems, and introduce a novel, unbiased metric for use in such situations.
Collapse
|
28
|
Li W, Ovchinnikov IV, Chen H, Wang Z, Lee A, Lee H, Cepeda C, Schwartz RN, Meier K, Wang KL. A Basic Phase Diagram of Neuronal Dynamics. Neural Comput 2018; 30:2418-2438. [PMID: 29894659 DOI: 10.1162/neco_a_01103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The extreme complexity of the brain has attracted the attention of neuroscientists and other researchers for a long time. More recently, the neuromorphic hardware has matured to provide a new powerful tool to study neuronal dynamics. Here, we study neuronal dynamics using different settings on a neuromorphic chip built with flexible parameters of neuron models. Our unique setting in the network of leaky integrate-and-fire (LIF) neurons is to introduce a weak noise environment. We observed three different types of collective neuronal activities, or phases, separated by sharp boundaries, or phase transitions. From this, we construct a rudimentary phase diagram of neuronal dynamics and demonstrate that a noise-induced chaotic phase (N-phase), which is dominated by neuronal avalanche activity (intermittent aperiodic neuron firing), emerges in the presence of noise and its width grows with the noise intensity. The dynamics can be manipulated in this N-phase. Our results and comparison with clinical data is consistent with the literature and our previous work showing that healthy brain must reside in the N-phase. We argue that the brain phase diagram with further refinement may be used for the diagnosis and treatment of mental disease and also suggest that the dynamics may be manipulated to serve as a means of new information processing (e.g., for optimization). Neuromorphic chips, similar to the one we used but with a variety of neuron models, may be used to further enhance the understanding of human brain function and accelerate the development of neuroscience research.
Collapse
Affiliation(s)
- Wenyuan Li
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Igor V Ovchinnikov
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Honglin Chen
- Department of Mathematics, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Zhe Wang
- Department of Mechanical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Albert Lee
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Houchul Lee
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Carlos Cepeda
- David Geffen School of Medicine, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Robert N Schwartz
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Karlheinz Meier
- Kirchhoff Institute for Physics, Heidelberg University, 69120 Heidelberg, Germany
| | - Kang L Wang
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| |
Collapse
|
29
|
Scarpetta S, Apicella I, Minati L, de Candia A. Hysteresis, neural avalanches, and critical behavior near a first-order transition of a spiking neural network. Phys Rev E 2018; 97:062305. [PMID: 30011436 DOI: 10.1103/physreve.97.062305] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Indexed: 06/08/2023]
Abstract
Many experimental results, both in vivo and in vitro, support the idea that the brain cortex operates near a critical point and at the same time works as a reservoir of precise spatiotemporal patterns. However, the mechanism at the basis of these observations is still not clear. In this paper we introduce a model which combines both these features, showing that scale-free avalanches are the signature of a system posed near the spinodal line of a first-order transition, with many spatiotemporal patterns stored as dynamical metastable attractors. Specifically, we studied a network of leaky integrate-and-fire neurons whose connections are the result of the learning of multiple spatiotemporal dynamical patterns, each with a randomly chosen ordering of the neurons. We found that the network shows a first-order transition between a low-spiking-rate disordered state (down), and a high-rate state characterized by the emergence of collective activity and the replay of one of the stored patterns (up). The transition is characterized by hysteresis, or alternation of up and down states, depending on the lifetime of the metastable states. In both cases, critical features and neural avalanches are observed. Notably, critical phenomena occur at the edge of a discontinuous phase transition, as recently observed in a network of glow lamps.
Collapse
Affiliation(s)
- Silvia Scarpetta
- Dipartimento di Fisica "E. Caianiello," Università di Salerno, Fisciano (SA), Italy
- INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Italy
| | - Ilenia Apicella
- Dipartimento di Fisica e Astronomia "G. Galilei," Università di Padova, Italy
| | - Ludovico Minati
- Complex Systems Theory Department, Institute of Nuclear Physics Polish Academy of Sciences (IFJ-PAN), Kraków, Poland
| | - Antonio de Candia
- INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Italy
- Dipartimento di Fisica "E. Pancini," Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy
| |
Collapse
|
30
|
Zhang R, Pei S. Dynamic range maximization in excitable networks. CHAOS (WOODBURY, N.Y.) 2018; 28:013103. [PMID: 29390628 DOI: 10.1063/1.4997254] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which a critical state is reached when the largest eigenvalue of the weighted non-backtracking matrix is close to one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintaining the largest size of the giant connected component.
Collapse
Affiliation(s)
- Renquan Zhang
- School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
| | - Sen Pei
- Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, New York 10032, USA
| |
Collapse
|
31
|
Yu S, Ribeiro TL, Meisel C, Chou S, Mitz A, Saunders R, Plenz D. Maintained avalanche dynamics during task-induced changes of neuronal activity in nonhuman primates. eLife 2017; 6. [PMID: 29115213 PMCID: PMC5677367 DOI: 10.7554/elife.27119] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Accepted: 10/28/2017] [Indexed: 11/24/2022] Open
Abstract
Sensory events, cognitive processing and motor actions correlate with transient changes in neuronal activity. In cortex, these transients form widespread spatiotemporal patterns with largely unknown statistical regularities. Here, we show that activity associated with behavioral events carry the signature of scale-invariant spatiotemporal clusters, neuronal avalanches. Using high-density microelectrode arrays in nonhuman primates, we recorded extracellular unit activity and the local field potential (LFP) in premotor and prefrontal cortex during motor and cognitive tasks. Unit activity and negative LFP deflections (nLFP) consistently changed in rate at single electrodes during tasks. Accordingly, nLFP clusters on the array deviated from scale-invariance compared to ongoing activity. Scale-invariance was recovered using ‘adaptive binning’, that is identifying clusters at temporal resolution given by task-induced changes in nLFP rate. Measures of LFP synchronization confirmed and computer simulations detailed our findings. We suggest optimization principles identified for avalanches during ongoing activity to apply to cortical information processing during behavior.
Collapse
Affiliation(s)
- Shan Yu
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States
| | - Tiago L Ribeiro
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States
| | - Christian Meisel
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States
| | - Samantha Chou
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States
| | - Andrew Mitz
- Laboratory of Neuropsychology, National Institute of Mental Health, Bethesda, United States
| | - Richard Saunders
- Laboratory of Neuropsychology, National Institute of Mental Health, Bethesda, United States
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, United States
| |
Collapse
|
32
|
Gollo LL. Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding. J R Soc Interface 2017; 14:20170207. [PMID: 28954848 PMCID: PMC5636266 DOI: 10.1098/rsif.2017.0207] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2017] [Accepted: 08/17/2017] [Indexed: 11/12/2022] Open
Abstract
The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.
Collapse
Affiliation(s)
- Leonardo L Gollo
- Systems Neuroscience Group, QIMR Berghofer Medical Research Institute, Brisbane, Australia
- The University of Queensland, Centre for Clinical Research, Brisbane, Australia
| |
Collapse
|
33
|
Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior. Sci Rep 2017; 7:7107. [PMID: 28769096 PMCID: PMC5541036 DOI: 10.1038/s41598-017-07135-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Accepted: 06/23/2017] [Indexed: 11/12/2022] Open
Abstract
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.
Collapse
|
34
|
Clawson WP, Wright NC, Wessel R, Shew WL. Adaptation towards scale-free dynamics improves cortical stimulus discrimination at the cost of reduced detection. PLoS Comput Biol 2017; 13:e1005574. [PMID: 28557985 PMCID: PMC5469508 DOI: 10.1371/journal.pcbi.1005574] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2017] [Revised: 06/13/2017] [Accepted: 05/15/2017] [Indexed: 11/18/2022] Open
Abstract
Fundamental to the function of nervous systems is the ability to reorganize to cope with changing sensory input. Although well-studied in single neurons, how such adaptive versatility manifests in the collective population dynamics and function of cerebral cortex remains unknown. Here we measured population neural activity with microelectrode arrays in turtle visual cortex while visually stimulating the retina. First, we found that, following the onset of stimulation, adaptation tunes the collective population dynamics towards a special regime with scale-free spatiotemporal activity, after an initial large-scale transient response. Concurrently, we observed an adaptive tradeoff between two important aspects of population coding-sensory detection and discrimination. As adaptation tuned the cortex toward scale-free dynamics, stimulus discrimination was enhanced, while stimulus detection was reduced. Finally, we used a network-level computational model to show that short-term synaptic depression was sufficient to mechanistically explain our experimental results. In the model, scale-free dynamics emerge only when the model operates near a special regime called criticality. Together our model and experimental results suggest unanticipated functional benefits and costs of adaptation near criticality in visual cortex.
Collapse
Affiliation(s)
- Wesley P. Clawson
- Department of Physics, University of Arkansas, Fayetteville, Arkansas, United States of America
| | - Nathaniel C. Wright
- Department of Physics, Washington University, Saint Louis, Missouri, United States of America
| | - Ralf Wessel
- Department of Physics, Washington University, Saint Louis, Missouri, United States of America
| | - Woodrow L. Shew
- Department of Physics, University of Arkansas, Fayetteville, Arkansas, United States of America
- * E-mail:
| |
Collapse
|
35
|
Del Papa B, Priesemann V, Triesch J. Criticality meets learning: Criticality signatures in a self-organizing recurrent neural network. PLoS One 2017; 12:e0178683. [PMID: 28552964 PMCID: PMC5446191 DOI: 10.1371/journal.pone.0178683] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Accepted: 05/17/2017] [Indexed: 11/23/2022] Open
Abstract
Many experiments have suggested that the brain operates close to a critical state, based on signatures of criticality such as power-law distributed neuronal avalanches. In neural network models, criticality is a dynamical state that maximizes information processing capacities, e.g. sensitivity to input, dynamical range and storage capacity, which makes it a favorable candidate state for brain function. Although models that self-organize towards a critical state have been proposed, the relation between criticality signatures and learning is still unclear. Here, we investigate signatures of criticality in a self-organizing recurrent neural network (SORN). Investigating criticality in the SORN is of particular interest because it has not been developed to show criticality. Instead, the SORN has been shown to exhibit spatio-temporal pattern learning through a combination of neural plasticity mechanisms and it reproduces a number of biological findings on neural variability and the statistics and fluctuations of synaptic efficacies. We show that, after a transient, the SORN spontaneously self-organizes into a dynamical state that shows criticality signatures comparable to those found in experiments. The plasticity mechanisms are necessary to attain that dynamical state, but not to maintain it. Furthermore, onset of external input transiently changes the slope of the avalanche distributions – matching recent experimental findings. Interestingly, the membrane noise level necessary for the occurrence of the criticality signatures reduces the model’s performance in simple learning tasks. Overall, our work shows that the biologically inspired plasticity and homeostasis mechanisms responsible for the SORN’s spatio-temporal learning abilities can give rise to criticality signatures in its activity when driven by random input, but these break down under the structured input of short repeating sequences.
Collapse
Affiliation(s)
- Bruno Del Papa
- Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt am Main, Germany
- International Max Planck Research School for Neural Circuits, Max Planck Institute for Brain Research, Frankfurt am Main, Germany
- * E-mail:
| | - Viola Priesemann
- Department of Non-linear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
| | - Jochen Triesch
- Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt am Main, Germany
| |
Collapse
|
36
|
Hahn G, Ponce-Alvarez A, Monier C, Benvenuti G, Kumar A, Chavane F, Deco G, Frégnac Y. Spontaneous cortical activity is transiently poised close to criticality. PLoS Comput Biol 2017; 13:e1005543. [PMID: 28542191 PMCID: PMC5464673 DOI: 10.1371/journal.pcbi.1005543] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Revised: 06/08/2017] [Accepted: 04/26/2017] [Indexed: 11/19/2022] Open
Abstract
Brain activity displays a large repertoire of dynamics across the sleep-wake cycle and even during anesthesia. It was suggested that criticality could serve as a unifying principle underlying the diversity of dynamics. This view has been supported by the observation of spontaneous bursts of cortical activity with scale-invariant sizes and durations, known as neuronal avalanches, in recordings of mesoscopic cortical signals. However, the existence of neuronal avalanches in spiking activity has been equivocal with studies reporting both its presence and absence. Here, we show that signs of criticality in spiking activity can change between synchronized and desynchronized cortical states. We analyzed the spontaneous activity in the primary visual cortex of the anesthetized cat and the awake monkey, and found that neuronal avalanches and thermodynamic indicators of criticality strongly depend on collective synchrony among neurons, LFP fluctuations, and behavioral state. We found that synchronized states are associated to criticality, large dynamical repertoire and prolonged epochs of eye closure, while desynchronized states are associated to sub-criticality, reduced dynamical repertoire, and eyes open conditions. Our results show that criticality in cortical dynamics is not stationary, but fluctuates during anesthesia and between different vigilance states.
Collapse
Affiliation(s)
- Gerald Hahn
- Unité de Neuroscience, Information et Complexité (UNIC), CNRS, Gif-sur-Yvette, France
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Adrian Ponce-Alvarez
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
| | - Cyril Monier
- Unité de Neuroscience, Information et Complexité (UNIC), CNRS, Gif-sur-Yvette, France
| | | | - Arvind Kumar
- Bernstein Center for Computational Neuroscience, Freiburg, Germany
- Dept. of Computational Science and Technology, School of Computer Science and Communication, KTH, Royal Institute of Technology, Stockholm, Sweden
| | - Frédéric Chavane
- Institut des Neurosciences de la Timone, CNRS, Marseille, France
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
- Institució Catalana de la Recerca i Estudis Avançats, Universitat Pompeu Fabra, Barcelona, Spain
- Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- School of Psychological Sciences, Monash University, Melbourne, Clayton, Victoria, Australia
| | - Yves Frégnac
- Unité de Neuroscience, Information et Complexité (UNIC), CNRS, Gif-sur-Yvette, France
| |
Collapse
|
37
|
Vallone F, Vannini E, Cintio A, Caleo M, Di Garbo A. Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice. Phys Rev E 2016; 94:032409. [PMID: 27739854 DOI: 10.1103/physreve.94.032409] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2016] [Indexed: 11/07/2022]
Abstract
Epilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (<20 ms), whereas an increase of the coupling is present for low frequencies (0.5-4 Hz) and long time lag (>40 ms). On the other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here.
Collapse
Affiliation(s)
- F Vallone
- Institute of Biophysics, CNR-National Research Council, 56124 Pisa, Italy.,The Biorobotics Institute, Scuola Superiore Sant'Anna, 56026 Pisa, Italy
| | - E Vannini
- Neuroscience Institute, CNR-National Research Council, 56124 Pisa, Italy
| | - A Cintio
- Institute of Biophysics, CNR-National Research Council, 56124 Pisa, Italy
| | - M Caleo
- Neuroscience Institute, CNR-National Research Council, 56124 Pisa, Italy
| | - A Di Garbo
- Institute of Biophysics, CNR-National Research Council, 56124 Pisa, Italy.,INFN-Section of Pisa, 56127 Pisa, Italy
| |
Collapse
|
38
|
Timme NM, Marshall NJ, Bennett N, Ripp M, Lautzenhiser E, Beggs JM. Criticality Maximizes Complexity in Neural Tissue. Front Physiol 2016; 7:425. [PMID: 27729870 PMCID: PMC5037237 DOI: 10.3389/fphys.2016.00425] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Accepted: 09/08/2016] [Indexed: 11/25/2022] Open
Abstract
The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity-an information theoretic measure-has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.
Collapse
Affiliation(s)
- Nicholas M. Timme
- Department of Psychology, Indiana University - Purdue University IndianapolisIndianapolis, IN, USA
| | | | | | - Monica Ripp
- Department of Physics, Syracuse UniversitySyracuse, NY, USA
| | | | - John M. Beggs
- Department of Physics, Indiana UniversityBloomington, IN, USA
- Biocomplexity Institute, Indiana UniversityBloomington, IN, USA
| |
Collapse
|
39
|
Girardi-Schappo M, Bortolotto GS, Gonsalves JJ, Pinto LT, Tragtenberg MHR. Griffiths phase and long-range correlations in a biologically motivated visual cortex model. Sci Rep 2016; 6:29561. [PMID: 27435679 PMCID: PMC4951650 DOI: 10.1038/srep29561] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Accepted: 06/15/2016] [Indexed: 12/21/2022] Open
Abstract
Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and 1/f (b) power spectrum in vivo and in vitro. We study an avalanching biologically motivated model of mammals visual cortex and find an extended critical-like region - a Griffiths phase - characterized by divergent susceptibility and zero order parameter. This phase lies close to the expected experimental value of the excitatory postsynaptic potential in the cortex suggesting that critical be-havior may be found in the visual system. Avalanches are not perfectly power-law distributed, but it is possible to collapse the distributions and define a cutoff avalanche size that diverges as the network size is increased inside the critical region. The avalanches present long-range correlations and 1/f (b) power spectrum, matching experiments. The phase transition is analytically determined by a mean-field approximation.
Collapse
Affiliation(s)
- M Girardi-Schappo
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - G S Bortolotto
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - J J Gonsalves
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - L T Pinto
- Departamento de Engenharia Química e Engenharia de Alimentos, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - M H R Tragtenberg
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| |
Collapse
|
40
|
Marshall N, Timme NM, Bennett N, Ripp M, Lautzenhiser E, Beggs JM. Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox. Front Physiol 2016; 7:250. [PMID: 27445842 PMCID: PMC4921690 DOI: 10.3389/fphys.2016.00250] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2016] [Accepted: 06/08/2016] [Indexed: 11/13/2022] Open
Abstract
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
Collapse
Affiliation(s)
- Najja Marshall
- Department of Neuroscience, Columbia University New York, NY, USA
| | - Nicholas M Timme
- Department of Psychology, Indiana University - Purdue University Indianapolis Indianapolis, IN, USA
| | | | - Monica Ripp
- Department of Physics, Syracuse University Syracuse, NY, USA
| | | | - John M Beggs
- Department of Physics, Indiana UniversityBloomington, IN, USA; Biocomplexity Institute, Indiana UniversityBloomington, IN, USA
| |
Collapse
|
41
|
Wang SJ, Ouyang G, Guang J, Zhang M, Wong KYM, Zhou C. Stochastic Oscillation in Self-Organized Critical States of Small Systems: Sensitive Resting State in Neural Systems. PHYSICAL REVIEW LETTERS 2016; 116:018101. [PMID: 26799044 DOI: 10.1103/physrevlett.116.018101] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Indexed: 06/05/2023]
Abstract
Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems, which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli.
Collapse
Affiliation(s)
- Sheng-Jun Wang
- Department of Physics, Shaanxi Normal University, Xi'An 710119, China
- 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
| | - Guang Ouyang
- 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
| | - Jing Guang
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China
| | - Mingsha Zhang
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China
| | - K Y Michael Wong
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, 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
- Beijing Computational Science Research Center, Beijing 100084, China
- Research Centre, HKBU Institute of Research and Continuing Education, Virtual University Park Building, South Area Hi-tech Industrial Park, Shenzhen 518057, China
| |
Collapse
|