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Venkadesh S, Shaikh A, Shakeri H, Barreto E, Van Horn JD. Biophysical modulation and robustness of itinerant complexity in neuronal networks. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1302499. [PMID: 38516614 PMCID: PMC10954887 DOI: 10.3389/fnetp.2024.1302499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 02/26/2024] [Indexed: 03/23/2024]
Abstract
Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability in the inhibitory population. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.
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Affiliation(s)
- Siva Venkadesh
- Department of Psychology, University of Virginia, Charlottesville, VA, United States
| | - Asmir Shaikh
- Department of Computer Science, University of Virginia, Charlottesville, VA, United States
| | - Heman Shakeri
- School of Data Science, University of Virginia, Charlottesville, VA, United States
- Biomedical Engineering, University of Virginia, Charlottesville, VA, United States
| | - Ernest Barreto
- Department of Physics and Astronomy and the Interdisciplinary Program in Neuroscience, George Mason University, Fairfax, VA, United States
| | - John Darrell Van Horn
- Department of Psychology, University of Virginia, Charlottesville, VA, United States
- School of Data Science, University of Virginia, Charlottesville, VA, United States
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2
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Lee H, Yi GS, Nam Y. Connectivity and network burst properties of in-vitro neuronal networks induced by a clustered structure with alginate hydrogel patterning. Biomed Eng Lett 2023; 13:659-670. [PMID: 37872997 PMCID: PMC10590365 DOI: 10.1007/s13534-023-00289-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Revised: 05/19/2023] [Accepted: 05/22/2023] [Indexed: 10/25/2023] Open
Abstract
Modularity is one of the important structural properties that affect information processing and other functionalities of neuronal networks. Researchers have developed in-vitro clustered network models for reproducing the modularity, but it is still challenging to control the segregation and integration of several sub-populations of them. We cultured clustered networks with alginate patterning and collected the electrophysiological signals to investigate the changes in functional properties during the development. We built inter-connected neuronal clusters using alginate micro-patterning with a circular shape on the surface of the micro-electrode array. The neuronal clusters were enabled to be connected at 3 or 10 days-in-vitro (DIV) by removing the barrier. The neuronal signals from different types of networks were collected from 16 to 34 DIV, and functional characteristics were examined. Connectivity and burst motif analysis were carried out to find out the relation between the structure and function of the networks. Neuronal networks with clustered structure showed different activity properties from the random networks along the development. The clustered networks had more short-range connections compared to the random networks. In the network burst motif analysis, the clustered networks showed more various patterns and a slower propagation of the activation patterns. In this study, we successfully cultured neuronal networks with clustered structure, and the structure affected the functional properties. The network model suggested in this study will be a good solution for observing the effect of structure on function during their development. Supplementary Information The online version contains supplementary material available at 10.1007/s13534-023-00289-5.
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Affiliation(s)
- Hyungsub Lee
- Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141 Republic of Korea
| | - Gwan-Su Yi
- Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141 Republic of Korea
| | - Yoonkey Nam
- Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141 Republic of Korea
- KAIST Institute for Health Science and Technology, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141 Republic of Korea
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3
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Ioannides G, Kourouklides I, Astolfi A. Spatiotemporal dynamics in spiking recurrent neural networks using modified-full-FORCE on EEG signals. Sci Rep 2022; 12:2896. [PMID: 35190579 PMCID: PMC8861015 DOI: 10.1038/s41598-022-06573-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 01/05/2022] [Indexed: 11/22/2022] Open
Abstract
Methods on modelling the human brain as a Complex System have increased remarkably in the literature as researchers seek to understand the underlying foundations behind cognition, behaviour, and perception. Computational methods, especially Graph Theory-based methods, have recently contributed significantly in understanding the wiring connectivity of the brain, modelling it as a set of nodes connected by edges. Therefore, the brain’s spatiotemporal dynamics can be holistically studied by considering a network, which consists of many neurons, represented by nodes. Various models have been proposed for modelling such neurons. A recently proposed method in training such networks, called full-Force, produces networks that perform tasks with fewer neurons and greater noise robustness than previous least-squares approaches (i.e. FORCE method). In this paper, the first direct applicability of a variant of the full-Force method to biologically-motivated Spiking RNNs (SRNNs) is demonstrated. The SRNN is a graph consisting of modules. Each module is modelled as a Small-World Network (SWN), which is a specific type of a biologically-plausible graph. So, the first direct applicability of a variant of the full-Force method to modular SWNs is demonstrated, evaluated through regression and information theoretic metrics. For the first time, the aforementioned method is applied to spiking neuron models and trained on various real-life Electroencephalography (EEG) signals. To the best of the authors’ knowledge, all the contributions of this paper are novel. Results show that trained SRNNs match EEG signals almost perfectly, while network dynamics can mimic the target dynamics. This demonstrates that the holistic setup of the network model and the neuron model which are both more biologically plausible than previous work, can be tuned into real biological signal dynamics.
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Affiliation(s)
- Georgios Ioannides
- Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK.
| | - Ioannis Kourouklides
- Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 33 Saripolou Street, 3036, Limassol, Cyprus
| | - Alessandro Astolfi
- Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK
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4
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Nobukawa S, Nishimura H, Wagatsuma N, Ando S, Yamanishi T. Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:3525-3537. [PMID: 32822305 DOI: 10.1109/tnnls.2020.3015208] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.
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5
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Zhang Y, Lai D, Han J, Wang X, Lin Q, Zhao X, Hu Z. Testing nonlinearity in topological organization of functional brain networks. Eur J Neurosci 2020; 52:4185-4197. [PMID: 32588503 DOI: 10.1111/ejn.14882] [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: 03/18/2020] [Revised: 06/13/2020] [Accepted: 06/15/2020] [Indexed: 10/24/2022]
Abstract
Aiming to provide an argumentation on the underlying nonlinearity of the overall functional brain network via surrogate data method and graph theory. Taking the functional magnetic resonance imaging data as original data set and then shuffled the time series of each region of interest to generate surrogate data sets, corresponding original network and its 400 surrogates were obtained via computing connectivity matrixes. The results show that both the global correlation level and corresponding small-world topological characters exhibited obvious differences between the original network and its surrogates. And the following statistical testing results demonstrate their significant distinction, and this topological difference has been proved to be caused by the intrinsic nonlinear dynamics. Accordingly, the nonlinearity of the original functional network and its superior dynamical complexity have been confirmed. The results of this study could provide a novel angle into exploring the underlying mechanism of the neural brain system and offer an essential evidence in explaining complex brain activities.
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Affiliation(s)
- Yan Zhang
- College of Optical and Electronic Technology, China Jiliang University, Hangzhou, China
| | - Dingyao Lai
- College of Optical and Electronic Technology, China Jiliang University, Hangzhou, China
| | - Jiahui Han
- College of Optical and Electronic Technology, China Jiliang University, Hangzhou, China
| | - Xuewei Wang
- Center for Optics and Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou, China
| | - Qiang Lin
- Center for Optics and Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou, China
| | - Xiaohu Zhao
- Department of Imaging, The Fifth People's Hospital of Shanghai, Fudan University, Shanghai, China
| | - Zhenghui Hu
- Center for Optics and Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou, China
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6
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Nobukawa S, Nishimura H, Yamanishi T. Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure. Sci Rep 2019; 9:12749. [PMID: 31484990 PMCID: PMC6726653 DOI: 10.1038/s41598-019-49286-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Accepted: 08/22/2019] [Indexed: 11/08/2022] Open
Abstract
Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.
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Affiliation(s)
- Sou Nobukawa
- Department of Computer Science, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba, 275-0016, Japan.
| | - Haruhiko Nishimura
- Graduate School of Applied Informatics, University of Hyogo, 7-1-28 Chuo-ku, Kobe, Hyogo, 650-8588, Japan
| | - Teruya Yamanishi
- AI & IoT Center, Department of Management and Information Sciences, Fukui University of Technology, 3-6-1 Gakuen, Fukui, 910-8505, Japan
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7
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Kim SY, Lim W. Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network. Neural Netw 2018; 106:50-66. [PMID: 30025272 DOI: 10.1016/j.neunet.2018.06.013] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Revised: 05/14/2018] [Accepted: 06/25/2018] [Indexed: 02/06/2023]
Abstract
We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.
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Affiliation(s)
- Sang-Yoon Kim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
| | - Woochang Lim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
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8
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Yamamoto H, Kubota S, Shimizu FA, Hirano-Iwata A, Niwano M. Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators. Front Comput Neurosci 2018; 12:17. [PMID: 29643771 PMCID: PMC5882810 DOI: 10.3389/fncom.2018.00017] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Accepted: 03/06/2018] [Indexed: 11/13/2022] Open
Abstract
A system consisting of interconnected networks, or a network of networks (NoN), appears diversely in many real-world systems, including the brain. In this study, we consider NoNs consisting of heterogeneous phase oscillators and investigate how the topology of subnetworks affects the global synchrony of the network. The degree of synchrony and the effect of subnetwork topology are evaluated based on the Kuramoto order parameter and the minimum coupling strength necessary for the order parameter to exceed a threshold value, respectively. In contrast to an isolated network in which random connectivity is favorable for achieving synchrony, NoNs synchronize with weaker interconnections when the degree distribution of subnetworks is heterogeneous, suggesting the major role of the high-degree nodes. We also investigate a case in which subnetworks with different average natural frequencies are coupled to show that direct coupling of subnetworks with the largest variation is effective for synchronizing the whole system. In real-world NoNs like the brain, the balance of synchrony and asynchrony is critical for its function at various spatial resolutions. Our work provides novel insights into the topological basis of coordinated dynamics in such networks.
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Affiliation(s)
- Hideaki Yamamoto
- Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan
| | - Shigeru Kubota
- Graduate School of Science and Engineering, Yamagata University, Yamagata, Japan
| | - Fabio A Shimizu
- Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
| | - Ayumi Hirano-Iwata
- Research Institute of Electrical Communication, Tohoku University, Sendai, Japan.,Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | - Michio Niwano
- Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
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9
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Fletcher JM, Wennekers T. From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity. Int J Neural Syst 2018; 28:1750013. [DOI: 10.1142/s0129065717500137] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory–inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to hold. We argue that the reason Katz centrality correlates so highly with neuronal activity compared to other centrality measures is because it nicely captures disinhibition in neural networks. In addition, we argue that these theoretical findings are applicable to neuroscientists who apply centrality measures to functional brain networks, as well as offer a neurophysiological justification to high level cognitive models which use certain centrality measures.
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Affiliation(s)
- Jack McKay Fletcher
- Centre for Robotic and Neural Systems, University of Plymouth, Drake Circus, Plymouth PL48AA, UK
| | - Thomas Wennekers
- Centre for Robotic and Neural Systems, University of Plymouth, Drake Circus, Plymouth PL48AA, UK
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10
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Kim SY, Lim W. Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity. Neural Netw 2017; 97:92-106. [PMID: 29096205 DOI: 10.1016/j.neunet.2017.09.016] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Revised: 08/17/2017] [Accepted: 09/29/2017] [Indexed: 10/18/2022]
Abstract
We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.
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Affiliation(s)
- Sang-Yoon Kim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
| | - Woochang Lim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
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11
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Mirzakhalili E, Gourgou E, Booth V, Epureanu B. Synaptic Impairment and Robustness of Excitatory Neuronal Networks with Different Topologies. Front Neural Circuits 2017; 11:38. [PMID: 28659765 PMCID: PMC5468411 DOI: 10.3389/fncir.2017.00038] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Accepted: 05/22/2017] [Indexed: 11/13/2022] Open
Abstract
Synaptic deficiencies are a known hallmark of neurodegenerative diseases, but the diagnosis of impaired synapses on the cellular level is not an easy task. Nonetheless, changes in the system-level dynamics of neuronal networks with damaged synapses can be detected using techniques that do not require high spatial resolution. This paper investigates how the structure/topology of neuronal networks influences their dynamics when they suffer from synaptic loss. We study different neuronal network structures/topologies by specifying their degree distributions. The modes of the degree distribution can be used to construct networks that consist of rich clubs and resemble small world networks, as well. We define two dynamical metrics to compare the activity of networks with different structures: persistent activity (namely, the self-sustained activity of the network upon removal of the initial stimulus) and quality of activity (namely, percentage of neurons that participate in the persistent activity of the network). Our results show that synaptic loss affects the persistent activity of networks with bimodal degree distributions less than it affects random networks. The robustness of neuronal networks enhances when the distance between the modes of the degree distribution increases, suggesting that the rich clubs of networks with distinct modes keep the whole network active. In addition, a tradeoff is observed between the quality of activity and the persistent activity. For a range of distributions, both of these dynamical metrics are considerably high for networks with bimodal degree distribution compared to random networks. We also propose three different scenarios of synaptic impairment, which may correspond to different pathological or biological conditions. Regardless of the network structure/topology, results demonstrate that synaptic loss has more severe effects on the activity of the network when impairments are correlated with the activity of the neurons.
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Affiliation(s)
- Ehsan Mirzakhalili
- Department of Mechanical Engineering, University of MichiganAnn Arbor, MI, United States
| | - Eleni Gourgou
- Department of Mechanical Engineering, University of MichiganAnn Arbor, MI, United States.,Division of Geriatrics, Department of Internal Medicine, Medical School, University of MichiganAnn Arbor, MI, United States
| | - Victoria Booth
- Department of Mathematics, University of MichiganAnn Arbor, MI, United States.,Department of Anesthesiology, Medical School, University of MichiganAnn Arbor, MI, United States
| | - Bogdan Epureanu
- Department of Mechanical Engineering, University of MichiganAnn Arbor, MI, United States
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12
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Kim SY, Lim W. Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network. Neural Netw 2017; 93:57-75. [PMID: 28544891 DOI: 10.1016/j.neunet.2017.04.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2016] [Revised: 02/22/2017] [Accepted: 04/11/2017] [Indexed: 10/19/2022]
Abstract
We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons, and investigate the effect of network architecture on emergence of synchronized brain rhythms by varying the fraction of LR interneurons plong. The betweenness centralities of the LR and SR interneurons (characterizing the potentiality in controlling communication between other interneurons) are distinctly different. Hence, in view of the betweenness, SWNs we consider are inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly the same betweenness centralities. For small plong, the load of communication traffic is much concentrated on a few LR interneurons. However, as plong is increased, the number of LR connections (coming from LR interneurons) increases, and then the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Sparsely synchronized rhythms are thus found to emerge when passing a small critical value plong(c)(≃0.16). The population frequency of the sparsely synchronized rhythm is ultrafast (higher than 100 Hz), while the mean firing rate of individual interneurons is much lower (∼30 Hz) due to stochastic and intermittent neural discharges. These dynamical behaviors in the inhomogeneous SWN are also compared with those in the homogeneous Watts-Strogatz SWN, in connection with their network topologies. Particularly, we note that the main difference between the two types of SWNs lies in the distribution of betweenness centralities. Unlike the case of the Watts-Strogatz SWN, dynamical responses to external stimuli vary depending on the type of stimulated interneurons in the inhomogeneous SWN. We consider two cases of external time-periodic stimuli applied to sub-populations of the LR and SR interneurons, respectively. Dynamical responses (such as synchronization suppression and enhancement) to these two cases of stimuli are studied and discussed in relation to the betweenness centralities of stimulated interneurons, representing the effectiveness for transfer of stimulation effect in the whole network.
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Affiliation(s)
- Sang-Yoon Kim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
| | - Woochang Lim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 42411, Republic of Korea.
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13
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Shein-Idelson M, Cohen G, Ben-Jacob E, Hanein Y. Modularity Induced Gating and Delays in Neuronal Networks. PLoS Comput Biol 2016; 12:e1004883. [PMID: 27104350 PMCID: PMC4841573 DOI: 10.1371/journal.pcbi.1004883] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Accepted: 03/24/2016] [Indexed: 11/23/2022] Open
Abstract
Neural networks, despite their highly interconnected nature, exhibit distinctly localized and gated activation. Modularity, a distinctive feature of neural networks, has been recently proposed as an important parameter determining the manner by which networks support activity propagation. Here we use an engineered biological model, consisting of engineered rat cortical neurons, to study the role of modular topology in gating the activity between cell populations. We show that pairs of connected modules support conditional propagation (transmitting stronger bursts with higher probability), long delays and propagation asymmetry. Moreover, large modular networks manifest diverse patterns of both local and global activation. Blocking inhibition decreased activity diversity and replaced it with highly consistent transmission patterns. By independently controlling modularity and disinhibition, experimentally and in a model, we pose that modular topology is an important parameter affecting activation localization and is instrumental for population-level gating by disinhibition. The capacity to transmit information between connected parts of a neuronal network is fundamental to its function. The organization of network connections (the topology of the network) is therefore expected to play an important role in determining network transmission. Since modular topology characterizes many brain circuits on multiple scales, investigating the role of modularity in activity gating is clearly desirable. By engineering such modular networks in vitro, we were able to perform such an investigation. Under these experimental conditions, we can independently control the degree of modularity, as well as inhibition in the network. We show that a combination of these two properties is highly beneficial from a communication perspective. Namely, it equips connected modules and large modular networks with the capacity to gate and temporally coordinate activity between the different parts of the network.
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Affiliation(s)
- Mark Shein-Idelson
- School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
- Tel Aviv University Center for Nanoscience and Nanotechnology, Tel Aviv, Israel
- Max Planck Institute for Brain Research, Frankfurt am Main, Germany
- * E-mail:
| | - Gilad Cohen
- School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
- Tel Aviv University Center for Nanoscience and Nanotechnology, Tel Aviv, Israel
| | - Eshel Ben-Jacob
- Tel Aviv University Center for Nanoscience and Nanotechnology, Tel Aviv, Israel
- School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
- Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
| | - Yael Hanein
- School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel
- Tel Aviv University Center for Nanoscience and Nanotechnology, Tel Aviv, Israel
- Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
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14
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Kim SY, Lim W. Effect of intermodular connection on fast sparse synchronization in clustered small-world neural networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052716. [PMID: 26651732 DOI: 10.1103/physreve.92.052716] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Indexed: 06/05/2023]
Abstract
We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength J(inter) and the average number of intermodular links per interneuron M(syn)(inter). In contrast to the case of nonclustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intramodular dynamics of subnetworks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intramodular dynamics of subnetworks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching degree between the instantaneous subpopulation spike rates of the subnetworks, and examine whether the sparse synchronization is global or modular. Depending on its magnitude, the intermodular coupling strength J(inter) seems to play "dual" roles for the pacing between spikes in each subnetwork. For large J(inter), due to strong inhibition it plays a destructive role to "spoil" the pacing between spikes, while for small J(inter) it plays a constructive role to "favor" the pacing between spikes. Through competition between the constructive and the destructive roles of J(inter), there exists an intermediate optimal J(inter) at which the pacing degree between spikes becomes maximal. In contrast, the average number of intermodular links per interneuron M(syn)(inter) seems to play a role just to favor the pacing between spikes. With increasing M(syn)(inter), the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes. Furthermore, we employ the realistic sub- and whole-population order parameters, based on the instantaneous sub- and whole-population spike rates, to determine the threshold values for the synchronization-unsynchronization transition in the sub- and whole populations, and the degrees of global and modular sparse synchronization are also measured in terms of the realistic sub- and whole-population statistical-mechanical spiking measures defined by considering both the occupation and the pacing degrees of spikes. It is expected that our results could have implications for the role of the brain plasticity in some functional behaviors associated with population synchronization.
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Affiliation(s)
- Sang-Yoon Kim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 705-115, Korea
| | - Woochang Lim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu 705-115, Korea
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15
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Stratton P, Wiles J. Global segregation of cortical activity and metastable dynamics. Front Syst Neurosci 2015; 9:119. [PMID: 26379514 PMCID: PMC4548222 DOI: 10.3389/fnsys.2015.00119] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Accepted: 08/07/2015] [Indexed: 11/23/2022] Open
Abstract
Cortical activity exhibits persistent metastable dynamics. Assemblies of neurons transiently couple (integrate) and decouple (segregate) at multiple spatiotemporal scales; both integration and segregation are required to support metastability. Integration of distant brain regions can be achieved through long range excitatory projections, but the mechanism supporting long range segregation is not clear. We argue that the thalamocortical matrix connections, which project diffusely from the thalamus to the cortex and have long been thought to support cortical gain control, play an equally-important role in cortical segregation. We present a computational model of the diffuse thalamocortical loop, called the competitive cross-coupling (CXC) spiking network. Simulations of the model show how different levels of tonic input from the brainstem to the thalamus could control dynamical complexity in the cortex, directing transitions between sleep, wakefulness and high attention or vigilance. The model also explains how mutually-exclusive activity could arise across large portions of the cortex, such as between the default-mode and task-positive networks. It is robust to noise but does not require noise to autonomously generate metastability. We conclude that the long range segregation observed in brain activity and required for global metastable dynamics could be provided by the thalamocortical matrix, and is strongly modulated by brainstem input to the thalamus.
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Affiliation(s)
- Peter Stratton
- Queensland Brain Institute, The University of Queensland Brisbane, QLD, Australia ; Centre for Clinical Research, The University of Queensland Brisbane, QLD, Australia
| | - Janet Wiles
- School of Information Technology and Electrical Engineering, The University of Queensland Brisbane, QLD, Australia
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16
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Barrett AB. Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052802. [PMID: 26066207 DOI: 10.1103/physreve.91.052802] [Citation(s) in RCA: 82] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2014] [Indexed: 05/04/2023]
Abstract
To fully characterize the information that two source variables carry about a third target variable, one must decompose the total information into redundant, unique, and synergistic components, i.e., obtain a partial information decomposition (PID). However, Shannon's theory of information does not provide formulas to fully determine these quantities. Several recent studies have begun addressing this. Some possible definitions for PID quantities have been proposed and some analyses have been carried out on systems composed of discrete variables. Here we present an in-depth analysis of PIDs on Gaussian systems, both static and dynamical. We show that, for a broad class of Gaussian systems, previously proposed PID formulas imply that (i) redundancy reduces to the minimum information provided by either source variable and hence is independent of correlation between sources, and (ii) synergy is the extra information contributed by the weaker source when the stronger source is known and can either increase or decrease with correlation between sources. We find that Gaussian systems frequently exhibit net synergy, i.e., the information carried jointly by both sources is greater than the sum of information carried by each source individually. Drawing from several explicit examples, we discuss the implications of these findings for measures of information transfer and information-based measures of complexity, both generally and within a neuroscience setting. Importantly, by providing independent formulas for synergy and redundancy applicable to continuous time-series data, we provide an approach to characterizing and quantifying information sharing amongst complex system variables.
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Affiliation(s)
- Adam B Barrett
- Sackler Centre for Consciousness Science, Department of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom and Department of Clinical Sciences, University of Milan, Milan 20157, Italy
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17
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Kim SY, Lim W. Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 2015; 9:179-200. [PMID: 25834648 DOI: 10.1007/s11571-014-9314-0] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Revised: 09/14/2014] [Accepted: 10/07/2014] [Indexed: 12/13/2022] Open
Abstract
We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.
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Affiliation(s)
- Sang-Yoon Kim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
| | - Woochang Lim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
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Samu D, Seth AK, Nowotny T. Influence of wiring cost on the large-scale architecture of human cortical connectivity. PLoS Comput Biol 2014; 10:e1003557. [PMID: 24699277 PMCID: PMC3974635 DOI: 10.1371/journal.pcbi.1003557] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2013] [Accepted: 02/17/2014] [Indexed: 12/30/2022] Open
Abstract
In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained ('random'), connection length preserving ('spatial'), and connection length optimised ('reduced') surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain.
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Affiliation(s)
- David Samu
- Sussex Neuroscience, CCNR, Informatics, University of Sussex, Falmer, Brighton, United Kingdom
- * E-mail:
| | - Anil K. Seth
- Sussex Neuroscience, CCNR, Informatics, University of Sussex, Falmer, Brighton, United Kingdom
- Sackler Centre for Consciousness Science, Informatics, University of Sussex, Falmer, Brighton, United Kingdom
| | - Thomas Nowotny
- Sussex Neuroscience, CCNR, Informatics, University of Sussex, Falmer, Brighton, United Kingdom
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19
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Glazebrook JF. Book review. COGN SYST RES 2014. [DOI: 10.1016/j.cogsys.2013.01.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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20
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Hu B, Ma J, Tang J. Selection of multiarmed spiral waves in a regular network of neurons. PLoS One 2013; 8:e69251. [PMID: 23935966 PMCID: PMC3732196 DOI: 10.1371/journal.pone.0069251] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2013] [Accepted: 06/06/2013] [Indexed: 11/18/2022] Open
Abstract
Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.
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Affiliation(s)
- Bolin Hu
- Department of Physics, Lanzhou University of Technology, Lanzhou, China
| | - Jun Ma
- Department of Physics, Lanzhou University of Technology, Lanzhou, China
- * E-mail:
| | - Jun Tang
- College of Science, China University of Mining and Technology, Xuzhou, China
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21
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Mäki-Marttunen T, Aćimović J, Ruohonen K, Linne ML. Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework. PLoS One 2013; 8:e69373. [PMID: 23935998 PMCID: PMC3723901 DOI: 10.1371/journal.pone.0069373] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Accepted: 06/07/2013] [Indexed: 11/25/2022] Open
Abstract
The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.
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Affiliation(s)
- Tuomo Mäki-Marttunen
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland.
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22
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Wildie M, Shanahan M. Metastability and chimera states in modular delay and pulse-coupled oscillator networks. CHAOS (WOODBURY, N.Y.) 2012; 22:043131. [PMID: 23278066 DOI: 10.1063/1.4766592] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Modular networks of delay-coupled and pulse-coupled oscillators are presented, which display both transient (metastable) synchronization dynamics and the formation of a large number of "chimera" states characterized by coexistent synchronized and desynchronized subsystems. We consider networks based on both community and small-world topologies. It is shown through simulation that the metastable behaviour of the system is dependent in all cases on connection delay, and a critical region is found that maximizes indices of both metastability and the prevalence of chimera states. We show dependence of phase coherence in synchronous oscillation on the level and strength of external connectivity between communities, and demonstrate that synchronization dynamics are dependent on the modular structure of the network. The long-term behaviour of the system is considered and the relevance of the model briefly discussed with emphasis on biological and neurobiological systems.
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Affiliation(s)
- Mark Wildie
- Department of Computing, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom.
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23
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Shanahan M, Wildie M. Knotty-centrality: finding the connective core of a complex network. PLoS One 2012; 7:e36579. [PMID: 22590571 PMCID: PMC3348887 DOI: 10.1371/journal.pone.0036579] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2011] [Accepted: 04/10/2012] [Indexed: 11/19/2022] Open
Abstract
A network measure called knotty-centrality is defined that quantifies the extent to which a given subset of a graph's nodes constitutes a densely intra-connected topologically central connective core. Using this measure, the knotty centre of a network is defined as a sub-graph with maximal knotty-centrality. A heuristic algorithm for finding subsets of a network with high knotty-centrality is presented, and this is applied to previously published brain structural connectivity data for the cat and the human, as well as to a number of other networks. The cognitive implications of possessing a connective core with high knotty-centrality are briefly discussed.
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Affiliation(s)
- Murray Shanahan
- Department of Computing, Imperial College London, London, United Kingdom.
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24
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Buzzi J, Zambotti L. Mean mutual information and symmetry breaking for finite random fields. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2012. [DOI: 10.1214/11-aihp416] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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25
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Wildie M, Shanahan M. Establishing Communication between Neuronal Populations through Competitive Entrainment. Front Comput Neurosci 2012; 5:62. [PMID: 22275892 PMCID: PMC3257854 DOI: 10.3389/fncom.2011.00062] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2011] [Accepted: 12/12/2011] [Indexed: 11/30/2022] Open
Abstract
The role of gamma frequency oscillation in neuronal interaction, and the relationship between oscillation and information transfer between neurons, has been the focus of much recent research. While the biological mechanisms responsible for gamma oscillation and the properties of resulting networks are well studied, the dynamics of changing phase coherence between oscillating neuronal populations are not well understood. To this end we develop a computational model of competitive selection between multiple stimuli, where the selection and transfer of population-encoded information arises from competition between converging stimuli to entrain a target population of neurons. Oscillation is generated by Pyramidal-Interneuronal Network Gamma through the action of recurrent synaptic connections between a locally connected network of excitatory and inhibitory neurons. Competition between stimuli is driven by differences in coherence of oscillation, while transmission of a single selected stimulus is enabled between generating and receiving neurons via Communication-through-Coherence. We explore the effect of varying synaptic parameters on the competitive transmission of stimuli over different neuron models, and identify a continuous region within the parameter space of the recurrent synaptic loop where inhibition-induced oscillation results in entrainment of target neurons. Within this optimal region we find that competition between stimuli of equal coherence results in model output that alternates between representation of the stimuli, in a manner strongly resembling well-known biological phenomena resulting from competitive stimulus selection such as binocular rivalry.
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Affiliation(s)
- Mark Wildie
- Department of Computing, Imperial College London London, UK
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26
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Seth AK, Barrett AB, Barnett L. Causal density and integrated information as measures of conscious level. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:3748-3767. [PMID: 21893526 DOI: 10.1098/rsta.2011.0079] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Because conscious scenes are distinguished by the same dynamical features, these measures are therefore good candidates for reflecting conscious level. After reviewing the theoretical background, we present new simulation results demonstrating similarities and differences between the measures, and we discuss remaining challenges in the practical application of the measures to empirically obtained data.
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Affiliation(s)
- Anil K Seth
- Sackler Centre for Consciousness Science, and School of Informatics, University of Sussex, Brighton BN1 9QJ, UK.
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27
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Shein-Idelson M, Ben-Jacob E, Hanein Y. Engineered neuronal circuits: a new platform for studying the role of modular topology. FRONTIERS IN NEUROENGINEERING 2011; 4:10. [PMID: 21991254 PMCID: PMC3180629 DOI: 10.3389/fneng.2011.00010] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/24/2011] [Accepted: 08/23/2011] [Indexed: 12/05/2022]
Abstract
Neuron–glia cultures serve as a valuable model system for exploring the bio-molecular activity of single cells. Since neurons in culture can be conveniently recorded with great fidelity from many sites simultaneously, it has long been suggested that uniform cultured neurons may also be used to investigate network-level mechanisms pertinent to information processing, activity propagation, memory, and learning. But how much of the functionality of neural circuits can be retained in vitro remains an open question. Recent studies utilizing patterned networks suggest that they provide a most useful platform to address fundamental questions in neuroscience. Here we review recent efforts in the realm of patterned networks’ activity investigations. We give a brief overview of the patterning methods and experimental approaches commonly employed in the field, and summarize the main results reported in the literature. The general picture that emerges from these reports indicates that patterned networks with uniform connectivity do not exhibit unique activity patterns. Rather, their activity is very similar to that of unpatterned uniform networks. However, by breaking the connectivity homogeneity, using a modular architecture, it is possible to introduce pronounced topology-related gating and delay effects. These findings suggest that patterned cultured networks may serve as a new platform for studying the role of modularity in neuronal circuits.
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28
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Hun Ki Lim, Keniston LP, Cios KJ. Modeling of Multisensory Convergence with a Network of Spiking Neurons: A Reverse Engineering Approach. IEEE Trans Biomed Eng 2011; 58:1940-9. [DOI: 10.1109/tbme.2011.2125962] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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29
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Lim HK, Keniston LP, Shin JH, Allman BL, Meredith MA, Cios KJ. Connectional parameters determine multisensory processing in a spiking network model of multisensory convergence. Exp Brain Res 2011; 213:329-39. [PMID: 21484394 DOI: 10.1007/s00221-011-2671-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2010] [Accepted: 03/30/2011] [Indexed: 02/02/2023]
Abstract
For the brain to synthesize information from different sensory modalities, connections from different sensory systems must converge onto individual neurons. However, despite being the definitive, first step in the multisensory process, little is known about multisensory convergence at the neuronal level. This lack of knowledge may be due to the difficulty for biological experiments to manipulate and test the connectional parameters that define convergence. Therefore, the present study used a computational network of spiking neurons to measure the influence of convergence from two separate projection areas on the responses of neurons in a convergent area. Systematic changes in the proportion of extrinsic projections, the proportion of intrinsic connections, or the amount of local inhibitory contacts affected the multisensory properties of neurons in the convergent area by influencing (1) the proportion of multisensory neurons generated, (2) the proportion of neurons that generate integrated multisensory responses, and (3) the magnitude of multisensory integration. These simulations provide insight into the connectional parameters of convergence that contribute to the generation of populations of multisensory neurons in different neural regions as well as indicate that the simple effect of multisensory convergence is sufficient to generate multisensory properties like those of biological multisensory neurons.
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Affiliation(s)
- H K Lim
- Department of Computer Science, School of Engineering, Virginia Commonwealth University School of Medicine, Richmond, VA, USA
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30
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Prettejohn BJ, Berryman MJ, McDonnell MD. Methods for generating complex networks with selected structural properties for simulations: a review and tutorial for neuroscientists. Front Comput Neurosci 2011; 5:11. [PMID: 21441986 PMCID: PMC3059456 DOI: 10.3389/fncom.2011.00011] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2010] [Accepted: 02/14/2011] [Indexed: 11/16/2022] Open
Abstract
Many simulations of networks in computational neuroscience assume completely homogenous random networks of the Erdös–Rényi type, or regular networks, despite it being recognized for some time that anatomical brain networks are more complex in their connectivity and can, for example, exhibit the “scale-free” and “small-world” properties. We review the most well known algorithms for constructing networks with given non-homogeneous statistical properties and provide simple pseudo-code for reproducing such networks in software simulations. We also review some useful mathematical results and approximations associated with the statistics that describe these network models, including degree distribution, average path length, and clustering coefficient. We demonstrate how such results can be used as partial verification and validation of implementations. Finally, we discuss a sometimes overlooked modeling choice that can be crucially important for the properties of simulated networks: that of network directedness. The most well known network algorithms produce undirected networks, and we emphasize this point by highlighting how simple adaptations can instead produce directed networks.
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Affiliation(s)
- Brenton J Prettejohn
- Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia Mawson Lakes, SA, Australia
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Barrett AB, Seth AK. Practical measures of integrated information for time-series data. PLoS Comput Biol 2011; 7:e1001052. [PMID: 21283779 PMCID: PMC3024259 DOI: 10.1371/journal.pcbi.1001052] [Citation(s) in RCA: 95] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2010] [Accepted: 12/06/2010] [Indexed: 11/29/2022] Open
Abstract
A recent measure of 'integrated information', Φ(DM), quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ(DM) is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ(DM) can rarely be measured in practice. Here, we describe two new measures, Φ(E) and Φ(AR), that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.
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Affiliation(s)
- Adam B Barrett
- Sackler Centre for Consciousness Science and School of Informatics, University of Sussex, Brighton, United Kingdom.
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Aleksander I, Gamez D. Informational theories of consciousness: a review and extension. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2011; 718:139-47. [PMID: 21744216 DOI: 10.1007/978-1-4614-0164-3_12] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
In recent years a number of people have suggested that there is a close link between conscious experience and the differentiation and integration of information in certain areas of the brain. The balance between differentiation and integration is often called information integration, and a number of algorithms for measuring it have been put forward, which can be used to make predictions about consciousness and to understand the relationships between neurons in a network. One of the key problems with the current information integration measures is that they take a lot of computer processing power, which limits their application to networks of around a dozen neurons. There are also more general issues about whether the current algorithms accurately reflect the consciousness associated with a system. This paper addresses these issues by exploring a new automata-based algorithm for the calculation of information integration. To benchmark different approaches we implemented the Balduzzi and Tononi algorithm as a plugin to the SpikeStream neural simulator, and used it to carry out some preliminary comparisons of the liveliness and Φ measures on simple four neuron networks.
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Affiliation(s)
- Igor Aleksander
- Department of Electrical Engineering, Imperial College, London SW7 2BT, UK.
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Meunier D, Lambiotte R, Bullmore ET. Modular and hierarchically modular organization of brain networks. Front Neurosci 2010; 4:200. [PMID: 21151783 PMCID: PMC3000003 DOI: 10.3389/fnins.2010.00200] [Citation(s) in RCA: 640] [Impact Index Per Article: 45.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2010] [Accepted: 11/17/2010] [Indexed: 11/13/2022] Open
Abstract
Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.
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Affiliation(s)
- David Meunier
- Centre for Speech, Language and the Brain, Department of Experimental Psychology, University of Cambridge Cambridge, UK
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Stratton P, Wiles J. Self-sustained non-periodic activity in networks of spiking neurons: The contribution of local and long-range connections and dynamic synapses. Neuroimage 2010; 52:1070-9. [DOI: 10.1016/j.neuroimage.2010.01.027] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2009] [Revised: 01/05/2010] [Accepted: 01/11/2010] [Indexed: 10/19/2022] Open
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Guo D, Li C. Self-sustained irregular activity in 2-D small-world networks of excitatory and inhibitory neurons. ACTA ACUST UNITED AC 2010; 21:895-905. [PMID: 20388595 DOI: 10.1109/tnn.2010.2044419] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
In this paper, we study the self-sustained irregular firing activity in 2-D small-world (SW) neural networks consisting of both excitatory and inhibitory neurons by computational modeling. For a proper proportion of unidirectional shortcuts, the stable self-sustained activity with irregular firing states indeed occurs in the considered network. By varying the shortcut density while keeping other system parameters fixed, different levels of irregular firing states, from weakly irregular to Poisson-like and burst firing states, are obtained in 2-D SW neural networks. It is also observed that this activity is sensitive to small perturbations, which might provide a possible mechanism for producing chaos. On the other hand, we find that several other system parameters, such as the network size and refractory period, have significant impact on this activity. Further simulation results show that the 2-D SW neural network can sustain such long-lasting firing behavior by using a smaller number of connections than the random neural network.
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Affiliation(s)
- Daqing Guo
- School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
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Barrett AB, Barnett L, Seth AK. Multivariate Granger causality and generalized variance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041907. [PMID: 20481753 DOI: 10.1103/physreve.81.041907] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2010] [Indexed: 05/04/2023]
Abstract
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy." Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.
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Affiliation(s)
- Adam B Barrett
- Sackler Centre for Consciousness Science, School of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom.
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Shanahan M. Metastable chimera states in community-structured oscillator networks. CHAOS (WOODBURY, N.Y.) 2010; 20:013108. [PMID: 20370263 DOI: 10.1063/1.3305451] [Citation(s) in RCA: 138] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
A system of symmetrically coupled identical oscillators with phase lag is presented, which is capable of generating a large repertoire of transient (metastable) "chimera" states in which synchronization and desynchronization coexist. The oscillators are organized into communities, such that each oscillator is connected to all its peers in the same community and to a subset of the oscillators in other communities. Measures are introduced for quantifying metastability, the prevalence of chimera states, and the variety of such states a system generates. By simulation, it is shown that each of these measures is maximized when the phase lag of the model is close, but not equal, to pi/2. The relevance of the model to a number of fields is briefly discussed with particular emphasis on brain dynamics.
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Affiliation(s)
- Murray Shanahan
- Department of Computing, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom
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Seth AK. A MATLAB toolbox for Granger causal connectivity analysis. J Neurosci Methods 2009; 186:262-73. [PMID: 19961876 DOI: 10.1016/j.jneumeth.2009.11.020] [Citation(s) in RCA: 452] [Impact Index Per Article: 30.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2009] [Revised: 11/21/2009] [Accepted: 11/23/2009] [Indexed: 10/20/2022]
Abstract
Assessing directed functional connectivity from time series data is a key challenge in neuroscience. One approach to this problem leverages a combination of Granger causality analysis and network theory. This article describes a freely available MATLAB toolbox--'Granger causal connectivity analysis' (GCCA)--which provides a core set of methods for performing this analysis on a variety of neuroscience data types including neuroelectric, neuromagnetic, functional MRI, and other neural signals. The toolbox includes core functions for Granger causality analysis of multivariate steady-state and event-related data, functions to preprocess data, assess statistical significance and validate results, and to compute and display network-level indices of causal connectivity including 'causal density' and 'causal flow'. The toolbox is deliberately small, enabling its easy assimilation into the repertoire of researchers. It is however readily extensible given proficiency with the MATLAB language.
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Affiliation(s)
- Anil K Seth
- Sackler Centre for Consciousness Science and School of Informatics, University of Sussex, Brighton, BN1 9QJ, UK.
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Barnett L, Buckley CL, Bullock S. Neural complexity and structural connectivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051914. [PMID: 19518487 DOI: 10.1103/physreve.79.051914] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2008] [Revised: 03/13/2009] [Indexed: 05/27/2023]
Abstract
Tononi [Proc. Natl. Acad. Sci. U.S.A. 91, 5033 (1994)] proposed a measure of neural complexity based on mutual information between complementary subsystems of a given neural network, which has attracted much interest in the neuroscience community and beyond. We develop an approximation of the measure for a popular Gaussian model which, applied to a continuous-time process, elucidates the relationship between the complexity of a neural system and its structural connectivity. Moreover, the approximation is accurate for weakly coupled systems and computationally cheap, scaling polynomially with system size in contrast to the full complexity measure, which scales exponentially. We also discuss connectivity normalization and resolve some issues stemming from an ambiguity in the original Gaussian model.
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Affiliation(s)
- L Barnett
- Department of Informatics, Centre for Computational Neuroscience and Robotics, School of Science and Technology, University of Sussex, Brighton BN1 9QH, United Kingdom.
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