1
|
Zhang R, Wang Z, Wu T, Cai Y, Tao L, Xiao ZC, Li Y. Learning spiking neuronal networks with artificial neural networks: neural oscillations. J Math Biol 2024; 88:65. [PMID: 38630136 DOI: 10.1007/s00285-024-02081-0] [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: 11/22/2022] [Revised: 06/30/2023] [Accepted: 03/05/2024] [Indexed: 04/19/2024]
Abstract
First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.
Collapse
Affiliation(s)
- Ruilin Zhang
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China
- Yuanpei College, Peking University, 100871, Beijing, China
| | - Zhongyi Wang
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China
- School of Mathematical Sciences, Peking University, 100871, Beijing, China
| | - Tianyi Wu
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China
- School of Mathematical Sciences, Peking University, 100871, Beijing, China
| | - Yuhang Cai
- Department of Mathematics, University of California, 94720, Berkeley, CA, USA
| | - Louis Tao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China.
- Center for Quantitative Biology, Peking University, 100871, Beijing, China.
| | - Zhuo-Cheng Xiao
- Courant Institute of Mathematical Sciences, New York University, 10003, New York, NY, USA.
| | - Yao Li
- Department of Mathematics and Statistics, University of Massachusetts Amherst, 01003, Amherst, MA, USA.
| |
Collapse
|
2
|
Xiao ZC, Lin KK. Multilevel monte carlo for cortical circuit models. J Comput Neurosci 2022; 50:9-15. [PMID: 35000059 DOI: 10.1007/s10827-021-00807-3] [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: 09/30/2020] [Revised: 11/18/2021] [Accepted: 11/24/2021] [Indexed: 11/25/2022]
Abstract
Multilevel Monte Carlo (MLMC) methods aim to speed up computation of statistics from dynamical simulations. MLMC is easy to implement and is sometimes very effective, but its efficacy may depend on the underlying dynamics. We apply MLMC to networks of spiking neurons and assess its effectiveness on prototypical models of cortical circuitry under different conditions. We find that MLMC can be very efficient for computing reliable features, i.e., features of network dynamics that are reproducible upon repeated presentation of the same external forcing. In contrast, MLMC is less effective for complex, internally generated activity. Qualitative explanations are given using concepts from random dynamical systems theory.
Collapse
Affiliation(s)
- Zhuo-Cheng Xiao
- Courant Institute of Mathematical Sciences, New York University, New York, USA.
| | - Kevin K Lin
- School of Mathematical Sciences, University of Arizona, Tucson, Arizona, USA
| |
Collapse
|
3
|
Cai Y, Wu T, Tao L, Xiao ZC. Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds. Front Comput Neurosci 2021; 15:678688. [PMID: 34489666 PMCID: PMC8418102 DOI: 10.3389/fncom.2021.678688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 07/23/2021] [Indexed: 12/02/2022] Open
Abstract
Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.
Collapse
Affiliation(s)
- Yuhang Cai
- Department of Statistics, University of Chicago, Chicago, IL, United States
| | - Tianyi Wu
- School of Mathematical Sciences, Peking University, Beijing, China.,Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, China
| | - Louis Tao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, China.,Center for Quantitative Biology, Peking University, Beijing, China
| | - Zhuo-Cheng Xiao
- Courant Institute of Mathematical Sciences, New York University, New York, NY, United States
| |
Collapse
|
4
|
Shao Y, Zhang J, Tao L. Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure. PLoS Comput Biol 2020; 16:e1007265. [PMID: 32516336 PMCID: PMC7304648 DOI: 10.1371/journal.pcbi.1007265] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Revised: 06/19/2020] [Accepted: 04/29/2020] [Indexed: 11/22/2022] Open
Abstract
Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.
Collapse
Affiliation(s)
- Yuxiu Shao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, China
| | - Jiwei Zhang
- School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, China
| | - Louis Tao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, China
- Center for Quantitative Biology, Peking University, Beijing, China
| |
Collapse
|
5
|
Li Y, Xu H. Stochastic neural field model: multiple firing events and correlations. J Math Biol 2019; 79:1169-1204. [PMID: 31292682 DOI: 10.1007/s00285-019-01389-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Revised: 03/05/2019] [Indexed: 11/28/2022]
Abstract
This paper studies a nonlinear dynamical phenomenon called the multiple firing event (MFE) in a spatially heterogeneous stochastic neural field model, which is extended from that in our previous paper (Li et al. in J Math Biol 78:83-115, 2018). MFEs are a partially synchronized spiking barrages that are believed to be responsible for the Gamma oscillation. Rigorous results about the stochastic stability and the law of large numbers are proved, which further imply the well-definedness and computability of many quantities related to MFEs. Then we devote to study spatial and temporal properties of MFEs. Our key finding is that MFEs are spatially correlated but the spatial correlation decays quickly. Detailed mathematical justifications are made based on our qualitative models that aim to demonstrate the mechanism of MFEs.
Collapse
Affiliation(s)
- Yao Li
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01002, USA.
| | - Hui Xu
- Department of Mathematics, Amherst College, Amherst, MA, 01002, USA
| |
Collapse
|
6
|
Xu ZQJ, Crodelle J, Zhou D, Cai D. Maximum entropy principle analysis in network systems with short-time recordings. Phys Rev E 2019; 99:022409. [PMID: 30934291 DOI: 10.1103/physreve.99.022409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Indexed: 11/07/2022]
Abstract
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in general is often required, e.g., hours of spiking recordings of neurons in neuronal networks. The issue of whether the MEP analysis can be successfully applied to network systems with data from short-time recordings has yet to be fully addressed. In this work, we investigate relationships underlying the probability distributions, moments, and effective interactions in the MEP analysis and then show that, with short-time recordings of network dynamics, the MEP analysis can be applied to reconstructing probability distributions of network states that is much more accurate than the one directly measured from the short-time recording. Using spike trains obtained from both Hodgkin-Huxley neuronal networks and electrophysiological experiments, we verify our results and demonstrate that MEP analysis provides a tool to investigate the neuronal population coding properties for short-time recordings.
Collapse
Affiliation(s)
- Zhi-Qin John Xu
- NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
| | - Jennifer Crodelle
- Courant Institute of Mathematical Sciences, New York University, New York, New York, USA
| | - Douglas Zhou
- School of Mathematical Sciences, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China
| | - David Cai
- NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.,Courant Institute of Mathematical Sciences, New York University, New York, New York, USA.,School of Mathematical Sciences, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China.,Center for Neural Science, New York University, New York, New York, USA
| |
Collapse
|
7
|
Zhang J, Shao Y, Rangan AV, Tao L. A coarse-graining framework for spiking neuronal networks: from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs. J Comput Neurosci 2019; 46:211-232. [PMID: 30788694 DOI: 10.1007/s10827-019-00712-w] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2018] [Revised: 01/27/2019] [Accepted: 01/31/2019] [Indexed: 11/29/2022]
Abstract
Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81-104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.
Collapse
Affiliation(s)
- Jiwei Zhang
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China.,Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China
| | - Yuxiu Shao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China.,Center for Quantitative Biology, Peking University, Beijing, 100871, China
| | - Aaditya V Rangan
- Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
| | - Louis Tao
- Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetic Engineering, School of Life Sciences, Peking University, Beijing, 100871, China. .,Center for Quantitative Biology, Peking University, Beijing, 100871, China.
| |
Collapse
|
8
|
Lei H, Yu Y, Zhu S, Rangan AV. Intrinsic and Network Mechanisms Constrain Neural Synchrony in the Moth Antennal Lobe. Front Physiol 2016; 7:80. [PMID: 27014082 PMCID: PMC4781831 DOI: 10.3389/fphys.2016.00080] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2015] [Accepted: 02/18/2016] [Indexed: 11/30/2022] Open
Abstract
Projection-neurons (PNs) within the antennal lobe (AL) of the hawkmoth respond vigorously to odor stimulation, with each vigorous response followed by a ~1 s period of suppression—dubbed the “afterhyperpolarization-phase,” or AHP-phase. Prior evidence indicates that this AHP-phase is important for the processing of odors, but the mechanisms underlying this phase and its function remain unknown. We investigate this issue. Beginning with several physiological experiments, we find that pharmacological manipulation of the AL yields surprising results. Specifically, (a) the application of picrotoxin (PTX) lengthens the AHP-phase and reduces PN activity, whereas (b) the application of Bicuculline-methiodide (BIC) reduces the AHP-phase and increases PN activity. These results are curious, as both PTX and BIC are inhibitory-receptor antagonists. To resolve this conundrum, we speculate that perhaps (a) PTX reduces PN activity through a disinhibitory circuit involving a heterogeneous population of local-neurons, and (b) BIC acts to hamper certain intrinsic currents within the PNs that contribute to the AHP-phase. To probe these hypotheses further we build a computational model of the AL and benchmark our model against our experimental observations. We find that, for parameters which satisfy these benchmarks, our model exhibits a particular kind of synchronous activity: namely, “multiple-firing-events” (MFEs). These MFEs are causally-linked sequences of spikes which emerge stochastically, and turn out to have important dynamical consequences for all the experimentally observed phenomena we used as benchmarks. Taking a step back, we extract a few predictions from our computational model pertaining to the real AL: Some predictions deal with the MFEs we expect to see in the real AL, whereas other predictions involve the runaway synchronization that we expect when BIC-application hampers the AHP-phase. By examining the literature we see support for the former, and we perform some additional experiments to confirm the latter. The confirmation of these predictions validates, at least partially, our initial speculation above. We conclude that the AL is poised in a state of high-gain; ready to respond vigorously to even faint stimuli. After each response the AHP-phase functions to prevent runaway synchronization and to “reset” the AL for another odor-specific response.
Collapse
Affiliation(s)
- Hong Lei
- Department of Neuroscience, The University of Arizona Tucson, AZ, USA
| | - Yanxue Yu
- Institute of Plant Quarantine, Chinese Academy of Inspection and Quarantine Beijing, China
| | - Shuifang Zhu
- Institute of Plant Quarantine, Chinese Academy of Inspection and Quarantine Beijing, China
| | - Aaditya V Rangan
- Department of Mathematics, Courant Institute of Mathematical Sciences, New York University New York, NY, USA
| |
Collapse
|
9
|
Newhall KA, Shkarayev MS, Kramer PR, Kovačič G, Cai D. Synchrony in stochastically driven neuronal networks with complex topologies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052806. [PMID: 26066211 DOI: 10.1103/physreve.91.052806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Indexed: 06/04/2023]
Abstract
We study the synchronization of a stochastically driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering. The synchrony is induced by cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is completely independent of the synaptic coupling, and depends solely on the external drive. On the other hand, the ability for the network to maintain synchrony depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability of repeated cascading total firing events, we go beyond mean-field and treelike approximations and conduct a detailed second-order calculation taking into account local clustering. Our explicit analytical results are shown to give excellent agreement with direct numerical simulations for the particular preferential-attachment network model investigated.
Collapse
Affiliation(s)
- Katherine A Newhall
- Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, USA
| | - Maxim S Shkarayev
- Department of Physics and Astronomy, Iowa State University, 12 Physics Hall, Ames, Iowa 50011-3160, USA
| | - Peter R Kramer
- Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA
| | - Gregor Kovačič
- Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA
| | - David Cai
- Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, 251 Mercer Street, New York, New York 10012, USA
- Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Dong Chuan Road 800, Shanghai 200240, China
- NYUAD Institute, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates
| |
Collapse
|
10
|
Cavallari S, Panzeri S, Mazzoni A. Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks. Front Neural Circuits 2014; 8:12. [PMID: 24634645 PMCID: PMC3943173 DOI: 10.3389/fncir.2014.00012] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2013] [Accepted: 02/07/2014] [Indexed: 11/13/2022] Open
Abstract
Models of networks of Leaky Integrate-and-Fire (LIF) neurons are a widely used tool for theoretical investigations of brain function. These models have been used both with current- and conductance-based synapses. However, the differences in the dynamics expressed by these two approaches have been so far mainly studied at the single neuron level. To investigate how these synaptic models affect network activity, we compared the single neuron and neural population dynamics of conductance-based networks (COBNs) and current-based networks (CUBNs) of LIF neurons. These networks were endowed with sparse excitatory and inhibitory recurrent connections, and were tested in conditions including both low- and high-conductance states. We developed a novel procedure to obtain comparable networks by properly tuning the synaptic parameters not shared by the models. The so defined comparable networks displayed an excellent and robust match of first order statistics (average single neuron firing rates and average frequency spectrum of network activity). However, these comparable networks showed profound differences in the second order statistics of neural population interactions and in the modulation of these properties by external inputs. The correlation between inhibitory and excitatory synaptic currents and the cross-neuron correlation between synaptic inputs, membrane potentials and spike trains were stronger and more stimulus-modulated in the COBN. Because of these properties, the spike train correlation carried more information about the strength of the input in the COBN, although the firing rates were equally informative in both network models. Moreover, the network activity of COBN showed stronger synchronization in the gamma band, and spectral information about the input higher and spread over a broader range of frequencies. These results suggest that the second order statistics of network dynamics depend strongly on the choice of synaptic model.
Collapse
Affiliation(s)
- Stefano Cavallari
- Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia Rovereto, Italy
| | - Stefano Panzeri
- Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia Rovereto, Italy ; Max Planck Institute for Biological Cybernetics Tübingen, Germany
| | - Alberto Mazzoni
- Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia Rovereto, Italy ; The BioRobotics Institute, Scuola Superiore Sant'Anna Pisa, Italy
| |
Collapse
|
11
|
Zhou D, Xiao Y, Zhang Y, Xu Z, Cai D. Granger causality network reconstruction of conductance-based integrate-and-fire neuronal systems. PLoS One 2014; 9:e87636. [PMID: 24586285 PMCID: PMC3929548 DOI: 10.1371/journal.pone.0087636] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2013] [Accepted: 12/25/2013] [Indexed: 12/18/2022] Open
Abstract
Reconstruction of anatomical connectivity from measured dynamical activities of coupled neurons is one of the fundamental issues in the understanding of structure-function relationship of neuronal circuitry. Many approaches have been developed to address this issue based on either electrical or metabolic data observed in experiment. The Granger causality (GC) analysis remains one of the major approaches to explore the dynamical causal connectivity among individual neurons or neuronal populations. However, it is yet to be clarified how such causal connectivity, i.e., the GC connectivity, can be mapped to the underlying anatomical connectivity in neuronal networks. We perform the GC analysis on the conductance-based integrate-and-fire (I&F) neuronal networks to obtain their causal connectivity. Through numerical experiments, we find that the underlying synaptic connectivity amongst individual neurons or subnetworks, can be successfully reconstructed by the GC connectivity constructed from voltage time series. Furthermore, this reconstruction is insensitive to dynamical regimes and can be achieved without perturbing systems and prior knowledge of neuronal model parameters. Surprisingly, the synaptic connectivity can even be reconstructed by merely knowing the raster of systems, i.e., spike timing of neurons. Using spike-triggered correlation techniques, we establish a direct mapping between the causal connectivity and the synaptic connectivity for the conductance-based I&F neuronal networks, and show the GC is quadratically related to the coupling strength. The theoretical approach we develop here may provide a framework for examining the validity of the GC analysis in other settings.
Collapse
Affiliation(s)
- Douglas Zhou
- Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
| | - Yanyang Xiao
- Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
| | - Yaoyu Zhang
- Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
| | - Zhiqin Xu
- Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
| | - David Cai
- Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China
- Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York, United States of America
- NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
| |
Collapse
|
12
|
A coarse-grained framework for spiking neuronal networks: between homogeneity and synchrony. J Comput Neurosci 2013; 37:81-104. [DOI: 10.1007/s10827-013-0488-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Revised: 11/06/2013] [Accepted: 11/11/2013] [Indexed: 10/25/2022]
|