1
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Ratas I, Pyragas K. Interplay of different synchronization modes and synaptic plasticity in a system of class I neurons. Sci Rep 2022; 12:19631. [PMID: 36385488 PMCID: PMC9668974 DOI: 10.1038/s41598-022-24001-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 11/08/2022] [Indexed: 11/17/2022] Open
Abstract
We analyze the effect of spike-timing-dependent plasticity (STDP) on a system of pulse-coupled class I neurons. Our research begins with a system of two mutually connected quadratic integrate-and-fire (QIF) neurons, which are canonical representatives of class I neurons. Along with various asymptotic modes previously observed in other neuronal models with plastic synapses, we found a stable synchronous mode characterized by unidirectional link from a slower neuron to a faster neuron. In this frequency-locked mode, the faster neuron emits multiple spikes per cycle of the slower neuron. We analytically obtain the Arnold tongues for this mode without STDP and with STDP. We also consider larger plastic networks of QIF neurons and show that the detected mode can manifest itself in such a way that slow neurons become pacemakers. As a result, slow and fast neurons can form large synchronous clusters that generate low-frequency oscillations. We demonstrate the generality of the results obtained with two connected QIF neurons using Wang-Buzsáki and Morris-Lecar biophysically plausible class I neuron models.
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Affiliation(s)
- Irmantas Ratas
- Center for Physical Sciences and Technology, 10257, Vilnius, Lithuania.
| | - Kestutis Pyragas
- Center for Physical Sciences and Technology, 10257, Vilnius, Lithuania
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2
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Kromer JA, Tass PA. Synaptic reshaping of plastic neuronal networks by periodic multichannel stimulation with single-pulse and burst stimuli. PLoS Comput Biol 2022; 18:e1010568. [PMID: 36327232 PMCID: PMC9632832 DOI: 10.1371/journal.pcbi.1010568] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 09/14/2022] [Indexed: 11/06/2022] Open
Abstract
Synaptic dysfunction is associated with several brain disorders, including Alzheimer's disease, Parkinson's disease (PD) and obsessive compulsive disorder (OCD). Utilizing synaptic plasticity, brain stimulation is capable of reshaping synaptic connectivity. This may pave the way for novel therapies that specifically counteract pathological synaptic connectivity. For instance, in PD, novel multichannel coordinated reset stimulation (CRS) was designed to counteract neuronal synchrony and down-regulate pathological synaptic connectivity. CRS was shown to entail long-lasting therapeutic aftereffects in PD patients and related animal models. This is in marked contrast to conventional deep brain stimulation (DBS) therapy, where PD symptoms return shortly after stimulation ceases. In the present paper, we study synaptic reshaping by periodic multichannel stimulation (PMCS) in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity (STDP). During PMCS, phase-shifted periodic stimulus trains are delivered to segregated neuronal subpopulations. Harnessing STDP, PMCS leads to changes of the synaptic network structure. We found that the PMCS-induced changes of the network structure depend on both the phase lags between stimuli and the shape of individual stimuli. Single-pulse stimuli and burst stimuli with low intraburst frequency down-regulate synapses between neurons receiving stimuli simultaneously. In contrast, burst stimuli with high intraburst frequency up-regulate these synapses. We derive theoretical approximations of the stimulation-induced network structure. This enables us to formulate stimulation strategies for inducing a variety of network structures. Our results provide testable hypotheses for future pre-clinical and clinical studies and suggest that periodic multichannel stimulation may be suitable for reshaping plastic neuronal networks to counteract pathological synaptic connectivity. Furthermore, we provide novel insight on how the stimulus type may affect the long-lasting outcome of conventional DBS. This may strongly impact parameter adjustment procedures for clinical DBS, which, so far, primarily focused on acute effects of stimulation.
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Affiliation(s)
- Justus A Kromer
- Department of Neurosurgery, Stanford University, Stanford, California, United States of America
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, California, United States of America
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3
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Khaledi-Nasab A, Kromer JA, Tass PA. Long-Lasting Desynchronization of Plastic Neuronal Networks by Double-Random Coordinated Reset Stimulation. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:864859. [PMID: 36926109 PMCID: PMC10013062 DOI: 10.3389/fnetp.2022.864859] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 03/18/2022] [Indexed: 11/13/2022]
Abstract
Hypersynchrony of neuronal activity is associated with several neurological disorders, including essential tremor and Parkinson's disease (PD). Chronic high-frequency deep brain stimulation (HF DBS) is the standard of care for medically refractory PD. Symptoms may effectively be suppressed by HF DBS, but return shortly after cessation of stimulation. Coordinated reset (CR) stimulation is a theory-based stimulation technique that was designed to specifically counteract neuronal synchrony by desynchronization. During CR, phase-shifted stimuli are delivered to multiple neuronal subpopulations. Computational studies on CR stimulation of plastic neuronal networks revealed long-lasting desynchronization effects obtained by down-regulating abnormal synaptic connectivity. This way, networks are moved into attractors of stable desynchronized states such that stimulation-induced desynchronization persists after cessation of stimulation. Preclinical and clinical studies confirmed corresponding long-lasting therapeutic and desynchronizing effects in PD. As PD symptoms are associated with different pathological synchronous rhythms, stimulation-induced long-lasting desynchronization effects should favorably be robust to variations of the stimulation frequency. Recent computational studies suggested that this robustness can be improved by randomizing the timings of stimulus deliveries. We study the long-lasting effects of CR stimulation with randomized stimulus amplitudes and/or randomized stimulus timing in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity. Performing computer simulations and analytical calculations, we study long-lasting desynchronization effects of CR with and without randomization of stimulus amplitudes alone, randomization of stimulus times alone as well as the combination of both. Varying the CR stimulation frequency (with respect to the frequency of abnormal target rhythm) and the number of separately stimulated neuronal subpopulations, we reveal parameter regions and related mechanisms where the two qualitatively different randomization mechanisms improve the robustness of long-lasting desynchronization effects of CR. In particular, for clinically relevant parameter ranges double-random CR stimulation, i.e., CR stimulation with the specific combination of stimulus amplitude randomization and stimulus time randomization, may outperform regular CR stimulation with respect to long-lasting desynchronization. In addition, our results provide the first evidence that an effective reduction of the overall stimulation current by stimulus amplitude randomization may improve the frequency robustness of long-lasting therapeutic effects of brain stimulation.
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Affiliation(s)
| | | | - Peter A. Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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4
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Aguilar-Canto F, Calvo H. A Hebbian Approach to Non-Spatial Prelinguistic Reasoning. Brain Sci 2022; 12:brainsci12020281. [PMID: 35204044 PMCID: PMC8870645 DOI: 10.3390/brainsci12020281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 02/12/2022] [Accepted: 02/15/2022] [Indexed: 02/01/2023] Open
Abstract
This research integrates key concepts of Computational Neuroscience, including the Bienestock-CooperMunro (BCM) rule, Spike Timing-Dependent Plasticity Rules (STDP), and the Temporal Difference Learning algorithm, with an important structure of Deep Learning (Convolutional Networks) to create an architecture with the potential of replicating observations of some cognitive experiments (particularly, those that provided some basis for sequential reasoning) while sharing the advantages already achieved by the previous proposals. In particular, we present Ring Model B, which is capable of associating visual with auditory stimulus, performing sequential predictions, and predicting reward from experience. Despite its simplicity, we considered such abilities to be a first step towards the formulation of more general models of prelinguistic reasoning.
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5
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Khaledi-Nasab A, Kromer JA, Tass PA. Long-Lasting Desynchronization Effects of Coordinated Reset Stimulation Improved by Random Jitters. Front Physiol 2021; 12:719680. [PMID: 34630142 PMCID: PMC8497886 DOI: 10.3389/fphys.2021.719680] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 08/12/2021] [Indexed: 12/30/2022] Open
Abstract
Abnormally strong synchronized activity is related to several neurological disorders, including essential tremor, epilepsy, and Parkinson's disease. Chronic high-frequency deep brain stimulation (HF DBS) is an established treatment for advanced Parkinson's disease. To reduce the delivered integral electrical current, novel theory-based stimulation techniques such as coordinated reset (CR) stimulation directly counteract the abnormal synchronous firing by delivering phase-shifted stimuli through multiple stimulation sites. In computational studies in neuronal networks with spike-timing-dependent plasticity (STDP), it was shown that CR stimulation down-regulates synaptic weights and drives the network into an attractor of a stable desynchronized state. This led to desynchronization effects that outlasted the stimulation. Corresponding long-lasting therapeutic effects were observed in preclinical and clinical studies. Computational studies suggest that long-lasting effects of CR stimulation depend on the adjustment of the stimulation frequency to the dominant synchronous rhythm. This may limit clinical applicability as different pathological rhythms may coexist. To increase the robustness of the long-lasting effects, we study randomized versions of CR stimulation in networks of leaky integrate-and-fire neurons with STDP. Randomization is obtained by adding random jitters to the stimulation times and by shuffling the sequence of stimulation site activations. We study the corresponding long-lasting effects using analytical calculations and computer simulations. We show that random jitters increase the robustness of long-lasting effects with respect to changes of the number of stimulation sites and the stimulation frequency. In contrast, shuffling does not increase parameter robustness of long-lasting effects. Studying the relation between acute, acute after-, and long-lasting effects of stimulation, we find that both acute after- and long-lasting effects are strongly determined by the stimulation-induced synaptic reshaping, whereas acute effects solely depend on the statistics of administered stimuli. We find that the stimulation duration is another important parameter, as effective stimulation only entails long-lasting effects after a sufficient stimulation duration. Our results show that long-lasting therapeutic effects of CR stimulation with random jitters are more robust than those of regular CR stimulation. This might reduce the parameter adjustment time in future clinical trials and make CR with random jitters more suitable for treating brain disorders with abnormal synchronization in multiple frequency bands.
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Affiliation(s)
- Ali Khaledi-Nasab
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Justus A Kromer
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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6
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Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity. Sci Rep 2021; 11:9840. [PMID: 33972613 PMCID: PMC8110549 DOI: 10.1038/s41598-021-89198-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Accepted: 04/20/2021] [Indexed: 11/09/2022] Open
Abstract
We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into \documentclass[12pt]{minimal}
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\begin{document}$$2^N$$\end{document}2N various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters \documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon$$\end{document}ε and \documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon$$\end{document}ε is the ratio of the time scales of the phase variables and synaptic weights, and \documentclass[12pt]{minimal}
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\begin{document}$$\mu$$\end{document}μ defines the sharpness of the plasticity boundary function. The limit \documentclass[12pt]{minimal}
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\begin{document}$$\mu \rightarrow 0$$\end{document}μ→0 corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with \documentclass[12pt]{minimal}
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\begin{document}$$2^N$$\end{document}2N various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.
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Khaledi-Nasab A, Kromer JA, Tass PA. Long-Lasting Desynchronization of Plastic Neural Networks by Random Reset Stimulation. Front Physiol 2021; 11:622620. [PMID: 33613303 PMCID: PMC7893102 DOI: 10.3389/fphys.2020.622620] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 12/23/2020] [Indexed: 12/19/2022] Open
Abstract
Excessive neuronal synchrony is a hallmark of neurological disorders such as epilepsy and Parkinson's disease. An established treatment for medically refractory Parkinson's disease is high-frequency (HF) deep brain stimulation (DBS). However, symptoms return shortly after cessation of HF-DBS. Recently developed decoupling stimulation approaches, such as Random Reset (RR) stimulation, specifically target pathological connections to achieve long-lasting desynchronization. During RR stimulation, a temporally and spatially randomized stimulus pattern is administered. However, spatial randomization, as presented so far, may be difficult to realize in a DBS-like setup due to insufficient spatial resolution. Motivated by recently developed segmented DBS electrodes with multiple stimulation sites, we present a RR stimulation protocol that copes with the limited spatial resolution of currently available depth electrodes for DBS. Specifically, spatial randomization is realized by delivering stimuli simultaneously to L randomly selected stimulation sites out of a total of M stimulation sites, which will be called L/M-RR stimulation. We study decoupling by L/M-RR stimulation in networks of excitatory integrate-and-fire neurons with spike-timing dependent plasticity by means of theoretical and computational analysis. We find that L/M-RR stimulation yields parameter-robust decoupling and long-lasting desynchronization. Furthermore, our theory reveals that strong high-frequency stimulation is not suitable for inducing long-lasting desynchronization effects. As a consequence, low and high frequency L/M-RR stimulation affect synaptic weights in qualitatively different ways. Our simulations confirm these predictions and show that qualitative differences between low and high frequency L/M-RR stimulation are present across a wide range of stimulation parameters, rendering stimulation with intermediate frequencies most efficient. Remarkably, we find that L/M-RR stimulation does not rely on a high spatial resolution, characterized by the density of stimulation sites in a target area, corresponding to a large M. In fact, L/M-RR stimulation with low resolution performs even better at low stimulation amplitudes. Our results provide computational evidence that L/M-RR stimulation may present a way to exploit modern segmented lead electrodes for long-lasting therapeutic effects.
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Affiliation(s)
- Ali Khaledi-Nasab
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Justus A Kromer
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
| | - Peter A Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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8
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Cabessa J, Tchaptchet A. Automata complete computation with Hodgkin-Huxley neural networks composed of synfire rings. Neural Netw 2020; 126:312-334. [PMID: 32278841 DOI: 10.1016/j.neunet.2020.03.019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2019] [Revised: 03/23/2020] [Accepted: 03/23/2020] [Indexed: 11/15/2022]
Abstract
Synfire rings are neural circuits capable of conveying synchronous, temporally precise and self-sustained activities in a robust manner. We propose a cell assembly based paradigm for abstract neural computation centered on the concept of synfire rings. More precisely, we empirically show that Hodgkin-Huxley neural networks modularly composed of synfire rings are automata complete. We provide an algorithmic construction which, starting from any given finite state automaton, builds a corresponding Hodgkin-Huxley neural network modularly composed of synfire rings and capable of simulating it. We illustrate the correctness of the construction on two specific examples. We further analyze the stability and robustness of the construction as a function of changes in the ring topologies as well as with respect to cell death and synaptic failure mechanisms, respectively. These results establish the possibility of achieving abstract computation with bio-inspired neural networks. They might constitute a theoretical ground for the realization of biological neural computers.
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Affiliation(s)
- Jérémie Cabessa
- Laboratory of Mathematical Economics and Applied Microeconomics (LEMMA), Université Paris 2, Panthéon-Assas, 75005 Paris, France; Institute of Computer Science of the Czech Academy of Sciences, P. O. Box 5, 18207 Prague 8, Czech Republic.
| | - Aubin Tchaptchet
- Institute of Physiology, Philipps University of Marburg, 35037 Marburg, Germany.
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9
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Effects of network topologies on stochastic resonance in feedforward neural network. Cogn Neurodyn 2020; 14:399-409. [PMID: 32399079 DOI: 10.1007/s11571-020-09576-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Revised: 01/26/2020] [Accepted: 03/05/2020] [Indexed: 01/06/2023] Open
Abstract
The effects of network topologies on signal propagation are studied in noisy feedforward neural network in detail, where the network topologies are modulated by changing both the in-degree and out-degree distributions of FFNs as identical, uniform and exponential respectively. Stochastic resonance appeared in three FFNs when the same external stimuli and noise are applied to the three different network topologies. It is found that optimal noise intensity decreases with the increase of network's layer index. Meanwhile, the Q index of FFN with identical distribution is higher than that of the other two FFNs, indicating that the synchronization between the neuronal firing activities and the external stimuli is more obvious in FFN with identical distribution. The optimal parameter regions for the time cycle of external stimuli and the noise intensity are found for three FFNs, in which the resonance is more easily induced when the parameters of stimuli are set in this region. Furthermore, the relationship between the in-degree, the average membrane potential and the resonance performance is studied at the neuronal level, where it is found that both the average membrane potentials and the Q indexes of neurons in FFN with identical degree distribution is more consistent with each other than that of the other two FFNs due to their network topologies. In summary, the simulations here indicate that the network topologies play essential roles in affecting the signal propagation of FFNs.
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10
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Papasavvas CA, Trevelyan AJ, Kaiser M, Wang Y. Divisive gain modulation enables flexible and rapid entrainment in a neocortical microcircuit model. J Neurophysiol 2020; 123:1133-1143. [PMID: 32023140 PMCID: PMC7099485 DOI: 10.1152/jn.00401.2019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Neocortical circuits exhibit a rich dynamic repertoire, and their ability to achieve entrainment (adjustment of their frequency to match the input frequency) is thought to support many cognitive functions and indicate functional flexibility. Although previous studies have explored the influence of various circuit properties on this phenomenon, the role of divisive gain modulation (or divisive inhibition) is unknown. This gain control mechanism is thought to be delivered mainly by the soma-targeting interneurons in neocortical microcircuits. In this study, we use a neural mass model of the neocortical microcircuit (extended Wilson-Cowan model) featuring both soma-targeting and dendrite-targeting interneuronal subpopulations to investigate the role of divisive gain modulation in entrainment. Our results demonstrate that the presence of divisive inhibition in the microcircuit, as delivered by the soma-targeting interneurons, enables its entrainment to a wider range of input frequencies. Divisive inhibition also promotes a faster entrainment, with the microcircuit needing less time to converge to the fully entrained state. We suggest that divisive inhibition, working alongside subtractive inhibition, allows for more adaptive oscillatory responses in neocortical circuits and, thus, supports healthy brain functioning.NEW & NOTEWORTHY We introduce a computational neocortical microcircuit model that features two inhibitory neural populations, with one providing subtractive and the other divisive inhibition to the excitatory population. We demonstrate that divisive inhibition widens the range of input frequencies to which the microcircuit can become entrained and diminishes the time needed to reach full entrainment. We suggest that divisive inhibition enables more adaptive oscillatory activity, with important implications for both normal and pathological brain function.
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Affiliation(s)
- Christoforos A Papasavvas
- CNNP Lab, Interdisciplinary Computing and Complex BioSystems Group, School of Computing, Newcastle University, Newcastle upon Tyne, United Kingdom.,Faculty of Medical Sciences, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Andrew J Trevelyan
- Faculty of Medical Sciences, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Marcus Kaiser
- CNNP Lab, Interdisciplinary Computing and Complex BioSystems Group, School of Computing, Newcastle University, Newcastle upon Tyne, United Kingdom.,Faculty of Medical Sciences, Newcastle University, Newcastle upon Tyne, United Kingdom.,Department of Functional Neurosurgery, Ruijin Hospital, School of Medicine, Shanghai Jiao Tong University, Shanghai, China
| | - Yujiang Wang
- CNNP Lab, Interdisciplinary Computing and Complex BioSystems Group, School of Computing, Newcastle University, Newcastle upon Tyne, United Kingdom.,Faculty of Medical Sciences, Newcastle University, Newcastle upon Tyne, United Kingdom.,UCL Queen Square Institute of Neurology, Queen Square, London, United Kingdom
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11
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From space to time: Spatial inhomogeneities lead to the emergence of spatiotemporal sequences in spiking neuronal networks. PLoS Comput Biol 2019; 15:e1007432. [PMID: 31652259 PMCID: PMC6834288 DOI: 10.1371/journal.pcbi.1007432] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Revised: 11/06/2019] [Accepted: 09/24/2019] [Indexed: 01/01/2023] Open
Abstract
Spatio-temporal sequences of neuronal activity are observed in many brain regions in a variety of tasks and are thought to form the basis of meaningful behavior. However, mechanisms by which a neuronal network can generate spatio-temporal activity sequences have remained obscure. Existing models are biologically untenable because they either require manual embedding of a feedforward network within a random network or supervised learning to train the connectivity of a network to generate sequences. Here, we propose a biologically plausible, generative rule to create spatio-temporal activity sequences in a network of spiking neurons with distance-dependent connectivity. We show that the emergence of spatio-temporal activity sequences requires: (1) individual neurons preferentially project a small fraction of their axons in a specific direction, and (2) the preferential projection direction of neighboring neurons is similar. Thus, an anisotropic but correlated connectivity of neuron groups suffices to generate spatio-temporal activity sequences in an otherwise random neuronal network model.
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12
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Hao Y, Huang X, Dong M, Xu B. A biologically plausible supervised learning method for spiking neural networks using the symmetric STDP rule. Neural Netw 2019; 121:387-395. [PMID: 31593843 DOI: 10.1016/j.neunet.2019.09.007] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Revised: 06/30/2019] [Accepted: 09/06/2019] [Indexed: 01/28/2023]
Abstract
Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.
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Affiliation(s)
- Yunzhe Hao
- Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences, 100190 Beijing, China; University of Chinese Academy of Sciences, 100049 Beijing, China
| | - Xuhui Huang
- Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences, 100190 Beijing, China.
| | - Meng Dong
- Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences, 100190 Beijing, China
| | - Bo Xu
- Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences, 100190 Beijing, China; University of Chinese Academy of Sciences, 100049 Beijing, China; CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, 100190 Beijing, China.
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13
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Brzosko Z, Mierau SB, Paulsen O. Neuromodulation of Spike-Timing-Dependent Plasticity: Past, Present, and Future. Neuron 2019; 103:563-581. [DOI: 10.1016/j.neuron.2019.05.041] [Citation(s) in RCA: 91] [Impact Index Per Article: 18.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Revised: 05/20/2019] [Accepted: 05/24/2019] [Indexed: 12/31/2022]
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14
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Ocker GK, Doiron B. Training and Spontaneous Reinforcement of Neuronal Assemblies by Spike Timing Plasticity. Cereb Cortex 2019; 29:937-951. [PMID: 29415191 PMCID: PMC7963120 DOI: 10.1093/cercor/bhy001] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Revised: 01/01/2018] [Accepted: 01/05/2018] [Indexed: 12/15/2022] Open
Abstract
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both microscopic and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly coupled neurons with shared stimulus preferences. After training, this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has often been associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.
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Affiliation(s)
- Gabriel Koch Ocker
- Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA, USA
- Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Mellon University, Pittsburgh, PA, USA
- Allen Institute for Brain Science, Seattle, WA, USA
| | - Brent Doiron
- Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Mellon University, Pittsburgh, PA, USA
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
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15
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Madadi Asl M, Valizadeh A, Tass PA. Dendritic and Axonal Propagation Delays May Shape Neuronal Networks With Plastic Synapses. Front Physiol 2018; 9:1849. [PMID: 30618847 PMCID: PMC6307091 DOI: 10.3389/fphys.2018.01849] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2018] [Accepted: 12/07/2018] [Indexed: 12/27/2022] Open
Abstract
Biological neuronal networks are highly adaptive and plastic. For instance, spike-timing-dependent plasticity (STDP) is a core mechanism which adapts the synaptic strengths based on the relative timing of pre- and postsynaptic spikes. In various fields of physiology, time delays cause a plethora of biologically relevant dynamical phenomena. However, time delays increase the complexity of model systems together with the computational and theoretical analysis burden. Accordingly, in computational neuronal network studies propagation delays were often neglected. As a downside, a classic STDP rule in oscillatory neurons without propagation delays is unable to give rise to bidirectional synaptic couplings, i.e., loops or uncoupled states. This is at variance with basic experimental results. In this mini review, we focus on recent theoretical studies focusing on how things change in the presence of propagation delays. Realistic propagation delays may lead to the emergence of neuronal activity and synaptic connectivity patterns, which cannot be captured by classic STDP models. In fact, propagation delays determine the inventory of attractor states and shape their basins of attractions. The results reviewed here enable to overcome fundamental discrepancies between theory and experiments. Furthermore, these findings are relevant for the development of therapeutic brain stimulation techniques aiming at shifting the diseased brain to more favorable attractor states.
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Affiliation(s)
- Mojtaba Madadi Asl
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
| | - Alireza Valizadeh
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran.,School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, CA, United States
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16
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Madadi Asl M, Valizadeh A, Tass PA. Propagation delays determine neuronal activity and synaptic connectivity patterns emerging in plastic neuronal networks. CHAOS (WOODBURY, N.Y.) 2018; 28:106308. [PMID: 30384625 DOI: 10.1063/1.5037309] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Accepted: 08/01/2018] [Indexed: 06/08/2023]
Abstract
In plastic neuronal networks, the synaptic strengths are adapted to the neuronal activity. Specifically, spike-timing-dependent plasticity (STDP) is a fundamental mechanism that modifies the synaptic strengths based on the relative timing of pre- and postsynaptic spikes, taking into account the spikes' temporal order. In many studies, propagation delays were neglected to avoid additional dynamic complexity or computational costs. So far, networks equipped with a classic STDP rule typically rule out bidirectional couplings (i.e., either loops or uncoupled states) and are, hence, not able to reproduce fundamental experimental findings. In this review paper, we consider additional features, e.g., extensions of the classic STDP rule or additional aspects like noise, in order to overcome the contradictions between theory and experiment. In addition, we review in detail recent studies showing that a classic STDP rule combined with realistic propagation patterns is able to capture relevant experimental findings. In two coupled oscillatory neurons with propagation delays, bidirectional synapses can be preserved and potentiated. This result also holds for large networks of type-II phase oscillators. In addition, not only the mean of the initial distribution of synaptic weights, but also its standard deviation crucially determines the emergent structural connectivity, i.e., the mean final synaptic weight, the number of two-neuron loops, and the symmetry of the final connectivity pattern. The latter is affected by the firing rates, where more symmetric synaptic configurations emerge at higher firing rates. Finally, we discuss these findings in the context of the computational neuroscience-based development of desynchronizing brain stimulation techniques.
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Affiliation(s)
- Mojtaba Madadi Asl
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195-1159, Iran
| | - Alireza Valizadeh
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45195-1159, Iran
| | - Peter A Tass
- Department of Neurosurgery, School of Medicine, Stanford University, Stanford, California 94305, USA
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17
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Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity. Sci Rep 2018; 8:12068. [PMID: 30104713 PMCID: PMC6089910 DOI: 10.1038/s41598-018-30565-9] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2018] [Accepted: 08/02/2018] [Indexed: 12/16/2022] Open
Abstract
Spike-timing-dependent plasticity (STDP) adjusts synaptic strengths according to the precise timing of pre- and postsynaptic spike pairs. Theoretical and computational studies have revealed that STDP may contribute to the emergence of a variety of structural and dynamical states in plastic neuronal populations. In this manuscript, we show that by incorporating dendritic and axonal propagation delays in recurrent networks of oscillatory neurons, the asymptotic connectivity displays multistability, where different structures emerge depending on the initial distribution of the synaptic strengths. In particular, we show that the standard deviation of the initial distribution of synaptic weights, besides its mean, determines the main properties of the emergent structural connectivity such as the mean final synaptic weight, the number of two-neuron loops and the symmetry of the final structure. We also show that the firing rates of the neurons affect the evolution of the network, and a more symmetric configuration of the synapses emerges at higher firing rates. We justify the network results based on a two-neuron framework and show how the results translate to large recurrent networks.
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18
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How stimulation frequency and intensity impact on the long-lasting effects of coordinated reset stimulation. PLoS Comput Biol 2018; 14:e1006113. [PMID: 29746458 PMCID: PMC5963814 DOI: 10.1371/journal.pcbi.1006113] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2017] [Revised: 05/22/2018] [Accepted: 04/03/2018] [Indexed: 12/31/2022] Open
Abstract
Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation.
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19
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Zhao J, Qin YM, Che YQ. Effects of topologies on signal propagation in feedforward networks. CHAOS (WOODBURY, N.Y.) 2018; 28:013117. [PMID: 29390642 DOI: 10.1063/1.4999996] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.
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Affiliation(s)
- Jia Zhao
- Key Laboratory of Cognition and Personality (Ministry of Education) and Faculty of Psychology, Southwest University, Chongqing 400715, China
| | - Ying-Mei Qin
- Tianjin Key Laboratory of Information Sensing and Intelligent Control, Tianjin University of Technology and Education, Tianjin 300222, China
| | - Yan-Qiu Che
- Tianjin Key Laboratory of Information Sensing and Intelligent Control, Tianjin University of Technology and Education, Tianjin 300222, China
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20
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Madadi Asl M, Valizadeh A, Tass PA. Dendritic and Axonal Propagation Delays Determine Emergent Structures of Neuronal Networks with Plastic Synapses. Sci Rep 2017; 7:39682. [PMID: 28045109 PMCID: PMC5206725 DOI: 10.1038/srep39682] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Accepted: 11/25/2016] [Indexed: 11/09/2022] Open
Abstract
Spike-timing-dependent plasticity (STDP) modifies synaptic strengths based on the relative timing of pre- and postsynaptic spikes. The temporal order of spikes turned out to be crucial. We here take into account how propagation delays, composed of dendritic and axonal delay times, may affect the temporal order of spikes. In a minimal setting, characterized by neglecting dendritic and axonal propagation delays, STDP eliminates bidirectional connections between two coupled neurons and turns them into unidirectional connections. In this paper, however, we show that depending on the dendritic and axonal propagation delays, the temporal order of spikes at the synapses can be different from those in the cell bodies and, consequently, qualitatively different connectivity patterns emerge. In particular, we show that for a system of two coupled oscillatory neurons, bidirectional synapses can be preserved and potentiated. Intriguingly, this finding also translates to large networks of type-II phase oscillators and, hence, crucially impacts on the overall hierarchical connectivity patterns of oscillatory neuronal networks.
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Affiliation(s)
- Mojtaba Madadi Asl
- Institute for Advanced Studies in Basic Sciences (IASBS), Department of Physics, Zanjan, 45195-1159, Iran
| | - Alireza Valizadeh
- Institute for Advanced Studies in Basic Sciences (IASBS), Department of Physics, Zanjan, 45195-1159, Iran.,Institute for Research in Fundamental Sciences (IPM), School of Cognitive Sciences, Tehran, 19395-5746, Iran
| | - Peter A Tass
- Institute of Neuroscience and Medicine - Neuromodulation (INM-7), Research Center Jülich, Jülich, 52425, Germany.,Stanford University, Department of Neurosurgery, Stanford, CA, 94305, USA.,University of Cologne, Department of Neuromodulation, Cologne, 50937, Germany
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21
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Martens MB, Houweling AR, E Tiesinga PH. Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks. J Comput Neurosci 2016; 42:87-106. [PMID: 27812835 PMCID: PMC5250670 DOI: 10.1007/s10827-016-0629-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2016] [Revised: 09/27/2016] [Accepted: 10/03/2016] [Indexed: 01/10/2023]
Abstract
Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.
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Affiliation(s)
- Marijn B Martens
- Department of Neuroinformatics, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands.
| | - Arthur R Houweling
- Department of Neuroscience, Erasmus University Medical Center, Rotterdam, Netherlands
| | - Paul H E Tiesinga
- Department of Neuroinformatics, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands
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22
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Zeitler M, Tass PA. Anti-kindling Induced by Two-Stage Coordinated Reset Stimulation with Weak Onset Intensity. Front Comput Neurosci 2016; 10:44. [PMID: 27242500 PMCID: PMC4868855 DOI: 10.3389/fncom.2016.00044] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Accepted: 04/18/2016] [Indexed: 11/16/2022] Open
Abstract
Abnormal neuronal synchrony plays an important role in a number of brain diseases. To specifically counteract abnormal neuronal synchrony by desynchronization, Coordinated Reset (CR) stimulation, a spatiotemporally patterned stimulation technique, was designed with computational means. In neuronal networks with spike timing–dependent plasticity CR stimulation causes a decrease of synaptic weights and finally anti-kindling, i.e., unlearning of abnormally strong synaptic connectivity and abnormal neuronal synchrony. Long-lasting desynchronizing aftereffects of CR stimulation have been verified in pre-clinical and clinical proof of concept studies. In general, for different neuromodulation approaches, both invasive and non-invasive, it is desirable to enable effective stimulation at reduced stimulation intensities, thereby avoiding side effects. For the first time, we here present a two-stage CR stimulation protocol, where two qualitatively different types of CR stimulation are delivered one after another, and the first stage comes at a particularly weak stimulation intensity. Numerical simulations show that a two-stage CR stimulation can induce the same degree of anti-kindling as a single-stage CR stimulation with intermediate stimulation intensity. This stimulation approach might be clinically beneficial in patients suffering from brain diseases characterized by abnormal neuronal synchrony where a first treatment stage should be performed at particularly weak stimulation intensities in order to avoid side effects. This might, e.g., be relevant in the context of acoustic CR stimulation in tinnitus patients with hyperacusis or in the case of electrical deep brain CR stimulation with sub-optimally positioned leads or side effects caused by stimulation of the target itself. We discuss how to apply our method in first in man and proof of concept studies.
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Affiliation(s)
- Magteld Zeitler
- Research Center Jülich, Institute of Neuroscience and Medicine, Neuromodulation (INM-7) Jülich, Germany
| | - Peter A Tass
- Research Center Jülich, Institute of Neuroscience and Medicine, Neuromodulation (INM-7)Jülich, Germany; Department of Neurosurgery, Stanford UniversityStanford, CA, USA; Department of Neuromodulation, University of CologneCologne, Germany
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23
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Lücken L, Popovych OV, Tass PA, Yanchuk S. Noise-enhanced coupling between two oscillators with long-term plasticity. Phys Rev E 2016; 93:032210. [PMID: 27078347 DOI: 10.1103/physreve.93.032210] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2015] [Indexed: 11/07/2022]
Abstract
Spike timing-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons.
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Affiliation(s)
- Leonhard Lücken
- Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
| | - Oleksandr V Popovych
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center, Jülich, Germany
| | - Peter A Tass
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center, Jülich, Germany.,Department of Neurosurgery, Stanford University, Stanford, California, USA.,Department of Neuromodulation, University of Cologne, Cologne, Germany
| | - Serhiy Yanchuk
- Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany.,Institute of Mathematics, Technical University of Berlin, Berlin, Germany
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24
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Liu H, Song Y, Xue F, Li X. Effects of bursting dynamic features on the generation of multi-clustered structure of neural network with symmetric spike-timing-dependent plasticity learning rule. CHAOS (WOODBURY, N.Y.) 2015; 25:113108. [PMID: 26627568 DOI: 10.1063/1.4935281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, the generation of multi-clustered structure of self-organized neural network with different neuronal firing patterns, i.e., bursting or spiking, has been investigated. The initially all-to-all-connected spiking neural network or bursting neural network can be self-organized into clustered structure through the symmetric spike-timing-dependent plasticity learning for both bursting and spiking neurons. However, the time consumption of this clustering procedure of the burst-based self-organized neural network (BSON) is much shorter than the spike-based self-organized neural network (SSON). Our results show that the BSON network has more obvious small-world properties, i.e., higher clustering coefficient and smaller shortest path length than the SSON network. Also, the results of larger structure entropy and activity entropy of the BSON network demonstrate that this network has higher topological complexity and dynamical diversity, which benefits for enhancing information transmission of neural circuits. Hence, we conclude that the burst firing can significantly enhance the efficiency of clustering procedure and the emergent clustered structure renders the whole network more synchronous and therefore more sensitive to weak input. This result is further confirmed from its improved performance on stochastic resonance. Therefore, we believe that the multi-clustered neural network which self-organized from the bursting dynamics has high efficiency in information processing.
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Affiliation(s)
- Hui Liu
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China
| | - Yongduan Song
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China
| | - Fangzheng Xue
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China
| | - Xiumin Li
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China
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25
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Bayati M, Valizadeh A, Abbassian A, Cheng S. Self-organization of synchronous activity propagation in neuronal networks driven by local excitation. Front Comput Neurosci 2015; 9:69. [PMID: 26089794 PMCID: PMC4454885 DOI: 10.3389/fncom.2015.00069] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Accepted: 05/20/2015] [Indexed: 12/30/2022] Open
Abstract
Many experimental and theoretical studies have suggested that the reliable propagation of synchronous neural activity is crucial for neural information processing. The propagation of synchronous firing activity in so-called synfire chains has been studied extensively in feed-forward networks of spiking neurons. However, it remains unclear how such neural activity could emerge in recurrent neuronal networks through synaptic plasticity. In this study, we investigate whether local excitation, i.e., neurons that fire at a higher frequency than the other, spontaneously active neurons in the network, can shape a network to allow for synchronous activity propagation. We use two-dimensional, locally connected and heterogeneous neuronal networks with spike-timing dependent plasticity (STDP). We find that, in our model, local excitation drives profound network changes within seconds. In the emergent network, neural activity propagates synchronously through the network. This activity originates from the site of the local excitation and propagates through the network. The synchronous activity propagation persists, even when the local excitation is removed, since it derives from the synaptic weight matrix. Importantly, once this connectivity is established it remains stable even in the presence of spontaneous activity. Our results suggest that synfire-chain-like activity can emerge in a relatively simple way in realistic neural networks by locally exciting the desired origin of the neuronal sequence.
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Affiliation(s)
- Mehdi Bayati
- Mercator Research Group "Structure of Memory", Ruhr-Universität Bochum Bochum, Germany
| | - Alireza Valizadeh
- Department of Physics, Institute for Advanced Studies in Basic Sciences Zanjan, Iran ; School of Cognitive Sciences, Institute for Research in Fundamental Sciences Tehran, Iran
| | | | - Sen Cheng
- Mercator Research Group "Structure of Memory", Ruhr-Universität Bochum Bochum, Germany ; Department of Psychology, Ruhr-Universität Bochum Bochum, Germany
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26
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Aoki T. Self-organization of a recurrent network under ongoing synaptic plasticity. Neural Netw 2015; 62:11-9. [DOI: 10.1016/j.neunet.2014.05.024] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2014] [Revised: 05/18/2014] [Accepted: 05/19/2014] [Indexed: 11/17/2022]
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27
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Aoki T, Yawata K, Aoyagi T. Self-organization of complex networks as a dynamical system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012908. [PMID: 25679683 DOI: 10.1103/physreve.91.012908] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2014] [Indexed: 06/04/2023]
Abstract
To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.
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Affiliation(s)
- Takaaki Aoki
- Faculty of Education, Kagawa University, Takamatsu 760-8521, Japan
| | - Koichiro Yawata
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Toshio Aoyagi
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan and CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
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28
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Popovych OV, Tass PA. Control of abnormal synchronization in neurological disorders. Front Neurol 2014; 5:268. [PMID: 25566174 PMCID: PMC4267271 DOI: 10.3389/fneur.2014.00268] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2014] [Accepted: 11/28/2014] [Indexed: 11/13/2022] Open
Abstract
In the nervous system, synchronization processes play an important role, e.g., in the context of information processing and motor control. However, pathological, excessive synchronization may strongly impair brain function and is a hallmark of several neurological disorders. This focused review addresses the question of how an abnormal neuronal synchronization can specifically be counteracted by invasive and non-invasive brain stimulation as, for instance, by deep brain stimulation for the treatment of Parkinson’s disease, or by acoustic stimulation for the treatment of tinnitus. On the example of coordinated reset (CR) neuromodulation, we illustrate how insights into the dynamics of complex systems contribute to successful model-based approaches, which use methods from synergetics, non-linear dynamics, and statistical physics, for the development of novel therapies for normalization of brain function and synaptic connectivity. Based on the intrinsic multistability of the neuronal populations induced by spike timing-dependent plasticity (STDP), CR neuromodulation utilizes the mutual interdependence between synaptic connectivity and dynamics of the neuronal networks in order to restore more physiological patterns of connectivity via desynchronization of neuronal activity. The very goal is to shift the neuronal population by stimulation from an abnormally coupled and synchronized state to a desynchronized regime with normalized synaptic connectivity, which significantly outlasts the stimulation cessation, so that long-lasting therapeutic effects can be achieved.
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Affiliation(s)
- Oleksandr V Popovych
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center , Jülich , Germany
| | - Peter A Tass
- Institute of Neuroscience and Medicine - Neuromodulation, Jülich Research Center , Jülich , Germany ; Department of Neurosurgery, Stanford University , Stanford, CA , USA ; Department of Neuromodulation, University of Cologne , Cologne , Germany
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29
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Rieubland S, Roth A, Häusser M. Structured connectivity in cerebellar inhibitory networks. Neuron 2014; 81:913-29. [PMID: 24559679 PMCID: PMC3988957 DOI: 10.1016/j.neuron.2013.12.029] [Citation(s) in RCA: 74] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/13/2013] [Indexed: 11/16/2022]
Abstract
Defining the rules governing synaptic connectivity is key to formulating theories of neural circuit function. Interneurons can be connected by both electrical and chemical synapses, but the organization and interaction of these two complementary microcircuits is unknown. By recording from multiple molecular layer interneurons in the cerebellar cortex, we reveal specific, nonrandom connectivity patterns in both GABAergic chemical and electrical interneuron networks. Both networks contain clustered motifs and show specific overlap between them. Chemical connections exhibit a preference for transitive patterns, such as feedforward triplet motifs. This structured connectivity is supported by a characteristic spatial organization: transitivity of chemical connectivity is directed vertically in the sagittal plane, and electrical synapses appear strictly confined to the sagittal plane. The specific, highly structured connectivity rules suggest that these motifs are essential for the function of the cerebellar network.
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Affiliation(s)
- Sarah Rieubland
- Wolfson Institute for Biomedical Research and Department of Neuroscience, Physiology and Pharmacology, University College London, Gower Street, London WC1E 6BT, UK
| | - Arnd Roth
- Wolfson Institute for Biomedical Research and Department of Neuroscience, Physiology and Pharmacology, University College London, Gower Street, London WC1E 6BT, UK.
| | - Michael Häusser
- Wolfson Institute for Biomedical Research and Department of Neuroscience, Physiology and Pharmacology, University College London, Gower Street, London WC1E 6BT, UK.
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30
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Popovych OV, Yanchuk S, Tass PA. Self-organized noise resistance of oscillatory neural networks with spike timing-dependent plasticity. Sci Rep 2013; 3:2926. [PMID: 24113385 PMCID: PMC4070574 DOI: 10.1038/srep02926] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Accepted: 09/25/2013] [Indexed: 01/01/2023] Open
Abstract
Intuitively one might expect independent noise to be a powerful tool for desynchronizing a population of synchronized neurons. We here show that, intriguingly, for oscillatory neural populations with adaptive synaptic weights governed by spike timing-dependent plasticity (STDP) the opposite is true. We found that the mean synaptic coupling in such systems increases dynamically in response to the increase of the noise intensity, and there is an optimal noise level, where the amount of synaptic coupling gets maximal in a resonance-like manner as found for the stochastic or coherence resonances, although the mechanism in our case is different. This constitutes a noise-induced self-organization of the synaptic connectivity, which effectively counteracts the desynchronizing impact of independent noise over a wide range of the noise intensity. Given the attempts to counteract neural synchrony underlying tinnitus with noisers and maskers, our results may be of clinical relevance.
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Affiliation(s)
- Oleksandr V. Popovych
- Institute of Neuroscience and Medicine – Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
| | - Serhiy Yanchuk
- Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany
| | - Peter A. Tass
- Institute of Neuroscience and Medicine – Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
- Department of Neuromodulation, University of Cologne, 50924 Cologne, Germany
- Clinic for Stereotactic and Functional Neurosurgery, University of Cologne, 50924 Cologne, Germany
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31
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Sadeghi S, Valizadeh A. Synchronization of delayed coupled neurons in presence of inhomogeneity. J Comput Neurosci 2013; 36:55-66. [PMID: 23744009 DOI: 10.1007/s10827-013-0461-9] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2013] [Revised: 05/02/2013] [Accepted: 05/09/2013] [Indexed: 10/26/2022]
Abstract
In principle, two directly coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators. Delay in communication, on the other hand, can exert phase shift in the activity of the coupled oscillators. In this study, we address the question of how phase locked, and in particular zero phase lag synchronization, can be achieved for a heterogeneous system of two delayed coupled neurons. We have analytically studied the possibility of inphase synchronization and near inphase synchronization when the neurons are not identical or the connections are not exactly symmetric. We have shown that while any single source of inhomogeneity can violate isochronous synchrony, multiple sources of inhomogeneity can compensate for each other and maintain synchrony. Numeric studies on biologically plausible models also support the analytic results.
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Affiliation(s)
- S Sadeghi
- Institute for Advanced Studies in Basic Sciences (IASBS), P. O. Box 45195-1159, Zanjan, Iran
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32
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Waddington A, Appleby PA, De Kamps M, Cohen N. Triphasic spike-timing-dependent plasticity organizes networks to produce robust sequences of neural activity. Front Comput Neurosci 2012; 6:88. [PMID: 23162457 PMCID: PMC3495293 DOI: 10.3389/fncom.2012.00088] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2012] [Accepted: 10/05/2012] [Indexed: 11/13/2022] Open
Abstract
Synfire chains have long been proposed to generate precisely timed sequences of neural activity. Such activity has been linked to numerous neural functions including sensory encoding, cognitive and motor responses. In particular, it has been argued that synfire chains underlie the precise spatiotemporal firing patterns that control song production in a variety of songbirds. Previous studies have suggested that the development of synfire chains requires either initial sparse connectivity or strong topological constraints, in addition to any synaptic learning rules. Here, we show that this necessity can be removed by using a previously reported but hitherto unconsidered spike-timing-dependent plasticity (STDP) rule and activity-dependent excitability. Under this rule the network develops stable synfire chains that possess a non-trivial, scalable multi-layer structure, in which relative layer sizes appear to follow a universal function. Using computational modeling and a coarse grained random walk model, we demonstrate the role of the STDP rule in growing, molding and stabilizing the chain, and link model parameters to the resulting structure.
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Davies S, Galluppi F, Rast AD, Furber SB. A forecast-based STDP rule suitable for neuromorphic implementation. Neural Netw 2012; 32:3-14. [PMID: 22386500 DOI: 10.1016/j.neunet.2012.02.018] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2011] [Revised: 01/15/2012] [Accepted: 02/07/2012] [Indexed: 11/17/2022]
Abstract
Artificial neural networks increasingly involve spiking dynamics to permit greater computational efficiency. This becomes especially attractive for on-chip implementation using dedicated neuromorphic hardware. However, both spiking neural networks and neuromorphic hardware have historically found difficulties in implementing efficient, effective learning rules. The best-known spiking neural network learning paradigm is Spike Timing Dependent Plasticity (STDP) which adjusts the strength of a connection in response to the time difference between the pre- and post-synaptic spikes. Approaches that relate learning features to the membrane potential of the post-synaptic neuron have emerged as possible alternatives to the more common STDP rule, with various implementations and approximations. Here we use a new type of neuromorphic hardware, SpiNNaker, which represents the flexible "neuromimetic" architecture, to demonstrate a new approach to this problem. Based on the standard STDP algorithm with modifications and approximations, a new rule, called STDP TTS (Time-To-Spike) relates the membrane potential with the Long Term Potentiation (LTP) part of the basic STDP rule. Meanwhile, we use the standard STDP rule for the Long Term Depression (LTD) part of the algorithm. We show that on the basis of the membrane potential it is possible to make a statistical prediction of the time needed by the neuron to reach the threshold, and therefore the LTP part of the STDP algorithm can be triggered when the neuron receives a spike. In our system these approximations allow efficient memory access, reducing the overall computational time and the memory bandwidth required. The improvements here presented are significant for real-time applications such as the ones for which the SpiNNaker system has been designed. We present simulation results that show the efficacy of this algorithm using one or more input patterns repeated over the whole time of the simulation. On-chip results show that the STDP TTS algorithm allows the neural network to adapt and detect the incoming pattern with improvements both in the reliability of, and the time required for, consistent output. Through the approximations we suggest in this paper, we introduce a learning rule that is easy to implement both in event-driven simulators and in dedicated hardware, reducing computational complexity relative to the standard STDP rule. Such a rule offers a promising solution, complementary to standard STDP evaluation algorithms, for real-time learning using spiking neural networks in time-critical applications.
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Affiliation(s)
- S Davies
- School of Computer Science, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom.
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34
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Aoki T, Aoyagi T. Self-organized network of phase oscillators coupled by activity-dependent interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:066109. [PMID: 22304157 DOI: 10.1103/physreve.84.066109] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2011] [Indexed: 05/23/2023]
Abstract
We investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators. We found that this coevolving dynamical system robustly yields three basic states of collective behavior with their self-organized interactions. The first is the two-cluster state, in which the oscillators are organized into two synchronized groups. The second is the coherent state, in which the oscillators are arranged sequentially in time. The third is the chaotic state, in which the relative phases between oscillators and their coupling weights are chaotically shuffled. Furthermore, we demonstrate that self-assembled multiclusters can be designed by controlling the weight dynamics. Note that the phase patterns of the oscillators and the weighted network of interactions between them are simultaneously organized through this coevolving dynamics. We expect that these results will provide new insight into self-assembly mechanisms by which the collective behavior of a rhythmic system emerges as a result of the dynamics of adaptive interactions.
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Affiliation(s)
- Takaaki Aoki
- Faculty of Education, Kagawa University, Takamatsu 760-8521, Japan.
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35
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ZHAO GANG. PROBABILITY OF ENTRAINMENT, SYNAPTIC MODIFICATION AND ENTRAINED PHASE ARE PHASE-DEPENDENT IN STDP. J BIOL SYST 2011. [DOI: 10.1142/s0218339010003354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Synaptic conductance can be modified in an activity dependent manner, in which the temporal relationship between pre- and post-synaptic spikes plays a major role. This spike timing dependent plasticity (STDP) has profound implications in neural coding, computation and functionality. Because the STDP learning curve is strongly nonlinear, initial state may have great impacts on the eventual state of the system. However, although this feature is intuitively clear, it has not been explored in detail before. This paper presents a preliminary numerical study in this direction. In a model of two pacemaker neurons and a synapse undergoing STDP, it is found that the probability of entrainment, direction of synaptic modification and entrained phase are all influenced by the initial relative phase. Based on these findings, it is reasonable to propose that the initial-state sensitive feature of STDP may contribute to its role of selective response in oscillatory neural networks.
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Affiliation(s)
- GANG ZHAO
- Institute of Complex Bio-Dynamics, Jiangxi Blue Sky University, Nanchang, Jiangxi, 330098, P. R. China
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36
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Hanuschkin A, Diesmann M, Morrison A. A reafferent and feed-forward model of song syntax generation in the Bengalese finch. J Comput Neurosci 2011; 31:509-32. [PMID: 21404048 PMCID: PMC3232349 DOI: 10.1007/s10827-011-0318-z] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2010] [Revised: 01/28/2011] [Accepted: 02/03/2011] [Indexed: 12/04/2022]
Abstract
Adult Bengalese finches generate a variable song that obeys a distinct and individual syntax. The syntax is gradually lost over a period of days after deafening and is recovered when hearing is restored. We present a spiking neuronal network model of the song syntax generation and its loss, based on the assumption that the syntax is stored in reafferent connections from the auditory to the motor control area. Propagating synfire activity in the HVC codes for individual syllables of the song and priming signals from the auditory network reduce the competition between syllables to allow only those transitions that are permitted by the syntax. Both imprinting of song syntax within HVC and the interaction of the reafferent signal with an efference copy of the motor command are sufficient to explain the gradual loss of syntax in the absence of auditory feedback. The model also reproduces for the first time experimental findings on the influence of altered auditory feedback on the song syntax generation, and predicts song- and species-specific low frequency components in the LFP. This study illustrates how sequential compositionality following a defined syntax can be realized in networks of spiking neurons.
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Affiliation(s)
- Alexander Hanuschkin
- Functional Neural Circuits Group, Faculty of Biology, Albert-Ludwig University of Freiburg, Schänzlestrasse 1, 79104 Freiburg, Germany.
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37
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Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks. J Comput Neurosci 2011; 32:309-26. [DOI: 10.1007/s10827-011-0353-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2010] [Revised: 05/17/2011] [Accepted: 07/06/2011] [Indexed: 10/17/2022]
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38
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Shore SE. Plasticity of somatosensory inputs to the cochlear nucleus--implications for tinnitus. Hear Res 2011; 281:38-46. [PMID: 21620940 DOI: 10.1016/j.heares.2011.05.001] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 04/29/2011] [Accepted: 05/01/2011] [Indexed: 11/26/2022]
Abstract
This chapter reviews evidence for functional connections of the somatosensory and auditory systems at the very lowest levels of the nervous system. Neural inputs from the dosal root and trigeminal ganglia, as well as their brain stem nuclei, cuneate, gracillis and trigeminal, terminate in the cochlear nuclei. Terminations are primarily in the shell regions surrounding the cochlear nuclei but some terminals are found in the magnocellular regions of cochlear nucleus. The effects of stimulating these inputs on multisensory integration are shown as short and long-term, both suppressive and enhancing. Evidence that these projections are glutamatergic and are altered after cochlear damage is provided in the light of probable influences on the modulation and generation of tinnitus.
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Affiliation(s)
- S E Shore
- Department of Otolaryngology, University of Michigan, 1150 W. Medical Center, Ann Arbor, MI 48109, USA
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39
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Kunkel S, Diesmann M, Morrison A. Limits to the development of feed-forward structures in large recurrent neuronal networks. Front Comput Neurosci 2011; 4:160. [PMID: 21415913 PMCID: PMC3042733 DOI: 10.3389/fncom.2010.00160] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2010] [Accepted: 12/25/2010] [Indexed: 11/25/2022] Open
Abstract
Spike-timing dependent plasticity (STDP) has traditionally been of great interest to theoreticians, as it seems to provide an answer to the question of how the brain can develop functional structure in response to repeated stimuli. However, despite this high level of interest, convincing demonstrations of this capacity in large, initially random networks have not been forthcoming. Such demonstrations as there are typically rely on constraining the problem artificially. Techniques include employing additional pruning mechanisms or STDP rules that enhance symmetry breaking, simulating networks with low connectivity that magnify competition between synapses, or combinations of the above. In this paper, we first review modeling choices that carry particularly high risks of producing non-generalizable results in the context of STDP in recurrent networks. We then develop a theory for the development of feed-forward structure in random networks and conclude that an unstable fixed point in the dynamics prevents the stable propagation of structure in recurrent networks with weight-dependent STDP. We demonstrate that the key predictions of the theory hold in large-scale simulations. The theory provides insight into the reasons why such development does not take place in unconstrained systems and enables us to identify biologically motivated candidate adaptations to the balanced random network model that might enable it.
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Affiliation(s)
- Susanne Kunkel
- Functional Neural Circuits Group, Faculty of Biology, Albert-Ludwig University of Freiburg Germany
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40
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Abstract
Tinnitus is a phantom sound (ringing of the ears) that affects quality of life for millions around the world and is associated in most cases with hearing impairment. This symposium will consider evidence that deafferentation of tonotopically organized central auditory structures leads to increased neuron spontaneous firing rates and neural synchrony in the hearing loss region. This region covers the frequency spectrum of tinnitus sounds, which are optimally suppressed following exposure to band-limited noise covering the same frequencies. Cross-modal compensations in subcortical structures may contribute to tinnitus and its modulation by jaw-clenching and eye movements. Yet many older individuals with impaired hearing do not have tinnitus, possibly because age-related changes in inhibitory circuits are better preserved. A brain network involving limbic and other nonauditory regions is active in tinnitus and may be driven when spectrotemporal information conveyed by the damaged ear does not match that predicted by central auditory processing.
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41
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Thivierge JP, Cisek P. Spiking neurons that keep the rhythm. J Comput Neurosci 2010; 30:589-605. [PMID: 20886275 DOI: 10.1007/s10827-010-0280-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2009] [Revised: 09/16/2010] [Accepted: 09/21/2010] [Indexed: 10/19/2022]
Abstract
Detecting the temporal relationship among events in the environment is a fundamental goal of the brain. Following pulses of rhythmic stimuli, neurons of the retina and cortex produce activity that closely approximates the timing of an omitted pulse. This omitted stimulus response (OSR) is generally interpreted as a transient response to rhythmic input and is thought to form a basis of short-term perceptual memories. Despite its ubiquity across species and experimental protocols, the mechanisms underlying OSRs remain poorly understood. In particular, the highly transient nature of OSRs, typically limited to a single cycle after stimulation, cannot be explained by a simple mechanism that would remain locked to the frequency of stimulation. Here, we describe a set of realistic simulations that capture OSRs over a range of stimulation frequencies matching experimental work. The model does not require an explicit mechanism for learning temporal sequences. Instead, it relies on spike timing-dependent plasticity (STDP), a form of synaptic modification that is sensitive to the timing of pre- and post-synaptic action potentials. In the model, the transient nature of OSRs is attributed to the heterogeneous nature of neural properties and connections, creating intricate forms of activity that are continuously changing over time. Combined with STDP, neural heterogeneity enabled OSRs to complex rhythmic patterns as well as OSRs following a delay period. These results link the response of neurons to rhythmic patterns with the capacity of heterogeneous circuits to produce transient and highly flexible forms of neural activity.
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Affiliation(s)
- Jean-Philippe Thivierge
- Department of Psychological and Brain Sciences, Indiana University, 1101 East Tenth Street, Bloomington, IN 47405, USA.
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42
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Gilson M, Burkitt A, van Hemmen LJ. STDP in Recurrent Neuronal Networks. Front Comput Neurosci 2010; 4. [PMID: 20890448 PMCID: PMC2947928 DOI: 10.3389/fncom.2010.00023] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2010] [Accepted: 06/28/2010] [Indexed: 11/13/2022] Open
Abstract
Recent results about spike-timing-dependent plasticity (STDP) in recurrently connected neurons are reviewed, with a focus on the relationship between the weight dynamics and the emergence of network structure. In particular, the evolution of synaptic weights in the two cases of incoming connections for a single neuron and recurrent connections are compared and contrasted. A theoretical framework is used that is based upon Poisson neurons with a temporally inhomogeneous firing rate and the asymptotic distribution of weights generated by the learning dynamics. Different network configurations examined in recent studies are discussed and an overview of the current understanding of STDP in recurrently connected neuronal networks is presented.
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43
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Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL. Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV: structuring synaptic pathways among recurrent connections. BIOLOGICAL CYBERNETICS 2009; 101:427-444. [PMID: 19937070 DOI: 10.1007/s00422-009-0346-1] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2009] [Accepted: 10/27/2009] [Indexed: 05/28/2023]
Abstract
In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.
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Affiliation(s)
- Matthieu Gilson
- Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia.
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44
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Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL. Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: Partially connected neurons driven by spontaneous activity. BIOLOGICAL CYBERNETICS 2009; 101:411-426. [PMID: 19937071 DOI: 10.1007/s00422-009-0343-4] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2009] [Accepted: 10/19/2009] [Indexed: 05/28/2023]
Abstract
In contrast to a feed-forward architecture, the weight dynamics induced by spike-timing-dependent plasticity (STDP) in a recurrent neuronal network is not yet well understood. In this article, we extend a previous study of the impact of additive STDP in a recurrent network that is driven by spontaneous activity (no external stimulating inputs) from a fully connected network to one that is only partially connected. The asymptotic state of the network is analyzed, and it is found that the equilibrium and stability conditions for the firing rates are similar for both full and partial connectivity: STDP causes the firing rates to converge toward the same value and remain quasi-homogeneous. However, when STDP induces strong weight competition, the connectivity affects the weight dynamics in that the distribution of the weights disperses more quickly for lower density than for higher density. The asymptotic weight distribution strongly depends upon that at the beginning of the learning epoch; consequently, homogeneous connectivity alone is not sufficient to obtain homogeneous neuronal activity. In the absence of external inputs, STDP can nevertheless generate structure in the network through autocorrelation effects, for example, by introducing asymmetry in network topology.
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Affiliation(s)
- Matthieu Gilson
- Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia.
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45
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Masuda N, Kawamura Y, Kori H. Analysis of relative influence of nodes in directed networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:046114. [PMID: 19905397 DOI: 10.1103/physreve.80.046114] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2009] [Revised: 09/01/2009] [Indexed: 05/28/2023]
Abstract
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PAGERANK. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.
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Affiliation(s)
- Naoki Masuda
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan
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46
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Waddington A, Cohen N. Capacity of networks to develop multiple attractors through STDP. BMC Neurosci 2009. [DOI: 10.1186/1471-2202-10-s1-p195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
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47
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Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL. Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity--strengthening correlated input pathways. BIOLOGICAL CYBERNETICS 2009; 101:81-102. [PMID: 19536560 DOI: 10.1007/s00422-009-0319-4] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2008] [Accepted: 05/13/2009] [Indexed: 05/27/2023]
Abstract
Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of "steady" inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.
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Affiliation(s)
- Matthieu Gilson
- Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia.
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48
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Takahashi YK, Kori H, Masuda N. Self-organization of feed-forward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051904. [PMID: 19518477 DOI: 10.1103/physreve.79.051904] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2008] [Indexed: 05/27/2023]
Abstract
Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly toward synchrony is not entirely clear. We examine relations between STDP and synchronous firing in spontaneously firing neural populations. Using coupled heterogeneous phase oscillators placed on initial networks, we show numerically that STDP prunes some synapses and promotes formation of a feedforward network. Eventually a pacemaker, which is the neuron with the fastest inherent frequency in our numerical simulations, emerges at the root of the feedforward network. In each oscillatory cycle, a packet of neural activity is propagated from the pacemaker to downstream neurons along layers of the feedforward network. This event occurs above a clear-cut threshold value of the initial synaptic weight. Below the threshold, neurons are self-organized into separate clusters each of which is a feedforward network.
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Affiliation(s)
- Yuko K Takahashi
- Faculty of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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49
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Aoki T, Aoyagi T. Co-evolution of phases and connection strengths in a network of phase oscillators. PHYSICAL REVIEW LETTERS 2009; 102:034101. [PMID: 19257356 DOI: 10.1103/physrevlett.102.034101] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2008] [Indexed: 05/15/2023]
Abstract
We investigate co-evolving dynamics in a weighted network of phase oscillators in which the phases of the oscillators at the nodes and the weights of the links interact with each other. We find that depending on the type of the dynamics of the weights, the system exhibits three kinds of asymptotic behavior: a two-cluster state, a coherent state with a fixed phase relation, and a chaotic state with frustration. Because of its structural stability, it is believed that our model captures the essential characteristics of a class of co-evolving and adaptive networks.
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Affiliation(s)
- Takaaki Aoki
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
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50
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Abstract
Neural synchronization is of wide interest in neuroscience and has been argued to form the substrate for conscious attention to stimuli, movement preparation, and the maintenance of task-relevant representations in active memory. Despite a wealth of possible functions, the mechanisms underlying synchrony are still poorly understood. In particular, in vitro preparations have demonstrated synchronization with no apparent periodicity, which cannot be explained by simple oscillatory mechanisms. Here, we investigate the possible origins of nonperiodic synchronization through biophysical simulations. We show that such aperiodic synchronization arises naturally under a simple set of plausible assumptions, depending crucially on heterogeneous cell properties. In addition, nonperiodicity occurs even in the absence of stochastic fluctuation in membrane potential, suggesting that it may represent an intrinsic property of interconnected networks. Simulations capture some of the key aspects of population-level synchronization in spontaneous network spikes (NSs) and suggest that the intrinsic nonperiodicity of NSs observed in reduced cell preparations is a phenomenon that is highly robust and can be reproduced in simulations that involve a minimal set of realistic assumptions. In addition, a model with spike timing-dependent plasticity can overcome a natural tendency to exhibit nonperiodic behavior. After rhythmic stimulation, the model does not automatically fall back to a state of nonperiodic behavior, but keeps replaying the pattern of evoked NSs for a few cycles. A cluster analysis of synaptic strengths highlights the importance of population-wide interactions in generating this result and describes a possible route for encoding temporal patterns in networks of neurons.
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