Phase Selective Oscillations in Two Noise Driven Synaptically Coupled Spiking Neurons

2015 ◽  
Vol 25 (07) ◽  
pp. 1540005
Author(s):  
Ilya Prokin ◽  
Ivan Tyukin ◽  
Victor Kazantsev

The work investigates the influence of spike-timing dependent plasticity (STDP) mechanisms on the dynamics of two synaptically coupled neurons driven by additive external noise. In this setting, the noise signal models synaptic inputs that the pair receives from other neurons in a larger network. We show that in the absence of STDP feedbacks the pair of neurons exhibit oscillations and intermittent synchronization. When the synapse connecting the neurons is supplied with a phase selective feedback mechanism simulating STDP, induced dynamics of spikes in the coupled system resembles a phase locked mode with time lags between spikes oscillating about a specific value. This value, as we show by extensive numerical simulations, can be set arbitrary within a broad interval by tuning parameters of the STDP feedback.

2008 ◽  
Vol 20 (4) ◽  
pp. 974-993 ◽  
Author(s):  
Arunava Banerjee ◽  
Peggy Seriès ◽  
Alexandre Pouget

Several recent models have proposed the use of precise timing of spikes for cortical computation. Such models rely on growing experimental evidence that neurons in the thalamus as well as many primary sensory cortical areas respond to stimuli with remarkable temporal precision. Models of computation based on spike timing, where the output of the network is a function not only of the input but also of an independently initializable internal state of the network, must, however, satisfy a critical constraint: the dynamics of the network should not be sensitive to initial conditions. We have previously developed an abstract dynamical system for networks of spiking neurons that has allowed us to identify the criterion for the stationary dynamics of a network to be sensitive to initial conditions. Guided by this criterion, we analyzed the dynamics of several recurrent cortical architectures, including one from the orientation selectivity literature. Based on the results, we conclude that under conditions of sustained, Poisson-like, weakly correlated, low to moderate levels of internal activity as found in the cortex, it is unlikely that recurrent cortical networks can robustly generate precise spike trajectories, that is, spatiotemporal patterns of spikes precise to the millisecond timescale.


2019 ◽  
Vol 30 (3) ◽  
pp. 952-968
Author(s):  
Christoph Pokorny ◽  
Matias J Ison ◽  
Arjun Rao ◽  
Robert Legenstein ◽  
Christos Papadimitriou ◽  
...  

Abstract Memory traces and associations between them are fundamental for cognitive brain function. Neuron recordings suggest that distributed assemblies of neurons in the brain serve as memory traces for spatial information, real-world items, and concepts. However, there is conflicting evidence regarding neural codes for associated memory traces. Some studies suggest the emergence of overlaps between assemblies during an association, while others suggest that the assemblies themselves remain largely unchanged and new assemblies emerge as neural codes for associated memory items. Here we study the emergence of neural codes for associated memory items in a generic computational model of recurrent networks of spiking neurons with a data-constrained rule for spike-timing-dependent plasticity. The model depends critically on 2 parameters, which control the excitability of neurons and the scale of initial synaptic weights. By modifying these 2 parameters, the model can reproduce both experimental data from the human brain on the fast formation of associations through emergent overlaps between assemblies, and rodent data where new neurons are recruited to encode the associated memories. Hence, our findings suggest that the brain can use both of these 2 neural codes for associations, and dynamically switch between them during consolidation.


2014 ◽  
Vol 18 (6) ◽  
pp. 2141-2166 ◽  
Author(s):  
Y. Elshafei ◽  
M. Sivapalan ◽  
M. Tonts ◽  
M. R. Hipsey

Abstract. It is increasingly acknowledged that, in order to sustainably manage global freshwater resources, it is critical that we better understand the nature of human–hydrology interactions at the broader catchment system scale. Yet to date, a generic conceptual framework for building models of catchment systems that include adequate representation of socioeconomic systems – and the dynamic feedbacks between human and natural systems – has remained elusive. In an attempt to work towards such a model, this paper outlines a generic framework for models of socio-hydrology applicable to agricultural catchments, made up of six key components that combine to form the coupled system dynamics: namely, catchment hydrology, population, economics, environment, socioeconomic sensitivity and collective response. The conceptual framework posits two novel constructs: (i) a composite socioeconomic driving variable, termed the Community Sensitivity state variable, which seeks to capture the perceived level of threat to a community's quality of life, and acts as a key link tying together one of the fundamental feedback loops of the coupled system, and (ii) a Behavioural Response variable as the observable feedback mechanism, which reflects land and water management decisions relevant to the hydrological context. The framework makes a further contribution through the introduction of three macro-scale parameters that enable it to normalise for differences in climate, socioeconomic and political gradients across study sites. In this way, the framework provides for both macro-scale contextual parameters, which allow for comparative studies to be undertaken, and catchment-specific conditions, by way of tailored "closure relationships", in order to ensure that site-specific and application-specific contexts of socio-hydrologic problems can be accommodated. To demonstrate how such a framework would be applied, two socio-hydrological case studies, taken from the Australian experience, are presented and the parameterisation approach that would be taken in each case is discussed. Preliminary findings in the case studies lend support to the conceptual theories outlined in the framework. It is envisioned that the application of this framework across study sites and gradients will aid in developing our understanding of the fundamental interactions and feedbacks in such complex human–hydrology systems, and allow hydrologists to improve social–ecological systems modelling through better representation of human feedbacks on hydrological processes.


2020 ◽  
Author(s):  
Yuko Koyanagi ◽  
Yoshiyuki Oi ◽  
Masayuki Kobayashi

Background: The general anesthetic propofol induces frontal alpha rhythm in the cerebral cortex at a dose sufficient to induce loss of consciousness. The authors hypothesized that propofol-induced facilitation of unitary inhibitory postsynaptic currents would result in firing synchrony among postsynaptic pyramidal neurons that receive inhibition from the same presynaptic inhibitory fast-spiking neurons. Methods: Multiple whole cell patch clamp recordings were performed from one fast-spiking neuron and two or three pyramidal neurons with at least two inhibitory connections in rat insular cortical slices. The authors examined how inhibitory inputs from a presynaptic fast-spiking neuron modulate the timing of spontaneous repetitive spike firing among pyramidal neurons before and during 10 μM propofol application. Results: Responding to activation of a fast-spiking neuron with 150-ms intervals, pyramidal cell pairs that received common inhibitory inputs from the presynaptic fast-spiking neuron showed propofol-dependent decreases in average distance from the line of identity, which evaluates the coefficient of variation in spike timing among pyramidal neurons: average distance from the line of identity just after the first activation of fast-spiking neuron was 29.2 ± 24.1 (mean ± SD, absolute value) in control and 19.7 ± 19.2 during propofol application (P < 0.001). Propofol did not change average distance from the line of identity without activating fast-spiking neurons and in pyramidal neuron pairs without common inhibitory inputs from presynaptic fast-spiking neurons. The synchronization index, which reflects the degree of spike synchronization among pyramidal neurons, was increased by propofol from 1.4 ± 0.5 to 2.3 ± 1.5 (absolute value, P = 0.004) and from 1.5 ± 0.5 to 2.2 ± 1.0 (P = 0.030) when a presynaptic fast-spiking neuron was activated at 6.7 and 10 Hz, respectively, but not at 1, 4, and 13.3 Hz. Conclusions: These results suggest that propofol facilitates pyramidal neuron firing synchrony by enhancing inhibitory inputs from fast-spiking neurons. This synchrony of pyramidal neurons may contribute to the alpha rhythm associated with propofol-induced loss of consciousness. Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New


2005 ◽  
Vol 17 (11) ◽  
pp. 2337-2382 ◽  
Author(s):  
Robert Legenstein ◽  
Christian Naeger ◽  
Wolfgang Maass

Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.


Author(s):  
Reimbay Reimbayev ◽  
Kevin Daley ◽  
Igor Belykh

Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. In this paper, we study the emergence of synchronization in networks of bursting neurons as a highly non-trivial, combined effect of electrical and inhibitory connections. We report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism, which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.


Neuroscience ◽  
2004 ◽  
Vol 126 (4) ◽  
pp. 1063-1073 ◽  
Author(s):  
A Szűcs ◽  
Á Vehovszky ◽  
G Molnár ◽  
R.D Pinto ◽  
H.D.I Abarbanel

2013 ◽  
Vol 25 (2) ◽  
pp. 450-472 ◽  
Author(s):  
Jun Hu ◽  
Huajin Tang ◽  
K. C. Tan ◽  
Haizhou Li ◽  
Luping Shi

During the past few decades, remarkable progress has been made in solving pattern recognition problems using networks of spiking neurons. However, the issue of pattern recognition involving computational process from sensory encoding to synaptic learning remains underexplored, as most existing models or algorithms target only part of the computational process. Furthermore, many learning algorithms proposed in the literature neglect or pay little attention to sensory information encoding, which makes them incompatible with neural-realistic sensory signals encoded from real-world stimuli. By treating sensory coding and learning as a systematic process, we attempt to build an integrated model based on spiking neural networks (SNNs), which performs sensory neural encoding and supervised learning with precisely timed sequences of spikes. With emerging evidence of precise spike-timing neural activities, the view that information is represented by explicit firing times of action potentials rather than mean firing rates has been receiving increasing attention. The external sensory stimulation is first converted into spatiotemporal patterns using a latency-phase encoding method and subsequently transmitted to the consecutive network for learning. Spiking neurons are trained to reproduce target signals encoded with precisely timed spikes. We show that when a supervised spike-timing-based learning is used, different spatiotemporal patterns are recognized by different spike patterns with a high time precision in milliseconds.


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