Current-based Synapses Research Articles

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes.

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Constructing functional models from biophysically-detailed neurons.

Improving biological plausibility and functional capacity are two important goals for brain models that connect low-level neural details to high-level behavioral phenomena. We develop a method called "oracle-supervised Neural Engineering Framework" (osNEF) to train biologically-detailed spiking neural networks that realize a variety of cognitively-relevant dynamical systems. Specifically, we train networks to perform computations that are commonly found in cognitive systems (communication, multiplication, harmonic oscillation, and gated working memory) using four distinct neuron models (leaky-integrate-and-fire neurons, Izhikevich neurons, 4-dimensional nonlinear point neurons, and 4-compartment, 6-ion-channel layer-V pyramidal cell reconstructions) connected with various synaptic models (current-based synapses, conductance-based synapses, and voltage-gated synapses). We show that osNEF networks exhibit the target dynamics by accounting for nonlinearities present within the neuron models: performance is comparable across all four systems and all four neuron models, with variance proportional to task and neuron model complexity. We also apply osNEF to build a model of working memory that performs a delayed response task using a combination of pyramidal cells and inhibitory interneurons connected with NMDA and GABA synapses. The baseline performance and forgetting rate of the model are consistent with animal data from delayed match-to-sample tasks (DMTST): we observe a baseline performance of 95% and exponential forgetting with time constant τ = 8.5s, while a recent meta-analysis of DMTST performance across species observed baseline performances of 58 - 99% and exponential forgetting with time constants of τ = 2.4 - 71s. These results demonstrate that osNEF can train functional brain models using biologically-detailed components and open new avenues for investigating the relationship between biophysical mechanisms and functional capabilities.

Fast Simulations of Highly-Connected Spiking Cortical Models Using GPUs.

Over the past decade there has been a growing interest in the development of parallel hardware systems for simulating large-scale networks of spiking neurons. Compared to other highly-parallel systems, GPU-accelerated solutions have the advantage of a relatively low cost and a great versatility, thanks also to the possibility of using the CUDA-C/C++ programming languages. NeuronGPU is a GPU library for large-scale simulations of spiking neural network models, written in the C++ and CUDA-C++ programming languages, based on a novel spike-delivery algorithm. This library includes simple LIF (leaky-integrate-and-fire) neuron models as well as several multisynapse AdEx (adaptive-exponential-integrate-and-fire) neuron models with current or conductance based synapses, different types of spike generators, tools for recording spikes, state variables and parameters, and it supports user-definable models. The numerical solution of the differential equations of the dynamics of the AdEx models is performed through a parallel implementation, written in CUDA-C++, of the fifth-order Runge-Kutta method with adaptive step-size control. In this work we evaluate the performance of this library on the simulation of a cortical microcircuit model, based on LIF neurons and current-based synapses, and on balanced networks of excitatory and inhibitory neurons, using AdEx or Izhikevich neuron models and conductance-based or current-based synapses. On these models, we will show that the proposed library achieves state-of-the-art performance in terms of simulation time per second of biological activity. In particular, using a single NVIDIA GeForce RTX 2080 Ti GPU board, the full-scale cortical-microcircuit model, which includes about 77,000 neurons and 3 · 108 connections, can be simulated at a speed very close to real time, while the simulation time of a balanced network of 1,000,000 AdEx neurons with 1,000 connections per neuron was about 70 s per second of biological activity.

The neurodynamics of epilepsy: a homotopy analysis between current-based and conductance-based synapses in a neural field model of epilepsy

Unlike Hodgkin-Huxley type spiking models, the overwhelming majority of neural field models use current-based synapses [1]. Although there exist neural field models that employ conductance-based synapses, it is not clear what their exact effects on the dynamics are, particularly with respect to epileptic dynamics. Neural field models of epilepsy typically describe the transition to seizure-like activity as a bifurcation [2]. This research examines the effects of conductance-based synapses on the transition from normal to seizure-like activity in neural field models.

Influence of different types of downscaling on a cortical microcircuit model

Neural network models are routinely downscaled in terms of numbers of neurons or synapses because of a lack of computational resources or the limited capacity of a given neuromorphic hardware. Unfortunately the downscaling is often performed without explicit mention of the limitations this entails [1]. This is relevant since downscaling can substantially affect the dynamics. For instance, reducing the number of neurons N while preserving in-degrees K increases shared inputs and hence correlations. Theoretical results on scaling are derived using simplifying assumptions. Therefore we use simulations to systematically investigate the effects of downscaling on the dynamics of a layered microcircuit model of early sensory cortex [2]. The model consists of eight excitatory and inhibitory populations of leaky integrate-and-fire point neurons with current-based synapses and homogeneous Poisson input. The full-scale network, comprising approximately 80,000 neurons and 0.3 billion synapses, is in the balanced state [3,4], displaying asynchronous irregular activity. For networks of binary or integrate-and-fire neurons in this state, the total current-based synaptic input to a given neuron is well approximated by a Gaussian noise, of which the mean and variance determine the firing rate. One way of preserving this mean and variance has been touched upon: reducing N but keeping K constant. For reduced K, firing rates can be preserved by an appropriate choice of synaptic weights, the ratio between excitatory and inhibitory weights, and mean external input [3,4]. However, these scaling methods are based on single-neuron dynamics and ignore network effects. For instance, scaling synaptic weights J and mean external input to preserve rates implies constant J2 K [3], which changes the feedback on the population level and hence qualitatively changes the network state [5]. An alternative that takes into account both single-neuron and network effects is to choose J so that J K is constant and adjusting the external drive to maintain the input variance. This preserves the shape of cross-correlation functions in balanced E-I networks [5]. However, the magnitude of the correlations increases as K decreases, and a restriction to positive external input variance limits the compensation for increased intrinsic variance. We consider the effects of the above scaling options on correlations, firing rates, synchrony, and irregularity of spiking activity. Although each method achieves near-constancy of one or more dynamical features, none preserves all of them. These results can be used to downscale networks of neurons with current-based synapses in the asynchronous irregular regime in a controlled manner. However, since it is not yet possible to analytically predict all the effects of scaling, it remains essential to compare down-scaled simulations with their full-scale counterparts.

The Neurodynamics of Epilepsy: Synaptic regulation and reversal potential modulation during seizures in a neural field model with conductance-based synapses

Recent experimental results have shown that during the initiation and termination of epileptic seizures there is a significant change in the micro-ionic environment of cortical neurons [1] that affects network balance between excitation and inhibition. This is evident through non-synaptic changes in the micro-ionic environment such as the excitatory and inhibitory reversal potentials and conductances that have been measured over the course of a seizure in an in vitro mouse model [2]. Although this phenomenon of a change in reversal potentials during seizures has recently been simulated numerically using a relatively small number of detailed multi-compartmental spiking models [3], it has not yet been modelled using larger scale mesoscopic neural field models within an analytical framework. This is because the majority of these models use current-based synapses, which do not take the reversal potentials into account [4] as they are more difficult to incorporate in mesoscopic models of brain dynamics. We present an analysis of a neural field model with conductance-based synapses that takes into account the reversal potentials and the nonlinear multiplicative effect that they have on the associated conductance. The conductance-based synapses model is derived, analysed and juxtaposed with the current-based synapses model and the results interpreted physiologically. A comparative bifurcation analysis of both models reveals that there are significant differences in the oscillatory behaviours that correspond to epileptic seizures [4]. In the conductance-based synapses model, there are endogenous anti-epileptic regulatory or control mechanisms that operate on the synaptic scale, whereas previously these were thought to be mainly on the network level; for example, in terms of feedback, feed-forward and surround inhibition [5]. Further, upon modulation of the reversal potentials, the new model exhibits seizure behaviour that initiates and terminates due to non-synaptic ionic mechanisms, similar to that measured in recent experiments [1]. Seizure dynamics in the brain are modulated by both synaptic regulatory mechanisms and non-synaptic homeostatic mechanisms, which play key roles during seizure initiation, spread and termination [5]. These mechanisms have been investigated using a novel analytical neural field model which has provided insights into understanding epileptic brain dynamics that are not currently observable in electrophysiological experiments and numerical simulations alone.

Key role of voltage-dependent properties of synaptic currents in robust network synchronization

Robust synchronized activity is ubiquitous in real neural networks. Diverse synaptic properties contribute to such robust synchronization. Synaptic current induced by an input spike is dependent on the voltage of post-synaptic neuron in real neural systems. Current-based synapse models, which neglect the voltage-dependent properties of synaptic currents, are widely used for analysis of robust synchronization in neural networks due to their simplicity. However, it was found in this paper that the voltage-dependent properties of synaptic currents play a key role in robust network synchronization in most cases, implying that current-based synapses are oversimplified for analysis of robust network synchronization.

RELATIONSHIP BETWEEN APPLICABILITY OF CURRENT-BASED SYNAPSES AND UNIFORMITY OF FIRING PATTERNS

The purpose of this paper is to identify situations in neural network modeling where current-based synapses are applicable. The applicability of current-based synapse model for studying post-transient behavior of neural networks is discussed in terms of average synaptic current strength induced by per spike during one firing cycle of a neuron (or briefly per spike synaptic current strength). It was found that current-based synapse models are applicable in both situations where both the interspike intervals of the neurons and the distribution of firing times of the neurons are uniform, and where the firing of all neurons is synchronized. If neither the interspike intervals nor the distribution of firing times of the neurons is uniform or the reversal potential is between the rest and threshold potentials, current-based synapse models may be oversimplified.

Dynamics of self-sustained activity in random networks with strong synapses

An understanding of short-term memory requires models of neural networks which are able to sustain activity in the absence of external input for several seconds. About half a century ago, [1] predicted the existence of self-sustained activity in neural networks with strong synapses. Despite this finding, most previous studies on the dynamics of neural networks are restricted to weak synapses, i.e. to a regime where the diffusion approximation is applicable. Recently, it has been shown in simulations that self-sustained activity emerges in networks of integrate-and-fire (IaF) neurons with strong synapses modeled as currents [2] (rather than as conductances, see [3]). Above a critical synaptic weight, the lifetime of self-sustained activity increases rapidly (Fig. ​(Fig.1C).1C). We present a stochastic model of the dynamics of a balanced random network of IaF neurons with current-based synapses in the strong-synapse regime. Based on the network's firing-rate transfer [4], we show that the firing-rate dynamics becomes bistable if the synapses are sufficiently strong: in addition to the quiescent state, a second stable fixed point at moderate firing rates is created (sketched in Fig. ​Fig.1A).1A). Firing-rate fluctuations can destabilize this fixed point, thereby limiting the lifetime of self-sustained activity (sketched in Fig. ​Fig.1B).1B). The magnitude of these fluctuations is mainly determined by the amount of spike-train correlations [5]. Our model explains the existence and the lifetime of self-sustained activity, and how the lifetime depends on the network size, the connectivity, the level of inhibition and the synapse strength. The results of our model are confirmed by network simulations. Figure 1 A. Phase space of the firing-rate dynamics. Dependence of the rate change dr/dt on the rate r (sketch). B. Firing-rate distribution in the self-sustained state (sketch). C. Dependence of the lifetime of self-sustained activity (color coded) on the level ...

A bifurcation analysis of a modified neural field model: conductance-based synapses act as an anti-epileptic regulatory mechanism

The spread of seizure-like behaviour through the cortex is facilitated not only by hyper-excitable, hyper-synchronous neuronal population firing, but by overcoming the regulatory mechanisms of the brain, such as feedback and feed-forward inhibition. These control mechanisms normally stabilise such pathological behaviour [1]. We suggest an additional network regulatory mechanism in the form of a ‘shunting’ effect based on the properties of conductance-based synapses, an important neurophysiological structure whose mechanism is often overlooked in macroscopic models of brain dynamics. A mathematical neural field model [2] is modified to include conductance-based synapses as opposed to current-based synapses. This is a more realistic description of synaptic dynamics that has a significant effect on the network behaviour [3]. A nonlinear summation of the synaptic currents is introduced that incorporates local feedback from the membrane potential and an ‘effective’ time constant that varies inversely with the amount of input. The result is a more physiologically detailed description of the synaptic current produced by post-synaptic potentials. The fixed-points of the new system are found and a perturbation analysis is performed. The stability of the system is determined and a bifurcation diagram is generated using the external input and network balance as bifurcation parameters. These results are then compared to that of the original model with current-based synapses and the differences interpreted physiologically. The fixed points, dynamics and oscillatory properties of the conductance-based model differ significantly from the current-based model. This is largely due to the ‘shunting’ effect of the synapses, which acts as a network regulatory mechanism. In particular, oscillatory behaviour in the conductance-based model is suppressed. Hence, conductance-based synapses are an important physiological structure whose mechanism of synaptic transmission should not be neglected in mean-field models, particularly when applied to epilepsy.

The perturbation response and power spectrum of a mean-field of IF neurons with inhomogeneous inputs

The aim of this study is to construct a bottom-up model of cortical dynamics that is capable of describing the same types of neural phenomena as top-down continuum models, namely the power spectrum, frequency response to perturbation and EEG time-series. The key difference between the two approaches is that the bottom-up approach preserves more of the intrinsic physiological details than the top-down models [1]. A stochastic Fokker-Planck modelling approach is used to describe a network of leak integrate-and-fire (IF) neurons with temporally inhomogeneous inputs. Previous work either calculated the response of a single neuron with conductance-based synapses, or the network with current-based synapses [2]. In this study we use and extend a recently published Fokker-Planck approach [3] within an analytical framework to calculate the dynamical firing-rate of a network with conductance-based synapses receiving temporally inhomogeneous synaptic input. In particular, the network has fully recurrent connectivity with both the steady-state and the dynamic perturbation response of the background activity fed back into the inputs. This is done in a self-consistent formalism [4] for a network of excitatory and inhibitory neurons. The Fokker-Planck formalism enables the calculation of the linear response of the firing-rate to perturbation with recurrent connections. The power spectrum and EEG time-series of the network are calculated by treating the synaptic inputs as an inhomogeneous Poisson process. From this we determine the auto-correlation function, which is identified as a cyclo-stationary process. The signal is then phase-averaged over its period and the Wiener-Khinchin theorem is used to determine the power spectrum from the autocorrelation function. The power spectrum is convolved with a filter to approximate the local field potential propagation through the extra-cellular fluid [5]. The analytical results of the frequency response of the dynamical firing rate and its power spectra are compared with numerical simulation results for a recurrently connected network with conductance-based synapses and temporally inhomogeneous inputs. Results are obtained using parameter values that represent typical cortical in vivo neurons [4]. This work is the first stage necessary for constructing a physiologically plausible mathematical model of a mesoscopic network of cortical columns.

High storage capacity of synfire chains in large-scale cortical networks of conductance-based spiking neurons

We demonstrate stable dynamics of synchronous pulse packet propagation and global asynchronous irregular (AI) activity in a sparse network of 105 neurons in which excitatory connectivity is derived from a random superposition of synfire chains having a total length of up to 80,000 pools. This is the largest amount of synfire chains to have been stably embedded in a network model of spiking neurons: about two orders of magnitude great than achieved previously [1-3]. Key features of the model which allow this high storage capacity are: (1) conductance-based rather than current-based synapses; and (2) inhibitory neurons in the synfire chain pools. As noted recently [3] the use of conductance over current based results in a narrower membrane potential distribution with a mean closer to threshold, which is more favourable for pulse-packet propagation at realistic levels of AI activity and background input. Recurrent dynamics of the AI state is driven by the propagating pulse packets which deliver random excitatory and inhibitory 'background input' to the rest of the network. The equilibrium dynamical behaviour of the network depends on a critical level of excitatory and inhibitory background input above which synfire wave propagation ceases to be viable. In our simulation protocol synfire waves are initiated by ongoing, intermittent delivery of external input pulses. In the stable regime, an upper limit in the number of simultaneously propagating pulse packets is reached, typically ~ 5-30 waves, above which further waves are only successfully initiated at the expense of existing waves. Using a semi-analytical framework, storage capacity, and the number of pulse packets that can propagate simultaneously, is calculated. Mean field analysis is used to estimate the stability and spiking rate of the AI state, combined with a numerical determination of the stability of wave propagation. Results agree qualitatively with simulations and correctly predict the order of magnitude of storage capacity. Departures from mean field theory are observed, most notably the greater fluctuations in the AI state particularly as the upper limit of storage is approached, which impacts upon the stability of pulse packet propagation and reduces the maximum number of simultaneously propagating waves. We also demonstrate in a modified version of this architecture that includes branching chains how synfire waves can be generated and maintained endogenously, using the same mechanism which stabilises the number of synfire waves at upper limit determined by the critical level of background input.

An Analytical Model for the ‘Large, Fluctuating Synaptic Conductance State’ Typical of Neocortical Neurons In Vivo

A model of in vivo-like neocortical activity is studied analytically in relation to experimental data and other models in order to understand the essential mechanisms underlying such activity. The model consists of a network of sparsely connected excitatory and inhibitory integrate-and-fire (IF) neurons with conductance-based synapses. It is shown that the model produces values for five quantities characterizing in vivo activity that are in agreement with both experimental ranges and a computer-simulated Hodgkin-Huxley model adapted from the literature (Destexhe et al. (2001) Neurosci. 107(1): 13-24). The analytical model builds on a study by Brunel (2000) (J. Comput. Neurosci. 8: 183-208), which used IF neurons with current-based synapses, and therefore does not account for the full range of experimental data. The present results suggest that the essential mechanism required to explain a range of data on in vivo neocortical activity is the conductance-based synapse and that the particular model of spike initiation used is not crucial. Thus the IF model with conductance-based synapses may provide a basis for the analytical study of the "large, fluctuating synaptic conductance state" typical of neocortical neurons in vivo.