Synaptic Parameters Research Articles

Stability and synchronization of coupled Rulkov map-based neurons with chemical synapses

The stability and synchronization analysis of two chaotic Rulkov maps coupled by bidirectional and symmetric chemical synapses are taken into account. As a function of intrinsic control parameters α, σ, η, reversal potential v, synaptic parameters θ, k, and external chemical coupling strength gc, conditions for stability of a fixed point for this system are derived. Some typical domains are chosen for numerical simulations which include time evolution of transmembrane voltages and phase portraits, and both of them are presented for theoretical analysis. Based on the master stability functions approach and calculation of the maximum Lyapunov exponents of synchronization errors, synchronized regions of the coupled neurons and a strip-shaped chaotic structure in parameter-space are obtained. Specially, given some values of control parameter α, we propose interval ranges of coupling strength gc in which the two chaotic Rulkov map-based neurons can be synchronized completely. It is shown that there exist different transition mechanisms of the neuronal spiking and bursting synchronization. The synchronized regions will become smaller and smaller as control parameter α or synaptic parameter θ increases. Nevertheless, the coupled neurons can at first transit from desynchrony to in-phase synchronization, and then to complete synchronization as chemical coupling strength gc increases. Compared with control parameter α and synaptic parameter θ, chemical coupling strength gc plays an opposite role in the process of synchronization transition. These findings could be useful for further understanding the role of two chaotic Rulkov maps coupled by bidirectional and symmetric chemical synapses in the field of cooperative behaviors of coupled neurons.

Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

Diffusive electrical connections in neuronal networks are instantaneous, while excitatory or inhibitory couplings through chemical synapses contain a transmission time-delay. Moreover, chemical synapses are nonlinear dynamical systems whose behavior can be described by nonlinear differential equations. In this work, neuronal networks with diffusive electrical couplings and time-delayed dynamic chemical couplings are considered. We investigate the effects of distributed time delays on phase synchronization of bursting neurons. We observe that in both excitatory and Inhibitory chemical connections, the phase synchronization might be enhanced when time-delay is taken into account. This distributed time delay can induce a variety of phase-coherent dynamical behaviors. We also study the collective dynamics of network of bursting neurons. The network model presents the so-called Small-World property, encompassing neurons whose dynamics have two time scales (fast and slow time scales). The neuron parameters in such Small-World network, are supposed to be slightly different such that, there may be synchronization of the bursting (slow) activity if the coupling strengths are large enough. Bounds for the critical coupling strengths to obtain burst synchronization in terms of the network structure are given. Our studies show that the network synchronizability is improved, as its heterogeneity is reduced. The roles of synaptic parameters, more precisely those of the coupling strengths and the network size are also investigated.

Shaping Neuronal Network Activity by Presynaptic Mechanisms

Neuronal microcircuits generate oscillatory activity, which has been linked to basic functions such as sleep, learning and sensorimotor gating. Although synaptic release processes are well known for their ability to shape the interaction between neurons in microcircuits, most computational models do not simulate the synaptic transmission process directly and hence cannot explain how changes in synaptic parameters alter neuronal network activity. In this paper, we present a novel neuronal network model that incorporates presynaptic release mechanisms, such as vesicle pool dynamics and calcium-dependent release probability, to model the spontaneous activity of neuronal networks. The model, which is based on modified leaky integrate-and-fire neurons, generates spontaneous network activity patterns, which are similar to experimental data and robust under changes in the model's primary gain parameters such as excitatory postsynaptic potential and connectivity ratio. Furthermore, it reliably recreates experimental findings and provides mechanistic explanations for data obtained from microelectrode array recordings, such as network burst termination and the effects of pharmacological and genetic manipulations. The model demonstrates how elevated asynchronous release, but not spontaneous release, synchronizes neuronal network activity and reveals that asynchronous release enhances utilization of the recycling vesicle pool to induce the network effect. The model further predicts a positive correlation between vesicle priming at the single-neuron level and burst frequency at the network level; this prediction is supported by experimental findings. Thus, the model is utilized to reveal how synaptic release processes at the neuronal level govern activity patterns and synchronization at the network level.

Prenatal choline supplementation attenuates spatial learning deficits of offspring rats exposed to low-protein diet during fetal period

Prenatal intake of choline has been reported to lead to enhanced cognitive function in offspring, but little is known about the effects on spatial learning deficits. The present study examined the effects of prenatal choline supplementation on developmental low-protein exposure and its potential mechanisms. Pregnant female rats were fed either a normal or low-protein diet containing sufficient choline (1.1g/kg choline chloride) or supplemented choline (5.0g/kg choline chloride) until delivery. The Barnes maze test was performed at postnatal days 31–37. Choline and its metabolites, the synaptic structural parameters of the CA1 region in the brain of the newborn rat, were measured. The Barnes maze test demonstrated that prenatal low-protein pups had significantly greater error scale values, hole deviation scores, strategy scores and spatial search strategy and had lesser random search strategy values than normal protein pups (all P<.05). These alterations were significantly reversed by choline supplementation. Choline supplementation increased the brain levels of choline, betaine, phosphatidylethanolamine and phosphatidylcholine of newborns by 51.35% (P<.05), 33.33% (P<.001), 28.68% (P<.01) and 23.58% (P<.05), respectively, compared with the LPD group. Prenatal choline supplementation reversed the increased width of the synaptic cleft (P<.05) and decreased the curvature of the synaptic interface (P<.05) induced by a low-protein diet. Prenatal choline supplementation could attenuate the spatial learning deficits caused by prenatal protein malnutrition by increasing brain choline, betaine and phospholipids and by influencing the hippocampus structure.

Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating

Seizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5–10min compared to approximately 1–2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated.

Early attenuation of long-term potentiation in senescence-accelerated mouse prone 8.

Senescence-accelerated mouse (SAM) is an experimental model animal showing a short lifespan and rapid advancement of senescence. Especially, SAM prone 8 (SAMP8) shows age-related impairment of learning and memory, and thus, it is a good model for age-related cognitive function. However, the synaptic characteristics related to cognitive function of SAMP8 have been poorly understood. In this study, we quantitatively evaluated the synaptic transmission and synaptic plasticity using hippocampal slices obtained from SAMP8 with electrophysiological methods to elucidate the synaptic features of SAMP8. We used the field recordings to measure some synaptic parameters. The slope of field excitatory postsynaptic potentials decreased with age in both SAMP8 and SAMresistant 1 (SAMR1), the control strain of SAMP8. The paired-pulse ratio (PPR), a representative of short-term synaptic plasticity, also decreased in both strains with age. On the other hand, although both SAMR1 and SAMP8 exhibited age-dependent decrease in long-term potentiation (LTP), a representative of long-term synaptic plasticity, the decrease in LTP in SAMP8 started at 6months of age, while in SAMR1, it was observed at 14months but not at 6months of age. The PPRs after high-frequency stimulation for LTP induction were smaller than those before the stimulation. These results indicate that synaptic plasticity in SAMP8 deteriorates at an earlier age compared to SAMR1, and are consistent with behavioral tests showing early impairment of learning and memory of SAMP8. Our study is the first report on quantitative analysis of synaptic function at SAMP8 hippocampus and corroborates the behavioral studies showing cognitive dysfunction with age; therefore, it will be helpful for future studies on aging.

Robustness of spiking Deep Belief Networks to noise and reduced bit precision of neuro-inspired hardware platforms.

Increasingly large deep learning architectures, such as Deep Belief Networks (DBNs) are the focus of current machine learning research and achieve state-of-the-art results in different domains. However, both training and execution of large-scale Deep Networks require vast computing resources, leading to high power requirements and communication overheads. The on-going work on design and construction of spike-based hardware platforms offers an alternative for running deep neural networks with significantly lower power consumption, but has to overcome hardware limitations in terms of noise and limited weight precision, as well as noise inherent in the sensor signal. This article investigates how such hardware constraints impact the performance of spiking neural network implementations of DBNs. In particular, the influence of limited bit precision during execution and training, and the impact of silicon mismatch in the synaptic weight parameters of custom hybrid VLSI implementations is studied. Furthermore, the network performance of spiking DBNs is characterized with regard to noise in the spiking input signal. Our results demonstrate that spiking DBNs can tolerate very low levels of hardware bit precision down to almost two bits, and show that their performance can be improved by at least 30% through an adapted training mechanism that takes the bit precision of the target platform into account. Spiking DBNs thus present an important use-case for large-scale hybrid analog-digital or digital neuromorphic platforms such as SpiNNaker, which can execute large but precision-constrained deep networks in real time.

DESIGN OF DETERMINISTIC MODEL OF SIGNAL TRANSDUCTION BETWEEN NEURONAL CELLS

Mathematical model describing signal transduction between neurons has been presented using the system of nonlinear ordinary differential equations. The Cauchy problem for the given system has been solved numerically and system parameters were adjusted to match the results of experimental measurements of extracellular postsynaptic potentials in rat hippocampus slices. While fitting model to the experimental data some values of synaptic parameters have been determined.

Role of synaptic structural plasticity in impairments of spatial learning and memory induced by developmental lead exposure in Wistar rats.

Lead (Pb) is found to impair cognitive function. Synaptic structural plasticity is considered to be the physiological basis of synaptic functional plasticity and has been recently found to play important roles in learning and memory. To study the effect of Pb on spatial learning and memory at different developmental stages, and its relationship with alterations of synaptic structural plasticity, postnatal rats were randomly divided into three groups: Control; Pre-weaning Pb (Parents were exposed to 2 mM PbCl2 3 weeks before mating until weaning of pups); Post-weaning Pb (Weaned pups were exposed to 2 mM PbCl2 for 9 weeks). The spatial learning and memory of rats was measured by Morris water maze (MWM) on PND 85–90. Rat pups in Pre-weaning Pb and Post-weaning Pb groups performed significantly worse than those in Control group (p<0.05). However, there was no significant difference in the performance of MWM between the two Pb-exposure groups. Before MWM (PND 84), the number of neurons and synapses significantly decreased in Pre-weaning Pb group, but not in Post-weaning Pb group. After MWM (PND 91), the number of synapses in Pre-weaning Pb group increased significantly, but it was still less than that of Control group (p<0.05); the number of synapses in Post-weaning Pb group was also less than that of Control group (p<0.05), although the number of synapses has no differences between Post-weaning Pb and Control groups before MWM. In both Pre-weaning Pb and Post-weaning Pb groups, synaptic structural parameters such as thickness of postsynaptic density (PSD), length of synaptic active zone and synaptic curvature increased significantly while width of synaptic cleft decreased significantly compared to Control group (p<0.05). Our data demonstrated that both early and late developmental Pb exposure impaired spatial learning and memory as well as synaptic structural plasticity in Wistar rats.

Tracking slow modulations in synaptic gain using dynamic causal modelling: Validation in epilepsy

In this work we propose a proof of principle that dynamic causal modelling can identify plausible mechanisms at the synaptic level underlying brain state changes over a timescale of seconds. As a benchmark example for validation we used intracranial electroencephalographic signals in a human subject. These data were used to infer the (effective connectivity) architecture of synaptic connections among neural populations assumed to generate seizure activity. Dynamic causal modelling allowed us to quantify empirical changes in spectral activity in terms of a trajectory in parameter space — identifying key synaptic parameters or connections that cause observed signals. Using recordings from three seizures in one patient, we considered a network of two sources (within and just outside the putative ictal zone). Bayesian model selection was used to identify the intrinsic (within-source) and extrinsic (between-source) connectivity. Having established the underlying architecture, we were able to track the evolution of key connectivity parameters (e.g., inhibitory connections to superficial pyramidal cells) and test specific hypotheses about the synaptic mechanisms involved in ictogenesis. Our key finding was that intrinsic synaptic changes were sufficient to explain seizure onset, where these changes showed dissociable time courses over several seconds. Crucially, these changes spoke to an increase in the sensitivity of principal cells to intrinsic inhibitory afferents and a transient loss of excitatory–inhibitory balance.

Zero-lag synchronization despite inhomogeneities in a relay system.

A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.

Modulation of a Single Neuron Has State-Dependent Actions on Circuit Dynamics,.

When does neuromodulation of a single neuron influence the output of the entire network? We constructed a five-cell circuit in which a neuron is at the center of the circuit and the remaining neurons form two distinct oscillatory subnetworks. All neurons were modeled as modified Morris-Lecar models with a hyperpolarization-activated conductance (ḡh ) in addition to calcium (ḡCa ), potassium (ḡK ), and leak conductances. We determined the effects of varying ḡCa , ḡK , and ḡh on the frequency, amplitude, and duty cycle of a single neuron oscillator. The frequency of the single neuron was highest when the ḡK and ḡh conductances were high and ḡCa was moderate whereas, in the traditional Morris-Lecar model, the highest frequencies occur when both ḡK and ḡCa are high. We randomly sampled parameter space to find 143 hub oscillators with nearly identical frequencies but with disparate maximal conductance, duty cycles, and burst amplitudes, and then embedded each of these hub neurons into networks with different sets of synaptic parameters. For one set of network parameters, circuit behavior was virtually identical regardless of the underlying conductances of the hub neuron. For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron. This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.

A TRPV Channel in Drosophila Motor Neurons Regulates Presynaptic Resting Ca2+ Levels, Synapse Growth, and Synaptic Transmission

Presynaptic resting Ca(2+) influences synaptic vesicle (SV) release probability. Here, we report that a TRPV channel, Inactive (Iav), maintains presynaptic resting [Ca(2+)] by promoting Ca(2+) release from the endoplasmic reticulum in Drosophila motor neurons, and is required for both synapse development and neurotransmission. We find that Iav activates the Ca(2+)/calmodulin-dependent protein phosphatase calcineurin, which is essential for presynaptic microtubule stabilization at the neuromuscular junction. Thus, loss of Iav induces destabilization of presynaptic microtubules, resulting in diminished synaptic growth. Interestingly, expression of human TRPV1 in Iav-deficient motor neurons rescues these defects. We also show that the absence of Iav causes lower SV release probability and diminished synaptic transmission, whereas Iav overexpression elevates these synaptic parameters. Together, our findings indicate that Iav acts as a key regulator of synaptic development and function by influencing presynaptic resting [Ca(2+)].

Stimulus dependence of local field potential spectra: experiment versus theory.

The local field potential (LFP) captures different neural processes, including integrative synaptic dynamics that cannot be observed by measuring only the spiking activity of small populations. Therefore, investigating how LFP power is modulated by external stimuli can offer important insights into sensory neural representations. However, gaining such insight requires developing data-driven computational models that can identify and disambiguate the neural contributions to the LFP. Here, we investigated how networks of excitatory and inhibitory integrate-and-fire neurons responding to time-dependent inputs can be used to interpret sensory modulations of LFP spectra. We computed analytically from such models the LFP spectra and the information that they convey about input and used these analytical expressions to fit the model to LFPs recorded in V1 of anesthetized macaques (Macaca mulatta) during the presentation of color movies. Our expressions explain 60%-98% of the variance of the LFP spectrum shape and its dependency upon movie scenes and we achieved this with realistic values for the best-fit parameters. In particular, synaptic best-fit parameters were compatible with experimental measurements and the predictions of firing rates, based only on the fit of LFP data, correlated with the multiunit spike rate recorded from the same location. Moreover, the parameters characterizing the input to the network across different movie scenes correlated with cross-scene changes of several image features. Our findings suggest that analytical descriptions of spiking neuron networks may become a crucial tool for the interpretation of field recordings.

Modeling Binaural Responses in the Auditory Brainstem to Electric Stimulation of the Auditory Nerve

Bilateral cochlear implants (CIs) provide improvements in sound localization and speech perception in noise over unilateral CIs. However, the benefits arise mainly from the perception of interaural level differences, while bilateral CI listeners' sensitivity to interaural time difference (ITD) is poorer than normal. To help understand this limitation, a set of ITD-sensitive neural models was developed to study binaural responses to electric stimulation. Our working hypothesis was that central auditory processing is normal with bilateral CIs so that the abnormality in the response to electric stimulation at the level of the auditory nerve fibers (ANFs) is the source of the limited ITD sensitivity. A descriptive model of ANF response to both acoustic and electric stimulation was implemented and used to drive a simplified biophysical model of neurons in the medial superior olive (MSO). The model's ITD sensitivity was found to depend strongly on the specific configurations of membrane and synaptic parameters for different stimulation rates. Specifically, stronger excitatory synaptic inputs and faster membrane responses were required for the model neurons to be ITD-sensitive at high stimulation rates, whereas weaker excitatory synaptic input and slower membrane responses were necessary at low stimulation rates, for both electric and acoustic stimulation. This finding raises the possibility of frequency-dependent differences in neural mechanisms of binaural processing; limitations in ITD sensitivity with bilateral CIs may be due to a mismatch between stimulation rate and cell parameters in ITD-sensitive neurons.

Altered synaptic structure in the hippocampus in a mouse model of Alzheimer's disease with soluble amyloid-β oligomers and no plaque pathology.

BackgroundMounting evidence suggests that soluble oligomers of amyloid-β (oAβ) represent the pertinent synaptotoxic form of Aβ in sporadic Alzheimer’s disease (AD); however, the mechanistic links between oAβ and synaptic degeneration remain elusive. Most in vivo experiments to date have been limited to examining the toxicity of oAβ in mouse models that also possess insoluble fibrillar Aβ (fAβ), and data generated from these models can lead to ambiguous interpretations. Our goal in the present study was to examine the effects of soluble oAβ on neuronal and synaptic structure in the amyloid precursor protein (APP) E693Q (“Dutch”) mouse model of AD, which develops intraneuronal accumulation of soluble oAβ with no detectable plaques in AD-relevant brain regions. We performed quantitative analyses of neuronal pathology, including dendrite morphology, spine density, and synapse ultrastructure in individual hippocampal CA1 neurons.ResultsWhen assessing neuronal morphology and complexity we observed significant alterations in apical but not in basal dendritic arbor length in Dutch mice compared to wild type. Moreover, Dutch mice exhibited a significant decrease in dendritic arborization with a decrease in dendritic length and number of intersections at 120 μm and 150 μm from the soma, respectively. We next examined synaptic parameters and found that while there were no differences in overall synaptic structure, Dutch mice displayed a significant reduction in the post-synaptic density (PSD) length of synapses on mushroom spines, in comparison to wild type littermates.ConclusionThe structural alterations to individual neurons in Dutch mice along with the changes in larger dendritic spines support the Aβ oligomer hypothesis, which postulates that the early cognitive impairments that occur in AD are attributed to the accumulation of soluble oAβ first affecting at the synaptic level with subsequent structural disturbances and cellular degeneration.Electronic supplementary materialThe online version of this article (doi:10.1186/1750-1326-9-41) contains supplementary material, which is available to authorized users.

Homeostasis vs allostasis: implications for brain function and mental disorders.

Most drugs that alter mental function, whether for recreational purposes or to treat mental disorders, affect synaptic transmission. Some drugs reshape the action potential, altering release of neurotransmitter; others antagonize or enhance the effect of a neurotransmitter on its synaptic receptor protein. Still other drugs inhibit reuptake of the neurotransmitter from the extracellular space, thus prolonging its action at the synapse. This leads naturally to the idea that disorders of thought, attention, and mood are fundamentally disorders of the synapse. Moreover, it presents a rationale for treating mental disorders by pharmacotherapy of the synapse. The rationale follows the venerable model of physiological regulation, homeostasis, where each parameter is supposed to maintain a certain value. A higher or lower value is considered “inappropriate” and thus potentially both a cause of disorder and a logical target for therapeutic readjustment. Normal mental functioning supposedly requires various synaptic parameters to hold their set values, whereas mental disorders supposedly result from “inappropriate” values. Certain neurons might release too much transmitter; others might release too little. A transmitter’s action might be too weak or too strong; or it might be too brief or too prolonged. Such are the hypothetical “inappropriate” values that drugs are sup

Unsupervised learnable neuron model with nonlinear interaction on dendrites

Recent researches have provided strong circumstantial support to dendrites playing a key and possibly essential role in computations. In this paper, we propose an unsupervised learnable neuron model by including the nonlinear interactions between excitation and inhibition on dendrites. The model neuron self-adjusts its synaptic parameters, so that the synapse to dendrite, according to a generalized delta-rule-like algorithm. The model is used to simulate directionally selective cells by the unsupervised learning algorithm. In the simulations, we initialize the interaction and dendrite of the neuron randomly and use the generalized delta-rule-like unsupervised learning algorithm to learn the two-dimensional multi-directional selectivity problem without an external teacher’s signals. Simulation results show that the directionally selective cells can be formed by unsupervised learning, acquiring the required number of dendritic branches, and if needed, enhanced and if not, eliminated. Further, the results show whether a synapse exists; if it exists, where and what type (excitatory or inhibitory) of synapse it is. This leads us to believe that the proposed neuron model may be considerably more powerful on computations than the McCulloch–Pitts model because theoretically a single neuron or a single layer of such neurons is capable of solving any complex problem. These may also lead to a completely new technique for analyzing the mechanisms and principles of neurons, dendrites, and synapses.

Parallel spike trains analysis using positive definite kernels

Since spikes are considered to be the fundamental element in neural systems, there has been a significant amount of work that analyzes the sequence of spike timings, or spike trains [1,2]. One important research question is to know how information is encoded in a spike train. There is an approach to construct a feature space that captures characteristics of spike trains, as is usually done in the field of pattern recognition. Another approach, which is increasingly becoming popular in recent years, is to find an appropriate similarity measure between spike trains [3,4]. This corresponds to constructing a model of information decoding done by the postsynaptic neurons. One promising way to define such similarity measures is to use positive definite kernels [5-7]. Since positive definite kernels are generalizations of inner products, they enable application of various linear methods used in machine learning (including regression, classification, and dimension reduction) to spike trains. Positive definite kernels are extensively used in kernel methods. While positive definite kernels on spike trains obtained from a single neuron have already been proposed [5-7], the extension of this to parallel spike trains obtained from multiple neurons has not been explored yet. Therefore, we defined such a kernel by extending the memoryless cross intensity kernel (mCI kernel) proposed by Paiva et al. [5]. To make the extension as natural as possible, we used a linear combination of cross-neuron interactions. We name the new kernel the linear combination of interactions kernel (LCIK) [9]. The parameters of the kernel can be set to make it positive definite. We applied this kernel to publicly available in vivo recordings taken from the primary visual field in macaque monkey brains [8]. The LCIK performed better than other possible kernels defined on a set of spike trains. When the parameters of the kernel were estimated using spike trains obtained from real neurons, we obtained biologically plausible values. For example, the estimated time constant was near the value commonly used in neural modeling. This indicates the possibility of using such kernels to look for an appropriate model of neurons based on observed spike recordings. We also simulated a simple neural network and generated spike trains to see the effect on the estimated values of the kernel parameters by changing the synaptic connection parameters. The result indicated that the kernel indirectly represents some of the internal parameters of the neural networks.

Modelling of neocortical neural dynamics during human focal seizures

Recent advances in microelectrode array (MEA) recordings have made possible the simultaneous recordings of spiking activity in ensembles of neocortical single neurons during human focal seizures. As a result, a much more detailed picture of seizure initiation and spread has begun to emerge [1]. Here, we combine single neuron spiking and local field potential (LFP) data obtained from 96-MEA recordings with mathematical modelling to characterize the synaptic coupling and parameters required to sustain the neural dynamics observed in the two main types of epileptic seizures identified in the studied patients: spike-wave-complex (SWCs ~2-3 Hz) seizures and gamma-band (40-60 Hz) seizures, respectively. We model the neocortex under a 96-MEA (4mm x 4mm) with Izhikevich type neurons [2,3]. There are 28x28 minicolumns in the model. Each minicolumn is 25μm apart from each other and has 12 excitatory neurons and 4 interneurons. The neurons are synaptically connected up to a radius of 75μm and a synaptic delay of 2ms. (Connectivity drops to zero close to the MEA boundaries). Each neuron is driven by an independent Poisson input simulating background synaptic activities (i.e. high Poisson rates close to a few kHz, but individual Poisson events are of small amplitude). We simulate each of the two types of epileptic seizures by controlling the synaptic strengths amongst neurons and the Poisson drive. Dynamics similar to that in gamma-band seizures (Fig. ​(Fig.1)1) were obtained in models that combined strong mutual inhibitory synaptic couplings (gi->i), strong inhibitory to excitatory synaptic couplings (gi->e), and strong Poisson drive to both the pyramidal and interneuronal populations. The resulting single neuron spiking patterns (in both the inhibitory and excitatory cases) remained irregular, despite that they lead to sustained narrow gamma band LFP oscillations, consistent with the observations from the neuronal spiking data recorded from the patients. Dynamics similar to SWC seizures were obtained by decreasing both mutual inhibitory coupling (gi->i ) and inhibitory to excitatory coupling (gi->e), as well as by reducing the Poisson drive to the inhibitory interneuron populations. During each SWC discharge (Figure ​(Figure1),1), we observed the spread of neuronal spiking activity and recruitment of pyramidal cells starting from a focus, accompanied by strong coherent LFP. In the model, the participation of interneurons in SWC generation is minimal due to the weak gi->i,e and low Poisson drive. Our model suggests that gamma-band seizures require strong inhibitory conductance and participation of both excitatory and inhibitory populations, while SWC seizures require weaker inhibitory conductances and are mostly driven by excitatory (pyramidal) neurons. We are working towards a conductance-based network model in which intra and extracellular ionic concentrations are included to explore how disregulation of ionic concentrations can trigger each of the two types of seizures. Figure 1 Neuronal spiking raster plots (gamma-band seizure: left; SWC seizure: right).