A homeostatic model of neuronal firing governed by feedback signals from the extracellular matrix

Estimation of cumulative amplitude distributions of miniature postsynaptic currents allows characterising their multimodality, quantal size and variability

A miniature postsynaptic current (mPSC) is a small, rare, and highly variable spontaneous synaptic event that is generally caused by the spontaneous release of single vesicles. The amplitude and variability of mPSCs are key measures of the postsynaptic processes and are taken as the main characteristics of an elementary unit (quantal size) in traditional quantal analysis of synaptic transmission. Due to different sources of biological and measurement noise, recordings of mPSCs exhibit high trial-to-trial heterogeneity, and experimental measurements of mPSCs are usually noisy and scarce, making their analysis demanding. Here, we present a sequential procedure for precise analysis of mPSC amplitude distributions for the range of small currents. To illustrate the developed approach, we chose previously obtained experimental data on the effect of the extracellular matrix on synaptic plasticity. The proposed statistical technique allowed us to identify previously unnoticed additional modality in the mPSC amplitude distributions, indicating the formation of new immature synapses upon ECM attenuation. We show that our approach can reliably detect multimodality in the distributions of mPSC amplitude, allowing for accurate determination of the size and variability of the quantal synaptic response. Thus, the proposed method can significantly expand the informativeness of both existing and newly obtained experimental data. We also demonstrated that mPSC amplitudes around the threshold of microcurrent excitation follow the Gumbel distribution rather than the binomial statistics traditionally used for a wide range of currents, either for a single synapse or when taking into consideration small influences of the adjacent synapses. Such behaviour is argued to originate from the theory of extreme processes. Specifically, recorded mPSCs represent instant random current fluctuations, among which there are relatively larger spikes (extreme events). They required more level of coherence that can be provided by different mechanisms of network or system level activation including neuron circuit signalling and extrasynaptic processes.

Artificial Neural Network Model with Astrocyte-Driven Short-Term Memory

In this study, we introduce an innovative hybrid artificial neural network model incorporating astrocyte-driven short-term memory. The model combines a convolutional neural network with dynamic models of short-term synaptic plasticity and astrocytic modulation of synaptic transmission. The model's performance was evaluated using simulated data from visual change detection experiments conducted on mice. Comparisons were made between the proposed model, a recurrent neural network simulating short-term memory based on sustained neural activity, and a feedforward neural network with short-term synaptic depression (STPNet) trained to achieve the same performance level as the mice. The results revealed that incorporating astrocytic modulation of synaptic transmission enhanced the model's performance.

STDP-Driven Rewiring in Spiking Neural Networks under Stimulus-Induced and Spontaneous Activity

Mathematical and computer simulation of learning in living neural networks have typically focused on changes in the efficiency of synaptic connections represented by synaptic weights in the models. Synaptic plasticity is believed to be the cellular basis for learning and memory. In spiking neural networks composed of dynamical spiking units, a biologically relevant learning rule is based on the so-called spike-timing-dependent plasticity or STDP. However, experimental data suggest that synaptic plasticity is only a part of brain circuit plasticity, which also includes homeostatic and structural plasticity. A model of structural plasticity proposed in this study is based on the activity-dependent appearance and disappearance of synaptic connections. The results of the research indicate that such adaptive rewiring enables the consolidation of the effects of STDP in response to a local external stimulation of a neural network. Subsequently, a vector field approach is used to demonstrate the successive "recording" of spike paths in both functional connectome and synaptic connectome, and finally in the anatomical connectome of the network. Moreover, the findings suggest that the adaptive rewiring could stabilize network dynamics over time in the context of activity patterns' reproducibility. A universal measure of such reproducibility introduced in this article is based on similarity between time-consequent patterns of the special vector fields characterizing both functional and anatomical connectomes.

Information Encoding in Bursting Spiking Neural Network Modulated by Astrocytes

We investigated a mathematical model composed of a spiking neural network (SNN) interacting with astrocytes. We analysed how information content in the form of two-dimensional images can be represented by an SNN in the form of a spatiotemporal spiking pattern. The SNN includes excitatory and inhibitory neurons in some proportion, sustaining the excitation-inhibition balance of autonomous firing. The astrocytes accompanying each excitatory synapse provide a slow modulation of synaptic transmission strength. An information image was uploaded to the network in the form of excitatory stimulation pulses distributed in time reproducing the shape of the image. We found that astrocytic modulation prevented stimulation-induced SNN hyperexcitation and non-periodic bursting activity. Such homeostatic astrocytic regulation of neuronal activity makes it possible to restore the image supplied during stimulation and lost in the raster diagram of neuronal activity due to non-periodic neuronal firing. At a biological point, our model shows that astrocytes can act as an additional adaptive mechanism for regulating neural activity, which is crucial for sensory cortical representations.

Toward Reflective Spiking Neural Networks Exploiting Memristive Devices

The design of modern convolutional artificial neural networks (ANNs) composed of formal neurons copies the architecture of the visual cortex. Signals proceed through a hierarchy, where receptive fields become increasingly more complex and coding sparse. Nowadays, ANNs outperform humans in controlled pattern recognition tasks yet remain far behind in cognition. In part, it happens due to limited knowledge about the higher echelons of the brain hierarchy, where neurons actively generate predictions about what will happen next, i.e., the information processing jumps from reflex to reflection. In this study, we forecast that spiking neural networks (SNNs) can achieve the next qualitative leap. Reflective SNNs may take advantage of their intrinsic dynamics and mimic complex, not reflex-based, brain actions. They also enable a significant reduction in energy consumption. However, the training of SNNs is a challenging problem, strongly limiting their deployment. We then briefly overview new insights provided by the concept of a high-dimensional brain, which has been put forward to explain the potential power of single neurons in higher brain stations and deep SNN layers. Finally, we discuss the prospect of implementing neural networks in memristive systems. Such systems can densely pack on a chip 2D or 3D arrays of plastic synaptic contacts directly processing analog information. Thus, memristive devices are a good candidate for implementing in-memory and in-sensor computing. Then, memristive SNNs can diverge from the development of ANNs and build their niche, cognitive, or reflective computations.

Controlling synchronization of gamma oscillations by astrocytic modulation in a model hippocampal neural network

Recent in vitro and in vivo experiments demonstrate that astrocytes participate in the maintenance of cortical gamma oscillations and recognition memory. However, the mathematical understanding of the underlying dynamical mechanisms remains largely incomplete. Here we investigate how the interplay of slow modulatory astrocytic signaling with fast synaptic transmission controls coherent oscillations in the network of hippocampal interneurons that receive inputs from pyramidal cells. We show that the astrocytic regulation of signal transmission between neurons improves the firing synchrony and extends the region of coherent oscillations in the biologically relevant values of synaptic conductance. Astrocyte-mediated potentiation of inhibitory synaptic transmission markedly enhances the coherence of network oscillations over a broad range of model parameters. Astrocytic regulation of excitatory synaptic input improves the robustness of interneuron network gamma oscillations induced by physiologically relevant excitatory model drive. These findings suggest a mechanism, by which the astrocytes become involved in cognitive function and information processing through modulating fast neural network dynamics.

Activity-dependent switches between dynamic regimes of extracellular matrix expression

Experimental studies highlight the important role of the extracellular matrix (ECM) in the regulation of neuronal excitability and synaptic connectivity in the nervous system. In its turn, the neural ECM is formed in an activity-dependent manner. Its maturation closes the so-called critical period of neural development, stabilizing the efficient configurations of neural networks in the brain. ECM is locally remodeled by proteases secreted and activated in an activity-dependent manner into the extracellular space and this process is important for physiological synaptic plasticity. We ask if ECM remodeling may be exaggerated under pathological conditions and enable activity-dependent switches between different regimes of ECM expression. We consider an analytical model based on known mechanisms of interaction between neuronal activity and expression of ECM, ECM receptors and ECM degrading proteases. We demonstrate that either inhibitory or excitatory influence of ECM on neuronal activity may lead to the bistability of ECM expression, so two stable stationary states are observed. Noteworthy, only in the case when ECM has predominant inhibitory influence on neurons, the bistability is dependent on the activity of proteases. Excitatory ECM-neuron feedback influences may also result in spontaneous oscillations of ECM expression, which may coexist with a stable stationary state. Thus, ECM-neuronal interactions support switches between distinct dynamic regimes of ECM expression, possibly representing transitions into disease states associated with remodeling of brain ECM.

Emergence of Relaxation Oscillations in Neurons Interacting With Non-stationary Ambient GABA

Dynamics of a homogeneous neural population interacting with active extracellular medium were considered. The corresponding mathematical model was tuned specifically to describe the behavior of interneurons with tonic GABA conductance under the action of non-stationary ambient GABA. The feedback provided by the GABA mediated transmembrane current enriched the repertoire of population activity by enabling the oscillatory behavior. This behavior appeared in the form of relaxation oscillations which can be considered as a specific type of brainwaves.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears as a functional property that is present everywhere.  Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.

Degradation of extracellular chondroitin sulfate delays recovery of network activity after perturbation

Chondroitin sulfate proteoglycans (CSPGs) are widely studied in vertebrate systems and are known to play a key role in development, plasticity, and regulation of cortical circuitry. The mechanistic details of this role are still elusive, but increasingly central to the investigation is the homeostatic balance between network excitation and inhibition. Studying a simpler neuronal circuit may prove advantageous for discovering the mechanistic details of the cellular effects of CSPGs. In this study we used a well-established model of homeostatic change after injury in the crab Cancer borealis to show first evidence that CSPGs are necessary for network activity homeostasis. We degraded CSPGs in the pyloric circuit of the stomatogastric ganglion with the enzyme chondroitinase ABC (chABC) and found that removal of CSPGs does not influence the ongoing rhythm of the pyloric circuit but does limit its capacity for recovery after a networkwide perturbation. Without CSPGs, the postperturbation rhythm is slower than in controls and rhythm recovery is delayed. In addition to providing a new model system for the study of CSPGs, this study suggests a wider role for CSPGs, and perhaps the extracellular matrix in general, beyond simply plastic reorganization (as observed in mammals) and into a foundational regulatory role of neural circuitry.

Seizure-like activity in hyaluronidase-treated dissociated hippocampal cultures

The extracellular matrix (ECM) plays an important role in use-dependent synaptic plasticity. Hyaluronic acid (HA) is the backbone of the neural ECM, which has been shown to modulate α-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate (AMPA) receptor mobility, paired-pulse depression, L-type voltage-dependent Ca(2+) channel (L-VDCC) activity, long-term potentiation and contextual fear conditioning. To investigate the role of HA in the development of spontaneous neuronal network activity, we used microelectrode array recording and Ca(2+) imaging in hippocampal cultures enzymatically treated with hyaluronidase. Our findings revealed an appearance of epileptiform activity 9 days after hyaluronidase treatment. The treatment transformed the normal network firing bursts and Ca(2+) oscillations into long-lasting "superbursts" and "superoscillations" with durations of 11-100 s. The changes in Ca(2+) transients in hyaluronidase-treated neurons were more prominent then in astrocytes and preceded changes in electrical activity. The Ca(2+) superoscillations could be suppressed by applying the L-VDCC blocker diltiazem, whereas the neuronal firing superbursts could be additionally suppressed by 6-cyano-7-nitroquinoxaline-2,3-dione as an antagonist of AMPA/kainate receptors. These results suggest that changes in the expression of HA can be epileptogenic and that hyaluronidase treatment in vitro provides a robust model for the dissection of the underlying mechanisms.