Novel Algorithm of Network Calcium Dynamics Analysis for Studying the Role of Astrocytes in Neuronal Activity in Alzheimer's Disease Models.

Accumulated experimental data strongly suggest that astrocytes play an important role in the pathogenesis of neurodegeneration, including Alzheimer's disease (AD). The effect of astrocytes on the calcium activity of neuron-astroglia networks in AD modelling was the object of the present study. We have expanded and improved our approach's capabilities to analyze calcium activity. We have developed a novel algorithm to construct dynamic directed graphs of both astrocytic and neuronal networks. The proposed algorithm allows us not only to identify functional relationships between cells and determine the presence of network activity, but also to characterize the spread of the calcium signal from cell to cell. Our study showed that Alzheimer's astrocytes can change the functional pattern of the calcium activity of healthy nerve cells. When healthy nerve cells were cocultivated with astrocytes treated with Aß42, activation of calcium signaling was found. When healthy nerve cells were cocultivated with 5xFAD astrocytes, inhibition of calcium signaling was observed. In this regard, it seems relevant to further study astrocytic-neuronal interactions as an important factor in the regulation of the functional activity of brain cells during neurodegenerative processes. The approach to the analysis of streaming imaging data developed by the authors is a promising tool for studying the collective calcium dynamics of nerve cells.

Inhibition of Neuronal Necroptosis Mediated by RIPK1 Provides Neuroprotective Effects on Hypoxia and Ischemia In Vitro and In Vivo.

Ischemic brain injury is a widespread pathological condition, the main components of which are a deficiency of oxygen and energy substrates. In recent years, a number of new forms of cell death, including necroptosis, have been described. In necroptosis, a cascade of interactions between the kinases RIPK1 and RIPK3 and the MLKL protein leads to the formation of a specialized death complex called the necrosome, which triggers MLKL-mediated destruction of the cell membrane and necroptotic cell death. Necroptosis probably plays an important role in the development of ischemia/reperfusion injury and can be considered as a potential target for finding methods to correct the disruption of neural networks in ischemic damage. In the present study, we demonstrated that blockade of RIPK1 kinase by Necrostatin-1 preserved the viability of cells in primary hippocampal cultures in an in vitro model of glucose deprivation. The effect of RIPK1 blockade on the bioelectrical and metabolic calcium activity of neuron-glial networks in vitro using calcium imaging and multi-electrode arrays was assessed for the first time. RIPK1 blockade was shown to partially preserve both calcium and bioelectric activity of neuron-glial networks under ischemic factors. However, it should be noted that RIPK1 blockade does not preserve the network parameters of the collective calcium dynamics of neuron-glial networks, despite the maintenance of network bioelectrical activity (the number of bursts and the number of spikes in the bursts). To confirm the data obtained in vitro, we studied the effect of RIPK1 blockade on the resistance of small laboratory animals to in vivo modeling of hypoxia and cerebral ischemia. The use of Necrostatin-1 increases the survival rate of C57BL mice in modeling both acute hypobaric hypoxia and ischemic brain damage.

Modeling Working Memory in a Spiking Neuron Network Accompanied by Astrocytes.

We propose a novel biologically plausible computational model of working memory (WM) implemented by a spiking neuron network (SNN) interacting with a network of astrocytes. The SNN is modeled by synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons via chemicals diffused in the extracellular space. Calcium elevations occur in response to the increased concentration of the neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strength of the synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organized by the application of a cue pattern representing one from the memory set distorted by noise. We found that successful retrieval with the level of the correlation between the recalled pattern and ideal pattern exceeding 90% is possible for the multi-item WM task. Having analyzed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in the SNN leading to successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Neuroprotective Effect of Kinase Inhibition in Ischemic Factor Modeling In Vitro.

The contribution of many neuronal kinases to the adaptation of nerve cells to ischemic damage and their effect on functional neural network activity has not yet been studied. The aim of this work is to study the role of the four kinases belonging to different metabolic cascades (SRC, Ikkb, eEF2K, and FLT4) in the adaptive potential of the neuron-glial network for modeling the key factors of ischemic damage. We carried out a comprehensive study on the effects of kinases blockade on the viability and network functional calcium activity of nerve cells under ischemic factor modeling in vitro. Ischemic factor modelling was performed on day 14 of culturing primary hippocampal cells obtained from mouse embryos (E18). The most significant neuroprotective effect was shown in the blockade of FLT4 kinase in the simulation of hypoxia. The studies performed revealed the role of FLT4 in the development of functional dysfunction in cerebrovascular accidents and created new opportunities for the study of this enzyme and its blockers in the formation of new therapeutic strategies.

Signatures of the Consolidated Response of Astrocytes to Ischemic Factors In Vitro.

Whether and under what conditions astrocytes can mount a collective network response has recently become one of the central questions in neurobiology. Here, we address this problem, investigating astrocytic reactions to different biochemical stimuli and ischemic-like conditions in vitro. Identifying an emergent astrocytic network is based on a novel mathematical approach that extracts calcium activity from time-lapse fluorescence imaging and estimates the connectivity of astrocytes. The developed algorithm represents the astrocytic network as an oriented graph in which the nodes correspond to separate astrocytes, and the edges indicate high dynamical correlations between astrocytic events. We demonstrate that ischemic-like conditions decrease network connectivity in primary cultures in vitro, although calcium events persist. Importantly, we found that stimulation under normal conditions with 10 µM ATP increases the number of long-range connections and the degree of corresponding correlations in calcium activity, apart from the frequency of calcium events. This result indicates that astrocytes can form a large functional network in response to certain stimuli. In the post-ischemic interval, the response to ATP stimulation is not manifested, which suggests a deep lesion in functional astrocytic networks. The blockade of Connexin 43 during ischemic modeling preserves the connectivity of astrocytes in the post-hypoxic period.

Anderson attractors in active arrays.

In dissipationless linear media, spatial disorder induces Anderson localization of matter, light, and sound waves. The addition of nonlinearity causes interaction between the eigenmodes, which results in a slow wave diffusion. We go beyond the dissipationless limit of Anderson arrays and consider nonlinear disordered systems that are subjected to the dissipative losses and energy pumping. We show that the Anderson modes of the disordered Ginsburg-Landau lattice possess specific excitation thresholds with respect to the pumping strength. When pumping is increased above the threshold for the band-edge modes, the lattice dynamics yields an attractor in the form of a stable multi-peak pattern. The Anderson attractor is the result of a joint action by the pumping-induced mode excitation, nonlinearity-induced mode interactions, and dissipative stabilization. The regimes of Anderson attractors can be potentially realized with polariton condensates lattices, active waveguide or cavity-QED arrays.

Distributed classifier based on genetically engineered bacterial cell cultures.

We describe a conceptual design of a distributed classifier formed by a population of genetically engineered microbial cells. The central idea is to create a complex classifier from a population of weak or simple classifiers. We create a master population of cells with randomized synthetic biosensor circuits that have a broad range of sensitivities toward chemical signals of interest that form the input vectors subject to classification. The randomized sensitivities are achieved by constructing a library of synthetic gene circuits with randomized control sequences (e.g., ribosome-binding sites) in the front element. The training procedure consists in reshaping of the master population in such a way that it collectively responds to the "positive" patterns of input signals by producing above-threshold output (e.g., fluorescent signal), and below-threshold output in case of the "negative" patterns. The population reshaping is achieved by presenting sequential examples and pruning the population using either graded selection/counterselection or by fluorescence-activated cell sorting (FACS). We demonstrate the feasibility of experimental implementation of such system computationally using a realistic model of the synthetic sensing gene circuits.

Assessing T cell clonal size distribution: a non-parametric approach.

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.

Pacemaker and network mechanisms of rhythm generation: cooperation and competition.

The origin of rhythmic activity in brain circuits and CPG-like motor networks is still not fully understood. The main unsolved questions are (i) What are the respective roles of intrinsic bursting and network based dynamics in systems of coupled heterogeneous, intrinsically complex, even chaotic, neurons? (ii) What are the mechanisms underlying the coexistence of robustness and flexibility in the observed rhythmic spatio-temporal patterns? One common view is that particular bursting neurons provide the rhythmogenic component while the connections between different neurons are responsible for the regularisation and synchronisation of groups of neurons and for specific phase relationships in multi-phasic patterns. We have examined the spatio-temporal rhythmic patterns in computer-simulated motif networks of H-H neurons connected by slow inhibitory synapses with a non-symmetric pattern of coupling strengths. We demonstrate that the interplay between intrinsic and network dynamics features either cooperation or competition, depending on three basic control parameters identified in our model: the shape of intrinsic bursts, the strength of the coupling and its degree of asymmetry. The cooperation of intrinsic dynamics and network mechanisms is shown to correlate with bistability, i.e., the coexistence of two different attractors in the phase space of the system corresponding to different rhythmic spatio-temporal patterns. Conversely, if the network mechanism of rhythmogenesis dominates, monostability is observed with a typical pattern of winnerless competition between neurons. We analyse bifurcations between the two regimes and demonstrate how they provide robustness and flexibility to the network performance.

Chaotic spatial bifurcation by complex coupling.

A spatial bifurcation (a transition from stationary to oscillatory regime) in a chain of unidirectionally coupled phase systems is studied. It is shown that complication of coupling terms can make this bifurcation spatially chaotic in contrast to the previously observed "regular" and "predictable" type. It is demonstrated that the found type of spatial bifurcation corresponds to a smooth (predictable) manifold in the parameter space, while its spatial location gets actually unpredictable being governed by regularities of chaotic behavior. We infer that complex collective dynamics may arise in networks with plain architecture and simple dynamics of individual elements if nontrivial coupling is realized.

Network mechanism for burst generation.

We report on the mechanism of burst generation by populations of intrinsically spiking neurons, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose synchronization at stronger coupling via spatiotemporal intermittency. The latter transition triggers fast repetitive spiking, which results in synchronized bursting. We present evidence that this mechanism is generic for various network topologies from regular to small-world and scale-free ones, different types of coupling and neuronal model.

Synchronization of spontaneous bursting in a CO2 laser.

We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.

Synchronized chaotic intermittent and spiking behavior in coupled map chains.

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

Phase synchronization in ensembles of bursting oscillators.

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles.

Phase synchronization of chaotic intermittent oscillations.

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.

Three types of transitions to phase synchronization in coupled chaotic oscillators.

We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.