We study the effect of introducing localized synapses on the astrocyte calcium activity. Instead of homogeneous excitation we include in the model well-defined synapses as sources of glutamate. Synaptic density was scaled according to the astrocyte morphology, in particular, surface-volume ratio in accordance with experimental data. Unlike uniform excitation model, where the calcium activity was dependent only on the astrocyte morphology, different localization of synapses causes the change in baseline calcium distribution. Localization of synapses leads to the decrease of baseline calcium levels in the peripheral regions of the astrocyte, while the dynamics of thick branches and soma does not change significantly. Introduction of synapses also affects the distribution of baseline calcium levels based on AVF parameter. Supposedly, this indicates the emergence of “microdomains” - regions of the astrocyte with the highest average activity.
Astrocytes not only provide for the transfer of nutrients between blood vessels and neurons, but also take part in signaling through nerve tissue and regulate formation, pruning, and plasticity of synapses. Analysis of the impact of the astrocytic domain organization on the local and collective dynamics of neurons is needed for both the fundamental understanding of the mechanisms underlying cognition and for the creation of new methods of neurodegenerative pathology treatment targeted at non-neuronal cells without direct effects on the neural network. Based on the available experimental data, we propose a model study of the role of astrocytic calcium signaling in the regulation of synaptic transmission between neurons in order to elucidate the role played by astrocyte calcium signaling in signaling pathways regulating neural activity. The proposed model is based on the following assumptions: (i) localized release of gliotransmitters depends on the spatiotemporal patterns of calcium activity and is determined by cell morphology and topology of the entire network; (ii) the release of gliotransmitters can lead to spatial segregation of the nervous tissue into regions in which different conditions are maintained, favoring for increased or decreased synaptic efficacy.
Most of the existing models of calcium dynamics of astrocytes do not take into account the effect of the Na/Ca- exchanger on the formation of calcium oscillations and their properties. However, recent experimental studies show that at an increased sodium concentration, the Na/Ca-exchanger works in the reverse mode, providing an additional calcium entry into the cell cytosol. In this work we study a model that simultaneously takes into account the IP3-mediated exchange with intracellular [Ca2+] stores and bidirectional [Ca2+] flow through Na/Ca-exchanger. We analyze the behavior of the system under stimulation with external glutamate- of the cell, explore the possible behavior regimes and reveal the effect of the cytosolic sodium concentration, the maximum current through the Na/Ca-exchanger, and the stimulus amplitude on the astrocytic calcium dynamics.
In theoretical consideration of the collective calcium dynamics in astrocytes, an adequate description of the properties of intercellular connections is as important as the details of intracellular dynamics. We propose and test two alternative approaches to connectivity modeling in a two-dimensional projection spatially detailed model of astrocytic networks. Both approaches are based on the creation of a system of densely packed cells with further detailing the diffusive exchange along the contact lines. The simplest way to organize intercellular communication is to change the degree of connectivity by changing the area of contact of cells without adding special case dynamics at the cell borders. Arguably a more advanced approach is to define a specialized model variant specifically for perimembrane layer at the neighboring cell interfaces. At the same time, we separately describe the dynamics of gap contacts. We compare the simulation results for both approaches and conclude that both methods can be useful at different levels of abstraction.
We simulate the formation and dynamics of calcium waves in a distributed astrocyte network. We take into account volume effects induced by the real morphology of an astrocyte cell. Astrocytes are sponge-like structures which do not occupy the entire volume of its compartment: astrocyte leaflets are surrounded by the neuropil. We introduce the astrocyte volume fraction (AVF) parameter which shows the part of the 2D template occupied by an astrocyte versus neuropil and correlates with this ratio in a real 3D structure. To describe the difference in the processes in branchlets and leaflets of an astrocyte and the continuous transition between them we use the surface-to-volume ratio (SVR) parameter.
We present a two-dimensional model of astrocytic Ca2+ dynamics. We take into account two main factors of the considered process: the IP3-mediated release from intracellular Ca2+ stores and the plasma membrane bidirectional exchange, i.e. the Na+/Ca2+-exchanger (NCX). We based on the Hodgkin - Huxley formalism to describe NCX effects and takes into account the glutamate transporter-mediated increase in Na+ during synaptic activity and Na+- and Ca2+-dependent regulation. The results of the unified model numerical solution confirm the emergence of calcium waves, which occur due to the synaptic activity and spread over the astrocyte network. The presence of NCX leads to a decrease in the average areas that are affected by a global calcium wave during excitation. However, the Na/Ca exchanger stimulates calcium waves, making possible the formation of more long-lived waves.
We present a composite model of astrocytic Ca2+ dynamics, which includes both IP3-mediated release from intracellular Ca2+ stores and bidirectional exchange through the plasma membrane, mediated by the Na+/Ca2+- exchanger (NCX). The NCX kinetic model is formulated in the Hodgkin/Huxley formalism, taking into account the glutamate transporter-mediated increase in Na+ during synaptic activity and Na+- and Ca2+-dependent regulation. We define main dynamic regimes and transitions in a point model, describing dynamics in an individual astrocyte segment. We demonstrate NCX-based modulation of store-mediated calcium oscillations (amplitude, frequency and amplitude-frequency), analyze and compare calcium dynamics in models with and without allosteric regulation of NCX by intracellular ions.
Spreading vascular reactions are mediated by electrical signals that are transmitted through the endothelial layer of blood vessels. The contraction of a vessel as a whole is impossible without the coordinated work of the smooth muscle cells of its wall, the study of the mechanisms and characteristics of their interconnection is important for understanding how their synchronized behavior is formed. In our work, we propose and investigate a mathematical model that focuses on taking into account the peculiarities of the interposition of endothelial cells and smooth muscle cells.
The most abundant non-neuronal cells in the brain, astrocytes, populate all parts of the central nervous system (CNS). Astrocytic calcium activity ranging from subcellular sparkles to intercellular waves is believed to be the key to a plethora of regulatory pathways in the central nervous system from synaptic plasticity to blood flow regulation. Modeling of the calcium wave initiation and transmission and their spatiotemporal dynamics is therefore an important step stone in understanding the crucial cogs of cognition. Astrocytes are active sensors of ongoing neuronal and synaptic activity, and neurotransmitters diffusing from the synaptic cleft make a strong impact on the astrocytic activity. Here we propose a model describing the patterns of calcium wave formation at a single cell level and discuss the interplay between astrocyte shape the calcium waves dynamics driven by local stochastic surges of glutamate simulating synaptic activity.
We study the features of formation and evolution of spatiotemporal chaotic regime generated by autonomous pacemakers in excitable deterministic and stochastic bistable active media using the example of the FitzHugh – Nagumo biological neuron model under discrete medium conditions. The following possible mechanisms for the formation of autonomous pacemakers have been studied: 1) a temporal external force applied to a small region of the medium, 2) geometry of the solution region (the medium contains regions with Dirichlet or Neumann boundaries). In our work we explore the conditions for the emergence of pacemakers inducing target patterns in a stochastic bistable excitable system and propose the algorithm for their analysis.
Cortical spreading depression (CSD) is an example of one of the most common abnormalities in biophysical brain functioning. Despite the fact that there are many mathematical models describing the cortical spreading depression (CSD), most of them do not take into consideration the role of redistribution of cerebral blood flow (CBF), that results in the formation of spatio-temporal patterns. The paper presents a mathematical model, which successfully explains the CBD role in the CSD process. Numerical study of this model has revealed the formation of stationary dissipative structures, visually analogous to Turing structures. However, the mechanism of their formation is not diffusion. We show these structures occur due to another type of spatial coupling, that is related to tissue perfusion rate. The proposed model predicts that at similar state of neurons the distribution of blood flow and oxygenation may by different. Currently, this effect is not taken into account when the Blood oxygen-level dependent (BOLD) contrast imaging used in functional magnetic resonance imaging (fMRI). Thus, the diagnosis on the BOLD signal can be ambiguous. We believe that our results can be used in the future for a more correct interpretation of the data obtained with fMRI, NIRS and other similar methods for research of the brain activity.
In recent decades modelling studies on cortical spreading depression (CSD) and migraine waves successfully contributed to formation of modern view on these fundamental phenomena of brain physiology. However, due to the extreme complexity of object under study (brain cortex) and the diversity of involved physiological pathways, the development of new mathematical models of CSD is still a very relevant and challenging research problem.
In our study we follow the functional modelling approach aimed to map the action of known physiological pathways to the specific nonlinear mechanisms that govern formation and evolution of CSD wave patterns. Specifically, we address the role of cerebral blood flow (CBF) redistribution that is caused by excessive neuronal activity by means of neurovascular coupling and mediates a spatial pattern of oxygen and glucose delivery. This in turn changes the local metabolic status of neural tissue. To build the model we simplify the web of known cell-to-cell interactions within a neurovascular unit by selecting the most relevant ones, such as local neuron-induced elevation of extracellular potassium concentration and biphasic response of arteriole radius. We propose the lumped description of distance-dependent hemodynamic coupling that fits the most recent experimental findings.
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