No abstract

Intracellular Ca2+ dynamics in astrocytes can be triggered by neuronal activity and in turn regulate a variety of downstream processes that modulate neuronal function. In this fashion, astrocytic Ca2+ signaling is regarded as a processor of neural network activity by means of complex spatial and temporal Ca2+ dynamics. Accordingly, a key step is to understand how different patterns of neural activity translate into spatiotemporal dynamics of intracellular Ca2+ in astrocytes. Here, we introduce a minimal compartmental model for astrocytes that can qualitatively reproduce essential hierarchical features of spatiotemporal Ca2+ dynamics in astrocytes. We find that the rate of neuronal firing determines the rate of Ca2+ spikes in single individual processes as well as in the soma of the cell, while correlations of incoming neuronal activity are important in determining the rate of “global” Ca2+ spikes that can engulf soma and the majority of processes. Significantly, our model predicts that whether the endoplasmic reticulum is shared between soma and processes or not determines the relationship between the firing rate of somatic Ca2+ events and the rate of neural network activity. Together these results provide intuition about how neural activity in combination with inherent cellular properties shapes spatiotemporal astrocytic Ca2+ dynamics, and provide experimentally testable predictions.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

We study the flow of signals through paths with the following condition: a node emits a signal if two incoming signals from other nodes arrive consecutively or if it receives an external stimuli. We apply our study to count and describe families of polychrony groups and we introduce triangular sequences.