Control and Plasticity of Intercellular Calcium Waves in Astrocytes: A Modeling Approach

Abstract

Intercellular Ca2+ waves in astrocytes are thought to serve as a pathway of long-range signaling. The waves can propagate by the diffusion of molecules through gap junctions and across the extracellular space. In rat striatal astrocytes, the gap-junctional route was shown to be dominant. To analyze the interplay of the processes involved in wave propagation, a mathematical model of this system has been developed. The kinetic description of Ca2+ signaling within a single cell accounts for inositol 1,4,5-trisphosphate (IP3) generation, including its activation by cytoplasmic Ca2+, IP3-induced Ca2+ liberation from intracellular stores and various other Ca2+ transports, and cytoplasmic diffusion of IP3 and Ca2+. When cells are coupled by gap junction channels in a two-dimensional array, IP3 generation in one cell triggers Ca2+ waves propagating across some tens of cells. The spatial range of wave propagation is limited, yet depends sensitively on the Ca2+-mediated regeneration of the IP3 signal. Accordingly, the term "limited regenerative signaling" is proposed. The gap-junctional permeability for IP3 is the crucial permissive factor for wave propagation, and heterogeneity of gap-junctional coupling yields preferential pathways of wave propagation. Processes involved in both signal initiation (activation of IP3 production caused by receptor agonist) and regeneration (activation of IP3 production by Ca2+, loading of the Ca2+ stores) are found to exert the main control on the wave range. The refractory period of signaling strongly depends on the refilling kinetics of the Ca2+ stores. Thus the model identifies multiple steps that may be involved in the regulation of this intercellular signaling pathway.

Functional Selectivity of G Protein Signaling by Agonist Peptides and Thrombin for the Protease-activated Receptor-1

“…5 is a scheme representing the proteins and interactions that were mathematically modeled. To construct the initial model, protein/protein interactions and enzymatic activations were translated into a system of ordinary differential reactions resembling well established models for receptor-G protein activation and calcium mobilization (72)(73)(74)(75). Activation of the IP 3 receptor of the endoplasmic reticulum by IP 3 and calcium was modeled according to equations proposed by De Young and Keizer (74).…”

Stochastic hybrid modeling of intracellular calcium dynamics

“…The influx across the plasma membrane consists of a nonspecific leakage flux and an ͓IP 3 ͔-dependent specific flux, which combines many fluxes including the entry through store-operated channels in response to the ER depletion and other effects. 25 Ca 2+ binds to buffer proteins in all three compartments, the cytosol, the ER, and the mitochondria, for which rapid buffering kinetics suggested earlier 26,27 is used. For a more detailed analysis of the perturbation of the calcium network, we refer the reader to Maurya and Subramaniam.…”

“…The model neglects molecular diffusion, the presence of IP 3 R clusters, and localconcentration effects in the mechanism for calcium release from the ER, 40 all of which are accounted for in the work by Greenstein et al, 35 Jafri et al, 41 and Puceat and Jaconi. 42 On the other hand, it includes detailed mechanisms of G-protein coupled receptor and G-protein activation and inactivation, which are absent in the works of Hofer et al, 25 Lemon et al, 27 Wiesner et al, 38 and Fink et al 39 The model enables the analysis of the effects of single and multiple knockdowns of proteins and subpopulational variability, i.e., to account for the fact that different cell-populations, when triggered by the same strength of a stimulus, result in quantitatively and qualitatively different responses ͑different peak-heights, risetimes, etc.͒. 43 Hence, we adopt the signaling network identified by Maurya and Subramaniam 3 as the basis for the present analysis.…”

Dynamics of a minimal neural model consisting of an astrocyte, a neuron, and an interneuron

“…In this model, the calcium fluxes through the membrane are the following: (1) a leakage Ca 2+ influx described by the rate ν LM ; (2) a capacitive calcium entry (CCE) of rate ν CCE ; (3) an extrusion across the plasma membrane described by the rate ν OUT ; (4) an influx of Ca 2+ mediated by the P2X ionotropic ATP receptor with rate ν ATP(P2X) . Following Höfer et al [37], two different biochemical processes mediating the production of IP 3 are included: PLCβ and PLCδ. The first one is responsible for the production of IP 3 in the presence of extracellular agonists and is activated through a G-protein-coupled receptor mechanism with rate ν PLCβ ; the second one describes the production of IP 3 arising from the [Ca 2+ ] i increase, and the corresponding rate is ν PLCδ .…”