Nonlinear gap junctions enable long-distance propagation of pulsating calcium waves in astrocyte networks

Abstract

A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca(2+) waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP(3)) through gap junctions that locally trigger Ca(2+) pulses via IP(3)-dependent Ca(2+)-induced Ca(2+) release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca(2+) waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca(2+) wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca(2+) dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca(2+) waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain.

Figure 1. Sketch of the signaling pathways considered in the ChI model.

(a) Ca²⁺-induced Ca²⁺ release (CICR) from the endoplasmic reticulum (ER) is the main mechanism responsible for intracellular Ca²⁺ dynamics in astrocytes. (b) Schematic of the coupling between Ca²⁺ dynamics and IP₃ metabolism in the astrocyte. (c) Endogenous IP₃ production is brought forth by hydrolysis of PIP₂ by PLCδ (the activity of which is regulated by Ca²⁺). (d) Degradation of IP₃ mainly occurs through IP₃ 3-kinase- (3K-) catalyzed phosphorylation and inositol polyphosphate 5-phosphatase (IP-5P)-mediated dephosphorylation. For simplicity, Ca²⁺-dependent PKC-mediated phosphorylation of IP₃-3K and competitive binding of IP₄ to IP-5P are not considered in this study. The legend of different arrows is given below (c).

Figure 2. The coupling functions used in the current study to model different types of gap-junctions.

Shown is the relative flux, i.e. the value the IP₃ flux divided by the coupling force F as a function of the IP₃ gradient (ΔIP₃) between two coupled cells, for linear, threshold-linear and sigmoidal coupling. Parameters: IP₃ ^thr = 0.3 µM, IP₃ ^scale = 0.05 µM.

Figure 3. Propagation patterns with linear (a, b) and non-linear sigmoidal (c, d) gap junctions.

The astrocyte chain was composed of 12 FM-encoding cells with reflective boundary conditions. Stimulation triggered by IP₃ ^bias = 1.0 µM from t = 0 s to t = 120 s applied to the first cell in the line.

Figure 4. Traveled distance for the propagation of Ca²⁺ waves as a function of stimulus intensity.

The stimulus is applied to the first cell and the traveled distance is expressed in number of cells. With moderate coupling strength (F = 2 µm/s) and N = 25 cells, long-range Ca²⁺ propagation is observed in the case of FM (a) but not AFM chains (b). Linear gap junctions (closed green circles) do not sustain propagation over long distances, whatever the encoding mode is. Long-range propagation is observed for AFM cells coupled by non-linear sigmoid (open magenta circles) or threshold-linear (times signs) gap junctions. Variation of the propagation range with F for 50 coupled FM cells (IP₃ ^bias = 2.0 µM) is shown in (c) for sigmoid and linear gap junctions. Panel (d) shows a map of the r_5P-ν_δ parameter space, where black dots correspond to waves propagating over all the cells, while white areas locate non-propagating waves. In these figures, a wave was considered to have reached a given cell whenever the amplitude of calcium variations in this cell was larger than 0.6 µM. Boundary conditions in these simulations were reflective.

Figure 5. Propagation patterns for linear (a, b) and non-linear sigmoidal (c, d) gap junctions.

The astrocyte chain was composed of 12 AFM astrocytes. Stimulus protocol and other parameters as in Figure 3.

Figure 6. Calcium (a–c) and IP₃ (d–f) traces for wave propagation in composite astrocyte chains.

Black traces locate FM cells while AFM cells are displayed with gray traces. (a, d) Alternating one FM with one AFM cell for example, may not allow propagation beyond the second AFM cell. (b, e) Larger propagation distances can be obtained by increasing the maximal rate of PLCδ in AFM cells. (c, f) Alternatively, longer traveling distances can be observed in chains where two AFM cells are separated by more than one FM cell. Parameters: a stimulus of IP₃ ^bias = 1.2 µM was applied between t = 10 and t = 300 s on the first cell of the chain (i.e. cell 1). Other parameters: v_δ ^(AFM) = 0.108 µM/s; v_δ ^(FM) = 0.832 µM/s; r_5P = 0.202 s⁻¹; IP₃ ^thr = 0.215 µM; (b, e): v_δ ^(AFM) = 0.15 µM/s. In all these simulations, a 5-minute-long stimulus was applied.

Figure 7. Complex behaviors at low coupling strength (F = 0.23 µM·s⁻¹).

The stimulus is an oscillatory input (positive square wave) applied to the central cell of an N = 41 cell chain. (a) Calcium concentration in cells 1 to 21 (cells 21 to 41, respectively, are identical). (b) The trajectory in the C-h-IP₃ phase space for cell 21 (i.e. the stimulated cell) and (c, d) the corresponding Ca²⁺ and IP₃ time series. Simulation performed on FM-encoding astrocytes with reflective boundary conditions and sigmoid gap junctions. Stimulus protocol: positive square wave of 50-second period and duty cycle of 0.4.