Figure 1.
The G-ChI model for glutamate-stimulation of intracellular calcium dynamics in astrocytes.
This graphical model introduces and summarizes the main variables and rate processes accounted for by the model. The stimulating neuron emits action potentials at times points given by the sequence s(t). The corresponding amount of released glutamate (Glu) is computed under the hypothesis of a dynamic synapse (Tsodyks-Markram model). Glutamate then activates group I metabotropic receptors (mGluRI) on the astrocyte membrane, thus activating Phospholipase Cβ (PLCβ), which results in the formation of IP3 with rate Jβ. IP3 is also synthesized with rate Jδ by calcium-activated Phospholipase Cδ (PLCδ) and transformed to other metabolites by two enzymes: IP3 3-kinase (rate J3K) and inositol polyphosphate 5-phosphatase (rate J5P). IP3 is also transported to other astrocytes to which the astrocyte is coupled via Gap Junction Channels (GJC) (flux Jij). The model moreover accounts for Calcium-Induced-Calcium-Release (CICR): Ca from intracellular stores (mostly the Endoplasmic Reticulum, ER) is pumped into the cytoplasm by Ca- and IP3-regulated IP3-Receptor Channels (IP3R, rate JC) of the ER membrane and reintegrated by sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) pumps (rate JP). The model also accounts for passive IP3 leak through the ER membrane (rate JL). The equations describing this graphical model are outlined in the main text (Methods section). More information can be found in Ref [34] and [35].
Figure 2.
Inference of model networks from experimental data.
A, The experimental culture of Fig. 2, with neurons segmented in red, astrocytes in green and unresponsive cells in blue. Scale bar is 75 µm. B, Model networks constructed using the experimental data of A. Fine grey lines delineate the Voronoi diagram computed from the experimental cell positions; green circles denote model astrocytes and dark green cells with a lightning symbol denote stimulated model astrocytes. Wide dark grey lines show the GJC connections between astrocytes. Scale bar is 75 µm. Model networks were inferred according to this process for each experiment. C, Close-up view of the Voronoi tesselation (light gray and blue lines) associated with an immunostaining image (in red the neuronal marker NeuN and in green the astrocytic marker GFAP). Astrocyte A will be GJC coupled to astrocytes B1 through B7 as they share boundaries of their anatomical domains (thick blue lines). D, Resulting distribution of astrocyte coupling degree. Most model astrocytes are connected to very few neighbors (n = 373). The inset shows the distribution of the size of connected astrocyte clusters (n = 146). It can be seen that most astrocytes are isolated but some experiments contain very large clusters of up to 60 astrocytes (indicated by stars).
Figure 3.
Geometric mapping of electrical activation.
A, Response probability color coded activation maps for different stimulation amplitudes showing a clear correlation between stimulation amplitude and number of activated neurons (scale bar 50 µm). B, Proportion of activated neurons as a function of stimulation amplitude, indicating a saturation zone. C, Recordings incorporating stimulations from different electrodes provide insight regarding mechanism of electrical stimulation. Each electrode activates a unique set of neurons with a very small neuronal population that responds to both.
Figure 4.
Astrocytic response to neuronal activity in the presence of neuronal AMPAR and NMDAR/kainate antagonists, and astrocytic mGluR1 and mGluR5 antagonists.
A, Ca2+ traces of two selected neurons (in red), showing stimulated activity according to a multi-frequency protocol, and seven selected astrocytes (in green) in presence of neuronal AMPAR and NMDAR/kainate antagonists. B, Representative traces of same cells and stimulation protocol as in A, showing no [Ca2+]i elevations in the presence of neuronal AMPAR and NMDAR/kainate antagonists, and astrocytic mGluR1 and mGluR5 antagonists.
Figure 5.
Frequency dependent astrocytic response to neuronal activity.
A, Ca2+ traces of two selected neurons (in red), showing stimulated activity according to a random multi-frequency protocol, and seven selected astrocytes (in green) showing frequency dependent [Ca2+]i elevations in response to neuronal activity. Experiments were performed in the presence of neuronal AMPAR and NMDAR/kainate antagonists. B, Ca2+ traces of same cells and stimulation protocol as in A, showing no astrocytic [Ca2+]i elevations in the presence of neuronal AMPAR and NMDAR/kainate antagonists, and astrocytic mGluR1 and mGluR5 antagonists. For each electrical stimulation frequency, single-cell astrocytes responsivenesses were very variable. Their distribution for the experiment displayed in A is shown in C, Increasing the stimulation frequency leads to increases in average astrocyte responsivenesses but it also increased responsiveness variability. D, Astrocytic population responsiveness versus stimulation frequency. Grey empty circles are population responsivenesses for experiments performed with NMDAR & AMPAR but without (astrocytic) mGluR antagonists (n = 284). Corresponding mean result, standard errors (black circles and bars), and sigmoid fit (black dashed line) are also illustrated. Turquoise empty squares are population responsivenesses obtained in the presence of both NMDAR & AMPAR and mGluR antagonists (n = 239). Corresponding mean results and standard errors and linear fit are shown as blue squares (with bars and dashed blue line, respectively).
Figure 6.
Spectral analysis of astrocytic [Ca2+]i oscillation with wavelet analysis.
A, Time frequency analysis of a representative astrocyte showing typical low frequency oscillation (Type I). B, Time frequency analysis of a representative astrocyte showing higher frequency response that increases with stimulation frequency (Type II). C, Histogram of the astrocyte maximal frequency (see Methods). Typical patterns are colored and fit by a Gaussian distribution (Type I cells in blue, and Type II cells in red). D, Distribution of astrocyte oscillation frequencies. Each column corresponds to one astrocyte and shows its oscillation frequency spectrum (binned at 0.02 Hz). Astrocytes were ranked according to their mean oscillating frequency; most of them oscillate at low frequencies but around one third (right part of the panel) responded to stimulations with oscillations as high as 0.2 Hz. (n = 284 cells).
Figure 7.
Model astrocytes also respond in a frequency-dependent manner to neuronal stimulation.
A, Astrocyte calcium signals (green traces) show a variety of responses, as in the experiments. Some of them start responding at frequencies as low as 2 Hz (top trace) while others need up to 20 Hz to elicit a significant response (bottom trace). Astrocytes were stimulated using the red neuronal spike train, stimulation frequencies are indicated on top of the figure. B, Using the same method as in the experiments (Fig. 3C), population responsiveness was computed in the simulations and plotted as a function of stimulation frequency for all modeled cultures. Grey circles denote population responsivenesses and black dots their average value. Error bars indicate standard error and the black dashed line shows the sigmoidal fit characterizing the frequency-dependent astrocyte response (n = 130 cells).
Figure 8.
Model astrocytes display a coupling degree-dependent onset.
A, Single-cell astrocyte responsiveness as a function of stimulation frequency and for different coupling degrees (i.e. number of unstimulated astrocytes to which the stimulated one is coupled). B, Normalized derivatives ((dR/dfs)/max(dR/dfs)) of the curves in A; peak values are denoted by stars (exact onset frequencies). Isolated astrocytes (k = 0, blue line) display a fast increase in responsiveness just before 2 Hz while astrocytes which are linked to one astrocyte (k = 1, green line) have a much later onset, around 5 Hz. For k = 2, red line the exact onset frequency is above 10 Hz.
Figure 9.
Network parameters affect astrocytic [Ca2+]i traces.
A, Ca2+ and B, IP3 traces of isolated astrocytes in response to different stimulation frequencies. Above 2 Hz, as shown on Fig. 7, astrocytes start responding with Ca2+ oscillations. Below 2 Hz, IP3 and Ca2+ levels reach a frequency-dependent steady-state; when these steady-state concentrations are high enough to trigger CICR (i.e. for high enough stimulation frequency), astrocytes respond with large Ca2+ oscillations. C, Increasing the stimulation frequency increases the astrocyte oscillation frequencies. Whatever the coupling degree k, the oscillation frequency reaches a plateau for high stimulation frequencies. The height of this plateau however strongly depends on the astrocyte coupling degree. Isolated astrocytes oscillate much faster than connected ones. Error bars denote standard deviation (n = 130 astrocytes).
Figure 10.
Spectral analysis of model astrocytic [Ca2+]i oscillations by wavelet analysis.
A, Time-frequency analysis of a representative astrocyte showing typical low frequency oscillation (Type I). B, Time-frequency analysis of a representative astrocyte showing typical high increasing frequency oscillation (Type II). C, Histogram of the maximal oscillation of astrocytic populations. Typical patterns are colored and fitted by a Gaussian distribution (Type I cells in blue, and Type II cells in red, total n = 373 cells). D, the distribution of astrocyte oscillation frequencies. Each column corresponds to one astrocyte and contains its oscillation spectrum (binned at 0.02 Hz). Astrocytes are ranked according to their mean oscillating frequency; most oscillate at low frequencies but around one third (right part of the panel) respond to stimulations with frequencies as high as 0.2 Hz, thus matching the experiments (cf. Fig. 4D).
Figure 11.
The oscillation frequency is significantly and negatively correlated to the onset frequency.
A, In the model, astrocytes that display high frequency oscillations also respond earlier (for smaller onset frequencies) than slowly oscillating astrocytes. The analysis was restricted to stimulated astrocytes (n = 130). B, The same effect is visible in experimental data; while the range of onset frequencies wider, the negative correlation between oscillation frequency and onset frequency is very significant. The analysis was restricted to strongly stimulated astrocytes, which responded to at least one stimulation in less than 1.5 s (n = 40). For A and B, grey circles denote single-cell astrocyte responses from all simulations or cultures, while black dots denote averages of the data after splitting in 4 classes. Error bars show corresponding standard deviation. Astrocytes were submitted to 10 Hz stimulations and onset values were computed as explained in the methods section.