Estimating integrated information in bidirectional neuron-astrocyte communication

There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of “integrated information.” We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.

Figure 1

Neuron-astrocytic networks: (a) six excitatory neurons connected all-to-all (exc-full), (b) six excitatory neurons connected by nearest neighbors (exc-nns), (c) one inhibitory neuron and five excitatory neurons connected by nearest neighbors (inh-nns). Connections without arrows are bidirectional. Astrocytes are associated to a single excitatory neuron and are connected between themselves through nearest-neighbor coupling. In (c) the inhibitory neuron is not linked to an astrocyte.

Figure 2

Simulated ${\mathrm{Ca}}^{2+}$ patterns in an astrocyte obtained for (a) unidirectional feedback $J_{\text{Glu}}=0$, $v_4=0.5\mu {\mathrm{M}\mathrm{s}}^{-1}$ and (b) bidirectional neuron-astrocyte coupling $J_{\text{Glu}}>0$, $v_4=0.3\mu {\mathrm{M}\mathrm{s}}^{-1}$. The neural network used is exc-nns with $g_s=3.42$.

Figure 3

Order parameter $\overline{r}$ as the coupling $g_s$ is varied. Inset: dependence of the average firing rate $v$ (${\mathrm{s}}^{-1}$) of the population of neurons upon $\overline{r}$. Plots are shown for (a) unidirectional and (b) bidirectional communication. Each marker represents a network architecture: black open circle [exc-full, Fig. 1], blue open square [exc-nns, Fig. 1], and red plus [inh-nns, Fig. 1].

Figure 4

Raster plots of (a) neuronal and (b) astrocytic activity at $g_s=3.4$ and $\lambda =20$ Hz with bidirectional coupling. Plots correspond to an excitatory network with all-to-all coupling [exc-full, Fig. 1]. Bottom figure (c) shows the instantaneous synchronization of the neurons defined according to Eq. (17).

Figure 5

Integrated information ${\mathrm{\Phi }}^{*}$ for different coupling values $g_s$ and timescales $\tau$. Each column indicates the network under consideration (shown in Fig. 1). Top row (a) shows the results for the unidirectional feedback from astrocytes and (b) the bidirectional neuron-astrocyte communication. Bright region of the heat plots corresponds to maximal ${\mathrm{\Phi }}^{*}$ around 2 ms and the shaded region around 20 ms indicates its second peak. Both peaks emerge as $g_s$ grows as described in the text.

Figure 6

Integrated information ${\mathrm{\Phi }}^{*}$ for different coupling values $g_s$ and varied timescales $\tau$. The network architecture corresponds to exc-full [Fig. 1] for (a) unidirectional and (b) bidirectional coupling.

Figure 7

Measures ${\mathrm{\Phi }}^{*}$ (integrated information), ${\mathrm{\Phi }}_{\text{WMS}}$ (net synergy), and $I_{AB}$ (mutual information). Left column: (a)–(c) indicate values associated with unidirectional feedback from astrocytes. Right column: (d)–(f) show values for the bidirectional neuron-astrocyte communication. ${\mathrm{\Phi }}^{*}$ and ${\mathrm{\Phi }}_{\text{WMS}}$ are reported at $\tau =2$ ms. Legends are defined as in Fig. 3.

Figure 8

(a)–(c) Integrated information ${\mathrm{\Phi }}^{*}$ for different stimulation frequencies $\lambda$ and timescales $\tau$: (a) exc-full network [Fig. 1] with fixed coupling $g_s=2.5$ and (b), (c) inh-nns network [Fig. 1] with $g_s=7.5$. Unidirectional feedback is denoted by (ud) and bidirectional (bd). (d) ${\mathrm{\Phi }}^{*}$ for fixed $\tau =2$ ms and varied $\lambda$. Markers: exc-full, open circle; inh-nns (ud), open square; and inh-nns (bd), plus. (a)–(c) Bright region of the heat plots corresponds to maximal ${\mathrm{\Phi }}^{*}$ around 2 ms and the shaded region around 20 ms indicates its second peak. Both peaks increase with $\lambda$ as described in the text.