Over the past few decades, astrocytes have raised a great concern (Volterra and Meldolesi, 2005; Sofroniew and Vinters, 2010; Molofsky and Deneen, 2015; Vainchtein and Molofsky, 2020). Increased evidence show that astrocytes actively participate in the brain functions (Hertz and Chen, 2016; Verkhratsky and Nedergaard, 2018; Deitmer et al., 2019) and importantly, they are hallmark of various brain diseases (Burda and Sofroniew, 2014; Verkhratsky et al., 2014; Sofroniew, 2015; Pekny et al., 2016). Astrocytes are electrically non-excitable cells that respond to stimulation with elevations of Ca²⁺ concentration. These Ca²⁺ signals appear as “global” and/or “focal” responses within the astrocyte complex (Guerra-Gomes et al., 2017). Three-dimensional Ca²⁺ imaging shows that 80% of total Ca²⁺ activity happens in fine processes which occupy 75% of cell volume and form the so-called spongiform domain (Bindocci et al., 2017). Understanding the Ca²⁺ signals involved is crucial to reveal the special role of astrocytes in health and diseases (Escartin et al., 2021).

Recently, great interests and technical advances have significantly promoted the topic. By taking advantage of high-resolution two-photon microscopy, Di Castro et al. found an intense local Ca²⁺ activity in the processes of mature astrocytes, called “focal” and “expanded” events due to the short duration and high frequency (Di Castro et al., 2011). Moreover, the local Ca²⁺ transients are closely associated with synaptic function. Bindocci et al. provided the first comprehensive 3D map of Ca²⁺ activity in an individual astrocyte, thereby demonstrating its complexity, heterogeneity, and locality, notably at the astrocyte-synapse interface, where activity is small, fast, and frequent (Bindocci et al., 2017). Stobart et al. identified, for the first time, fast astrocyte Ca²⁺ microdomains in fine processes and endfeet by using novel combinations of genetically encoded Ca²⁺ indicators (Stobart et al., 2018). They provided new insight into the timing of activity in the fine structures of astrocyte and neuron, suggesting that astrocyte signaling is fast enough to play a role in synaptic modulation. Arizono et al. performed 3D-STED microscopic imaging of the spongiform domain of astrocytes and observed a reticular meshwork of nodes and shafts that often formed loop-like structures (Arizono et al., 2020). The work also shows that nodes not only host highly localized spontaneous Ca²⁺ transients but also are likely functional components of tripartite synapses. Ding et al. investigated the Ca²⁺ transient changes in the subcellular domain of astrocytes during brain aging (Ding et al., 2022). The results suggest that aging-induced changes of Ca²⁺ transient types are heterogeneous within astrocytic subcellular domains. Despite these advances, established optical techniques typically break down at this nanoscale due to the diffraction limit, making difficult to understand the mechanistic link between their morphology and Ca²⁺ signals.

Computational modeling is an effective way to understand complex systems with a much more systematic and controlled way than what could be done experimentally. The same hold true for studying cellular signalling in astrocytes. In this vein, Cresswell-Clay et al. proposed a minimal compartmental model for astrocytes that can qualitatively reproduce essential hierarchical features of spatiotemporal Ca²⁺ dynamics in astrocytes (Cresswell-Clay et al., 2018). Savtchenko et al. systematically incorporated multi-scale, 3D astroglial architecture into a realistic multi-compartmental cell model (Savtchenko et al., 2018). It is detailed but also much computationally demanding. Gordleeva et al. introduced a spatially extended astrocyte model to study the effects of interplay of Ca²⁺ signals in processes and in Soma mediating correlations between local signals and the cell-level response of the astrocyte (Gordleeva et al., 2019). Denizot et al. used a stochastic spatially explicit individual-based strategy and proposed an IP₃R-mediated Ca²⁺ signaling model for dynamics in fine processes (Denizot et al., 2019). Subsequently, they modelled node-shaft geometries of the gliapil by designing an isolated fine process containing five identical nodes and four identical shafts based on their super-resolution study (Denizot et al., 2022). Verisokin et al. flattened astrocyte images used as spatial templates to reduce the 3D of realistic astrocytes to 2D allowing for smaller computational costs than Savtchenko et al. (2018), Verisokin et al. (2021).

As there are only limited spatial models without full consideration of the morphological parameters on Ca²⁺ activity the integration of experimental data to computational approaches is required Here, to clarify how nano-morphology of astrocytes controls Ca²⁺ activity, we gave a more complete picture by proposing a structurally similar model of realistic astrocytic fine processes using published data from live tissue (Arizono et al., 2020). The model consisted of initial sites of Ca²⁺ microdomains, nodes, connecting shafts, and a section of large process. The variable size of nodes and shafts could cause the diffusion changes of whole dynamics and finally powerfully affected the Ca²⁺ activity involved. Simulations allowed for the explanations of complicated relations between astrocytic morphology and excitability, such as the effect of nano-morphology of fine processes on local Ca²⁺ activity, interactions between fine and larger processes and how pathological morphological deficits of astrocytes affect glutamate-mediated tripartite synapses.

To recap, our study aims to shed light on the effect of the nano-morphology of astrocytic fine processes on local Ca²⁺ microdomain activity and synaptic transmission. We posit this integrated approach could help understand certain mechanisms such as plasticity of astrocyte dynamical processes and pathological morphological changes in brain disorders like Alzheimer’s disease (AD) and inspire new insights into therapies for unsolved neurological diseases (Zhang et al., 2022).

Astrocytes display a complex morphology characterized by distinct compartments: the Soma, primary processes, and numerous fine processes which form the astrocytic spongiform domain resembling a reticular meshwork of dividing and merging astrocytic processes. Most of those compose tripartite synapses with their neuron partners where they sense neuronal activity and process this information as a Ca²⁺ signal (Semyanov et al., 2020). Super-resolution imaging shows the anatomical units of those fine processes: nodes and shafts (Arizono et al., 2020). These nodes and shafts constitute a network featuring closely spaced bulbous node-like enlargements that frequently form branch points from which several thinner connecting shaft-like processes emerge. Nodes are simultaneously locations of initial sites of Ca²⁺ signals and the participant of tripartite synapses while shafts may not be capable of generating Ca²⁺ events spontaneously (Arizono et al., 2020).

Considering these, we constructed two submodels, a node-shaft model and a tripartite synapse model. The former investigated how the morphology of fine processes affects Ca²⁺ activity at the astrocyte scale. The node-shaft model consisted of spherical structures, nodes, connected to each other or the parent process with cylindrical structures, shafts. We then extended the original model by adding a neuronal component, hoping to further study the effect of morphological changes of fine processes on neuronal activity in the tripartite synaptic structure. The tripartite synapse model was composed of one of nodes in the former model, a presynaptic bouton and a postsynaptic spine. Nodes possess endoplasmic reticulum (ER) so that Ca²⁺ signals can occur when IP₃Rs on the ER membrane are at open state. Shafts contain no organelles but IP₃ and Ca²⁺ can diffuse through them. In the model, the width of nodes was set to greater than or equal to the width of shafts. In summary, these two parts together form the node-based tripartite synapse model.

Our model produced consistent Ca²⁺ signals essentially in agreement with results of experiments in live tissue (Arizono et al., 2020). Each node exhibited unique pattern of Ca²⁺ signal which were fast and small. While in the parent astrocytic process that nodes connected to, Ca²⁺ transients were larger both in amplitude and interval indicating significant differences in Ca²⁺ signals between the microdomain and larger astrocytic processes (Figure 3).

Astrocytes use “Ca²⁺ language” to process information and most of the basal Ca²⁺ activity occurs in their fine structures where they compose the spongiform domain (Bindocci et al., 2017). This attractive area has gained great attention but also faced challenges and difficulties from techniques. Deciphering the mechanistic link between nano-morphology and intracellular Ca²⁺ signals is essential yet hard to analyze experimentally. In this study, we studied the role of fine morphology of astrocytes by using computational tools and data from super-resolution microscopy. Our model validated the effect of morphology of astrocytic fine processes on local Ca²⁺ activity and further showed that the width ratio between nodes and shafts determined the shape of Ca²⁺ signals in microdomain. How the inextricably related players, fine and large processes, interact remains unclear. Here we provided a computational study indicating that the differences between compartmental diffusion might be an explanation and the number of fine processes connected to the large processes could affect the mutual Ca²⁺ activity. Since astrocytic fine processes actively participate in the synaptic communication forming the so-called tripartite synapse, we associated the node-shaft model with the existing tripartite synapse model. No doubt, this could be an essential model of astrocyte-neuron networks. The results showed the strong influence of reduced morphology of nodes on synaptic transmission.

Actually, Denizot et al. have proposed a model with realistic 3D geometries of fine processes after their super-resolution investigation (Arizono et al., 2020; Denizot et al., 2022). They designed an isolated section of fine process with five identical nodes connected by four identical shafts. Nodes are approximated as spheres of width d 0 = 0.38 μ m and shafts as 1 μm-long cylinders. The width of shafts has three different values: d s h a f t = d 0 , d s h a f t = d 0 / 2 and d s h a f t = d 0 / 3 . They focused on the effect of shaft width on Ca²⁺ signals. They found that thin shafts favor node compartmentalization and more robust signal propagation, simultaneously enhance Ca²⁺ activity in nodes. Contrastly, we here built a more comprehensive model of the spongiform structure and investigated the width of nodes and the length of shafts. Our model showed that large nodes were also beneficial for enhancing Ca²⁺ activity while shaft length had no effect. Besides, we studied the crosstalk between the fine and large processes. We also discussed the role of morphological changes in fine processes on synapses. Although Denizot et al. mentioned the impact of astrocytic nano-morphology on astrocyte activity at tripartite synapses in health and disease, it seems to lack more detailed analysis and validation.

In addition, Savtchenko et al. and Denizot et al.‘s earlier studies also proposed astrocyte models associated with the nano-morphology of astrocytic fine processes (Savtchenko et al., 2018; Denizot et al., 2019). Savtchenko et al. transformed polygonal z-stacks representing 3D-reconstructed processes from electron microscopy into z-stacks of cylindrical slabs in silico. They only briefly compared two modelled astrocytes with different stem trees that were populated with the same nanoscopic processes. Collectively, the contribution of this work is more for a powerful tool provided to study functions of astrocytes than astrocytic physiology itself. Denizot et al. mimicked an astrocytic process consisting of a cylinder of length 1 μm and radius 0.1 μm. They investigated some mechanisms on astrocyte Ca²⁺ microdomains including clustering of IP₃R channels, endogenous buffers, etc. The two studies are helpful but they both only regard the processes as simple cylindrical structures, also do not allow for that nodes are preferential sites of Ca²⁺ initialization and synaptic transmission. One necessary task of computational biology is to incorporate the latest experimental data into our modeling work to advance the construction and validation of models.

Astrocytic fine processes possess a very high surface-to-volume ratio, and this parameter determines the probability of Ca²⁺ events initiation (Wu et al., 2019) and is necessary for efficient glutamate uptake (Patrushev et al., 2013). In our simulations, we found a specific width ratio of nodes to shafts, about 3, was the most favorable structural ratio under which the local Ca²⁺ activity was the most active. We thought this ratio presented in astrocytes might be advantageous to diffusion and explained why Ca²⁺ events more frequently start in thin astrocytic processes (with a higher ratio) than in thick processes or Soma (Semyanov, 2019). Especially, when astrocytes exhibit morphological deficits or undergo reactive response in diseases, their volumes and structures change, which is sure to induce the alterations in Ca²⁺ activity, eventually leads to behavioral modification of astrocytes like the loss of functions or enhanced protection.

Astrocytic Ca²⁺ activity seems to be compartmentalized. Experiments show that most of Ca²⁺ signals that reach the interface between two structures (like Soma and processes) stop there just like some forms of physical and/or biological barrier are presented at the interfaces (Bindocci et al., 2017; Arizono et al., 2020). How the other small portion of events crosses the barrier and propagates from one to another compartments, such as processes to Soma, remains unanswered, which still needs more experimental explorations. Therefore, in this model, the assumed compartments were all non-confined. We mainly focused on the crosstalk between the fine and large processes and found that the connectivity of nodes to larger processes markedly shaped the Ca²⁺ signal of the large structures. This finding may make sense because in many neurodegenerative instances, the change in number of astrocytic processes is a frequent occurrence, for example, reactive astrocytes always have more complex branchy degree while atrophic astrocytes have less processes because of morphological deficits (Zhou et al., 2019).

Astrocytes are important shapeshifters which allow them to respond to the changing environment during development, injury and disease. Their morphological changes have been observed in various experiments especially in pathological conditions, but most mechanisms remain unknown. For example, hypertrophic reactive astrocytes are always thought to be a hallmark in many neurodegenerative diseases, while the atrophic astrocytes are presented earlier in AD (Verkhratsky et al., 2016; Jones et al., 2017; Escartin et al., 2021). So far, the molecular basis for astrocyte atrophy preceding astrogliosis, and what is the contribution of this phenotype to the onset of AD are still puzzles. Moreover, the apparent morphological deficits including reduced volumes of fine processes are also observed in Huntington’s disease (Octeau et al., 2018). Instead, in Parkinson’s disease, there is a significant expansion of the coverage by astrocyte processes of striatal tripartite synapse with unknown of the underlying mechanisms (Villalba and Smith, 2011). According to our simulations, the atrophy of astrocytic fine processes altered astrocytic Ca²⁺ activity thereby affecting the release of glutamate. The degradation of the excitability was hence the possible reason for early cognitive disorder and memory loss in the early stage of AD. This conclusion is an interesting idea but we realize and believe that more wet-lab design and data are required to address this specific clinical question. On the other hand, our model explained that the increase of the astrocytic coverage could enhance glutamate uptake in the synaptic cleft and decrease the high extracellular glutamate levels and overall neuronal hyperactivity which was consistent with the experimental results in the parkinsonian state (Villalba and Smith, 2011). Overall, the agreement between our model and experiments potentially illustrates that astrocyte-induced synaptic impairment may be responsible for the dysfunction of advanced brain abilities such as cognition, memory, etc. Rescuing the morphological deficits and guarantying the morphological integrality are potentially the cure for neurological disorders.

Knowledge about Ca²⁺ microdomain is rapidly increasing. A recent study indicates that ER is observed in only ∼45% of fine processes (Aboufares El Alaoui et al., 2020) and other sources of these dynamics are therefore revealed. Clear evidence has shown that extracellular Ca²⁺ influx through cell membrane ion channels can contribute to astrocytic microdomain events with fast dynamics, such as TRPA1 and Na⁺/Ca²⁺ exchanger (Ahmadpour et al., 2021). Besides, Agarwal et al. (Agarwal et al., 2017) found that in the absence of IP₃-dependent release, microdomain Ca²⁺ transients still occur due to the opening of the mitochondrial permeability transition pore. These various fluxes can also induce cascade reaction. For instance, once store-operated Ca²⁺ entry is activated, the depletion of ER activates the ER Ca²⁺ sensors stromal interaction molecules 1 and 2, then the molecules translocate to the junctional ER to interact with and activate store-operated Ca²⁺ release-activated Ca²⁺ channels (Toth et al., 2019), suggesting that intracellular release and transmembrane influxes coordinately contribute to Ca²⁺ microdomains. Considering a complete picture of the Ca²⁺ microdomain would definitely help better understand the theme but also is challenging due to the missing explanation of some mechanisms. In this study, we aimed to provide a biologically plausible theoretical framework that could provide reasonable predictions on the morphology-defined Ca²⁺ microdomains that are difficultly enabled in experiments.

In fact, our model leaves much to be desired and needs further improvement. Firstly, our node-shaft model is only an approximation of the astrocyte microdomains and cannot fully reflect the morphology of fine processes. Secondly, our model does not fully consider the factors affecting astrocyte Ca²⁺ dynamics. In astrocytes, in addition to glutamate, ATP, GABA and other signaling pathways also affect Ca²⁺ signalization and contribute to the regulation of a number of both physiological and pathophysiological processes in the nervous system as well (Chen et al., 2023). The model only examined a subset of the astrocyte microdomains and did not take into account the extracellular Ca²⁺ diffusion. Thirdly, Some details of the model are not rigorous enough. The presence of ER in the fine processes is controversial, but there is evidence that Ca²⁺ microdomains can have a pure intracellular or extracellular Ca²⁺ source (Lia et al., 2021). And we chose to add ER in the thinnest astrocyte processes for some considerations, thus ignoring another possibility. What’s more, we did not consider ryanodine receptors in our modeling, which is something we need to explore in the future. The Hodgkin-Huxley model is used to generate presynaptic spikes without using a fluctuating applied current. Instead a constant current is used here because we found that even substituting 1, 2, and 5 times the noise of the 0–1 uniformly distributed current has little effect on the results. This may be partly due to the short current window we applied. Finally, astrocytes share their cytoplasm through gap junctional coupling into a syncytium. The node-shaft model can be extended to describe the communication between two astrocyte microdomains, and even to astrocyte networks. On the other hand, our tripartite synaptic model, as the smallest unit of signal propagation of astrocyte-neuron network, is also helpful for future network construction. By further understanding the astrocyte microdomain in the future, we hope to build more realistic astrocyte models with more comprehensive signaling pathways.

Although many questions and challenges exist, Ca²⁺ signals in astrocyte microdomains have gained a decade of significant advances, as said, a new decade of great discoveries has just begun (Lia et al., 2021). We need fruitful partnerships between tool generators, modellers and experimentalists to catalyze major breakthroughs in biology, physiology and pathology of astrocytes.