Interrogating functional connectivity of in vitro neural glia tissue model modulated through integrative control of matrix stiffness and a neurotrophic factor

Abstract

Brain function emerges from intricate cellular communication within neural networks. Both In silico neuronal models and primary neuron cells have revealed that the branching architecture of individual neurons determines the bioelectrical signal propagation pattern and dynamics. However, whether stem cell-differentiated neurons can build functional connectivity regulated by neuronal morphology has yet to be determined. Here, we hypothesized that neurite length, branching, or both factors would regulate the functional connectivity of the stem cell-differentiated neural network. We examined this hypothesis by differentiating mouse cortical neural stem cells (NSCs) on Matrigel substrates with varying storage moduli, both with and without basic fibroblast growth factor (bFGF). Interestingly, with bFGF, Matrigel with a storage modulus (G′) of 100 Pa drives NSCs to differentiate into neurons with more dendritic branches, while the gel with G′ of 50 Pa led to the development of longer neurites with fewer branches. Notably, branch-rich neural networks exhibited an increased frequency of calcium transients. Using a MATLAB-based analysis pipeline incorporating graph theory, we constructed spatial and temporal calcium activity maps, revealing that branching complexity, more than neurite length, correlates with the density and strength of functional neural circuits. Overall, this study demonstrates that the dendritic branching of neurons, modulated with matrix stiffness and neurotrophic factors, is a key element in enhancing the electrophysiological functionality of the stem cell-differentiated neural network. This finding will have a significant impact on efforts to reconstruct functional neural tissue models, advancing both regenerative therapies and unexplored applications, including biological computing.

1. Introduction

Behavior, cognition, and intelligence emerge from intricate cellular communication within neural networks [1–3]. Individual “living” neurons work as a building block of bioelectrical circuits and form a neural network. Since neural activity results from bioelectrical signal transmission among individual neurons, the architecture of the neuronal network significantly influences its functionality [4,5]. For instance, whole-brain scanning studies uncovered a correlation between distinct neural firing patterns and varied brain regions at tissue levels [6,7]. In vivo studies using rats and mice revealed that local neuron firing patterns contribute to behavioral performance [8]. However, these studies have yet to address how the architecture of individual neurons influences the functional connectivity of neuronal networks.

Several studies using in silico neuronal models have reported that branching morphology of individual neurons plays a crucial role in the dynamics of signal propagation [9–12]. Specifically, dendritic area modulates a neuronal firing rate [10]. Additionally, the width ratio between mother and daughter branches influences signal propagation patterns [9]. Separately, experimental studies combining microelectrode array (MEA) and morphological imaging of primary cortical cells in rats reported that the axonal length, thickness, and branch order regulate propagation velocity and magnitude of the neuronal signal [13,14]. Although these studies demonstrated that neuronal morphology influences the electrical activities of single neurons, further research is needed to understand how the configuration of individual neurons affects the correlation of neural signal transmission within the neural network. For instance, is the functional connectivity improved by increasing neurite length, branch number, or both?

To modulate the morphology of the neurons in vitro, researchers have been exploring external cues to change neuronal architecture [15,16], especially with neural stem cell (NSC) derived neurons [17,18]. In the past, mechanical and biochemical cues have been used to modulate neuronal architecture. For instance, an elastic modulus of the neuronal cell culture substrate can alter differentiation yield and neurite outgrowth of NSCs [18–21]. Increasing the elastic modulus of a fibronectin-coated polydimethylsiloxane (PDMS) substrate from 12kPa to 750 kPa decreased neurite length from 80 to 40 μm of NSC differentiated neurons [21]. Additionally, certain soluble factors, such as the basic fibroblast-like factor (bFGF), have been used to promote migration and survival of NSC and regulate neuronal differentiation [22–25]. In particular, bFGF can increase the neural differentiation yield of NSCs [22–25], and when combined with electrical stimulation, it establishes highly branched neurites [24]. A mixture of bFGF and retinoic acid further increased the percentage of neurons and mean neurite length [22]. However, there has been limited research on how the neuronal architectures, modulated by mechanical and chemical cues, affect the functionality of neural networks.

Here, we hypothesized that the morphological features of individual neurons, specifically neurite length and dendritic branching, are regulated by both soluble and insoluble extracellular cues, and that these features, in turn, influence the functional connectivity of stem cell-derived neural networks. To investigate this, we differentiated mouse cortical neural stem cells (NSCs) on Matrigel substrates with distinct storage moduli and supplemented the culture medium with varying concentrations of basic fibroblast growth factor (bFGF). While a variety of soluble factors have been implicated in neural differentiation [26–28], including retinoic acid, EGF, BDNF, and VEGF, bFGF was selected for this study as a representative neurotrophic factor due to its dual role in supporting both neural progenitor proliferation and neuronal maturation, particularly its impact on neurite outgrowth and branching. We quantitatively profiled neurite outgrowth and branching complexity under each condition and performed calcium imaging coupled with graph theory-based analysis to assess multicellular network dynamics [29,30]. By integrating structural and functional measurements, our study reveals how matrix mechanics and trophic signaling together shape both neuronal morphology and the emergent connectivity patterns within neural networks, offering insight into the design of more physiologically relevant in vitro brain models.

2. Results

2.1. The concentration of extracellular matrix proteins of the Matrigel modulates its rheological properties but does not affect its permeability

First, viscoelastic properties of the Matrigel matrices—hereafter referred to simply as Matrigel—with varying concentrations of extracellular matrix (ECM) proteins were characterized. Specifically, we measured the storage modulus (G′) and loss modulus (G″) as a function of the frequency during small-amplitude oscillatory tests (Figure 1A). G′ remained constantly larger than G″ for both ECM protein concentrations. No crossover point was observed between G′ and G″ for the tested frequencies [31]. Increasing ECM protein concentrations from 6 to 10 mg/ml elevated G′ of the Matrigel from 50 to 100 Pa.

Figure 1. Rheological properties and diffusivity of the Matrigel matrix with controlled ECM protein concentrations.

Storage modulus G’ (Filled symbols) and loss modulus G’ (hollow symbols) as a function of frequency and (A) as a function of shear strain amplitude. (B) for 6 mg/ml (triangle) and 10 mg/ml (square) Matrigel matrices. (C) Fluorescence recovery curve of FITC-dextran loaded in 6 mg/ml (triangle) and 10 mg/ml (square) Matrigel matrices and (D) diffusion coefficient of the FITC-dextran in Matrigel matrices. Each value and error bar in (C) and (D) represent average values and standard deviation of 5 samples per condition.

We also investigated effects of ECM protein concentration on the strain dependence of G′ and G″ of the Matrigel (Figure 1B). G′ and G″, which remained independent of the strain within a linear viscoelastic region, became dependent as the strain exceeded a critical strain. G′ decreased with strain, while G″ rose to a peak followed by a decrease. The critical strains of the Matrigel were reduced from 24.8 % to 9.9 % by increasing the ECM protein concentration from 6 to 10mg/ml. A strain where G′ and G″ crossed was also decreased by increasing the ECM protein concentration.

In parallel, the permeability of the Matrigel was evaluated by measuring the diffusivity of the fluorescein-labeled dextran (FITC-dextran) with a molecular weight of 40 kDa using a microscope equipped with the fluorescence recovery after photobleaching (FRAP) analysis module (Figure 1C). The photo-bleached region of the Matrigel recovered more than 80% of the original fluorescence intensity within 20 seconds, regardless of the ECM protein concentration. Diffusion coefficients of the dextran were determined by fitting fluorescent recovery from FRAP analysis to equation (1). The diffusion coefficients were 46 μm²/s and 43 μm²/s in the Matrigel with ECM protein concentrations of 6 and 10 mg/m, respectively (Figure 1D).

2.2. bFGF and rheological properties of the Matrigel regulate differentiation of NSCs.

Mouse NSCs adhered to Matrigel substrates with G′ of 50 and 100 Pa and were cultured in neural differentiation media, either supplemented with 20 mg/ml bFGF or without it. While cells were initially plated on the surface rather than embedded within the gel, they progressively infiltrated the matrix over the course of differentiation, forming a 3D network structure. A side-view image of the culture is provided in Supplementary Figure S1. After 14 days, immunofluorescence images showed multiple cell populations, including neurons and glial cells, stained positively for β-III tubulin (TUJ1) and glial fibrillary acidic protein (GFAP), respectively (Figure 2A). Notably, in bFGF-free neural differentiation media, differentiated cells aggregated into bundles where neurons were minimally stretched and branched. In contrast, bFGF promoted formation of a neuronal cell sheet with interconnected networks associated with glial cells.

Figure 2. Analysis of mouse NSC differentiation after culture in neural differentiation media supplemented without and with 20ng/ml bFGF.

(A) Immunofluorescent images of NSC-derived neural cells on Matrigel substrates with G′ of 50 and 100 Pa. The neuronal biomarker β-III tubulin (Tuj1, green), the astrocyte-specific glial fibrillary acidic protein (GFAP, red), and DAPI (blue) are shown in images taken at Days 14 and 21 of differentiation. Scale bar: 50μm. (B-1) and (C-1) Quantification of the number of Tuj1-positive cells per unit area at Days 14 and 21. (B-2) and (C-2) The neuron to astrocyte ratio at Days 14 and 21. Each value and error bar in (B)-(C) represent the mean and standard deviation of 3 samples per condition (*p < 0.05, ordinary one-way ANOVA)

According to quantitative analysis, by counting the number of TUJ1-positive neurons and GFAP-positive glial cells, bFGF supplementation increased the neuron population. To further distinguish between proliferation and differentiation effects, we also quantified the total number of cells (Figure S2). This analysis confirmed that bFGF treatment increased overall cell numbers, supporting its role in promoting neural stem/progenitor cell proliferation and neural differentiation. This effect was particularly pronounced when NSCs were differentiated on the Matrigel with G′ of 100 Pa (Figure 2B-1 and 2C-1). Furthermore, with bFGF, increasing G′ of Matrigel from 50 to 100 Pa quadrupled the neuron-to-glial ratio by Day 21. Without bFGF, the neuron-to-glial ratio significantly decreased from Day 14 to Day 21, regardless of G′ of the Matrigel. This result was attributed to the fast proliferation of glial cells (Figure 2B-2 and 2C-2)

2.3. The architecture of NSC-derived neurons is modulated by bFGF and rheological properties of the Matrigel substrates.

Neurites of differentiated neurons were examined using the IMARIS neurite tracing tool. TUJ1 was used for structural analysis. We also performed immunostaining for MAP2, a marker of mature neurons. MAP2 expression was prominently observed in TUJ1-positive cells in conditions treated with bFGF, confirming that a significant fraction of the differentiated neurons had reached a mature state (Figure S3). We traced and reconstructed TUJ1-positive neurons that had differentiated in the bFGF-supplemented media (Figure 3A). No traceable neurites were found in the absence of bFGF, regardless of G′ of the Matrigel. Therefore, our analysis focused on whether G′ of the gel influenced neurite stretching and branching in the presence of bFGF. On Day 14, neurons differentiated on the Matrigel with G′ of 100Pa exhibited a longer maximum neurite length than those on the gel with G′ of 50Pa. However, no significant difference was found in the average neurite length between these two conditions (Figure 3B). By Day 21, neurons cultured on the gel with G′ of 50Pa showed a doubling in both maximum and average neurite length, while those on the gel with G′ of 100Pa maintained similar lengths to those observed on Day 14. Notably, the maximum and average neurite lengths on the gel with G′ of 50Pa were significantly higher than those on the gel with G′ of 100 Pa.

Figure 3. Morphological analysis of the NSC-derived neurons on Days 14 and 21 of differentiation.

(A) Immunofluorescent image of NSC-derived TUJ1-positive neurons (green) alongside computer- reconstructed neurons (red) on Matrigel substrates with varying G’. Scale bar: 50μm. (B) Profile of neurite length of the reconstructed neurons. (C) Sholl analysis mask showing the correlation between the number of Sholl intersections and Matrigel G’ of to 50Pa and 100Pa, with radii increasing in 10 μm increments. (D-E) Mean number of branches in NSC-derived neurons on Matrigel substrates with different G” on (D) Day 14 and (E) Day 21 of differentiation. Each value and error bar in (B), (D), and (E) represent average values and standard deviation of 3 samples per condition (*p <0.05, unpaired, heteroscedastic student’s t-test).

We further evaluated the extent to which G′ of the gel modulates neurite branching by counting the number of Sholl intersections and branches per cell in the reconstructed neurons (Figure 3C–E). The Sholl analysis measures the number of neurites intersecting concentric circles of increasing radii from the soma, thus allowing us to quantify the dendritic branching patterns of neurons. Figure 3C displays reconstructed neurons within Sholl circles, with radii increasing in 10-μm increments. Neurons differentiated on the gel with G′ of 50Pa exhibited branching points closer to the soma within 20μm on Day 14 and within 10μm on Day 21. In contrast, neurites on the gel with G′ of 100 Pa displayed branching points spread over a wider distance from the soma within 30μm on both Days 14 and 21. Additionally, neurites on the gel with G′ of 100 Pa exhibited branching approximately twice as much as those on the gel with G′ of 50 Pa (Figure 3D & E). To directly assess the role of laminin, we performed an additional experiment in which a laminin-blocking antibody was incorporated into the 100 Pa Matrigel substrate, with and without bFGF supplementation (Figure S4). Laminin blocking resulted in reduced cell adhesion and inhibited neurite sprouting in both conditions. While bFGF increased cell attachment compared to cultures without bFGF, neurite extensions remained absent in both conditions.

2.4. Calcium activity of neural networks is correlated with the number of neural branches.

We investigated the effects of bFGF and G′ of Matrigel on the calcium activity of NSC-derived neural networks. As shown in time-lapse images capturing dynamic changes in calcium flux, neural networks formed without bFGF supplementation exhibited minimal changes in intracellular calcium levels (Figure 4A and Video S1). In contrast, neural networks formed in the media supplemented with bFGF showed active propagation of calcium transient along neurons. Fluorescence traces were recorded from 100 different regions of interest (ROI). Figures 4B illustrate the changes in fluorescent intensity for each ROI over time. The peaks of calcium transient, which varied over time, were plotted as raster plots of spike times. Without bFGF supplementation, the neural networks displayed no active calcium flux across the observed area, regardless of G′ of the Matrigel on which NSCs were differentiated. Conversely, bFGF increased the number of ROIs showing active calcium flux in neurons. Notably, the gel with G′ of 100 Pa resulted in more ROIs exhibiting active calcium flux than the gel with G′ of 50 Pa.

Figure 4. Effects of bFGF and G’ of Matrigel on calcium flux activity in NSC-derived neural networks.

(A) Time-lapse images capturing calcium flux for a 10-second period. The white boxes in the first column indicate neurons highlighted in the time-lapse images, while the white arrows in the 2nd-to 7th columns point to areas where calcium concentration is maximal at specific time points. Scale bar: 50μm. (B) Calcium fluorescent traces and raster plots displaying calcium transient peaks from 100 regions of interest (ROIs) over a 1-minute duration. (C) Average calcium increases in the neural network. (D) Correlation between average calcium rises and the number of neuronal branches within the neural network. Each value and error bar in (C) and (D) represent average values and standard deviation of 3 samples per condition (*p <0.05, ordinary one-way ANOVA).

We also measured the average calcium rise, which was quantified by calculating the average number of calcium spikes across 100 ROIs within a specific time frame (Figure 4C). Neural networks formed in bFGF-supplemented media exhibited a higher frequency of calcium events than those formed in media without bFGF supplementation. With bFGF supplementation, the gel with G′ of 100 Pa enabled the formation of neural networks with an increased frequency of calcium firing compared to the gel with G′ of 50 Pa (Figure 4C). Interestingly, the average calcium rise was linearly correlated with the number of branches analyzed in Figure 3 but not the length of axons (Figure 4D).

2.5. Neuron architecture shapes functional connectivity.

Functional correlations between individual ROIs were used to construct a functional connectivity map that quantifies neuronal activity across different regions. Figure 5A illustrates the process of calculating functional connectivity from calcium flux images, where calcium transients were recorded from 100 ROIs in time-lapse calcium images. These calcium transients were used to calculate pairwise Pearson correlation coefficients, which were then organized into a correlation matrix. This matrix served as the adjacent matrix to create a weighted adjacent graph. In this graph, each node represents an ROI, and the correlation values between two ROIs determine the weight of the edges. This weighted adjacent graph represents the functional connectivity of the neural network. Figure 5B shows the Pearson correlation matrices from calcium activities of neural networks formed in the differentiation media supplemented with bFGF. Pearson plots could not be made for neural networks formed without bFGF supplementation due to minimal calcium activity, as shown in Figures 5B & C.

Figure 5. Functional connectivity analysis of NSC-derived neural networks.

(A) A schematic illustration of the procedure used to determine functional connectivity from calcium flux images. (B) Pearson correlation coefficient map of 100 ROIs within the neural network formed on gels with G’ of 50 and 100 Pa in the presence of bFGF. The color bar represents the Pearson correlation value. (C) Functional connectivity graph of neural networks formed on gels with G’ of 50 and 100 Pa in the presence of bFGF. The yellow boxes in the upper images mark the zoomed-in section of the functional connectivity graph. Node size indicates the number of correlated nodes, while the line width represents the magnitude of the Pearson correlation value between two nodes. (D) The mean number of functional connections (edge) and (E) are the mean number of ROIs with more than 5 edges in neural networks formed on gels with G’ of 50 and 100 Pa in the presence of bFGF. Each value and error bar in (B), (D), and (E) represent average values and standard deviation from 3 samples per condition (*p <0.05, unpaired, heteroscedastic student’s t-test)

The correlation matrices were used to develop the functional connectivity map shown in Figure 5C. As overviewed in Figure S5, this functional connectivity graph is based on graph theory [29,30], where each region of interest (ROI) is referred to as a “node.” Each node has a correlation value representing pairwise functional interactions with other nodes, presented in a matrix format (Figure S5A). These interactions are represented as a graph, with the corresponding matrix termed the adjacency matrix. In Supplemental Figure S5A, a correlation value of 1 between nodes A and B in the matrix is illustrated as a connected line, referred to as an edge, in the graph. The edges represent functional connections between nodes and are weighted by the corresponding correlation values from the adjacency matrix, which are reflected by the thickness of the lines. Supplemental Figure S5B displays correlation values ranging from 0 to 1, with increasing edge thickness signifying stronger correlations. Additionally, the number of edges linked to a node reflects how many connections the node has with other nodes. As shown in Supplementary Figure S5C, this degree of connectivity is represented by node size in the functional connectivity graph. In summary, edges (connected lines) represent functional connections between nodes, edge thickness corresponds to correlation strength, and node size indicates the number of connected nodes. Together, these visual cues in the functional connectivity graph, derived from the functional correlation adjacency matrix, provide comprehensive representation of the overall functional connectivity of the neural network.

Accordingly, with a correlation threshold of 0.6, the average number of functional connections in the neural network formed on the gel with G′ of 50 Pa was 56. In contrast, the neural network formed on the gel with G′ of 100Pa was 510 (Figure 5D). The neural network on the gel with G′ of 100Pa exhibited an average of 54 nodes functionally connected to more than 5 distinct regions. In contrast, the neural network on the gel with G′ of 50Pa has fewer than 10 such connections (Figure 5E). To assess the robustness of our network analysis, we performed the functional connectivity analysis using other correlation thresholds (e.g., 0.4 and 0.8), as shown in Supplementary Figure S6. This analysis demonstrated that the overall network trends, particularly differences in average node count and the presence of highly connected nodes, remained consistent across thresholds. These findings support that functional connectivity patterns can be captured without introducing significant bias or altering the interpretation of key results.

3. Discussion

This study utilized Matrigel, a 3D gel network formed from the physical association of natural ECM proteins, as a substrate for NSC differentiation. Our small-amplitude oscillatory frequency sweep and oscillation amplitude sweep tests disclosed that ECM protein concentration controls stiffness and yield strain of the gel, likely due to variations in entangled fibrous networks. The gel with a higher G′ at 100 Pa exhibited a higher critical strain than that of Matrigel with G′ of 50 Pa. Despite the differences in the rheological properties of Matrigel, the diffusivity showed negligible difference. Therefore, we focused on examining effects of G′ of the gel on neuronal differentiation, structure, and function.

Interestingly, when bFGF was present in the media, NSCs cultured on softer gel with G′ of 50 Pa differentiated to neurons with longer, less branched neurites, while those on stiffer gels with G′ of 100Pa developed more extensively branched neurites. In contrast, in the absence of bFGF, gel stiffness had no apparent effect, highlighting synergistic interaction where mechanical cues modulate the influence of neurotrophic signaling on neurite outgrowth and branching [17,32]. In this context, it is notable that the storage modulus values tested in this study (50 and 100 Pa) fall within the mechanical range of the neonatal rat cortical tissue at postnatal Days 4 and 12 [33]. Additionally, bFGF is endogenously expressed in the developing cortex and plays a well-established role in regulating neural progenitor proliferation and neuronal maturation [34]. Taken together, the extracellular microenvironment engineered in this study exhibits biochemical and biomechanical relevance to developing brain tissue. This finding contributes to a growing recognition that both mechanical and biochemical components of the extracellular environment play integrative roles in neural development, which is a relationship that remains underexplored compared to studies of each cue [32,35,36].

Matrigel contains endogenous growth factors, including less than 0.1 pg/mL of bFGF according to manufacturer specifications. As such, inclusion of a 0 ng/mL exogenous bFGF control condition allowed us to isolate the effects of added bFGF. The observed differences in neuronal morphology and network activity were only present under exogenous bFGF treatment, confirming that endogenous factors in Matrigel did not significantly influence our outcomes. Additionally, this finding can be extended to other soluble factors involved in neural differentiation, such as retinoic acid, EGF, NGF, BDNF, and VEGF, each of which influences various aspects of neuronal development via distinct pathways [26–28,37,38]. Future studies should explore how these factors compare or interact with bFGF in similar experimental contexts, potentially disclosing synergistic effects or alternative strategies for regulating neural differentiation.

Varying the Matrigel concentration to modulate stiffness may also alter the density of cell adhesion motifs, such as laminin and collagen IV, thereby influencing neuronal behavior through integrin-mediated signaling. These biochemical changes could mediate neural differentiation and network formation, in conjunction with stiffness. Our finding that laminin blocking reduces cell adhesion and limits neurite sprouting indicates that laminin-mediated adhesion plays a significant role in enabling stiffness-regulated neurite extension. These findings suggest that stiffness and ligand-mediated cues act in parallel to regulate neuronal differentiation and morphology. To further clarify the respective roles of mechanical and biochemical signals, future studies should systematically analyze cell-matrix signaling pathways (e.g., focal adhesion kinase phosphorylation) and utilize matrix systems that allow independent tuning of stiffness and ligand density. Such approaches will be critical for refining our understanding of how the extracellular microenvironment regulates neural development.

A central and novel finding of this study is that the branching architecture of “living” neurons, engineered through the combination of bFGF and the storage modulus, enhanced functional connectivity (Figure 5) and increased neural activity, as measured by the synchronized frequency of calcium transients (Figure 4). This experimental validation aligns with prior in silico studies[9,39,40]. The structure of neural circuits is known to play a crucial role in physiological functions, including computation and information processing [41,42], and morphological parameters of individual neurons modulate their electrophysiological activity [43–46]. The morphology of neural networks reflects that of their individual neurons, with computational models predicting connectivity patterns [44]. While branching morphology has been proposed as a key determinant of signal propagation in silico [9,39,40], this study is the first to validate this effect using stem cell-derived neurons experimentally. These temporal differences in neurite morphology likely reflect the combined influence of progressive neuronal maturation and activitydependent remodeling. For example, in our cultures, neurons on the softer gel exhibited pronounced neurite elongation over time, consistent with intrinsic maturation processes. In contrast, neurons on the stiffer gel maintained similar neurite lengths but displayed greater branching complexity that was established early and subsequently stabilized. This morphological stabilization coincided with elevated spontaneous calcium activity, which in turn may reinforce neurite extension on softer gels and branching refinement on stiffer gels. This interpretation aligns with prior studies demonstrating that neuronal firing activity promotes dendritic elaboration and stabilization [47,48].

Notably, the functional connectivity map generated by combining calcium imaging and group-based theory in this study proved highly effective in assessing the correlation of neural circuits. According to this map, neural networks with branch-rich neurons displayed higher functional connectivity, indicating that each network region is functionally related. This result suggests that the structural characteristics of neurons within a network, particularly the number of branches, are closely linked to the network’s functional properties. However, further research is needed to investigate how additional structural factors, such as branching points (the locations where neurites branch), branch order (the hierarchical numbering from the neuron cell body to the branches), and neurite width, correlate with neuronal functionality. The properties and population of astrocytes would be additional variables because cells significantly affect the signaling and electrophysiological properties of the neural network.

This study also emphasized the importance of neuronal maturity in neural network function. We used TUJ1 to visualize overall neuronal architecture and MAP2 to assess maturity. The presence of MAP2-positive cells, particularly under bFGF-treated conditions, confirms that the neurons had progressed to a mature state by the time of functional analysis. These findings reinforce our interpretation that the observed network activity, measured through calcium imaging and graph theory-based analysis, reflects interactions among mature and functionally competent neurons.

An important consideration in biomaterial-based neural cultures is the potential degradation of the extracellular matrix over time. Since Matrigel is a biologically derived hydrogel, its composition and mechanical properties may change during prolonged culture, influencing neural differentiation and network activity. Although our study examines neural development at a single time point (day 21), future investigations should explore how matrix degradation influences the long-term maturation and functionality of neural networks. Recent studies underscore the importance of characterizing the stability of hydrogels used in neural cultures [49]. Investigating the progressive changes in substrate stiffness, biochemical composition, and their interaction with neural cells over time could provide valuable insights into optimizing the extracellular environment for sustained culture. Future experiments incorporating multiple time points, advanced imaging techniques, and mechanical testing would help determine the extent to which matrix degradation influences neural network development and plasticity.

While our threshold-based approach for detecting calcium transients was effective, the spike detection method can influence the interpretation. Deconvolution-based algorithms, such as the Oasis method [50], can offer improved temporal precision of calcium spike timing by modeling the dynamics of calcium indicators. Future studies could benefit from systematically comparing threshold-based and model-based methods to determine their impact on downstream analysis, including calcium activity and functional connectivity patterns. Such comparisons may further improve the accuracy and robustness of calcium imaging-based assessments in in vitro neuronal systems.

Our study also used OG488 BAPTA-1, a calcium indicator that requires culture termination after each recording. This limitation prevented longitudinal tracking of neural network development. Given that neural activity and connectivity are dynamic and evolve throughout network maturation, the ability to monitor the same cultures over extended periods would provide deeper findings into these processes, including maturation processes and synaptic plasticity. A promising direction for future studies is the use of genetically encoded calcium indicators (GECIs), such as GCaMP6, which enable repeated calcium imaging in living cultures. Prior research [51] has shown that neuronal activity and functional connectivity undergo significant changes during network development. Incorporating GECIs in future work would allow for real-time tracking of these temporal dynamics, thereby offering a more comprehensive understanding of how extracellular factors influence neural circuit maturation and plasticity.

Finally, additional network-level analyses could further deepen our understanding of functional architecture. For instance, quantifying functional communities and computing network metrics such as global efficiency, as explored in recent studies [49,52], could allow for a more detailed understanding of communication within the neural network. These approaches may elucidate how different regions of the network interact and how extracellular microenvironment variables such as matrix stiffness or neurotrophic factor modulate overall network function. Although these advanced analyses are beyond the scope of the present work, they represent an important direction for future investigation.

In conclusion, this study provides significant insights into how the structural properties of individual neurons, influenced by both bFGF and mechanical cues, regulate network functionality. Our finding also bridges the gap between in vitro experiments and in silico models, providing a foundation for extending this research to human systems using human-derived neural cells. Additionally, these insights can be applied to therapeutic strategies or biocomputing design aimed at enhancing or evaluating neural network functionality through structural modulation of individual neurons.

4. Materials and Methods

4.1. Characterization of rheological properties of Matrigel

The rheological properties of Matrigel were evaluated using a discovery hybrid rheometer (DHR-3, TA Instruments). The pre-gel solutions of Matrigel with concentrations of 6mg/ml and 10mg/ml were directly deposited on the rheometer and cured at room temperature for 40 minutes. The storage and loss moduli were measured by conducting a frequency sweep test in the 0.01-10 rad/s frequency range at a fixed strain of 0.02. Additionally, storage and loss moduli altered with oscillatory shear deformation were characterized by conducting the strain sweep measurement in the strain range of 0.0001-100 at a fixed angular frequency of 1 rad/s. Samples were kept at room temperature in all experiments.

4.2. Characterization of gel permeability

The diffusivity of fluorescein-labeled dextran (FITC-dextran) in Matrigel was measured by conducting the fluorescence recovery after photobleaching (FRAP) analysis. The pre-gel Matrigel solution was mixed with 2 mg/ml FITC-dextran before curing to form the gel. The FRAP test was performed using a multiphoton confocal microscope equipped with a FRAP module (LSM 710, Zeiss). A bleach spot of 31.5μm diameter was selected for all measurements and bleached with laser at 488nm. The diffusion coefficient for each Matrigel with different concentrations was calculated as described previously by Yu-Tong Hong et al. [53]. Briefly, the diffusion time (${\tau }_D$) was calculated by least-squares fitting of the fluorescence intensity (F) over time (t) to equation (1).

$$F(t)=I_0+I_1{e}^{\frac{-{\tau }_D}{2t}}$$ (1)

Where $I_0$ is the initial fluorescence intensity and $I_1$ is the modified Bessel function. The diffusion coefficient (D) was then calculated using equation (2).

$$D=R^2/{\tau }_D$$ (2)

Where R is the radius of the photobleached spot.

4.3. Mouse neural stem cell (NSC) expansion and differentiation.

Mouse cortical neural stem cells (NSC002, R&D Systems) were cultured and proliferated following the manufacturer’s protocol. Briefly, the mouse cortical NSCs were cultured as neutrospheres on a culture plate with DMEM/F-12 media supplemented with N2-Max media supplements. The media was supplemented with basic fibroblast growth factor (bFGF) and epidermal growth factor. After expansion, NSCs were cultured on a Matrigel substrate prepared on a glass slide. To assemble the culture platform, a 1 mm- thick silicone spacer with a 5 mm inner diameter was placed on the glass surface to define a cylindrical well. A pre-gelled Matrigel solution was cast into the spacer and allowed to polymerize. NSCs were dissociated into single cells and seeded on top of the Matrigel at a density of 500,000 cells/cm². Differentiation was induced by changing the growth media to differentiation media. The differentiation media were supplemented with 20 ng/ml bFGF or without bFGF for the entire differentiation period (i.e., 14 and 21 days). To assess the role of laminin-mediated cue in neurite branching pattern, Matrigel substrates with a storage modulus of 100 Pa were prepared in the culture platform as described above. A laminin γ1-blocking antibody (Santa Cruz biotechnology) was applied to the gels at a concentration of 1 μg per 100 μg of Matrigel protein. The substrate was incubated at room temperature for 2 h to allow binding to exposed matrix ligands. Following incubation, excess antibody was gently removed, and mouse cortical NSCs were seeded onto the antibody-treated substrates either supplemented with 20 ng/ml bFGF or without bFGF. Cultures were maintained under the same differentiation conditions as described above for 14 days prior to imaging and analysis.

4.4. Immunostaining of NSC-derived neuronal networks

Cells were fixed with 2% paraformaldehyde (Sigma) in 1X DPBS (Thermo Fisher) for 30 minutes at room temperature. The fixed cells were permeabilized by 0.1% Triton X-100 (Sigma) for 10 minutes at room temperature, followed by a 45-minute incubation with 2% bovine serum albumin (Sigma). The samples were allowed to react with primary antibodies overnight at room temperature using rabbit anti-beta III tubulin 1:2000 (Abcam) as a neuron marker and chicken anti-glial fibrillary acidic protein (GFAP) 1:1000 as an astrocyte marker (Abcam). After Dulbecco’s Phosphate-Buffered Saline washes, samples were treated with the secondary antibodies, donkey anti-rabbit Alexa Fluor 488 (Abcam) and goat anti-chicken Alexa Fluor 594 (Abcam), for 2 hours at room temperature. DAPI was incubated with neural networks for 15 minutes at room temperature to stain the nuclei of the fixed cells. Then, samples were stored on the glass-bottom dish with a mounting medium.

4.5. Morphological analysis of NSC-derived neuronal networks

The immunofluorescent images were captured using the inverted laser-scanning confocal microscope (Zeiss LSM 900). The numbers of neurons and astrocytes were quantified by counting DAPI-stained nuclei along with TUJ1-positive neurons and GFAP-positive astrocytes. Neurites on the immunofluorescent images were reconstructed by neurite tracking function in IMARIS. The nuclei were considered as a starting point, and the TUJ1-positive sites as neurites in IMARIS. The length of each neurite and branch order were provided by the built-in analysis tool in IMARIS. The Sholl analysis, originally introduced by Sholl, quantifies neuronal complexity by measuring the number of neurites intersecting concentric circles of increasing radii from the soma [54]. For our analysis, Sholl circles were defined as concentric circles with radii increasing in 1 μm increments. For each neuron, the number of neurite intersections within each Sholl circle was quantified and averaged.

4.6. Calcium imaging of NSC-derived neuronal networks

Calcium imaging of neuronal networks was performed using a cell-permeable fluorescent calcium indicator dye, OG488 BAPTA-1 (AAT Bioquest). The dye generates a fluorescence signal upon binding with calcium ions, thus allowing for the monitoring of intracellular calcium flux and release. The NSC-derived neuronal networks were incubated with the calcium dye in the neural medium at a final concentration of 4 μM and 37°C for 40 minutes. Following incubation, the cultures were washed twice with phosphate buffer saline (PBS), and fresh media were added. Spontaneous calcium activity was recorded using an epifluorescent microscope (Nikon EclipseTi) equipped with a fluorescein isothiocyanate filter, capturing 10 frames per second for 1 minute.

4.7. Calcium flux and functional connectivity analysis

The calcium transients were traced by measuring the calcium fluorescent intensity of 100 regions of interest (ROIs) within time-lapse calcium flux images. Circular ROIs, evenly distributed in a 10 by 10 grid across the image frame, were selected. The dynamic mean intensity change within each ROI was calculated for one minute using Fiji, an image processing software. The calcium transient was filtered using custom MATLAB code with detrending and a moving average filter to reduce noise. Subsequently, pairwise Pearson correlation coefficients were calculated for the calcium activity of each ROI. An absolute threshold of 0.6 for the Pearson correlation value was applied to generate the functional connectivity map. The map was illustrated an undirected graph, where the thresholded Pearson correlation array served as an adjacency array. In this graph, nodes represent the ROIs, and edges represent the functional connectivity between pairs of ROIs. The size of each circle (node) reflects the node degree, indicating the number of paired ROIs with a Pearson correlation value higher than the threshold. The width of the connecting lines (edges) represents the Pearson correlation value between the two connected ROIs.

Data and materials availability

Data will be made available on request.