A stamp mold for printing axon guidance reagents was fabricated on a silicon wafer with standard photolithography techniques using negative photoresist SU-8 2010 (Microchem, United States), and molding polydimethoxysilane (PDMS) into a stamp through curing overnight at 60^oC, as previously described (Joo et al., 2015; Ryu et al., 2016; Ryu et al., 2019) (Supplementary Figure 2). A poly-l-lysine (1 mg/mL) coated coverslip was required for patterning. The 10-μg/mL Semaphorin 3F (3237-S3, R & D Systems) ink was poured onto the surface of a stamp for 1 h at 37^oC. The stamps were rinsed with distilled water and air-dried. The ink-loaded stamp was placed on the PLL-coated coverslips for printing and was slightly pressed using a 20-g weight for 10 min. The printed coverslip was ready for culture after rinsing with Dulbecco’s phosphate-buffered saline.

Hippocampi were isolated from E18 embryonic Sprague–Dawley rats (timed-mated) and dissociated into single cells, as previously described (Ryu et al., 2016; Ryu et al., 2019). Neural cells in MEM-based culture media (10% FBS, 1% penicillin–streptomycin [PS], 1% N2 supplement, and 3.6 mg/mL glucose) were seeded in culture dishes at a density of 39.5–78.9 cells/mm². Culture media were replaced with incomplete culture media (ICM) (2% B-27 supplement, 0.5% L-glutamax, and 1% PS in Neurobasal media) 3 h after plating. CultureOne^TM supplement (A3320201, Gibco) was added to the ICM to obtain pure neuron culture to avoid micropatterns covered by astrocytes. CultureOne supplement drives the differentiation of neuroprogenitor cells to neurons without side effects on neuronal morphology (Thermofisherscientific, 2017). B-27 supplement was replaced with B-27plus supplement (A3582801, Gibco) to improve the survival rate of cultured neurons. Animal care and euthanasia protocols followed the Korea University guidelines and were approved by the Korea University Institutional Animal Care and Use Committee.

Recombinant adeno-associated viruses (AAVs) were generated through transfection of HEK293T cells using polyethylenimine (PEI) and purified using ultracentrifugation (Ti70 rotor, Beckman) over iodixanol (D1556, Sigma-Aldrich), as described in Challis et al. (2019). The four-vector mix of pAAV-hSyn1-tTA (Addgene plasmid # 99119), pAAV-TRE-mRuby2 (Addgene plasmid # 99114), pAAV-TRE-EGFP (Addgene plasmid # 89875), and pAAV-TRE-mTurquoise2 (Addgene plasmid # 99113) was packaged into the AAV-PHP.eB capsid (CLOVER, Caltech). The pAAV-hSyn1-tTA, pAAV-TRE-mTurquoise2, pAAV-TRE-mRuby2, pAAV-PHP.eB capsids were provided by Viviana Gradinaru, and pAAV-TRE-EGFP was provided by Hyungbae Kwon. Cultured neurons were transfected with 0.5–1.5 × 10¹³ vg/well (for 15,000 cells) at days in vitro (DIV) 3–7. Cells were fixed with 4% paraformaldehyde and 4% sucrose in 0.1 M phosphate buffer (PBS) (pH 7.4) at DIV 21, as previously described (Ryu et al., 2016), and were mounted on microscope slides after immunostaining when necessary. For immunocytochemistry, the fixed samples were incubated with primary antibodies in blocking solution (3% bovine serum albumin, 0.2% Triton X-100 in Tris-buffered saline (TBS) overnight at 4^oC after 30 min blocking. Samples were washed three times with 0.05% Triton X-100 in TBS for 10 min each under gently shaking, and then stained with appropriate secondary antibodies for 30 min. Antibodies against GFAP (rabbit, 1:10000, z0334, DAKO), MAP2 (chick, 1:500, AB5543, Millipore), and Tuj1 (mouse, 1:2000, T8660, Sigma-Aldrich) were used. The slides were imaged with a slidescanner (Axio Scan.Z1, Zeiss) using a 10× objective lens or a confocal microscope (TCS SP8, Leica) using a 63× objective lens for imaging synapses.

(Image rotation) Initially, neuron images with patterns were rotated to facilitate image processing. The rotational angle was obtained using Fast Fourier Transform (FFT) on a pattern image. FFT is useful for identifying repetitive patterns and determining their alignment angle.

(Pattern detection) 2D cross correlation between the rotated pattern image and a template pattern image was calculated. Finally, the positions of individual patterns were obtained by detecting circles from the 2D cross correlation image circles and were indexed.

(Cell, dendrite, and axon segmentation) Cells, dendrites, and axons were manually segmented using in-house GUI MATLAB codes. During segmentation, the cell image with a pattern was scanned through zooming and shifting of the field of view. To discriminate individual cells by color, we adjusted color balance between three colors: red, green blue, and brightness of the pattern in each field of view. The positions of cellular components of each neuron were obtained by placing the cursor on the pattern with the desired cellular components, and on the keyboard pressing the “c” button for cells, “d” button for dendrites, and “a” button for axons. The pattern positions with dendrites or axons were matched to the pattern indices. As all synapses were formed in patterns, the positions of patterns with dendrites and axons annotated with a cell index were sufficient for reading synaptic connections.

(Network analysis) Based on our observations, two neurons considered synaptically connected when the dendrites of one cell met the axons of the other cell within the pattern. Co-location of Synapsin and PSD95 signals was observed in most patterns, where the axons of one neuron and the dendrites of another neuron coexisted. A table of connected cell pairs was imported using Cytoscape (Shannon et al., 2003) to visualize the reconstructed networks and analyze degree, eccentricity, and centralities. The mathematical definitions of the analytic terms are:

where s and t are nodes in the network different from n, σ_st is the total number of shortest paths from s to t, and σ_st(n) is the number of shortest paths from s to t passing through n.

(Three-node motif analysis) We selected triplet node sets from the adjunct matrix and investigated which classes were included among 13 classes of three-node motifs using in-house MATLAB codes.

Microcontact printing is a simple technique for micrometer-level processing of the surface of a culture substrate. In this study, the pattern of permissive PLL dots surrounded by Sema3F for repulsive axon guidance cues was used. The Sema3F-negative PLL dot array patterns allow the allocation of synapses in the dot pattern compartmentalized from long, complex growing axons (Ryu et al., 2016). In addition, axons can grow to be very long, but they cannot extend very far from the cell body owing to entrapment of the PLL dots, which facilitates obtaining simplified artificial neuronal circuits. First, we observed the ways in which axons interacted with Sema3F-negative dot array patterns (Supplementary Figure 3). During the maturation of the neural circuits on micropatterns, axons grew radially from the cell body and where the axon terminal met the interface between Sema3F and PLL zones, it grew along the interface line (0–120 min in Supplementary Figure 3). Axons often escaped from the permissive to repulsive zone at the sharp angular point of the triangle pattern (630 min in Supplementary Figure 3) and extended into a neighboring pattern (990 min in Supplementary Figure 3). We speculated that the shape of pattern with a smaller angle made it easier to escape axons from the pattern. Conversely, larger-angled patterns could better capture axons inside the pattern than smaller-angled ones. As a results, the distances from the cell body to the maximal extension of the axon in hexagon (120^o) and square (90^o) were significantly shorter than triangle (60^o) (Supplementary Figure 4). The difference between the square pattern and the hexagonal pattern is not very significant, but the hexagonal pattern was empirically easier to analyze. Based on these observations, we adopted a honeycomb pattern to reduce the chance of maintaining axons within one hexagonal pattern (Figures 1A,B). Maturing patterns of DIV 21 neurons in honeycomb patterns are shown in Figures 1C–E. The rate of the cells inside the patterns was 64.3 ± 8.2% (Figure 1G). Though both axons and dendrites remained inside hexagonal patterns (Figures 1C–E) under our experimental conditions, axons often migrated to other hexagonal patterns. In addition, synapses were well established inside the permissive area, as previously reported (Ryu et al., 2016) (Figure 1F). An axon intruded into a receptive pattern area (RPA) of blue colored cells (yellow arrow in Figure 1F) and formed synaptic connections with blue cells. The co-location of synapsin (red) and PSD95 (green) signals is shown in the inset of Figure 1F. We found that >90% of hexagonal patterns with both axons and dendrites exhibited synapse formation, suggesting that most of the spatial contact resulted in synapse formation. As we expected, using hexagonal patterns, the complexity of neuronal network was obviously reduced suitable for the further quantitative analysis (Supplementary Figure 5).

To estimate the range of diversity of artificial neural circuits, we quantified the occupancy of patterns by cell bodies, dendrites, and axons from 14 different samples, cultured on hexagonal patterns with 55-μm edge length (L) of a hexagon and a 70-μm gap between hexagons (D). The occupancy values were 9.0–19.5% (average ± SD: 15.7 ± 3.4%) for cell bodies, 28.0–49.0% (average ± SD: 39.6 ± 6.7%) for dendrites, and 57.4–76.4% (average ± SD: 68.7 ± 7.3%) for axons (Figure 1H). We counted patterns occupied by the dendrite/axon of each neuron to assess the coverage of dendrites and axons of each neuron (Figures 1I,J). The number of patterns occupied by the dendrites of a cell is equivalent to the number of RPAs. This does not mean that the number of RPAs is the capacity of synaptic connections, but a large number (area) of RPAs provide a greater chance of building synaptic connections. A total of 76.2% of neurons formed one or two RPAs (Figure 1I). The cell outside pattern tended to make a more RPA owing to its easy accessibility to many neighboring patterns. A neuron occupied an average of 6.7 patterns with its axon. The number of patterns occupied by axons per cell varied from 1 to 25, and neurons tended to cover 2–4 patterns; meanwhile, most neurons (80.8%) covered fewer than 10 patterns (Figure 1J). Collaboration of axon coverage of each cell and the distance between neighboring cells contributed to the complexity of the circuit. The average distance from the cell to the three closest neighboring cells was determined (Figure 1K). The average distance of 59.5% was in the range 60–120 μm, indicating that neurons with this patterning condition had a high chance of reaching synaptic partners, since neurons had neighboring cells in the nearest hexagonal patterns. The distances from the center of a hexagon to the closest or furthest edge of the neighboring hexagon (l₁ and l₂ in Figure 1B) were 117.6/212.8 μm, respectively, in this pattern condition; the edge of the hexagon (L) was 55 μm, and the gap between hexagons (D) was 70 μm.

The stochastic multicolor labeling technique endows cells with a color that is randomly composed of several colors, such as red, green, and blue. Recently, since the introduction of Brainbow, several improved techniques have been suggested (Livet et al., 2007; Cai et al., 2013; Chan et al., 2017). A two-component inducer system using the tetracycline (tet)-inducible system is reportedly better for various color expressions (Chan et al., 2017). In addition, the PHP.eB serotype of AAVs efficiently produced higher CNS transduction than other serotypes in in vivo studies (Chan et al., 2017; Dayton et al., 2018; Mathiesen et al., 2020). This multicolor labeling system was applied to the primary culture of pure neurons, and individual neurons were easily discriminated from each other (see Figure 2A). However, the fluorescence intensities in different compartments of the same cell varied, and local aggregation of similar colors through global optimization of fluorescence intensities often reduced the fidelity of cell identification. To precisely mark the cell-to-cell connectivity, we developed MATLAB codes, enabling the manual labeling of cell bodies, dendrites, and axons by locally adjusting the color balance and recording their pattern position, as described in the Materials and Methods section of this manuscript. Through post-processing, most connectivity in the in vitro neural circuits could be interpreted at cellular resolution. A representative network reconstructed from an image of cultured neurons in 397 hexagonal patterns (n = 12) is shown in Figure 2B. The color of a node indicates the in-degree value of a node, and the size of a node reflects the out-degree value of the node. The direction of the arrow is from the presynaptic neurons to postsynaptic neurons. The network consisted of 15 large and small network segments and 6 isolated nodes. The degree distribution of the six different cultures of neurons is shown in Supplementary Figure 5.

Surprisingly, the rules of connection between neurons did not seem straightforward despite the neural circuits established on micropatterns being very simple; indeed, there was only a weak correlation between the number of RPAs of a cell and in-degree values of that cell (Figure 2C), since axons from different neurons can penetrate the same RPA, as previously mentioned. Similarly, axon coverage of a cell did not correlate with the out-degree value of that cell (Figure 2D). The reason appears to be that even if axons grow long and cover a wide area, the cell cannot synapse with other cells without any target cell in the growth area of the axon. Cells in neighboring patterns can be candidates for pre/post-synaptic neurons. However, the number of cells in the nearest neighboring patterns (in a circle with radius r₁; Figure 1B) did not have a significant correlation with the in-degree value (Figure 2E), and the number of cells in patterns in the range of the next nearest neighboring patterns (in a circle with radius r₂; see Figure 1B) did not correlate with the out-degree value (Figure 2F). Therefore, the formation of synaptic connections in the micropatterns did not simply depend on the growth range of the cells or the number of neighboring cells (cell density).

Networks of various sizes and structures were observed under the same micropatterning conditions. To determine the characteristics of the reconstructed network from cultured neuronal circuits, a graph theory analysis was applied. Though the analysis of a neuron’s wiring pattern alone cannot explain the functional roles of the neuron, it offers the possibility of a functional role of the neuron in the network. Therefore, it is necessary to understand the anatomical structure of neuronal networks in order to understand their function. The number of nodes and edges, eccentricity, in-degree, out-degree, closeness centrality, and betweenness centrality were analyzed in eight different network segments from six different samples cultured on honeycomb patterns (L = 55 μm, D = 70 μm) (Figure 3; also shown in Figure 4). Regardless of the network sizes and number of nodes/edges or eccentricities, the density values of the networks were diverse (line graph in Figures 3A,B). The eccentricity of a node is the distance from the node to the farthest node, and the minimum and maximum values of eccentricity are defined as the radius and diameter of the network, respectively. Thus, the distribution of eccentricity provides an estimation of the network size. The network diameters of the sample networks ranged from 3 to 8 (Figure 3B). In/out-degree values are important basic indicators of local centrality in a directed network. Nodes with more than 4 or 5 in/out degrees depend on the networks (Figures 3C,D) and are tagged by red and green, respectively (see Figure 4). While nodes with a large in-degree can integrate information from neighboring nodes, nodes with a large out-degree can constitute information sources by distributing information to neighbors. These large in/out-degree cells are defined as local hubs, and hub cells are readily identifiable. For example, Cell #74 in Net #2 (in-degree 5), Cell #58 in Net #4 (in-degree 6), and Cell #67 in Net #6 (in-degree 6) are representative examples of the local (integrator) hub (Figure 4). Net #1-Cell #30 (out-degree 6), Net #2-Cell #95 (out-degree 5), and Net #3-Cell #18 (out-degree 5) are examples of the local (distributor) hub (Figure 4). To investigate global efficiency or influence, closeness centrality and betweenness centrality were analyzed (Figures 3E,F). For example, Cell #30 in Net #1 in Figure 4 had a high out-degree value (6) and high closeness centrality (1). These results indicate that Cell #30 could drive many local neighbor cells (high out-degree), while simultaneously having easy access to other nodes (high closeness centrality). We empirically defined cells with these features as pacemaker, or driver, cells. Information from a source (pacemaker) travels through the network. During information transmission, important nodes have high betweenness centrality or stress values. The nodes with high betweenness centrality, tagged in purple in Figure 4, are recruited in the shortest path lengths among the nodes, indicating that heavy information flows through that node. Therefore, these cells may play an important role in information transmission or serve as bottlenecks. In Net #1, Cells #24, #44, #42, #33, and #35 also exhibited high betweenness centrality. Among these, the route from Cell #24 to #35 appears as the main path among local networks, such as an express highway connecting cities (Figure 4). In addition, Cell #42 has a high out-degree value (4), and it can be regarded as a connector hub that connects the local network modules (Bullmore and Sporns, 2009). Therefore, information from Cell #30 flows to Cell #15 via the connecting route, including the Cell #42 connector hub. Cell #15 can be readout of Net #1, since information in Net #1 gathers in Cell #15.

It is believed that structural motifs have functional significance owing to over-representation of a certain motif in a network. In particular, in the study of the relationship between the structure of a neural circuit and its function (Sporns and Kotter, 2004; Tremblay et al., 2016; English et al., 2017), analysis of structural motifs can be a useful quantitative measure. Analysis of small motifs can quantify interactions between neighboring nodes (Bullmore and Sporns, 2009). Interestingly, common characteristics were found in the analysis of motif profiles across different species/networks. For example, classes 4, 6, and 9 of three-node motifs were frequently observed in four different functional networks of the brain (macaque visual cortex, macaque cortex, fine-grained macaque cortex, and cat cortex) (Sporns and Kotter, 2004; Gollo et al., 2014); meanwhile, class 7 was very rare across the five brain networks (C. elegans, macaque visual cortex, macaque cortex, fine-grained macaque cortex, and cat cortex). We analyzed size 3 motifs (M3) in our simplified neuronal circuits and attempted to identify common features across different neural circuits as well as circuit-dependent characteristics. The difference in distribution of motif classes between neural networks and random, or lattice, structures was apparent (Sporns and Kotter, 2004). In general, classes 7–13 of the 13 different three-node motifs occurred less frequently. In particular, class 7 was very rare. Surprisingly, this may be an indication of the existence of a ubiquitous wiring rule in neural networks, avoiding the recurrent relation of the three nodes. However, eight networks showed clear differences in the three-node motif profiles (Figure 5B). For example, the representative types of neural circuit structures are the feedforward motif (m³₅) and feedback motif (m³₆) (Tremblay et al., 2016). While the feedback structure (m³₆) was frequently observed in Nets #1, #5, and #7, the feedforward structure (m³₅) was more dominant in Net #6. Therefore, motif analysis can be considered a useful tool for quantitatively measuring network structures, such as using basis vectors in linear algebra.

The accuracy of this new analysis system for neuronal connections is largely dependent on the quality of microcontact printing and multicolor cell labeling. Improvement in patterning with microfluidics (Lee et al., 2018), for example, may improve the quality of patterning. The acuity of tracing individual neurons may also be improved through time-lapse imaging.

This in vitro network analysis system cannot determine the ways in which the artificial neuronal network can mimic “real” neural circuits. Though there exists possible differences between the artificial neuronal circuits and brain circuits in not only the neuronal morphology but also their electrophysiological properties (Zhu et al., 2016), the benefits of in vitro experimental systems are irrefutable.