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We studied effective connectivity in rat cortical cultures with various degrees of spatial aggregation, ranging from homogeneous networks to highly aggregated ones. We considered small cultures 3 mm in diameter and that contained about $2,000$ neurons. Spatial inhomogeneity favored an increase of metric correlations and connectivity among neighboring neurons. Effective connectivity was determined from spontaneous activity recordings using calcium fluorescence imaging. We used generalized transfer entropy as tool to infer the effective connectivity. We carried out numerical simulations to build networks that mimicked the experimental ones and to test the reliability of the connectivity–inference algorithm. Effective connectivity traits were investigated during the development of the cultures over two weeks, and along the gradual blockade of excitatory connections through CNQX. We observed that the average effective connectivity rapidly increased during culture development. At day in vitro (DIV) 15 the average excitatory in–degree was measured as $\bar{k}^{\mathrm{in}}_E \simeq 50$ for homogeneous and semi aggregated networks, and $\bar{k}^{\mathrm{in}}_E \simeq 120$ for aggregated ones, and with 20 percent inhibition. Aggregated cultures exhibited assortative traits and a high resilience to chemical damage, while the other cultures were dissassortative or neutral, and less resilient. Our work illustrates the role of metric correlations in spatially embedded networks in shaping connectivity and activity traits in living neuronal networks.

Scaffolds and patterned substrates are among the most successful strategies to dictate the connectivity between neurons in culture. Here, we used numerical simulations to investigate the capacity of physical obstacles placed on a flat substrate to shape structural connectivity, and in turn collective dynamics and effective connectivity, in biologically-realistic neuronal networks. We considered μ-sized obstacles placed in mm-sized networks. Three main obstacle shapes were explored, namely crosses, circles and triangles of isosceles profile. They occupied either a small area fraction of the substrate or populated it entirely in a periodic manner. From the point of view of structure, all obstacles promoted short length-scale connections, shifted the in- and out-degree distributions toward lower values, and increased the modularity of the networks. The capacity of obstacles to shape distinct structural traits depended on their density and the ratio between axonal length and substrate diameter. For high densities, different features were triggered depending on obstacle shape, with crosses trapping axons in their vicinity and triangles funneling axons along the reverse direction of their tip. From the point of view of dynamics, obstacles reduced the capacity of networks to spontaneously activate, with triangles in turn strongly dictating the direction of activity propagation. Effective connectivity networks, inferred using transfer entropy, exhibited distinct modular traits, indicating that the presence of obstacles facilitated the formation of local effective microcircuits. Our study illustrates the potential of physical constraints to shape structural blueprints and remodel collective activity, and may guide investigations aimed at mimicking organizational traits of biological neuronal circuits. publishedVersion