Predicting Macroscopic Axon Topology from Microscopic Kinematics: An Interactive Tracking and Random Walk Pipeline for Substrate-Dependent Cortical Neurospheres

The cortical neuron is a fundamental building block of the mammalian brain, and the morphology of its axonal projections is central to how functional circuits assemble. The trajectory along which an axon grows is a key determinant of connectivity, yet the kinematics of cortical axon outgrowth remain poorly quantified. Characterizing these dynamics is most tractable in vitro, where axonal growth can be measured directly and under controlled, reproducible conditions. Even in culture, however, this remains challenging because cortical neurons require dense plating for viability, and their soma is motile, so growth behavior is highly sensitive to local density and population context, complicating reproducible measurement of intrinsic dynamics. To overcome these limitations, we used size-controlled cortical neurospheres, which provide a fixed spatial origin and a reproducible environment, together with a custom semi-automated tracking pipeline to quantify single-axon kinematics across two functionalized substrates and two developmental phases. This approach revealed a substrate-dependent divergence in outgrowth: during the later developmental phase, axons on poly-D-lysine with laminin (PDL-LA) substrate grew faster than those on PDL, with a mean step size of 0.436 versus 0.339 {micro}m /min. Decomposing trajectories into Katz dynamic states, we built a generative biased random walk model that reproduces axonal behavior at both microscopic (single-axon) and macroscopic (network topology) scales. This open, reproducible framework links single-axon kinematics to network architecture, enabling the structural connectivity of neurospherebased circuits in vitro to be predicted from measurable growth dynamics, a necessary foundation for future studies linking circuit structure to emergent function.