Loewner Equation With Chaotic Driving Function Describes Neurite Outgrowth Mechanism

A new physical description for neurite morphogenesis was investigated in the framework of the Loewner equation. We applied the Loewner equation to the traces of the neurites of in vitro cultured Neuro2A cells and numerically obtained the driving functions corresponding to them. Then, we examined the statistical properties of the driving functions using root mean square fluctuation, which showed that they differ from those of stochastic Loewner evolution and there exists some deterministic mechanism behind neurite morphogenesis. Additionally, a kind of attractor was reconstructed from the time differences of the driving functions of the analyzed neurites, and its evaluated Lyapunov exponents suggested a chaotic property in the dynamics of the morphogenesis.