Role of geometrical cues in neuronal growth

I will present a systematic experimental and theoretical investigation of neuronal growth on micro-patterned surfaces. The experimental results show that neurons cultured on surfaces with periodic geometrical patterns display a significant increase in the total length of axons, as well as axonal alignment along preferred growth directions, which are controlled by the surface geometry. We demonstrate that axonal dynamics is governed by non-linear stochastic differential equations, and use this theoretical model to measure key dynamical parameters: angular distributions, correlation functions, diffusion coefficients and cell-surface coupling forces. Our results show that neuronal alignment on these surfaces is completely determined by the surface geometry, and that the growth dynamics can be quantified by a minimal set of experimentally measurable parameters. I will also discuss how to generalize this approach to include mechanical and biochemical external cues, and introduce a general framework for the quantitative description of neuronal growth and self-organization in complex environments.