An analytical study of growth cone pathfinding

During development and regeneration the neuronal growth cone is responsible for guiding the axon to its final target. Much of our insight into this process is from experimental studies, both in vitro and in vivo. Additional understanding is possible through quantitative models of growth cone guidance. This work focuses on the development of a model for growth cone guidance based on accounts of growth cone guidance in literature and measurements of growth cone migration from our laboratory. The mechanistic basis of this model is a well-documented guidance mechanism termed “bias in veil extension”, where growth cone lamellar extension is either accelerated or blocked in discrete regions around the growth cone.; Model parameters are developed to define factors important for guidance by bias in veil extension. Simulation algorithms are designed to quantify the effect of bias in veil extension on growth cone migratory patterns. Migration is simulated in the presence of an attractive cue and in the presence of a repulsive cue. Simulation results suggest guidance by an attractive cue is far more predictable than guidance by a repulsive cue. Guidance by a repulsive cue exhibits a strong but unexpected dependence on the ratio of stochastic to deterministic motion driving growth cone migratory dynamics.; Further simulations are run to investigate this dependence. A dimensionless indicator Ψ of the growth cone migratory response &phis; is developed, and when Ψ is plotted against &phis;, a stochastic dominated migration state and a deterministic dominated migration state are seen. It is in the transition between these two states that sustained growth cone guidance by a repulsive cue is possible and controllable. We speculate that while in a stochastic state the growth cone is in a “search” mode looking for a target cue and that while in a deterministic state the growth cone is migrating along a tract separating targets. We further speculate that the nervous system may make use of a mechanism to control the balance between stochastic and deterministic migration to regulate which neurons growth steadily and which may pause to explore their environment.