Computer simulation of nerve growth cone filopodial dynamics for visualization and analysis

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Abstract
The neuronal growth cone plays a fundamental role in nerve development and regeneration. A sensory-motile structure, it determines the path of axonal extension through its interactions with the extracellular environment, ultimately directing the formation of functional connections in the nervous system. Though several mechanisms of interaction have been proposed, these have been difficult to describe quantitatively due to the complexity of growth cone behavior, as manifested in the randomly and rapidly changing shape of the growth cone. The application of mathematical techniques to model growth cone shape and motility in terms of underlying processes represents a promising approach with untapped potential for helping to unravel this complexity while revealing new insights into axonal pathfinding events. This paper presents a simulation model for filopodial dynamics, a primary feature of the motile growth cone. The model produces realizations of dynamic filopodial structure on representative growth cones for a given set of model parameters, which include the rates of filopodial initiation, extension, and retraction, filopodial length at maximum extension, and angular orientation. These parameters are based on recent experimental characterization of filopodial dynamics [Buettner et al., 1994: Dev. Biol. 163:407–422]. The mathematical relationship between the model parameters and average filopodial number and length per growth cone is described, and the contribution of individual parameters to overall filopodial morphology is illustrated both visually and numerically. In addition, the model is used to simulate filopodial encounter with a target for various conditions of filopodial dynamics. The result is characterized in terms of a mean encounter time for a population of growth cones and provides an indication of the effect of individual parameters of filopodial dynamics on the encounter process. Future experimental testing will be required to develop the model further. However, in its current form, the model enables a first approximation analysis of many hypotheses of growth cone migration and pathfinding and offers insight into the the underlying mechanismes of nerve growth and regeneration.