title: A mathematical framework for modeling axon guidance.
abstract: In this paper, a simulation tool for modeling axon guidance is presented. A mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms. In our framework, models can be defined that consist of concentration fields of guidance molecules in combination with finite-dimensional state vectors. These vectors can characterize migrating growth cones, target neurons that release guidance molecules, or other cells that act as sources of membrane-bound or diffusible guidance molecules. The underlying mathematical framework is presented as well as the numerical methods to solve them. The potential applications of our simulation tool are illustrated with a number of examples, including a model of topographic mapping.
authors.affiliation: Center for Mathematics and Computer Science, MAS, PO Box 94079, 1090 GB, Amsterdam, The Netherlands. johannes.krottje@gmail.com
authors.forename: Johannes K
authors.initials: JK
authors.lastname: Krottje
authors.forename: Arjen
authors.initials: A
authors.lastname: van Ooyen
mesh_terms: D000465:Algorithms; D000818:Animals; D001369:Axons / Q000502:physiology*; D002465:Cell Movement / Q000502:physiology; D003198:Computer Simulation; D020439:Growth Cones / Q000502:physiology; D008959:Models, Neurological