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A mathematical framework for modeling axon guidance.

Krottje JK, van Ooyen A - Bull. Math. Biol. (2006)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Center for Mathematics and Computer Science, MAS, PO Box 94079, 1090 GB, Amsterdam, The Netherlands. johannes.krottje@gmail.com

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.

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Node distribution (left) and solution of the concentration field (right).
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Fig4: Node distribution (left) and solution of the concentration field (right).

Mentions: In the simulation we solved the diffusion profile using 1514 nodes with six attracting rings and two non-attracting rings around the source location. This gives a refinement such that the node density inside the source support is about 100 times higher than far away from the source. In Fig. 4 the distribution of nodes is displayed together with the field solution that was obtained.Fig. 4


A mathematical framework for modeling axon guidance.

Krottje JK, van Ooyen A - Bull. Math. Biol. (2006)

Node distribution (left) and solution of the concentration field (right).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2806218&req=5

Fig4: Node distribution (left) and solution of the concentration field (right).
Mentions: In the simulation we solved the diffusion profile using 1514 nodes with six attracting rings and two non-attracting rings around the source location. This gives a refinement such that the node density inside the source support is about 100 times higher than far away from the source. In Fig. 4 the distribution of nodes is displayed together with the field solution that was obtained.Fig. 4

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Center for Mathematics and Computer Science, MAS, PO Box 94079, 1090 GB, Amsterdam, The Netherlands. johannes.krottje@gmail.com

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.

Show MeSH