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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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An example configuration of the vectors z and zg.
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Fig3: An example configuration of the vectors z and zg.

Mentions: To formulate an ODE for ϕ that depends on the value of ϕg, we use the mapping ϕ → (sin(ϕ), cos(ϕ)) to view the growth directions as two-dimensional unit vectors, z and zg, respectively. The ideal direction zg can be split in a part parallel to the growth direction z and a part that is perpendicular to it, . An illustration of this is shown in Fig. 3. We assume that . Returning to angles ϕ and ϕg this results in .Fig. 3


A mathematical framework for modeling axon guidance.

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

An example configuration of the vectors z and zg.
© Copyright Policy
Related In: Results  -  Collection

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

Fig3: An example configuration of the vectors z and zg.
Mentions: To formulate an ODE for ϕ that depends on the value of ϕg, we use the mapping ϕ → (sin(ϕ), cos(ϕ)) to view the growth directions as two-dimensional unit vectors, z and zg, respectively. The ideal direction zg can be split in a part parallel to the growth direction z and a part that is perpendicular to it, . An illustration of this is shown in Fig. 3. We assume that . Returning to angles ϕ and ϕg this results in .Fig. 3

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