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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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Example of a setting with three dynamic states and two fields.
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Fig2: Example of a setting with three dynamic states and two fields.

Mentions: The coupling between the states and the fields occurs through the arguments ρj(ri) and ∇ρj(ri) in G and the functions σ(si) in Stot. An example of the coupling is depicted in Fig. 2, where we have three states and two concentration fields. Here an arrow from one object to another means that the dynamics of the latter object depend on the former. For example, the dynamics of state 1 is determined by itself and the fields A and B, whereas the dynamics of field A depend on states 1 and 2.Fig. 2


A mathematical framework for modeling axon guidance.

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

Example of a setting with three dynamic states and two fields.
© Copyright Policy
Related In: Results  -  Collection

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

Fig2: Example of a setting with three dynamic states and two fields.
Mentions: The coupling between the states and the fields occurs through the arguments ρj(ri) and ∇ρj(ri) in G and the functions σ(si) in Stot. An example of the coupling is depicted in Fig. 2, where we have three states and two concentration fields. Here an arrow from one object to another means that the dynamics of the latter object depend on the former. For example, the dynamics of state 1 is determined by itself and the fields A and B, whereas the dynamics of field A depend on states 1 and 2.Fig. 2

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