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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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Examples of biological concepts that can be incorporated in our framework.
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Fig1: Examples of biological concepts that can be incorporated in our framework.

Mentions: In this section, we will describe a modeling framework for axon guidance. In the models that can be defined within this framework one can incorporate different biological processes and mechanisms, some of which are displayed in Fig. 1. From a mathematical perspective the framework consists of states, fields and their coupling. We will now discuss these components and their biological interpretation, as well as show how they are related through the model equations.Fig. 1


A mathematical framework for modeling axon guidance.

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

Examples of biological concepts that can be incorporated in our framework.
© Copyright Policy
Related In: Results  -  Collection

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

Fig1: Examples of biological concepts that can be incorporated in our framework.
Mentions: In this section, we will describe a modeling framework for axon guidance. In the models that can be defined within this framework one can incorporate different biological processes and mechanisms, some of which are displayed in Fig. 1. From a mathematical perspective the framework consists of states, fields and their coupling. We will now discuss these components and their biological interpretation, as well as show how they are related through the model equations.Fig. 1

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