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Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis.

Causin P, Facchetti G - PLoS Comput. Biol. (2009)

Bottom Line: We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor.The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization.Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics F Enriques, Università degli Studi di Milano, Milano, Italy. Paola.Causin@unimi.it

ABSTRACT
The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

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GC schematization.The GC is represented in the mathematical model as a disk subdivided in angular sectors. We consider the settings of the chemotactic assay for neural cells, where a pipette (here on the right) establishes a steady graded field of a chemotropic molecule.
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pcbi-1000479-g001: GC schematization.The GC is represented in the mathematical model as a disk subdivided in angular sectors. We consider the settings of the chemotactic assay for neural cells, where a pipette (here on the right) establishes a steady graded field of a chemotropic molecule.

Mentions: Polar coordinates are used, the origin of the axes being positioned in the center of the GC. The angle denotes the azimuthal coordinate on the membrane and its origin is set along the direction connecting the GC center with the pointwise source, which we always suppose to lay on the right hand side of the cell (see Fig. 1). We denote by the radius of the GC.


Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis.

Causin P, Facchetti G - PLoS Comput. Biol. (2009)

GC schematization.The GC is represented in the mathematical model as a disk subdivided in angular sectors. We consider the settings of the chemotactic assay for neural cells, where a pipette (here on the right) establishes a steady graded field of a chemotropic molecule.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2722090&req=5

pcbi-1000479-g001: GC schematization.The GC is represented in the mathematical model as a disk subdivided in angular sectors. We consider the settings of the chemotactic assay for neural cells, where a pipette (here on the right) establishes a steady graded field of a chemotropic molecule.
Mentions: Polar coordinates are used, the origin of the axes being positioned in the center of the GC. The angle denotes the azimuthal coordinate on the membrane and its origin is set along the direction connecting the GC center with the pointwise source, which we always suppose to lay on the right hand side of the cell (see Fig. 1). We denote by the radius of the GC.

Bottom Line: We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor.The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization.Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics F Enriques, Università degli Studi di Milano, Milano, Italy. Paola.Causin@unimi.it

ABSTRACT
The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

Show MeSH