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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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Study of the effect of the [cAMP]/[cGMP] ratio.Top: [cAMP]/[cGMP] ratio as a function of time (in minutes) for different values of  (reported in the legend). Bottom. Position  of the abscissa of the barycenter of the open calcium channels (in ) as a function of the ratio [cAMP]/[cGMP] after . Each marker corresponds to a simulation carried out with a different value of .
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pcbi-1000479-g014: Study of the effect of the [cAMP]/[cGMP] ratio.Top: [cAMP]/[cGMP] ratio as a function of time (in minutes) for different values of (reported in the legend). Bottom. Position of the abscissa of the barycenter of the open calcium channels (in ) as a function of the ratio [cAMP]/[cGMP] after . Each marker corresponds to a simulation carried out with a different value of .

Mentions: Using the DCC-UNC5 model, we can analyze more in detail the role of second messengers cyclic AMP and GMP (activated by DCC and DCC–UNC5 pathways, respectively) in modulating the response. We explore a large set of values of in the range and we compute from each corresponding simulation the ratio as a function of time (see Fig. 14, (left)). Moreover, in Fig. 14 (right), we show the position of the barycenter of the open calcium channels as a function of the [cAMP]/[cGMP] ratio after . The position of the barycenter indicates here the direction of incipient motion and thus the type of response. These results quantify the idea of Nishlyama-et-al-2003, where the chemotactic response (experimental measure of the axon turning angle) is qualitatively connected to the ratio. In particular, the model quantitatively explains the presence of extremal points in the curve reported in [28, Fig.4c] as the outcome of the synergistic interaction of receptors, which enhances the polarization produced in the single receptor case, and of the characteristics of the internal amplification process, which is nonlinear.


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

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

Study of the effect of the [cAMP]/[cGMP] ratio.Top: [cAMP]/[cGMP] ratio as a function of time (in minutes) for different values of  (reported in the legend). Bottom. Position  of the abscissa of the barycenter of the open calcium channels (in ) as a function of the ratio [cAMP]/[cGMP] after . Each marker corresponds to a simulation carried out with a different value of .
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000479-g014: Study of the effect of the [cAMP]/[cGMP] ratio.Top: [cAMP]/[cGMP] ratio as a function of time (in minutes) for different values of (reported in the legend). Bottom. Position of the abscissa of the barycenter of the open calcium channels (in ) as a function of the ratio [cAMP]/[cGMP] after . Each marker corresponds to a simulation carried out with a different value of .
Mentions: Using the DCC-UNC5 model, we can analyze more in detail the role of second messengers cyclic AMP and GMP (activated by DCC and DCC–UNC5 pathways, respectively) in modulating the response. We explore a large set of values of in the range and we compute from each corresponding simulation the ratio as a function of time (see Fig. 14, (left)). Moreover, in Fig. 14 (right), we show the position of the barycenter of the open calcium channels as a function of the [cAMP]/[cGMP] ratio after . The position of the barycenter indicates here the direction of incipient motion and thus the type of response. These results quantify the idea of Nishlyama-et-al-2003, where the chemotactic response (experimental measure of the axon turning angle) is qualitatively connected to the ratio. In particular, the model quantitatively explains the presence of extremal points in the curve reported in [28, Fig.4c] as the outcome of the synergistic interaction of receptors, which enhances the polarization produced in the single receptor case, and of the characteristics of the internal amplification process, which is nonlinear.

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