Limits...
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.

Show MeSH
DCC model: concentration profiles as a function of time (in minutes).Curves are relative to the four most representative angular sectors, perceiving a cue concentration ranging from minimal to maximal value, respectively. Legend: green [Netrin] = 9.52 nM (max value), cyan [Netrin] = 9.36 nM, blue [Netrin] = 9.16 nM, magenta [Netrin] = 9.08 nM, red [Netrin] = 9.07 nM (min value).
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2722090&req=5

pcbi-1000479-g004: DCC model: concentration profiles as a function of time (in minutes).Curves are relative to the four most representative angular sectors, perceiving a cue concentration ranging from minimal to maximal value, respectively. Legend: green [Netrin] = 9.52 nM (max value), cyan [Netrin] = 9.36 nM, blue [Netrin] = 9.16 nM, magenta [Netrin] = 9.08 nM, red [Netrin] = 9.07 nM (min value).

Mentions: We first demonstrate that the model correctly achieves polarization and reaches a steady state condition, where front–back differentiation is established. In Fig. 4, we plot the concentration profiles as a function of time, obtained from simulations carried out till . In Fig. 5, we plot for the different species the abscissa of the barycenter of the molecules as a function of time. Since at the initial time the distribution of molecules is homogeneous, the displacement of their spatial barycenter from represents an index of the intensity of the polarization. In Fig. 6, we plot the concentrations after as a function of . Significant polarization of the receptors takes place in tenth of minutes; polarization is inherited by all the internal species. An interesting behavior is shown by calcium channels, which undergo in all sectors a first phase of opening, reaching a fairly similar maximum value, followed by closure, more pronounced in the rear side. This mechanism might represent a sort of LEGI, global “inhibition” being constituted by collective opening and local “activation” by differential closure. Note that this is to be intended only as a qualitative interpretation (see also the discussion in [11]). The position of the barycenter of bound receptors presents a sigmoid behavior, which is characteristic of autocatalyzing processes: a first phase of relatively slow accumulation (lag time) followed by a quick growth till a steady state. This is in agreement with the experimental result of [19, Fig.1e]. In Fig. 7, we plot the concentration profiles as a function of time for a simulation with a longer integration interval . A steady state is definitely reached.


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

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

DCC model: concentration profiles as a function of time (in minutes).Curves are relative to the four most representative angular sectors, perceiving a cue concentration ranging from minimal to maximal value, respectively. Legend: green [Netrin] = 9.52 nM (max value), cyan [Netrin] = 9.36 nM, blue [Netrin] = 9.16 nM, magenta [Netrin] = 9.08 nM, red [Netrin] = 9.07 nM (min value).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000479-g004: DCC model: concentration profiles as a function of time (in minutes).Curves are relative to the four most representative angular sectors, perceiving a cue concentration ranging from minimal to maximal value, respectively. Legend: green [Netrin] = 9.52 nM (max value), cyan [Netrin] = 9.36 nM, blue [Netrin] = 9.16 nM, magenta [Netrin] = 9.08 nM, red [Netrin] = 9.07 nM (min value).
Mentions: We first demonstrate that the model correctly achieves polarization and reaches a steady state condition, where front–back differentiation is established. In Fig. 4, we plot the concentration profiles as a function of time, obtained from simulations carried out till . In Fig. 5, we plot for the different species the abscissa of the barycenter of the molecules as a function of time. Since at the initial time the distribution of molecules is homogeneous, the displacement of their spatial barycenter from represents an index of the intensity of the polarization. In Fig. 6, we plot the concentrations after as a function of . Significant polarization of the receptors takes place in tenth of minutes; polarization is inherited by all the internal species. An interesting behavior is shown by calcium channels, which undergo in all sectors a first phase of opening, reaching a fairly similar maximum value, followed by closure, more pronounced in the rear side. This mechanism might represent a sort of LEGI, global “inhibition” being constituted by collective opening and local “activation” by differential closure. Note that this is to be intended only as a qualitative interpretation (see also the discussion in [11]). The position of the barycenter of bound receptors presents a sigmoid behavior, which is characteristic of autocatalyzing processes: a first phase of relatively slow accumulation (lag time) followed by a quick growth till a steady state. This is in agreement with the experimental result of [19, Fig.1e]. In Fig. 7, we plot the concentration profiles as a function of time for a simulation with a longer integration interval . A steady state is definitely reached.

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