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A frequency-dependent decoding mechanism for axonal length sensing.

Bressloff PC, Karamched BR - Front Cell Neurosci (2015)

Bottom Line: We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network.If the protein output were thresholded, then this could provide a mechanism for axonal length control.We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Utah Salt Lake City, UT, USA.

ABSTRACT
We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network. We showed that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. In this paper, we explore how frequency-encoding of axonal length can be decoded by a frequency-modulated gene network. If the protein output were thresholded, then this could provide a mechanism for axonal length control. We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network.

No MeSH data available.


A gene promoter driven by the oscillatory retrograde signal uI(t). Adapted and redrawn from Tostevin et al. (2012).
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Figure 5: A gene promoter driven by the oscillatory retrograde signal uI(t). Adapted and redrawn from Tostevin et al. (2012).

Mentions: In order to investigate the effects of intrinsic noise, we consider an extended version of the network analyzed in Section 2.2 in which we explicitly include the dynamics of gene activation. Suppose that a gene promoter has two states: an inactive state Q and an active state Q*. In the active state, the gene produces the protein C at a rate of μ, and the protein subsequently decays at a rate λ. The promoter is activated in response to the pulsatile retrograde signal uI(t) and deactivates at a constant rate of β, see Figure 5:


A frequency-dependent decoding mechanism for axonal length sensing.

Bressloff PC, Karamched BR - Front Cell Neurosci (2015)

A gene promoter driven by the oscillatory retrograde signal uI(t). Adapted and redrawn from Tostevin et al. (2012).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4508512&req=5

Figure 5: A gene promoter driven by the oscillatory retrograde signal uI(t). Adapted and redrawn from Tostevin et al. (2012).
Mentions: In order to investigate the effects of intrinsic noise, we consider an extended version of the network analyzed in Section 2.2 in which we explicitly include the dynamics of gene activation. Suppose that a gene promoter has two states: an inactive state Q and an active state Q*. In the active state, the gene produces the protein C at a rate of μ, and the protein subsequently decays at a rate λ. The promoter is activated in response to the pulsatile retrograde signal uI(t) and deactivates at a constant rate of β, see Figure 5:

Bottom Line: We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network.If the protein output were thresholded, then this could provide a mechanism for axonal length control.We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Utah Salt Lake City, UT, USA.

ABSTRACT
We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network. We showed that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. In this paper, we explore how frequency-encoding of axonal length can be decoded by a frequency-modulated gene network. If the protein output were thresholded, then this could provide a mechanism for axonal length control. We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network.

No MeSH data available.