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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.


Schematic diagram illustrating how the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold is crossed. An analogous result applies to decoding of protein concentration gradients.
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Figure 7: Schematic diagram illustrating how the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold is crossed. An analogous result applies to decoding of protein concentration gradients.

Mentions: By analogy with the effects of intrinsic noise in protein concentration gradients (Howard, 2012), the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold c0 is crossed. This is illustrated schematically in Figure 7. Although the time-averaged protein output is still approximately a monotonically decreasing function of axonal length L on large length-scales, fluctuations due to intrinsic noise mean that it is non-monotonic on smaller length scales. It follows that the protein output can cross threshold several times over small changes in L resulting in an uncertainty ΔL with regards to the critical axonal length. The uncertainty ΔL can be estimated as follows: Suppose that in the absence of noise . Denoting the variance in the concentration due to intrinsic noise by , we then have the approximation


A frequency-dependent decoding mechanism for axonal length sensing.

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

Schematic diagram illustrating how the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold is crossed. An analogous result applies to decoding of protein concentration gradients.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 7: Schematic diagram illustrating how the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold is crossed. An analogous result applies to decoding of protein concentration gradients.
Mentions: By analogy with the effects of intrinsic noise in protein concentration gradients (Howard, 2012), the presence of noise in the protein output leads to an uncertainty ΔL in the critical axonal length L0 at which the threshold c0 is crossed. This is illustrated schematically in Figure 7. Although the time-averaged protein output is still approximately a monotonically decreasing function of axonal length L on large length-scales, fluctuations due to intrinsic noise mean that it is non-monotonic on smaller length scales. It follows that the protein output can cross threshold several times over small changes in L resulting in an uncertainty ΔL with regards to the critical axonal length. The uncertainty ΔL can be estimated as follows: Suppose that in the absence of noise . Denoting the variance in the concentration due to intrinsic noise by , we then have the approximation

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.