Limits...
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.


Relationship of the mean protein output  and axonal length L, obtained by time averaging the solution to Equation (5) for several values of τ. Function definitions and parameter values are as in Figures 2, 4. The existence of a threshold protein output c0 could provide a mechanism for determining a critical length L0.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4508512&req=5

Figure 4: Relationship of the mean protein output and axonal length L, obtained by time averaging the solution to Equation (5) for several values of τ. Function definitions and parameter values are as in Figures 2, 4. The existence of a threshold protein output c0 could provide a mechanism for determining a critical length L0.

Mentions: Equation (9) suggests that if the protein decay rate λ, the rate of protein activation A, and the pulse-width η are constant, then the mean protein output is a monotonically decreasing function of the period T of the pulsatile retrograde signal. In the context of the delayed feedback model, this means that is a monotonically decreasing function of axonal length L. Although the analytical representation of was obtained by making assumptions that simplified the analysis of Equation (5), and the pulse-width η is not fixed (see Figure 2), one still finds numerically that decreases monotonically with L, see Figure 4. (As shown by Krakauer et al. (2002), it is also possible to modify the simple gene network so that the protein output becomes independent of pulse width). Note that if UM is sufficiently large, then A ≈ h* due to the saturating nature of h. What is more, changing the value of UM will not alter significantly unless it is reduced by a considerable amount. Thus, the mean protein output of the system is relatively insensitive to the amplitude of the input signal and responds only to the frequency of the input signal, making the feed forward serial network a plausible means by which a neuron can decode the oscillating retrograde signal from the delayed feedback model.


A frequency-dependent decoding mechanism for axonal length sensing.

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

Relationship of the mean protein output  and axonal length L, obtained by time averaging the solution to Equation (5) for several values of τ. Function definitions and parameter values are as in Figures 2, 4. The existence of a threshold protein output c0 could provide a mechanism for determining a critical length L0.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 4: Relationship of the mean protein output and axonal length L, obtained by time averaging the solution to Equation (5) for several values of τ. Function definitions and parameter values are as in Figures 2, 4. The existence of a threshold protein output c0 could provide a mechanism for determining a critical length L0.
Mentions: Equation (9) suggests that if the protein decay rate λ, the rate of protein activation A, and the pulse-width η are constant, then the mean protein output is a monotonically decreasing function of the period T of the pulsatile retrograde signal. In the context of the delayed feedback model, this means that is a monotonically decreasing function of axonal length L. Although the analytical representation of was obtained by making assumptions that simplified the analysis of Equation (5), and the pulse-width η is not fixed (see Figure 2), one still finds numerically that decreases monotonically with L, see Figure 4. (As shown by Krakauer et al. (2002), it is also possible to modify the simple gene network so that the protein output becomes independent of pulse width). Note that if UM is sufficiently large, then A ≈ h* due to the saturating nature of h. What is more, changing the value of UM will not alter significantly unless it is reduced by a considerable amount. Thus, the mean protein output of the system is relatively insensitive to the amplitude of the input signal and responds only to the frequency of the input signal, making the feed forward serial network a plausible means by which a neuron can decode the oscillating retrograde signal from the delayed feedback model.

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.