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.


Plot of mean protein output  vs. axonal length L. Results are based on simulations of the chemical master Equation (14) using the Gillespie algorithm with input s(t) = h[uI(t)]. Parameter values used to generate retrograde signal uI(t) are the same as in Figure 2. Other parameter values are β = 1, μ = 0.1, λ = 0.01, and N = 1000.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: Plot of mean protein output vs. axonal length L. Results are based on simulations of the chemical master Equation (14) using the Gillespie algorithm with input s(t) = h[uI(t)]. Parameter values used to generate retrograde signal uI(t) are the same as in Figure 2. Other parameter values are β = 1, μ = 0.1, λ = 0.01, and N = 1000.

Mentions: The dependence of on axonal length L in the presence of intrinsic noise is shown in Figure 6. The general inverse relationship is still prevalent in this situation, but fluctuates due to the stochasticity in the gene switching.


A frequency-dependent decoding mechanism for axonal length sensing.

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

Plot of mean protein output  vs. axonal length L. Results are based on simulations of the chemical master Equation (14) using the Gillespie algorithm with input s(t) = h[uI(t)]. Parameter values used to generate retrograde signal uI(t) are the same as in Figure 2. Other parameter values are β = 1, μ = 0.1, λ = 0.01, and N = 1000.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: Plot of mean protein output vs. axonal length L. Results are based on simulations of the chemical master Equation (14) using the Gillespie algorithm with input s(t) = h[uI(t)]. Parameter values used to generate retrograde signal uI(t) are the same as in Figure 2. Other parameter values are β = 1, μ = 0.1, λ = 0.01, and N = 1000.
Mentions: The dependence of on axonal length L in the presence of intrinsic noise is shown in Figure 6. The general inverse relationship is still prevalent in this situation, but fluctuates due to the stochasticity in the gene switching.

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.