A frequency-dependent decoding mechanism for axonal length sensing.
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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.
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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. |
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Mentions: where ω denotes the frequency of the periodic solution and for P = E, I and the steady state of the corresponding chemical signal. We immediately notice two facts from Equation (4). First, if τ = 0, then the bifurcation conditions cannot be satisfied, suggesting that there exists a critical delay τc past which Equations (1) and (2) have periodic solutions. This corresponds with the existence of some critical axonal length Lc past which signals will oscillate. Second, the bifurcation conditions can only be satisfied if . It follows that the feedback strengths WP must be sufficiently large and/or the Hill function must be sufficiently steep. The latter implies that oscillations are facilitated if the chemical signal interactions are cooperative in nature, as reflected by the value of n in the delayed feedback model. The existence of the Hopf bifurcation point does not in itself guarantee the onset of stable limit cycles for τ > τc. However, this can be verified numerically, and one finds that the frequency of the oscillation beyond the bifurcation point is a monotonically decreasing function of L, see Figure 2. |
View Article: PubMed Central - PubMed
Affiliation: Department of Mathematics, University of Utah Salt Lake City, UT, USA.
No MeSH data available.