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.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.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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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. |
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Mentions: Hence, c(t) converges to a T-periodic solution following any transient dynamics, as shown in Figure 3. More significantly, there is now a strong DC component to the signal so that the relative amplitude of the oscillatory part has been suppressed. Indeed it is possible to find parameter values for which , where is the time-averaged protein output (Krakauer et al., 2002). Therefore, in order to characterize the protein output in terms of the frequency ω of uI(t), we find the time average of c(t) post transience. This can be done by simply integrating Equation (5) over a period of uI(t): |
View Article: PubMed Central - PubMed
Affiliation: Department of Mathematics, University of Utah Salt Lake City, UT, USA.
No MeSH data available.