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Spatial trigger waves: positive feedback gets you a long way.

Gelens L, Anderson GA, Ferrell JE - Mol. Biol. Cell (2014)

Bottom Line: Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances.Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs.Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves-spatial switches, pulses, and oscillations-and to show how they arise.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305-5174 Applied Physics Research Group, Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium.

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Trigger waves tend to self-organize. (A) Self-organizing trigger waves in an oscillatory FHN model with the model's parameters assumed to be inhomogeneous in space. A single focus of oscillations eventually dominates the whole system. (B) Self-organizing mitotic waves in Xenopus egg extracts in Teflon tubes. The red circles mean that a reporter nucleus at that position entered mitosis at that time. The blue circles denote mitotic exit. In cycle 1, there is no obvious relationship between position and time of mitotic entry or exit, but by cycle 6, a wave of mitosis starting near the top of the tube dominates the whole system. The arrows denote positions from which waves apparently originate. (Adapted from Chang and Ferrell, 2013.)
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Figure 5: Trigger waves tend to self-organize. (A) Self-organizing trigger waves in an oscillatory FHN model with the model's parameters assumed to be inhomogeneous in space. A single focus of oscillations eventually dominates the whole system. (B) Self-organizing mitotic waves in Xenopus egg extracts in Teflon tubes. The red circles mean that a reporter nucleus at that position entered mitosis at that time. The blue circles denote mitotic exit. In cycle 1, there is no obvious relationship between position and time of mitotic entry or exit, but by cycle 6, a wave of mitosis starting near the top of the tube dominates the whole system. The arrows denote positions from which waves apparently originate. (Adapted from Chang and Ferrell, 2013.)

Mentions: This question is addressed for an oscillatory FHN system in Figure 5A. Rather than starting with two discrete domains with different initial conditions, we assume that there are small, random variations in initial conditions and parameter values throughout the system. As the system begins to oscillate, the noise makes it unclear whether there are trigger waves or not (Figure 5A). Eventually, discrete foci from which oscillations emerge become apparent, and eventually a single focus, where the oscillation frequency happened to be highest, dominates the behavior of the whole tube. Similar behavior is seen in biological trigger waves. In the experiment shown in Figure 5B, mitotic waves become apparent after a couple of cell cycles and self-organize so that they emerge from three discrete foci by cycle 4, two foci by cycle 5, and 1 focus by cycle 6 (Figure 5B, arrows). Thus trigger waves do not just propagate information relatively quickly; they can also make noisy events become more orderly.


Spatial trigger waves: positive feedback gets you a long way.

Gelens L, Anderson GA, Ferrell JE - Mol. Biol. Cell (2014)

Trigger waves tend to self-organize. (A) Self-organizing trigger waves in an oscillatory FHN model with the model's parameters assumed to be inhomogeneous in space. A single focus of oscillations eventually dominates the whole system. (B) Self-organizing mitotic waves in Xenopus egg extracts in Teflon tubes. The red circles mean that a reporter nucleus at that position entered mitosis at that time. The blue circles denote mitotic exit. In cycle 1, there is no obvious relationship between position and time of mitotic entry or exit, but by cycle 6, a wave of mitosis starting near the top of the tube dominates the whole system. The arrows denote positions from which waves apparently originate. (Adapted from Chang and Ferrell, 2013.)
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Related In: Results  -  Collection

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Figure 5: Trigger waves tend to self-organize. (A) Self-organizing trigger waves in an oscillatory FHN model with the model's parameters assumed to be inhomogeneous in space. A single focus of oscillations eventually dominates the whole system. (B) Self-organizing mitotic waves in Xenopus egg extracts in Teflon tubes. The red circles mean that a reporter nucleus at that position entered mitosis at that time. The blue circles denote mitotic exit. In cycle 1, there is no obvious relationship between position and time of mitotic entry or exit, but by cycle 6, a wave of mitosis starting near the top of the tube dominates the whole system. The arrows denote positions from which waves apparently originate. (Adapted from Chang and Ferrell, 2013.)
Mentions: This question is addressed for an oscillatory FHN system in Figure 5A. Rather than starting with two discrete domains with different initial conditions, we assume that there are small, random variations in initial conditions and parameter values throughout the system. As the system begins to oscillate, the noise makes it unclear whether there are trigger waves or not (Figure 5A). Eventually, discrete foci from which oscillations emerge become apparent, and eventually a single focus, where the oscillation frequency happened to be highest, dominates the behavior of the whole tube. Similar behavior is seen in biological trigger waves. In the experiment shown in Figure 5B, mitotic waves become apparent after a couple of cell cycles and self-organize so that they emerge from three discrete foci by cycle 4, two foci by cycle 5, and 1 focus by cycle 6 (Figure 5B, arrows). Thus trigger waves do not just propagate information relatively quickly; they can also make noisy events become more orderly.

Bottom Line: Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances.Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs.Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves-spatial switches, pulses, and oscillations-and to show how they arise.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, CA 94305-5174 Applied Physics Research Group, Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium.

Show MeSH