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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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Three types of trigger waves from coupling the FHN reactions to diffusion. The system is assumed to have one spatial dimension (represented on the y-axis); it is essentially a long, thin tube. The values of u as a function of time and position are represented by a heat map color scale. In all cases we assumed that the system has a high initial value of u in the middle of the tube over a width of 40 units (u(t = 0) = 1) and a low initial value of u elsewhere (u(t = 0) = –0.6). The initial value for v is the same everywhere (v(t = 0) = –0.3). For the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube (b = 0.5) than in the rest of the tube (b = 1), acting as a pacemaker for the whole system. In the top panels there is no diffusive coupling (D = 0), while in the bottom panels diffusion is included (D = 1). The FHN parameters are the same as those shown in Figure 2.
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Figure 3: Three types of trigger waves from coupling the FHN reactions to diffusion. The system is assumed to have one spatial dimension (represented on the y-axis); it is essentially a long, thin tube. The values of u as a function of time and position are represented by a heat map color scale. In all cases we assumed that the system has a high initial value of u in the middle of the tube over a width of 40 units (u(t = 0) = 1) and a low initial value of u elsewhere (u(t = 0) = –0.6). The initial value for v is the same everywhere (v(t = 0) = –0.3). For the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube (b = 0.5) than in the rest of the tube (b = 1), acting as a pacemaker for the whole system. In the top panels there is no diffusive coupling (D = 0), while in the bottom panels diffusion is included (D = 1). The FHN parameters are the same as those shown in Figure 2.

Mentions: These can be solved numerically for some choice of parameters and initial conditions. For each of the simulations shown in Figure 3, we assumed that we have a long, one-dimensional tube (like an axon) with the system in a low-u state (u(t = 0) ∼ –0.6, v(t = 0) ∼ –0.3) everywhere except for a small region in the middle of the tube, where the system has a higher membrane potential (u(t = 0) = 1). In Figure 3D, the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube than in the other regions. We then assumed that either there was no diffusive coupling (top, D = 0) or there was diffusive coupling (bottom, D = 1) and examined how the systems evolved with time. We represent the value of u at each point in space and time by a heat map color scale.


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

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

Three types of trigger waves from coupling the FHN reactions to diffusion. The system is assumed to have one spatial dimension (represented on the y-axis); it is essentially a long, thin tube. The values of u as a function of time and position are represented by a heat map color scale. In all cases we assumed that the system has a high initial value of u in the middle of the tube over a width of 40 units (u(t = 0) = 1) and a low initial value of u elsewhere (u(t = 0) = –0.6). The initial value for v is the same everywhere (v(t = 0) = –0.3). For the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube (b = 0.5) than in the rest of the tube (b = 1), acting as a pacemaker for the whole system. In the top panels there is no diffusive coupling (D = 0), while in the bottom panels diffusion is included (D = 1). The FHN parameters are the same as those shown in Figure 2.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

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Figure 3: Three types of trigger waves from coupling the FHN reactions to diffusion. The system is assumed to have one spatial dimension (represented on the y-axis); it is essentially a long, thin tube. The values of u as a function of time and position are represented by a heat map color scale. In all cases we assumed that the system has a high initial value of u in the middle of the tube over a width of 40 units (u(t = 0) = 1) and a low initial value of u elsewhere (u(t = 0) = –0.6). The initial value for v is the same everywhere (v(t = 0) = –0.3). For the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube (b = 0.5) than in the rest of the tube (b = 1), acting as a pacemaker for the whole system. In the top panels there is no diffusive coupling (D = 0), while in the bottom panels diffusion is included (D = 1). The FHN parameters are the same as those shown in Figure 2.
Mentions: These can be solved numerically for some choice of parameters and initial conditions. For each of the simulations shown in Figure 3, we assumed that we have a long, one-dimensional tube (like an axon) with the system in a low-u state (u(t = 0) ∼ –0.6, v(t = 0) ∼ –0.3) everywhere except for a small region in the middle of the tube, where the system has a higher membrane potential (u(t = 0) = 1). In Figure 3D, the oscillatory case, we also assumed that the frequency of the oscillations is higher in the middle of the tube than in the other regions. We then assumed that either there was no diffusive coupling (top, D = 0) or there was diffusive coupling (bottom, D = 1) and examined how the systems evolved with time. We represent the value of u at each point in space and time by a heat map color scale.

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
Related in: MedlinePlus