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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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Diffusion can push the system across a threshold. (A, B) Diffusive spreading of a high-u state in the absence of reaction for two different diffusion coefficients. The values of u as a function of position and time are depicted both as curves and in a simplified red-green-blue heat map representation. Increasing the diffusion coefficient allows some regions within the low-u region to attain moderately high (green) levels of u more quickly, but for a shorter duration. (C) Phase plot for one point in space that is initially in the low-u region. Diffusion moves the value of u across the threshold into the green region, but in the absence of reaction, eventually returns it to the blue region. If the FHN reactions are fast enough, they can capture the suprathreshold trajectory and convert this point in space to a high-u (red) state. (D, E) Diffusion plus reaction allows self-regenerating trigger waves to propagate outward (D) unless the diffusion coefficient is too high (E).
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Figure 4: Diffusion can push the system across a threshold. (A, B) Diffusive spreading of a high-u state in the absence of reaction for two different diffusion coefficients. The values of u as a function of position and time are depicted both as curves and in a simplified red-green-blue heat map representation. Increasing the diffusion coefficient allows some regions within the low-u region to attain moderately high (green) levels of u more quickly, but for a shorter duration. (C) Phase plot for one point in space that is initially in the low-u region. Diffusion moves the value of u across the threshold into the green region, but in the absence of reaction, eventually returns it to the blue region. If the FHN reactions are fast enough, they can capture the suprathreshold trajectory and convert this point in space to a high-u (red) state. (D, E) Diffusion plus reaction allows self-regenerating trigger waves to propagate outward (D) unless the diffusion coefficient is too high (E).

Mentions: Diffusion provides a mechanism for crossing the threshold. This is illustrated in Figure 4 for the case of the bistable FHN system. Diffusion mixes nearby values such that a point in space within the low-u region will have its value of u initially increase as the high-u region mixes with it and then eventually fall back down (Figure 4, A–C). The higher the diffusion coefficient, the faster is the initial increase, but the fall back down is faster as well (Figure 4, A–C). Diffusion can therefore allow the value of u to increase above the threshold (or, in phase space, to cross the separatrix) for some period of time. If the time is sufficient, the FHN reactions can convert that region of space into an even higher level of u (Figure 4, C and D). The entire process is repeated in the next region of space and then the next, resulting in a trigger wave of bistable switching that never slows down and never peters out (Figure 4C). Similar arguments can be made for the excitable and oscillatory cases.


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

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

Diffusion can push the system across a threshold. (A, B) Diffusive spreading of a high-u state in the absence of reaction for two different diffusion coefficients. The values of u as a function of position and time are depicted both as curves and in a simplified red-green-blue heat map representation. Increasing the diffusion coefficient allows some regions within the low-u region to attain moderately high (green) levels of u more quickly, but for a shorter duration. (C) Phase plot for one point in space that is initially in the low-u region. Diffusion moves the value of u across the threshold into the green region, but in the absence of reaction, eventually returns it to the blue region. If the FHN reactions are fast enough, they can capture the suprathreshold trajectory and convert this point in space to a high-u (red) state. (D, E) Diffusion plus reaction allows self-regenerating trigger waves to propagate outward (D) unless the diffusion coefficient is too high (E).
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Related In: Results  -  Collection

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Figure 4: Diffusion can push the system across a threshold. (A, B) Diffusive spreading of a high-u state in the absence of reaction for two different diffusion coefficients. The values of u as a function of position and time are depicted both as curves and in a simplified red-green-blue heat map representation. Increasing the diffusion coefficient allows some regions within the low-u region to attain moderately high (green) levels of u more quickly, but for a shorter duration. (C) Phase plot for one point in space that is initially in the low-u region. Diffusion moves the value of u across the threshold into the green region, but in the absence of reaction, eventually returns it to the blue region. If the FHN reactions are fast enough, they can capture the suprathreshold trajectory and convert this point in space to a high-u (red) state. (D, E) Diffusion plus reaction allows self-regenerating trigger waves to propagate outward (D) unless the diffusion coefficient is too high (E).
Mentions: Diffusion provides a mechanism for crossing the threshold. This is illustrated in Figure 4 for the case of the bistable FHN system. Diffusion mixes nearby values such that a point in space within the low-u region will have its value of u initially increase as the high-u region mixes with it and then eventually fall back down (Figure 4, A–C). The higher the diffusion coefficient, the faster is the initial increase, but the fall back down is faster as well (Figure 4, A–C). Diffusion can therefore allow the value of u to increase above the threshold (or, in phase space, to cross the separatrix) for some period of time. If the time is sufficient, the FHN reactions can convert that region of space into an even higher level of u (Figure 4, C and D). The entire process is repeated in the next region of space and then the next, resulting in a trigger wave of bistable switching that never slows down and never peters out (Figure 4C). Similar arguments can be made for the excitable and oscillatory cases.

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