Spatial trigger waves: positive feedback gets you a long way.
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.
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
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Mentions: Here we assume a = 0.1 and e = 0.01 and change the behavior by varying the parameter b. Note that all parameters and variables are dimensionless throughout. When b is relatively large (b > 1.8), the system is bistable. Depending on the initial conditions, the system will settle down into one of two alternative stable steady states, one with a negative membrane potential (Figure 2A) and one with a positive membrane potential. For the initial value of v assumed here (v = −0.3), all trajectories that start with u > −0.3 (the threshold shown by the dashed line in Figure 2A) will approach the positive-potential steady state (Figure 2A, red curve), and all trajectories that start with u < −0.3 will end up at the negative-potential steady state (Figure 2A, blue curve). Thus a small perturbation that pushes the system across the threshold will be amplified into a large difference in the system's ultimate fate.
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.