title: Coexistence of multiple propagating wave-fronts in a regulated enzyme reaction model: link with birhythmicity and multi-threshold excitability.
abstract: We analyze the spatial propagation of wave-fronts in a biochemical model for a product-activated enzyme reaction with non-linear recycling of product into substrate. This model was previously studied as a prototype for the coexistence of two distinct types of periodic oscillations (birhythmicity). The system is initially in a stable steady state characterized by the property of multi-threshold excitability, by which it is capable of amplifying in a pulsatory manner perturbations exceeding two distinct thresholds. In such conditions, when the effect of diffusion is taken into account, two distinct wave-fronts are shown to propagate in space, with distinct amplitudes and velocities, for the same set of parameter values, depending on the magnitude of the initial perturbation. Such a multiplicity of propagating wave-fronts represents a new type of coexistence of multiple modes of dynamic behavior, besides the coexistence involving, under spatially homogeneous conditions, multiple steady states, multiple periodic regimes, or a combination of steady and periodic regimes.
authors.affiliation: Departamento de Bioquimica, Faculdad de Quimicas, Universidad Complutense, E-28040 Madrid, Spain.
authors.forename: C
authors.initials: C
authors.lastname: Pérez-Iratxeta
authors.forename: J
authors.initials: J
authors.lastname: Halloy
authors.forename: F
authors.initials: F
authors.lastname: Morán
authors.forename: J L
authors.initials: JL
authors.lastname: Martiel
authors.forename: A
authors.initials: A
authors.lastname: Goldbeter