Scientific article

Mathematical modeling of Erk activity waves in regenerating zebrafish scales

Published inBiophysical journal, vol. 120, no. 19, p. 4287-4297
Publication date2021-10-05
First online date2021-05-20

Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration of osteoblast tissue in zebrafish scales. These waves originate from a central source region, propagate as expanding rings, and impart cell growth, thus controlling tissue morphogenesis. Here, we present a minimal reaction-diffusion model for Erk activity waves. The model considers three components: Erk, a diffusible Erk activator, and an Erk inhibitor. Erk stimulates both its activator and inhibitor, forming a positive and negative feedback loop, respectively. Our model shows that this system can be excitable and propagate Erk activity waves. Waves originate from a pulsatile source that is modeled by adding a localized basal production of the activator, which turns the source region from an excitable to an oscillatory state. As Erk activity periodically rises in the source, it can trigger an excitable wave that travels across the entire tissue. Analysis of the model finds that positive feedback controls the properties of the traveling wavefront and that negative feedback controls the duration of Erk activity peak and the period of Erk activity waves. The geometrical properties of the waves facilitate constraints on the effective diffusivity of the activator, indicating that waves are an efficient mechanism to transfer growth factor signaling rapidly across a large tissue.

Affiliation Not a UNIGE publication
Citation (ISO format)
HAYDEN, Luke D. et al. Mathematical modeling of Erk activity waves in regenerating zebrafish scales. In: Biophysical journal, 2021, vol. 120, n° 19, p. 4287–4297. doi: 10.1016/j.bpj.2021.05.004
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Article (Published version)
ISSN of the journal0006-3495

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