2022/08/19 by Carles Tardío Pi, Pi, Carles Tardío, Jorge Castillo Medina +3
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2208.09119
openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, based on spatially distributed limit-cycle oscillators, that allows us to capture the dynamics of synchronization fronts by taking the continuum limit as the number of coupled oscillators tends to infinity. We explore analytically a family of wavefront-type solutions to the system in terms of model parameters and corroborate its validity via a numerical finite-difference method algorithm. Finally, we review our results in light of some experimental systems in synthetic biology based on a synchronised quorum of genetic clocks, coupled via a diffusive auto-inducer signalling molecule analogue to our Hooke-like coupling scheme within the proposed hybrid Rayleigh-van der Pol model.