A simple mechanism for controlling the onset and arrest of collective oscillations in genetic circuits

TL;DR

This paper presents a simple control mechanism for initiating and stopping collective oscillations in coupled genetic circuits, using a single bifurcation parameter to modulate dynamics and produce complex transient behaviors.

Contribution

It introduces a novel bifurcation-based control method for collective oscillations in genetic networks, highlighting the role of network topology and coupling in dynamic regulation.

Findings

Control of oscillations via a single bifurcation parameter

Rich out-of-equilibrium dynamics with multiple time scales

Observation of transient patterns like self-organized pacemakers

Abstract

We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for an intermediate period between collective fixed-point behavior. The control mechanism works by monotonically increasing a single bifurcation parameter. Both the onset and arrest of oscillations are due to bifurcations. Depending on the coupling strength, the network topology and the tuning speed, our numerical simulations reveal a rich dynamics out-of-equilibrium with multiple inherent time scales, long transients towards the stationary states and interesting transient patterns like self-organized pacemakers. Zooming into the transition regime, we pursue the arrest of oscillations along the arms of spirals. We point out possible relations to the genetic network of segmentation clocks.