摘要：AbstractAs many disorders have been correlated with dysfunctional biophysical rhythms, new therapies based on the control of clock functions are emerging for the slowdown of disease progression. In this context, a general disrupted biological clock is modeled by the canonical form of a genetic negative feedback loop. When the unique fixed point of thisN-dimensional non-linear differential system is stable, the model reproduces accurately the damped oscillations observed in a damaged oscillator. First, a synthetic modification of the network is proved to generate sustained oscillations and allow to recover a functional clock. The desired periodic trajectories are obtained by destabilizing the fixed point of the model and monotone properties are applied for global results. In a limit case, this modification of the loop is shown to be equivalent to an external piecewise constant control law, supporting the conjecture that simple qualitative control strategies may be able to guarantee sustained oscillations. From the perspective of a biological implementation, this result is promising as these types of control are well adapted to experimental constraints. To support this theoretical work, the methods are applied to the disrupted circadian clock observed in human cancer cells.
关键词：KeywordsFeedback loopsOscillatorsBio controlNonlinear systemsQualitative control
