Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

Abstract

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus–response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus–response curves with sigmoidal shape.

Keywords

• Finite-time Lyapunov spectrum
• transient dynamics
• sigmoidal response curve
• nonautonomous dynamical system