On amplitude-timescale constraints in a pulse generating biomolecular circuit

An incoherent feed-forward loop is an important pulse-generating biomolecular circuit. However, the factors constraining the peak amplitude and timescale parameters asuch as rise time, pulse width, and decay time are generally unclear. Here we address this using a control-theoretic tools to analyze a standard computational model of a feedforward loop. We compute the dependence of the amplitude and timescale parameters on system parameters. The area under the curve is solved analytically to establish parametric dependence of pulse shape. We use a co-ordinate change to transform the system into an integral feedback system. We use the transformed system to understand factors constraining the amplitude and timescale parameters. These results should help in understanding the interdependence of key systems-level parameters in a pulsing biomolecular circuit.