Design of a sequestration-based network with tunable pulsing dynamics

Incoherent feedforward networks exhibit the ability to generate temporal pulse behavior. However, exerting control over specific dynamic properties, such as amplitude and rise time, poses a challenge and is intricately tied to the network's implementation. In this study, we focus on analyzing sequestration-based networks capable of exhibiting pulse behavior. By employing time-scale separation in the fast sequestration regime, we approximate the temporal dynamics of these networks. This approach allows us to establish a mapping that elucidates the impact of varying the kinetic rates and pulse specifications, including amplitude and rise time. Furthermore, we introduce a positive feedback mechanism to regulate the amplitude of the pulsing response.