Designing generative dissipative networks for programming complex temporal dynamics and functions

Complex temporal dynamics orchestrated by natural networks are essential for cellular functions. Replicating these dynamics in simplified synthetic networks could elucidate underlying mechanisms, facilitating the creation of life-like systems. Herein, we introduce a versatile, modular, and programmable framework for constructing hierarchical and multifunctional generative dissipative networks (GDNs) capable of producing complex temporal dynamics. This framework involves two types of modules. Generative modules produce fuels, and dissipative modules consume these fuels to activate transient signals. By integrating multiple modules, hierarchical GDNs with diverse compositions, sizes, connections, and topologies were constructed to produce controllable complex temporal dynamics, like precise pulse-multiphase control, pulse-repetition frequency modulation, and programmed timing of multiple pulses. These dynamics stem from coordination among heterogeneous modules and competition among homogeneous modules, as corroborated by kinetic modeling. Furthermore, GDNs offer a robust platform for programming autonomous temporal functions, exemplified by GDN-mediated temporal programming of RNA transcription and DNA condensate dynamics.