Biochemical Computing Mode for Sequential Logic

Recent years have witnessed the growing scholarly interest in the next-generation general-purpose computers. Various innovative computing modes have been proposed, such as optical, quantum phenomena, and DNA-based modes. Sequential logic circuits are a critical factor that enables these modes to function as general-purpose computers, given their essential role in facilitating continuous computation and memory storage through their ability to store states. However, compared to computability, it is often overlooked due to the difficulty of its implementation. In this paper, we first demonstrate sequential mapping, a crucial necessary condition for electronic computers to realize sequential logic circuits, and highlight this distinctive property of general-purpose computers in the context of logic gate circuits. To achieve computational functionalities comparable to those of electronic computers, we utilize the control effect of enzymes on enzymatic reactions to design a logic gate model that is composed of small molecules and driven by enzymes, subsequently propose a biochemical computing mode. Furthermore, we mathematically analyze the static and dynamic input-output properties of biochemical logic gate components and prove that the biochemical computing mode satisfies sequential mapping similar to electronic computers. When combined with the storage characteristics of NOT-AND gates, it can realize sequential logic circuits. The findings can serve as a theoretical foundation for developing general-purpose biochemical computers.