The proper functioning of the organism relies on various cell behaviors, such as chemotaxis, biological rhythms, and migration. The execution of these biological functions is closely related to biochemical processes within the cell. Specifically, receptors on the cell membrane sense changes in the environment and transmit signals to downstream signaling molecules, regulating gene expression levels. Proteins translated from gene transcription can further regulate signaling pathways and metabolic networks. Moreover, biochemical molecules involved in the above cellular networks are usually not uniformly distributed within the cell, and many of them can form assemblies. Given the complexity of these cellular networks, mathematical models are widely used to model the cellular network and reveal the principles behind biological functions. By building mathematical models of signaling pathways, gene networks, and molecular assemblies, we have studied the mechanisms of biological functions such as adaptability, noise resistance, oscillations, pattern formation, cell migration, and anti-phase oscillation. These studies have revealed the formation mechanisms of complex biological phenomena and provided an important theoretical foundation for biomedicine.
