The article by Béla Novak and John J. Tyson explores the design principles of biochemical oscillators, which are essential for various cellular processes such as signaling, motility, development, and cell cycle control. They identify three key requirements for biochemical oscillations: delayed negative feedback, sufficient "nonlinearity" in reaction kinetics, and proper balancing of time scales of opposing chemical reactions. Positive feedback is highlighted as a mechanism to delay the negative feedback signal. The authors classify biological oscillators based on the topology of positive and negative feedback loops, including delayed negative feedback loops, amplified negative feedback loops, and incoherently amplified negative feedback loops. They also discuss the role of nonlinearity in oscillations, which can arise from various sources such as multimeric transcription factors, allosteric enzymes, and reversible phosphorylation. The article concludes by emphasizing the importance of quantitative modeling in understanding and predicting cellular oscillations, and suggests that biochemical oscillators may have evolved repeatedly through genetic changes that destabilized steady states and generated sustained oscillations.The article by Béla Novak and John J. Tyson explores the design principles of biochemical oscillators, which are essential for various cellular processes such as signaling, motility, development, and cell cycle control. They identify three key requirements for biochemical oscillations: delayed negative feedback, sufficient "nonlinearity" in reaction kinetics, and proper balancing of time scales of opposing chemical reactions. Positive feedback is highlighted as a mechanism to delay the negative feedback signal. The authors classify biological oscillators based on the topology of positive and negative feedback loops, including delayed negative feedback loops, amplified negative feedback loops, and incoherently amplified negative feedback loops. They also discuss the role of nonlinearity in oscillations, which can arise from various sources such as multimeric transcription factors, allosteric enzymes, and reversible phosphorylation. The article concludes by emphasizing the importance of quantitative modeling in understanding and predicting cellular oscillations, and suggests that biochemical oscillators may have evolved repeatedly through genetic changes that destabilized steady states and generated sustained oscillations.