Scale-invariant dissipation underlies enzyme catalytic performance

The role of energy dissipation in the evolution of living systems remains a subject of ongoing debate. Here, we quantify the dissipation associated with enzyme catalysis using minimalistic models of enzyme kinetics and a complete set of microscopic rate constants. We identify a power-law proportionality between total dissipated energy and key kinetic parameters- specifically, the catalytic constant and the specificity constant. These scale-invariant relationships hold across enzyme classes, biological domains, and natural or engineered enzymes. Consistent with Jensen's hypothesis, specialized enzymes display greater catalytic efficiency and higher dissipation. Yet, the wide range of observed efficiencies and dissipation values suggests that scale-independent organizational principles govern enzyme catalysis. Our findings indicate that biological evolution has not merely tolerated dissipation but has actively harnessed and regulated it within constraints imposed by functional and environmental demands. The scale-invariant perspective provides a unifying view of physical (dissipative) and biological (adaptive) evolutionary processes in the emergence of enzymatic function.