Visual Interpretation of the Meaning of kcat/KM in Enzyme Kinetics

Abstract

Abstractkcat and kcat/KM are the two fundamental kinetic parameters in enzyme kinetics. kcat is the first-order rate constant that determines the reaction rate when the enzyme is fully occupied at a saturating concentration of the substrate. kcat/KM is the second-order rate constant that determines the reaction rate when the enzyme is mostly free at a very low concentration of the substrate. Both parameters provide critical information on how the enzyme lowers the energy barriers along the reaction pathway for catalysis. However, it is surprising how often kcat/KM is used inappropriately as a composite parameter derived by dividing kcat with KM to assess both catalytic power and affinity to the substrate of the enzyme. The main challenge in explaining the true meaning of kcat/KM is the difficulty to demonstrate how the reaction energetics of enzyme catalysis determines kcat/KM in a simple way. Here, I report a step-by-step demonstration on how to visualize the meaning of kcat/KM on the reaction energy diagram. By using the reciprocal form of the expression of kcat/KM with the elementary rate constants in kinetic models, I show that kcat/KM is a harmonic sum of several kinetic terms that correspond to the heights of the transition states relative to the free enzyme. Then, I demonstrate that the height of the highest transition state has the dominant influence on kcat/KM, i. e. the step with the highest transition state is the limiting step for kcat/KM. The visualization of the meaning of kcat/KM on the reaction energy diagram offers an intuitive way to understand all the known properties of kcat/KM, including the Haldane relationship.