Rate constants determined by nuclear magnetic resonance

Fast kinetic methods are used to measure reactions that take place in less time than required to mix the reagents manually and to measure the reaction by usual methods, like UV-visible spectrophotometry and fluorescence. The best known of them are rapid-mixing and relaxation methods, which are used for reactions with half-times in the millisecond and microsecond ranges, respectively. The picosecond range is usually measured with electrical field and ultrasonic waves (A. Cornish-Bowden, 1976, Principles of Enzyme Kinetics, pp. 164-167, Butterworths, London). Normally these very fast rates occur when a ligand binds to or dissociates from a protein. When the binding is mediated only by the diffusion, the lower limit of the association rate constant (k(on)) should not exceed the value of a diffusion-controlled reaction (around 10(10) M(-1) s(-1)). Therefore, the values most frequently found for these rate constants, for example, in the association of a substrate with an enzyme, are in the range 10(6) to 10(9) M(-1) s(-1) (M. Eigen and G. G. Hammes, 1963, Adv. Enzymol. 25, 1-38). The values for the dissociation rate constants (k(off)) for these reactions, which depend on the equilibrium constant for the enzyme-substrate complex interaction, are in the range 10(1) to 10(5) s(-1), most often between 10(3) and 10(4) s(-1) (A. Fersht, 1999, Structure and Mechanism in Protein Science, pp. 164-165, Freeman, New York). If the equilibrium constant is known, and the value of koff is determined by nuclear magnetic resonance (NMR), as described in this chapter, the value of k(on) can be calculated; this should not exceed the value of diffusion rate in the media in which the reaction is performed.