Direct Measurements of the Dissociation-Rate Constant for Inhibitor-Enzyme Complexes via the T1ρ and T2 (CPMG) Methods

Abstract

The unimolecular dissociation rate constant, k−1, for the inhibitor-enzyme complex tubercidin-Escherichia coli purine nucleoside phosphorylase (PNPase) has been determined directly via two related 1H NMR methods for studying exchange-mediated transverse relaxation. One method involves measurements of the decay rate, 1/T1ρ, of spin-locked magnetization in the rotating frame as a function of the strength of the spin-locking field, ωSL The second method involves measurements of the Carr-Purcell-Meiboom-Gill (CPMG) spin-echo decay rate, 1/TCPMG2 as a function of the repetition rate, 1/tcp, of the refocusing pulses. Expressions describing the dependence of TCPMG2 as a function of 1/tcp and k−1 have been previously derived with sufficient generality to include the two-site inhibitor-enzyme exchange case. Existing expressions for T1ρ as a function of kex and ωSL, however, had to be reformulated to take into account differences between Tb2 and Tb1 for the bound form of the inhibitor as well as offset corrections important at low values of ωSL A new expression for exchange-mediated T1ρ has been derived to take these factors into account and is shown to provide a more accurate description of observed T1ρ data than previous models. Numerical analysis of relaxation rates, measured independently by either the rotating-frame or the spin-echo method for the H1′ and H2 protons of tubercidin at different inhibitor:enzyme ratios, yields comparable values for k−1 of 2400 (±350) and 900 (±80) s−1 at 20 and 10°C, respectively. The merits of both methods are compared and suggestions for optimizing the experiments are discussed.