Time Course Analysis of Enzyme-Catalyzed DNA Polymerization

Extracting kinetic parameters from DNA polymerase-catalyzed processive polymerization data using traditional initial-rate analysis has proven to be problematic for multiple reasons. The first substrate, DNA template, is a heterogeneous polymer and binds tightly to DNA polymerase. Further, the affinity and speed of incorporation of the second substrate, deoxynucleoside triphosphate (dNTP), vary greatly depending on the nature of the templating base and surrounding sequence. Here, we present a mathematical model consisting of the DNA template-binding step and a Michaelis–Menten-type nucleotide incorporation step acting on a DNA template with a finite length. The model was numerically integrated and globally fitted to experimental reaction time courses. The time courses were determined by monitoring the processive synthesis of oligonucleotides of lengths between 50 and 120 nucleotides by DNA polymerase I (Klenow fragment exo^–) using the fluorophore PicoGreen. For processive polymerization, we were able to estimate an enzyme–template association rate k₁ of 7.4 μM^–1 s^–1, a disassociation rate k_–1 of 0.07 s^–1, and a K_d of 10 nM, and the steady-state parameters for correct dNTP incorporation give k_cat values of 2.5–3.3 s^–1 and K_m values of 0.51–0.86 μM. From the analysis of time courses measured between 5 and 25 °C, an activation energy for k_cat of 82 kJ mol^–1 was calculated, and it was found that up to 73% of Klenow fragment becomes inactivated or involved in unproductive binding at lower temperatures. Finally, a solvent deuterium kinetic isotope effect (KIE) of 3.0–3.2 was observed under processive synthesis conditions, which suggests that either the intrinsic KIE is unusually high, at least 30–40, or previous findings, showing that the phosphoryl transfer step occurs rapidly and is flanked by two slow conformational changes, need to be re-evaluated. We suggest that the numerical integration of rate equations provides a high level of flexibility and generally produces superior results compared to those of initial-rate analysis in the study of DNA polymerase kinetics and, by extension, other complex enzyme systems.