Kinetic assays of DNA polymerase fidelity: A theoretical perspective beyond Michaelis-Menten kinetics

The high fidelity of DNA polymerase (DNAP) is critical for the faithful replication of DNA. There are several quantitative approaches to measure DNAP fidelity. Directly counting the error frequency in the replication products gives the true fidelity but it turns out very hard to implement in practice. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using kinetic theories combined with the measured apparent kinetic rates. However, whether it is equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies using these assays to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. In this paper, we make a comprehensive examination on the theoretical foundation of the two kinetic assays, based on the theory of DNAP fidelity recently proposed by us. Our studies show that while the conventional kinetic assays are generally valid to quantify the discrimination efficiency of DNAP, they are valid to quantify the proofreading efficiency of DNAP only when the kinetic parameters satisfy some constraints which will be given explicitly in this paper. These results may inspire more carefully-designed experiments to quantify DNAP fidelity.

Figure 1

The minimal reaction scheme of DNA replication. $E$: the enzyme DNAP. $D_i$: the primer-template duplex with primer terminal at the template site $i$.

Figure 2

The three-step reaction scheme of the competitive incorporation of dRTP and dWTP. $E$: ${\text{exo}}^{-}$-DNAP. $D_i$: the primer-template duplex with the matched(R) terminal at site $i$. For brevity, the subscript $i$ in each rate constant is omitted.

Figure 3

(a) The multistep reaction scheme of ${\text{exo}}^{+}$-DNAP including the multistep incorporation process [indicated by $k^{*}$ and details are shown in panel (b)], the intramolecular/intermolecular transfer (i.e., without/with DNAP dissociation) of the primer terminal between Pol and Exo and the excision of the primer terminal nucleotide. (b) The multistep incorporation scheme. The enzyme-substrate complex ($ED$) goes through $N$ states (indicated by subscripts $1,...,N$) to successfully incorporate a single dNTP (indicated by subscript $i$). To simplify the notation, the superscripts indicating the template nucleotide $X_i$ and the subscripts indicating the primer nucleotide ${\alpha }_i$ are omitted. This rule also applies to other figures in this paper, unless otherwise specified.

Figure 4

The reaction scheme for the steady-state assay to measure the specificity constant of the nucleotide incorporation reaction of DNAP with deficient exonuclease domain. The omitted multistep incorporation process is shown in Fig. 3.

Figure 5

The reaction scheme for the steady-state assay to measure the effective excision rate of ${\text{exo}}^{+}$-DNAP.

Figure 6

The ratio $F/f_{\mathrm{ss}}$ may become larger than 10 when $k_{pe}^{†}\ll k_{pe}$ and $k_{\text{off}}^{p†}\ll k_{\text{off}}^p$. The kinetic rates are set as $q=1$, $k_{ep}=k_{ep}^{†}=1$, $k_{pe}=0.1$, $k_{\text{off}}^e=k_{\text{off}}^{e†}=1$, $k_{\text{off}}^p=0.1$, $k_{\text{on}}^p={10}^3$. $k_{\text{on}}^e$ is calculated according to the thermodynamic constraint ($k_{\text{on}}^e=k_{\text{on}}^p{k}_{pe}{k}_{\text{off}}^e/k_{\text{off}}^p{k}_{ep}={10}^3$). The binding rates are large enough, i.e., $k_{\text{on}}^e>k_{\text{off}}^e$ and $k_{\text{on}}^p>k_{\text{off}}^p,k_{pe}$.

Figure 7

The reaction scheme for the transient-state assay to measure the specificity constant of the nucleotide incorporation reaction of DNAP with deficient exonuclease domain. The omitted multistep incorporation process is shown in Fig. 3.

Figure 8

The reaction scheme for the transient-state assay to measure the effective excision rate of ${\text{exo}}^{+}$-DNAP.

Figure 9

The ratio $F/f_{\mathrm{ts}}$ may become larger than 10 when $q,{\tilde{k}}_{ep}<{\tilde{k}}_{pe}$. The kinetic rates are set as $q=1$, $k_{\text{off}}^e=1$, $k_{\text{off}}^p=0.1$, $k_{\text{on}}^p={10}^3$. $k_{\text{on}}^e$ is calculated by the thermodynamic constraint ($k_{\text{on}}^e=k_{\text{on}}^p{k}_{pe}{k}_{\text{off}}^e/k_{\text{off}}^p{k}_{ep}$). The binding rates are always large enough when adjusting $k_{pe}$ and $k_{ep}$, i.e., $k_{\text{on}}^e>k_{\text{off}}^e$ and $k_{\text{on}}^p>k_{\text{off}}^p,k_{pe}$.

Figure 10

The multistep reaction scheme of ${\text{exo}}^{+}$-DNAP including the translocation step.

Figure 11

The ratio $F/f_{\mathrm{ts}}$ becomes larger than 10 when $k_t$ and $r_t$ get small enough. The kinetic rates (for terminal mismatch $RW$) : $q=1$, $k_{pe}=0.1$, $k_{ep}=1$, $k_{\text{off}}^e=1$, $k_{\text{off}}^{\text{pre}}=0.1$, $k_{\text{off}}^{\text{post}}=0.001$, $k_{\text{on}}^{\text{pre}}={10}^3$. $k_{\text{on}}^e$ and $k_{\text{on}}^{\text{post}}$ are calculated by thermodynamic constraints ($k_{\text{on}}^e=k_{\text{on}}^p{k}_{pe}{k}_{\text{off}}^e/k_{\text{off}}^{\text{pre}}{k}_{ep}={10}^3$, $k_{\text{on}}^{\text{post}}=k_{\text{on}}^{\text{pre}}{k}_t{k}_{\text{off}}^{\text{post}}/k_{\text{off}}^{\text{pre}}{r}_t$). The binding rates are always large enough when adjusting $k_t$ and $r_t$ to ensure $k_{\text{on}}^a>k_{\text{off}}^a,a=\text{pre},\text{post},e,$ and $k_{\text{on}}^{\text{pre}}>k_{pe}$.

Figure 12

The ratio $F/f_{\mathrm{ts}}$ may become larger than 10 when $k_{pe}$ gets large enough. The kinetic rates (for terminal mismatch $RW$): $q=1$, $k_{ep}=1$, $k_{\text{off}}^e=1$, $k_{\text{off}}^{\text{pre}}=0.1$, $k_{\text{off}}^{\text{post}}=0.1$, $k_t=10$, $k_{\text{on}}^{\text{pre}}={10}^3$. $k_{\text{on}}^e$ and $k_{\text{on}}^{\text{post}}$ are calculated by thermodynamic constraints($k_{\text{on}}^e=k_{\text{on}}^p{k}_{pe}{k}_{\text{off}}^e/k_{\text{off}}^{\text{pre}}{k}_{ep}$, $k_{\text{on}}^{\text{post}}=k_{\text{on}}^{\text{pre}}{k}_t{k}_{\text{off}}^{\text{post}}/k_{\text{off}}^{\text{pre}}{r}_t$). The binding rates are always large enough when adjusting $k_{pe}$ and $r_t$ to ensure $k_{\text{on}}^a>k_{\text{off}}^a,a=\text{pre},\text{post},e,$ and $k_{\text{on}}^{\text{pre}}>k_{pe}$.