Minimalist model for force-dependent DNA replication

Abstract

In experiments using optical or magnetic tweezers, investigators have monitored the rate at which polymerase enzymes catalyze DNA replication when the template strand is subjected to a stretching force. For T7, Klenow, and Sequenase polymerases, the replication rate increases modestly at low tension and then decreases markedly at higher tension. Molecular-dynamics (MD) simulations using x-ray structure data for the open and closed complexes of the Taq enzyme with DNA revealed that the dependence of replication rate on tension could be accounted for in terms of the induced enthalpy changes for the two DNA segments adjacent to the site of the added nucleotide. Here, we present a simple, minimalist two-segment local model (M2L) derived from some striking features seen in the MD simulations. The model predicts the tension dependence of the replication rate using only structural data and a critical tension, f(∗), without recourse to MD simulations. At f(∗), the outermost DNA segment undergoes a large angular reorientation in the open conformation of the enzyme. We give a generic plot for the M2L model, apply it to family A and B polymerases and HIV reverse transcriptase, and discuss factors that may govern the f(∗) flip parameter.

Figure 1

Results for Taq replication activity. (A) The dependence on tension force of the enthalpy of activation for converting the open complex to a closed one. Solid and dashed curves represent enthalpy contributions from DNA segments in the open and closed conformations, respectively, obtained from an average of MD simulations from Andricioaei et al. (16) and this study. For segments a, a′, and b′, at forces up to 20 pN, the dependence is nearly linear, indicating that the orientation of these segments is insensitive to the force; however, segment b undergoes a marked reorientation at f^∗ = 9.5 ± 1.5 pN that shifts the activation enthalpy from negative to positive values. (B) Corresponding results from the M2L model (Eq. 7) for the activation enthalpy. (C) Comparison of results for the DNA replication rate, obtained from Eq. 1 using the MD simulation data (full curve) with that obtained from the M2L model (dashed; Eq. 8).

Figure 2

Generic plots for dependence on applied tension force according to M2L model. (A) From Eq. 7, for enthalpy of activation. (B) From Eq. 8, for replication rate constant. Both are plotted against dimensionless tension, ξ = fd/k_BT. Plots pertain to five values of ξ^∗ = 0, 0.5, 1, 1.5, and 2, the parameter that specifies the tension at which an angular “flip” of the b segment occurs. In both A and B, the width parameter Δξ = 0.4 for all five values of ξ^∗.

Figure 3

Dependence on tension force obtained from the M2L model for kinetics of DNA replication catalyzed by the T7 and Klenow DNA polymerases. Activation enthalpies (A and B) and rate constants (C and D) are calculated from the structural parameters found in Table 1. Corresponding M2L coefficients are given in Eqs. 9 and 10. Rate constant results (solid curves) from M2L are compared with previous experimental data (points) (1,2). Dashed curves for T7 indicate the bound given by 1 SD of the open conformation parameters.

Figure 4

Dependence on the tension force of HIV-RT and ϕ29 replication activity. (A) For HIV-RT, circles with error bars show data obtained from the flow-cell experiments of Kim et al. (36); dashed curves indicate the range of results (10–90%) derived from the atomic force microscopy data of Lu et al. (35). Solid curves were obtained from the M2L model with flip parameter ξ^∗ = 0 or ξ^∗ = 4 used in Eq. 11. (B) For ϕ29, circles show data obtained from the optical tweezer experiments of Ibarra et al. (37), and the solid line indicates the M2L prediction with no flip occurring, as described by Eq. 12.

Figure 5

Taq, HIV-RT, and ϕ29 DNA undergo different changes to convert the open conformation to the closed conformation. The 0 nucleotide (plain numbers) and the incoming nucleotide (primed numbers) are shown at two or three time steps in the process: 1), open; 2), post-flip; and 3), closed. (A) In Taq, the 0 nucleotide first undergoes an abrupt flip that brings it inward, closer to the closed form. It must then undergo a rotation and further inward motion to reach the closed conformation. (B) On the other hand, in HIV-RT, the 0 nucleotide only needs a single downward motion to move it into the closed conformation. (C) Lastly, in ϕ29, no flip is required, and the 0 nucleotide only undergoes a small translational motion. The HIV-RT and ϕ29 open structures do not contain an incoming nucleotide.