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. 2015 Jul 21;109(2):220-30.
doi: 10.1016/j.bpj.2015.05.020.

Helicase processivity and not the unwinding velocity exhibits universal increase with force

David L Pincus  1 , Shaon Chakrabarti  2 , D Thirumalai  3
Affiliations

Helicase processivity and not the unwinding velocity exhibits universal increase with force

David L Pincus et al. Biophys J. .

Abstract

Helicases, involved in a number of cellular functions, are motors that translocate along single-stranded nucleic acid and couple the motion to unwinding double-strands of a duplex nucleic acid. The junction between double- and single-strands creates a barrier to the movement of the helicase, which can be manipulated in vitro by applying mechanical forces directly on the nucleic acid strands. Single-molecule experiments have demonstrated that the unwinding velocities of some helicases increase dramatically with increase in the external force, while others show little response. In contrast, the unwinding processivity always increases when the force increases. The differing responses of the unwinding velocity and processivity to force have lacked explanation. By generalizing a previous model of processive unwinding by helicases, we provide a unified framework for understanding the dependence of velocity and processivity on force and the nucleic acid sequence. We predict that the sensitivity of unwinding processivity to external force is a universal feature that should be observed in all helicases. Our prediction is illustrated using T7 and NS3 helicases as case studies. Interestingly, the increase in unwinding processivity with force depends on whether the helicase forces basepair opening by direct interaction or if such a disruption occurs spontaneously due to thermal fluctuations. Based on the theoretical results, we propose that proteins like single-strand binding proteins associated with helicases in the replisome may have coevolved with helicases to increase the unwinding processivity even if the velocity remains unaffected.

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Figures

Figure 1
Figure 1
A schematic illustration of the extension of the Betterton and Jülicher model for helicases. The position of the helicase (black circle) on an underlying one-dimensional lattice representing the nucleic acid substrate is denoted by the variable n, while the variable m refers to the location of the ss-dsNA junction. At infinite separation between the helicase and ss-ds NA junction, n → n + 1 transitions occur at rate k+, while n → n − 1 transitions occur at rate k−. Similarly, m → m + 1 transitions occur at rate α, and m → m − 1 transitions occur at rate β. The tension F is applied to the ends of the nucleic acid. To see this figure in color, go online.
Figure 2
Figure 2
Unwinding velocity V1(F,U0) as a function of the tension (FΔx/kBT), for various coupling potentials U0/kBT = 0 (red circles), 1 (orange squares), 2 (yellow diamonds), 3 (green down-triangles), 4 (green up-triangles), and 5 (cyan rectangles). (Solid black lines) Numerical results obtained using Eqs. 9 and 11. Each symbol represents an average of 1000 independent KMC simulations. For forces exceeding FΔx/kBT = 1.9, the duplex melts and it is no longer possible to numerically solve the system given by Eq. 11, but the robustness of our simulation algorithm allows us to explore this regime confirming that the duplex has melted. The parameters used were f = 0.01, α = 105 s−1, β = 7 × 105 s−1, k+ = 1 bp/s, k− = 0.01 bp/s, γ = 0.01 s−1, and j0 = 1. To see this figure in color, go online.
Figure 3
Figure 3
Ratio of the mean attachment time of an active to a passive helicase 〈τ〉/〈τ〉HW as a function of FΔx/kBT, for U0/kBT = 1 (black solid line), 2 (orange dashed line), 3 (green short and long dashed line), 4 (blue short dashed line), and 5 (red dotted line). The value 〈τ〉/〈τ〉HW increases with FΔx/kBT and decreases with increasing U0/kBT. Interestingly, the mean attachment time is unaffected by f (all curves with the same value of U0/kBT can be superimposed). Parameters used to solve Eq. 11 were α = 105 s−1, β = 7 × 105 s−1, k+ = 1 bp/s, k− = 0.01 bp/s, γ = 0.01 s−1, j0 = 1, and M = 104. (a)–(d) correspond to f = 0.01, 0.05, 0.25, and 0.5, respectively. To see this figure in color, go online.
Figure 4
Figure 4
Mean unwinding processivity of an active helicase (relative to that of a passive helicase) as a function of FΔx/kBT, for U0/kBT = 1, 2, 3, 4, 5, 10, 15, and 20. For all values of U0, the processivity always increases with increasing tension destabilizing the ss-dsNA junction and decreases with increasing step height. Unlike the mean attachment time (Fig. 3), the unwinding processivity is highly sensitive to the kinetic parameter f, further confirming that the processivity is likely to exert a strong influence over the kinetics of unwinding. Parameters used to solve Eq. 11 were α = 105 s−1, β = 7 × 105 s−1, k+ = 1 bp/s, k− = 0.01 bp/s, γ = 0.01 s−1, j0 = 1, and M = 104. (a)–(d) correspond to f = 0.01, 0.05, 0.25, and 0.5, respectively. To see this figure in color, go online.
Figure 5
Figure 5
Plots of the mean unwinding processivity of a helicase as a function of the applied tension, for U0/KBT = 0 (passive), 1, 2, 3, 4, 5, 10, 15, and 20. The processivity always increases with increasing tension destabilizing the ss-dsNA junction and decreases with increasing step height. We used the same parameters as in Fig. 4. (a)–(d) correspond to f = 0.01, 0.05, 0.25, and 0.5, respectively. To see this figure in color, go online.
Figure 6
Figure 6
The dependence of 〈τ〉, 〈δm〉, and 〈δm〉/〈τ〉 on the step-height (U0/KBT) for varying amounts of GC content for the sequence given in the text. Simulations were performed at U0/kBT = 0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Each data point corresponds to an average over 1000 independent KMC simulations. All quantities decrease with increasing %GC. Interestingly, the mean attachment time 〈τ〉 is again very insensitive to f. The value 〈δm〉 is, however, sensitive to f, leading to disparate behaviors for 〈δm〉/〈τ〉. When f = 0.25, 〈δm〉/〈τ〉 shows a very distinct maximum when %GC = 0.0 but a very weak maximum when %GC = 1.0. When f = 0.01, 〈δm〉/〈τ〉 shows saturating behavior with increasing U0. Thus, sequence plays a crucial role in determining the kinetics of unwinding. Parameters used in the simulations were α = 105 s−1, β = 7 × 105 s−1, k+ = 1 bp/s, k− = 0.01 bp/s, γ = 0.01 s−1, and j0 = 1. (a), (c), and (e) correspond to f = 0.01, while (b), (d), and (f) correspond to f = 0.25. To see this figure in color, go online.
Figure 7
Figure 7
(a) Dependence of eΔGF on F for two models: ΔGF = FΔx (blue curve), and ΔGF=2L/llog(1/(Fl)sinh(Fl)) (red curve). The parameters Δx = 0.594 nm, L = 0.6 nm/nucleotide, and l = 1.3 nm were chosen such that for both models, the critical force (force at which ΔG = ΔGF) is 13.5 pN, a typical value for DNA hairpins. To be consistent with the rest of our analysis, ΔG was chosen to be 1.95 kBT. (b and c) Experimental data suggesting a universal behavior of the unwinding processivity as a function of force. Velocity (blue) and processivity (red) data on (b) the T7 helicase (28) and (c) the NS3 helicase (40). The data shows that the unwinding velocity of the two helicases can be strongly or weakly dependent on external force. The processivity clearly increases as F increases, for both the helicases. To see this figure in color, go online.
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