Remote control of DNA-acting enzymes by varying the Brownian dynamics of a distant DNA end

Abstract

Enzyme rates are usually considered to be dependent on local properties of the molecules involved in reactions. However, for large molecules, distant constraints might affect reaction rates by affecting dynamics leading to transition states. In single-molecule experiments we have found that enzymes that relax DNA torsional stress display rates that depend strongly on how the distant ends of the molecule are constrained; experiments with different-sized particles tethered to the end of 10-kb DNAs reveal enzyme rates inversely correlated with particle drag coefficients. This effect can be understood in terms of the coupling between molecule extension and local molecular stresses: The rate of bead thermal motion controls the rate at which transition states are visited in the middle of a long DNA. Importantly, we have also observed this effect for reactions on unsupercoiled DNA; other enzymes show rates unaffected by bead size. Our results reveal a unique mechanism through which enzyme rates can be controlled by constraints on macromolecular or supramolecular substrates.

Fig. 1.

Experiment setup and supercoil relaxation assay. (A) A supercoiled dsDNA is tethered between a surface and a paramagnetic bead. As plectonemic supercoils are introduced, DNA extension is reduced. (B) When supercoiling is relaxed, an increase in DNA extension is observed. (C) Relaxation mechanism for topo IB and topo V. Cleavage of one strand covalently links one end to the topo (open circle), and allows the other to rotate about the unbroken strand (blue), relaxing stored ΔLk. (D) Bxb1 integrase: A tethered dsDNA (dotted lines) with attP (red arrow) and a short DNA fragment with attB (blue arrow) form a synapse with two Bxb1 integrase dimers. Cleavage of all four strands is accompanied by covalent attachment of each 5′ end to an integrase subunit; supercoils on the tethered DNA then relax by rotation about the protein interface that holds the two halves of the complex together (21). Reactions in C and D are reversible (i.e., the cleaved strands may religate to recover the torsional stiffness of the dsDNA). (E) Nicking enzyme Nt.AlwI (9) binds to a dsDNA and cuts only one strand, producing irreversible nicking.

Fig. 2.

Real-time traces for supercoil relaxation by topo IB (0.5 pN, ΔLk = -30). (A) A 1 μm-diameter bead; relaxation leads to bead velocity of 21 ± 1 μm/s. (B) A 2.8 μm-diameter tethered bead; relaxation occurs with bead velocity of 5.6 ± 0.4 μm/s.

Fig. 3.

Dependence of supercoil relaxation velocity on the inverse of effective bead diameter (0.5 pN, ΔLk = -30). For each enzyme, a well-defined slope (in units of μm²/s) was obtained from a two-parameter linear fit to the velocities averaged over series of experiments. Bead diameters of 0.7 μm, 0.8 μm, 1.0 μm, 1.2 μm, and 2.8 μm were used; the slowest velocities were obtained using paired 2.8-μm beads (two beads stuck together). All error bars indicate standard errors determined from the number of measurements listed below. Pink: Bxb1 integrase. The slope of the velocity vs. effective bead diameter is 9.4 ± 0.8 μm²/s, lower than all other enzymes studied, indicating that Bxb1 integrase has the largest barriers to rotational relaxation among all enzymes studied in this paper. (Number of measurements: n = 7 and 26 for 1- and 2.8-μm beads, respectively). Purple: topo V, slope 25.4 ± 0.9 μm²/s (n = 11 and 23 for 1- and 2.8-μm beads, respectively). Red: vaccinia topo IB, slope 29.2 ± 0.8 μm²/s, close to that for topo V (n = 7, 5, 8, 5, 9, and 5 for 0.7-, 0.8-, 1.0-, 1.2-, and 2.8-μm beads, respectively; n = 5 for the double 2.8-μm bead). Blue: nicking enzyme Nt.AlwI, slope 35 ± 1 μm²/s, the highest among all supercoil relaxation enzymes studied, consistent with its having the lowest barriers to rotational relaxation (n = 10 and 8 for 1- and 2.8-μm beads, respectively; n = 9 for doublets of 2.8-μm beads). Green: bead release velocities obtained by cutting the dsDNA with restriction enzyme PvuII. Again, a simple linear dependence is found with slope 72 ± 2 μm²/s. As expected, this is higher than that of any supercoil relaxation experiments (n = 10 and 8 for 1- and 2.8-μm beads, respectively). Black: theoretical limit for bead release velocity based on estimated bead terminal velocity at 0.5-pN pulling force (constant in our experiments), water viscosity (6.9•10^-4 Pa·s for water at 37 °C), bead size, and proximity to surface (7). Expected velocity is linear in the inverse of effective bead diameter with slope 76.6 μm²/s, in accord with results for bead release (green).

Fig. 4.

Religation times (“open” times) and corresponding rates for Bxb1 integrase depends on bead size. Following double-strand cleavage and supercoil relaxation, attP–Bxb1 integrase–attB–CT synapses usually religate, leading to recovery of torsional stiffness. A series of waiting times between relaxation and religation (constant 0.5-pN force) was measured and was well-fit by a exponential decay corresponding to a single-step chemical process. All error bars show standard errors. (A) Average waiting time for 2.8 μm-diameter beads was 225 ± 54 s. The exponential fit rate was 3.6 ± 0.3•10^-3 s^-1 (n = 11). (B) Average waiting time for 1 μm-diameter beads was 61 ± 17 s. The exponential fit rate was 14 ± 2•10^-3 s^-1 (n = 21). (C) Plot of religation rates indicates a linear dependence on the inverse of effective bead diameter.