The rotation-coupled sliding of EcoRV

It has been proposed that certain type II restriction enzymes (REs), such as EcoRV, track the helical pitch of DNA as they diffuse along DNA, a so-called rotation-coupled sliding. As of yet, there is no direct experimental observation of this phenomenon, but mounting indirect evidence gained from single-molecule imaging of RE–DNA complexes support the hypothesis. We address this issue by conjugating fluorescent labels of varying size (organic dyes, proteins and quantum dots) to EcoRV, and by fusing it to the engineered Rop protein scRM6. Single-molecule imaging of these modified EcoRVs sliding along DNA provides us with their linear diffusion constant (D1), revealing a significant size dependency. To account for the dependence of D1 on the size of the EcoRV label, we have developed four theoretical models describing different types of motion along DNA and find that our experimental results are best described by rotation-coupled sliding of the protein. The similarity of EcoRV to other type II REs and DNA binding proteins suggests that this type of motion could be widely preserved in other biological contexts.


Dynamics of the linker-label complex
With the exception of the EcoRV-scRM6 fusion protein, the fluorescent labels were attached to the enzyme via a flexible linker which was either an N-terminal His 6 -tag or a biotin and polyethylene glycol (PEG, n = 2 or n = 11) containing spacer. Recently, we developed a model to estimate the impact of such a flexible linker on the dynamics of a protein-label complex sliding along DNA (22). We showed that the Brownian motion of the label can be partially decoupled from that of the protein if 1) the relaxation time τ R of the linker-label complex is small compared to the time τ S the protein needs to slide over one DNA base-pair and 2) the end-to-end length z 0 of the linker is larger than the length a ≈ 0.34 nm of a DNA base-pair. When these two assumptions are fulfilled, the friction coefficient ξ of the proteinlabel complex can be written as , where ξ p and ξ l are the 3D friction coefficients of the protein and of the label, respectively, and f > 1 accounts for the DNAprotein friction.
We now investigate the validity of these two assumptions (τ S ≫ τ R and z 0 > a) in our experiments. To estimate the end-to-end length z 0 of a PEG linker, we model it as a polymer with a contour length L and a persistence length l p . For such a polymer, p Ll z 2 0 (31). The persistence length l p for a linear carbon chain ranges from 0.3 to 0.5 nm (32), whereas l p ≈ 0.38 nm for a PEG molecule (33). Thus we assume l p ≈ 0.4 nm for the linkers used in our experiments, which gives z 0 ≈ 1.5 nm for the PEG 2 linker (L ≈ 3 nm) and z 0 ≈ 2 nm for the PEG 11 linker (L ≈ 6 nm). To estimate the end-to-end length z 0 of a His 6 -tag, we used the crystal structure of the protein G with a similar tag (34), and derived z 0 ≈ 2 nm. The hypothesis z 0 > a is thus fulfilled.
The relaxation time τ R of the linker-label complex depends on the size of the label. For a label of radius r l much smaller than z 0 , the relaxation time of the linker-label complex is that of the polymer T k z B R / 3 0 η τ (31), where η is the viscosity of the buffer (η = 8.9x10 -4 Pa s for water at T = 298 K) and k B is the Boltzmann constant. For z 0 ≈ 2 nm, one gets τ R ≈ 2 ns. For a label of radius r l much larger than z 0 , the relaxation time of the linker-label complex is given by T k r z B l R / 6 2 0 πη τ (35). For the largest label used (QD655), one gets τ R ≈ 140 ns with r l = 15 nm and z 0 = 1.5 nm. For a label whose size is in the order of z 0 , one expects τ R to be in the ns range. In comparison, the time EcoRV needs to slide over a is 5 2 / 2 ≈ D a S τ µs assuming D 1 ≈ 10 -2 µm 2 s -1 , which is the largest value of the linear diffusion coefficient we measured. Thus τ S ≫ τ R , for whatever the size of the label used in our experiments is.

Measuring the radii of the labels by Fluorescent Correlation Spectroscopy (FCS)
The hydrodynamic radii of the fluorescent labels were measured by FCS with a home-built two-photon setup (36). Fluorescence excitation at 780 nm was achieved by a Ti:Sapphire laser (Mira 900; Coherent, Auburn, CA) using a 60X water immersion objective (UPlan apo, NA 1.2; Olympus, Rungis, France). The fluorescence signal, after collection by the same objective, was passed through two filters (dichroic filter 680DCSPXR and emission filter HQ 560/80; Chroma Technology, Rockingham, VT) and was split for detection by two avalanche photodiodes (SPCM-AQR-14, Perkin Elmer, Wellesley, MA). The auto-correlation function from the photodiode signals was calculated by an ALV-6000 digital correlator (ALV, Langen, Germany).
For each label the auto-correlation curve (Fig. S1) was fitted by (37): where N is the average number of fluorescent labels in the excitation volume, described as a 2D Gaussian beam, and τ l is the diffusion time of the label through the beam waist ω. Under two-photon excitation the diffusion time is given by where r FITC = 0.577 ± 0.002 nm is the radius of FITC, derived from the Stokes-Einstein relation using η = 8.9x10 -4 Pa s for PBS and the reference value of the diffusion constant of the dye, D FITC = 425 ± 1 µm 2 s -1 at T = 298 K (39). The uncertainty in the estimation of r l is about 10 %, as the main uncertainties (≈ 5 %) come from the measurements of τ l and τ FITC . As we measured τ l at different times, implying different laser waists ω and thus different diffusion times τ FITC , in Table 1 we give the values of τ FITC and τ l from which we derived r l for streptavidin-Cy3 (sav-Cy3) and QDs of various sizes (QDEO6, QD605 and QD655).
The 3D diffusion coefficient of the EcoRV-scRM6 fusion protein (RV-FP) The hydrodynamic radius of the EcoRV fusion protein was measured by FCS on a home-built one-photon setup (dichroic filter Q505LP ; Chroma Technology, Rockingham, VT) (36). Samples were excited at 488 nm (163-C12, Spectra Physics, Irvine, CA) using a 60X water immersion objective (UPlan apo, NA 1.2; Olympus, Rungis, France). The fluorescence signal, after collection by the same objective, passed through an emission filter (HQ 560/80 ; Chroma Technology) and was then split to allow simultaneous acquisition on two avalanche photodiodes (SPCM-AQR-14; Perkin Elmer, Wellesley, MA). For each run, the auto-correlation function from the two photodiodes was calculated by an ALV-6000 digital correlator (ALV, Langen, Germany). Sixty runs of 90 s were averaged to yield the final data.
The auto-correlation curve (Fig. S2) was fitted by : where N is the average number of fluorescent labels in the excitation volume, described as a 2D Gaussian beam, p the fraction of molecules in the triplet state, τ t the relaxation time of the triplet state and τ l is the diffusion time of the label through the beam waist ω. Under onephoton excitation the diffusion time is given by l l D 4 / 2 ω τ = (38), where D l is the 3D diffusion coefficient of the fluorescent label in the buffer (PBS). The calibration of the FCS setup, as well as the calculation of the hydrodynamic radius of the fusion protein EcoRV-scRM6 labeled with Cy3B, were done as previously described for the two-photon setup. Note that the diffusion times measured with the one-photon setup are not comparable with those measured with the two-photon setup, since the focal volume is much larger in the former case than in the latter one. Figure S2. FCS auto-correlation curves for EcoRV labeled with Cy3B and the fusion protein EcoRV-scRM6 labeled with Cy3B. The curves were normalized to 1. Calibration was performed using fluorescein. Solid lines are fit of the experimental data. Figure S3. A schematic display of EcoRV-scRM6 fusion protein. EcoRV is presented in magenta and scRM6 in orange. r p and r l are the radii of protein and label, respectively.
In order to measure the effective radius r l of one of the two scRM6 proteins fused to EcoRV, we used FCS to measure the 3D translational diffusion coefficient D RV-FP of the fusion protein double labeled with Cy3B. Comparison of D RV-FP with the 3D translational diffusion coefficient D RV of EcoRV-Cy3B, also measured by FCS, gives access to r l assuming that the linear friction coefficient ξ RV-FP of the fusion protein can be established as a function of r l and the radius of EcoRV r p .
Assuming that r l < r p, the linear friction coefficients of the fusion protein along x-and y-axes ( Figure S3) are the same, and depend on both the radius of EcoRV and the label, whereas the friction coefficient along the z-axis is independent of the label radius:  can be directly derived from the ratio τ RV-FP / τ RV .

Sliding of EcoRV-QD605 PEG 11 and EcoRV-scRM6
Single EcoRV molecules sliding along DNA were observed using a previously described setup (8). Typical movie sequences and single enzyme trajectories along the DNA are shown in Figure S4.