Nonspecifically bound proteins spin while diffusing along DNA

Abstract

It is known that DNA-binding proteins can slide along the DNA helix while searching for specific binding sites, but their path of motion remains obscure. Do these proteins undergo simple one-dimensional (1D) translational diffusion, or do they rotate to maintain a specific orientation with respect to the DNA helix? We measured 1D diffusion constants as a function of protein size while maintaining the DNA-protein interface. Using bootstrap analysis of single-molecule diffusion data, we compared the results to theoretical predictions for pure translational motion and rotation-coupled sliding along the DNA. The data indicate that DNA-binding proteins undergo rotation-coupled sliding along the DNA helix and can be described by a model of diffusion along the DNA helix on a rugged free-energy landscape. A similar analysis including the 1D diffusion constants of eight proteins of varying size shows that rotation-coupled sliding is a general phenomenon. The average free-energy barrier for sliding along the DNA was 1.1 +/- 0.2 k(B)T. Such small barriers facilitate rapid search for binding sites.

Figure 1

Models and definitions. (a) Schematic of linear diffusion model. Protein with radius R translates parallel to DNA axis (D₁ for the linear model is independent of protein offset from the DNA axis; an offset of zero is depicted here). (b) Schematic of helical diffusion model. Protein center of mass translates along a helical path. The width of the helical path is parameterized by R_OC, the minimum distance between the protein’s center of mass and the DNA axis. The protein’s DNA-binding site always faces the DNA axis, imposing coupling between protein translation and protein body-centric rotation. (c) Cartoon of rugged free-energy landscape U(z) experienced by sliding protein molecule according to the helical diffusion model. System free energy and barrier heights to translocation are heterogeneous, depending on protein position in a heterogeneous base sequence. Each minimum corresponds to binding in register with a particular base pair, while each maximum corresponds to the transition state for sliding to the adjacent position. The rms variation of landscape energy is parameterized as ε. To slide along z to the adjacent base pair register, the protein must rotate by about 2π/10 radians in order to maintain contact between the protein’s DNA-binding site and the newly targeted base pair in the DNA helix. The hydrodynamic friction on the protein opposing this rotation-coupled movement along the DNA helix dominates the resistance to translocation of the protein molecule.

Figure 2

Schematic of the flow-stretching and fluorescence imaging apparatus (reproduced from ref. 3) and diffusion of hOggl. (a) Inverted microscope fitted for total internal reflection fluorescence imaging with mounted flow cell. (b) Flow cell detail. (c) Schematic of flow-stretched λ DNA molecule (not to scale). Buffer solution flows over glass coverslip to which double-stranded λ DNA, 16 µm in length, is attached by one end. (d) One-dimensional diffusion trajectories of hOgg1 conjugates of two different sizes, hOgg1-Cy3B (black lines) and hOggl-PEG-streptavidin-Alexa Fluor 546 (gray lines), diffusing along DNA. Upper traces on left axis correspond to motion along the DNA, ‘x(t) (bp)’. Lower traces on right axis correspond to motion transverse to DNA, ‘y(t) (bp)’.

Figure 3

Test of the diffusion models by protein size dependence with consistent (hOgg1) DNA-binding interface. (a) Test of the linear diffusion model. One-dimensional diffusion constants of hOggl and hOggl-streptavidin sliding along double-stranded DNA versus the inverse protein radius, 1/R, which is expected to give a linear relationship for molecules sliding along DNA with no rotational coupling. The fit, with just one adjustable parameter, is very poor, giving a reduced χ² value of 386. The ordinal error bars represent 95% confidence intervals for D₁ based on the single-molecule data, while the error bars on the abscissa indicate uncertainty in 1/R. (b) Test of the helical diffusion model. The same diffusion constant data from a plotted versus 1/[R³ + ¾R(R_OC)²], which is expected to give a linear relationship for molecules undergoing rotation-coupled sliding along the DNA helix, where the DNA-binding site on the protein maintains contact with the DNA. Most of the energy dissipated by such a sliding molecule is consumed by friction from protein rotation and circumnavigation of the DNA axis. The fit, with just one adjustable parameter, is satisfactory, giving a reduced χ² value of 0.75. The error bars here are similar to those of a except that uncertainty in R_OC is additionally reflected.

Figure 4

Global analysis of a diverse set of DNA-binding proteins according to the linear and helical models. Plotted are values of D₁ for the human hOgg1-Cy3B, hOgg1-streptavidin (this work), B. st. MutY (this work) and E. coli MutM M74A (this work) DNA glycosylases, adenoviral AVP-pVIc complex (this work), E. coli LacI-YFP dimers, the BamHI restriction endonuclease dimer (this work), and the Klenow fragment of E. coli DNA polymerase I (this work). (a) Comparison of the data with the linear diffusion model (values of D₁ versus 1/R). The fit, with just one adjustable parameter, is incongruent with the trend in the data (coefficient of determination, R² = 0.52), revealing a poor description of the size dependence in this dataset by the linear diffusion model. (b) Comparison of the data with the helical diffusion model (values of D₁ versus 1/[R³ + ¾R(R_OC)²]). This fit, with just one adjustable parameter, quite satisfactorily describes the trend in the data (coefficient of determination, R² = 0.94), indicating the consistency of these data with the rotation-coupled sliding model. The error bars for each data point describe the same uncertainties represented in Figure 3. The gray dashed lines represent bounds on the model prediction reflecting the observational variation in ε. (c) ε calculated for sliding on a rough energy landscape for the eight proteins appearing in b. The error bars correspond to 95% confidence intervals.