Single Molecule Measurements of Repressor Protein 1D Diffusion on DNA

We used single-molecule imaging techniques and measured the one-dimensional diffusion of LacI repressor proteins along elongated DNA to address the long-standing puzzle of why some proteins find their targets faster than allowed by 3D diffusion. Our analysis of the LacI transcription factor’s diffusion yielded four main results: (1) LacI diffuses along nonspecific sequences of DNA in the form of 1D Brownian motion; (2) the observed 1D diffusion coefficients $D_1$ vary over an unexpectedly large range, from $2.3\times {10}^{-12}{\mathrm{cm}}^2/\mathrm{s}$ to $1.3\times {10}^{-9}{\mathrm{cm}}^2/\mathrm{s}$; (3) the lengths of DNA covered by these 1D diffusions vary from 120 nm to 2920 nm; and (4) the mean values of $D_1$ and the diffusional lengths indeed predict a LacI target binding rate 90 times faster than the 3D diffusion limit.

Figure 1

(a) Schematics of a GFP-LacI (green) bound $lac{O}_{256}$-DNA monomer and dimer (red). (b) Elongation of the DNA. (c) Frame averaged superposed image of GFP-LacI bound to an elongated $lac{O}_{256}$-DNA dimer. The scale bar is $1\mu \mathrm{m}$. (d) A GFP-LacI monomer of frequent blinking and unitary bleaching. (e) A GFP-LacI monomer that blinked, recovered the first bleaching in 3 s, and finally irreversibly bleached. (f) The GFP-LacI dots for the first 12 frames of (e), showing blinking at frames 2 and 7, and bleaching at frame 10. (g) A GFP-LacI dimer with two bleaching events.

Figure 2

(a) Frame averaged, superposed image of a GFP-LacI molecule diffusing along DNA. The two large dots at the DNA ends are LacI-$lac{O}_{256}$ sites, and the green segment on the nonspecific DNA (arrow) is the trace of the diffusing GFP-LacI. (b) Image series of the diffusing protein (arrow) of selected clear relative displacements corresponding to green dots in (c), the displacement vs $t$ curve of the diffusing protein. (d) Fluorescence time trace of the diffusing GFP-LacI. It is a dimer. (e) Gaussian distribution of $x_i-x_{i-1}$. The scale bar is $0.5\mu \mathrm{m}$.

Figure 3

(a) $x$ vs $t$ for 70 trajectories. (b) Nondegenerate $x_i-x_{i-n}$ distributions. (c) ${\mathrm{MSD}}_{(n,N)}$ vs $n$ for the 15 colored walks in linear scale and (d) in log-log scale. The arrows in (a), (c), and (d) denote the walk in Fig. 2. The dashed lines in (c) and (d) are the fit of Eq. (2) to the top trajectory.

Figure 4

(a) $D_1$ distribution of the 15 trajectories. (b) $D_1$ vs fractional bound location on the nonspecific segment of the $Lac{O}_{256}$-DNA dimer. The error bars were obtained from the fit of ${\mathrm{MSD}}_{(n,N)}$ to $n$ with weighted errors at each $n$ given by Eq. (3). (c) Histogram of $x_{\max }-x_{\min }=l_d$ for the 70 trajectories. The solid line is a Gaussian fit with a mean of $500\pm 220\mathrm{nm}$ ($\mathrm{mean}\pm \mathrm{SD}$). Values in (a) and (c) have been adjusted to DNA contour length.