Base-sequence-dependent sliding of proteins on DNA

The possibility that the sliding motion of proteins on DNA is influenced by the base sequence through a base pair reading interaction, is considered. Referring to the case of the T7 RNA-polymerase, we show that the protein should follow a noise-influenced sequence-dependent motion which deviate from the standard random walk usually assumed. The general validity and the implications of the results are discussed.

Figure 1

Four base pairs. Arrows indicate the location of the hydrogen accepting

Figure 2

Diffusion dynamics for the T7 RNA-polymerase-DNA interaction (symbols), for energy parameters: $E_t=E_{\mathit{min}}$, $\beta ϵ=0.5$ (squares); $E_t=E_{\mathit{min}}$, $\beta ϵ=1$ (open circles); $E_t=E_{\mathit{max}}$, $\beta ϵ=1$ (triangles). Time is measured in time units. Solid lines show the dynamics obtained on an artificial Gaussian energy landscape with $E_{\mathit{min}}=-Nϵ$, $E_{\mathit{max}}\approx Nϵ∕2$ (see the discussion in Sec. 4).

Figure 3

$2D*=⟨{(n-n_0)}^2⟩∕T_{n0}^n$ as a function of the adimensional parameter $\beta ϵ$ (full lines), and the corresponding $2D$ directly evaluated by fitting the large time diffusion (symbols), for corresponding different values of the threshold energy: $E_t=E_{\mathit{min}}$ (open circles), $E_t=0$ (triangles) and $E_t=E_{\mathit{max}}$ (diamonds). Time is measured in time units (t.u.) and mean square displacement in squared base pairs $\left({\mathrm{bps}}^2\right)$.

Figure 4

Dispersion (in ${\mathrm{bps}}^2$) versus time (in time units t.u.) for our model (upper curve), and for linear diffusion (straight line), for $\beta ϵ=1$. The linear diffusion approximation systematically overestimates the time needed for an enzyme to diffuse over a distance $l=\sqrt{{\left(\Delta n\right)}^2}$ base pairs along DNA. Segments between the two curves show differences between the two descriptions. The relative mistake $\Delta t∕t$ is $\approx 70\%$ for $l=30$ and $\approx 37\%$ for $l=50$.

Figure 5

Dynamic behavior, obtained on the artificial Gaussian energy landscape, for $N=10$ (full circles), $N=14$ (open circles), $N=20$ (squares), with $\beta ϵ=1$ (upper curves) or 0.2 (lower curves). Time is measured in time units (t.u.) and mean squared distance in squared base pairs $\left({\mathrm{bps}}^2\right)$; see the text for details.