Nonspecific DNA-Protein Interaction: Why Proteins Can Diffuse along DNA

Recent single molecule experiments have reported that DNA binding proteins (DNA-BPs) can diffuse along DNA. This suggests that interactions between proteins and DNA play a role during the target search even far from their specific site on DNA. Here we show by means of Monte Carlo simulations and analytical calculations that there is a counterintuitive repulsion between the two oppositely charged macromolecules at a nanometer range. For the concave shape of DNA-BPs, and for realistic protein charge densities, we find that the DNA-protein interaction free energy has a minimum at a finite surface-to-surface separation, in which proteins can easily slide. When a protein encounters its target, the free energy barrier is completely counterbalanced by the H-bond interaction, thus enabling the sequence recognition.

Figure 1

Influence of protein shape on the interaction. (a) Schematic view of the model proteins. The height and diameter of the cylindrical proteins (2,3) are both 5 nm, as well as the side of the cubic protein (4) and the radius of the sphere. The hollow cylindrical proteins (3) have a cylindrical cavity, of curvature $C_{\perp }=0$, $-0.25$, $-0.5$, or $-1{\mathrm{nm}}^{-1}$. (b) Free energy of the DNA-protein systems computed by MC simulations. The protein and DNA are immersed in a monovalent salt whose Debye length ${\lambda }_D=1\mathrm{nm}$ [27] corresponds to physiological conditions. The standard deviation of the free energy is $0.2k_{B}T$.

Figure 2

Influence of protein charge on the interaction. Free energy of the DNA-protein system for a set of protein charge densities obtained by PB theory (curves) and by MC simulations (squares). The area of the concave protein surface $S_{\mathrm{int}}$ is $15{\mathrm{nm}}^2$. The charge density is ${\sigma }_{\mathrm{prot}}=Z_{\mathrm{prot}}/S_{\mathrm{int}}$, where $Z_{\mathrm{prot}}$ is the charge of the protein at the interface. The charge density of DNA is ${\sigma }_{\mathrm{DNA}}=-1.0e{\mathrm{nm}}^{-2}$. In the MC simulations, the shape of the model DNA-BP is a cylinder of height 5 nm, with a concave interface ($C_{\perp }=-1/R_{\mathrm{DNA}}$, $C_{\parallel }=0$). The protein charges are distributed on a pattern of 16 sites, 0.1 nm below the surface of the cylindrical cavity.

Figure 3

Ionic density fields. The density is obtained by PB theory (a), and by MC simulations (b) for two protein charge densities and two distances $L$. The unit is ${\rho }^0=0.2\mathrm{mol}·{\mathrm{L}}^{-1}$ In the PB treatment, the density along the $x$ direction, perpendicular to the plates, is plotted ($x=0$ on the protein and $x=L$ on DNA). In the simulations, the ionic density in the plane perpendicular to the DNA axis is plotted.

Figure 4

Free-energy landscape. The free energy is computed along a 30 bp DNA sequence, as a function of $L$ and of the protein coordinates along DNA ($z$), for ${\sigma }_{\mathrm{prot}}=0.17|{\sigma }_{\mathrm{DNA}}|$. The gap between level lines is $k_{B}T$. The lower graph displays the free energy as a function of $L$ for each $z$ value. In both graphs, the black curve corresponds to a randomly chosen nonspecific coordinate, while the red curve corresponds to the specific site.