How a protein searches for its specific site on DNA: The role of intersegment transfer

Proteins are known to locate their specific targets on DNA up to two orders of magnitude faster than predicted by the Smoluchowski three-dimensional diffusion rate. One of the mechanisms proposed to resolve this discrepancy is termed “intersegment transfer.” Many proteins have two DNA binding sites and can transfer from one DNA segment to another without dissociation to water. We calculate the target search rate for such proteins in a dense globular DNA, taking into account intersegment transfer working in conjunction with DNA motion and protein sliding along DNA. We show that intersegment transfer plays a very important role in cases where the protein spends most of its time adsorbed on DNA.

Figure 1

(Color online) A DNA globule. The long DNA is forced to return many times by the wall of a prokaryotic cell. On the right, a blown-up view shows a typical region of the transient network at a scale much smaller than the DNA persistence length $p$. This figure represents a very dense case, where the nearest-neighbor distance between DNA segments, each of length $p$, is shorter than $p$.

Figure 2

Schematic dependences of the acceleration rate on the adsorption strength $y$, with (solid line) or without (dashed line) DNA motion and intersegment transfer. Both the acceleration rate $t_s∕t$ and $y$ are given in logarithmic scale.

Figure 3

“Phase diagram” for the acceleration rate $t_s∕t$ in the plane of $y$ and $N{l}^3$, where $l$ is held constant. Both the $y$ and $N{l}^3$ axes are in the logarithmic scale. The ratio $t_s∕t$ is shown in black on the background of each region. (a) Shows scaling dependences without inter-DNA transfer; (b) gives results with inter-DNA transfer, where $t_s∕t$ saturates at large $y$.

Figure 4

Schematic dependences of acceleration rate on $y$ for a semidilute $\left(N{l}^3>1\right)$ solution of short DNA pieces (a) without inter DNA transfer; (b) and (c) with inter DNA transfer. The fraction next to each curve shows its slope (the power dependence of $t_s∕t$ on $y$).

Figure 5

(Color online) Collision of a DNA molecule with its nearest neighbor at distance $r_p$ (other DNA molecules are not shown).

Figure 6

“Phase diagram” for the dissociation rate under the influence of inter DNA transfer.

Figure 7

(Color online) “Phase diagram” for the acceleration rate at large $y$ on globular DNA, where the intersegment transfer plays an important role in the target search.