Effects of isolated nonspecific binders upon the search for specific targets: Absolute rates versus competition between the targets

Many biological processes involve macromolecules searching for their specific targets that are surrounded by other objects, and binding to these objects affects the target search. Acceleration of the target search by nonspecific binders was observed experimentally and analyzed theoretically, for example, for DNA-binding proteins. According to existing theories this acceleration requires continuous transfer between the nonspecific binders and the specific target. In contrast, our analysis predicts that (i) nonspecific binders could accelerate the search without continuous transfer to the specific target provided that the searching particle is capable of sliding along the binder; (ii) in some cases such binders could decelerate the target search, but provide an advantage in competition with the “binder-free” target; (iii) nonbinding objects decelerate the target search. We also show that although the target search in the presence of binders could be considered as diffusion in inhomogeneous media, in the general case it cannot be described by the effective diffusion coefficient.

Figure 1

Specific target surrounded by obstacles. (a) Obstacles are isolated from each other and from the specific target. (b) Both the obstacles and the specific target are actually the parts of the same molecule (e.g., DNA) (top), but can be represented as isolated from each other (bottom).

Figure 2

Alternative representations for the searching particle and an obstacle at the moment of collision. Left: The searching particle is represented as a point object and an obstacle is represented as a sphere of the radius $a$. Right: An obstacle is represented as a point object and the searching particle is represented as a sphere of the radius $a$. Note that coordinates of the centers for both objects remain the same for both representations.

Figure 3

Transferring of the searching particle as a result of collision. Trajectory of the particle is shown as a dashed line. For designations see the main text. Azimuthal angle is not shown. (a) Collision in the absence of sliding. (b) Collision in the presence of sliding. Sliding regions of the trajectory are shown as the dashed lines stretched parallel to the surface.

Figure 4

Positions of colliding obstacle and the searching particles relative to the center of the specific target. For designations see the main text. Azimuthal angle is not shown.

Figure 5

Dependence of the probability of reaching the target upon the volume concentration of spherical obstacles. The dependencies are normalized upon the probability for zero concentration of obstacles.

Figure 6

Distribution of obstacles around two specific targets. These targets could be viewed as representatives of multiple targets distributed in solution with the average distance 2R between them.

Figure 7

Dependence of the first-passage time to reach the target upon the volume concentration of spherical obstacles. The dependencies are normalized upon the first-passage time for zero concentration of obstacles.

Figure 8

Rod-shaped obstacles. (a) Cylindrical representation. (b) Representation as a string of beads.

Figure 9

Dependence of the probability of reaching the target upon the volume concentration of spherical and rod-shaped obstacles. The dependencies are normalized upon the probability for zero concentration of obstacles.