Target search of N sliding proteins on a DNA

Abstract

At low to moderate ambient salt concentrations, DNA-binding proteins bind relatively tightly to DNA, and only very rarely detach. Intersegmental transfer due to DNA-looping can be excluded by applying an external pulling force to the DNA molecule. Under such conditions, we explore the targeting dynamics of N proteins sliding diffusively along DNA in search of their specific target sequence. At lower densities of binding proteins, we find a reduction of the characteristic search time proportional to N(-2), with corrections at higher concentrations. Rates for detachment and attachment of binding proteins are incorporated in the model. Our findings are in agreement with recent single molecule studies in the presence of bacteriophage T4 gene 32 protein for which the unbinding rate is much lower than the specific binding rate.

FIGURE 1

Classical Berg/von Hippel model of target search.

FIGURE 2

Optical tweezers setup (30). Single λ-DNA molecules are attached at the 3′ ends of each strand to two polystyrene beads. One bead is held by a glass micropipette by suction, whereas the other bead is held in an optical trap, formed by two counter-propagating laser beams focused to a common point. Force-extension curves were obtained by moving the micropipette and measuring the resulting force on the bead via the displacement relative to the focus of the optical trap. From the force-extension data, the binding rates displayed in Fig. 3 could be determined as described in Pant et al. (22,23). (Inset) Melting of the double-strand by gp32 or ^*I occurs from the pre-existing boundaries at the ends of the molecule.

FIGURE 3

Measured rate of binding of the T4 gene 32 protein truncate ^*I as a function of protein concentrations in 75 mM salt (solid square), 100 mM salt (solid triangle), 150 mM salt (open square), and 200 mM salt (open triangle). The fitted lines have slopes of 1.74 ± 0.35, 1.85 ± 0.24, 2.08 ± 0.39, and 1.95 ± 0.17, respectively. The data obtained at 100 mM salt are fitted by the theoretical model in Fig. 5.

FIGURE 4

Mean first passage time T(n₀) of target search on a large, one-sided system (one target located at x = 0), as a function of the density n₀ of excluding walkers that cannot occupy the same lattice site. The maximum density is n₀ = 30%. The dashed line corresponds to the exact result for dimensionless diffusion coefficient from Eq. 16 obtained in the continuum approximation. We see a slight deviation for larger densities. Each data point corresponds to 10⁵ runs, except for 10³ realizations for the lowest density. Note the comparatively small error bars.

FIGURE 5

Dimensional binding rate k_a in 1/s as function of protein concentration C in M, converted from Fig. 4 for parameters corresponding to 100 mM salt. The fitted one-dimensional diffusion constant for sliding along the dsDNA is D_1d = 3.3 · 10⁻⁹cm²/s, located nicely within the experimental value 10⁻⁸…10⁻⁹ cm²/s (see Refs. 22,23).

FIGURE 6

Behavior of the mean first passage time T(N) as a function of the number N of TFs attached to a DNA of length 1000b according to Eq. 2, for the dilute case (solid line), TF-size λ = b (long-dashed line) and λ = 10b (short-dashed line). Excluded volume effects reduce the target search time T(N).