Search by proteins for their DNA target site: 1. The effect of DNA conformation on protein sliding

Abstract

The recognition of DNA-binding proteins (DBPs) to their specific site often precedes by a search technique in which proteins slide, hop along the DNA contour or perform inter-segment transfer and 3D diffusion to dissociate and re-associate to distant DNA sites. In this study, we demonstrated that the strength and nature of the non-specific electrostatic interactions, which govern the search dynamics of DBPs, are strongly correlated with the conformation of the DNA. We tuned two structural parameters, namely curvature and the extent of helical twisting in circular DNA. These two factors are mutually independent of each other and can modulate the electrostatic potential through changing the geometry of the circular DNA conformation. The search dynamics for DBPs on circular DNA is therefore markedly different compared with linear B-DNA. Our results suggest that, for a given DBP, the rotation-coupled sliding dynamics is precluded in highly curved DNA (as well as for over-twisted DNA) because of the large electrostatic energy barrier between the inside and outside of the DNA molecule. Under such circumstances, proteins prefer to hop in order to explore interior DNA sites. The change in the balance between sliding and hopping propensities as a function of DNA curvature or twisting may result in different search efficiency and speed.

Figure 1.

Structural characterization of linear (length, 100 bp) and circular (circumference, 100 bp) DNA molecules. (A) Conformations of an ideal B-DNA (partly shown) and circular DNA. Unlike the uniform major groove widths (W_B-DNA = 10.8 Å) observed in linear B-DNA, circular DNA shows wider major grooves on the exterior of the DNA circle (W_out) and narrower major groove widths inside (W_in) the circle. (B) Correlations between the major groove widths (black) and the electrostatic potential (red) for a linear (upper panel) and circular (lower panel) DNA molecule calculated at the reference points shown by the blue spheres in (A) (see Materials and Methods section for details). (C) Correlation between the circumference (in bp) of circular DNA and its curvature (defined as 1/r, where r is the radius of the circular DNA). The curvature of linear DNA is 0 by definition. (D) Correlations between the changes in major groove width (black) and potential energy (EP; red) with the curvature of the circular DNA. The change in width and potential energy are determined by ΔW = W_out− W_in and ΔEP = EP_out − EP_in.

Figure 2.

Effect of salt concentration on the interplay between sliding (S), hopping (H) and 3D diffusion (D) for the Sap1 protein on (A) linear DNA molecule of length 100 bp and (B) circular DNA molecule with circumference 100 bp.

Figure 3.

Effect of DNA curvature on DBP search dynamics. (A) Proportion of sliding (S), hopping (H) and 3D diffusion (D) dynamics adopted by the DBP as a function of the difference between the widths of exterior and interior major grooves (ΔW; caused by changes in DNA curvature) for circular DNA molecules (circumference, 50–500 bp) at 0.02 M salt concentration. (B) Sliding and hopping dynamics are further characterized depending on the position of Sap-1 with respect to circular DNA. Triangles and circles represent the fraction of sliding and hopping events during which the protein is located outside and inside of the circular DNA, respectively. Gray shaded region denotes DNA minicircles of circumference ≤ 100 bp (also characterized by large DNA curvatures).

Figure 4.

Role of DNA curvature in determining the efficiency of DNA search performed by Sap-1 at Cs = 0.02 M. (A) The efficiency is measured by the number of base pairs probed by Sap-1 using sliding dynamics during the simulation and presented as a function of the difference between the outer and inner major groove widths, ΔW (caused by changes in DNA curvature). (B) The one-dimensional diffusion coefficient D₁ calculated for the portions of the simulation during which Sap-1 scanned the DNA contour via pure sliding (blue circles) and for the portions during which Sap-1 was bound to the DNA (green circles) by either the sliding or hopping modes of dynamics. As sliding frequency decreases sharply for ΔW ≥ 1.8 Å, D₁ values were not calculated beyond this point. The extreme right point (close to ΔW = 4.0) is an outlier, which represents the results for a circular DNA with a circumference of 50 bp. The inner core of this DNA is smaller than the size of Sap-1, which forces Sap-1 to diffuse freely and prevents sliding and hopping interactions. Gray shaded region denotes DNA minicircles of circumference ≤ 100 bp.

Figure 5.

Trace of the search path of Sap1 around circular DNA of circumference (A) 200 bp, (B) 100 bp, (C) 70 bp and (D) 60 bp at 0.02 M salt concentration. DNA is colored orange, while cyan and green represent the sliding and hopping modes, respectively. The low salt concentration causes 3D diffusion events to occur only very rarely, which facilitates characterization of the bound protein–DNA state.

Figure 6.

Free-energy surfaces F(E_DH, R) for circular DNA structures of circumference (A) 100 bp, (B) 70 bp and (C) 60 bp, where E_DH is the electrostatic energy calculated using Debye–Hückel relations (see Materials and Methods section) at a salt concentration of 0.02 M. R represents the distance between the center of mass of the recognition helix of Sap-1 and the center of the closest base pairs in the circular DNA. Therefore, minima correspond to a small R, which denotes sliding, whereas the existence of hopping dynamics can be found at higher R. kT denotes Boltzmann constant times temperature, where the temperature is set such that Sap-1 is in a fully folded state during the simulations.

Figure 7.

Role of DNA supercoiling on search dynamics of DBPs. (A) Variation in major groove width for minicircle DNA with linking number (Δlk) of −1, 0 and 3. (B) Major groove widths located inside the DNA circle (W_in) and the associated electrostatic potential (EP_in) are presented as a function of change in linking number (Δlk). (C) Proportion of sliding, hopping and diffusion dynamics as a function of Δlk (and, hence, as a function of W_in) in circular DNA at Cs = 0.02 M. (C) Number of base pairs probed by Sap-1 using sliding, hopping and 3D diffusion dynamics on 100 bp circular DNA conformations with varying numbers of helical twists (Δlk). (D) Diffusion coefficient (D₁) calculated for the portions of the simulation during which Sap-1 scanned the DNA contour via pure sliding (blue circles) and for the portions during which Sap-1 was bound to the DNA (green circles) by either the sliding or hopping mode of dynamics. As sliding frequency decreases sharply for Δlk ≥ 1, D1 values were not calculated beyond this point.

Figure 8.

Traces of the search path of Sap-1 on 100 bp circular DNA twisted to various extents around the double helix. A DNA conformation with Δlk < 0 denotes an under-twisted DNA structure having wider internal groove widths into which DBPs fit easily to perform smooth sliding. A DNA conformation with Δlk > 0 represents an over-twisted structure. With increasing DNA twisting, groove widths become narrower and therefore prevent sliding dynamics by not allowing DBPs to fit well inside the major groove.