Strong physical constraints on sequence-specific target location by proteins on DNA molecules

Abstract

Sequence-specific binding to DNA in the presence of competing non-sequence-specific ligands is a problem faced by proteins in all organisms. It is akin to the problem of parking a truck at a loading bay by the side of a road in the presence of cars parked at random along the road. Cars even partially covering the loading bay prevent correct parking of the truck. Similarly on DNA, non-specific ligands interfere with the binding and function of sequence-specific proteins. We derive a formula for the probability that the loading bay is free from parked cars. The probability depends on the size of the loading bay and allows an estimation of the size of the footprint on the DNA of the sequence-specific protein by assaying protein binding or function in the presence of increasing concentrations of non-specific ligand. Assaying for function gives an 'activity footprint'; the minimum length of DNA required for function rather than the more commonly measured physical footprint. Assaying the complex type I restriction enzyme, EcoKI, gives an activity footprint of approximately 66 bp for ATP hydrolysis and 300 bp for the DNA cleavage function which is intimately linked with translocation of DNA by EcoKI. Furthermore, considering the coverage of chromosomal DNA by proteins in vivo, our theory shows that the search for a specific DNA sequence is very difficult; most sites are obscured by parked cars. This effectively rules out any significant role in target location for mechanisms invoking one-dimensional, linear diffusion along DNA.

Figure 1

Diffusion mechanisms for a protein (oval) to reach its DNA target site (black rectangle) on a segment of DNA (open rectangle). The leftmost protein is using linear diffusion (sliding) to randomly search along the DNA molecule for the target. The middle protein is using multiple dissociation/association (hopping) events. It takes two random steps towards the target but then hops away from the target and then onto another DNA segment. The rightmost protein has two DNA-binding sites and can bridge between different DNA segments during its search for the target.

Figure 2

Non-specific DNA-binding ligands (small ovals) bind to a DNA segment (open rectangle) containing a target site (black rectangle) for a site-specific protein (large shaded oval). The small ligands cover n base pairs of DNA and the large protein covers g base pairs. The upper DNA molecule is coated with perfectly ‘parked’ ligands and the target site for the site-specific protein is blocked. The middle panel shows sub-optimal parking as gaps between consecutive ligands that are not multiples of n. Complete coverage of this DNA molecule with ligands is impossible and one of the ligands is obstructing the target site of the site-specific protein. The lower panel shows sub-optimal coverage by the small ligands but the site-specific protein has been able to bind to its unobstructed target site.

Figure 3

Theoretical curves for the probability, p_per(g; B, N), of a gap of g base pairs completely encompassing the loading bay for the truck as a function of the fractional coverage (nB/N) of the DNA lattice by cars, calculated using Equation 3. There are B cars bound to a lattice of N = 4000 bp. The solid lines are for car size n = 10 bp and loading bay gap size, g, varying from 100, 20, 10, 5 and 1 bp from left to right. The dashed lines are for n = 4 with g = 100 (left-hand curve) and 20 (right-hand curve). The dotted lines are for n = 1 with g = 100 (left-hand curve) and 20 (right-hand curve). (Note that complete saturation of the lattice is reached at B/N = 0.1 for n = 10 as nB/N = 1 and in general at 1/n. Curves for g = 1 are independent of n.)

Figure 4

Activity footprint determination, using Equation 3 and the law of mass action (Supplementary Data, Equation S18), for the inhibition of EcoKI activity on circular plasmid DNA as a function of saturation of the plasmid with the intercalating dye molecule YOYO. The ordinate axis shows the experimental rate constants for ATP hydrolysis (filled circles) and DNA cleavage (open circles) expressed as fractions of the rate constants measured in the absence of YOYO. The DNA (N = 4361 bp) has one target site for the enzyme and YOYO is assumed to be a car binding irreversibly with n = 4 bp. The binding affinity, K_d, of EcoKI for its target was fixed at 2 nM (17) with [EcoKI] = 67 nM and [DNA] = 50 nM. The only variables in fitting were the loading bay gap size, g, and an ordinate scaling factor which deviated <15% from the expected value of 0.02 (given by 1/[DNA]). Data at high saturation are taken from Keatch et al. (31); data at low saturation have been added using the same experimental methods as used previously (31).

Figure 5

The average size (N/B − n), in base pairs, of a gap between consecutive cars as a function of lattice (N = 4000) saturation with cars of different sizes. The curves from left to right have cars sizes of n = 1, 4, 10 and 100. The E.coli chromosome has a fractional coverage varying between 0.1 and 0.5 depending upon growth conditions.