Kinetics of target site localization of a protein on DNA: a stochastic approach

It is widely recognized that the cleaving rate of a restriction enzyme on target DNA sequences is several orders-of-magnitude faster than the maximal one calculated from the diffusion-limited theory. It was therefore commonly assumed that the target site interaction of a restriction enzyme with DNA has to occur via two steps: one-dimensional diffusion along a DNA segment, and long-range jumps coming from association-dissociation events. We propose here a stochastic model for this reaction which comprises a series of one-dimensional diffusions of a restriction enzyme on nonspecific DNA sequences interrupted by three-dimensional excursions in the solution until the target sequence is reached. This model provides an optimal finding strategy which explains the fast association rate. Modeling the excursions by uncorrelated random jumps, we recover the expression of the mean time required for target site association to occur given by Berg et al. in 1981, and we explicitly give several physical quantities describing the stochastic pathway of the enzyme. For competitive target sites we calculate two quantities: processivity and preference. By comparing these theoretical expressions to recent experimental data obtained for EcoRV-DNA interaction, we quantify: 1), the mean residence time per binding event of EcoRV on DNA for a representative one-dimensional diffusion coefficient; 2), the average lengths of DNA scanned during the one-dimensional diffusion (during one binding event and during the overall process); and 3), the mean time and the mean number of visits needed to go from one target site to the other. Further, we evaluate the dynamics of DNA cleavage with regard to the probability for the restriction enzyme to perform another one-dimensional diffusion on the same DNA substrate following a three-dimensional excursion.     

Searching target sites on DNA by proteins: Role of DNA dynamics under confinement

DNA-binding proteins (DBPs) rapidly search and specifically bind to their target sites on genomic DNA in order to trigger many cellular regulatory processes. It has been suggested that the facilitation of search dynamics is achieved by combining 3D diffusion with one-dimensional sliding and hopping dynamics of interacting proteins. Although, recent studies have advanced the knowledge of molecular determinants that affect one-dimensional search efficiency, the role of DNA molecule is poorly understood. In this study, by using coarse-grained simulations, we propose that dynamics of DNA molecule and its degree of confinement due to cellular crowding concertedly regulate its groove geometry and modulate the inter-communication with DBPs. Under weak confinement, DNA dynamics promotes many short, rotation-decoupled sliding events interspersed by hopping dynamics. While this results in faster 1D diffusion, associated probability of missing targets by jumping over them increases. In contrast, strong confinement favours rotation-coupled sliding to locate targets but lacks structural flexibility to achieve desired specificity. By testing under physiological crowding, our study provides a plausible mechanism on how DNA molecule may help in maintaining an optimal balance between fast hopping and rotation-coupled sliding dynamics, to locate target sites rapidly and form specific complexes precisely.     

Sliding of Proteins Non-specifically Bound to DNA: Brownian Dynamics Studies with Coarse-Grained Protein and DNA Models

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.     

Linear diffusion of the restriction endonuclease EcoRV on DNA is essential for the in vivo function of the enzyme.

Linear diffusion along DNA is a mechanism of enhancing the association rates of proteins to their specific recognition sites on DNA. It has been demonstrated for several proteins in vitro, but to date in no case in vivo. Here we show that the restriction endonuclease EcoRV slides along the DNA, scanning approximately 1000 bp in one binding event. This process is critically dependent on contacts between amino acid residues of the protein and the backbone of the DNA. The disruption of single hydrogen bonds and, in particular, the alteration of electrostatic interactions between amino acid side chains of the protein and phosphate groups of the DNA interfere with or abolish effective sliding. The efficiency of linear diffusion is dependent on salt concentration, having a maximum at 50 mM NaCl. These results suggest that a nonspecific and mobile binding mode capable of linear diffusion is dependent on a subtle balance of forces governing the interaction of the enzyme and the DNA. A strong correlation between the ability of EcoRV mutants to slide along the DNA in vitro and to protect Escherichia coli cells from phage infection demonstrates that linear diffusion occurs in vivo and is essential for effective phage restriction.     

The Role of Noncognate Sites in the 1D Search Mechanism of EcoRI

A one-dimensional (1D) search is an essential step in DNA target recognition. Theoretical studies have suggested that the sequence dependence of 1D diffusion can help resolve the competing demands of a fast search and high target affinity, a conflict known as the speed-selectivity paradox. The resolution requires that the diffusion energy landscape is correlated with the underlying specific binding energies. In this work, we report observations of a 1D search by quantum dot-labeled EcoRI. Our data supports the view that proteins search DNA via rotation-coupled sliding over a corrugated energy landscape. We observed that whereas EcoRI primarily slides along DNA at low salt concentrations, at higher concentrations, its diffusion is a combination of sliding and hopping. We also observed long-lived pauses at genomic star sites, which differ by a single nucleotide from the target sequence. To reconcile these observations with prior biochemical and structural data, we propose a model of search in which the protein slides over a sequence-independent energy landscape during fast search but rapidly interconverts with a “hemispecific” binding mode in which a half site is probed. This half site interaction stabilizes the transition to a fully specific mode of binding, which can then lead to target recognition.     

Tracking of Single Quantum Dot Labeled EcoRV Sliding along DNA Manipulated by Double Optical Tweezers

Fluorescence microscopy provides a powerful method to directly observe single enzymes moving along a DNA held in an extended conformation. In this work, we present results from single EcoRV enzymes labeled with quantum dots which interact with DNA manipulated by double optical tweezers. The application of quantum dots facilitated accurate enzyme tracking without photobleaching whereas the tweezers allowed us to precisely control the DNA extension. The labeling did not affect the biochemical activity of EcoRV checked by directly observing DNA digestion on the single molecule level. We used this system to demonstrate that during sliding, the enzyme stays in close contact with the DNA. Additionally, slight overstretching of the DNA resulted in a significant decrease of the 1D diffusion constant, which suggests that the deformation changes the energy landscape of the sliding interaction. Together with the simplicity of the setup, these results demonstrate that the combination of optical tweezers with fluorescence tracking is a powerful tool for the study of enzyme translocation along DNA.     

Protein Sliding along DNA: Dynamics and Structural Characterization

Efficient search of DNA by proteins is fundamental to the control of cellular regulatory processes. It is currently believed that protein sliding, hopping, and transfer between adjacent DNA segments, during which the protein nonspecifically interacts with DNA, are central to the speed of their specific recognition. In this study, we focused on the structural and dynamic features of proteins when they scan the DNA. Using a simple computational model that represents protein-DNA interactions by electrostatic forces, we identified that the protein makes use of identical binding interfaces for both nonspecific and specific DNA interactions. Accordingly, in its one-dimensional diffusion along the DNA, the protein is bound at the major groove and performs a helical motion, which is stochastic and driven by thermal diffusion. A microscopic structural insight into sliding from our model, which is governed by electrostatic forces, corroborates previous experimental studies suggesting that the active site of some regulatory proteins continually faces the interior of the DNA groove while sliding along sugar-phosphate rails. The diffusion coefficient of spiral motion along the major groove of the DNA is not affected by salt concentration, but the efficiency of the search can be significantly enhanced by increasing salt concentration due to a larger number of hopping events. We found that the most efficient search comprises ∼ 20% sliding along the DNA and ∼ 80% hopping and three-dimensional diffusion. The presented model that captures various experimental features of facilitated diffusion has the potency to address other questions regarding the nature of DNA search, such as the sliding characteristics of oligomeric and multidomain DNA-binding proteins that are ubiquitous in the cell.     

A Model of Sequence-Dependent Protein Diffusion Along DNA

We introduce a probabilistic model for protein sliding motion along DNA during the search of a target sequence. The model accounts for possible effects due to sequence-dependent interaction between the nonspecific DNA and the protein. Hydrogen bonds formed at the target site are used as the main sequence-dependent interaction between protein and DNA. The resulting dynamical properties and the possibility of an experimental verification are discussed in details. We show that, while at large times the process reaches a linear diffusion regime, it initially displays a sub-diffusive behavior. The sub-diffusive regime can last sufficiently long to be of biological interest.     

The rotation-coupled sliding of EcoRV

It has been proposed that certain type II restriction enzymes (REs), such as EcoRV, track the helical pitch of DNA as they diffuse along DNA, a so-called rotation-coupled sliding. As of yet, there is no direct experimental observation of this phenomenon, but mounting indirect evidence gained from single-molecule imaging of RE-DNA complexes support the hypothesis. We address this issue by conjugating fluorescent labels of varying size (organic dyes, proteins and quantum dots) to EcoRV, and by fusing it to the engineered Rop protein scRM6. Single-molecule imaging of these modified EcoRVs sliding along DNA provides us with their linear diffusion constant (D(1)), revealing a significant size dependency. To account for the dependence of D(1) on the size of the EcoRV label, we have developed four theoretical models describing different types of motion along DNA and find that our experimental results are best described by rotation-coupled sliding of the protein. The similarity of EcoRV to other type II REs and DNA binding proteins suggests that this type of motion could be widely preserved in other biological contexts.     

Searching DNA via a “Monkey Bar” Mechanism: The Significance of Disordered Tails

The search through nonspecific DNA for a specific site by proteins is known to be facilitated by sliding, hopping, and intersegment transfer between separate DNA strands, yet the driving forces of these protein dynamics from the molecular perspective are unclear. In this study, molecular features of the DNA search mechanism were explored for three homologous proteins (the HoxD9, Antp, and NK-2 homeodomains) using a simple computational model in which protein-DNA interactions are represented solely by electrostatic forces. In particular, we studied the impact that disordered N-terminal tails (N-tails), which are more common in DNA-binding proteins than in other proteins, have on the efficiency of DNA search. While the three homeodomain proteins were found to use similar binding interfaces in specific and nonspecific interactions with DNAs, their different electrostatic potentials affect the nature of their sliding dynamics. The different lengths and net charges of the N-tails of the homeodomains affect their motion along the DNA. The presence of an N-tail increases sliding propensity but slows linear diffusion along the DNA. When the search is performed in the presence of two parallel DNA molecules, a direct transfer, which is facilitated by the protein tail, from one nonspecific DNA to another occurs. The tailed proteins jump between two DNA molecules through an intermediate in which the recognition helix of the protein is adsorbed to one DNA fragment and the N-tail is adsorbed to the second, suggesting a “monkey bar” mechanism. Our study illustrates how the molecular architecture of proteins controls the efficiency of DNA scanning.     

Obstacle bypass in protein motion along DNA by two-dimensional rather than one-dimensional sliding

Site-specific DNA-binding proteins locate their target sites by facilitated diffusion. Several proteins have been shown to slide along DNA in vitro. However, whereas sliding is often envisaged as one-dimensional tracking of the DNA major groove, such a mechanism would not allow linear diffusion over long distances in vivo, where short stretches of free DNA are delimited by bound proteins. I propose a two-dimensional sliding mechanism, in which the protein diffuses freely on the cylindrical DNA surface, and I present experiments that can distinguish between one- and higher-dimensional diffusion along the DNA contour length. At 100 mm NaCl, translocation of EcoRI restriction endonuclease between sites on two DNA helices connected by a Holliday junction is as efficient as between sites on the same helix, indicating a three-dimensional mechanism. At 25 mm NaCl, translocation between sites on the same DNA helix is more efficient, indicating a role for sliding at low ionic strength. Obstacles attached to the major groove of one face of the DNA helix did not interfere with sliding, regardless of their orientation relative to the cleavage sites. This result is compatible with two-dimensional but not one-dimensional sliding. As illustrated by Monte-Carlo simulation, two-dimensional sliding may not only allow proteins to move around nucleosomes in vivo but also reduce the redundancy of their search for the target site.     

Timing facilitated site transfer of an enzyme on DNA

Many enzymes that react with specific sites in DNA have the property of facilitated diffusion, in which the DNA chain is used as a conduit to accelerate site location. Despite the importance of such mechanisms in gene regulation and DNA repair, there have been few viable approaches to elucidate the microscopic process of facilitated diffusion. Here we describe a new method in which a small-molecule trap (uracil) is used to clock a DNA repair enzyme as it hops and slides between damaged sites in DNA. The 'molecular clock' provides unprecedented information: the mean length for DNA sliding, the one-dimensional diffusion constant, the maximum hopping radius and the time frame for DNA hopping events. In addition, the data establish that the DNA phosphate backbone is a sufficient requirement for DNA sliding.     

Binding and recognition of GATATC target sequences by the EcoRV restriction endonuclease: a study using fluorescent oligonucleotides and fluorescence polarization

Oligonucleotides labeled with hexachlorofluorescein (hex) have enabled the interaction of the restriction endonuclease EcoRV with DNA to be evaluated using fluorescence anisotropy. The sensitivity of hex allowed measurements at oligonucleotide concentrations as low as 1 nM, enabling K(D) values in the low nanomolar range to be measured. Both direct titration, i.e., addition of increasing amounts of the endonuclease to hex-labeled oligonucleotides, and displacement titration, i.e., addition of unlabeled oligonucleotide to preformed hex-oligonucleotide/EcoRV endonuclease complexes, have been used for K(D) determination. Displacement titration is the method of choice; artifacts due to any direct interaction of the enzyme with the dye are eliminated, and higher fluorescent-labeled oligonucleotide concentrations may be used, improving signal-to-noise ratio. Using this approach (with three different oligonucleotides) we found that the EcoRV restriction endonuclease showed a preference of between 1.5 and 6.5 for its GATATC target sequence at pH 7.5 and 100 mM NaCl, when the divalent cation Ca2+ is absent. As expected, both the presence of Ca2+ and a decrease in pH value stimulated the binding of specific sequences but had much less effect on nonspecific ones.     

How do site-specific DNA-binding proteins find their targets?

Essentially all the biological functions of DNA depend on site-specific DNA-binding proteins finding their targets, and therefore ‘searching’ through megabases of non-target DNA. In this article, we review current understanding of how this sequence searching is done. We review how simple diffusion through solution may be unable to account for the rapid rates of association observed in experiments on some model systems, primarily the Lac repressor. We then present a simplified version of the ‘facilitated diffusion’ model of Berg, Winter and von Hippel, showing how non-specific DNA–protein interactions may account for accelerated targeting, by permitting the protein to sample many binding sites per DNA encounter. We discuss the 1-dimensional ‘sliding’ motion of protein along non-specific DNA, often proposed to be the mechanism of this multiple site sampling, and we discuss the role of short-range diffusive ‘hopping’ motions. We then derive the optimal range of sliding for a few physical situations, including simple models of chromosomes in vivo, showing that a sliding range of ~100 bp before dissociation optimizes targeting in vivo. Going beyond first-order binding kinetics, we discuss how processivity, the interaction of a protein with two or more targets on the same DNA, can reveal the extent of sliding and we review recent experiments studying processivity using the restriction enzyme EcoRV. Finally, we discuss how single molecule techniques might be used to study the dynamics of DNA site-specific targeting of proteins.     

EcoRV restriction endonuclease binds all DNA sequences with equal affinity

In the presence of MgCl2, the EcoRV restriction endonuclease cleaves its recognition sequence on DNA at least a million times more readily than any other sequence. In this study, the binding of the EcoRV restriction enzyme to DNA was examined in the absence of Mg2+. With each DNA fragment tested, several DNA-protein complexes were detected by electrophoresis through polyacrylamide. No differences were observed between isogenic DNA molecules that either contained or lacked the EcoRV recognition site. The number of complexes with each fragment varied with the length of the DNA. Three complexes were formed with a DNA molecule of 55 base pairs, corresponding to the DNA bound to 1, 2, or 3 molecules of the protein, while greater than 15 complexes were formed with a DNA of 381 base pairs. A new method was developed to analyze the binding of a protein to multiple sites on DNA. The method showed that the EcoRV enzyme binds to all DNA sequences, including the EcoRV recognition site, with the same equilibrium constant, though two molecules of the protein bind preferentially to adjacent sites on the DNA in a cooperative fashion. All of the complexes with a substrate that contained the EcoRV site dissociated upon addition of competitor DNA, but when the competitor was mixed with MgCl2, a fraction of the substrate was cleaved at the EcoRV site. The fraction cleaved was due mainly to the translocation of the enzyme from nonspecific sites on the DNA to the specific site.     

Molecular enzymology of the EcoRV DNA-(Adenine-N (6))-methyltransferase: kinetics of DNA binding and bending, kinetic mechanism and linear diffusion of the enzyme on DNA

The EcoRV DNA-(adenine-N(6))-methyltransferase recognizes GATATC sequences and modifies the first adenine residue within this site. We show here, that the enzyme binds to the DNA and the cofactor S-adenosylmethionine (AdoMet) in an ordered bi-bi fashion, with AdoMet being bound first. M.EcoRV binds DNA in a non-specific manner and the enzyme searches for its recognition site by linear diffusion with a range of approximately 1800 bp. During linear diffusion the enzyme continuously scans the DNA for the presence of recognition sites. Upon specific M.EcoRV-DNA complex formation a strong increase in the fluorescence of an oligonucleotide containing a 2-aminopurine base analogue at the GAT-2AP-TC position is observed which, most likely, is correlated with DNA bending. In contrast to the GAT-2AP-TC substrate, a G-2AP-TATC substrate in which the target base is replaced by 2-aminopurine does not show an increase in fluorescence upon M.EcoRV binding, demonstrating that 2-aminopurine is not a general tool to detect base flipping. Stopped-flow experiments show that DNA bending is a fast process with rate constants >10 s(-1). In the presence of cofactor, the specific complex adopts a second conformation, in which the target sequence is more tightly contacted by the enzyme. M.EcoRV exists in an open and in a closed state that are in slow equilibrium. Closing the open state is a slow process (rate constant approximately 0.7 min(-1)) that limits the rate of DNA methylation under single turnover conditions. Product release requires opening of the closed complex which is very slow (rate constant approximately 0.05-0.1 min(-1)) and limits the rate of DNA methylation under multiple turnover conditions. M.EcoRV methylates DNA sequences containing more than one recognition sites in a distributive manner. Since the dissociation rate from non-specific DNA does not depend on the length of the DNA fragment, DNA dissociation does not preferentially occur at the ends of the DNA.     

Mg2+ confers DNA binding specificity to the EcoRV restriction endonuclease.

The EcoRV mutant D90A which carries an amino acid substitution in its active center does not cleave DNA. Therefore, it is possible to perform DNA binding experiments with the EcoRV-D90A mutant both in the absence and in the presence of Mg2+. Like wild-type EcoRV [Taylor et al. (1991) Biochemistry 30, 8743-8753], it does not show a pronounced specificity for binding to its recognition site in the absence of Mg2+ as judged by the appearance of multiple shifted bands in an electrophoretic mobility shift assay with a 377-bp DNA fragment carrying a single EcoRV recognition sequence. In the presence of Mg2+, however, only one band corresponding to a 1:1 complex appears even with a high excess of protein over DNA. This complex most likely is the specific one, because its formation is suppressed much more effectively by a 13-bp oligodeoxynucleotide with an EcoRV site than by a corresponding oligodeoxynucleotide without an EcoRV site. The preferential interaction of the EcoRV-D90A mutant with specific DNA in the presence of Mg2+ was also demonstrated directly: a 20-bp oligodeoxynucleotide with an EcoRV site is bound with KAss = 4 x 10(8) M-1, while a corresponding oligodeoxynucleotide without an EcoRV site is bound with KAss less than or equal to 1 x 10(5) M-1. From these data it appears that Mg2+ confers DNA binding specificity to this mutant by lowering the affinity to nonspecific sites and raising the affinity to specific sites as compared to binding in the absence of Mg2+. It is concluded that this is also true for wild-type EcoRV.