Analysis of a one-dimensional random walk with irreversible losses at each step: applications for protein movement on DNA

Correlated Target Search by Vaccinia Virus Uracil-DNA Glycosylase, a DNA Repair Enzyme and a Processivity Factor of Viral Replication Machinery

The protein encoded by the vaccinia virus D4R gene has base excision repair uracil-DNA N-glycosylase (vvUNG) activity and also acts as a processivity factor in the viral replication complex. The use of a protein unlike PolN/PCNA sliding clamps is a unique feature of orthopoxviral replication, providing an attractive target for drug design. However, the intrinsic processivity of vvUNG has never been estimated, leaving open the question whether it is sufficient to impart processivity to the viral polymerase. Here, we use the correlated cleavage assay to characterize the translocation of vvUNG along DNA between two uracil residues. The salt dependence of the correlated cleavage, together with the similar affinity of vvUNG for damaged and undamaged DNA, support the one-dimensional diffusion mechanism of lesion search. Unlike short gaps, covalent adducts partly block vvUNG translocation. Kinetic experiments show that once a lesion is found it is excised with a probability ~0.76. Varying the distance between two uracils, we use a random walk model to estimate the mean number of steps per association with DNA at ~4200, which is consistent with vvUNG playing a role as a processivity factor. Finally, we show that inhibitors carrying a tetrahydro-2,4,6-trioxopyrimidinylidene moiety can suppress the processivity of vvUNG.

Distinct Mechanisms of Target Search by Endonuclease VIII-like DNA Glycosylases

Proteins that recognize specific DNA sequences or structural elements often find their cognate DNA lesions in a processive mode, in which an enzyme binds DNA non-specifically and then slides along the DNA contour by one-dimensional diffusion. Opposite to the processive mechanism is distributive search, when an enzyme binds, samples and releases DNA without significant lateral movement. Many DNA glycosylases, the repair enzymes that excise damaged bases from DNA, use processive search to find their cognate lesions. Here, using a method based on correlated cleavage of multiply damaged oligonucleotide substrates we investigate the mechanism of lesion search by three structurally related DNA glycosylases—bacterial endonuclease VIII (Nei) and its mammalian homologs NEIL1 and NEIL2. Similarly to another homologous enzyme, bacterial formamidopyrimidine–DNA glycosylase, NEIL1 seems to use a processive mode to locate its targets. However, the processivity of Nei was notably lower, and NEIL2 exhibited almost fully distributive action on all types of substrates. Although one-dimensional diffusion is often regarded as a universal search mechanism, our results indicate that even proteins sharing a common fold may be quite different in the ways they locate their targets in DNA.

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.

Mechanisms of diffusional search for specific targets by DNA-dependent proteins

To perform their functions, many DNA-dependent proteins have to quickly locate specific targets against the vast excess of nonspecific DNA. Although this problem was first formulated over 40 years ago, the mechanism of such search remains one of the unsolved fundamental problems in the field of protein-DNA interactions. Several complementary mechanisms have been suggested: sliding, based on one-dimensional random diffusion along the DNA contour; hopping, in which the protein "jumps" between the closely located DNA fragments; macroscopic association-dissociation of the protein-DNA complex; and intersegmental transfer. This review covers the modern state of the problem of target DNA search, theoretical descriptions, and methods of research at the macroscopic (molecule ensembles) and microscopic (individual molecules) levels. Almost all studied DNA-dependent proteins search for specific targets by combined three-dimensional diffusion and one-dimensional diffusion along the DNA contour.

Speed-selectivity paradox in the protein search for targets on DNA: is it real or not?

Protein search for targets on DNA starts all major biological processes. Although significant experimental and theoretical efforts have been devoted to investigation of these phenomena, mechanisms of protein-DNA interactions during the search remain not fully understood. One of the most surprising observations is known as a speed-selectivity paradox. It suggests that experimentally observed fast findings of targets require smooth protein-DNA binding potentials, while the stability of the specific protein-DNA complex imposes a large energy gap which should significantly slow down the protein molecule. We developed a discrete-state stochastic approach that allowed us to investigate explicitly target search phenomena and to analyze the speed-selectivity paradox. A general dynamic phase diagram for different search regimes is constructed. The effect of the target position on search dynamics is investigated. Using experimentally observed parameters, it is found that slow protein diffusion on DNA does not lead to an increase in the search times. Thus, our theory resolves the speed-selectivity paradox by arguing that it does not exist. It is just an artifact of using approximate continuum theoretical models for analyzing protein search in the region of the parameter space beyond the range of validity of these models. In addition, the presented method, for the first time, provides an explanation for fast target search at the level of single protein molecules. Our theoretical predictions agree with all available experimental observations, and extensive Monte Carlo computer simulations are performed to support analytical calculations.

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.

Timing facilitated site transfer of an enzyme on DNA

Many enzymes that react with specific sites in DNA exhibit the property of facilitated diffusion, where 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 where 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 1D sliding constant, the maximum hopping radius and time frame for DNA hopping events. In addition, the data establish that the DNA phosphate backbone is a sufficient requirement for DNA sliding.

MOLECULAR DYNAMICS STUDY OF THE TRANSCRIPTIONAL RECOGNITION MECHANISM OF HEME ACTIVATE PROTEIN (HAP)

The heme activate protein (HAP) is a model system for understanding protein–DNA interactions and allosteric mechanisms in gene regulation. Despite the wealth of biochemical data provided by extensive mutations of HAP, the specific recognition mechanism of the target DNA by HAP has remained elusive. This paper gives the results of a study using molecular dynamics simulations performed for a single DNA fragment (USACYC7) and three protein–DNACYC7complex crystal structures: the HAP-wt and two HAP mutants — HAP-PC7: S63G; HAP-18: S63R. Comparative molecular dynamics simulations reveal that the distributions of protein–DNA interactions recognizing the key base steps (CGC) are consistent with their transcriptional activities. Relative to the similar conformations of three bound DNA, the different flexibilities in involving DNA recognition regions: N-term Arm and Zn 2 Cys 6 Binuclear Cluster in three HAPs may result in a variety of protein–DNA recognitions. Despite different intensities of motions, the essential dynamics (ED) analysis shows that the internal motions of three protein–DNA complexes are similar: three proteins all slide along DNA to find their target sites. Thus, under this condition, during the recognition process, the flexibility of the DNA recognizing regions (N-term Arm and Zn 2 Cys 6 Binuclear Cluster regions) plays a crucial role in determining the abilities of protein's recognizing DNA: the higher is its flexibility, the faster it slides along the DNA to find the targeted DNA.

Mechanism of translocation of uracil-DNA glycosylase from Escherichia coli between distributed lesions

Uracil-DNA glycosylase (Ung) is a DNA repair enzyme that excises uracil bases from DNA, where they appear through deamination of cytosine or incorporation from a cellular dUTP pool. DNA repair enzymes often use one-dimensional diffusion along DNA to accelerate target search; however, this mechanism remains poorly investigated mechanistically. We used oligonucleotide substrates containing two uracil residues in defined positions to characterize one-dimensional search of DNA by Escherichia coli Ung. Mg(2+) ions suppressed the search in double-stranded DNA to a higher extent than K(+) likely due to tight binding of Mg(2+) to DNA phosphates. Ung was able to efficiently overcome short single-stranded gaps within double-stranded DNA. Varying the distance between the lesions and fitting the data to a theoretical model of DNA random walk, we estimated the characteristic one-dimensional search distance of ~100 nucleotides and translocation rate constant of ~2×10(6) s(-1).

Dynamic strategies for target-site search by DNA-binding proteins

Gene regulatory proteins find their target sites on DNA remarkably quickly; the experimental binding rate for lac repressor is orders-of-magnitude higher than predicted by free diffusion alone. It has been proposed that nonspecific binding aids the search by allowing proteins to slide and hop along DNA. We develop a reaction-diffusion theory of protein translocation that accounts for transport both on and off the strand and incorporates the physical conformation of DNA. For linear DNA modeled as a wormlike chain, the distribution of hops available to a protein exhibits long, power-law tails that make the long-time displacement along the strand superdiffusive. Our analysis predicts effective superdiffusion coefficients for given nonspecific binding and unbinding rate parameters. Translocation rate exhibits a maximum at intermediate values of the binding rate constant, while search efficiency is optimized at larger binding rate constant values. Thus, our theory predicts a region of values of the nonspecific binding and unbinding rate parameters that balance the protein translocation rate and the efficiency of the search. Published data for several proteins falls within this predicted region of parameter values.

Diffusion of the restriction nuclease EcoRI along DNA

Many specific sequence DNA binding proteins locate their target sequence by first binding to DNA nonspecifically, then by linearly diffusing or hopping along DNA until either the protein dissociates from the DNA or it finds the recognition sequence. We have devised a method for measuring one-dimensional diffusion along DNA based on the ratio of the dissociation rate of protein from DNA fragments containing one specific binding site to the dissociation rate from DNA fragments containing two specific binding sites. Our extensive measurements of dissociation rates and specific-nonspecific relative binding constants of the restriction nuclease EcoRI enable us to determine the diffusion rate of nonspecifically bound protein along the DNA. By varying the distance between the two binding sites, we confirm a linear diffusion mechanism. The sliding rate is relatively insensitive to salt concentration and osmotic pressure, indicating that the protein moves smoothly along the DNA probably following the helical phosphate-sugar backbone of DNA. We calculate a diffusion coefficient for EcoRI of 3 x 10(4) bp(2) s(-)(1) EcoRI is able to diffuse approximately 150 bp, on average, along the DNA in 1 s. This diffusion rate is about 2000-fold slower than the diffusion of free protein in solution. A factor of 40-50 can be accounted for by rotational friction resulting from following the helical path of the DNA backbone. Two possibilities could account for the remaining activation energy: salt bridges between the DNA and the protein are transiently broken, or the water structure at the protein-DNA interface is disrupted as the two surfaces move past each other.

The effects of intersegmental transfers on target location by proteins

We study a model of protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding--in which the protein diffuses along the contour of the DNA, (b) jumping--where the protein travels between two sites along the DNA by three-dimensional diffusion and finally (c) intersegmental transfer--which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably, (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependences, for example on the DNA length.

A model for the mediation of processivity of DNA-targeting proteins by nonspecific binding: dependence on DNA length and presence of obstacles

A physical and mathematical model is presented to explain processivity of proteins on DNA. In this model, a DNA-targeting protein such as a restriction enzyme can diffuse to the DNA surface and nonspecifically bind to it. Once on the DNA surface it will either move along the DNA or equilibrate with the surrounding region. Owing to the nonspecific binding, the search for a specific site on the DNA occurs in a reduced dimensionality, and the protein appears processive when moving from one specific site to another. The simplest version of this nonspecific-binding-facilitated diffusion model is solved and the results quantitatively explain experimentally observed dependence of the processivity ratio on the intervening DNA length between two specific sites.

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 approximately 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.