One-dimensional Diffusion of Proteins along DNA

Evidence for sliding of proteins along DNA has been provided by many kinetic studies, but single-molecule-based measurements have uncovered distinct problems, the solutions of which may lead us to an understanding of new mechanisms for gene regulation. Furthermore, they reveal a deep problem lying between chemistry and physics regarding the seemingly simple binding between DNA and protein. Single-molecule dynamics provides a tool to solve this problem without prejudgments or unsound assumptions.


Importance of Single-molecule-based Analysis
Single-molecule dynamics is the most powerful, and probably the only direct, method for analyzing a biological phenomenon in which the history of a single molecule appears at macroscopic level. The long-standing question as to whether or not proteins slide along nonspecific parts of DNA provides an excellent example of the power of the new method and its complementarity to classic kinetics. The sliding of a protein (a microscopic history) can macroscopically enhance the formation of specific complexes, as described below (see also Ref. 1 for review). The histories of individual molecules have traditionally been considered unimportant in chemistry, because the differences in histories of different molecules are normally obliterated due to numerous random collisions with solvent molecules. The resulting group of molecules with a unified average history is considered as a single chemical species. In practice, however, a chemical species is usually arbitrarily defined, and such a theoretical uncertainty causes a serious problem in kinetics, because kinetic analysis is based on hypotheses of mechanisms. Direct observation of individual molecules, on the other hand, requires no theoretical assumptions. This is the most important reason for the application of single-molecule dynamics to a problem like sliding.
The limitation of space here has urged exclusion of the sliding of DNA clumps and of the energy-driven translocation of enzymes such as helicases and RNA polymerase being engaged in RNA synthesis; the successful single-molecule studies of the latter have been recently reviewed (2).

Practical Definitions of Translocation Mechanisms
To avoid serious confusion due to the variable terminology used in past discussions of protein sliding, specific terms should first be defined clearly. One-dimensional diffusion of a protein here includes all mechanisms of translocation along a single DNA molecule that do not involve a free state of the protein. These mechanisms are classified into sliding and intersegment transfer (Fig. 1). The latter is here supposed to require at least two DNA binding sites on the protein molecule as in the general theory (3,4), excluding a transient interaction as a secondary binding. Sliding and hopping are taken to imply, respectively, a helical movement due to tracking a groove of DNA or a non-helical movement parallel to the DNA axis (5, 6), although they have been differently defined theoretically (3). These distinctions are sacrificed here for simplicity, because a simple microscopic observation cannot distinguish them.

Single-molecule Dynamics of RNA Polymerase, CamR, and Photolyase
To visualize movement of a single molecule of protein using a commercially available fluorescent microscope, the molecule must be made strongly fluorescent. This can be done by attaching several tens of fluorophores per molecule (7,8). The clearest visual assay of sliding movement is to let DNA take up a special geometry as in Fig. 2A and to detect the traces of protein molecules moving with the same geometry. A DNA concentration of 10 -100 g/ml is required to observe binding events at a significant frequency. These requirements were satisfied by applying dielectrophoresis to align extended DNA molecules in parallel (9).
Fluorescently labeled Escherichia coli RNA polymerase holoenzyme was injected so as to flow at an angle across the array of DNA molecules (8). Linear motions parallel to DNA were observed in half of the traces passing through the DNA region ( Fig. 2A). The linear motions disappeared when holoenzyme was preincubated with heparin or with a short DNA fragment harboring a strong promoter. Furthermore, neither the IgG used for fluorescent labeling nor microcrystals of rhodamine showed linear motions. These negative controls, together with the quantitative agreement between the lifetimes of the observed sliding complexes and those previously measured for nonspecific holoenzyme-DNA complexes (10), prove that the observed movement is a true sliding of holoenzyme along DNA and not a hydrodynamic artifact such as rectification of flow in the DNA region. The sliding complex is the only complex observed in nonspecific regions of the DNA, and stably bound complexes form only at the promoter. Moreover, a typical bacterial repressor, Pseudomonas putida CamR, which is a small homodimeric protein with a helix-turn-helix DNA binding motif, shows very similar movements. 1 These results suggest that sliding is a general property of DNA-binding proteins, although not all might be able to slide.
The flow introduced in the above assay, or asymmetric collisions with solvent molecules, converts otherwise bidirectional sliding movements into a large unidirectional travel of several micrometers. The length of travel should not be confused with the sliding distance, which is defined as the mean size of DNA segment scanned per binding event (in the absence of flow), and has been kinetically estimated as 350 -1000 base pairs for RNA polymerase (11,12).
Atomic force microscopy can measure the movement of single molecules trapped on a flat surface at a resolution smaller than 1 nm. By fixing DNA on a mica surface, the random displacements due to sliding of Aspergillus nidulans photolyase have been directly detected (13). The drawback of this method is slowing down of the movements of molecules because of interaction with a surface.

Single-molecule Dynamics and Kinetics Are Complementary
The relationship between the new single-molecule-based techniques and classic kinetics resembles that between the new techniques developed in molecular biology and classical genetics, which have become fused and essential to modern biology. Kinetics can compensate for the defects of single-molecule dynamics, namely the heavy modification used for visualizing and detecting target molecules, and the unusual experimental conditions.

Merits and Demerits of Kinetic Techniques Used in the Test for Sliding
Several quantitative techniques to detect DNA-protein complexes have been used in the kinetic test for sliding. The filterbinding technique has been widely used (14,15,18,24,26,29,31,34,37) but is open to misinterpretation if there are two or more types of complexes that are trapped with different efficiencies (37). If practicable, the gel shift assay (38,39) is an excellent choice (24,37,40), because it can be made highly quantitative by introducing a competition between two DNA fragments (41). An up-to-date method, surface plasmon resonance, needs special care when applied to rapid reactions such as the binding of protein and DNA. The binding kinetics can be disturbed by mass transportation to the surface of detection and by rebinding events (42). Rapid mixing techniques have been successfully combined with DNase I footprinting (30) and UV flash photo-cross-linking (Fig. 2E) (10,11,23). Notably the latter can directly detect nonspecific complexes.
The formation of a specific complex of an enzyme can be kinetically monitored by its catalytic consequences, provided that the catalytic reaction is more rapid than the breakdown of the specific complex, a condition called diffusion control (16,18,20,22,32). A better designed enzyme assay shown in Fig. 2F is free from this limitation. Interestingly a groove-tracking type of sliding was shown for EcoRI (5) and BssHII (6) endonucleases by this assay. Notably this processivity assay is also possible in vivo (21,33,36).

Biological Significance of Sliding: Kinetic Contribution, Processivity, and More?
Sliding along DNA obviously can kinetically affect a biological process through the acceleration of association, if bimolecular association is the rate-limiting step of the process. This situation, however, may only apply to limited cases in vivo. For example, transcription initiation includes several time-consuming elementary reaction steps. As a result the association of RNA polymerase with a promoter is rarely rate-limiting, FIG. 1. One-dimensional diffusion mechanism. Mechanisms of transfer within the same DNA molecule are here classified into sliding and intersegment transfer. The latter requires two DNA binding sites such as LacI tetramer (24,37,40) and steroid receptor dimer (44). The green ovals are protein molecules, and DNAs are shown as the double lines.
FIG. 2. The experimental designs to test for the existence of sliding. The yellow boxes denote specific sites. A, the experimental design used in the direct visualization (7,8). B, the faster association to a specific site on a longer DNA fragment is the most naive kinetic assay (5, 16, 18, 20 -22, 26, 29 -32, 34). C, sliding makes binding to a specific site flanked by a long nonspecific segment more rapid than to one flanked by a short nonspecific segment on the same DNA molecule (5,12,22). D, if a protein slides on DNA fragments of the same length, it should bind to all specific sites with similar rates irrespective of their number on a DNA fragment (24). E, time courses of association and positions of complexes can be monitored by rapid UV photo-crosslinking (10,11,23) and by rapid DNase I footprinting (30). The crosslinking between protein and DNA is marked by an X. F, sliding enables the enzyme to catalyze preferentially at two or more sites on the same DNA molecule rather than others (5,6,17,19,33,35,36). The red boxes are the specific sites modified by an enzyme action. making the acceleration of association by sliding less significant. However, sliding may be more general in the production of processivity, as evidenced in restriction (21,31,32) and repair (33,36) of DNA.

The Antenna Effect and a New Role of Sliding
If a protein slides from its specific site into nonspecific sites (Fig. 3A), longer DNA will accelerate the overall dissociation from the specific site. This length effect compensates the kinetic length effect on association (Fig. 2B), and binding affinity will be unchanged. Indeed such absence of the enhancement of affinity by sliding has been reported for EcoRI (18) and Cro repressor (34).
However, there are several cases showing enhancement of affinity by the extension of DNA (Fig. 3C); the observed enhancements are 20-fold for EcoRI methylase (31, 32), 10-fold for human immunodeficiency virus type 1 integrase (43), more than 100-fold for CamR, 1 and 10 -30-fold for LacI (26,29). Interestingly the existence of sliding by RNA polymerase was detected by preferential occupancies among several identical promoters on the same DNA, using a design similar to that shown in Fig. 2C (12). Nonspecific DNA up to 350 base pairs in length enhanced affinity for its flanking promoter in an equilibrium condition, although this applied only when it was placed downstream of the promoter. These examples indicate that an extended region of nonspecific DNA can work as an antenna to harvest protein for binding to a flanking specific site.
To investigate this antenna effect without making any theoretical assumptions, the movement traces of molecules of CamR and RNA polymerase were compared, following dissociation from their specific sites in the presence of bulk flow. Most of the traces of CamR showed direct dissociation into bulk, or sliding movements too small to be resolved by the microscope, prior to complete dissociation (Fig. 3B). 1 In contrast the traces of RNA polymerase showed sliding during the two-step dissociation (Fig. 3A) (8) almost as extensive as during association. Accordingly the dissociation of CamR will be less enhanced than association by increases in DNA length, consistent with the observed large enhancement of its affinity. The asymmetry of the small antenna effect found for RNA polymerase (12) can also be explained along these lines. If RNA polymerase slides off the promoter more frequently in an upstream than a downstream direction because of the asymmetry of the promoterholoenzyme interaction, the extension of downstream DNA would enhance the promoter affinity more than extension upstream, making the antenna effect asymmetric.
An alternative explanation for the antenna effect is that the additional length of DNA loops back onto the specific complex, permitting a transient secondary contact, which further stabilizes the specific complex. If longer DNA stabilizes the complex 100-fold by this mechanism, dissociation occurs only from a 1% fraction of complexes that are not looped, reducing the overall dissociation rate to 1% of that in the absence of looping (or less, if unlooping is rate-limiting in the overall dissociation process). This prediction, however, contradicts the observation that the dissociation rate is independent of DNA length in the case of EcoRI methylase (31). Furthermore, this model cannot explain the asymmetric antenna effect seen with RNA polymerase or the apparent absence of sliding upon dissociation of CamR. Therefore, sliding is the primary candidate as the basis of the antenna effect. If so, the role of sliding would be much more important than previously speculated; affinities for specific sites could be reduced by limitation of sliding movements (Fig.  3D). In fact EcoRI endonuclease is inhibited by various protein complexes locating near the cleavage site, as well as unusual DNA structures such as pseudo-recognition sites and triple helices (5). This is "action at a distance" in the true sense, which could be implicated in many gene regulation mechanisms such as nucleosome remodeling in transcription.

A Deep Insight into the Chemistry of Sliding Is Also Gained from Single-molecule Dynamics
In most kinetic studies nonspecific complexes are supposed to form a single chemical species, giving a two-step model: free components 7 nonspecific complex 7 specific complex. This assumption has been made arbitrarily, ignoring the definition of a chemical species, which states that every member of the species has an equal probability of conversion. Because nonspecific complexes at distal and proximal sites have different probabilities of sliding into a specific site, the above assumption in effect excludes the possibility of sliding from the outset.
Alternatively a nonspecific complex at any position on DNA could be considered a distinct chemical species, as has been supposed in a general theory (see the "Appendix" of Ref. 3) (4). If so, the energy barrier between contiguous nonspecific positions should be high enough to allow sufficient collisions with solvent molecules to randomize the histories of individual protein molecules while they remain at a nonspecific site. On the other hand the single-molecule assay revealed that this barrier is so small that the speed of sliding is about half of the parallel component of bulk flow (8). In other words, polymerase molecules move "half-freely" along DNA consisting of nonspecific sites. This may or may not contradict the distinct species at each position model but raises the third possibility that a group of nonspecific complexes within the sliding distance would more truly represent a chemical species than one at each position. Therefore, the true chemical status of nonspecific complexes is not yet clear.
The largest problem of the antenna effect, as has already been briefly noted (31), is a seeming contradiction to a basic assumption of chemistry. The principle of microreversibility, which is derived from the second law of thermodynamics and the definition of chemical species, demands an equal influx and efflux between a specific complex and the bulk free pool in There are two mechanisms of dissociation from specific sites (yellow). A protein molecule (green) first slides into nonspecific sites and then dissociates into bulk (A). The dissociation rate of this mechanism depends on the length of nonspecific DNA, whereas it becomes independent by the direct dissociation mechanism (B). If this direct dissociation is combined with an association mediated by the sliding mechanism, a specific site on a longer DNA should have stronger affinity than the identical site on a shorter DNA, which is the antenna effect (C). A similar decrease in the affinity is expected when sliding movements are limited by the bindings of other proteins (pink) near the specific site (D), causing an action at a distance. The seeming violation of the microreversibility in the antenna effect is discussed in the text. equilibrium if these two states constitute two chemical species that are directly connected by an elementary chemical step. The larger accumulation of a specific complex by the antenna effect should concomitantly increase the efflux from the specific site, k d ϫ [specific complex]. In contrast the influx from the free state, k a ϫ [free protein], should be unchanged because both k a and [free protein] are independent of the antenna effect, contradicting the principle. Therefore, something is missing in the chemical interpretation of the antenna effect.
This contradiction could be resolved in two ways, both proposing the existence of an additional chemical species. The looped complex model is easier to be understood but cannot explain some experimental results, as mentioned above. In an alternative model, the chemical species of the specific complex is defined similarly to the third possibility mentioned above so that it includes all complexes within the sliding distance from the specific site. In addition, an elongated space surrounding a DNA chain, which can be termed the "DNA domain," is proposed to exist, and the protein molecules dissociating from the extended specific site initially enter this space and diffuse in it. As a distinct chemical species, the protein in this DNA domain can equilibrate both with free protein and with the extended specific complex. Increasing the length of DNA up to the sliding distance would also elongate the DNA domain and thus increase the influx from free state into the domain. The increased influx satisfies the principle because in equilibrium it becomes equal to the efflux into and the influx from the specific site, which are increased by the antenna effect.
Experimentally a space of this sort was found in rapid UV photo-cross-linking studies of sliding (10,11,23). RNA polymerase in a rapid flow was confined to this space yet in a state such that cross-linking was impossible, and the postulation of such a space was needed for numerical simulation.
More experiments would prove or disprove this model in the future, and they are very likely to be single-molecule measurements, because they should be designed so as to be free from traditional chemical assumptions. The above examples claim that the world of molecules may not always harmonize with our ordinary macroscopic experience not only in quantum mechanics but also in the chemistry and biology of seemingly simple DNA-protein interaction.