- Measurement of the contributions of 1D and 3D pathways to the translocation of a protein along DNA

Facilitated Diffusion by BbvCI. The properties of a recently characterized restriction enzyme, BbvCI (30, 31), yielded a general method for analyzing the diffusional translocation of proteins on DNA. Many restriction enzymes are dimers of identical subunits that recognize palindromic sequences (4, 5), but BbvCI is a heterodimer that recognizes a nonpalindromic site. The restriction enzymes that recognize nonpalindromic targets are often monomers (5), and two monomers, each bound to a separate recognition site (38), have to associate to cut the DNA. In contrast, a single molecule of the BbvCI enzyme cleaves both strands of the DNA at an individual site by using different subunits to attack each strand: its R2 subunit cuts the CC strand, and R1 cuts the GC strand (30, 31). Consequently, the degree of processivity of BbvCI on DNA with two sites in repeat orientation, relative to the isogenic DNA with inverted sites (Fig. 1), reveals whether the enzyme stays in contact with the DNA as it moves from one site to another or whether it loses track of the path of the intervening DNA during the transfer.

If the sole pathway for the intramolecular transfer of a protein along DNA is 1D diffusion, then BbvCI may be able to cut the DNA with repeated sites processively, but it can only cut the DNA with inverted sites by distributive reactions at each site, and not by processivity. Conversely, if the protein dissociates from the DNA at least once during the transfer, then BbvCI may still be able to act processively on the two-site DNA, by reassociating back to the same chain. The DNA with inverted sites then must give the same level of processivity as the DNA with repeated sites. A third possibility is that some translocation events involve only sliding steps, whereas others include one or more hopping/jumping step(s). In this case, the fP value for inverted sites will be lower than that on repeated sites, but not zero. The ratios of the fP values on repeated and inverted sites (Fig. 3) thus indicate the contributions of 1D sliding and 3D hopping/jumping to the translocation of the protein along DNA

Under certain circumstances, higher levels of processivity were observed on DNA molecules with two BbvCI sites in repeat orientation than on the isogenic DNA with sites in inverted orientation (Table 1). This result proves that, on a DNA with two sites, the BbvCI endonuclease can cleave one site and then translocate to the other while staying in contact with the DNA throughout the transfer. It has been argued that an enzyme catalyzing processive reactions on a DNA with multiple sites may move along DNA by a different mechanism from that during its motion from its initial random site to its first target site; in particular, that processivity cannot arise from sliding if there is an obligatory dissociation at the end of each catalytic cycle (17). The data presented here show that this scheme is not the case: processivity by BbvCI can involve 1D sliding. However, the differences in the fP values for repeated and inverted sites were observed only with closely spaced sites, up to 45 bp apart, but not at 75 bp, and at low ionic strengths, at 60 mM NaCl, but not at 150 mM. BbvCI thus translocates along DNA by 1D diffusion only over short distances, <75 bp, at low salt concentrations, <150 mM NaCl.

Outside these limits, its motion from one site to another always involves at least one event where the enzyme loses track of the path of the DNA between the sites, i.e., a dissociation/reassociation step. Buffers containing 150 mM NaCl exclude 1D diffusion over distances of ≥30 bp yet have a lower ionic strength than the cytoplasm of Escherichia coli (39). If the cytoplasm of the bacterium that produces the BbvCI enzyme, Bacillus brevis, has a similar composition to that of E. coli, then it is unlikely that 1D diffusion plays a significant role for BbvCI in vivo. Moreover, elevated fP values from repeated sites, relative to inverted sites, do not necessarily imply no reorientation events during translocations between repeated sites and one or more reorientations with the inverted sites, as proposed here. Instead, the difference in fP values could be due to x reorientation events with repeated sites and x + y events on inverted sites, where x and y are even and odd numbers, respectively. If so, the distance that this protein can travel along DNA by 1D diffusion will be even shorter than the 30-bp limit identified here.

Facilitated Diffusion by Other Systems. This work describes just one DNA-binding protein, the BbvCI restriction endonuclease. Nevertheless, the results obtained with this protein match closely the general conclusions from a number of recent theoretical studies of DNA–protein association rates (8, 28, 29). In particular, at the high DNA concentrations found in vivo, the maximal association rate arises when sliding is limited to relatively short distances, typically ≈10 times longer than the length of the target sequence (8). Hence, the overall conclusions from this study, that proteins find their target sites primarily by hopping/jumping interspersed with sliding over short distances, may be applicable to many DNA-binding proteins. However, the actual path length for sliding, and the effect of salt on this process, are likely to vary from one protein to the next. Some DNA-binding proteins may stay in contact with the DNA for translocations over longer distances than BbvCI, as reported for certain proteins in low salt buffers (10, 18), whereas others may dissociate after shorter distances. The key factor in determining the mean path length for 1D diffusion by a protein on DNA is its affinity for nonspecific DNA (811). In this respect, BbvCI is comparable with other restriction enzymes (3437).

The above strategy for analyzing facilitated diffusion originated from the properties of BbvCI, but it is applicable to any enzyme that interacts differently with each DNA strand. For example, it could be applied to a repair enzyme that removes damaged bases from DNA, by examining its processivity on substrates with two target bases, either one in each strand or two in one strand. Likewise, it could be used on enzymes that act at hemi-methylated sites, by constructing DNA substrates where either some sites are methylated in one strand and others in the opposite strand or where one strand is methylated at all sites and the other fully unmethylated, as is the case in vivo after the semiconservative replication of fully methylated DNA (4, 5).

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