On the Processive Mechanism of Escherichia coZi DNA Polymerase I QUANTITATIVE

Comparison of the rates of polymerization catalyzed by DNA polymerases in the presence of a limited and a com- plete complement of the four deoxynucleoside triphosphates permits accurate measurement of the processivity of polymerization. The each the polymerase the DNA template, may be measured in a range from 1.0 to several hundred for as great

of a stationary DNA polymerase molecule bound to DNA, with the "kinetic affinity" of a polymerase in the course of synthesis. For E. coli DNA polymerase I, the static affinity is usually severalfold greater than the kinetic affinity.
A method has also been developed to measure the average template length available to a DNA polymerase for synthesis at individual 3' termini of any DNA substrate, and the effect of temperature and ionic strength on this available length. Results of such measurements show that the processivity values reported here are an intrinsic property of the DNA polymerase and are not determined by the available template length.
We have previously described a method to assess whether polymerization of nucleotides by DNA polymerases is processive; that is, whether a succession of nucleotides is polymerized before the enzyme is released from the template (1 In an earlier publication, Gass and Cozzarelli (2) suggested that measurement of the rate of DNA synthesis in the presence of one, two, or three dNTPs compared to that measured with all four dNTPs could provide a quantitative determination of processivity over a large range of values tone to several hundred). The basic point of their analysis was that reaction rate is determined in part by processivity, and that the rate with a full as compared to a partial complement of dNTPs could be used to distinguish processivity from other factors affecting polymerization rate. However, processivity can be derived quantitatively from such an analysis only if the rate of reaction is proportional to the number of nucleotides added to individual DNA molecules. Since this proportionality was not demonstrated in the original analysis, Gass and Cozzarelli (2) pointed out that the values which they calculated for Bacillus subtilis DNA polymerases might not represent the true processivity of polymerization.
In this report, we have extended the original proposal of Gass and Cozzarelli (2) into a theory and an experimental method which have allowed us to measure unambiguously values of the processivity of nucleotide polymerization by DNA polymerases. When applied to E. coli DNA polymerase I, this analysis has confirmed that polymerization of nucleotides by this enzyme is processive. It has further indicated that under certain conditions the processivity exceeds 180 nucleotides. The results have also shown that reaction conditions and template structure can affect the processivity of this polymerase. In contrast, DNA polymerase p from KB cells (3) is nonprocessive; that is, the enzyme dissociates following addition of each nucleotide, under all of the conditions tested.
The analysis permits a comparison of the "static affinity" of a bound DNA polymerase molecule for a primer-terminus, to the "kinetic affinity" of an actively polymerizing enzyme. It also allows determination of the "average available template length"; i.e. the total number of nucleotides which may be added to each primer-terminus of a DNA template by an excess of enzyme molecules over primer-termini under specific conditions. With this new information we are able to obtain a much clearer picture of the microscopic movement of DNA polymerases as they synthesize DNA than was heretofore available. THEORY With a large excess of primer-termini over enzyme molecules, nucleotide polymerization may be considered to be a two-phase, cyclic process. In the first phase, free enzyme diffuses to and binds the primer-template (4). In the second phase, the enzyme catalyzes an ordered succession of dNTP binding, nucleotide condensation, and translocation until the enzyme dissociates from the primer-template (5). The entire cycle is then repeated. We define the average increment of time elapsed during one complete cycle, from the binding and reaction of the DNA polymerase with a 3'-primer terminus capable of supporting DhrA synthesis, through the dissociation and diffusion steps, to the rebinding of the enzyme to another reactive 3' terminus, as the "cycling time." The polymerization rate when x dNTPs are present may then be expressed as follows: where P, is the rate of polymerization, E the number of active enzyme molecules, N, the average number of nucleotides incorporated per polymerization cycle, and T, the cycling time. This is a general expression that applies to both synthesis with a limited complement of dNTPs (X = 1, 2, or 3 for native DNA) and synthesis with a complete complement of dNTPs (3~ = 4 for native DNA).' For native DNA, N, is the average number of nucleotides polymerized with a complete complement of dNTPs, and is therefore the processivity of polymerization.
The goal of these calculations is to express N, in terms of parameters which can be measured experimentally.
The ratio of polymerization rates with a limited uersus a complete complement of dNTPs for native DNA (P,,,) may be expressed as: is: (x=l,Z,or 3) Returning to Equation 3, it is possible to relate the measured reaction rates P,, Pa, P,,;, and P,,i to the processivity of polymerization as follows: This expression is rearranged as follows: lFyx] N4 = Nx FX] Note that all right-hand terms are either calculated or experimentally determined. Equation 13 may also be rewritten as follows: (15) where P',:, = P,:,T,/T,.
Since only a single triphosphate is labeled in all experiments, a correction is made to allow use of the ratio of radioactivity incorporation rates (R',:,). This factor (L) is explained under "Theory" and relates R',:, to P',:, as follows: This expression is incorporated into Equation 15 to yield: The theoretical relationship between N, and R',:, is shown for calf thymus DNA in Fig. 1

and for poly[d(A-T)]
in Fig. 2. In order to use these figures to determine enzyme processivity, it is necessary to calculate the value of R',:, which is: where R,:, is the ratio of label incorporated in limited (X = 1, 2, or 3) as compared to complete (3~ = 4) reactions and T,/T, is calculated from Equation 11.
There are two practical limitations to such an analysis. (a) Cross-contamination of one dNTP with another will produce an erroneously high polymerization rate during limited synthesis, and as a consequence, the apparent processivity will be correspondingly lowered. Reaction 1; Reaction 3, a mixture containing a limited complement of dNTPs and primer-template DNA only; and Reaction 4, a mixture containing a complete complement of dNTPs and primer-template DNA only. Rates of these reactions were used to calculate relative cycling times and processivity.
The relative concentrations of enzyme and DNA in all reactions were maintained such that the amount of DNA synthesis was less than 10% of the amount of synthesis that the DNA could support with a large excess of E. coli DNA polymerase I.
The concentration of activated DNA in inhibited reactions was lower than in the uninhibited reactions. This was done: (a) to increase inhibition by raising the inhibitor/activated DNA ratio; (b) to compensate for the higher activity of the DNA polymerase in the uninhibited reaction so the DNA would react to less than 10% of its capacity; and (c) to help compensate for any effects the concentration of 3'-phosphoryl ends might have on processivity.* Both untreated and micrococcal nuclease-treated DNAs present in processivity experiments contained a low level of active 3'-hydroxyl primer-termini.
Since synthesis on this DNA contributed slightly to the processivity value, all DNAs in any single determination were from the same source (e.g. synthesis on ColEl DNA was inhibited by 3'-phosphorylterminated ColEl DNA).
Nicked DNA Templates -Processivity and relative cycling times were measured with nicked ColEl DNA and activated calf thymus DNA as primer-templates (Table I). Activated calf thymus DNA may contain gaps (areas of single strands) in addition to nicks (breaks with no nucleotides removed), while nicked ColEl DNA contains essentially no gaps (9). Processivity was determined by comparing rates of synthesis with one and four dNTPs, as well as with three and four dNTPs.  values of processivity were found with activated calf thymus DNA compared with nicked ColEl DNA. This may reflect a somewhat different structure of the calf thymus DNA, perhaps due to the presence of some gaps in addition to nicks. This interpretation is consistent with the processivity measurements with gapped DNA (below).
The relative cycling time (TX/T,) values with nicked DNA ranged from 4 to 6, suggesting that the enzyme dissociates relatively slowly in the absence of all four dNTPs. Indeed, binding of enzyme to DNA in the absence of polymerization (static affinity) may be much greater than binding during polymerization (kinetic affinity). Since enzyme is constantly releasing and rebinding the growing primer-terminus in the course of polymerization, its affinity for DNA during synthesis would be expected to be decreased relative to its affinity in the absence of catalysis. Gapped DNA Template -The processivity of polymerization with a gapped primer-template structure was tested using nicked ColEl DNA that had been digested with exonuclease III (9). As shown in Table I, DNA polymerase I was more processive by approximately 2.5-fold on a template containing primarily gaps than on one which was completely nicked. The relative cycling time (TJT,) was substantially lower with gapped compared with nicked DNA as primer-template. This suggested that (a) the kinetic affinity for gapped DNA is greater than that for nicked DNA; (b) the static affinity for gapped structures is less than that for nicked structures; or (c) both of the above.

Poly[d(A-T)] Template
-Experiments with the polyld(A-'I)1 The procedures for determination of processivity and relative cycling time were the same as described in the legend for Table I (Table I). The kinetic affinity of the enzyme for the alternating co-polymer was nearly equal to the static affinity.
Processivity was greatly diminished at 5" compared to 37 (Table II). Also, the relative cycling time was greater at the lower temperature, suggesting that under these conditions the static affinity of the enzyme becomes significantly higher than the. kinetic affinity of the enzyme for poly[d (A-T)].
An increase in ionic strength from approximately 0.125 to 0.315 p also reduced considerably the value of processivity, but did not affect the relative cycling time.
The striking temperature effects apparent with poly[d(A-T)] were probably the result of stabilization of the secondary structure of the co-polymer at 5", thus preventing "slippage" or "creeping" which would have allowed further DNA synthesis by reiteration and elimination of "barriers" to polymerization (13,15). These experiments show that the particular reaction conditions and primer-template selected for analysis can have profound effects on processivity. In this case, DNA polymerase I appeared processive for only three nucleotides at 5" and an ionic strength of 0.312 CL, yet was processive for 188 nucleotides at 37" and an ionic strength of 0.11 p.
Experiments were attempted on gapped ColEl DNA at low temperature (5", 0.1 ~1 but the enzyme appears to have dissociated so slowly from reactive 3'-hydroxyl termini that it did not cycle and thus inhibition could not be measured accurately. Such effects have been observed using the cohesive ends of DNA as primer-template at 6" (1).  Fig. 5 shows the effect of ionic strength on processivity and relative cycling time with activated calf thymus DNA as template. The values for the ratio of relative cycling times approached 1 as ionic strength was increased, but the processivity did not drop significantly until the ionic strength was increased to greater than 0.35 p. Processivity then decreased with increasing salt to a minimum value of approximately 1. Hence, at -very high ionic strength (>0.7 ~1, the enzyme polymerized in a nonprocessive manner. The effect of ionic strength on the activity of DNA polymerase I is also shown in Fig. 5. From these data, it is evident that while processivity must affect the overall rate of polymerization (SeeJ'Theory"), these two parameters need not show a direct correspondence.
Under conditions in which processivity approached 1, it IONIC STRENQTH (Jo) FIG. 5. Effect of ionic strength on processivity and relative cycling time of Escherichia coli DNA polymerase I with activated calf thymus DNA. Reaction mixtures were identical with those described in the legend to Table I  Effect of DNA concentration on rate of synthesis by KB cell DNA polymerase p. Reaction mixtures were as described in the legend to Table IV with 100 mM KC1 added. Aliquots (50 ~1) were removed after 10 min and acid-insoluble radioactivity was determined. Mixtures contained either 13HldlTP alone (0) or all four dNTPs (0). was possible to verify measurements of processivity by an independent means. If the static and kinetic affinity of DNA polymerase for DNA are very low, then the great majority of the time the DNA polymerase is not bound to DNA. If the binding step is by far the slowest, then cycling times must be essentially equivalent in the presence of a limited and complete complement of dNTPs. This condition manifests itself as a linear dependence of rate on DNA concentration, since the DNA is a second order reactant for the binding reaction. Fig.  6 shows that there is a nearly linear dependence of rate on DNA concentration at 0.725 p ionic strength and 0 to 6 PM DNA concentration. Under these conditions, relative rates all show a value of approximately 1.0 for processivity.
Effective Template Lengths of DNA A method is described under "Theory" for determination of the average available template length for DNA synthesis at each 3' terminus of a substrate DNA under specific conditions. It involves calculation of extents of polymerization in the presence of both a limited and complete complement of dNTPs using an excess of the DNA polymerase. Apparent template lengths for the DNA used in the experiments described above were calculated accordingly, and are shown in Table III. In general, these lengths are severalfold higher than the values of processivity obtained for the same DNA. This result indicates that values of processivity were not limited by the available template length, but instead were properties intrinsic to DNA polymerase I under the conditions specified.

Nonprocessivity of DNA Polymerase /3 from KB Cells
The DNA polymerase p from KB cells when polymerizing on activated calf thymus DNA gave a processivity value of about one, i.e. is nonprocessive. There was an essentially The procedure for calculating the effective template length is presented under "Theory." Reaction mixtures (40 ~1) to which 0.25 to 0.50 pg of DNA polymerase I were added, contained salt and buffer components identical with those used for processivity measurements under the conditions described (refer to the legend to Table I (Fig. 7), suggesting that binding of enzyme to DNA was rate-determining.
Hence, omission of dNTPs should not have perturbed the cycling time. Lowering ionic strength to increase the affinity of the enzyme for DNA had no effect on processivity ( These workers suggested that the decrease in rate of synthesis could be interpreted in terms of processivity of polymerization.
However, since duration of binding of enzyme to DNA could in some manner have been affected by dNTP omission, unambiguous interpretation of the data was not possible. In this report we have provided the theoretical and experimental framework with which to analyze such data, and thus to determine precisely the processivity of polymerization.
The critical aspect of the analysis is a correction for perturbations in polymerase "cycling time," which account for any effects dNTP omission might have on DNA binding with DNA polymerase. By this analysis, E. coli DNA polymerase I may be processive for up to 188 nucleotides. However, processivity was shown to be highly sensitive to ionic strength, temperature, and the structure of the DNA template. The results suggest that, in general, higher ionic strength, and lower temperature decrease processivity.
Increase of ionic strength alone was sufficient to change the mechanism of polymerization from processive to nonprocessive (processivity = 1.0). Shielding of ionic interactions by salt ions apparently decreased the affinity for DNA. This alone could account for the altered processivity since lowered affinity for DNA could decrease the binding time to the point where the enzyme did not have time to translocate and catalyze polymerization of more than a single nucleotide. The effect of lowered temperature on processivity may have resulted from (a) a decreased ability of the DNA polymerase to displace DNA strands; (b) effects of temperature on 5' + 3' exonuclease function; or (c) temperature-induced structural changes in the primer-template or DNA polymerase. The lower processivity observed with nicked DNA substrates, compared to values obtained with gapped DNA substrates suggests that the affinity for primer-template is lowered if 5' += 3' exonuclease activity or strand displacement activity occurs concommitantly with polymerization (17).
In all of these experiments we have found that the relative cycling time (TX/T,) is near or greater than 1. This indicates that the "kinetic affinity" of the actively polymerizing enzyme molecule for the template is generally lower than the "static Since actively polymerizing enzyme must assume such a configuration at least once for each nucleotide polymerized, whereas stationary enzyme need not assume such a configuration at all, it is not surprising that the kinetic affinity is generally lower than the static affinity. The numerical value of T,/T, is not indicative of a quantitative relationship between kinetic and static affinity because some synthesis does occur even when a limited complement of dNTPs is used in the reaction.
Examination of the data shows that T,/T, is much higher on the nicked DNA substrate than on the gapped DNA substrate. This suggests that the process of continual removal of DNA ahead of the growing primer diminishes the kinetic affinity relative to static affinity. Our experiments with the DNA polymerase /3 from KB cells show that regardless of temperature and ionic strength, the mechanism of this enzyme is nonprocessive (N, = 1).
The analysis presented above allows calculation of the average template length available for polymerization beyond each primer-terminus of the substrate DNA. Results from these experiments show that processivity is not limited by the template length, but is instead an accurate indication of the propensity of DNA polymerase I to translocate along the DNA template. The ability to determine available template length may be useful in other aspects of nucleic acid research. For example, it may be possible to determine template lengths available to DNA polymerases after radiation, chemical, or mechanical damage, and during repair and recombination events.
Processivity of DNA polymerization has been actively investigated by a number of laboratories in recent years. McClure and Jovin (13) showed that with poly[d(A-T)] at 4" and ionic strength approximately 0.25 p, DNA polymerase I is essentially nonprocessive. Results at higher temperatures were consistent with increased processivity. Our findings of low processivity (N, = 3.3) with poly[d(A-T)] at low temperature and high processivity (N, = 188) at higher temperature, are in reasonable agreement with their findings.
Chang (18) and Sherman and Gefter (15) have shown that polymerase I will extend an excess of primer strands in a synchronous manner over short time intervals (several minutes). These experiments, however, cannot be interpreted quantitatively.
Some ambiguity occurs because the time intervals examined were presumably much longer than the cycling time of DNA polymerase I, even if polymerization were processive for more than 100 nucleotides.
Thomas and Olivera have devised a method to measure the processivity of nucleases on homopolymer templates. Although their results are not directly comparable to ours, since we cannot measure processivity on homopolymers, they have shown that at 37" and approximately 0.09 p ionic strength, the 5' -+ 3' exonuclease of DNA polymerase I is processive for less than approximately 20 bases during nick translation. Such a value is consistent with our results on nicked DNA substrates.
The finding that the DNA polymerase /3 from KB cells is nonprocessive is in agreement with an earlier report that an analogous enzyme purified from calf thymus extended a 3' terminus of DNA for only one nucleotide before dissociating (18).
Finally, it is clear from recent work (15,19,20) that proteins associated with DNA replication, for example, E. coli DNA-binding protein, can affect processivity. The simple, rapid method described here for quantitative measurement of processivity provides a useful tool to assess the effects of these proteins on the mechanism of DNA polymerases. The advantage of the method described here is that virtually no restriction is placed either on the choice of primer-template or reaction conditions.

Acknowledgments
-We wish to thank Dr. I. R. Lehman for his interest and encouragement.
We also thank Dr.  Figs. 1 and 2. These curves show the relationship between the ratio of reaction rates with a limited uersus complete complement of dNTPs and the processivity of polymerization.
To simplify the analysis, the relative cycling time (TX/T,) is assumed to be 1.0. The relationship can be corrected for other values of relative cycling time as described under "Theory" and below.
Determination of Processivity with ColEl DNA and Activated Calf Thymus DNA-In this case, the rate of limited synthesis with one, two, or three dNTPs is compared to the rate of complete synthesis when all four dNTPs are provided. As mentioned under "Theory," the rate of polymerization with any number of dNTPs may be generalized as follows: E Nx Px = 7, (X=l,2,3or4) (1) where the subscript x denotes the number of dNTPs, P is the polymerization rate, E, is the number of enzyme molecules, N, is the average number of nucleotides polymerized during each polymerization cycle, and T is the cycling time. The term N, may be expressed in the following manner: where N is the processivity. The value of S, is determined by the deoxynucleoside triphosphates present and the base composition of the template. Values of S, are shown in Table V for the cases of calf thymus DNA, ColEl DNA, and polyld(A-Tll. When all four dNTPs are present, S,=, = 1 and the expression for N, becomes: N,z4 = ,il (1 + l2 + l3 +...+ 1") D, = y nD,, n=l (22) =N This simply shows that the average number of nucleotides incorporated per polymerization cycle with all four dNTPs is, indeed, the processivity. When one, two, or three dNTPs are present (X = 1, 2, or 3, respectively), the expression for N, may be rewritten: When only a single deoxynucleoside triphosphate is radioactive, a correction factor (L) must be incorporated into the expression. The ratio of rates of radioactivity incorporated in limited versus complete synthetic reactions may then be expressed as: to directly determine processivity from the curves in Fig. 1.
Determination of Processivity with PoZy[d(A-T)] -In this case, limited synthesis with d'M'P is compared to complete synthesis with dATP and dTTP. With limited synthesis on this defined primer-template, only a single nucleotide may be incorporated on one-half of the primer-templates, and none can be added to the remainder. Thus, the average number of nucleotides incorporated per polymerization cycle is 0.5. The polymerization rates for synthesis in the presence of a limited and full complement of dNTPs may then be expressed as follows: Limited synthesis:  Table V. In order to reduce the number of variables so that the expression could be graphed, it was assumed that T,/T, = 1. This means that cycling time is unaffected by omission of any of the deoxynucleoside triphosphates. Equation 10 then reduces to:  Table V were used to generate the curves shown in Fig. 1.
In order to use the figure to calculate processivity it is necessary to calculate (R 's:4) from: (181 Since R,., and T,/T, are all measurable values, it is possible Moreover, the correction factor, L, with label only in d'ITP, is 2. When L is incorporated into the ratio expression to yield the ratio of label incorporation (RI,,), the expression becomes: For purposes of illustrating the relationship, we assume (T,/ T,) = 1. Then R',:2 = l/N. This expression was used to generate the curve shown in Fig. 2. The correction for cycling time can be made as shown for calf thymus DNA in Equation 18, and processivity may be calculated from measured values of reaction rate.