©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Gel Kinetic Analysis of DNA Polymerase Fidelity in the Presence of Proofreading Using Bacteriophage T4 DNA Polymerase (*)

(Received for publication, July 26, 1994; and in revised form, December 18, 1994)

Steven Creighton (§) Myron F. Goodman (¶)

From the Department of Biological Sciences, University of Southern California, Los Angeles, California 90089-1340

ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
FOOTNOTES
REFERENCES

ABSTRACT

A gel fidelity assay, previously used in the analysis of DNA polymerases having no associated 3` to 5` exonuclease activity, has been generalized for use with polymerases that contain exonucleolytic proofreading. The main purpose of this study was the development of a general analysis, using a standard Markov model, to convert experimentally observed DNA primer gel bands arising from insertion and proofreading of right and wrong deoxyribonucleotides, into nucleotide incorporation velocities and, most importantly, fidelities. The model has been applied primarily to an analysis of polymerase kinetics and fidelity in the presence of a next correct rescue dNTP, but the model can be conveniently modified to investigate other experimental designs. In the presence of rescue dNTP, direct competition occurs between excision or extension of a mismatch. At concentrations of rescue dNTP sufficient to suppress the gel band intensity at the mismatch target site, nucleotide incorporation and misincorporation rates can be obtained from the ratios of gel band intensities 3` (downstream) and 5` (upstream) to the target site, measured as a function dNTP concentration for ``wrong'' and ``right'' dNTP substrates. The polymerase misincorporation efficiency, in the presence of proofreading, is given by the ratio of wrong to right incorporation efficiencies, V(max)/K, obtained from the gel band ratios. The bacteriophage T4 polymerase with a highly active 3`-exonuclease activity was used to illustrate the assay. Nucleotide misincorporation efficiencies measured at several template sites were dCMPbulletA 10, dGMPbulletA 10, dTMPbulletT 2 times 10, and dAMPbulletA < 10. Proofreading of the dGMPbulletA mispair was suppressed by about 3-fold in the presence of high concentrations of next correct ``rescue'' dNTP causing a concomitant reduction in the fidelity of dGMPbulletA to about 3 times 10.


INTRODUCTION

A large number of studies on the fidelity of DNA synthesis using purified DNA polymerase have been performed over the past 30 years (1, 2) . An initial experiment performed by Kornberg and co-workers (3) measured the frequency of mispairing of the mutagenic base analogue bromouracil with G using Escherichia coli DNA pol I. (^1)Hall and Lehman(4) , compared misincorporation of dTMP opposite G using DNA polymerases purified from wild-type and mutator (tsL56) T4 bacteriophage. E. coli pol I and T4 polymerases contain 5` 3` polymerase and 3` 5` proofreading exonuclease activities on a single polypeptide chain. Biochemical studies using pol I (5) and T4 mutator, wild-type, and antimutator polymerases (6, 7, 8, 9, 10) were crucial in demonstrating that discrimination against non-Watson-Crick base pairs occurred during nucleotide insertion and excision, and the combined action of both steps produced a high fidelity DNA product. Subsequent experiments using a wide variety of DNA polymerases and reverse transcriptases showed that the spectrum of errors and their template locations could differ widely among polymerases; recent reviews dealing with DNA synthesis fidelity are contained in Refs. 1, 2, 11, and 12.

Although DNA polymerase errors occur infrequently, different types of errors (e.g. transitions, transversion, and frameshifts) cover a wide range of frequencies and are distributed nonrandomly in DNA. Many factors, perhaps involving subtle differences in the interactions linking polymerase, matched and mismatched dNTP substrates, and primer-template DNA, can contribute to enzyme-specific variations in mutational spectra and nonrandom error distributions. Examples include fluctuations in base stacking that can perturb nucleotide insertion rates and fidelities(13) , primer-template slippage events that can lead both to base substitution and frameshift errors(14, 15, 16) , and sequence context effects (e.g. A-T or G-C ``richness'' that can influence proofreading efficiencies (17, 18, 19, 20, 21, 22) ).

The availability of a rapid assay measuring fidelity at arbitrary template locations would be useful for analyzing how differences in polymerases and primer template sequences contribute to each individual type of base substitution and frameshift mutation. Direct observations of incorporation fidelity, e.g. using two radioactive labels to measure the relative incorporation of mismatched and matched base pairs(9, 10) , are simple in concept but difficult in practice. In experiments where there is direct competition between matched versus mismatched dNTPs for incorporation into DNA, it is often difficult to detect misincorporations, even when dNTP pool concentrations are biased to favor insertion of a mispaired dNTP substrate(23) .

A ``gel kinetic'' assay, in which incorporation of matched and mismatched dNTP substrates are measured, in separate reactions, as a function of dNTP concentration, has been used as an alternative method of deducing insertion fidelity for polymerases (2, 24, 25) . In the gel kinetic assay, extension of P-labeled primers by the addition of either matched or mismatched unlabeled nucleotides opposite a template target site can be visualized using polyacrylamide gel electrophoresis to resolve primers differing in length by one or more nucleotides. In the absence of exonuclease activity, the origin of each gel band results from either a newly inserted ``right'' or ``wrong'' nucleotide or from polymerase dissociation. The assay can be performed rapidly, and the kinetic analysis leads to simple expressions for insertion rates and fidelities in terms of gel band intensity ratios(2, 24, 25) . However, the presence of proofreading adds considerable complexity to the kinetic analysis, because gel bands can arise from either insertion or excision of a nucleotide or from polymerase dissociation(2) . In this paper, we provide a detailed kinetic analysis of the gel fidelity assay for DNA synthesis in the presence of exonucleolytic proofreading. We use the assay to measure the fidelity of synthesis by T4 DNA polymerase at several defined template sites.


EXPERIMENTAL PROCEDURES

Materials

Purified wild-type T4 DNA Polymerase and an exonuclease-deficient mutant T4 polymerase, D112A,E114A was the kind gift of Dr. Linda Reha-Krantz. Fast protein liquid chromatography-purified dNTP substrates were purchased from Pharmacia Biotech Inc. and were used without further purification. Radioactive [-P]ATP was purchased from ICN Radiochemicals Inc. T4 polynucleotide kinase for 5`-end labeling was purchased form U. S. Biochemical Corp.

The primers and templates used were synthesized by Dr. Linda B. Bloom, University of Southern California, on an Applied Biosystems Inc. 381A DNA synthesizer, and by Dr. Lynn Williams (Comprehensive Cancer Center, University of Southern California, Los Angeles) and used after gel purification. The 30-mer template sequence was 5`-TCATCGAGCATGATCACGTCGTGACTGGGA-3`. The 15-mer primer used for the primer extension and turnover experiments was 5`-TCCCAGTCACGACGT-3`. Additional 18-mer primers used for the exonuclease partitioning experiments had the sequences 5`-TCCCAGTCACGACGTGAT-3` and 5`-TCCCAGTCACGACGTGAG-3`.

Reaction Conditions for Primer Extension Measurements

The procedures for 5`-end labeling and primer-template annealing were identical to those described previously(13, 24) . The concentration of primer-template after annealing was 270 nM. The 3times reaction buffer consisted of 120 mM Tris-Cl, pH 8.0, 30 mM MgCl(2), 2 mg/ml bovine serum albumin, and 25 mM dithiothreitol. T4 Polymerase (stock concentration, 100 µM) was diluted 10,000-fold in 3times reaction buffer on ice. For running-start primer extension reactions(13, 24) , a 3-µl volume of 3times dNTP substrate (in 5 mM Tris-Cl, pH 7.5) was added to 3 µl of the annealed primer-template and placed in water bath at 37 °C. Reactions were initiated by the addition of 3 µl of the enzyme/reaction buffer mixture and quenched by adding 9 µl of 95% formamide, 20 mM EDTA. The final reaction mixture had 90 nM primer-template and 3 nM T4 DNA polymerase. A series of running-start reactions run for different lengths of time determined that reactions carried out for approximately 1 min were sufficient to resolve primer elongation bands corresponding to incorporation of either correct or incorrect deoxynucleotides and subsequent elongation. Under these conditions, less than 20% of the input P/T (DNA primer-template) molecules were elongated by polymerase, satisfying ``single completed hit'' conditions (2) (see ``Markov Model Analysis'').

Polymerase-Exonuclease Partitioning Measurements

Primers (18-mers) were annealed to the template forming either a correctly matched, T(primer)bulletA, or mismatched, G(primer)bulletA, base pair at the 3`-primer terminus. Except for the different primers used, the reactions were performed in the same manner as the primer extension experiments. To measure the competition between extension and excision at the GbulletA mismatched terminus, it was necessary to run the experiment for 5 min in order to observe measurable extension of the mismatch in the presence of 50 µM dCTP, present in the reaction as the next correct ``rescue'' nucleotide (for example, see Fig. 7b).


Figure 7: Partitioning between polymerizaton and proofreading at matched and mismatched primer termini from a standing start. T4 DNA polymerase was presented with preformed correctly paired or mispaired P/T termini. a, correctly paired dTMPbulletA primer-3` terminus; b, incorrectly paired dGMPbulletA primer-3` terminus. The ratio of the extended primers (the sum of bands after the primer band) to degraded primers (the sum of bands before the primer band) is plotted as a function of the concentration of the next correct nucleotide, dCTP.



Gel Electrophoresis and Quantitation

For both the primer extension and exonuclease partitioning experiments, after quenching the final reaction mixture was heated to 100 °C for 5 min and cooled on ice for 1 min, and a 4-µl aliquot was loaded on a 16% polyacrylamide gel (40 times 30 times 0.07 cm) containing 8 M urea. Electrophoresis was carried out for about 4 h at 2000 V; the gel was dried, and the radiation in each band was measured using a Molecular Dynamics PhosphorImager (Sunnyvale, CA) and the software provided.

Analysis of Gel Band Intensities

For all primer extension experiments, the gel band intensities were converted into relative V(max)/K(m) values as follows. We define I as the sum of the integrated intensities of gel bands corresponding to nucleotide incorporations at a target site T and primers extended past T (i.e.I = I+I+I+. . . ). For each target nucleotide, in the absence of proofreading 3`-exonuclease, the value of v=I/Iis plotted versusthe concentration of the target nucleotide. The data are plotted either in double reciprocal Lineweaver-Burk form or as a nonlinear least squares fit to a rectangular hyperbola, I/I=Vbullet[dNTP]/(K+[dNTP]), where Vis the relative maximum velocity for incorporation of dNMP at the target site T(2) . The ratio V/Kis obtained from either the reciprocal of the yaxis intercept of the Lineweaver-Burk plot or from the slope in the linear region of the rectangular hyperbola(13, 24) . The values of V/Kfor a single determination are reproducible to ±30%. The misinsertion efficiency, f, of a nucleotide at site Tin the absence of proofreading is given by the ratio (V/K)/(V/K)for incorporation of wrong (W) and right (R) nucleotides, measured in separatereactions (2, 10, 26) (see ). The misincorporation efficiency, f, in the presence of proofreading is obtained in the same manner as the misinsertion efficiency, except that the values of I/Iare plotted as a function of the concentrations of wrong and right nucleotides incorporated opposite a target site T, where a band at Tis absent in the presence of high concentrations of next correct rescue dNTP (see Fig. 1and ).


Figure 1: Sketch of gel kinetic DNA polymerase fidelity assay. A 5` P-labeled primer annealed to DNA template is extended by polymerase in a running-start reaction. The running-start deoxynucleoside triphosphate substrates G (dGTP) and A (dATP) are present at concentrations required to achieve nearly maximum forward polymerization rates. The dNTPs, dTTP (right) and dGTP (wrong), to be inserted at the template target site T (the target base is A for this example), are measured as a function of concentration, in separate reactions, in the presence of a rescue substrate (dCTP) present at a concentration required to achieve approximately maximum rates of extension of the mismatched primer terminus. The ratio of gel bands, I/I, is plotted as a function of target dNTP concentrations, and the values of V(max)/K are determined separately for the right and wrong incorporations; (I = I + I + I + . . . ). The expected gel band patterns for correct insertions (dTMPbulletA) yield a relatively large value of I compared with a low intensity band at T - 1; see Fig. 4a. For incorrect insertions (dGMPbulletA), I is small compared with a high intensity band at T - 1; (see Fig. 4b where the T - 1 band corresponds to the intense AbulletT band located 2 nucleotides downstream of the primer-3` terminus). Ideally, the band at the target site T is either missing or small compared with the bands at T + 1 and T - 1. To satisfy SCH conditions, see ``Markov Model Analysis,'' less than 20% of the input P-labeled primer band is extended during the course of the reaction. The misincorporation efficiency, f, is determined from the V(max)/Kratios for wrong and right incorporations.




Figure 4: Incorporation of one right and three wrong nucleotides opposite a single site on the template. Primer extension experiments were performed with 30 µM dGTP, 30 µM dATP and varying amounts of the nucleotide to be inserted opposite template A, as well as varying amounts of the next correct nucleotide (dCTP). In a, the incorporation of the correct dTMP opposite A (the third nucleotide to be added) in the presence of dCTP (30 µM) is shown. In b, the misincorporation of dGMP in the absence and presence of dCTP (30 µM) is shown, while in c, the concentration of dCTP was varied and served as both the misincorporated nucleotide and the next correct nucleotide. The relative velocity of misincorporation of dCTP, at low concentrations, was fit accurately by the quadratic expression v = (2.0 times 10 µM)[dCTP]^2. Paneld, shows the incorporation of the incorrect dAMP in the absence and presence of the rescue nucleotide (dCTP). Note that the incorporation in the lanes with the rescue nucleotide present were caused by the misincorporation of dCMP.




RESULTS

Extension of 5` P-labeled primers by incorporation of matched and mismatched deoxyribonucleotides opposite individual template target sites can be visualized directly by polyacrylamide gel electrophoresis(24, 27, 28) . Measurements of the dependence of integrated gel band intensities as a function of the concentration of right and wrong dNTP substrates have been used to deduce the fidelity of nucleotide insertion for DNA polymerases devoid of 3`-exonucleolytic proofreading activity(13, 24, 25) . Our primary experimental objective in this paper is to investigate the use of a gel kinetic assay to measure DNA polymerase fidelity in the presence of proofreading. A sketch illustrating the fidelity measurement is shown in Fig. 1. Wild-type bacteriophage T4 DNA polymerase, known to contain a relatively active associated 3`-exonuclease (nuclease/polymerase ratio 0.1, see (6) and (10) ) has been used in the analysis.

Observation of Misincorporation by T4 DNA Polymerase

A series of initial experiments were aimed at determining whether T4 polymerase-catalyzed insertion errors were detectable by polyacrylamide gel electrophoresis. Ideally, the assays should be run to conform to single completed hit (SCH) conditions(2) . Single-hit conditions reflect a situation in which most P/T molecules (>90%) encounter a polymerase at most once but where each polymerase can extend or degrade many different P/T DNA molecules. Single-hit conditions are met either when less than 20% of the primer molecules are extended or when trapping molecules (e.g. unlabeled DNA, heparin) are present to sequester enzyme molecules free in solution. The requirement for completed hits guarantees that gel band intensities result primarily from polymerases that have dissociated from P/T DNA rather than from polymerases that remain bound to the DNA when the reaction is quenched. A high P/T to polymerase ratio (30:1) ensures that less than 1/30th of the intensity of any gel band is derived from the presence of bound polymerasebulletP/T complexes at the end of the reaction.

The T4 proofreading exonuclease has been shown to excise a sizable fraction (10-20%) of correctly inserted nucleotides during rapid forward synthesis(9, 10) , and it was therefore important to investigate whether misincorporation bands could be detected in the presence of an active proofreading exonuclease (Fig. 2). The template sequence is shown at the right-hand side, and the primer-3` terminus is indicated by the intense band located opposite template site A (e.g. see lane1, None). A band corresponding to correct incorporation opposite template C was observed only when dGTP was present (Fig. 2, lane2, G). No detectable primer extension was observed when either dATP, dTTP, or dCTP was included as the sole source of substrate (Fig. 2, lanes3-5). Extensive primer degradation caused by the action of the polymerase associated 3` 5` exonuclease was detected in the absence of dGTP (lanes3-5), while the only detectable degradation band in the presence of dGTP corresponded to removal of a single dTMP at the primer-3`-terminus (lane2).


Figure 2: Observation of misincorporations by T4 DNA polymerase. Each gel lane illustrates a primer extension reaction containing 70 µM of each of the nucleotides shown. The template sequence is given at the right-handside, and the primer-3` terminus is indicated by the intense band located opposite template site A (e.g. see lane1, None).



Primer extension was measured in the presence of various combinations of two dNTP substrates (Fig. 2, lanes6-11). The gel patterns revealed the presence of a variety of misincorporation events. The upperband opposite the template A position (lane7, ) arose from misincorporation opposite template T followed by extension of the mismatched primer terminus by the correct incorporation of dTMP opposite A. A band of barely detectable intensity located opposite template T (lane7) reflects a low probability of polymerase dissociation from the P/T, prior either to excision or extension of the mispair. A point of interest concerning the T4 polymerase is that, contrary to expectations, the identity of the mispair appears to be dTMPbulletT rather than dGMPbulletT. Primer extension was observed to increase with increasing concentrations of dTTP but not dGTP (data not shown). The formation of a dCMPbulletT mismatch is indicated by the band opposite template T (lane8, ). The primer terminated following formation of the CbulletT mispair (lane8) because, unlike the case of extension of the TbulletT mispair (lane7, ), the next correct nucleotide, dTTP, was absent from the reaction shown in lane 8. Misincorporation bands were also observed in the absence of the nucleotide (dGTP) required for insertion at the primer-3` terminus (lanes 9-11). Thus, the presence of detectable misincorporation gel bands provides a means for analyzing the fidelity of polymerases in the presence of exonucleolytic proofreading by using a gel kinetic analysis analogous to the assay developed to measure fidelity in the absence of proofreading(13, 24, 25) .

In comparison with reactions carried out with two substrates, combinations of three substrates resulted in a small fraction of primers extended by as many as 9 nucleotides containing at least one misincorporation band (data not shown). A reaction containing all four dNTP substrates (lane12, All) showed prominent pause bands at template incorporation sites 2, 12, 14, and 15 (e.g. template incorporation site 2 refers to the template T site 2 nucleotides downstream from the primer-3` terminus A site, lane1). Thus, during a single hit, a majority of primers can be extended by at least 12 nucleotides, but the T4 polymerase also has a small (10%) probability of dissociating following addition of 2 nucleotides.

Misincorporation Kinetics of Wild-type T4 DNA Polymerase

An experiment was carried out to compare the kinetics of incorporation of right (dAMPbulletT) and wrong (dTMPbulletT) base pairs at a template target site, T, 2 nucleotides downstream from the primer-3` terminus (Fig. 3). The running-start nucleotide dGTP was present in all reactions. The kinetics of incorporating dAMP opposite T was carried out in the absence and presence of the rescue nucleotide dTTP (Fig. 3a). A plot of relative incorporation velocity, v (see ), given by the ratio of integrated band intensities at the target site and beyond compared with the integrated intensity one base before the target, I/I, versus[dATP]is well fit by a rectangular hyperbola (Fig. 3a, right-handside). The kinetics of incorporating dAMP at the target T site were the same in the presence or absence of rescue dTTP (Fig. 3a, right-handside). The band at the template target persists in the presence of dTTP because (i) this specific target appears to be a pause site attributable to relatively rapid dissociation of T4 polymerase (Fig. 2, lane12, All) and (ii) the low concentration of rescue dTTP, 3 µM, may be insufficient to catalyze complete primer extension prior to polymerase dissociation.


Figure 3: T4 DNA polymerase incorporation kinetics. Primer extension experiments were run for 1 min with 30 µM dGTP and varying amounts of the nucleotide substrate to be inserted opposite template T. Shown to the left of each gel is the nucleotide inserted on the primer strand and the template base corresponding to each band (i.e. AbulletT represents dAMP inserted opposite T). In a, the substrate was dATP, present at the concentrations indicated, both with (closedcircles) and without (opencircles) the next correct nucleotide dTTP (3 µM). A plot showing the ratio (I(2) + I(3))/I(1) was fit (in the presence and absence of rescue dTTP) to a rectangular hyperbola. A least-squares fit gave a relative V(max) = 45 and K = 12 µM (V(max)/K = 3.8 µM). In b, the substrate for misincorporation was dTTP, which served as its own next correct rescue nucleotide. The ratio I(3)/I(1) was plotted, and a linear fit was obtained corresponding to V(max)/K = 6 times 10 µM. Reaction conditions are described under ``Experimental Procedures,'' see ``Reaction Conditions for Primer Extension Measurements.''



For misincorporation of dTMP opposite template T, the target and rescue substrates were both dTTP (Fig. 3b). Rescue bands at site T +1 are clearly visible at the two highest concentrations of dTTP, 100 and 300 µM, and a very weak, but measurable, band is present at 30 µM dTTP (Fig. 3b). The misincorporation velocities were a linear function of [dTTP], with no detectable curvature to permit an estimate of K(m) (Fig. 3b, right-handside). An important point to emphasize is that the absence of a detectable primer extension band at the target site implies that the rescue nucleotide was present at high enough concentration (>30 µM) to allow extension of the mismatched primer-3` terminus prior to polymerase dissociation and that the complete removal of a mismatched dTTPbulletT by the exonuclease, prior to polymerase dissociation, created a band at site T -1 by removing the remaining unextended portion of the primer band at the target T.

The fidelity analysis is simplified when a target band at T is either absent, or more generally, small compared with the integrated intensities at both T +1 and T -1. The presence of an appreciable target band leads to potential ambiguities in the analysis (see ``Markov Model Analysis'') because a band at T can arise either from incorporation at the target site followed by polymerase dissociation or from exonucleolytic excision at the rescue site. Proofreading of a next correct rescue nucleotide could occur with relatively high efficiency because it is likely to be destabilized when located next to a mispair. Thus, the origin of the target band will be ambiguous unless additional measurements are made, specifically, a measurement of polymerase rate of dissociation at the target site (2, 29, 30) and a measurement of turnover of rescue dNTP dNMP(9, 10) . For the case of the correct nucleotide, however, the target band T was used in the analysis because the kinetics for incorporation of the correct nucleotide were essentially the same in the presence and absence of the next correct nucleotide (Fig. 3a, right-handside).

The misincorporation efficiency, f, defined as the reciprocal of the incorporation fidelity, is equal to the ratio of dTMP/dAMP incorporation opposite T, and is expressed as a ratio of V(max)/K(m) values for TbulletT (Wrong) compared with AbulletT (Right) base pairs.

A value of f 1.6 times 10 was obtained from the data in Fig. 3, a and b.

Insertion of all four nucleotides was measured opposite template A, three nucleotides downstream from the primer-3` terminus (Fig. 4). Two running-start nucleotides, dGTP and dATP were present at concentrations geq30 µM, and the concentration of each of the four dNTPs was varied as shown. Misincorporation kinetics for dGTP and dATP were measured in the presence and absence of the rescue nucleotide, dCTP geq 30 µM, under multiple-hit conditions (there was an average of about 1.5 hits/extended primer). The SCH approximation is extremely useful for describing the assay; however, accurate fidelity determinations can be made when multiple hits have occurred (see ``Correcting for Multiple Hits'' under ``Appendix'')

DNA synthesis was first carried out in the presence of all four dNTPs, with increasing concentrations of the correct substrate, dTTP (Fig. 4a). An increase in the primer extension band corresponding to dGMPbulletA misincorporation was observed with increasing dGTP concentration in the absence of rescue dCTP (Fig. 4b). There appeared to be no detectable primer extension continuing beyond the GbulletA mismatch in the absence of dCTP. When dCTP was included in the reaction, the dGMPbulletA misincorporation band diminished significantly, and a trace dGMPbulletA band was observed only at the highest concentration of dGTP (1000 µM).

A small fraction of primers was extended by the addition of at least 10 nucleotides beyond the initial mismatch in the presence of the rescue nucleotide, and these contained at least two, and possibly three, additional mismatches located opposite the three template A sites downstream from the initial target A site. At each site, the band opposite A was missing (dTTP was absent from the reaction in Fig. 4b), suggesting that the enzyme excised the misinserted nucleotide with high efficiency, giving rise to a relatively intense band, at T -1, 1 base before the target site, and extended the mismatch at lower efficiency giving rise to a band at T +1. Note that the excision bands corresponding to 1 base prior to each A template site increased in intensity with increasing dGTP concentration. It is therefore likely that the mispairs were predominantly dGMPbulletA, but some dCMPbulletA mispairs may also have occurred. We estimated the efficiency of misincorporating dGMP opposite A located 9 nucleotides from the primer terminus by summing the integrated intensities of all the bands downstream of the dGMPbulletA site, dividing by the integrated intensity of the band prior to the mispair site, I/I, and plotting the ratio as a function of the dGTP concentration (see and ). The efficiency of incorporating dTMP opposite A can be determined in the same manner (Fig. 4a; note that inclusion of the low intensity (TbulletA) band, I, at the target site has a negligible effect on the value of V/Kfor the correct insertion (see ``Markov Model Analysis'')). For this template A site, V/K(dGMPbulletA) =1.5 times10, V/K(dTMPbulletA) =1.6 times10, resulting in f10.

The misincorporation of dCMP opposite A as a function of increasing dCTP concentration is shown in Fig. 4c. Significant primer extension beyond the four template A sites (sites 3, 6, 9, and 13) was observed, with a much greater extent of misincorporation and continued synthesis past the site of the mispair occurring at higher rescue dCTP levels (Fig. 4c). Summation of the integrated intensities of bands extending beyond the first A site (site 3) resulted in a quadratic dependence of mispair extension efficiency as a function of dCTP concentration, in the low dCTP concentration range (data not shown). A quadratic dependence is expected to occur at low concentration of rescue dNTP when the target and rescue dNTPs are the same(31) .

Misincorporation of dAMP opposite A was not detected using dATP concentrations up to 1000 µM (Fig. 4d, NoRescue). The absence of a detectable dAMPbulletA band at high concentrations of dATP was not likely to have been caused by substrate inhibition of the polymerase because primer extension bands were observed in the presence of rescue dCTP (Fig. 4d, Rescue). Therefore, the misincorporation of dCMP opposite template A sites were most likely to be responsible for primer elongation past the first two A sites in the absence of dTTP. From the data in Fig. 4, the misincorporation efficiencies () were estimated as dCMPbulletA 10 and dGMPbulletA 3 times 10 and 1 times 10, in the presence and absence of rescue dCTP, respectively. The absence of a detectable primer extension band corresponding to misincorporation of dAMP opposite A (Fig. 4d, NoRescue) places an approximate upper limit on the value of f (dAMPbulletA) < 10.

Dependence of Misincorporation Efficiency, f, on the Concentration of Rescue dNTP

We investigated the efficiency of incorporating dGMP opposite A as a function of the concentration of rescue dCTP (Fig. 5). When synthesis was carried out in the presence of 100 µM target dGTP, there was a clear dGMPbulletA misincorporation band observed in the absence of dCTP (Fig. 5a, see also Fig. 4b, NoRescue). The band corresponding to dGMPbulletA misincorporation diminished in intensity with increasing concentration of rescue dCTP and was accompanied by an increase in the extent of primer elongation beyond the mismatch. The ratio I/I, plotted in Fig. 5b, is proportional to the rate of misinsertion of dGMPbulletA multiplied by the probability that either polymerase dissociation or continued extension by the rescue base occurred relative to excision of the misinserted nucleotide. The misincorporation rate increased nearly 3-fold as the level of rescue dCTP was increased between 0 and 10 µM(Fig. 5b) as a result of inhibition of proofreading. The ratio I/I, plotted in Fig. 5c, represents the ratio of the rate of polymerization of the rescue nucleotide relative to polymerase dissociation at the target misincorporation site (template A, site 3). The maximum polymerization/dissociation rate was about 30; this rate is an order of magnitude less than that observed for dTMPbulletA correct incorporation at the same template site (Fig. 4a). However, the Kfound for the rescue reaction was approximately 2 µM(Fig. 5b), which was considerably lower than expected.


Figure 5: Kinetics of the rescue of a mismatch by the next correct nucleotide. In the primer extension reaction, the substrate concentrations were dGTP = 100 µM and dATP = 30 µM, and dCTP concentration was varied as shown. In a, the gel bands are shown; in b, I(3)/I(2) is plotted as a function of dCTP concentration. Note that in the absence of rescue nucleotide, some of the mismatches escaped cleavage because of polymerase dissociation. In c, the value of I/Iis plotted versusdCTP concentration, and this ratio reflects the kinetics of incorporation of the rescue nucleotide.



We considered the obvious possibility that a small fraction of rescue dCTP could have undergone deamination to dUTP as an explanation for the low K(m) observed for extension of the GbulletA mispair. In the presence of low contaminating levels of dUTP, UbulletA correct pairs could have been formed in preference to GbulletA mispairs, and rescue of the UbulletA pairs could then have occurred at much lower dCTP concentrations than required for rescuing GbulletA mispairs, since the addition of dCMP opposite G would occur after a correct base pair (UbulletA). Since the K(m) for the addition of dCMP would be in the micromolar range, the rescue should be saturated at [dCTP] above 1 µM. However, the absence of a detectable incorporation band opposite A at 10 µM dCTP (Fig. 4c) argues against this possibility because the rescue reaction is approximately saturated in the presence of 10 µM dCTP (Fig. 5b). A second argument against the presence of dUTP contamination is that as the concentration of dCTP is increased between 0 and 10 µM in Fig. 5a, there is no increase in insertion opposite A above the level of incorporation of dGMP, where an increase would be expected if the dCTP was contaminated with dUTP.

A comparison between wild-type and an exonuclease-deficient T4 polymerase for dGMPbulletA misincorporation showed that f (dGMPbulletA) 5 times 10 measured for the exonuclease-deficient enzyme was about 2-fold higher than the wild-type error rate measured in the presence of 30 µM dCTP rescue nucleotide and was about 5-fold higher than the wild-type rate measured in the absence of rescue dCTP (Fig. 4b). The total amount of primer extension for the exonuclease-deficient polymerase was essentially independent of the concentration of rescue dCTP (Fig. 6), whereas primer extension increased appreciably for the wild-type polymerase (Fig. 4b, Rescue). A second misincorporation, either dGMPbulletG or possibly dAMPbulletG, formed immediately adjacent to the dGMPbulletA misincorporation band, was clearly observed in the banding pattern for the exonuclease-deficient enzyme (Fig. 6, position indicated by an arrow) but was not present in case of wild-type T4 polymerase (Fig. 4b). The mispair was most likely to be GbulletG because dGTP was present at a 30-fold higher concentration than dATP.


Figure 6: Misincorporation by a T4 exonuclease-deficient polymerase and the effect of the next correct nucleotide. In the primer extension reaction, the substrate concentrations were dGTP = 100 µM and dATP = 30 µM, and dCTP concentration was varied as shown. The arrow indicates the location of a band in the 0 µM dCTP lane that corresponds most likely to the misincorporation of dGMP opposite G (or possibly to the misincorporation of dAMP opposite template G) following the formation of the GbulletA mismatch.



Partitioning between Polymerization and Exonucleolytic Cleavage from a Standing Start

The probability of exonucleolytic cleavage versus polymerization when T4 polymerase initially encounters a primer template from a standing start was investigated using primers terminating with T (forming a TbulletA base pair) or G (forming a GbulletA mispair) opposite the template A target investigated in Fig. 4. Partitioning between polymerization and proofreading was measured by comparing the the amount of primer degraded to the amount extended as a function of the concentration of next correct dCTP. The ratio of the extended/degraded primer was plotted as a function of dCTP concentration for both matched (Fig. 7a) and mismatched (Fig. 7b) primer termini. The polymerase-to-exonuclease partitioning for the correct nucleotide leveled off at a ratio of 3 (Fig. 7a), suggesting that the polymerase adds the next correct nucleotide 75% of the time after correctly inserting a nucleotide at T, while excising the just incorporated nucleotide only 25% of the time. In contrast, partitioning for the incorrect nucleotide remained linear up to concentration of 1 mM next correct dCTP (Fig. 7b); at 1 mM rescue dCTP, 1 dCMP was added for every 3 misinserted (dGMP) nucleotides removed. These data contrast with the low concentration of rescue dCTP (K(m) 2 µM) required to extend a dGMPbulletA mismatch in a running-start reaction (Fig. 5b). This difference may reflect a requirement for an additional kinetic step when polymerase initially binds a P/T compared with a bound enzyme approaching a target from a running start. Perhaps the polymerase binds to DNA in a loose binding mode prior to polymerization and in a tighter binding mode once polymerization has begun. Capson et al.(32) have shown that there is a change in the polymerasebulletP/T complex following addition of the first dNMP resulting in an increased affinity of the enzyme for DNA.

Markov Model Analysis

During polymerization, right and wrong nucleotides are inserted and excised opposite template strand bases and, at each P/T DNA site, polymerases generally have sequence-dependent probabilities of dissociation(29, 33) . Starting with identical P-labeled P/T DNA, the insertion, excision, and dissociation events give rise to a series of discrete bands on a polyacrylamide gel. The objective is to deduce the incorporation fidelity of DNA polymerases at an arbitrary template site in the presence of 3` 5` exonuclease proofreading activity. Primer extension measurements are made as a function of wrong and right dNTP substrate concentrations run in separate reactions. A model is required to interpret gel band origins, quantitatively, in terms of insertion and excision efficiencies for wrong and right nucleotides and to deduce site-specific nucleotide misincorporation efficiencies, f ().

SCH Approximation

In the analysis, we have assumed that the kinetics experiments are run under SCH conditions; later we will discuss the ramifications of this approximation. SCH conditions are satisfied if a great majority of P/T molecules encounter a DNA polymerase at most only once during the course of a primer extension reaction. Gel bands are assumed to result from a ``completed'' hit, which takes place when the polymerase dissociates following one or more insertion or excision reactions. An ``incompleted'' hit refers to an enzyme still in the process of polymerization or excision when the reaction is quenched. The fraction of bands arising from incompleted hits depends on the ratio of polymerase/DNA and on the K(d) of the polymerase for P/T termini. SCH conditions are met if less than 20% of the input primer molecules are extended and when reactions contain either a high primer-template/DNA polymerase ratio or if a trap is present to bind free polymerases in solution(2) .

The probability of a P/T being hit n times by polymerase is given by a Poisson distribution, p(n) = (µ^n/n!) exp (-µ), assuming that the interaction between polymerase and any given P/T is independent of the identity of the P/T and of the number of times it was previously hit. The probability that any P/T is not extended is p(o) = exp (-µ), where µ is equal to the average number of hits/primer, µ = -ln(p(o)). The probability that a primer is not extended during the reaction, p(o), is measured as the fraction of unextended primers present at the end of the reaction. The distribution of bands provides an accurate reflection of the probabilities that a polymerase dissociates at a particular template site, and the band intensities reflect the probability that polymerase either inserts or excises a right or wrong dNMP to reach a particular template site prior to dissociation. For example, if the integrated intensities the bands are: I(+0) = 100, I(+1) = 20, I(+2) = 10, and I(+3) = 30, then the relative probabilities of a polymerase incorporating a given number of nucleotides during a single hit are: P(+1) = 33%, P(+2) = 17%, and P(+3) = 50%. These probabilities result from a single polymerasebulletP/T encounter and do not depend on any specific polymerization model. An explicit model is required for the interpretation of band intensities in terms of an underlying kinetic scheme. The effect of multiple encounters between polymerase and P/T DNA is discussed below (see ``Correcting for Multiple Hits'' under ``Appendix'').

Relating Misincorporation Efficiency to Gel Band Ratios in the Absence of 3` 5` Exonuclease Activity

Consider a running-start reaction in which at least 1 nucleotide is added prior to reaching a template target site (T) at which the incorporation fidelity is to be determined (see Fig. 1, top, sketch of P/T DNA). Each P-labeled gel band corresponds either to unextended primers or to primers extended by the addition of 1 or more nucleotides to reach the target site and beyond. In the absence of exonuclease, at each site T along the template the polymerase will either dissociate at a rate k or it will insert a dNMP residue with rate k, i.e. the polymerase either inserts a nucleotide opposite the target base (and continues beyond) contributing to I or dissociates from the template contributing to I(see Fig. 8a). The polymerase dissociation rate, k, and nucleotide insertion rate, k, are dependent on sequence context(29, 33) . Iis proportional to the probability of insertion k/(k+k), and Iis proportional to the probability of dissociation, k/(k+k). Thus, insertion velocity under SCH, in the absence of exonuclease, is expressed in terms of the gel bands as .


Figure 8: Markov models for DNA polymerase. In all figures, transient states are indicated by largegraycircles, absorbing states by smallwhitecircles, and transitions by single arrows labeled with the rate of the transition. The polymerase is assumed to reach the site immediately before the target site by adding the running start nucleotides (doublearrows). a, polymerase without an exonuclease. The polymerase begins in transient state 3. It will either make a transition to absorbing state 1 by dissociating with rate k or to absorbing state 2 by adding the next nucleotide with rate k. b, polymerase possessing an exonuclease. This is a minimal model for a DNA polymerase possessing an associated 3`-exonuclease. The system begins in transient state 4, from which it will either make a transition to absorbing state 1 with rate k by dissociating or make a transition to transient state 5 with rate k by adding the target nucleotide. If the polymerase is in transient state 5, it will either return to transient state 4 with rate k by excising the target nucleotide, go to absorbing state 2 with rate k by dissociating, or go to absorbing state 3 with rate k by adding the next correct rescue nucleotide. c, polymerase possessing an exonuclease with discreet states for the binding of the target nucleotide. The model is similar to the one shown in b, except that the transient states have been expanded to include association of a dNTP (indicated by N) with a polymerasebulletP/T complex, initially in transient state 3, to make a transition to transient state 4 (polymerasebulletP/TbulletdNTP complex) and dissociation of dNTP to make the reverse transition from state 4 back to state 3. Polymerase dissociation from either state 3 or state 4 into the absorbing state 1 will give rise to a gel band at template site T - 1. The polymerase can incorporate N, with rate constant k, to enter state 5. Once in state 5, the 3`-exonuclease can excise the newly incorporated N, with rate constant k, to return to state 3, or the polymerase can insert a rescue nucleotide, with rate constant k, to enter the absorbing state 2, giving rise to a gel band at template site T + 1. It is assumed that, while in state 3, the dissociation of the polymerase is small, i.e.k (k + k).



A knowledge of k rates at specific P/T sites, which can be evaluated by measuring the decrease in primer utilization as a function of time caused by polymerase dissociation(2, 33) , is not required to measure fidelity(2) . The polymerase is bound at the same correctly matched P/T terminus when making either right or wrong insertions, and thus k cancels from the expression for fidelity (). The relative misincorporation efficiency, f, is expressed as the ratio of apparent second order rate constants(26) , [(V(max)/K(m))(W)/(V(max)/K(m))(R)] giving the efficiency of insertion of wrong compared with right dNMPs at the target site (). V(max)/K(m) is given by the slope of the linear portion of the rectangular hyperbola plot, k versus dNTP concentration. A measurement of the ratio I/Iis sufficient to obtain the polymerase insertion fidelity in the absence of proofreading.

Relating Misincorporation Efficiency to Gel Band Ratios in the Presence of 3` 5` Exonuclease Activity: Markov Analysis Under SCH Conditions

In the presence of an exonuclease, it is no longer possible to identify a gel band at T with polymerase dissociation following insertion of a nucleotide, and a gel band at T -1 with dissociation prior to insertion at T. For example, a band at T -1 can arise, during a single hit, either from dissociation at T -1 prior to insertion at T or from dissociation at T -1 following insertion and then excision at T. To provide a model for the conversion of integrated gel band intensities into velocities and fidelities in the presence of proofreading, transitions coupling three sites on the template will be considered. The three template sites are T (target site at which f is evaluated); T -1, one nucleotide upstream from T; and T +1, one nucleotide downstream from T. The T +1 position is especially important in the misincorporation analysis because it can be used to analyze partitioning between two competing reactions occurring at T, mismatch extension versus proofreading. It has been shown that exonucleolytic excision of both matched and mismatched primer termini are inhibited with increasing concentrations of next correct dNTP. Thus, fidelity in the presence of exonuclease depends explicitly on the absolute level of rescue dNTP(10, 34) . Although proofreading can be suppressed, it is generally not eliminated even at saturating levels of rescue dNTP(10) .

In order to determine the relative band intensities in the presence of proofreading, we have used a Markov model to describe the system (see ``Appendix'' and (34) ). Solution of the model requires some simple matrix manipulations and gives the final distribution of band intensities in terms of the rate constants of the individual microscopic steps in the model (see Fig. 8b). Basically, solution of the model is accomplished by determining the final distribution of states of the system after an large amount of time has elapsed, assuming all systems initially prepared were polymerases located at template position T -1. The evolution of the ensemble of systems into the final distribution is governed by the multiplication of the vector corresponding to the initial state by a matrix that depends on the rates of transition between the states of the system. The final distribution of states when all polymerases have dissociated from their templates is identified with the gel band intensities. This corresponds to the completed hit approximation given earlier.

The model analysis in the presence of proofreading is strongly influenced by experimental conditions. At a concentration of rescue dNTP high enough to compete effectively with polymerase dissociation at T, (k + k) k, the band at T was not detected above background (Fig. 3b and 4, b and d). The probability of making a transition from states 4 to 1 contributing to Iis proportional to k(k+k), and the probability to go from states 4 to 3 contributing to Iis proportional to kk(see ). Thus, the ratio of T +1to T -1is

The ratio k/k is multiplied by a factor that gives the probability that the polymerase adds a rescue nucleotide to go from T T +1 prior to exonucleolytic excision of the inserted nucleotide to go from T T -1.

If the binding of the nucleotide is explicitly included in the model for the exonuclease (Fig. 8c), the apparent nucleotide incorporation rate (k) for the model is

where V(max) is the V(max) for the enzyme without an exonuclease, and dNTP is the nucleotide inserted at the target site T (see ``Appendix'' and ). The exonuclease reduces the apparent V(max) by the factor k/(k + k) leaving K(m) unchanged. The misincorporation efficiency in the presence of proofreading is determined from by varying the concentration of target dNTP (for right and wrong nucleotides separately) at a constant concentration of rescue dNTP. Values of V(max)/K(m) are obtained from the linear portion of a plot of I/IversusdNTP concentration.

Approximating Fidelity when a Band Is Present at T, I>0

The presence of a nonnegligible band intensity at the T position, caused by polymerase dissociation prior to either rescue or excision, can lead to potential ambiguities in the analysis of the gel bands caused by an uncertainty in whether a band at T would have been rescued or excised if the polymerase had not dissociated. If I>0, then upper and lower bounds for k, can be determined by adding the band at Tto that at T +1or to that at T -1, respectively. Thus, the misincorporation efficiency can be bracketed first by calculating fby adding the band intensity at Tto the intensity at T +1(the upper limit) and then comparing it with the value calculated by adding the band intensity at Tto that at T -1(the lower limit). In practice, except for the most distributive enzymes, differences between upper and lower misincorporation efficiency limits are likely to be within a factor of 2. If the rate of dissociation at Tis measured(29, 33) , then the fidelity can be calculated directly by using procedures outlined in (2) . However, the experimental effort to carry out the more complete analysis is substantial, and for most purposes the upper and lower limits for fidelity should be adequate.

The addition of a band at T to that at T +1 (and beyond) is not likely to alter the kinetics of correct incorporation significantly because less than 20% of correctly inserted nucleotides are typically excised(10) . In the case of incorporation of dAMP opposite T, no significant differences were observed comparing the polymerization kinetics carried out either in the absence or presence of rescue dNTP (Fig. 3a, right-handside). In contrast, the presence of a rescue dNTP markedly affected the kinetics for incorrect incorporations (Fig. 5c).


DISCUSSION

Mutations occur nonrandomly in DNA. The types and magnitudes of base substitution and frameshift errors can vary widely depending on polymerase properties (1, 2) and local behavior of P/T DNA termini(22, 33, 35) . Previously, we introduced a gel kinetic assay to measure DNA polymerase fidelity at arbitrary template sites in the absence of exonuclease proofreading(24, 25) . Misincorporations of normal nucleotides are rare events that are difficult to measure in assays in which right and wrong nucleotides compete directly for insertion into DNA, even in the absence of proofreading. A gel kinetic assay, in which incorporation of wrong and right nucleotides are measured in separate reactions, is designed to avoid many of the problems inherent in a direct competition assay.

A greater latitude in experimental design and gel band interpretation is possible using proofreading-proficient polymerases in contrast to the straightforward design and interpretation of fidelity measurements in the absence of proofreading(2) . In this paper, we have generalized the gel assay to measure fidelity in the presence of 3` 5` exonuclease activity using wild-type T4 DNA polymerase. A Markov model is used to convert experimentally observed primer extension gel band intensities, arising from insertion or excision of right and wrong nucleotides, into nucleotide incorporation velocities (see Markov Model Analysis). If primer extension bands corresponding to correct and incorrect nucleotide incorporations at defined template sites are detectable by polyacrylamide gel electrophoresis (Fig. 2Fig. 3Fig. 4Fig. 5Fig. 6), then incorporation efficiencies, V(max)/K(m) values, can be determined and the relative misincorporation efficiency (the reciprocal of incorporation fidelity) can be evaluated as the ratio of V(max)/K(m) for wrong compared with right incorporations ( Fig. 1and ).

Kinetically Determined Misincorporation Efficiencies in the Presence of Proofreading

Experiments are most easily analyzed when carried out under SCH conditions (see ``Markov Model Analysis''), so that the ratios of band intensities reflect the relative insertion and excision rates taking place on individual P/T DNA molecules and not steady-state product release rates(2) . Nucleotide misincorporation efficiencies, f (), were measured at three template sites. In contrast to misincorporation efficiencies, which are independent of absolute dNTP concentrations in the absence of 3`-exonuclease(26) , values of f obtained in the presence of proofreading depend explicitly on the concentration of next correct rescue dNTP(10, 34) . At saturating concentrations of rescue dNTP, it was generally possible to eliminate the band arising from polymerase dissociation at the target site T, leaving bands at the rescue site T +1 site and beyond, following extension of wrong and right primer termini, and at site T -1 following nucleolytic excision of mismatched or matched primer termini (Fig. 3b and Fig. 4, b-d). In the absence of a significant band at T, misincorporation efficiencies are determined from by plotting the ratios I/Ias a function of target dNTP concentration and fitting the data to a rectangular hyperbola to obtain values of V/Kfor wrong compared with right incorporations.

Using T4 polymerase, containing an active proofreading exonuclease, we measured misincoporation efficiencies at several P/T sites in the presence of saturating concentrations of rescue dNTP. Compared with dTMP incorporation opposite A, dGMPbulletA (Fig. 4b, Rescue) and dCMPbulletA (Fig. 4c), misincorporation efficiencies were approximately 3 times 10 and 10, respectively. Misincorporation of dAMP opposite A was not detected (Fig. 4d), f (dAMPbulletA) < 10. A value of f (dGMPbulletA) 10 was measured at a target A site 9 nucleotides downstream from the first A site (Fig. 4b). A value of f 1.6 times 10 was determined for dTMPbulletT misincorporation (Fig. 3, a and b). In contrast to the high misincorporation of dTMP opposite T, misincorporation of dGMP opposite T was at least a factor of 100 less efficient at this site, using either wild-type or exonuclease-deficient mutant T4 polymerases (data not shown). It has been observed that other proofreading-deficient polymerases have considerably less difficulty making and extending GbulletT compared with TbulletT mismatches(13, 36, 37) .

A defining hallmark of the next nucleotide effect is that primer extension competes with nucleotide excision, and thus proofreading should be reduced as levels of rescue dNTP are increased leading to increased misincorporation rates (10, 31) (see Fig. 3b). Values of V(max)/K(m) for misincorporation are predicted to increase quadratically with low increasing concentrations of rescue dNTP when the identity of the misincorporated and rescue nucleotides are the same(31) . The kinetics of dCMPbulletA mispair formation (Fig. 5c) was found to agree with this prediction (data not shown). When misincorporated and rescue nucleotides differ in identity, misincorporation efficiencies are expected to increase linearly at low increasing concentrations of rescue dNTP(10, 31) , as observed in Fig. 5c.

Applications of the Model to Experimental Design and Analysis

We suggest that use of high concentrations of rescue dNTP to eliminate, or at least reduce, the intensity of the band at a template target T is not only easiest to analyze, but is perhaps most biologically relevant. In vivo conditions are likely to favor rapid and highly processive synthesis. There is evidence in vitro, supported by data presented in this paper, demonstrating that T4 polymerase can switch between synthetic and degradative modes while remaining bound to a primer-3` terminus(38) . However, the analysis does not require the absence of a gel band at T (see ``Markov Model Analysis'' and (2) ), nor is it limited by restrictions contained in the models shown in Fig. 8.

An important advantage of the Markov analysis is that it is straightforward in principle and practice to introduce modifications into the model. Modifications are made directly in the transition matrix P (see and for the proofreading model used in this paper) to incorporate changes in the model with respect to number of states and transitions between states. The final state populations are arrived at by simple operations performed using P. This approach is considerably less cumbersome, much less time consuming, and much more intuitively understandable than formulating and solving a new series of rate equations for each alteration made to the model. To cite a single example, we have ignored the possibility of excision of the rescue nucleotide in the basic model (Fig. 8b). Although there is unlikely to be excision of the rescue nucleotide following incorporation of a correct nucleotide opposite the target template site T, the situation could be different following a misincorporation at T. The presence of an unstable base pair at T could lead to excision of a ``stable'' base pair at T +1. To allow for this possibility, one would allow for a transition from state 3 to state 5 (rate constant k), and since state 3 would now become a transient state, the polymerase would dissociate from state 3 (k) to a newly defined absorbing state to create a band at T +1, or it could add another dNMP to create a band at T +2. The remainder of the analysis to compute the matrix NR () required to express integrated gel band intensities in terms of the insertion and excision parameters would be carried out as described under ``Appendix.''

As the model becomes increasingly complex, additional experiments would be required to obtain values for the newly defined rate constants, e.g. measuring integrated band intensities at several concentrations of rescue dNTP, determining polymerase dissociation rates at various template sites (see (2) ). However, the data reported in this paper suggest that the simple kinetic model, using gel band intensity ratios to characterize wrong and right incorporation, (Fig. 8b), may be sufficient to measure polymerase fidelity in the presence of proofreading at arbitrarily chosen template locations. Two other model based approximations, an analysis of multiple hits and exonuclease cycling, have been dealt with in the final two sections under ``Appendix.'' Multiple hits, which increase the apparent rate of synthesis by allowing primer templates that have been hit once to be re-engaged by a polymerase and further extended, have no affect on fidelity, provided that the average number of hits is similar for right and wrong insertions. The kinetics experiments can easily be designed to satisfy this condition. Exonuclease cycling occurs when a nucleotide is inserted and excised multiple times during a single hit. If a high concentration of rescue dNTP is present in the assay, then cycling is unlikely to occur for insertion of a correct nucleotide. Practically speaking, if the concentrations of the target dNTP are chosen so that the amount of incorporation for either right or wrong nucleotides remains in the linear region, then the effect of cycling on determinations of V(max)/K(m) is negligible (see ``Appendix'').

The measurements carried out with T4 polymerase containing a highly active 3` to 5` exonuclease suggests that the gel assay may be useful for measuring the fidelity of a wide variety of proofreading and nonproofreading polymerases. It should be possible to use the assay in a running-start mode to measure fidelities for polymerases with subunits that greatly enhance processivity, e.g. T7 polymerase, T4, or E. coli pol III holoenzyme. To measure the fidelity of highly processive polymerases by the gel kinetic assay will require that a careful balance be maintained between the concentrations of target and rescue dNTPs so that measurable bands at the T +1 and T -1 template positions can be observed.


APPENDIX

The ``Appendix'' contains six sections. The first section describes the formal steps in the solution of a Markov model. In the second section, the solution is used to express nucleotide misincorporation efficiency, f (), in the presence of proofreading, in terms of measured gel band intensity ratios; is derived under ``Appendix'' as . The third section contains a Markov model derivation of polymerase incorporation velocity in the presence of proofreading, and explicit binding of the target nucleotide () for the model, Fig. 8c, is derived in under ``Appendix'' as . The fourth section presents a general model for relating the experimental V(max)/K(m) values to fidelity. The fifth section analyzes the effects of multiple hits on the determination of fidelity by the kinetic assay. The sixth section contains a brief analysis of the effects of dNTP dNMP cycling.

Markov Models of Enzymatic Processes

Markov methods, which are well known in physics and engineering(39) , can be applied to studies of macromoleclar systems. These models assume that the systems that they describe obey a no memory property. At any time, the behavior of the system is determined solely by the state of the system at that time, and the previous history of the system does not affect its behavior.

The main elements of a Markov model are (i) the ensemble of systems, (ii) the states of the systems of the ensemble, and (iii) the transitions between these states. Since the Markov model deals with an ensemble of systems, the actual description of the ensemble is in terms of a set of probabilities of finding any randomly selected system in any given state. This set of probabilities is given by the state vector V(t) = [p(1)(t) . . . p(n)(t)], where T denotes the transpose of the vector, n is the total number of states in the system, and p(i)(t) is the probability of finding a randomly chosen system in state i at time t.

The transitions are assumed to occur randomly over any given time interval dt. Transitions are between two given states, and the probability of a transfer between these states in the time interval dt (assumed to be very small) is given as P(dt). Since there are n states in the system, there are n^2 possible transitions between these states (note that the probability of a transition from a state back to itself must be specified). These probabilities are organized into the time-independent matrix P(dt)

where i and j are arbitrary states. The probabilities must meet the condition

which ensures that the total probability that a system in state i makes any transition is 1. Typically, states are divided up into transient and absorbing states on the basis of the number of transitions out of the state. If there are no transitions out of a state j, then P(dt) = 1, and the state is classified as an absorbing state. Otherwise, the state is classified as transient state. The major distinction between transient and absorbing states is that in the limit of infinite time, any system will be found only in an absorbing state. The states of the systems are enumerated such that all absorbing states are listed before any transient states. Thus, if there are three states in the system and two are absorbing, the states 1 and 2 are the absorbing ones, and 3 is the transient one.

The time evolution of the state vector is given by the difference equation

In the single completed hit approximation, we are interested in the infinite time limit for the behavior of the polymerase on the template. That is, when we specify a completed hit, this is formally equivalent to determining the state vector at infinite time (where all transitions out of transients states (states in which the polymerase is still ``on the DNA'') have occurred. The formal steps to arrive at the infinite time state vector are as follows.

1) Construct the partitioned transition matrix P.

P has been subdivided into the identity matrix I representing transitions of absorbing states to absorbing states, the zero matrix 0 representing transitions from absorbing states to transient states, the matrix R(dt) representing transitions from transient states to absorbing states, and the matrix Q(dt) representing transitions among transient states.

2) Calculate the final state vector, i.e. the vector containing the final distribution of states for the system. The final distribution is determined by the application of an infinite number of infinitesimal transition operations to the initial state vector,

where P(dt)^n is the matrix product of P(dt) with itself n times. The value of the P matrix after an infinite amount of multiplications is given by (40) .

The matricies R and Q are obtained from the transition matrix P (). Q represents transitions between transient states and approaches 0 in the limit of infinite time, as it must to ensure the convergence of N. The matrix NR is is the only ``nontrivial'' part of P, and represents the transitions from the initial to the final states.

These concepts are illustrated using the model presented in Fig. 8a. We take as our system our earlier model for polymerase action in the absence of exonucleolytic proofreading(2) . The system is assumed to have three states: state 1, polymerase dissociated from unextended DNA; state 2, DNA extended by the polymerase; and state 3, polymerase bound to unextended DNA. There are two transitions in this model: the ``off'' transition between states 3 and 1, where the polymerase dissociates from unextended DNA, and the ``pol'' transition between states 3 and 2, where the polymerase adds a base to the DNA (further dissociation or polymerization is not considered). Thus state 3 is a transient state and states 1 and 2 are absorbing. The rate of the off transition is k, and its probability in a small time interval is kdt. Similarly, the rate and probability of the polymerase transition are k and kdt.

Initially, the ensemble is set up so that all systems are in state 3 (V^T(0) = [0 0 1]). The P matrix for the system is

The submatrices of this matrix are

The matricies N and NR are thus

The matrix Pis

Finally, the infinite time state vector V() is

Thus, in the limit of infinite time, the ratio of extended to unextended DNA (states 2 and 1) is just k/k, in agreement with our previous results(2) .

Markov Model Relating Integrated Gel Band Intensities to Polymerase Rate Constants for Polymerases Possessing a 3` 5` Exonuclease

In Fig. 8b, we present the model for a polymerase possessing an exonuclease inserting a base at location T on the template. Three absorbing states, 1, 2, and 3, are defined to correspond with gel bands at T -1, T, and T +1, and represent the polymerase either dissociating at locations T -1 or T or reaching location T +1 by adding the rescue base (from which it cannot return). The two transient states, 4 and 5, reflect addition of the target base by the polymerase and excision of the target base by the exonuclease. The population of each of the states is contained in a state vector V(t) = [p(1)p(2)p(3)p(4)p(5)]. Initially at time 0, a running-start nucleotide is inserted at template position T -1, and the system enters transient state 4. The state vector at time t = 0 is, therefore, V(0) = [0 0 0 1 0]. The system can cycle between transient states 4 and 5 until entering an absorbing state, which ends the hit. Since all completed hits on P/T molecules will eventually result in a transition to an absorbing state, the form of the final state vector is V() = [V(1)V(2)V(3) 0 0]. The final distribution is the experimentally observed quantity, where V(1), V(2), and V(3) are proportional to the integrated band intensities at T -1, T, and T +1, respectively, at the completion of the experiment. For the fidelity analysis in this paper, we have used sufficiently high concentrations of rescue dNTP so that the band at T is absent for the case of wrong incorporations, i.e. V(2) 0.

In the model, the polymerase enters state 4 by incorporating a running-start nucleotide opposite template site T -1. The enzyme has two choices while in state 4; it can either dissociate from the DNA with rate constant k to enter state 1, resulting in a labeled gel band at position T -1, or it can insert a nucleotide (right or wrong) opposite the target site T to enter state 5. The insertion rate, k, depends on dNTP concentration in accordance with Michaelis-Menten kinetics. The enzyme has a choice of three transitions while in state 5; it can dissociate (k), resulting in a gel band at T (entering state 2), it can excise the newly incorporated nucleotide and return to state 4 (transition rate constant k), or it can add the next correct rescue nucleotide (k) resulting in a gel band at T +1 (entering state 3).

The transition matrix for this system is

The submatrix R(dt) is

The matrix N(dt) is given by

where the normalization factor det(I - Q) is

The final step of the analysis is to obtain the matrix NR, which contains the transitions from initial to final states.

The object of the analysis is to determine the misincorporation efficiency at a template target site T, f (, see ``Results''), from the integrated gel band intensities corresponding to primers extended to T -1, T, and T +1. The first row of NR is the probability that a primer extended by incorporation of a running-start nucleotide opposite template site T -1 (system initially in transient state 4, Fig. 8b) reaches the states giving rise to gel bands T -1, T, and T +1 respectively. The final state vector is given by

The first three elements of V(), representing the absorbing state populations, are proportional to the integrated band intensities I, I, and I, respectively. In the absence of proofreading and when there is no rescue dNTP present the reaction, k=k=0, the ratio of target to previous band intensities is given by , (see also under ``Results''). The relationship of the gel bands at Tand T -1to polymerase misinsertion efficiency in the absence of exonuclease is, for the most part, independent of the model used for analysis(2) .

In the presence of proofreading and in the presence of rescue dNTP, the condition that the band at T be small, IIimplies that kk. When this condition is satisfied,

where k/(k + k) is the probability that a primer band extended to the target site is rescued by the addition of the next correct nucleotide before proofreading occurs at site T.

Markov Model Derivation of Kinetics for DNA Polymerases Containing Proofreading Including a Separate State for Nucleotide Binding

Next, we derive an expression for the ratio of gel band intensities, I/I, showing the explicit dependence on concentration of dNTP inserted at the target site T, for a polymerase containing 3`-exonuclease proofreading activity. The states of the system are shown in Fig. 8c. The system is partitioned into absorbing states 1 and 2, which correspond to polymerase dissociations giving rise to observable primer extension bands on a polyacrylamide gel, Iand I. We will assume for simplicity that the band at Tis either absent or small compared with the bands at T -1and T +1, k(k+k. The dependence on dNTP concentration (the dNTP substrate is indicated in Fig. 8cby N) can be made explicit in the model by including states from which the polymerasebulletP/T complex can either bind or release the substrate N, states 4 and 3, respectively. The Pmatrix can be written down by inspection and is given by

Application of the steps described in the previous section leads to an expression for the infinite time population vector

where the first and second elements are proportional to the integrated gel band intensities at sites T -1 and T +1, respectively,

Thus, the polymerization rate is

This is the expression given in (see ``Results'') showing that the effect of the exonuclease in the simple model described by Fig. 8b is to cause a reduction in the apparent maximum velocity of the incorporation reaction in the absence of exonuclease activity, leaving the Michaelis constant unchanged.

The Generality of Fidelities Determined from V(max)/K(m) Measurements

We have derived expressions showing that determination of the ratio V(max)/K(m) values for two different substrates will give the fidelity provided the assumption of single complete hits is met. As shown by Fersht(26) , determination of V(max)/K(m) ratios give polymerase fidelity in both the absence and presence of proofreading. Fig. 9represents a generalization of the polymerase-proofreading model presented on page 361 in (26) .


Figure 9: General model for incorporation of a single substrate molecule. This is a general model for chemical processes in which the incorporation of a single substrate molecule, not bound in a cooperative fashion, distinguishes initial material from the final product. The initial states are represented by the leftmosttwocircles and the squigglyarrows between them, with the arrows representing any number of states and transitions between the input material and state alpha (the state in which initial material can bind the substrate before incorporating it). The final states are represented by the rightmosttwocircles and the arrows between them. The state beta is the state immediately following the first irreversible step after the incorporation of the substrate. The grayrectangle between states alpha and beta represents the states between the binding of the substrate and the irreversible step following its incorporation.



Consider a series of chemical reactions in which initial material, e.g. P/T DNA (Fig. 9, farleftcircle) is converted to a final product (the two rightcircles) by a series of reactions in which the bottleneck is the addition of a critical substrate (denoted by the grayrectangle). Connecting the two left and two rightcircles are squigglyarrows that denote any number of transitions, possibly branching, between the states denoted by the circles. State alpha is defined as the population of P/T DNA that have been extended to the T -1 position and remain bound to a polymerase molecule, ready to receive a nucleotide to insert at position T. State alpha is represented in the model by transient state 4 (Fig. 8b). State beta is the population of P/T DNA that have been extended to the T +1 position by incorporation of a rescue nucleotide and are assumed to be refractory to exonucleolytic attack. State beta represents initial material that has been irreversibly converted to final product (polymerase bound to site Tafter releasing the PP(i), assuming [PP(i)] = 0, in the polymerase-only model, Fig. 8a, and polymerase bound to site T +1 after incorporating the rescue base in the polymerase-exonuclease model, Fig. 8b). The irreversible step, e.g. release of PP(i) or DNA product, need not be the same for incorporation of right and wrong substrates.

The arrow labeled k denotes a series of steps occurring between the binding of the incoming substrate and the irreversible step after its incorporation. These steps occurring within the grayrectangle (corresponding to transient state 5, Fig. 8b) include, but are not limited to, conformational changes occurring in the insertion pathway that might differ substantially for right and wrong substrates (32, 41, 42, 43, 44) , and branching reactions such as exonucleolytic proofreading(26) . At low concentrations of the substrate, k will be the slowest step in the entire system and will have a rate kappa(s)[S], since (assuming no cooperative interactions between the incoming substrates) the rate can always be made to fall within the linear region (which indicates that substrate/enzyme association rate constants dominate the reaction) by suitable choice of substrate concentration. The arrow labeled k denotes steps that convert final material back to initial material and is assumed to have a rate of zero in the absence of accumulated byproducts.

Thus, two critical assumptions are made in the model (Fig. 9). First the concentration of the substrate is low enough that the formation of beta is a linear function of [S]. The initial velocity is in the V(max)/K(m) domain when binding of the substrate is rate-limiting. Second, the concentration of the byproducts of the incorporation of the substrate is zero, removing the possibility of conversion of any beta formed back to alpha. Given these conditions, there will be a time profile for the concentration of initial material in the alpha state. If the rate of conversion from alpha to beta is very low, then the dynamics of alpha(t) will only depend on the steps occurring prior to the formation of alpha. The dynamics will be the same no matter what the nature of the substrate is and is denoted alpha(0)(t). The formation of beta is given by the following equations.

Note that since the value of alpha(t`)dt` will be the same for right and wrong dNTP substrates, the ratio of the incorporation efficiencies is

In the model, we denote beta(S)(t)/[S] as V(max)/K(m), which gives

where V(max)/K(m) is an experimentally observed quantity, and kappa is the actual rate of conversion of the bound substrate into product. kappa(S)[S] is the rate of going from states alpha to beta (), and kappa(S) is proportional to the probability of a single nucleotide being incorporated per nucleotide binding event. kappa(W)/kappa(R) is the ratio of probabilities for incorporation of right versus wrong nucleotides per binding event (i.e. the fidelity); thus, measurement of V(max)/K(m) ratios will give the fidelity in this general model.

Correcting for Multiple Hits

In specific sequence contexts, proofreading efficiencies may be too high to observe extension at the T +1 position under single-hit conditions, while a T +1 band can be observed under multiple-hit conditions. It is therefore important to have a means of calculating fidelity using multiple hit data, and the development in the previous section can be used to demonstrate that the ratio of V(max)/K(m) values will give the fidelity of incorporation when templates are subjected to multiple hits. As before, the rate k, which is the total rate of the process of binding and incorporating the target base, in the presence of proofreading, as well as that of binding and incorporating the rescue nucleotide (assuming no band at T) can be made arbitrarily small by limiting the concentration of the target nucleotide. The rate k is zero since we are assuming that the exonuclease cannot act on molecules extended to the T +1 position.

Thus, the conditions of the previous section are met if it is assumed that polymerase molecules that hit a template always extend to at least position T -1, that no band is observed at position T, that primers that are extended to T +1 and beyond never go back, and that in a single hit, negligable amounts of T +1 are observed. Note from that if reactions for the right and wrong nucleotides are run for the same time (i.e. same number of multiple hits), using the results of the previous section, it can be seen that determination of the ratio of V(max)/K(m) (from the concentration behavior of Iand I) for the correct and incorrect nucleotide in this multiple hit situation will give the misincorporation efficiency, since the assumptions behind Fig. 9are satisfied. Only the band following the initial misincorporation (T +1band) can be analyzed using multiple hits since for misincorporations subsequent to the first, the rate of reaching the alpha-state does depend on the identity of the right or wrong nucleotide. This restriction, however, does not apply in the single completed hit approximation where bands downstream from T +1are amenable to analysis.

Exonuclease Cycling

After the polymerase inserts a base, the exonuclease may excise it, and the polymerase may again insert another base. In vivo, this process would initiate a new round of competition for insertion between all possible nucleotides. In the gel assay, however, there is only one nucleotide present at high enough relative concentration to be effectively inserted. This restriction leads to the phenomenon of exonuclease cycling where the polymerase keeps adding and removing the same base until it dissociates. Cycling results in an apparent higher efficiency of incorporation since the polymerase will attempt to again add the same base after the exonuclease acts. The observed efficiency of incorporation lies in between that of the full polymerase/exonuclease system and that of the polymerase alone. Thus, it becomes important to determine if cycling is occurring in a given reaction and, if so, its magnitude and possible effect on incorporation efficiency.

A simplified model of the cycling can be derived by considering Fig. 8b. Initially, the polymerase is in state 4, where it may add the target base with rate k or dissociate with rate k. If a nucleotide is added, then the polymerase will be at state 5 and either excise the newly inserted nucleotide with rate k or it will either add the next base or dissociate with rate (k + k). If the exonuclease does act, the polymerase will generate a dNMP molecule and return to state 4.

The number of polymerase cycles from state 4 to 5 and back to 4 can be counted as follows(45) . First define the probability that the polymerase makes a transition from 4 to 5 as p = k/(k + k) and the probability that the polymerase goes from state 5 to 4 as p = k/(k + k + k). The probability that a polymerase makes at least n cycles during its time on the template is then (pp)^n. The average number of cycles completed by the polymerase is the sum of the product of the number of cycles, and the probability of making that number of cycles, or (n)(1 - pp)(pp)^n, which reduces to pp/(1 - pp). The ideal situation of zero cycles during a single hit is approached if either p or p approaches zero. The value of p can be made small only if (k + k) k, which is hard to guarantee since one does not know what the relative values are of k and k. However, p = k/(k + k) can be made as small as necessary by reducing the concentration of the target nucleotide.

Thus, the rule is to approximate the competitive conditions in a noncompetition experiment, make all measurements at low dNTP substrate concentrations. While this condition leads to a conclusion similar to that of the previous section (namely, carry out kinetic measurements only in the V(max)/K(m) region of substrate concentration), in this case, the motivation is to make the series of states between alpha and beta the same in the noncompetition experiment as would be the case in an experiment where right and wrong dNTP substrates are in direct competition by polymerase.


FOOTNOTES

*
This research was supported by National Institutes of Health Grants GM21422, GM42554, and AG11398. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§
Present address: NeXagen, Inc., 2860 Wilderness Pl., Boulder, CO 80301.

To whom correspondence should be addressed: Dept. of Biological Sciences, University of Southern California, ACB Rm. 239, University Park, Los Angeles, California 90089-1340. Tel.: 213-740-5190; Fax: 213-740-8631.

(^1)
The abbreviations used are: pol I, DNA polymerase I from E. coli; pol III, E. coli DNA polymerase III; P/T, primer-template DNA in which a 30-mer template strand is annealed to a 15-mer primer for running-start reactions or to a 18-mer primer for standing-start reactions; T, T -1, T +1, template target site, an adjacent 3` (upstream) site, and an adjacent 5` (downstream) site, respectively; SCH, single completed hit conditions required for expressing integrated gel band intensities in terms of polymerase-associated insertion, excision, and dissociation rate constants.


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