Modulation of DNA Polymerase Noncovalent Kinetic Transitions by Divalent Cations*

Replicative DNA polymerases (DNAPs) require divalent metal cations for phosphodiester bond formation in the polymerase site and for hydrolytic editing in the exonuclease site. Me2+ ions are intimate architectural components of each active site, where they are coordinated by a conserved set of amino acids and functional groups of the reaction substrates. Therefore Me2+ ions can influence the noncovalent transitions that occur during each nucleotide addition cycle. Using a nanopore, transitions in individual Φ29 DNAP complexes are resolved with single-nucleotide spatial precision and sub-millisecond temporal resolution. We studied Mg2+ and Mn2+, which support catalysis, and Ca2+, which supports deoxynucleoside triphosphate (dNTP) binding but not catalysis. We examined their effects on translocation, dNTP binding, and primer strand transfer between the polymerase and exonuclease sites. All three metals cause a concentration-dependent shift in the translocation equilibrium, predominantly by decreasing the forward translocation rate. Me2+ also promotes an increase in the backward translocation rate that is dependent upon the primer terminal 3′-OH group. Me2+ modulates the translocation rates but not their response to force, suggesting that Me2+ does not affect the distance to the transition state of translocation. Absent Me2+, the primer strand transfer pathway between the polymerase and exonuclease sites displays additional kinetic states not observed at >1 mm Me2+. Complementary dNTP binding is affected by Me2+ identity, with Ca2+ affording the highest affinity, followed by Mn2+, and then Mg2+. Both Ca2+ and Mn2+ substantially decrease the dNTP dissociation rate relative to Mg2+, while Ca2+ also increases the dNTP association rate.

DNA polymerases (DNAPs) 4 are responsible for accurate replication of DNA genomes. Replicative DNAPs achieve this by catalyzing template-directed polymerization of deoxyribonucleoside triphosphates (dNTPs) with extremely high fidelity (with error rates of ϳ10 Ϫ6 to ϳ10 Ϫ8 ) (1,2). Phosphodiester bond formation, the chemical transformation during polymerization, is catalyzed in the polymerase active site, in the 5Ј to 3Ј direction. Many replicative DNAPs also catalyze a second nucleotidyl transfer reaction, the exonucleolytic cleavage of the primer strand in the 3Ј to 5Ј direction. This editing reaction allows for removal of incorrect nucleotides inserted during polymerization, contributing ϳ1-2 orders of magnitude to replication fidelity (1). Exonucleolytic editing occurs in a separate active site that is typically ϳ30 -40 Å from the polymerase site (3)(4)(5)(6)(7)(8)(9), and it requires that ϳ3 base pairs of the nascent primertemplate duplex be melted to allow the primer strand to be transferred from the polymerase site to the exonuclease site.
An essential role for two divalent metal cations (Me 2ϩ ions) in the mechanism of numerous enzyme-catalyzed nucleotidyl transfer reactions has been characterized (10), in which one Me 2ϩ ion (termed metal A) serves primarily to activate the nucleophile, whereas the other (termed metal B) mitigates the negative charge that builds in the transition state (10,11). For replicative DNAPs, this two Me 2ϩ ion mechanism applies to both phosphodiester bond formation in the polymerase site, and to hydrolysis of the primer terminal dNMP residue in the exonuclease site (12,13). In accord with their roles in the chemical transformations, the Me 2ϩ ions are intimate architectural components of each of the active sites. They are coordinated by a highly conserved set of acidic amino acid side chains in each site, as well as by specific functional groups of the reaction substrates. Therefore, in addition to their essential role in the chemical reactions, Me 2ϩ ions may also influence the reversible noncovalent transitions that govern the fate of DNAP-DNA complexes after each covalent nucleotide addition. These transitions include (i) the primer strand transfer between the polymerase and exonuclease sites, (ii) the translocation fluctuations, in which the DNA substrate moves between the pretranslocation and post-translocation states in the DNAP polymerase site, a spatial displacement of the distance of a single nucleotide, and (iii) dNTP binding in the polymerase site. In contrast to the roles of the Me 2ϩ ions in the chemical steps of dNTP polymerization and exonucleolysis, much less is known about the effects of Me 2ϩ ions on these noncovalent transitions in DNAP complexes.
The conserved architecture of the DNAP domain that contains the polymerase active site resembles a partially closed hand, comprising palm, thumb, and fingers subdomains (3,4,9,14,15). The palm subdomain contains residues that participate in catalysis of phosphodiester bond formation, including the acidic residues involved in Me 2ϩ coordination. The fingers subdomain contains residues essential for binding incoming nucle-otide substrates. When dNTP binds to the polymerase active site in the post-translocation state, elements of the fingers subdomain move relative to their position in complexes lacking dNTP, closing in toward the active site to achieve a tight steric fit for the nascent base pair. In the fingers-closed dNTP-bound complex, the 3Ј-OH group of the DNA primer strand and a non-bridging oxygen of the ␣ phosphate are ligands for one of the Me 2ϩ ions (metal A) and non-bridging oxygens of all three phosphate groups are ligands for the metal B ion (4,(15)(16)(17).
A hypothesis for the structural basis of translocation in the B family of replicative DNAPs has been proposed (3). The B family includes pol ⑀ and pol ␦, the enzymes that catalyze leading and lagging strand genomic replication, respectively, in eukaryotes (18,19). Core structure, catalytic mechanisms, and functional properties are highly conserved in this DNAP family (2,3,8,9,20,21). Based upon the comparison of crystal structures of the DNAP from bacteriophage ⌽29 in the fingers-open, post-translocation state DNAP-DNA binary complex or in the fingers-closed, post-translocation state DNAP-DNA-dNTP ternary complex (3), it was proposed that the post-translocation state ternary complex can serve as a model for the structure of a fingers-closed, pre-translocation state complex. In this view, the nascent base pair between the templating base at n ϭ 0 and the incoming complementary dNTP in the post-translocation state ternary complex occupies the site that would be occupied by the terminal base pair of the primer-template duplex in the pre-translocation state complex. The structure of the binary complex in the fingers-open, post-translocation state indicates that the pre-translocation state in the fingersopen conformation is sterically precluded, and hence fingers opening was proposed to accompany the forward translocation (3). Little is known about whether Me 2ϩ ions that interact with complexes in the polymerase active site in the pre-translocation or post-translocation states exert any influence on the translocation fluctuations. For the X-family mammalian repair DNAP, pol ␤, there is evidence that Me 2ϩ can stabilize the pre-translocation state in DNAP-DNA binary complexes (22).
We have developed a single-molecule approach using a nanoscale pore (Fig. 1, A and B) that permits quantification of the rates of translocation fluctuations, rates of the primer strand transfer between the polymerase and exonuclease sites, and rates of dNTP binding, in individual DNAP-DNA complexes (23)(24)(25)(26). We used the B-family replicative ⌽29 DNAP, which serves as an excellent model system for leading strand DNA synthesis catalyzed in more complex B family replisomes. It catalyzes highly processive DNA synthesis while remaining tightly associated with its DNA substrate and promoting downstream strand displacement during replication (3,(27)(28)(29)(30), obviating the need for accessory proteins such as sliding clamps or helicases. Primer strand transfer between the ⌽29 DNAP polymerase and exonuclease sites is an intramolecular process (31).
When a complex formed between ⌽29 DNAP and a primer template DNA substrate (Fig. 1C) is captured atop an ␣-hemolysin nanopore in an applied electric field (Fig. 1, A and B), it FIGURE 1. Capture of individual DNAP complexes. A, a single ␣-hemolysin nanopore is inserted in a ϳ25-m diameter lipid bilayer separating two chambers (cis and trans) containing buffer solution. A patch clamp amplifier applies voltage across the bilayer and measures ionic current carried through the pore by K ϩ and Cl Ϫ ions. B, ionic current time trace for a binary complex formed between wild type ⌽29 DNAP and a DNA substrate (DNA1-H_H, in panel C) captured at 180 mV applied potential in buffer containing 10 mM K-Hepes, pH 8.0, 0.3 M KCl, 1 mM EDTA, 1 mM DTT, and 11 mM MgCl 2 . ⌽29 DNAP and DNA1-H_H were added to the nanopore cis chamber to final concentrations of 0.75 and 1 M, respectively. Schematics above the current trace illustrate the sequence of events: (i) the ionic current through the open nanopore; (ii) the current drops rapidly when a complex is captured. The enzyme is too large to enter the nanopore, and therefore the complex, with the enzyme bound at the primer-template junction of the DNA substrate, perches atop the pore. The DNA template strand of the complex is suspended through the nanopore lumen, which is just wide enough to accommodate a single strand of DNA. Individual complexes reside atop the nanopore for tens of seconds, during which the measured ionic current fluctuates on the millisecond time scale between two amplitude levels (inset). Transition between the two amplitudes corresponds to movement of the DNA substrate relative to the enzyme and the nanopore by the distance of a single nucleotide (23,35,39). This spatial displacement of the DNA substrate that occurs during the translocation is detected in the time traces of ionic current by the use of a reporter group of five consecutive abasic (1Ј-H, 2Ј-H) residues in the template strand (red circles in the schematic). The fluctuations between the two amplitudes continue until complexes dissociate or are ejected, after which another complex can be captured. C, DNA hairpin substrates comprise a 14-base pair duplex region and a single-stranded template region of 35 nucleotides. The reporter group of five abasic (1Ј, 2Ј-H) residues spans positions ϩ8 to ϩ12 (red Xs in the sequence). DNA1-H_OH bears a 2Ј-H, 3Ј-OH primer terminus and DNA1-H_H bears a 2Ј-H, 3Ј-H primer terminus.
undergoes iterative fluctuations across the translocation step. The forward and reverse fluctuations across the translocation step are recorded as discrete transitions between two amplitudes in time traces of ionic current (Figs. 1B, ii, inset, and 2A). Each individual captured complex resides atop the nanopore and undergoes the amplitude fluctuations for several seconds, and in each experiment, hundreds of DNAP-DNA complexes can be captured and examined one-by-one, in series. Dwell time samples of each amplitude level are extracted from the ionic current time traces and used to quantify transitions with sub-millisecond temporal resolution and single nucleotide spatial precision.
Complexes formed between ⌽29 DNAP and DNA1-H_H captured in the presence of 10 mM Mg 2ϩ fluctuate rapidly between the two ionic current amplitudes (Figs. 1B and 2A, i). Addition of dNTP complementary to the templating base at n ϭ 0 (dGTP) stabilizes the lower amplitude post-translocation state ( Fig. 2A, ii) (23,25). In contrast to complexes formed with DNA1-H_H ( Fig. 2A, i), complexes formed with DNA1-H_OH display an additional kinetic state at the upper amplitude. The presence of this state can be directly observed in the time traces as pauses of tens to hundreds of milliseconds that punctuate intervals of rapid fluctuation between the two amplitudes ( Fig.  2A, iii). We showed that the periods of rapid fluctuation are due to transitions between the pre-translocation and post-translocation states and that the pauses in the upper amplitude arise when the primer strand is transferred from the polymerase active site to the exonuclease site (26). Thus, the upper amplitude comprises the pre-translocation state in the polymerase site and the state in which the primer strand occupies the exonuclease site; the lower amplitude comprises the post-translocation state in the polymerase site (23)(24)(25)(26).
When an individual DNAP-DNA complex is held atop the nanopore, the applied voltage exerts a force on the complex along the direction of the translocation. This applied force shifts the translocation equilibrium toward the upper amplitude, pre-translocation state (23,24); it impedes the rate of the forward translocation and increases the rate of the reverse translocation (23,24), but it does not affect the rates of dNTP binding (25) or the rates of primer strand transfer between the polymerase and exonuclease sites (26). Based on translocation fluctuations measured under varying opposing force loads and in the presence of varying nucleotide concentrations, we established the kinetic relationship of the translocation to the step of nucleotide binding and to the step of primer strand transfer between the polymerase and exonuclease sites (Fig. 2B). Specifically, we showed that the forward translocation precedes dNTP binding; the translocation fluctuation is rectified but not driven by dNTP binding, and dNTP has no influence on the rates of the translocation fluctuations ( Fig. 2B) (25). Furthermore, we established that transfer of the primer strand from the polymerase to the exonuclease site occurs prior to the forward translocation fluctuation; the pre-translocation state is therefore the branch point between the DNA synthesis and editing pathways ( Fig. 2B) (26). We developed mathematical methods to determine the forward (r 1 ) and reverse (r 2 ) rates of translocation fluctuations, the forward (r 3 ) and reverse (r 4 ) rates of primer strand transfer between the polymerase and exonuclease sites, and the rates of dNTP or rNTP association (k on ) and dissociation (k off ) in individual DNAP complexes (Fig. 2B) (24 -26, 32).
In prior studies (23,24,26,32,33), we applied these capabilities to examine the kinetic mechanisms by which mutations of highly conserved DNAP residues, alterations in DNA substrate (iii) DNA1-H_H. In (iii) 4 M dGTP was present in the cis chamber. The two red dashed lines indicate the two amplitude levels between which the measured current fluctuates; at 180 mV, the upper amplitude is centered at ϳ32 pA, and the lower amplitude is centered at ϳ26 pA at 180 mV. B, four-state model for the reversible, noncovalent transitions that govern the fate of replicative DNAP complexes following each covalent nucleotide addition. The model shows the kinetic relationships among the steps of translocation, primer strand transfer between the polymerase and exonuclease active sites, and dNTP binding. Transfer of the primer strand from the polymerase to the exonuclease site precedes the forward translocation (26), and the forward translocation precedes dNTP binding; the translocation is rectified but not driven by dNTP binding, and dNTP has no influence on the rates across the translocation step (25). The kinetic model comprises six transition rates: the rates of translocation (r 1 , r 2 ), the rates of primer stand transfer between the pre-translocation state polymerase site and the exonuclease site (r 3 , r 4 ), and the rates of dNTP binding to post-translocation state complexes (k on [dNTP] and k off ). The mathematical framework based on the model allows these rates to be determined from experimental measurements (24 -26). Each of the three unshaded ellipses corresponds to a state (pre-translocation state, post-translocation state, or dNTP-bound post-translocation state) in which the primer strand, in duplex with the template strand, resides in the polymerase site; the ellipse that is shaded gray corresponds the state in which the primer terminus resides in the exonuclease site. sequence or structure, or alterations in nucleotide substrate structure exert their influence on DNAP function. The majority of these studies were conducted using complexes captured in the presence of a high concentration of Mg 2ϩ (10 mM). In the current study, we have examined the effects of Me 2ϩ ions on noncovalent transitions that are essential to DNAP function. We determined the concentration-dependent effects of Mg 2ϩ , Mn 2ϩ , and Ca 2ϩ on the translocation fluctuations, on primer strand transfer between the polymerase and exonuclease sites, and on dNTP binding, in individual ⌽29 DNAP-DNA complexes. Mg 2ϩ and Mn 2ϩ are metals that support catalysis in both the polymerase and exonuclease active sites, whereas Ca 2ϩ supports nucleotide binding but not catalysis in either the polymerase or the exonuclease active sites (34).

Experimental Procedures
DNA and Enzymes-DNA substrates were synthesized at Stanford Protein and Nucleic Acid Facility and purified by denaturing PAGE. DNA hairpins were annealed by heating at 90°C for 4 min followed by snap cooling in ice water. Wild type ⌽29 DNAP was obtained from Enzymatics (Beverly, MA). The D12A/D66A mutant was obtained from XPol Biotech (Madrid, Spain).
Nanopore Methods-Nanopore experiments were conducted as described (23,25,(35)(36)(37)(38). A single ␣-hemolysin nanopore is inserted in a ϳ25-m diameter lipid bilayer that separates two chambers (cis and trans) containing buffer solution (10 mM K-Hepes, pH 8.0, 0.3 M KCl, and 1 mM DTT). DNA and ⌽29 DNAP were added to the cis chamber to final concentrations of 1 and 0.75 M, respectively. MgCl 2 , CaCl 2 , MnCl 2 , or EDTA were added to the cis well as indicated in the text and figure legends. Ionic current was measured with an integrating patch clamp amplifier (Axopatch 200B, Molecular Devices) in voltage clamp mode. Data were sampled using an analog-to-digital converter (Digidata 1440A, Molecular Devices) at 100 kHz in whole cell configuration and filtered at 5 kHz using a low pass Bessel filter.
Detection of the Translocation in Captured DNAP-DNA Complexes-The displacement of the DNA relative to the enzyme that occurs during translocation is detected with single nucleotide spatial precision and sub-millisecond temporal resolution by the use of a reporter group in the template strand of the DNA substrate, and has been described in detail (23-26, 32, 33, 35, 39). Briefly, the reporter comprises five consecutive abasic (1Ј,2Ј-H) residues (shown as red Xs in the sequence in Fig.  1C and as solid red circles in the schematic in Fig. 1B). When the reporter resides within the pore lumen, the abasic residues allow more ions to flow through the channel than a strand composed of normal DNA residues alone. The extent to which the abasic reporter augments the amplitude of captured complexes depends upon its position relative to the limiting aperture of the nanopore lumen. Thus, displacement of the abasic reporter group in the nanopore lumen is manifested as a change in measured ionic current (23,35).
Analysis of Ionic Current Time Traces-The extraction of the dwell time samples of the upper and lower amplitudes from recorded time traces of ionic current, and the calculation of kinetic transition rates, has been described in detail (26,32).
Estimating Free [dNTP] in Bulk Phase-Due to the high affinity of ⌽29 DNAP-DNA complexes for dNTP in Mn 2ϩ and Ca 2ϩ it was necessary to measure complementary dNTP binding by adding very low concentrations of dGTP to the bulk phase in the cis well (Fig. 10). In bulk phase, dGTP may bind onto complexes to form ternary complexes. As a result, not all added dGTP molecules are free in bulk. When the added dGTP concentration is lower than the enzyme concentration, the concentration of free dGTP in bulk may be significantly different from that of added dGTP. Therefore, we need to calculate the free dGTP concentration.
Let p ϭ probability of lower amplitude (post-translocation state, with or without dNTP bound); [dGTP] 0 ϭ concentration of added dGTP in bulk; [DNAP⅐DNA] 0 ϭ concentration of added enzyme-DNA complexes in bulk; [dGTP] Free ϭ concentration of free dGTP in bulk; K d (bulk) ϭ apparent binding affinity of dGTP onto enzyme-DNA complexes in bulk; and K d ϭ binding affinity of dGTP onto an enzyme-DNA complex that is captured atop the pore and is in the post-translocation configuration. Note that K d (bulk) may be different from K d because in bulk, not all enzyme molecules are necessarily at the primertemplate junction, and for complexes with enzyme at the primer-template junction, not all of them are in the post-translocation state (the state competent to bind dNTP) at all times. So, in our model, we allow K d (bulk) to be different from K d . In experiments, [DNAP⅐DNA] 0 is fixed at 0.75 M and [dGTP] 0 is a control variable. As a function of [dGTP] 0 and K d (bulk) , the concentration of free dGTP in bulk has the following expression.
Previously (23) we established that the normalized p/(1 Ϫ p) is related to the free dGTP concentration by Equation 2.

Results
When ⌽29 DNAP complexes are captured atop the nanopore in the absence of added Me 2ϩ , the measured ionic current fluctuates between the two amplitudes that are characteristic of the fluctuations across the translocation step observed in the presence of Me 2ϩ (26). Neither the forward nor reverse translocation displacement requires Me 2ϩ . However, in the absence of Me 2ϩ , the probability of occupancy of the lower amplitude, post-translocation state (p) is higher than when complexes are captured in the presence of Me 2ϩ (Fig. 3). Addition of Me 2ϩ to the bulk phase elicits a decrease in p for complexes formed with both DNA1-H_OH, which bears a natural 2Ј-H, 3Ј-OH primer terminus, or DNA1-H_H, which bears a 2Ј-H, 3Ј-H primer terminus (Fig. 1C). This is illustrated in amplitude histograms for complexes formed between the D12A/D66A mutant of ⌽29 DNAP and DNA1-H_OH (Fig. 3A) or DNA1-H_H (Fig. 3B), captured in either the absence of Me 2ϩ (Fig. 3, A, i, and B, i) or in the presence of 6 mM Mg 2ϩ (Fig. 3, A, ii, and B, ii), 6 mM Ca 2ϩ (Fig. 3, A, iii, and B, iii), or 6 mM Mn 2ϩ (Fig. 3, A, iv, and B, iv). The D12A/D66A mutant lacks two of the ligands for the catalytic Me 2ϩ ions in the exonuclease active site and thus has negligible exonucleolytic activity (40,41). This permits experiments to be conducted with DNA1-H_OH in the presence of Mg 2ϩ or Mn 2ϩ , conditions under which the 2Ј-H, 3Ј-OH terminated primer strand would be degraded in the bulk phase by the wild type enzyme (26,35). The extent to which p was decreased for the D12A/D66A complexes varied with the identity of the metal species; for both DNA1-H_OH and DNA1-H_H, Mn 2ϩ caused the largest decrease in p, followed by Ca 2ϩ and then Mg 2ϩ (Fig. 3).
We examined the effects of Me 2ϩ concentration on the probability of the post-translocation state in ⌽29 DNAP complexes by performing titration experiments spanning five orders of magnitude, from 0.2 to 10,000 M Me 2ϩ . For DNA1-H_OH, we used the wild type enzyme in Ca 2ϩ titration experiments, and the D12A/D66A enzyme in titration experiments with Mg 2ϩ , Ca 2ϩ , and Mn 2ϩ (Fig. 4A). Because the 2Ј-H, 3Ј-H primer terminus of DNA1-H_H inhibits the onset of ⌽29 DNAP-catalyzed exonucleolytic digestion of the primer strand relative to substrates bearing 2Ј-H, 3Ј-OH termini (35), it affords protection for DNA in experiments conducted with the wild type enzyme in the presence of Mg 2ϩ or Mn 2ϩ . This protection permitted us to examine the effects of all three metals (Mg 2ϩ , Ca 2ϩ , and Mn 2ϩ ) on complexes formed between DNA1-H_H with the wild type enzyme and those with D12A/D66A enzyme in the titration experiments (Fig. 4B).
For complexes formed with DNA1-H_OH in the absence of Me 2ϩ , but not those formed with DNA1-H_H in the absence of Me 2ϩ , the identity of the enzyme causes a difference in p; for wt ⌽29 DNAP at 0 Me 2ϩ , p Ϸ 45% (Fig. 4A), whereas for the D12A/D66A mutant at 0 Me 2ϩ p Ϸ 30% (Figs. 3A, i, and 4B).
For all complexes examined, formed with either the wild type or D12A/D66A enzyme, and either the DNA1-H_OH or DNA1-H_H substrate, Me 2ϩ causes a concentration-dependent decrease in p. For most of the complexes, the decrease in p occurs primarily within the concentration range of ϳ10 to 1000 M Me 2ϩ (Fig. 4); the exception is the response of p to Ca 2ϩ for the complexes of the wild type enzyme with DNA1-H_OH (Fig.  4A). For this complex, the decrease in p begins at a lower concentration (between ϳ6 and 8 M) than it does for D12A/D66A complexes formed with DNA1-H_OH (ϳ10 M). Furthermore, for the wild type complexes formed with DNA1-H_OH, p drops precipitously in response to Ca 2ϩ , reaching a lower level than for the D12A/D66A enzyme at concentrations above ϳ60 -80 M. At [Ca 2ϩ ] Ն ϳ1000 M, p for the wild type enzyme resolves to ϳ1-2 and ϳ4 -5% for the D12A/D66A enzyme.
Me 2ϩ Concentration-dependent Resolution of Kinetic Complexity in the Primer Strand Transfer Pathway-We sought to determine the kinetic mechanisms that contribute to the Me 2ϩ -dependent decrease in probability of post-translocation state occupancy. Although the net effect of Me 2ϩ for each DNAP-DNA complex is a decrease in p relative to the same complex in the absence of Me 2ϩ , any subset of the noncovalent transitions that govern the probability of the post-translocation state could be affected by Me 2ϩ (Fig. 2B), and the magnitude and Me 2ϩ -concentration dependence of effects on each transition could vary depending upon the identity of the partners in the DNAP-DNA complex and upon the identity of the metal. We first examined the survival probability versus dwell time of upper amplitude dwell time samples and that of lower amplitude dwell time samples, extracted from ionic current traces for complexes captured in the Me 2ϩ titration experiments (Figs. 5 and 6). The survival probability as a function of time t is defined as the probability that the dwell time is larger than t. The observed survival probability is calculated as the fraction of dwell time samples larger than t.   In the presence of 10 mM Mg 2ϩ , the upper amplitude survival probability for binary complexes formed between the D12A/ D66A enzyme with DNA1-H_OH is well fit by a model of two exponential modes (26) (Fig. 5A). We have shown that these two kinetic states in the upper amplitude correspond to (i) stays of the complex in the pre-translocation state in the polymerase site, and (ii) stays of the complex in the state in which the primer strand occupies the exonuclease site (26). Upper amplitude survival probability for complexes captured in 10 mM Ca 2ϩ , formed between DNA1-H_OH and either the wild type enzyme (Fig. 5B) or the D12A/D66A enzyme (Fig. 5C), are also well fit by a model of two exponential modes, as are complexes of the D12A/D66A enzyme with DNA1-H_OH captured in 10 mM Mn 2ϩ (Fig. 5D).
However, in the absence of Me 2ϩ (Fig. 6A, i), and across a wide range of [Me 2ϩ ] up to almost 1000 M the distribution of upper amplitude dwell time for complexes formed with the DNA1-H_OH substrate deviates from a distribution of two exponential modes. This is illustrated in Fig. 6A, i-iv, for complexes captured in 0, 1, 10, and 100 M Mg 2ϩ . The upper amplitude survival probability contains more than two exponential modes, suggesting the possibility that at low [Me 2ϩ ], residence in the exonuclease site may be described by multiple kinetic states, rather than a single kinetic state. As [Mg 2ϩ ] is increased into the mmiilmolar range (Figs. 5A and 6A, v and vi), survival probability of the upper amplitude converges to a model of two exponential modes.
Qualitatively similar kinetic complexity (deviation from two exponential modes) at Me 2ϩ concentrations below ϳ1000 M was observed for the upper amplitude for all of the complexes examined in the Mg 2ϩ , Ca 2ϩ , or Mn 2ϩ titration experiments. In addition, as we have previously reported, when complexes formed between either the wild type or D12A/D66A enzyme and the DNA1-H_H substrate are captured in the presence of high [Me 2ϩ ], plots of survival probability versus dwell time of the upper amplitude are fit by a single exponential decay function. This decay rate corresponds to the inverse of the forward translocation rate (24,26). Thus, for the DNA1-H_H complexes at high [Me 2ϩ ], a population of dwell time samples that corresponds to stays of the primer strand in the exonuclease site cannot be resolved. This, combined with the kinetic complexity in the upper amplitude observed in the presence of 0 or submillimolar Me 2ϩ for complexes formed with either DNA1-H_OH or DNA1-H_H, precludes our ability to reliably quantify the effects of Me 2ϩ on the rates of primer strand transfer between the polymerase and exonuclease site (Fig. 2B, r 3  and r 4 ).
Despite the kinetic complexity in the upper amplitude, the effects of Me 2ϩ ions on the forward and reverse rates of translocation can be reliably determined. First, for each of the complexes examined, in the absence of Me 2ϩ , and across the entire range of [Me 2ϩ ], survival probability of the lower amplitude is well fit by a single exponential decay function (Fig. 6B) (24,26); thus the reverse translocation rate (r 2 ) can be calculated from the data. Second, despite the complexity of the upper amplitude dwell time distribution observed at 0 Me 2ϩ and at Me 2ϩ concentrations below ϳ1000 M (Fig. 6A, i-iv), r 1 can also be determined across the [Me 2ϩ ] titration series. This is illustrated using a hypothetical example for the kinetic complexity of the upper amplitude dwell time cluster (Fig. 7), in which the upper amplitude comprises four kinetic states: A, B, C, and D, where state A is the pre-translocation state. The forward translocation rate (r 1 ) is the rate of escaping from state A to the lower amplitude, and can be accurately determined from the measured survival probability. Let S(t) be the upper amplitude survival probability as a function of dwell time t. Mathematically, no matter how kinetically complex the upper amplitude is, it holds for Equation 5.
That is, the forward translocation rate r 1 is the initial decay rate of the survival probability.
The Influence of Me 2ϩ on ⌽29 DNAP Translocation Rates-Me 2ϩ ions have notable effects on both forward rate (r 1 ) and reverse rate (r 2 ) of the translocation fluctuations (Fig. 8). For all complexes examined, formed between either the wild type or D12A/D66A enzymes, with either the DNA1-H_OH or DNA1-H_H substrates, Me 2ϩ causes a concentration-dependent decrease in r 1 . The [Me 2ϩ ]-dependent decreases in r 1 (Fig. 8, A and C) largely mirror the [Me 2ϩ ]-dependent decreases in p (Fig.  4, A and B); the decrease in the forward translocation rate (r 1 ) makes the dominant contribution to the decrease in the probability of the post-translocation state (p). As with the decrease in p, the effects of Me 2ϩ on r 1 occur primarily within the concentration regime of ϳ10 to ϳ1000 M Me 2ϩ (Fig. 8, A and C). Also in accord with the decrease in p, the extent to which r 1 was decreased for the D12A/D66A complexes varied with the identity of the metal species; for both DNA1-H_OH and DNA1-H_H, Mn 2ϩ elicited the greatest decrease in r 1 , followed by Ca 2ϩ and then Mg 2ϩ (Fig. 8, A and C). In complexes formed with DNA1-H_OH, the higher value of p observed in the absence of Me 2ϩ for the wild type enzyme relative to the D12A/ , the upper amplitude dwell time shows more than two exponential modes (Fig. 6), which indicates that the primer strand transfer pathway between the polymerase and exonuclease sites contains multiple kinetic states, and is no longer described by a pair of transition rates (r 3 and r 4 as in Fig. 2B). Even in that case, the forward translocation rate r 1 can still be reliably calculated from measured dwell time samples (see "Results").
D66A enzyme (Fig. 4) is also accounted for, at least in part, by a difference in r 1 for the two enzymes in the absence of Me 2ϩ (Fig.  8A). For wild type complexes formed with DNA1-H_OH at 0 Me 2ϩ , r 1 Ϸ 3400/s, whereas for D12A/D66A complexes formed with DNA1-H_OH at 0 Me 2ϩ , r 1 Ϸ 2700/s. With DNA1-H_OH, the effects of Me 2ϩ on complexes formed with both enzymes can only be compared for Ca 2ϩ ; we note that the Ca 2ϩ concentration at which r 1 begins to decrease differs for the two enzymes, with the decrease in r 1 beginning at ϳ0.2 M Ca 2ϩ for the wild type enzyme and at ϳ1 M for the D12A/D66A enzyme. At Ca 2ϩ concentrations above ϳ1 M, the values of r 1 for the two enzymes converge (Fig. 8A).
For complexes formed with either the wild type or D12A/ D66A enzymes, Me 2ϩ causes a concentration-dependent increase in r 2 that is dependent upon the presence of the primer terminal 3Ј-OH group: the increase is observed for complexes formed with DNA1-H-OH (Fig. 8B) but not for complexes formed with DNA1-H_H (Fig. 8D). The increase in r 2 is much more modest than the decrease in r 1 . The Me 2ϩ -dependent increase in r 2 becomes detectable at ϳ100 M Me 2ϩ , an order of magnitude higher than the concentration required to observe the decrease in r 1 . In complexes formed with the D12A/D66A enzyme, r 2 continues to increase as a function of either Mg 2ϩ or Mn 2ϩ up to at least 10,000 M, the highest concentration tested. In contrast, the ability of Ca 2ϩ to cause an increase in r 2 , in complexes formed with either the wild type or D12A/D66A enzymes, appeared to saturate above ϳ2000 M (Fig. 8B). Like the decrease in r 1 , the extent to which r 2 was increased for the D12A/D66A complexes varied with the identity of the metal species, but the rank order of effectiveness among the three metal ions at eliciting the increase in r 2 differs from the effect on r 1 ; Ca 2ϩ elicited the greatest increase in r 2 , followed by Mn 2ϩ , and then by Mg 2ϩ , which had modest effects (Fig. 8B).
The Relationship Among the Effects of Me 2ϩ , the Identity of the Primer Terminus, and the Translocation Energy Landscape-The influence of Me 2ϩ ions on the magnitude of both r 1 and r 2 uncovered in the Me 2ϩ titration experiments (Fig. 8) prompted us to examine the effect of Me 2ϩ ions on the energy landscape across the translocation step (Fig. 9). The Me 2ϩ titration experiments were conducted by capturing ⌽29 DNAP complexes at a single applied voltage (180 mV). When complexes are held atop the nanopore, the force applied by the voltage impedes the rate of the forward translocation (r 1 ) and increases the rate of the reverse translocation (r 2 ). Plots of log(r 1 ) versus voltage and log(r 2 ) versus voltage both fit to straight lines, indicating that the force is applied along the direction of the translocation (24). The Me 2ϩ ions could influence both the rate at a given voltage and the dependence of the rates on voltage. The slope of log(r 1 ) versus voltage is negative and proportional to the distance between the pre-translocation state and the transition state for the translocation step; the slope of log(r 2 ) versus voltage is positive and proportional to the distance between the transition state and the post-translocation state (24).
We showed previously that the primer terminal 3Ј-OH group is a determinant in the energy landscape of the translocation (26). When complexes are captured at 180 mV in the presence of 10 mM Mg 2ϩ , r 1 is ϳ3.8-fold faster in complexes with DNA1- H_OH than it is in complexes of DNA1-H_H. The 3Ј-OH group causes a decrease in the slope of log(r 1 ) versus voltage and an increase in the slope of log(r 2 ) versus voltage, indicating that in 10 mM Mg 2ϩ , along the coordinate of the translocation displacement, the transition state is closer to the pre-translocation state for complexes formed with DNA1-H_OH than it is for complexes formed with DNA1-H_H (26). Because the increase in r 2 observed at high [Me 2ϩ ] in the Me 2ϩ titration experiments is dependent upon the presence of the primer terminal 3Ј-OH group (Fig. 8, B and D), it was of particular interest to compare the effects of Me 2ϩ ions on the energy landscape between complexes formed with DNA1-H_OH and complexes formed with DNA1-H_H. Is the influence of the 3Ј-OH group on the energy landscape of the translocation affected by the presence of Me 2ϩ ? Does the influence of the 3Ј-OH group in the translocation depend upon an interaction between the primer terminus and a Me 2ϩ ion (or ions), or is it an inherent property of the interaction of the DNA substrate with the enzyme?
We examined the influence of Me 2ϩ on the response of the translocation rates to applied force by comparing complexes captured at 0 Me 2ϩ to those captured at 10 mM Mg 2ϩ , across the range of voltages from 140 to 220 mV (Fig. 9). Experiments were conducted in the absence of Me 2ϩ with both the wild type and the D12A/D66A enzymes, for complexes formed with both DNA1-H_OH and DNA1-H_H; in 10 mM Mg 2ϩ with both enzymes for complexes formed with DNA1-H_H; and in 10 mM Mg 2ϩ with the D12A/D66A enzyme for complexes formed with DNA1-H_OH. The higher values for r 1 in the absence of Me 2ϩ relative to values for r 1 in 10 mM Me 2ϩ that were ob-served in the Me 2ϩ titration experiments conducted at 180 mV (Fig. 8, A and C) hold across the voltage range examined, for complexes formed with either DNA-H_OH or DNA1-H_H (Fig. 9A). In addition, as previously observed for complexes captured in the presence of 10 mM Mg 2ϩ , in the absence of Me 2ϩ , r 1 is faster in complexes formed with DNA1-H_OH than it is for complexes formed with DNA1-H_H. For complexes formed with DNA1-H_OH, there is a modest decrease in the slope of log(r 1 ) versus voltage relative to that for complexes formed with DNA1-H_H, in the absence of Me 2ϩ or in the presence of 10 mM Mg 2ϩ (Fig. 9A). The 3Ј-OH group exerts an effect on the slope of log(r 2 ) versus voltage that is more substantial in relative magnitude to its effect on the slope of log(r 1 ) versus voltage. In complexes with DNA1-H_OH, the slope of log(r 2 ) versus voltage is increased relative to that for complexes formed with DNA1-H_H, in the presence of 10 mM Mg 2ϩ or the absence of Me 2ϩ (Fig. 9B).
We compared the absolute values of the slopes of the fitting lines in the log(rate) versus voltage plots (Fig. 9, C and D). The slope values for log(r 1 ) versus voltage as well as those for log(r 2 ) versus voltage show two discrete clusters. For r 1 , a cluster for complexes formed with DNA1-H_OH is centered at ϳ0.019, and a cluster for complexes formed with DNA1-H_H is centered at ϳ0.028 (Fig. 9C). In the case of r 2 , a cluster for complexes formed with DNA1-H_OH is centered at ϳ0.02, and a cluster for complexes formed with DNA1-H_H is centered at ϳ0.008 (Fig. 9D). For both log(r 1 ) versus voltage and log(r 2 ) versus voltage, the dependence of slope on force is a function of the primer terminus identity, regardless of the presence or absence of Me 2ϩ .
The Influence of Me 2ϩ on Complementary dNTP Binding-Me 2ϩ ions are essential for both dNTP binding and catalysis in the polymerase active site. The identity of the Me 2ϩ ions bound in the polymerase active site can strongly influence dNTP binding affinity and binding rates (33), as well as the fidelity of dNTP selection and the ability to catalyze phosphodiester bond formation (see Refs. 10, 42, and 43 and references therein). Because the forward translocation fluctuation precedes dNTP binding, dNTP binds to complexes only when they are in the post-translocation state (Fig. 2B) (25). In the nanopore assay the two translocation states are fully resolved and the effects of dNTP on the equilibrium between the two translocation states can be quantified. Furthermore, because dNTP stabilizes the lower amplitude, post-translocation state ( Fig. 2A, ii) by extracting and analyzing dwell time samples in a stochastic model, the rates of dNTP binding to and dissociating from the post-translocation state can be quantified (25).
We compared the binding affinity for dGTP (complementary to dCMP at n ϭ 0 of DNA1 in Fig. 1C) and dGTP binding rates, in complexes formed with D12A/D66A enzyme, captured in the presence of 10 mM Mg 2ϩ , Mn 2ϩ , or Ca 2ϩ ( Fig. 10; Table 1).
For Ca 2ϩ , we conducted dGTP titration experiments with both DNA1-H_OH and DNA1-H_H; for Mg 2ϩ and Mn 2ϩ , we used DNA1-H_H in dGTP titration experiments. The affinity for dNTP among different DNAP-DNA complexes can be directly compared by plotting the normalized p/ (1 Ϫ p), where p is the probability of post-translocation state occupancy. The normalized p/(1 Ϫ p) is defined as the value of p/ (1 Ϫ p) in the presence of a given concentration of dNTP, divided by the value of p/(1 Ϫ p) for the same complex captured in the absence of dNTP (in the presence of Me 2ϩ of the same identity and concentration). The normalized p/ (1 Ϫ p) is independent of the transitions between the two translocation states in the absence of dNTP (23,32), which vary among the complexes and conditions compared. In addition, we have shown that (normalized is the concentration of dNTP (23). This theoretical expression predicts that the log-log plot of (normalized p/(1 Ϫ p) Ϫ 1) versus [dNTP] is a straight line with slope ϭ 1 and vertical intercept ϭ -log(K d ) at [dNTP] ϭ 1 M. Thus K d is determined from the vertical intercept at [dNTP] ϭ 1 M, obtained in fitting observed data points to the theoretical expression. A higher vertical position in the log-log plot of (normalized p/(1 Ϫ p) Ϫ 1) versus [dNTP] corresponds to a smaller value for K d and a stronger binding affinity ( Fig. 10; Table 1).
For D12A/D66A complexes formed with DNA1-H_H in Mg 2ϩ , the dNTP binding affinity is K d Ϸ 1 M (in Mg 2ϩ ) ( Table  1) (33). Both Mn 2ϩ and Ca 2ϩ cause an enhancement in dNTP binding affinity compared with complexes captured in Mg 2ϩ , with Mn 2ϩ yielding a decrease in the value of K d by ϳ25-fold, to K d Ϸ 0.04 M (in Mn 2ϩ ), and Ca 2ϩ decreasing the value of K d more significantly, by an additional order of magnitude to K d Ϸ 0.004 M (in Ca 2ϩ ). The stronger affinity afforded in Mn 2ϩ relative to Mg 2ϩ is primarily due to an ϳ18-fold decrease in the dNTP dissociation rate, in good accord with an earlier comparison between dNTP binding parameters for the D12A/D66A mutant captured in 10 mM Mg 2ϩ or in 2 mM Mn 2ϩ (33). The more substantial enhancement in dNTP binding affinity for complexes captured in Ca 2ϩ occurs due to a combination of an ϳ9-fold increase in the dNTP association rate constant and an ϳ23-fold decrease in the dNTP dissociation rate, relative to the binding rates for complexes captured in Mg 2ϩ . Because Ca 2ϩ supports dNTP binding but does not support phosphodiester bond formation, this afforded an opportunity to examine the effect of the primer terminal 3Ј-OH group, a ligand for metal A (15), on dNTP binding by comparing complexes formed with FIGURE 10. Complementary dNTP binding affinity compared as a function of Me 2؉ species and primer terminus identity. Complexes were formed between the D12A/D66A mutant of ⌽29 DNAP and DNA1-H-OH in 10 mM Ca 2ϩ (black unfilled sideways triangles), or with DNA1-H_H in 10 mM Ca 2ϩ (red filled triangles), 10 mM Mg 2ϩ (blue filled triangles), or 10 mM Mn 2ϩ (yellow filled triangles). The binding affinity is examined using the log-log plot of (normalized p/(1 Ϫ p) Ϫ 1) versus dGTP concentration. We have shown that the vertical intercept of the log-log plot at [dGTP] ϭ 1 M is given by -log(K d ) (23). The higher the log-log plot is vertically, the smaller the value of K d and the stronger the binding affinity. Error bars show the standard errors.

TABLE 1
Complementary dNTP binding rates in complexes formed with the D12A/D66A mutant of ⌽29 DNAP Rates were determined using dwell time samples extracted from ionic current traces (see "Experimental Procedures") and a three-state kinetic model (consisting of transitions r 1 , r 2 , k on , and k off in the model diagram in Fig. 1A). Complexes were captured at 180 mV in the presence of 1 mM EDTA, with 11 mM MgCl 2 , or 11 mM CaCl 2 , or 11 mM MnCl 2 as indicated; K d , k on ͓dNTP͔, and k off are independent of the applied voltage (23,25). All values are reported with the standard error.  Fig. 2B). The plot of (normalized p/(1Ϫp) Ϫ1) versus ͓dGTP͔ is shown in Fig. 10.

DNA
DNA1-H_OH or with DNA1-H_H. The presence or absence of the primer terminal 3Ј-OH group does not significantly affect the ground state dNTP binding parameters ( Fig. 10; Table 1); k on , k off, and K d are each very similar for complexes formed with both DNA substrates.

Discussion
In this study, we hypothesized that because the divalent cations (Me 2ϩ ions) that are essential for catalytic function in both the polymerase and exonuclease active sites of replicative DNAPs serve as intimate components of the architecture in each of the sites, they may exert significant influence on the noncovalent transitions that occur in DNAP-DNA complexes during each nucleotide addition cycle. To test this, we applied a nanopore-based, single molecule approach that features singlenucleotide spatial precision and sub-millisecond temporal resolution to determine the effects of Mg 2ϩ , Ca 2ϩ , and Mn 2ϩ on the kinetic transitions of translocation, dNTP binding, and primer strand transfer between the polymerase and exonuclease active sites (Fig. 2B), in individual complexes formed with ⌽29 DNAP, a B-family replicative DNAP.

Me 2ϩ Ions Alter the Equilibrium Across the Translocation
Step, and the Forward and Reverse Translocation Rates-Fluctuations across the translocation step, during which the DNAP moves with respect to its DNA substrate by the distance of a single nucleotide, occur in the absence of Me 2ϩ , indicating that the translocation fluctuations are an activity inherent to the DNAP-DNA complex. Nonetheless, Me 2ϩ ions have a significant influence on the translocation. For all ⌽29 DNAP-DNA complexes examined, formed with either the wild type or D12A/D66A enzyme, and either the DNA1-H_OH or DNA1-H_H substrate, Me 2ϩ causes a concentration-dependent decrease in the probability of the post-translocation state (p) (Fig. 4). This shift in equilibrium is promoted by Mg 2ϩ and Mn 2ϩ , which support DNAP catalysis, and Ca 2ϩ , which supports dNTP binding but not catalysis. It is caused primarily by a [Me 2ϩ ]-dependent decrease in the forward translocation rate (r 1 ) (Fig. 8, A and C). The Me 2ϩ -dependent decrease in r 1 may be attributable to stabilization of the fingers-closed pre-translocation state, which would be predicted to slow the forward translocation (3). The pre-translocation state that is sampled during the nanopore experiments corresponds to the product of the covalent addition of the primer terminal residue during DNA synthesis, after pyrophosphate has dissociated from the complex (presumably complexed with the metal B ion) (26,35). Although we cannot assign whether the Me 2ϩ -dependent decrease in r 1 is caused by binding of Me 2ϩ at the metal A or metal B site, the Me 2ϩ -dependent effects on the escape from the pre-translocation state suggest that while the environment of both metal binding sites necessarily changes significantly after catalysis, at least one of the sites retains affinity for Me 2ϩ .
Each of the three metals examined also promoted a modest concentration-dependent increase in the backward transition rate from the post-translocation to pre-translocation state (r 2 ) that is dependent upon the presence of a 3Ј-OH group at the primer terminus of the DNA substrate (Fig. 8, B and D). The dependence of the increase in r 2 on the primer strand 3Ј-OH implicates this group as a ligand for the metal ion that elicits the increase, suggesting that it is the post-translocation state metal A ion and implying that the metal A ion binds to the ⌽29 DNAP-DNA complexes independent of the presence of dNTP. In complexes formed with a DNA substrate bearing a 3Ј-H primer terminus, where the increase in r 2 is not observed (Fig.  8D), we cannot distinguish between the case in which metal A does not bind, or the case in which it binds but does not cause an increase in r 2 .
In the nanopore experiments, the applied voltage exerts a force on the captured DNAP-DNA complex along the direction of the translocation. Although Me 2ϩ modulates the translocation rates at a given applied force (Fig. 8), it does not alter the dependence of the rates on force, for complexes formed with either DNA1-H_OH or with DNA1-H_H (Fig. 9). The primer terminal 3Ј-OH group is a determinant in the energy landscape of the translocation (26); its presence alters the slopes of both log(r 1 ) versus voltage and log(r 2 ) versus voltage. When complexes captured at 0 Me 2ϩ are compared with those captured at 10 mM Mg 2ϩ , across a range of applied voltages from 140 to 220 mV (Fig. 9, A and B), the dependence of the slopes of both log(r 1 ) versus voltage and log(r 2 ) versus voltage are observed to be a function of the primer terminus identity, regardless of the presence or absence of Me 2ϩ (Fig. 9, C and D). The smaller slope of log(r 1 ) versus voltage and larger slope of log(r 2 ) versus voltage for complexes formed with DNA1-H_OH relative to complexes formed with DNA1-H_H indicates that the transition state for the translocation is closer to the pre-translocation state when the DNA substrate bears a primer terminal 3Ј-OH group than when the DNA substrate bears a primer terminal 3Ј-H group, independent of the presence or absence of Me 2ϩ . Thus, Me 2ϩ affects the translocation rates at each given voltage, but not the dependence of the rates on force, indicating that Me 2ϩ does not perturb the translocation distances among the pre-translocation state well, the post-translocation state well, and the transition state, which are strongly influenced by the primer terminal 3Ј-OH group. Like the translocation fluctuations, the influence of the primer terminal 3Ј-OH on the energy landscape of the translocation is inherent to the DNAP-DNA complex.
Me 2ϩ Ion Identity Affects Complementary dNTP Binding Equilibrium and Rates-Complementary dNTP binding in the post-translocation state polymerase active site is strongly affected by Me 2ϩ identity, with Ca 2ϩ affording the highest affinity, followed by Mn 2ϩ , and then Mg 2ϩ ( Fig. 10; Table 1). Both Ca 2ϩ and Mn 2ϩ substantially decrease the dNTP dissociation rate relative to Mg 2ϩ ; Ca 2ϩ also yields an increase in the dNTP association rate constant. In contrast to Mn 2ϩ and Mg 2ϩ , Ca 2ϩ does not support phosphodiester bond formation, yielding the opportunity to examine the effect of the primer terminal 3Ј-OH group, which is a ligand for metal A (15), on dNTP binding. Somewhat surprisingly, the presence or absence of the primer terminal 3Ј-OH group does not significantly affect the ground state dNTP binding parameters ( Fig. 10; Table 1), which are very similar for complexes formed with DNA1-H_OH or DNA1-H_H. This indicates that the presence or absence of the primer terminal 3Ј-OH group is not a determinant for ground state dNTP binding in Ca 2ϩ .
Because selective stabilization of the transition state over the ground state contributes to catalytic efficiency and specificity (44), it is possible that the enhanced ground state stabilization effected by both Mn 2ϩ and Ca 2ϩ contributes to the effects of these metals on phosphodiester bond formation. Because k off reflects the free energy difference between the dNTP-bound post-translocation state and the dNTP-unbound post-translocation state, the smaller values of k off for complexes formed in Mn 2ϩ or Ca 2ϩ relative to complexes formed in Mg 2ϩ may obtain, at least in part, from a deeper free energy well for the dNTP-bound ground state. In addition to affecting the free energy difference between the dNTP-bound and unbound states, a deeper free energy well could affect the free energy difference between the dNTP-bound ground state and the transition state for catalysis. Among the three metals we examined, the largest stabilization of ground state dNTP binding is caused by Ca 2ϩ , and this metal does not support catalytic function. Ground state stabilization by Mn 2ϩ , while an order of magnitude more modest than Ca 2ϩ , is almost 20-fold greater than that afforded by Mg 2ϩ ; while Mn 2ϩ supports catalysis, it is at a cost to fidelity in nucleotide selection.
The relationship among Me 2ϩ ions, dNTP binding, and conformational transitions associated with dNTP binding has been studied for pol ␤ (45), for the Klenow fragment of DNA polymerase I (an A-family repair DNAP) (46), and for the B-family replicative DNAP from bacteriophage RB69 (47,48). Not surprisingly, details vary among these enzymes, which have different functional roles and are from different DNAP families. Nonetheless, the studies are consistent with a general scenario in which metal B is sufficient to support dNTP binding and the associated fingers-closing conformational change, whereas both metals A and B are required for phosphodiester bond formation.
The effects of Me 2ϩ ions on dNTP binding or on the translocation that we have measured in ⌽29 DNAP-DNA complexes may be related, at least in part, to Me 2ϩ -dependent effects on the rates of fingers opening and closing. Based on earlier findings that both r 1 and k off are slower for complexes captured in 2 mM Mn 2ϩ than for complexes captured in 10 mM Mg 2ϩ , we had hypothesized that Mn 2ϩ may exert its effects on both r 1 and k off by decreasing the rate of fingers opening from the closed complex (33). This hypothesis is based upon the structural model proposed for translocation (3), which predicts that decreasing the rate of fingers opening in the pre-translocation state would lead to a decrease in the rate of the forward translocation (r 1 ). Similarly, because it is reasonable to assume that dNTP dissociation requires fingers opening, a decrease in the rate of fingers opening could yield a decrease in the dissociation rate of dNTP (k off ) from the dNTP-bound post-translocation state. The findings in the current study that both r 1 and k off are lower in Ca 2ϩ ( Fig. 8; Table 1) than they are in Mg 2ϩ provides further evidence supporting the hypothesis.
Complex Effects of Me 2ϩ on the Primer Strand Transfer Pathway between the Polymerase and Exonuclease Active Sites-We previously established the correspondence between a second kinetic state in the upper amplitude and the primer strand transfer between the polymerase and exonuclease sites (26). In the current study, we examined the effects of Me 2ϩ ions on primer strand transfer by applying approaches developed in the prior study, which revealed that the primer strand pathway displays significant Me 2ϩ -concentration dependent kinetic complexity. In the absence of Me 2ϩ , or when the [Me 2ϩ ] is low, the pathway for primer strand transfer between the polymerase and exonuclease sites displays more than two kinetic states (Fig.  6A). For complexes formed with DNA1-H_OH, this complexity resolves to two states (the pre-translocation state in the polymerase site, and the state in which the primer has been transferred to the exonuclease site) when the [Me 2ϩ ] is above ϳ1 mM (Figs. 5 and 6A) (26). For complexes formed with DNA1-H_H captured in the presence of high [Me 2ϩ ], dwell time samples that correspond to stays of the primer strand in the exonuclease site cannot be resolved from the dwell time samples that decay at a single exponential rate that corresponds to the inverse of the forward translocation rate (24,26). Although these observed effects of [Me 2ϩ ] are intriguing, we are not yet able to speculate about the mechanisms governing the effects of Me 2ϩ on the kinetics of the primer strand transfer pathway. Detailed dissection of the effects of [Me 2ϩ ] on this pathway will require biochemical and mathematical models significantly more complex than the four-state model shown in Fig. 2B, which we will pursue in future studies.
Finally, it is not yet known how generally applicable our findings regarding the effects of Me 2ϩ ions on translocation, dNTP binding, or primer strand transfer with the ⌽29 DNAP will be to other DNAPs, in large part because most techniques that have been employed to examine DNAPs cannot resolve and quantify the translocation step and the kinetic transitions that it coordinates with both single nucleotide precision and sub-millisecond temporal resolution. However, given the structural and functional conservation of the polymerase and exonuclease active sites in the B-family replicative DNAPs, it is reasonable to expect that these effects will apply to other enzymes in this family. This includes the eukaryotic nuclear leading strand and lagging strand replicative DNAPs, pol ⑀ and pol ␦, respectively (18,19). In light of the finding that Me 2ϩ , which stabilizes the pre-translocation state in ⌽29 DNAP-DNA complexes (Fig. 8, A and C), can also stabilize the pre-translocation state in DNAP-DNA complexes of the X-family mammalian repair DNAP, pol ␤ (22), it is also possible that our findings will extend more broadly to other DNAP families.