Standard Free Energy for the Hydrolysis of Adenylylated T4 DNA Ligase and the Apparent pK a of Lysine 159*

Equilibrium constants for the adenylylation of T4 DNA ligase have been measured at 10 pH values. The values, when plotted against pH, fit a titration curve corresponding to a pK a of 8.4 ± 0.1. The simplest interpretation is that the apparent pK a is that of the 6-amino group of the AMP-accepting residue Lys159. Based on the pH dependence of the equilibrium constants, the value at pH 7.0 is 0.0213 at 25 °C, corresponding to ΔG′o = +2.3 kcal mol−1. From this value and the standard free energy change of –10.9 kcal mol−1 for the hydrolysis of ATP to AMP and PPi, we calculate that ΔG′o for the hydrolysis of the adenylyl-DNA ligase is –13.2 kcal mol−1. The presence of conserved basic amino acid residues in the catalytic domain, which are proximal to the active site in the homologous catalytic domain of T7 DNA ligase, suggests that the pK a of Lys159 is perturbed downward by the electrostatic effects of nearby positively charged amino acid side chains. The lower than normal pK a 8.4 compared with 10.5 for the 6-amino group of lysine and the high energy of the α,β-phosphoanhydride linkage in ATP significantly facilitate adenylylation of the enzyme.

DNA ligases catalyze phosphodiester-bond formation between the adjacent 5Ј-phosphate and 3Ј-hydroxyl ends of the nicked DNA chains (1,2). DNA ligases were first identified in 1967 (3)(4)(5)(6)(7)(8) and shown to play essential roles in DNA replication, repair, and recombination. Recently, interest in DNA ligases has been expanded by new information regarding the connections between human cancers and DNA repair systems (9,10). The two types of DNA ligases are ATP-dependent and NAD ϩ -dependent, respectively. ATP-dependent ligases are from eukaryotic cells, certain prokaryotes, and bacteriophages of the T series; NAD ϩ -dependent enzymes are from other prokaryotic cells. DNA ligases require a divalent cation for activity, and the optimum concentration of Mg 2ϩ for the T4 DNA ligase is 10 mM (2). Molecular weights of DNA ligases vary considerably, from 41 kDa in T7 to more than 100 kDa for the mammalian DNA ligases. The T4 DNA ligase is a single polypeptide with the molecular weight of 68,000 (11). The crystal structure of T4 DNA ligase has not been determined; however, that of T7 DNA ligase has been solved at 2.6 Å (10).
DNA ligation proceeds in three reversible steps by a ping pong kinetic mechanism (2,12) as shown in Eqs. 1a-1c for ATP-dependent ligases.
E-Lys-NH 2 ϩ ATP 7 E-Lys-NH-AMP ϩ PP i (Eq. 1a) DNA ligase reacts with ATP in the first step to displace PP i and generate an AMP enzyme (adenylyl enzyme) complex in which the AMP is linked to the 6-amino group of a lysine residue of the enzyme through a phosphoramide bond (13). The AMP enzyme then binds nicked DNA and transfers the AMP group to the 5Ј-phosphoryl group in the nick. The resulting adenosine-5Ј-pyrophosphoryl moiety in the nick activates the phosphate group at the 5Ј terminus of the DNA by supplying AMP as a good leaving group. The final step is a nucleophilic attack by the 3Ј-hydroxyl group on this activated phosphorus atom to displace AMP and form the 3Ј-5Ј-phosphodiester bound. The second and the third steps (Eqs. 1b and 1c) are thermodynamically spontaneous reactions (i.e. Ϫ⌬GЈ°). However, the adenosine-5Ј-phosphoramidate formed in the first step is expected to be a high energy intermediate. The standard free energy change for the hydrolysis of E-Lys-NH-AMP (nucleoside-5Ј-phosphoramidate) has not been known; however, it could be calculated from the equilibrium constant for adenylylation of the enzyme at pH 7.0 and the standard free energy change of Ϫ10.9 kcal mol Ϫ1 for the hydrolysis of ATP to AMP and PP i (14). In this study, we report the equilibrium constants for the adenylylation of T4 DNA ligase at ten different pH values, the apparent pK a for dissociation of the protonated lysine residue of the T4 DNA ligase, and the standard free energy change for the hydrolysis of adenylylated T4 DNA ligase.

EXPERIMENTAL PROCEDURES
Materials-ATP, CHES, 1 HEPES, dithiothreitol, ovalbumin, and DNase were purchased from Sigma. The following were obtained from the vendors indicated: Mg acetate from Aldrich; pET21 vector from Novagen; YM30 filtration membrane from Amicon; [ 3 H]ATP from ARC; Ultrafree-MC 30K filter unit from Millipore; and Bio-Safe II from Research Products International Corp.
Preparation of DNA Ligase-T4 DNA ligase was purified from Escherichia coli BL21(DE3) transformed with plasmid pEAW128. To construct pEAW128, the gene encoding T4 DNA ligase was inserted into pET21A (Novagen) in two PCR fragments. Genomic DNA of E. coli strain BNN67, in which the T4 ligase gene is inserted as a bacteriophage lysogen (15), was used as the template for both PCR reactions. Genomic DNA was prepared using a published procedure (16). The 256 base pairs of the T4 ligase gene defining the N terminus of the protein from the initiation codon to the MfeI site were inserted into pET21A, replacing sequences from the NdeI to the BamHI sites. The 5Ј-PCR primer corresponded to bases 1-18 of the T4 ligase gene, with 5Ј-CTCGAGCCAT added to the 5Ј end to provide a clamp and an NdeI site. * Supported by Grant GM 30480 from the National Institute of General Medical Sciences. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
The 3Ј-PCR primer corresponded to bases 261-247 of the T4 ligase gene, with 5Ј-CGGGATCC added to the 5Ј end to provide a BamHI site and clamp. With the first fragment inserted, the modified pET21A was digested at MfeI and HindIII, and the remaining base pairs of the gene were inserted. The 5Ј-PCR primer for this second fragment corresponded to bases 254 -265 of the T4 ligase gene. The 3Ј-primer corresponded to bases 1460 -1455 of the T4 ligase gene, with 5Ј-CCCAAGCTTTCA added to provide a clamp and HindIII site. DNA ligase was purified by a modification of the procedure of Davis et al. (15). Cells were disintegrated by addition of DNase and then sonicated for 4 min in 1 min bursts. At the early stage of purification two ammonium sulfate fractionations were performed. The last step of the procedure, hydroxylapatite chromatography, was omitted because the enzyme was essentially pure as indicated by gel electrophoresis. Purified enzyme was concentrated in an Amicon ultrafiltration device using the YM30 filtration membrane.
Equilibrium Constant for Adenylylation of DNA Ligase-The equilibrium constants (K pHx ) for the reaction of DNA ligase and [ 3 H]ATP⅐Mg to produce the covalent AMP enzyme and pyrophosphate according to Eq. 2 were measured at ten different pH values. The solutions were filtered through Ultrafree-MC (30-kDa cutoff) filter units, which separated the enzyme from the small molecules. Ultrafree-MC filter units with a low binding regenerated cellulose membrane are essentially a 1.5-ml polypropylene conical microcentrifuge tube into which a 400-l chamber with the membrane forming its bottom is inserted. An aliquot of the reaction mixture (300 l) was transferred from the reaction vessel into the upper chamber of the filter unit, and the tube was subjected to centrifugation at 2,000 ϫ g for 30 min in a microcentrifuge (MicroV; Denver Instrument Company). The sample was completely centrifuged through the filter. The upper chamber was then transferred to a fresh microcentrifuge tube. An aliquot of 50 mM buffer (300 l) was added to the concentrate to initiate the washing, and the tube was centrifuged at 2,000 ϫ g for 20 min in a microcentrifuge. This procedure was repeated three times. After the final wash, the upper chamber containing the concentrate was transferred into a scintillation vial, then 400 l of 10% (w/v) SDS was added to the upper chamber inside the vial. After 1 h, 600 l of the 50 mM buffer and 15 ml of Bio-Safe II counting mixture were added into the scintillation vial, which was then counted for [ 3 H]AMP ligase. Nonspecific binding to the filter was determined in the same way using samples in which chicken ovalbumin was substituted for DNA ligase. To confirm that the reactions had reached equilibrium in 20 min, two of the reactions (0.04 and 0.1 mM ATP at pH 8.5) were carried out for three different reaction periods (20, 30, and 40 min). The results showed no significant differences in the production of 3  Assuming that only the unprotonated form of Lys 159 reacts with Mg⅐ATP, the apparent dissociation constant for Lys 159 , K a , is given by Eq. 5, where K pHx is the apparent equilibrium constant at pH ϭ x, and K eq is the pH-independent overall equilibrium constant.

Equilibrium Constants for the Formation of E-Lys 159 -NH-AMP-
The covalent intermediate is produced in the reaction of DNA ligase with ATP according to Eq. 1a. The apparent equilibrium constant at a given pH ϭ x, K pHx , can be measured by use of radiolabeled ATP as described under "Experimental Procedures." The equilibrium constants for adenylylation of DNA ligase were determined at ten different pH values and have been plotted against pH in Fig. 1.
The Apparent pK a for Lys 159 of T4 DNA Ligase-The data for apparent equilibrium constants, K pHx were fitted to Eq. 5 to obtain the apparent K a . The value of the apparent pK a of Lys 159 is 8.40 Ϯ 0.09 at 25°C. This value is 2.1 units less than the normal pK a for dissociation of the protonated 6-amino group of a lysine residue, which is 10.5 (17). The simplest interpretation of the results in Fig. 1 is that the apparent pK a observed is that for the dissociation of the 6-ammonium group of Lys 159 .
A value of pK a 2.1 units lower than usual can be rationalized on the basis of the existence of a net positive charge in the active site of the free enzyme. Although the structure of the T4 DNA ligase is not available, the crystal structure of T7 DNA ligase has been solved at 2.6 Å resolution (10). Aside from the differences in molecular weights of the two enzymes, the amino acid sequence alignment of T4 and T7 DNA ligases revealed the existence of conserved motifs in the catalytic domain (18). The crystal structure of T7 DNA ligase complexed with ATP shows an excess of positive charges surrounding the nucleotide molecule (19), and almost all lysine and arginine residues at the active site of T7 and T4 DNA ligase are conserved (18). These residues include, in addition to the AMP-accepting Lys 159 (20), Lys 375 , Lys 277 , Arg 182 , and Arg 164 of T4 DNA ligase. A lowered FIG. 1. K pHx versus pH for adenylation of DNA ligase. The apparent equilibrium constants, K pHx , were measured as described under "Experimental Procedures." The results were then plotted as K pHx versus pH. Then from fitting the data to Eq. 5 the line was computed as well as the apparent pK a for Lys 159 . The pK a value resulting from this fitting procedure was 8.40 Ϯ 0.09.

TABLE I Standard free energy change for reactions of DNA ligase and ATP
value of pK a for Lys 159 in the active site of the T4 DNA ligase, from 10.5 to 8.4, could well be caused by electrostatic destabilization of the lysine-6-ammonium group by the nearby positively charged, basic amino acids. The positive electrostatic field would favor proton dissociation and a lowered pK a . This effect might not be confined to Lys 159 and would perturb the acid dissociation constants of the other basic residues as well, it is only the effect on the pK a of Lys 159 that would be detected by our chemical test of adenylylating the enzyme. Standard Free Energy Change for Hydrolysis of Adenylylated DNA Ligase-The recommendation of the International Union of Pure and Applied Chemistry is that ⌬GЈ o refers to total concentrations of the ionic species of each component of the reaction at pH 7.0, 25°C, and 1 mM free Mg 2ϩ (21). In this study, standard free energy changes follow this recommendation. The standard free energy change for hydrolysis of adenylylated DNA ligase, ⌬GЈ o , can be calculated from the free energies of the reaction studied here, Eq. 1a, and that for the hydrolysis of ATP to AMP and PP i (22). To determine the ⌬GЈ o , the value for K pH7 at pH ϭ 7 for the adenylylation of DNA ligase was calculated using Eq. 5 and found to be K pH7 ϭ 0.0213. Then the ⌬GЈ o for Eq. 1a was calculated as ϩ2.3 kcal mol Ϫ1 from ⌬GЈ o ϭ ϪRT ln K pH7 . The standard free energy change (⌬GЈ o°) for hydrolysis of adenylylated DNA ligase, Eq. 8, can be calculated as the sum of Eqs. 6 and 7 as shown in Table I. The value of ⌬GЈ o is Ϫ13.2 kcal mol Ϫ1 , which indicates that E-Lys-NH-AMP is a high-energy compound. As we expected (14) the standard free energy of hydrolysis of adenylylated DNA ligase is in the same range as the value of ⌬GЈ o for the hydrolysis of UMP-imidazolide to UMP and imidazole, which is Ϫ14.7 kcal mol Ϫ1 (22).
Although adenylyl-DNA ligase is high energy, it is not so high as to be inaccessible by cleavage of the phosphoanhydride bond linking P ␣ and P ␤ in Mg⅐ATP, which is 2.3 kcal mol Ϫ1 lower in energy when expressed as the standard free energy of hydrolysis. The difference can be overcome by the millimolar concentration of Mg⅐ATP in a cell and the very favorable free energy changes for the coupled reactions Eqs. 1b and 1c. The low apparent pK a of Lys 159 is a significant factor in bringing the value of ⌬GЈ o near enough to that of Mg⅐ATP for cleavage to AMP and Mg⅐PP i . If the apparent pK a of Lys 159 had been normal for the 6-amino group (10.5), ⌬GЈ o for the hydrolysis of adenylyl-DNA ligase would have been Ϫ16.1 kcal mol Ϫ1 , a value that would make the formation of the adenylyl-DNA ligase intermediate very difficult. Therefore, it seems that electrostatic pK a perturbation of Lys 159 at the active site of DNA ligase is significant in facilitating the action of this enzyme.
Another factor favoring the adenylylation of DNA ligase is the energy of the ␣,␤-phosphoanhydride linkage in ATP. The standard free energy of hydrolysis has recently been found to be Ϫ10.9 kcal mol Ϫ1 (14), which is significantly more negative than the Ϫ7.8 kcal mol Ϫ1 for hydrolysis of the ␤,␥-phosphoanhydride linkage (21). The combined effects of the high energy ␣,␤-phosphoanhydride linkage in ATP and the low value of pK a for Lys 159 in T4 DNA ligase facilitate the formation of the intermediate AMP ligase.
Another high energy intermediate in the action of DNA ligase is the adenylylated DNA produced by transfer of the AMP-group from the adenylyl-DNA ligase to the 5Ј-P of nicked DNA. The resulting phosphoanhydride linkage is a P 1 ,P 2 -dialkyl diphosphate, and as such can be expected to display a similar value of ⌬GЈ°to that for the hydrolysis of UDP-glucose to UMP and glucose-1-phosphate, which is Ϫ10.3 kcal mol Ϫ1 (14). This is 2.9 kcal mol Ϫ1 less negative than ⌬GЈ°for the hydrolysis of adenylyl-DNA ligase, so that the transfer of the AMP group from the adenylylated enzyme to nicked DNA appears to be spontaneous.