Stimulated Interaction between (cid:1) and (cid:2) Subunits of Tryptophan Synthase from Hyperthermophile Enhances Its Thermal Stability*

Tryptophan synthase from hyperthermophile, Pyrococcus furiosus , was found to be a tetrameric form ( (cid:1) 2 (cid:2) 2 ) composed of (cid:1) and (cid:2) 2 subunits. To elucidate the rela- tionship between the features of the subunit association and the thermal stability of the tryptophan synthase, the subunit association and thermal stability were examined by isothermal titration calorimetry and differential scanning calorimetry, respectively, in comparison with those of the counterpart from Escherichia coli . The association constants between the (cid:1) and (cid:2) subunits in the hyperthermophile protein were of the order of 10 8 M (cid:3) 1 , which were higher by two orders of magnitude than those in the mesophile one. The negative values of the heat capacity change and enthalpy change upon the subunit association were much lower in the hyperthermophile protein than in the mesophile one, indicating that the conformational change of the hyperthermophile protein coupled to the subunit association is slight. The denaturation temperature of the (cid:1) subunit from the hyperthermophile was enhanced by 17 °C due to the formation of the (cid:1) 2

؊1 , which were higher by two orders of magnitude than those in the mesophile one. The negative values of the heat capacity change and enthalpy change upon the subunit association were much lower in the hyperthermophile protein than in the mesophile one, indicating that the conformational change of the hyperthermophile protein coupled to the subunit association is slight. The denaturation temperature of the ␣ subunit from the hyperthermophile was enhanced by 17°C due to the formation of the ␣ 2 ␤ 2 complex. This increment in denaturation temperature due to complex formation could be quantitatively estimated by the increase in the association constant compared with that of the counterpart from E. coli.
Hyperthermophilic proteins, which retain the folded conformation and maximally express their function near the boiling point of water, have been the target of extensive studies on protein stabilization, folding, structure, and evolutionary aspects over the past decade. Much work has been done to determine the three-dimensional structures of hyperthermophile proteins and to identify the structural determinants of the enhanced stability. A comparison of the structures of proteins from hyperthermophiles with their mesophilic counterparts has led to a better understanding of several features of the hyperthermophile proteins (1, 2, 19 -22). One of these is that several hyperthermophile proteins have structures with a higher degree of oligomerization compared with the mesophilic homologues. Triose phosphate isomerase from hyperthermophiles is found to be tetrameric in contrast to the dimeric form from mesophilic sources (3)(4)(5)(6). Hyperthermophilic phosphoribosylanthranilate isomerase is dimeric, but the proteins from mesophilic organisms are monomeric (7). Hyperthermophilic lactate dehydrogenase exists as tetrameric or octameric forms (8). Moreover, extra ion pairs or hydrophobic interactions have often been found in the subunit/subunit interface of proteins from hyperthermophiles (9 -18). On the bases of these observations, a hypothesis has been proposed that the higher order oligomerization of subunits and strong subunit association are potentially important for enhanced stability of hyperthermophile proteins (19 -22). However, there are few studies that characterize the strength of the subunit association in the hyperthermophile proteins and quantitatively elucidate the correlation between the subunit association and stability. Elucidating the subunit association feature in hyperthermophile proteins is an important subject for understanding the mechanism of anomalous stability and of protein-protein recognition itself in oligomeric proteins. Isothermal titration calorimetry is a powerful method for thermodynamically assessing proteinprotein interactions, which are especially useful for measuring association parameters. There has been little application of isothermal titration calorimetry to characterize subunit association in hyperthermophile proteins.
We are now focusing our attention on the subunit association in tryptophan synthase from the hyperthermophile, Pyrococcus furiosus, in connection with thermal stability. Prokaryotic tryptophan synthase (EC 4.2.1.20) with the subunit composition ␣ 2 ␤ 2 is a multifunctional and allosteric enzyme. This ␣ 2 ␤ 2 complex has an ␣␤␤␣ arrangement (23) and can be isolated as the ␣ monomer and ␤ 2 . The ␣ and ␤ 2 subunits catalyze inherent reactions (for reviews, see Refs. 24 -28). When the ␣ and ␤ 2 subunits associate to form the ␣ 2 ␤ 2 complex, the enzymatic activity of each subunit is enhanced by 1 to 2 orders of magnitude (for reviews, see Refs. 24 -28). The ␣/␤ subunits interaction is important for the mutual activation of the each subunit in prokaryotic tryptophan synthase. We found that tryptophan synthase (PfTSase) 1 from P. furiosus was also composed of ␣ 2 ␤ 2 , and the enzymatic activities of the ␣ and ␤ 2 subunits separated in their active forms were stimulated by the formation of the ␣ 2 ␤ 2 complexes as well as the reported mesophilic prokaryotic bacterial tryptophan synthases (for reviews, see Refs. 24 -28). The thermal stability of the ␣ subunit of PfTSase is remarkably higher than that from Escherichia coli (29).
Tryptophan synthase from hyperthermophiles is an attractive model system for seeking correlation between subunit association and stability.
In this report, to elucidate the subunit interaction feature in PfTSase in connection with thermal stability and tryptophan synthase from E. coli (EcTSase), the subunit association and thermal stability were measured by isothermal titration calorimetry and differential scanning calorimetry, respectively. The results revealed that the binding between the ␣ and ␤ subunits in PfTSase was strong compared with that in EcTSase, leading to the enhanced stability of the protein and the high temperature adaptation of the tryptophan synthase function.

EXPERIMENTAL PROCEDURES
Expression and Purification of ␣, ␤ 2 , and ␣ 2 ␤ 2 from P. furiosus-The ␣ subunit (Pf␣) from P. furiosus was expressed in the E. coli strain JM109/p␣1974 (30) and purified as described previously (29). Each of the genes of trpB and trpBA from P. furiosus was transformed into the E. coli strain JM109 (30). E. coli, harboring each of the genes, was grown in 15 liters of Luria-Bertani medium supplemented with ampicillin at 100 mg/liter culture medium at 37°C. The expressions of trpB and trpBA were induced by isopropyl-␤-D(Ϫ)-thiogalactopyranoside added at a concentration of 1 mM to the culture medium 1 h after starting the culture. After culturing for 20 h, the cells were harvested and suspended in 100 ml of 20 mM potassium phosphate buffer (pH 7.0) containing 0.02 mM PLP, 1 mM EDTA, and 5 mM DTT. After sonication and heat treatment of the homogenized solution for 10 min at 75°C, cell debris and denatured E. coli proteins were removed by centrifugation at 15,000 rpm for 30 min at 4°C.
For Pf␤ 2 , the precipitate with ammonium sulfate at 60% saturation was dissolved in 50 ml of 25 mM potassium phosphate buffer (pH 7.0) containing 0.02 mM PLP, 5 mM EDTA, and 1 mM DTT and dialyzed against the same buffer overnight at 4°C. The dialyzed sample was applied on a column (2.5 ϫ 27 cm) of DEAE-Sephacel (Amersham Biosciences) and eluted with a linear gradient of 25 to 500 mM potassium phosphate buffer (pH 7.0) containing 5 mM EDTA and 1 mM DTT. The active fractions of the eluted solutions were concentrated and applied to a gel filtration column (Superdex TM200 26/60, Amersham Biosciences) and separated using 25 mM potassium phosphate buffer (pH 7.0) containing 5 mM EDTA and 1 mM DTT. The collected active fractions were finally purified by ion exchange chromatography (Q Sepharose 26/10, Amersham Biosciences) with a linear gradient of 25 to 200 mM potassium phosphate buffer (pH 7.0) containing 5 mM EDTA and 1 mM DTT.
For Pf␣ 2 ␤ 2 , the precipitate with ammonium sulfate at 60% saturation was dissolved in 50 ml of 10 mM potassium phosphate buffer (pH 7.0) containing 0.02 mM PLP, 5 mM EDTA, and 1 mM DTT and dialyzed against the same buffer overnight at 4°C. The sample was separated on a column (2.5 ϫ 27 cm) of DEAE-Sephacel (Amersham Biosciences) with a linear gradient of 10 to 500 mM potassium phosphate buffer (pH 7.0) containing 5 mM EDTA and 1 mM DTT. Next, the collected active fractions were separated by gel filtration (Superdex TM200 26/60, Amersham Biosciences) and finally purified by ion exchange chromatography (Q Sepharose 26/10, Amersham Biosciences) with a linear gradient of 10 to 300 mM potassium phosphate buffer (pH 7.0) containing 5 mM EDTA and 1 mM DTT. PLP at a concentration of 0.1 mM was added to the solutions of the purified Pf␤ 2 and Pf␣ 2 ␤ 2 .
The ␣ subunit from E. coli was purified as already described (31). The ␤ 2 subunit (32) from E. coli was purified as already described (33). All the purified proteins showed a single band on SDS-PAGE.
Protein Concentrations-The protein concentrations were estimated from the absorbance of the protein solution at pH 7.0 using a cell with a light path length of 1 cm. The values of OD 1 cm 1% were 6.92 for Pf␣, 10.18 for Pf␤ 2 subunit, and 9.94 for Pf␣ 2 ␤ 2 . These values were determined based on protein assay by the Lowry method using bovine serum albumin as the standard protein. The concentrations of Ec␣, Ec␤ 2 , and Ec␣ 2 ␤ 2 were determined using OD 1 cm 1% values 4.4 (34), 6.5, and 6.0 (35), respectively.
Ultracentrifugation Analysis-Ultracentrifugation analysis was carried out in a Beckman Optima model XL-A. Sedimentation equilibrium experiments were performed at 20°C using an An-60 Ti rotor at a speed of 7,000 -32,000 ϫ g. Before taking the measurements, the protein solutions were dialyzed overnight against the desired buffer at 4°C. The experiments at three different protein concentrations between 1.8 and 0.5 mg/ml were run in Beckman 4-sector cells. The partial specific volumes of 0.751 cm 3 /g for Pf␣, 0.743 for Pf␤ 2 , and 0.747 for Pf␣ 2 ␤ 2 were calculated from the amino acid compositions (36). Analysis of the sedimentation equilibria was performed using the program XLAVEL (Beckman, version 2).
Isothermal Titration Calorimetry-Isothermal titration calorimetry (ITC) was performed using an Omega Isothermal Titration Calorimeter (Microcal, Northampton, MA). Prior to the measurements, the solutions of the ␣ and ␤ 2 subunits were dialyzed against 50 mM potassium phosphate buffer (pH 7.0) containing 1 mM EDTA, 0.1 mM DTT, and 0.02 mM PLP. The dialyzed samples were filtered through a 0.22-m pore size membrane and then degassed in a vacuum. A 10-l volume of the ␤ 2 subunit at a high concentration was injected into the 1.3155-ml sample cell containing the ␣ subunit with a 170-s equilibration period between injections. Integration of the thermogram and the binding isotherm were analyzed using the ITC data analysis module in ORIGIN software (Microcal Software, Northampton, MA).
Differential Scanning Calorimetry-Differential scanning calorimetry (DSC) was carried out using differential scanning microcalorimeters, VP-DSC (Microcal) and Nano-DSC II model 6100 (Calorimetry Science Corp.) at a scan rate of 1°C/min. Prior to the measurements, the protein solution was dialyzed against buffer described in the legend of Fig. 5. The dialyzed sample was filtered through a 0.22-m pore size membrane and then degassed in a vacuum. The protein concentrations during the measurements were 0.2-1.4 mg/ml.

Confirmation of Association States of Recombinant ␤ 2 and
␣ 2 ␤ 2 from P. furiosus-Pf␣, which consists of 248 residues and has a molecular weight of 27,500, is found to exist in a monomer form in solution (29). Ultracentrifugation analysis was used to determine the association forms of the proteins translated by the trpB and trpBA gens from P. furiosus, which were expressed in E. coli. The apparent molecular weights (M r app ) at various pHs are shown in Fig. 1. The ␤ chain is comprised of 388 residues and the calculated molecular weight is 42,500 (30). The M r app of the recombinant ␤ was 84,000 -88,000 in the pH region above 4.7, indicating that the ␤ chain exists in a dimeric form (Pf␤ 2 ). The M r app of the recombinant complex of ␣ with ␤ subunits was almost nearly equal to 2-fold (140,000) the calculated value for ␣␤ around pH 7. These results show that tryptophan synthase from P. furiosus forms a complex of ␣ 2 ␤ 2 (Pf␣ 2 ␤ 2 ) as observed for prokaryotic tryptophan synthases from mesophiles (24 -28) and from the hyperthermophile (37,38). The M r app of the Pf␤ 2 decreased with decreasing pH below 4.0, resulting in dissociation to a monomer at pH 3.0. As shown in Fig. 1, the M r app of Pf␣ 2 ␤ 2 decreased with decreasing pH between pH 5 and 4, although that of Pf␤ 2 did not change. Binding Titration of ␣ with ␤ 2 Subunits by Isothermal Titration Calorimetry-To examine the inherent feature of the interaction between Pf␣ and Pf␤ 2 in comparison with EcTSase, an isothermal titration calorimetry (ITC) was used in the absence of any substrates or ligands, and the thermodynamic parameters of the binding of Pf␣ with Pf␤ 2 were estimated. The titration in this study was performed by injecting the ␤ 2 subunit into the ␣ subunit, in the calorimetry cell, at various temperatures and pH 7.0, because the solubility of Pf␣ was not sufficient for making a solution with a high concentration at pH 7.0. This was contrary to the injection used in our previous studies (33,39). Fig. 2A displays the typical raw data for the calorimetric titration of the ␣ subunit with the ␤ 2 subunit at 40°C. The binding of Pf␣ with Pf␤ 2 was exothermic. In Fig. 2B the titration curves are plotted as the sum of the heat released by each injection, normalized by the concentration of the ␣ subunit. The ITC titration curves for both PfTSase and EcT-Sase fitted well to a model of one set site (␣ ϩ ␤^␣␤) (Fig. 2B) and permitted the extraction of the enthalpy change (⌬H) upon formation of the complex, the association constant (K), and the stoichiometry (n) (40). The Gibbs energy change (⌬G) and the entropy change (⌬S) upon the subunit association can be evaluated using the following equation, where T and R are the absolute temperature and the gas constant, respectively. The thermodynamic parameters for the subunit association at various temperatures are listed in Table I. The stoichiometry (molar ratio of ␤/␣) of association between Pf␣ and Pf␤ was similar to unity and did not depend on temperature. The stoichiometry for EcTSase was 1.5. In a previous study in which Ec␣ is injected into the Ec␤ 2 solution, the stoichiometry is 1.4 (33,39). The deviation from unity may be due to a decrease in the binding ability of the ␤ subunit with PLP, because both Ec␣ and Ec␤ 2 showed a single band on SDS-PAGE (33). The K values were of the order of 10 8 M Ϫ1 in the temperature region of 40 -60°C for PfTSase and of the order of 10 6 M Ϫ1 in the temperature region of 20 -40°C for EcTSase (Table I and Fig. 3A). The K values of PfTSase were 2 orders higher than those of EcTSase. The negative values of ⌬H for the interaction between Pf␣ and Pf␤ were smaller that those in EcTSase (Table I and Fig. 3B). In both cases of PfTSase and EcTSase, the ⌬H values linearly correlated with temperature (Fig. 3B). The heat capacity change (⌬Cp) obtained from the slope of the linear correlation was estimated to be Ϫ1.96 and Ϫ5.56. kJ/K per mole of ␣ subunit for PfTSase and EcT-Sase, respectively. Fig. 4 shows the temperature dependences of ⌬G and ⌬S together with ⌬H. In the case of PfTSase, the summation of small values of Ϫ⌬H and ϪT⌬S yielded the Gibbs energy (⌬G) for the subunit binding reaction. In contrast, for EcTSase, the large negative values of ⌬H were compensated by using the large values of ϪT⌬S, resulting in a smaller negative ⌬G. The subunit association in PfTSase was characterized by a large K, small negative ⌬H, small negative ⌬Cp, and small ⌬S in comparison with EcTSase.
Thermal Stability of Subunits Alone and the Complex-To explore the relationship between the K values and the stability of PfTSase, the thermal stability of each subunit and complex was measured by differential scanning calorimetry (DSC). The DSC measurement was carried out in the alkaline region, because the proteins became turbid by heating at neutral pH and they do not form a complex in the acidic region (Fig. 1). Fig.  5A shows the DSC curves for Pf␣, Pf␤ 2 , and Pf␣ 2 ␤ 2 at pH 9.3-9.4. The Pf␣ exhibited a DSC curve with a single peak at 87.2°C (curve a in Fig. 5A). For Pf␤ 2 , a major peak appeared at 112.2°C accompanied by a minor broad peak at 94.6°C (curve b in Fig. 5A). It was confirmed that the major and minor peaks came from the holo-Pf␤ 2 and apo-Pf␤ 2 removing cofactor PLP, respectively. In the case of Pf␣ 2 ␤ 2 , separate two peaks appeared at 104.6 and 112.5°C (curve c in Fig. 5A). The peak on the higher temperature can be assigned to that coming from Pf␤ 2 , because the peak temperature (112.5°C) was quite similar to that of Pf␤ 2 alone (112.2°C). Therefore, the peak temperature at the lower temperature could be considered to arise from Pf␣.  Fig. 5B and Table II). The T d value of Ec␤ 2 (80.3°C) at pH 8.2 did not change by complex formation (curves b and c in Fig. 5B and Table II). The stabilization of Pf␣ due to the complex formation might be correlated with a strong subunit association with a higher K value obtained by ITC. Pf␣ and Pf␤ 2 were drastically higher by 34.2 and 31.9°C than those of Ec␣ and Ec␤ 2 , respectively.

ITC and DSC Measurements of Hybrid Complex between Pf Subunits and Ec Subunits-To explore which of the ␣ and (or)
␤ subunits corresponds to the strong association in PfTSase, the interaction between the Pf subunits and Ec subunits was examined by ITC. The ITC data at 40°C demonstrated that the K values upon formation of the hetero complex between the Pf subunits and Ec subunits were lower than those of the homo complexes (Table I). The K value strongly decreased by 4 and 3 orders of magnitude for the Pf␤ 2 -Ec␣ and Ec␤ 2 -Pf␣ associations, respectively, compared with that for the Pf␣-Pf␤ 2 association. These results suggest that the conformation of the subunit interface in PfTSase differs from that in EcTSase.  5C shows the DSC curves of the complexes with hetero subunits. The peak positions for both Pf␣ 2 Ec␤ 2 and Ec␣ 2 Pf␤ 2 appeared at temperatures corresponding to each of the component subunits (Table II), indicating that the interaction between the subunits in the hybrid complexes did not contribute to enhancing the thermal stability of the subunits in contrast to the Pf␣ 2 ␤ 2 ( Fig. 5A and Table II). DISCUSSION The Conformational Change upon the Subunit Association of PfTSase-The K values of PfTSase in the range from 40 to 60°C were of the order of 10 8 M Ϫ1 and 2 orders higher than those of EcTSase in the range from 20 to 40°C (Table I and Fig.  3A). This means that the interaction between the ␣ and ␤  subunits from the hyperthermophile is extremely strong. The protein-protein association with a K value of 8 orders or over has been reported in the hen egg white lysozyme, its antibody (42)(43)(44)(45), barnase-barstar (46), and transthyretin-retinol binding protein (47) interactions, which are highly specific for biological significance. The association between the subunits in PfTSase is equivalent to such a highly specific interaction.
The negative value of ⌬Cp of the subunit association for PfTSase (Ϫ1.96 kJ/K mol of ␣) was less than half of that for EcTSase (Ϫ5.56 kJ/K mol of ␣) (Table I and Fig. 3B). In the cases of TSases from mesophiles, Hiraga and Yutani (39) have reported that a heat capacity change (⌬Cp est ) is estimated to be Ϫ1.05 kJ/K mol from the values of the water-accessible nonpolar (⌬A np ) and polar (⌬A p ) surface areas buried upon subunit association in the ␣/␤ subunit interface in the crystal structure of the StTSase complex. The negative values of ⌬Cp experimentally obtained upon the subunit association for EcTSase and StTSase (Ϫ7.29 and Ϫ6.83 kJ/K mol, respectively) are much larger than the estimated one (Ϫ1.05 kJ/mol) mentioned above.
It has been evaluated that this difference comes from the folding of many residues coupled to the ␣/␤ subunit association in EcTSase and StTSase (39), according to the method of Spolar and Record (48). ⌬A np and ⌬A p in the ␣/␤ interface for PfTSase complex can not be estimated, because the structure of the PfTSase complex has not yet been determined. However, the number of residues of local folding coupled to the subunit association in PfTSase might be postulated to be slight, because of the smaller negative ⌬Cp (Ϫ1.96 kJ/K mol of ␣). For a rigid body association in which a specific site is recognized by a "lock and key" interaction, an experimental ⌬Cp value might be similar to the ⌬Cp est predicted from ⌬A np and ⌬A p resulting from burial of the pre-existing complementary surface (48).
Negative ⌬Cp values of association corresponding to the concept of "induced fit" are larger than the negative ⌬Cp est predicted from ⌬A np and ⌬A p . In this case, the folding of many residues is coupled to the association and creates key parts of the protein-protein, protein-ligand, and protein-DNA interface (48). According to this criteria, the subunit association in PfTSase resembles a rigid body association. In contrast, the subunit association in EcTSase corresponds to an "induced fit" with large conformational changes.
The smaller negative ⌬H of the subunit association for PfTSase relative to that for EcTSase (Table I and Fig. 3B) also indicates that the conformational changes upon the subunit association are much smaller in PfTSase than in EcTSase, because the negative value of the enthalpy change due to protein folding is high (49). In PfTSase, the small values of negative ⌬H and positive ⌬S yield the negative value of ⌬G for driving the subunit association (Fig. 4A). The association constant between the hetero subunits from PfTSase and EcTSase at 40°C were drastically decreased relative to those for PfTSase and EcTSase, resulting in the decreases in the negative ⌬G (Table I). The negative ⌬H for the hetero subunit associations also decreased. These results indicate that the ␣ and ␤ subunits of PfTSase cannot strongly bind to each of subunits from EcTSase. The thermodynamic parameters of the subunit associations revealed that the binding between the ␣ and ␤ subunits was much tighter in PfTSase than in EcTSase, and the conformational change coupled with the subunit association was low in PfTSase.
Structural Bases of Strong Subunit Association in PfTSase-The structures of the St␣ 2 ␤ 2 complex form (23, 50 -52) and an isolated Pf␣ monomer (29) have been determined by x-ray analysis. We tried to explore the cause responsible for the strong subunit association in PfTSase from comparison of the structures of the subunit interfaces in Pf␣ and Ts␣. The crystal structure of Pf␣ alone (29) is the same topological pattern to that of St␣ in the St␣ 2 ␤ 2 complex form (23). Pf␣, St␣, and Ec␣ consist of 248, 268, and 268 residues, respectively. The sequence identities between Pf␣ and St␣ and between Ec␣ and St␣ are 31.5 and 85.1%, respectively.
We can find out the differences in the two structures as follows. The loops 2 and 6 in the St␣, which play an important role in the catalysis and allosteric communication between the active sites of the ␣ and ␤ subunits, contact with St␤ (23, 50 -52). The B-factor averaged for the main-chain atoms of the loop 2 in Pf␣ is considerably lower than that in St␣ (29), indicating that the loop 2 is less mobile in Pf␣ than in St␣. The loop 6 of St␣ is highly mobile and 12 residues in the loop 6 have not been determined due to a weak electron density (23). In Pf␣, only three residues are not determined, although Pf␣ does not form a complex with the ␤ subunit, indicating that the number of mobile residues in Pf␣ is drastically reduced (29). The amino acid residues of the loop 6 in Pf␣ exchange by polar to nonpolar, acidic to basic, or less to more hydrophobic resi- dues from those in StTSase, although the amino acid sequence of the loop 2 is highly conserved in both ␣ subunits (Fig. 6). In other regions of the subunit interface in StTSase, six hydrogen bonds are formed (53). The corresponding residues in PfTSase are presented in Fig. 6. The hydrogen bonding residues in StTSase are not conserved in both the ␣ and ␤ subunits in PfTSase except for the Asn ␣104 -Gly ␤292 pair in StTSase. The remarkable deviations in the root mean square deviations of the C␣ atoms between Pf␣ and St␣ are found in the loop 2 and in the residues of Val 119 , Phe 120 , and His 121 in Pf␣ (29), which are the residues in St␣ forming hydrogen bonds with the residues in St␤. From these observations, it seems that the conformations of the subunit interface in Pf␣ substantially differ from those in St␣, and the rigidly ordered conformations of the loops 2 and 6 in Pf␣ might contribute to creating the key part of the interface responsible for the strong subunit association in PfTSase.
Correlation between Subunit Association Constant and Protein Stability-For dimeric phosphoribosylanthranilate isomerase (7) and tetrameric pyrrolidone carboxyl peptidases (54) from hyperthermophiles and dimeric 3-isopropylmalate dehydrogenase from thermophiles (55), the experimental data have shown that the subunit interaction is important to the increase in thermal stability in solution. For these proteins, however, the relationship between subunit association and stability has not been quantitatively evaluated. Schellman (56,57) has developed an equation for the relationship between the binding constant of a ligand to a biopolymer and the melting temperature of a biopolymer as follows, where T o and T are the melting temperatures in the absence and presence of a ligand, respectively, L is the ligand concentration, ⌬H°is the denaturation enthalpy in the absence of a ligand, ⌬n is the difference in the number of bound molecules of a ligand in the unfolded and folded states, K is a binding constant, and R is the gas constant. This equation is applicable only when the enthalpy change of binding is negligible compared with the enthalpy change of the transition (57). Because the ⌬H values of the subunit association for PfTSase were small, although the values for EcTSase were large (Table I), we used Equation 2 to verify whether the enhancement in the T d value of Pf␣ in the complex form ( Fig. 5 and Table II) is due to the large K value of the subunit association. In the present case, a biopolymer and a ligand are the ␣ and ␤ subunits, respectively. Table III   The T d values represent the peak temperature of the DSC profiles measured at scan rate of 1°C/min. a From panels A and B in Fig. 5. b From panel C in Fig. 5 for the hybrid complexes between the Pf subunits and Ec subunits. c The differences in the T d values of individual subunits in the isolated and homo complex forms.   (Table I). The K used in Equation 2 was obtained by ITC measurements at various temperatures listed in Table I. ⌬T was calculated assuming ⌬n of 1.0. ⌬n was calculated using 17.4°C as ⌬T (ϭT Ϫ T 0 ). M Ϫ1 . Because the conformational change coupled to the subunit association in PfTSase was low as judged from the thermodynamic parameters for the subunit association, it was proved that the increase in T d of Pf␣ due to the complex formation is not due to the subunit binding-induced conformational stabilization of the subunits but due to the shift in the equilibrium toward the native state, which is caused by the increase in the association constant. This reveals that the enhancement in the thermal stability of subunit resulting from subunit association can be quantitatively evaluated by the subunit association constant.
The T d values of the Pf␤ monomer in the acidic region remarkably decreased with lower pH levels, 2 suggesting the importance of the ␤-␤ subunit interaction for the higher stability of Pf␤ 2 compared with Pf␣. The T d (80.3°C) value of Ec␤ 2 at pH 8.4 was higher than that of Ec␣ and comparable to that of Pf␣ at pH 9.4 (Fig. 5, A and B). The interaction between the ␤ subunits from the mesophile also enhances the stability of this dimeric protein.
Conclusion-The present study proved four significant aspects of the subunit association in the PfTSase compared with EcTSase: 1) Pf␣ and Pf␤ 2 tightly bind by the K value of the order of 10 8 M Ϫ1 ; 2) The negative values of ⌬Cp and ⌬H on the subunit association were low, indicating that the conformational change coupled to the subunit association is low; 3) The T d of Pf␣ was drastically enhanced by 17°C in the ␣ 2 ␤ 2 complex form; 4) This increment could be quantitatively evaluated from the remarkably increased K value. It was found that the stimulated interaction between the subunits with the order of 10 8 M Ϫ1 or over of K values remarkably enhances the thermal stability of a protein without conformational changes.