Tsukuba Life Science Center, The Institute of Physical and Chemical Research (RIKEN), 3-1-1 Koyadai, Tsukuba, Ibaraki 305-0074, Japan 1 Present address: Faculty of Science and Technology, Meijo University,1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan
![]() |
Abstract |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Keywords: amino acid properties/buried and partially buried mutants/local sequence and structural effects/multiple regression technique/protein stability/unfolding free energy change
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
It has been shown that changes in stability caused by mutations in the buried and partially buried regions of proteins are affected by different types of interactions. The contribution made by hydrophobicity to changes in stability of proteins caused by buried mutations has been emphasized by several investigators (Yutani et al., 1987; Matsumura et al., 1988
; Shortle et al., 1990
; Takano et al., 1995
, 1997
; Akasako et al., 1997
; Xu et al., 1998
). Moreover, the contributions of buried hydrogen bonds (H bonds) and salt bridges to protein stability have also been elucidated (Chen et al., 1993
; Tissot et al., 1996
). In the case of partially buried and surface mutations, the contribution made by H bonds to the stability of T4 lysozyme was extensively studied by Alber et al. (1987), who replaced Thr157 with 13 other amino acids. Electrostatic interactions (surface salt bridges and helixdipole interactions) also play important roles in protein stability changes caused by partially buried and surface mutations (Akke and Forsen, 1990
; Serrano et al., 1990
; Nicholson et al., 1991
; Sun et al., 1991
).
On the other hand, Gills and Rooman (1997) derived torsion and distance potentials and then applied them to predict the stability of seven proteins with mutations in the buried and partially buried regions of the molecules. They found that distance potentials, which are dominated by hydrophobic interactions, represent the strongest interactions stabilizing the protein core; whereas torsion potentials, which are defined by local interactions along the chain, represent the strongest interactions at the protein surface. Combining the distance potentials with the torsion potentials, weighted by 0.4 and 0.7, respectively, for buried and partially buried mutations, yielded correlations between computed and measured changes in folding free energy with correlation coefficients (r) of 0.80 and 0.71, respectively.
In spite of these studies, the relationship between the specific properties of amino acid residues and the stability (in terms of melting temperature and free energy) of protein mutants has yet to be fully explored. In the present work, we analyzed the correlation between stability changes of proteins caused by buried and partially buried mutations and the changes in 48 physicochemical, energetic and conformational properties. Multiple regression analysis was performed with selected groups of three properties obtained from among all possible combinations of the total 48. Finally, inclusion of information about local sequence and structural effects increased the r value of partially buried mutations to 0.97, which reflects a higher level of accuracy than has been obtained using other published methods. We observed that hydrophobicity is the major factor with respect to buried mutations, but hydrogen bonds, other polar interactions and hydrophobic interactions are all important determinants of the stability changes caused by partially buried mutations.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
A database was set up for protein mutants from 103 different proteins. It includes the thermodynamic data for more than 4000 mutants (Gromiha et al., 1999). In the present study, we selected data for different solvent accessibility between: (i) 0 and 2% for completely buried mutations; (ii) 2 and 20% for intermediate between buried and partially buried mutations; (iii) 20 and 50% for partially buried mutations and (iv) more than 50% for exposed mutations. We considered the data for all pH values in the native state.
Furthermore, we have used a subset of data obtained for pH values between 5 and 9 in our analysis and the number of buried and partially buried mutations for each protein is given in Table I. The complete information is available at http://www.rtc.riken.go.jp/~gromiha/table.html and the experimental data (
Tm,
G and
GH2O) can be obtained at the URL, http://www.rtc.riken.go.jp/protherm.html (Gromiha et al., 1999
). We then subdivided the data set into hydrophobic mutations and mutations in selected secondary structural regions (helix, strand, coil or turn). Mutations were defined as hydrophobic when both the mutant and wild-type residues were hydrophobic; Ala, Cys, Phe, Gly, Ile, Leu, Met, Val, Trp and Tyr were considered to be hydrophobic (nonpolar), and all other residues were considered to be polar.
Computation of accessibility
Solvent accessibility (%) was defined as the ratio of the solvent accessible surface area (ASA) of a residue in the native state and that of the residue in an extended tripeptide (Ala-X-Ala) conformation. The solvent accessible surface areas of all atoms were computed using the program ASC (Eisenhaber and Argos, 1993; Eisenhaber et al., 1995
) with the van der Waals radii of the atoms given by Ooi et al. (1987). The extended state coordinates were computed using the ECEPP/2 algorithm (Momany et al., 1975
) with the dihedral angles of Oobatake and Ooi (1993).
Amino acid properties
It has been shown that there are specific cooperativities among amino acid residues, which due to similarities in their various physical, chemical, energetic and conformational properties, enable them to preserve their specific, preferred environments and spatial positions in the folded conformation of proteins (Prabakaran and Ponnuswamy, 1979). We considered a set of 48 diverse amino acid properties, which fall into various clusters analyzed by Tomii and Kanehisa (1996). Detailed descriptions of the properties have already been published (Gromiha and Ponnuswamy, 1993; Oobatake and Ooi, 1993
) and the numerical values are available at http://www.rtc.riken.go.jp/~gromiha/table.html. The selected 48 amino acid properties were normalized between 0 and 1.
Computation procedure
We computed the mutation-induced changes in property values, P(i), using the equation,
![]() |
where Pmut (i) and PWT (i) are, respectively, the normalized property value of the ith mutant and wild-type residues; i varies from 1 to N; N being the total number of mutants. The computed differences in property values (P) were related to the changes in experimental stability values (
Tm,
G or
GH2O) using the correlation coefficient.
Local sequence and structural effects
The effect of local sequence, Pseq(i), was included using the equation
|
where Pmut (i) is the property value of the ith mutant residue, and Pj(i) is the total property value of a segment of (2k + 1) residues, ranging from i k to i + k about the ith wild-type residue. We used windows of 3 and 9 (k = 1, 4) residues to include the influence of short and medium-range interactions (Ponnuswamy et al., 1973
, 1980
; Gromiha and Selvaraj, 1997
).
The structural information was included as follows. Each residue in the protein was represented by its C atom. Using the C
coordinates, a volume with a radius of 8 Å was fixed around the mutant residue, and the residues occurring within this volume were identified. From the analysis of a set of three-dimensional structures of globular proteins, Manavalan and Ponnuswamy (1977, 1978) showed that the influence of each residue over the surrounding medium extends effectively up to 8 Å; hence, we used an 8 Å radius rather than 6 or 10 Å, as was previously used for barnase (Serrano et al., 1992
) and staphylococcal nuclease (Shortle et al., 1990
), respectively. The residues surrounding the mutant residue were assigned their property values, and the total property value, Psur(i), was computed using the equation
![]() |
where nij is the total number of type j residues surrounding the ith residue of the protein, and Pj is the property value of the type j residue. The structural information, Pstr(i), was included using the equation
![]() |
where Pmut(i) is the property value of the ith mutant residue. The computed Pseq(i) and Pstr(i) were related to the changes in experimental stability values (Tm,
G or
GH2O) using correlation coefficients.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Correlation of stability with properties of amino acids
We observed a significant correlation for several properties of amino acids and stability. The results are similar for each of the three measures of stabilityTm,
G and
GH2O. Hence, we only discuss the results obtained for
Tm.
The correlation coefficients (r), relating changes in each of the selected 13 properties (Eqn 1) to experimental Tm values, are given in Table II
. In the case of buried mutations, the chromatographic index (Rf, the characteristic migration rate in a solvent-absorbent system) has the highest value (r = 0.59). Surrounding hydrophobicity (Hp), bulkiness (Bl, the ratio of side chain volume to length), normalized consensus hydrophobicity (Hnc), long range non-bonded energy (El), mean r.m.s. fluctuation displacement (F), solvent accessible reduction ratio (Ra), average number of surrounding residues (Ns), unfolding solvent accessible surface area change (
ASA), unfolding entropy change of hydration (T
Sh), and unfolding hydration heat capacity change (
Cph) are the other 10 properties that correlate significantly (|r | > 0.5) with
Tm (Table II
).
|
When we generated 48 sets of random numbers, and calculated the correlation with the experimental stability changes (Tm,
G and
GH2O), the average r value fell within a range between 0.07 ± 0.05 and 0.39 ± 0.18 for all data sets, which emphasizes the validity of selecting various amino acid properties.
Mutation in helical segments
Considering the mutations in helical segments of partially buried mutations, the strongest positive correlation was observed for ASA, whereas the strongest negative correlation was for T
Sc (Table II
). Three other properties, T
Sh,
Cph and V0, also showed significant correlations (r > 0.5). We noted that all of these properties were related to thermodynamic parameters, and that the conformational parameter, P
, was not correlated with stability, as was the case for buried mutations.
Mutations in strand segments
When we analyzed the effects of partially buried mutations within strand segments, ß-strand tendency (Pß) showed the strongest single-property correlation with Tm (r = 0.67). Interestingly, properties responsible for accessibility and long range interactions (Ra, Hp, Bl and Ns) also correlated significantly (r > 0.5) with experimental thermal stability, which demonstrates the importance of long range interactions for the stability of globular proteins (Gromiha and Selvaraj, 1997
, 1998
, 1999a
,Gromiha and Selvaraj, b
; Selvaraj and Gromiha, 1998
). We found that F, Pc, Pt and
c had strong negative correlations with
Tm. Thus, strand (Pß) and coil (Pc) tendency (Fasman, 1989
) have opposing influences on stability. In buried mutations, long-range non-bonded energy, El, correlated most strongly with
Tm.
Mutations in coil regions
No significant correlation was observed between any of the amino acid properties and Tm when partially buried mutations within coil regions were treated as a single group. Mutations within regions of a coil were, therefore, further subdivided based on the H-bond forming capability of the amino acids involved: set 1 included mutations from a residue with H-bond forming capability (hb) to another hb residue (hb
hb); set 2 included mutations from a residue without H-bond forming capability (nhb) to another nhb residue (nhb
nhb); set 3 contained mutations from an hb residue to a nhb residue (hb
nhb); and set 4 contained mutations from a nhb residue to an hb residue (nhb
hb). We considered Asp, Cys, Glu, His, Lys, Met, Asn, Gln, Arg, Ser, Thr, Trp and Tyr to belong to the hb group, as suggested by Vogt et al. (1997).
Within set 1, the strongest positive and negative correlations were with TSc (r = 0.72) and Ca (r = 0.91), respectively.
Hh, Esm and
Gh also showed significant positive correlations with
Tm, while
Hc showed a strong negative correlation (r = 0.83). Thus stability is favored by the chain entropic contribution (T
Sc) and disfavored by chain enthalpic terms (
Hc). Multiple regression analysis strengthened the correlation (r = 0.95), and inclusion of local sequence information yielded a still stronger correlation (r = 0.97).
The single-property correlations for set 2 were weak, but significant single-property correlations were obtained for sets 3 and 4. Inclusion of local sequence information increased r values to 0.97, 0.78 and 0.95, respectively, for sets 2, 3 and 4. A similar strengthening of the correlation with stability was obtained when structural information was included.
![]() |
Discussions |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
A perusal of the top four properties (Rf, El, Ra and Cph) that showed the strongest correlation with
Tm and
G of buried mutation shows that for all of the properties, the nonpolar residues (A, V, M, Y, I, W, L and F) had higher values; charged residues had lower values; and polar residues had intermediate values. Also, we observed a direct relation between property values and the number of carbon atoms. For instance, considering the negatively charged residues, Asp and Glu, the Glu residue, which has more carbon atoms than Asp, acquires a higher value. Similar trends were observed between Lys and Arg [P(Arg) > P(Lys)] and between Asn and Gln [P(Gln) > P(Asn)], among others. An in-depth analysis of nonpolar residues shows a similar pattern: P(Ala) > P(Gly); P(Leu) > P(Val); P(Ile) > P(Val); and P(Trp) > P(Tyr). Thus, hydrophobic residues play a major role in explaining the changes in stability caused by buried mutations, which is consistent with the well-known fact that hydrophobicity, defined as a measure of transfer free energy change, varies linearly with the number of methylene carbons (Tanford, 1980
).
With respect to GH2O, we observed a better single-property correlation for buried mutations in ß-strand segments than for those in
-helical segments (Table II
), which may be due to the stronger hydrophobicity of ß-strands (Ponnuswamy et al., 1980
; Gromiha and Ponnuswamy, 1995
). These authors showed that ß-strand segments have higher average Hp values than do
-helical segments, which explains the stronger hydrophobicity of ß-strands and the stronger correlation between mutations within ß-strand regions and stability.
Subgrouping secondary structures strengthens correlation for partially buried mutations
The analysis carried out based on the secondary structure (helix, strand, coil and turn) yielded good correlations between amino acid properties and protein stability changes caused by partially buried mutations (Table II); moreover, multiple regression analysis using three properties substantially strengthened these correlations. When the analysis was carried out using the complete data set, the correlation was poor (data not shown), which may have been due to combining the effects of irregular structures (coil) with those of ordered structures (helix, strand and turn): the two structure types have opposing roles in the folding and stability of protein molecules, and hence their contributions to stability might offset one another. The present study, therefore, suggests that mutations in ordered and disordered structures should be considered separately, and that classification based on secondary structures is necessary for better understanding of the relationship between the structure and stability of proteins.
Coil has different tendency
The r values obtained for the 17 selected properties in all of the respective subgroups are given in Table II. It is evident from this table that the mechanism responsible for changes in stability caused by partially buried mutations within coil segments is the opposite of that in helical and strand segments. Within coil segments, T
Sc was the property most strongly correlated with stability (Table II
), which was indicative of the importance of entropic effects in the stability of mutations within coil regions. Interestingly, we note that the signs for the properties governing stability of coil regions are the opposite of those observed in all the other segments.
The relationship among the subgroups for all 48 properties with respect to GH2O is shown in Figure 1
. In this figure, we show the relation between the r values obtained for hydrophobic mutations and those for mutations in secondary structures. We found a direct relationship between hydrophobicity and ordered structures, indicating that hydrophobicity plays a role in stabilizing the structures of mutations in ordered structures. On the other hand, the inverse was found for coil regions, which are destabilized by hydrophobicity. We also observed that a coil behaves in a manner opposite to that of a helix, strand or turn; r values are 0.82, 0.68 and 0.71, respectively.
|
![]() |
Importance of hydrogen bonds for protein stability changes |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
![]() |
Importance of sequence and structural information |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
In Figure 2, the relationship between the experimental and computed
GH2O values for mutations in coil regions (set 4, nhb
hb) are depicted; Figure 2a
shows the correlation without sequence and structural information, while Figure 2b
shows the correlation when structural information is included. The r values obtained for the two sets of data are 0.71 and 0.95, respectively. Note that in Figure 2a
some of the mutants are substantially displaced from the diagonal line (G234D of 1WSY; G34D, G34K and V36T of 1BNI; and G121H and G121S of 1DYJ). Inspection of residues surrounding the mutant residue showed that along the sequence, more than 50% of both the nearby and more distant residues were polar. Furthermore, we noted the presence of at least one aromatic residue nearby most of the mutants. The inclusion of the information about the polar and aromatic residues (structural effect) strengthened the correlation, and all six mutants moved toward the diagonal line (Figure 2b
). This finding emphasizes the importance of structural effects for improving the correspondence between experimental and computed stabilities. We observed a similar improvement using information about sequence. Information about the surrounding residues and three-dimensional structures yields better results with respect to partially buried mutations than to buried ones. This may be due to the fact that in partially buried regions, mutants are more likely to be surrounded by both hydrophobic and polar residues.
|
Comparison among different measures of stability
We observed basically the same conclusions for all three measures of stability, Tm,
G and
GH2O. Specifically, hydrophobicity (Bl, Rf,
ASA, T
Sh and
Cph) and entropy (T
Sc) are the dominant factors, respectively, in all data sets of buried mutations and in coil regions of partially buried mutations, for these three measures of stability. Interestingly, for
Tm and
G (the data obtained from thermal denaturation experiments), thermodynamic parameters, T
Sh and
Cph have more influence than other hydrophobic properties, whereas other properties reflecting hydrophobicity (Bl and Rf) are dominants for
GH2O to the stability of hydrophobic buried mutations. The cross correlation between single property correlation of subgroups in partially buried mutations shows that the r values obtained for
GH2O are better than those of
Tm and
G. This may be due to the fact that most of the amino acid properties were derived at room temperature.
Conclusions
Hydrophobicity was the major factor determining the stability of buried mutations, whereas hydrogen bonds, long-range interactions and hydrophobic interactions were all important determinants of stability for partially buried mutations. Subgroups based on secondary structure yielded significantly better results. The strongest correlations between partially buried mutations within helix, strand and turn and changes in protein stability are governed by hydrophobicity, whereas a coil has the opposite (destabilizing) tendency with respect to hydrophobicity. As compared to helix, strand and turn, regions of coil were inversely related to stability, indicating that the mechanism underlying coil stability is different from those of other secondary structures; a coil is strongly influenced by the effects of entropy. Information about sequence and structure was very important for predicting stability changes caused by partially buried mutations, but did not significantly strengthen the correlation for buried mutations.
![]() |
Acknowledgments |
---|
![]() |
Notes |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Akke,M. and Forsen,S. (1990) Proteins Struct. Funct. Genet., 8, 2329.[ISI][Medline]
Alber,T., Dao-pin,S., Wilson,K., Wozniak,J.A., Cook,S.P. and Matthews,B.W. (1987) Nature, 330, 4146.[ISI][Medline]
Bash,P.A., Singh,U.C., Langridge,R. and Kollman,P.A. (1987) Science, 236, 564568.[ISI][Medline]
Bhaskaran,R. and Ponnuswamy,P.K. (1984) Int. J. Pept. Protein Res., 24, 180191.[ISI][Medline]
Chen,Y.W., Fersht,A.R. and Henrick,K. (1993) J. Mol. Biol., 234, 11581170.[ISI][Medline]
Chou,P.Y. and Fasman,G.D. (1978) Adv. Enzymol., 47, 45148.[Medline]
Dang,L., Merz,K.M. and Kollman,P.A. (1989) J. Am. Chem. Soc., 111, 85058508.[ISI]
Dill,K.A. (1990) Biochemistry, 29, 71337155.[ISI][Medline]
Eisenberg,D., Weiss,R.M., Terwilliger,T.C. and Wilcox,W. (1982) Faraday Symp. Chem. Soc., 17, 109120.
Eisenhaber,F. and Argos,P. (1993) J. Comp. Chem., 14, 12721280.[ISI]
Eisenhaber,F., Lijnzaad,P., Argos,P., Sander,C. and Scharf,M. (1995) J. Comp. Chem., 16, 273284.
Fasman,G.D. (1989) In Fasman,G.D. (ed.), Prediction of Protein Structure and Principles of Protein Conformation. Plenum press, New York, pp. 193316.
Gills,D. and Rooman,M. (1996) J. Mol. Biol., 257, 11121126.[ISI][Medline]
Gills,D. and Rooman,M. (1997) J. Mol. Biol., 272, 276290.[ISI][Medline]
Gromiha,M.M. and Ponnuswamy,P.K. (1993) J. Theor. Biol., 165, 87100.[ISI]
Gromiha,M.M. and Ponnuswamy,P.K. (1995) Int. J. Pept. Protein Res., 45, 225240.[ISI][Medline]
Gromiha,M.M. and Selvaraj,S. (1997) J. Biol. Phys., 23, 151162.[ISI]
Gromiha,M.M. and Selvaraj,S. (1998) Protein Engng, 11, 249251.[Abstract]
Gromiha,M.M. and Selvaraj,S. (1999a) Biophys Chem., 77, 4968.[ISI][Medline]
Gromiha,M.M. and Selvaraj,S. (1999b) Prep. Biochem. Biotech., in press.
Gromiha,M.M., An,J., Kono,H., Oobatake,M., Uedaira,H. and Sarai,A. (1999) Nucleic Acids Res., 27, 286288.
Iqbal,M. and Verrall,R.E. (1988) J. Biol. Chem., 263, 41594165.
Lee,C. and Levitt,M. (1991) Nature, 352, 448451.[ISI][Medline]
Manavalan,P. and Ponnuswamy,P.K. (1977) Arch. Biochem. Biophys, 184, 476487.[ISI][Medline]
Manavalan,P. and Ponnuswamy,P.K. (1978) Nature, 275, 673674.[ISI][Medline]
Matsumura,M., Becktel,W.J. and Matthews,B.W. (1988) Nature, 334, 406410.[ISI][Medline]
Matthews,B.W. (1995) Adv. Protein Chem., 46, 249278.[ISI][Medline]
Miyazawa,S. and Jernigan,R.L. (1994) Protein Engng, 7, 12091220.[Abstract]
Momany,F.A., McGuire,R.F., Burgess,A.W. and Scheraga,H.A. (1975) J. Phys. Chem., 79, 23612381.[ISI]
Nicholson,H., Anderson,D.E., Dao-pin,S. and Matthews,B.W. (1991) Biochemistry, 30, 98169828.[ISI][Medline]
Oobatake,M. and Ooi,T. (1977) J. Theor. Biol., 67, 567584.[ISI][Medline]
Oobatake,M. and Ooi,T. (1993) Prog. Biophys Mol. Biol., 59, 237284.[ISI][Medline]
Ooi,T., Oobatake,M., Némethy,G. and Scheraga,H.A. (1987) Proc. Natl Acad. Sci. USA, 84, 30863090.[Abstract]
Pace,C.N., Shirely,B.A., McNutt,M. and Gajiwala,K. (1996) FASEB J., 10, 7583.
Ponnuswamy,P.K. (1993) Prog. Biophys Mol. Biol., 59, 57103.[ISI][Medline]
Ponnuswamy,P.K. and Gromiha,M.M. (1993) Int. J. Pept. Protein Res., 42, 326341.[ISI][Medline]
Ponnuswamy,P.K. and Gromiha,M.M. (1994) J. Theor. Biol., 166, 6374.[ISI]
Ponnuswamy,P.K., Warme,P.K. and Scheraga,H.A. (1973) Proc. Natl Acad. Sci. USA, 70, 830833.[Abstract]
Ponnuswamy,P.K., Prabhakaran,M. and Manavalan,P. (1980) Biochim. Biophys. Acta, 623, 301316.[ISI][Medline]
Prabhakaran,M. and Ponnuswamy,P.K. (1979) J. Theor. Biol., 80, 485504.[ISI][Medline]
Rose,G.D. and Wolfenden,R. (1993) Annu. Rev. Biophys Biomol. Str., 22, 381415.
Rose,G.D., Geselowitz,A.R., Lesser,G.J., Lee,R.H. and Zehfus,M.H. (1985) Science, 229, 834838.[ISI][Medline]
Selvaraj,S. and Gromiha,M.M. (1998) J. Protein Chem., 17, 691697.[ISI][Medline]
Serrano,L., Horovitz,A., Avron,B., Bycroft,M. and Fersht,A.R. (1990) Biochemistry, 29, 93439352.[ISI][Medline]
Serrano,L., Kellis,J.T.,Jr., Cann,P., Matouschek,A. and Fersht,A.R. (1992) J. Mol. Biol., 224, 783804.[ISI][Medline]
Shortle,D., Stites,W.E. and Meeker,A.K. (1990) Biochemistry, 29, 80338041.[ISI][Medline]
Simonson,T. and Brunger,A.T. (1992) Biochemistry, 31, 86618674.[ISI][Medline]
Sober,H.A. (1970) Handbook of Biochemistry: Selected Data for Molecular Biology, 2nd edn. The Chemical Rubber Co., Cleveland, Ohio.
Sun,D.P., Sauer,U., Nicholson,H. and Matthews,B.W. (1991) Biochemistry, 30, 71427153.[ISI][Medline]
Takano,K., Ogasahara,K., Kaneda,H., Yamagata,Y., Fujii,S., Kanaya,E., Kikuchi,M., Oobatake,M. and Yutani,K. (1995) J. Mol. Biol., 254, 6276.[ISI][Medline]
Takano,K., Yamagata,Y., Fujii,S. and Yutani,K. (1997) Biochemistry, 36, 688698.[ISI][Medline]
Tanford,C. (1980) The Hydrophobic Effect. Wiley & Sons, New York.
Tidor,B. and Karplus,M. (1991) Biochemistry, 30, 32173228.[ISI][Medline]
Tissot,A.C., Vuilleumier,S. and Fersht,A.R. (1996) Biochemistry, 35, 67866794.[ISI][Medline]
Tomii,K. and Kanehisa,M. (1996) Protein Engng, 9, 2736.[Abstract]
Topham,C.M., Srinivasan,N. and Blundell,T.L. (1997) Protein Engng, 10, 721.[Abstract]
van Gunsteren,W.F. and Mark,A.E. (1992) J. Mol. Biol., 227, 389395.[ISI][Medline]
Vogt,G., Woell,S. and Argos,P. (1997) J. Mol. Biol., 269, 631643.[ISI][Medline]
Wetzel,R., Perry,L.J., Baase,W.A. and Becktel,W.J. (1988) Proc. Natl Acad. Sci. USA, 85, 401405.[Abstract]
Xu,J., Baase,W.A., Baldwin,E. and Matthews,B.W. (1998) Protein Sci., 7, 158177.
Yutani,K., Ogasahara,K., Tsujita,T. and Sugino,Y. (1987) Proc. Natl Acad. Sci. USA, 84, 44414444.[Abstract]
Zimmerman,J.M. Eliezer,N. and Simha,R. (1968) J. Theor. Biol., 21, 170201.[ISI][Medline]
Received December 22, 1998; revised March 24, 1999; accepted March 30, 1999.