Department of Chemistry, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
1 To whom correspondence should be addressed. Present address: Center for Biomolecular Structure Analysis, Department of Biochemistry, Allied Health Building, University of Texas Health Science Center at San Antonio, San Antonio, TX 78229-3900, USA. e-mail: sdeep{at}instinct.v24.uthscsa.edu
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Abstract |
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Keywords: atomic solvation parameter sets/chain free energy/free energy of solvation of folding/hydrogen bonding/solvent-accessible surface area
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Introduction |
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The alternative approach to calculate the solvent contribution is based on the Kauzmann formalism (Kauzmann, 1959). To quantify the contributions of hydrophobic free energy (
GH
) to the observed standard free energy change for the folding of proteins, most work has been focused on analyzing the free energy of transfer (
G°tr) of amino acids or their analogues from water to an organic solvent (Nozaki and Tanford, 1971
) or the gas phase (Wolfenden et al., 1981
). Various hydrophobicity scales have been proposed that rank amino acids according to either their experimental transfer behavior or their observed distribution in protein crystal structures between exterior and interior of the folded form (Bull and Breese, 1974
; Fendler et al., 1975
; Tanford, 1978
; Janin, 1979
; Rose et al., 1985
; Damodaran and Song, 1986
). However a comparison of the hydrophobicity scales reveals that in general, values of
G°tr from different scales do not correlate well with each other and that even the relative ranking of amino acid varies from one scale to another.
Hermann (Hermann, 1972) developed an implicit method for treating water molecules, whereby the area of various hydrocarbons could be quantitatively related to their solubilities. Chothia (Chothia, 1974
) found a linear relationship between surface areas of amino acid residues and free energy changes associated with the transfer of amino acids from organic solvent to water. The slope of this line corresponds to a free energy change of about 25 cal/mol.Å2 for non-polar residues.
Assuming that the thermodynamic component or the free energy of the folded protein molecule is proportional to the total protein surface that is accessible to water, regardless of whether the exposed surface is apolar, polar or charged, is an oversimplification. Eisenberg and McLachlan (Eisenberg and McLachlan, 1986) computed the free energy of interaction of water with the protein as the sum of energies of atomic groups. They considered the process of transferring atoms or the groups from the interior of a protein to aqueous solution and used transfer free energies of amino acids from n-octanol to water as reported by Fauchere and Plisca (Fauchere and Plisca, 1983
). The solvent contribution to the free energy of folding of a protein (
Gs,f) can be expressed simply in terms of reduction in its solvent-accessible area of folding multiplied by the solvation free energy per unit area.
, where
i is the atomic solvation parameter of the atom i of the given type,
Ai is the change in solvent-accessible surface area upon folding and
Gs,f is the change in solvation energy of folding (Eisenberg and McLachlan, 1986
).
Atomic solvation parameters (ASPs) are widely used to estimate the solvation contribution to the thermodynamic stability of proteins and the results obtained are generally promising (Wesson and Eisenberg, 1992; Williams et al., 1992
; Schiffer et al., 1993
; Stouten et al., 1993
). These parameters are used to rationalize the changes in protein stability that result from single-site mutations (Kellis et al., 1989
; Eriksson et al., 1992
; Lee, 1993
; Blaber et al., 1994
; Huang et al., 1995
) and to predict thermodynamic properties of compact denatured states and partially folded states or molten-globule states of proteins (Xie and Freire, 1994
; Freire, 1995
; Hilser and Freire, 1996
).
Many workers have pursued this approach, which led to a dissemination/proliferation of several different atomic solvation parameter sets; some of them are listed by Juffer et al. (Juffer et al., 1995). All ASP sets are derived by a least-squares fitting of experimentally observed changes in free energies upon transfer of a simple model compound from an organic solvent to water.
However, recent reports showed that large discrepancies exist between results using different atomic solvation parameter sets. It has also been shown that the use of atomic solvation parameters often does not contribute to the ability to estimate accurately the energetics of ligand binding or protein association (Horton and Lewis, 1992; von Freyberg et al., 1993
; Janin, 1995
; Karplus, 1997
).
In view of discrepancies in the results of free energies of solvation for various proteins obtained using different atomic solvation parameter sets, it was felt desirable to carry out systematic studies on the calculation of accessible surface area and the changes in free energy of folding of a large number of proteins. Since experimental values for free energy of solvation of proteins are not available for comparison with the values calculated using ASPs, it was thought worthwhile to calculate the changes in free energy of folding of proteins on mutations, where the calculated results can be compared with the experimental results. This would give a better perception of the suitability and limitations of the various ASP sets for modeling folding processes and proteinligand binding.
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Materials and methods |
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The Sch3 and WE sets were derived by Wesson and Eisenberg (Wesson and Eisenberg, 1992) from Wolfendens measurement data on transfer free energies of small solutes from vacuum to water, which were adjusted for the entropy of mixing by Kyte and Doolittle (Kyte and Doolittle, 1982
) and Sharp et al. (Sharp et al., 1991a
,b), respectively. A solvent potential function was introduced that describes proteinwater interactions based solely on the position of protein atoms and on atomic solvation parameters, as an alternative to including explicit water molecules in a simulation. The potential function and its derivative are added to the CHARMm force field (Brooks et al., 1983
) for simulation of protein in a vacuum; the total potential describes a protein solvated in water.
The Sch4 set was derived by Schiffer et al. (Schiffer et al., 1993) by comparison of simulations using an ASP solvation term based on different octanolwater transfer data as complements to the AMBER potential function in a protein folding/molecular dynamics study.
The Oons atomic solvation parameter set was established by Ooi et al. (Ooi et al., 1987) to supplement the ECEPP/2 (empirical conformational energy programs for peptides) algorithm (Momany et al., 1975
; Némethy et al., 1983
) that computes the intramolecular energy of the folded protein molecule. It was derived from the transfer free energies of small solute molecules from vacuum to water, as given by Cabani et al. (Cabani et al., 1981
) and supplemented with data from Wolfenden et al. (Wolfenden et al., 1981
) on transfer energies for the partition of amino acids between water and vapour phase (vacuum). While the EM set was derived by assuming that there are no significant changes in conformation of amino acids during the transfer process, possible shifts of the distribution among various conformations were taken into account in the Oons set.
In a similar approach, the Jrf set was derived by Vila et al. (Vila et al., 1991) by adding a solvation potential function based on the Connolly molecular surface areas and its derivative to the ECEPP/2 program. The solvation models were evaluated by the concordance between solvation free energy and root mean square deviation from the crystal structure in 39 near-native conformations of bovine pancreatic trypsin inhibitor.
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Results and discussion |
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where Gmf and
Gwf are the free energies of folding of the mutant and wild-type lysozyme T4, respectively.
Since (Gmf
Gwf) > 0, it means that all the mutants of T4 lysozyme are less stable than the wild-type lysozyme T4. In order to quantify the relative contribution of the hydrophobic interactions, hydrogen bonding, etc., to the stability of these mutants, the changes in accessible surface areas of folding and the changes in free energies of solvation of folding of mutants of lysozyme T4 were calculated.
The values of mw
A of folding calculated using two radii sets are listed in Table IV and Table V and are found to be negative for all mutants except for the mutant where threonine is replaced by cysteine. The negative values of
mw
A of folding appear to arise from the increase in the extent of the burial of polar nitrogen atoms (both charged and uncharged) in mutants leading to a decrease in stability, although it is partly compensated by exposure of oxygen atoms.
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A protein structure is stabilized not only by buried hydrophobic residues but also by buried polar residues with hydrogen bonds. The X-ray crystal structure of lysozyme T4 shows that Thr157 is located in an irregular loop on the surface of the protein and is involved in hydrogen bonding with Thr155 and Asp159 as shown in Figure 1. The substitution of Thr157 by amino acid alters the geometry of the hydrogen bonding network (as shown in Figure 2 for Ile), resulting in a change of several interactions in the folded state, i.e. hydrogen bonding, van der Waals, hydrophobic and electrostatic interactions. When Thr157 is replaced by Asn (T157N), Ser (T157S), Asp (T157D) or Arg (T157R), the buried backbone amide of Asp159 is hydrogen bonded (Alber et al., 1987). The substitution of Thr157 by Phe (T157F), I1e (T157I), Leu (T157L), Val (T157V), Cys (T157C), Glu (T157E) or His (T157H) results in the loss of the hydrogen bond to the amide of Asp159 while the hydroxyl oxygen of Thr155 forms a new hydrogen bond with a water molecule in place of the hydroxyl hydrogen of Thr157. The mutants with or without a hydrogen bond to the amide of Asp159 will be subsequently referred to as type A and type B mutants. The loss of one hydrogen bond destabilizes type B mutants by 1 kcal (Fersht et al., 1985
; Shirley et al., 1992
).
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The most striking X-ray crystal structure of this series is that of T157G. The absence of a side chain on glycine leaves a gap on the surface of the enzyme that is filled by a new bound water molecule (Alber et al., 1987). The water molecule is positioned to interact with the same hydrogen-bonded partners as Thr157 in wild-type protein. The average geometry of the hydrogen-bonded network is improved, apparently because the solvent molecule is not covalently bonded to the protein. With two protons to donate, the new water can form a hydrogen bond with the side-chain carboxylate of Asp159. Similarly, Asn has two protons to donate and hence can form an extra hydrogen bond with the side-chain carboxylate of Asp159. The formation of one extra hydrogen bond is correlated with the decrease in
mw
Gf, leading to higher stability of mutants T157G and T157E.
The major force opposing protein folding is the loss of conformational entropy (Doig and Sternberg, 1995). Since, in the wild-type lysozyme T4, Thr157 is conformationally restricted owing to its ß-branched side chain compared with most of the amino acids, it is expected that the contribution of the chain entropy term will be significant. The values of
mw
Gc,f were calculated using the value of side-chain entropy for different amino acids (Pickett and Sternberg, 1993
).
Another factor affecting the stability of mutants is the change in the volume of the cavity. The change in the volume of the cavity upon mutation of lysozyme T4 is essentially very small so it was not included in the calculation of mw
Gf.
Table VII summarizes the contributions of various stabilization factors to the overall stability of mutants relative to the wild-type lysozyme T4. The values of the calculated mw
Gf, the sum of
mw
Gs,f,
mw
GHB,
mw
GH2O and
mw
Gc, for different mutants are given in Table VIII. All atomic solvation parameter sets except Jrf predict wild-type lysozyme to be more stable than its mutants. However, the values of
mw
Gf differ for different ASP sets.
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The correlation coefficients between the experimental and calculated mw
Gf data sets are listed in Table VIII. It is clear that octanol to water-based atomic solvation parameter sets Sch1 and EM are more consistent than other atomic solvation parameter sets in predicting
mw
Gf. EM gives a slightly higher value of
mw
Gf. Figure 3 shows the correlation between the experimental and calculated
mw
Gf values based on the Sch1 set. The only mutant for which the experimental and calculated
mw
Gf values differ considerably is T157I. The bulkier ethyl substituent of Ile forces the side chain of Asp 159 to move 1.1 Å away from its position in the wild-type protein (Alber et al., 1987
). The unusually large motion of Asp159 disturbs the intramolecular network of hydrogen bonding in that region, leading to a large reduction in stability.
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The octanol to water-based ASP set Jrf predicts all mutants to be more stable than wild-type lysozyme T4. Mutations of lysozyme T4 are accompanied by burial of charged/uncharged N that is partly compensated for by exposure of O atoms. Most ASP sets assign almost equal ASP to N and O. Since Jrf assigns ASP of O three times ASP of N, the solvation free energy will be determined more or less by the changes in the accessible surface area of the O atoms and hence mutants are predicted to be more stable than wild-type lysozyme T4.
Vacuum to water-based ASP sets WE and Sch3 predict all mutants to be less stable than the wild-type lysozyme T4. However, the mw
Gf values obtained are higher in magnitude, which can be attributed to the higher ASP assigned to charged nitrogen atoms. If vacuum to water transfer is used to define hydrophobicity, then the solvation enthalpy makes a large contribution to the net free energy change, partially cancelling the solvation entropy. As a result, the hydrophobic effect becomes smaller than when defined in terms of octanol to water transfer. This will result in a higher ASP of polar atoms than non-polar atoms. Based on the definition involving vacuum to water transfer, Privalov and co-workers have argued that the hydrophobic effect makes only a small contribution to protein stability (Privalov and Gill, 1988
; Makhatdze and Privalov, 1993
; Privalov and Makhatdze, 1993
). However, exclusion of T157N, T157H and T157R and T157C from the experimental data does not improve the correlation coefficient significantly. This clearly indicates that factors other than the hydrophobic effect are responsible for the poor performance of vacuum to water-based ASP sets. The change of mode to define hydrophobicity also affects the contribution of hydrogen bonds to the overall stability. Since vacuum has a lower dielectric constant than octanol, the hydrogen bond contribution to
mw
Gf is expected to be higher in the case of vacuum to water-related ASP sets. This can explain why type B mutants are predicted to be more stable than type A mutants. Also, the contribution of hydrogen bonding to
mw
Gf will vary significantly owing to the changes in hydrogen bond geometry and type of hydrogen bonds. Burial of polar and charged polar atoms in the interior of the mutants may result in good geometry of the already existing hydrogen-bond network of the protein and therefore a higher negative value of
mw
GHB, which will lower the predicted large value of
mw
Gf for mutants. Similarly, the calculated higher value of
mw
Gf for T157R, T157H and T157N can be compensated. The strength of proteinprotein and proteinwater hydrogen bonds will be considerably different. The low strength of proteinwater hydrogen bonds compared with proteinprotein hydrogen bonds can explain the calculated low value of
mw
Gf for T157G compared with T157D and T157S.
The WE and Sch3 ASP sets have been derived using the transfer free energy that was corrected to exclude the effect of differences in molar volume between solute and solvent. The volume effect is not considered when deriving other ASP sets. The volume effect is particularly large upon transfer of the solute from vacuum to water. This is one of the reasons for the poor performance of ASP sets Sch4 and Oons. The values of the calculated mw
Gf using Sch4 and Oons defy the logic that has been used to describe the difference in the experimental and calculated values using WE and Sch3. The ASP set Sch4 assigns higher ASP to charged N/O than uncharged N/O and predicts T157R and T157D to be the least stable mutants. Similarly, the ASP set Oons assigns higher ASP to carbonyl carbon and predicts T157D to be more stable than T157S.
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Conclusions |
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The vacuum to water-based atomic solvation parameter sets WE and Sch3 predict a higher magnitude of the hydrophobic contribution to mw
Gf, leading to a higher value of
mw
Gf. This is due to the different definition used to describe hydrophobicity. However, a higher
mw
Gs,f is partly compensated by negative
mw
GHB. The contribution of hydrogen bonds to the stability of proteins is much higher when defined in terms of vacuum to water transfer. Also, the contribution of hydrogen bonds to
mw
Gf will vary significantly owing to the changes in hydrogen bond geometry and type of hydrogen bonds. Hence the use of vacuum to water-based atomic solvation parameter sets should be avoided for the prediction of the stability of mutants until a more accurate method to determine the strength of hydrogen bond is in place. The ASP sets WE and Sch3 sets are better than Sch4 and Oons because they are derived from the transfer free energies that are corrected to exclude the volume effect. The ASP set Sch4 assigns higher ASP to charged N/O relative to uncharged N/O whereas Oons assigns a higher ASP to carbonyl carbon.
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Acknowledgements |
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References |
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Received February 26, 2002; revised December 5, 2002; accepted April 15, 2003.