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Theoretical binding energies of inhibitors to enzymes
Biochimica et Biophysica Acta 870 (1986) 177-179
177
Elsevier BBA 30131
BBA
Report
Theoretical binding energies of inhibitors to enzymes I. Saira Mian and W. Graham Richards * Physical Chemistry Laboratory, South Parks Road, Oxford, OXI 3QZ (U.K.) (Received October 16th, 1985) Key words: Lysozyme; Molecular orbital calculation; Binding enthalpy; Enzyme inhibition
Modified quantum mechanical calculations predict the binding enthalpies of saccharide inhibitors of lysozyme to within a few kilocalories of experimental measurements.
If ever drugs or other useful inhibitors of enzymes are to be designed theoretically then it is important to be able to calculate the binding enthalpy between the inhibitor and the protein. In principle it ought to be possible to start with the refined X-ray crystal structure of an enzyme and to compute the binding energy of a small molecule to the macromolecule using the methods of quantum mechanics, avoiding the host of adjustable parameters employed in empirical potential functions. In an approximation to this procedure we have earlier calculated the binding energy of the drug methotrexate to dihydrofolate reductase and have obtained an enthalpy of binding within 2 kcal. tool -1 of the experimental value [1]. In that case, however, we were forced to incorporate a number of approximations which are hard to justify, so that the suspicion remains that the excellent agreement is fortuitous. Here we take a better test case, the much studied [2-5] enzyme lysozyme with saccharide inhibitors, N-acetylglucosamine (GlcNAc) and its polymeric forms. The calculated binding energies again show an accuracy of a few kilocalories per mole, lending credence to this technique as a vehicle for the design of novel inhibitors. The coordinates of the hen egg-white lysozyme and the enzyme-inhibitor complexes with N-
acetylglucosamine (monomer and trimer; dimer coordinates not available) at 2 A resolution were used (Artymuik and Phillips, unpublished work/ personal communication). The hydrogen atoms were added to the substrate following standard valence procedures and the enzyme cleft was considered to involve the residues Leu-56, Gln-57, I1e-58, Asn-59, Trp-62, Trp-63, Leu-75, Ile-98, Asp-101, Gly-102, Asn-103, Ala-107, Trp-108, Arg-ll2 and Arg-125 for the trimer and Glu-35, Ash-44, Asn-46, Asp-52, Leu-56, Gln-57, Ile-58, Asn-59, Trp-62,Ile-98, Ala-107, Trp-108 and Vail09 for the monomer. Each atom of this portion of the enzyme is incorporated into an ab initio molecular orbital calculation by treating it as a fixed partial charge at the crystal position, the value of the partial positive or negative charge coming from a library of previously computed values for tripeptides [6]. The inhibitors are treated in a full ab initio fashion as nuclei plus the appropriate number of electrons, although due to their size each saccharide molecule is split into fragments whose energies are summed. The binding enthalpy is the difference between the energy of the isolated inhibitor and its energy in the electrostatic enzyme pocket, or Binding energy = ~ [ E T (i, HEWL) - E T ( i ) ] i=1
* To whom correspondence should be addressed. 0167-4838/86/$03.50 © 1986 Elsevier Science Publishers B.V. (Biomedical Division)
- [ E T (H-HEWL) - E T (H) ]
178
Fig. 1. Illustration of the amino acids involvedin the binding site of lysozymetogether with the substrate (GicNAc) in bold.
with n being the number of fragments, ET(i ) the total energy of fragment i and ET(i-HEWL) its energy in the site. The second term arises because in making the fragments satisfy fully their valences, extra hydrogens have to be added, giving as a small correction term the difference in the energy of these extra hydrogens when isolated or in the site. The calculations were performed with a modified version of the Gaussian '70 program' [7,8] implemented on an ICL 2988 computer. The fragments were located in the enzyme binding site
CHzOH
CHzOH
.~ .............
"'..-
.A nu
J=0
,\:,,
, ...... ""/..
'
"..
~
~'-I .... '
"OH
i'
/
I
.
0
I'N'I .... ' "J
CHzOH
o~ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
,
H
using molecular graphics techniques employing an ICL PERQ computer and an Evans and Sutherland PS 300 system. Fig. 1 gives some idea of the complexity of the system included in the quantum mechanical calculations. The results are not particularly sensitive to how the fragments are created. Thus, if the trimer (tri-GlcNAc) is bound to the subsites of the enzyme conventionally labelled A, B and C, then different modes of creating fragments (see Fig. 2) yield theoretical binding energies of - 1 3 . 2 kcalmo1-1 (case a), - 1 3 . 5 kcal. mo1-1 (case b) and - 1 2 . 4 kcal. mol~ 1 (case c) as compared with an experimental [5] enthalpy of binding of - 14.3 + 0.6 kcal. mo1-1. Inclusion of only those residues involved in hydrogen bonding to trimer (Asn-59, Trp-62, Trp-63, Asp-101, Ala-107 and Arg-125) yields a binding energy of - 10.3 kcal. mol- 1. The a- and fl-anomeric forms of GlcNAc bind in different but related ways [5]; in the fl form, GIcNAc binds with its acetamido side-chain making essentially the same hydrogen bonds with the enzyme as those observed for a-GlcNAc but oriented so as to make two additional hydrogen bonds. The flanomer is predicted to bind by - 2 . 8 kcal. mol-1, whilst our calculations do not predict a stable bound a-anomeric form indicated by a positive enthalpy of binding of 0.7 kcal. mo1-1. The experimental values [5], for which the mode of binding is unspecified, is - 6.1 + 0.8 kcal. mol- 1. Estimates of the binding energies of the monomer or dimer into specific sub-binding sites of the enzyme may be made using the calculated interac-
"xi
I
....
I.
NH
.
.
.
.
.
.
CH3
.
'\t=
, ..... ,
I
.... I . . . . . . . . C--'-O
I
,
:
0 "':,¢'... i ' /
0.0.
--.-
....
"OH ~ "
. . . . . .,," 7
"~'-I . . . . x4
,
I
I ....
NH I. . . . . . . . C--O
I
CH3
,"
s
"
""/'-.. /-"
/
....
I ....
NH I .... C~O
I
CH3
Fig. 2. Diagram illustrating the three different modes of creating the tri-GlcNAc fragments. Case (a) . . . . . ; case (b) . . . . . . ; case (c) . . . . . . .
179
tion between trimer fragments in sub-binding sites A, B and C. Thes e values may be compared with experimental measurements: the dimer in sites B and C is estimated to bind by -11.5 kcal. mol-1; in sites A and B by - 4 . 1 kcal. mo1-1. The experimental value [5], for which the location of binding is unsure, is - 1 1 . 4 + 0.4 kcal. mo1-1. In the case of the monomer we predict binding energies for sites A, B and C to be - 3 . 4 kcal.mo1-1, - 2 . 1 kcal. mol- 1 and - 12.3 kcal- mol- 1, respectively, in agreement with experimental evidence that the monomer is most firmly attached to site C. In all cases our predicted binding energies are better than _+7 kcal. mol- 1. The calculations incorporate the electrostatic contribution to binding, the polarization of the substrate by the enzyme and hydrogen bonding in so far as this is electrostatic in origin. Solvent effects are not included, but these are more likely to contribute to entropic rather than enthalpic aspects of binding. The accuracy of the predictions is sufficient to encourage the use of this method in a predictive manner, especially for estimating the relative binding energies of a series of similar compounds such as are frequently synthesized in the pharmaceutical industry.
This work was conducted pursuant to a contract from the National Foundation for Cancer Research. We should also like to thank Dr. P. Artymuik and Prof. Sir David Phillips, Laboratory of Molecular Biophysics, Oxford University, for the coordinates of the enzyme and of the bound complexes. References 1 Richards, W.G. and Cuthbertson, A.F. (1984) J. Chem. Soc. Chem. Commun. 167-168 2 A discussion on the Structure and Function of Lysozyme, organised by Perutz, M. F. (1967) Proc. R. Soc. B 167, 349-448 3 Kelly, K.A., Sielecki, A.R., Sykes, B.D. and James, M.N.G. (1979) Nature 282, 875-877 4 Hornbeck, P.V. and Wilson, A.C. (1984) Biochemistry 23, 998-1002 5 Imoto, T., Johnson, L.N., North, A.C.T., Phillips, D.C. and Rupley, J.A. (1972) in The Enzymes, Vol. VIII (Boyer, P.D., ed.), pp. 666-868, Academic Press, New York 6 Blaney, J.M., Weiner, P.K., Dearing, A., Kollman, P.A., Jorgensen, E.C., Oatley, S.J., Burridge, J.M. and Blake, C.C.F. (1982) J. Am. Chem. Soc. 104, 6424-6434 7 Hehre, W.J., Eathan, W.A., Ditchfield, R., Newton, M.D. and Pople, J.A. (1973) QCPE Bull. 11, 236 8 Lambros, S.A. and Richards, W.G. (1984) J. Molec. Struc. (Theochem.) 109, 61-71
177
Elsevier BBA 30131
BBA
Report
Theoretical binding energies of inhibitors to enzymes I. Saira Mian and W. Graham Richards * Physical Chemistry Laboratory, South Parks Road, Oxford, OXI 3QZ (U.K.) (Received October 16th, 1985) Key words: Lysozyme; Molecular orbital calculation; Binding enthalpy; Enzyme inhibition
Modified quantum mechanical calculations predict the binding enthalpies of saccharide inhibitors of lysozyme to within a few kilocalories of experimental measurements.
If ever drugs or other useful inhibitors of enzymes are to be designed theoretically then it is important to be able to calculate the binding enthalpy between the inhibitor and the protein. In principle it ought to be possible to start with the refined X-ray crystal structure of an enzyme and to compute the binding energy of a small molecule to the macromolecule using the methods of quantum mechanics, avoiding the host of adjustable parameters employed in empirical potential functions. In an approximation to this procedure we have earlier calculated the binding energy of the drug methotrexate to dihydrofolate reductase and have obtained an enthalpy of binding within 2 kcal. tool -1 of the experimental value [1]. In that case, however, we were forced to incorporate a number of approximations which are hard to justify, so that the suspicion remains that the excellent agreement is fortuitous. Here we take a better test case, the much studied [2-5] enzyme lysozyme with saccharide inhibitors, N-acetylglucosamine (GlcNAc) and its polymeric forms. The calculated binding energies again show an accuracy of a few kilocalories per mole, lending credence to this technique as a vehicle for the design of novel inhibitors. The coordinates of the hen egg-white lysozyme and the enzyme-inhibitor complexes with N-
acetylglucosamine (monomer and trimer; dimer coordinates not available) at 2 A resolution were used (Artymuik and Phillips, unpublished work/ personal communication). The hydrogen atoms were added to the substrate following standard valence procedures and the enzyme cleft was considered to involve the residues Leu-56, Gln-57, I1e-58, Asn-59, Trp-62, Trp-63, Leu-75, Ile-98, Asp-101, Gly-102, Asn-103, Ala-107, Trp-108, Arg-ll2 and Arg-125 for the trimer and Glu-35, Ash-44, Asn-46, Asp-52, Leu-56, Gln-57, Ile-58, Asn-59, Trp-62,Ile-98, Ala-107, Trp-108 and Vail09 for the monomer. Each atom of this portion of the enzyme is incorporated into an ab initio molecular orbital calculation by treating it as a fixed partial charge at the crystal position, the value of the partial positive or negative charge coming from a library of previously computed values for tripeptides [6]. The inhibitors are treated in a full ab initio fashion as nuclei plus the appropriate number of electrons, although due to their size each saccharide molecule is split into fragments whose energies are summed. The binding enthalpy is the difference between the energy of the isolated inhibitor and its energy in the electrostatic enzyme pocket, or Binding energy = ~ [ E T (i, HEWL) - E T ( i ) ] i=1
* To whom correspondence should be addressed. 0167-4838/86/$03.50 © 1986 Elsevier Science Publishers B.V. (Biomedical Division)
- [ E T (H-HEWL) - E T (H) ]
178
Fig. 1. Illustration of the amino acids involvedin the binding site of lysozymetogether with the substrate (GicNAc) in bold.
with n being the number of fragments, ET(i ) the total energy of fragment i and ET(i-HEWL) its energy in the site. The second term arises because in making the fragments satisfy fully their valences, extra hydrogens have to be added, giving as a small correction term the difference in the energy of these extra hydrogens when isolated or in the site. The calculations were performed with a modified version of the Gaussian '70 program' [7,8] implemented on an ICL 2988 computer. The fragments were located in the enzyme binding site
CHzOH
CHzOH
.~ .............
"'..-
.A nu
J=0
,\:,,
, ...... ""/..
'
"..
~
~'-I .... '
"OH
i'
/
I
.
0
I'N'I .... ' "J
CHzOH
o~ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
,
H
using molecular graphics techniques employing an ICL PERQ computer and an Evans and Sutherland PS 300 system. Fig. 1 gives some idea of the complexity of the system included in the quantum mechanical calculations. The results are not particularly sensitive to how the fragments are created. Thus, if the trimer (tri-GlcNAc) is bound to the subsites of the enzyme conventionally labelled A, B and C, then different modes of creating fragments (see Fig. 2) yield theoretical binding energies of - 1 3 . 2 kcalmo1-1 (case a), - 1 3 . 5 kcal. mo1-1 (case b) and - 1 2 . 4 kcal. mol~ 1 (case c) as compared with an experimental [5] enthalpy of binding of - 14.3 + 0.6 kcal. mo1-1. Inclusion of only those residues involved in hydrogen bonding to trimer (Asn-59, Trp-62, Trp-63, Asp-101, Ala-107 and Arg-125) yields a binding energy of - 10.3 kcal. mol- 1. The a- and fl-anomeric forms of GlcNAc bind in different but related ways [5]; in the fl form, GIcNAc binds with its acetamido side-chain making essentially the same hydrogen bonds with the enzyme as those observed for a-GlcNAc but oriented so as to make two additional hydrogen bonds. The flanomer is predicted to bind by - 2 . 8 kcal. mol-1, whilst our calculations do not predict a stable bound a-anomeric form indicated by a positive enthalpy of binding of 0.7 kcal. mo1-1. The experimental values [5], for which the mode of binding is unspecified, is - 6.1 + 0.8 kcal. mol- 1. Estimates of the binding energies of the monomer or dimer into specific sub-binding sites of the enzyme may be made using the calculated interac-
"xi
I
....
I.
NH
.
.
.
.
.
.
CH3
.
'\t=
, ..... ,
I
.... I . . . . . . . . C--'-O
I
,
:
0 "':,¢'... i ' /
0.0.
--.-
....
"OH ~ "
. . . . . .,," 7
"~'-I . . . . x4
,
I
I ....
NH I. . . . . . . . C--O
I
CH3
,"
s
"
""/'-.. /-"
/
....
I ....
NH I .... C~O
I
CH3
Fig. 2. Diagram illustrating the three different modes of creating the tri-GlcNAc fragments. Case (a) . . . . . ; case (b) . . . . . . ; case (c) . . . . . . .
179
tion between trimer fragments in sub-binding sites A, B and C. Thes e values may be compared with experimental measurements: the dimer in sites B and C is estimated to bind by -11.5 kcal. mol-1; in sites A and B by - 4 . 1 kcal. mo1-1. The experimental value [5], for which the location of binding is unsure, is - 1 1 . 4 + 0.4 kcal. mo1-1. In the case of the monomer we predict binding energies for sites A, B and C to be - 3 . 4 kcal.mo1-1, - 2 . 1 kcal. mol- 1 and - 12.3 kcal- mol- 1, respectively, in agreement with experimental evidence that the monomer is most firmly attached to site C. In all cases our predicted binding energies are better than _+7 kcal. mol- 1. The calculations incorporate the electrostatic contribution to binding, the polarization of the substrate by the enzyme and hydrogen bonding in so far as this is electrostatic in origin. Solvent effects are not included, but these are more likely to contribute to entropic rather than enthalpic aspects of binding. The accuracy of the predictions is sufficient to encourage the use of this method in a predictive manner, especially for estimating the relative binding energies of a series of similar compounds such as are frequently synthesized in the pharmaceutical industry.
This work was conducted pursuant to a contract from the National Foundation for Cancer Research. We should also like to thank Dr. P. Artymuik and Prof. Sir David Phillips, Laboratory of Molecular Biophysics, Oxford University, for the coordinates of the enzyme and of the bound complexes. References 1 Richards, W.G. and Cuthbertson, A.F. (1984) J. Chem. Soc. Chem. Commun. 167-168 2 A discussion on the Structure and Function of Lysozyme, organised by Perutz, M. F. (1967) Proc. R. Soc. B 167, 349-448 3 Kelly, K.A., Sielecki, A.R., Sykes, B.D. and James, M.N.G. (1979) Nature 282, 875-877 4 Hornbeck, P.V. and Wilson, A.C. (1984) Biochemistry 23, 998-1002 5 Imoto, T., Johnson, L.N., North, A.C.T., Phillips, D.C. and Rupley, J.A. (1972) in The Enzymes, Vol. VIII (Boyer, P.D., ed.), pp. 666-868, Academic Press, New York 6 Blaney, J.M., Weiner, P.K., Dearing, A., Kollman, P.A., Jorgensen, E.C., Oatley, S.J., Burridge, J.M. and Blake, C.C.F. (1982) J. Am. Chem. Soc. 104, 6424-6434 7 Hehre, W.J., Eathan, W.A., Ditchfield, R., Newton, M.D. and Pople, J.A. (1973) QCPE Bull. 11, 236 8 Lambros, S.A. and Richards, W.G. (1984) J. Molec. Struc. (Theochem.) 109, 61-71