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Theoretical calculations on enzyme—substrate interactions: The binding of n-alkylboronic acids to α-chymotrypsin A
Journal of Molecular Structure (Theochem),
109 (1984) 61-71 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THEORETICAL CALCULATIONS ON ENZYME-SUBSTRATE INTERACTIONS: THE BINDING OF n-ALKYLBORONIC ACIDS TO a-CHYMOTRYPSIN A
SANDRA A. LAMBROS and W. GRAHAM RICHARDS
Physical Chemistry Labomtory,
Oxford, Oxon (Ct. Britain)
ANTHONY F. MARCHINGTON
I.C.I. Plant Protection Division, Jealotts Hill Research Station, Bracknell, Berkshire (G t. Britain) (Received 1 December 1983)
ABSTRACT Modified ab initio SCF calculations are presented for the binding of n-alkylboronic acids to wchymotrypsin A. The enzyme active site is represented by 214 binding site atoms each carrying an effective point-charge incorporated into the one-electron Hamiltonian. The procedure requires only five per cent more CPU time than a typical calculation on the isolated molecule. INTRODUCTION
The rapid increase over the last few years in the knowledge of protein structures has prompted much theoretical interest in the binding of small substrates to biological binding sites. Enzyme-substrate complexes are too large to be studied using quantum-mechanical techniques directly and consequently much of the current work in this area is centred upon the use of molecular mechanics. The method presented here extends the work of Hayes and Kollman [l] in using modified ab initio SCF calculations to study the docking problem. Theoretical calculations on biological systems are usually concerned only with isolated molecules, whereas clearly it is the interactions of these molecules with three-dimensional macromolecules which is of importance. Solvation and entropy effects are normally ignored due to difficulties inherent in their calculation. A method of representing the environment, whether it be crystal [ 2, 31 solvent [4] or protein is by the use of partial point charges. These charges can then be incorporated into the one-electron Hamiltonian and in this way the electrostatic interaction and the polarisation of the substrate by its environment can be calculated. The reverse polarisation of the environment by the substrate, charge transfer and the exchange energy are neglected, although the latter can be explicitly con0166-1280/84/$03.00
o 1984 Elsevier Science Publishers B.V.
62
sidered by not allowing the substrate to penetrate within the van der Waals radii of surrounding atoms. EXPERIMENTAL
The enzyme--substrate system For a valid assessment of this technique for the calculation of binding energies, the chosen model system needs to conform to five main criteria. These are: (i) A knowledge of crystallographic structure, preferably for both the free enzyme and for enzyme-substrate complexes. (ii) The structural transitions which occur in the process of complexation should be small. (iii) The mechanism for binding should be well understood with measured thermodynamic quantities for the binding of similar substrates. (iv) There should be no allosteric effects. (v) In addition there are those limits imposed by the use of the ab initio method. The study, therefore, has been limited to those substrates which may be adequately described by 70 minimal basis functions and since the programme does not explicitly include d orbitals it was preferred that the enzyme system should contain no transition metal. The binding of the inhibitors, n-alkylboronic acids (B(OH),(CH,),H where n = O-8), to cu-chymotrypsin conforms to these criteria. The binding energies have been determined experimentally by Antonov et al. [5] using an aqueous solution of 0.1 M sodium chloride with 10% methanol present as solvent and p-nitrophenyltrimethylacetate, N-acetyl-ctyrosine ethyl ester and N-( 3 carboxypropionyl)-L-phenylalanine-p-nitroanilide as substrates. It was demonstrated that two competitive reactions occur: (i) Enzyme catalysis E+S
k, + E + P1 + P2 k-,
and (ii) Enzyme inhibition E + I k? EI i
The inhibition equilibrium constant ki is highly dependent upon the n-alkyl chain length as shown in Fig. 1. cu-Chymotrypsin is an endopeptidase with well studied kinetics from which a mechanism of action has been proposed [6-111. The general reaction scheme initially involves the formation of an enzyme-substrate complex. The charge-relay system of the enzyme is then activated enhancing the nucleophilicity of the serine-195 oxygen leading to the formation of a
63 -AG 15.c
I0.C
.
5.c 112345678 ”
Fig. 1. Graph of experimental binding energies of n-alkylboronic acids to cu-chymotrypsin as a function of chain length (ref. 5).
tetrahedral adduct. This tetrahedral intermediate then decomposes to the acyl enzyme which then undergoes deacylation. The boronic acids have been shown to be transition-state analogue inhibitors [12-141 and are consequently of importance in understanding the formation of the acyl intermediate. The energies calculated here are those for the formation of enzyme-substrate non-covalently bonded complex before and after activation of the chargerelay system. The formation of this complex can be seen to be a consequence of electrostatic, hydrophobic and steric interactions with also small conformational changes in the enzyme and substrate. Of those, the electrostatic component is implicitly considered in the calculation whilst the hydrophobic effect which is largely due to entropic changes in solvent is primarily considered through a thermodynamic correction term devised to correlate with the changes in free energy of solvation upon binding. Steric forces between enzyme and substrate are considered initially through the use of computer graphics by ensuring that there is no overlap of van der Waals radii. Modified ab initio calculations are then only performed on these configurations. In this case, changes in bond lengths and bond angles of the active site and substrate are ignored although conformational changes in the substrate are allowed. For this system such an approximation is justifiable since, from crystallographic studies [7, 15, 161 it is known that there are no large conformational changes upon complexation except for the charge-relay system. Also, previous molecular mechanical studies for the binding of ~-amino acids have found good agreement with experiment without geometry relaxation [ 171. Choice of poin t-charge model The crystallographic co-ordinates of cY-chymotrypsin A were obtained from the Brookhaven database from which the co-ordinates of the amino
64
acid active site residues were extracted. The catalytic pocket was taken to consist of histidine 57, aspartate 102, serine 189-serine 195, serine 214, cystine 220 and valine 227, i.e. 17 residues in total. The water molecules present in the crystallographic protein active site are not considered. As in previous work by Hayes and Kollman [ 181 charges can be assigned to each residue as determined from ab initio STO-3G calculations on the specimen structures NH?-CO-CHR-NH-CHO using the crystallographic coordinates of the amino acid main atoms with the hydrogens placed on the heavy atoms using standard bond lengths and angles. The Mulliken net atomic charges can be similarly adjusted to give neutrality for the unit -NH-CHR-CO-. Also, to assess the sensitivity of the results to the actual value used for the point charges, parallel calculations were performed using the set of charges as defined by Kolhnan which are invariant to conformational changes. The charge distribution is clearly different for the inactive and activated forms of the charge-relay system. Nucleophilic attack on the substrate results in the hydroxyl proton of serine 195 being transferred to histidine 57 which consequently becomes positively charged. The aspartate 102 residue is believed to maintain its negative charge [19, 201. This study examines the initial complex before the onset of covalent binding, therefore both serine 195 and histidine 57 are taken to be the neutral species whilst aspartate 102 (and also 194) is regarded as monoanionic. Determination of the position and conformation of the substrates in the binding site The docking of substrates [ 211 into the enzyme pocket (ca. 12 WX 6.5 A X 4.0 A) is best achieved using real-time computer graphics. In this case a PDPl1/60 with a DEC VT11 graphics terminal was used. Initially a least-squares fit is performed between the known position of a bound substrate, N-formyl-L-tryptophan and the alkylboronic acid. Standard geometries were used for the latter [22]. Where the boronic acid extends beyond the position occupied by the known substrate the method developed by Barry may be used to enable the sampling of the conformational and translational space without incurring unfavourable steric interactions with the protein [23]. The active site of the enzyme is displayed as a surface given by the sum of the van der Waals radii of the enzyme atoms plus that for a carbon atom. The stick model of the substrate can then be manipulated so that at no time does it protrude through this surface of effective van der Waals contact. Alternatively, force field calculations [24] could be used for further conformational adjustments and for optimising the internal energy. Since this was a test study the final conformational adjustments were made using the modified ab initio programme. As an example, Fig. 2 shows an ORTEP diagram of the lowest energy conformation of n-hexylboronic acid when bound to a-chymotrypsin A.
65
Fig. 2. An ORTEP diagram of n-hexylboronic the enzyme-substrate complex.
acid energy minimum conformation
in
Calculations The total energy of the substrate molecules both in free space and when perturbed by the point-charge model of the active site was calculated using a full SCF computation with an STO-3G basis set. The Hamiltonian to be solved is
electronic terms
nuclear terms where qv represents the partial point charges modelling the catalytic site, i and j are electron indicies and or and w nuclei. The binding energy so determined may be divided into its electrostatic and polarisation components. The electrostatic contribution is derived directly from the free space substrate wavefunction using the Hamiltonian for the enzyme complex. The polarisation component is then available by subtraction from the calculated total.
66
AE TOTAL
=AEELJNXROSTATIC
+AEPOLARISATION
Due to limits on computational time n-heplyl- and n-octylboronic acid substrates were studied using a fragmentation method, with n-hexylboronic acid also studied for comparison. The substrates were divided into the molecular fragments B(OH)z(CH2)4H and H(CH2),-4H. The binding energies of these two fragments, from the comparative study, were approximately additive (within 0.08 kcal moT’) for the point charge models used (see Tables 1 and 2). TABLE 1 Binding energies in kcal mol-’ for the formation of the enzyme-substrate cY-chymotrypsin in its natural form Substrate
Binding energy (kcal mol-’ ) a
WOW,
B(CH),CH, B(OH),CH,CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + HtCH,),H
complex with
-2.729 -2.083 -2.358 -2.410 -2.420 -2.590 -2.816 -2.867 -2.809 -2.848
b
-2.59 -1.852 -2.144 -2.215 -2.215 -2.449 -2.764 -2.691 -2.580 -2.661
%dculated involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated with the active site charges derived from the conformationally averaged amino acid residues. TABLE 2 Binding energies in kcal mol-’ for the formation of the enzyme-substrate the activated charge-relay system of cu-chymotrypsin Substrate
Binding energy (kcal mol-’ ) a
NOW,
B(CH),CH, B( OH),CH,CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,)$H, B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + HtCH,),H B(CH),(CH,),H + H(CH,),H
complex using
-2.143 -1.447 -1.515 -1.605 -1.648 -1.841 -2.081 -2.103 -1.754 -1.77
b
-2.065 -1.147 -1.205 -1.314 -1.353 -1.642 -1.923 -1.843 -1.74 -1.821
Walculated involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated with the active site charges derived from the conformationally averaged amino acid residues.
67 RESULTS
The calculated binding energies in kilocalories for the substrate--enzyme complex with the charge-relay system in its inactive form and the partial point-charges derived from Mulliken population analysis of the amino acid residues using crystallographic co-ordinates and the conformationally averaged charges are shown in Table 1. Table 2 indicates the binding energies after the charge-relay system has been activated. The results show similar trends for the pointcharge models used although they differ in their absolute values, with the most favourable initial binding occurring before the chargerelay system has been activated. This would agree with the mechanism of action proposed for a-chymotrypsin, namely that the serine 195 OH rotates and activates the substrate only after the initial recognition of the enzymesubstrate complex has occurred The binding energies for all the n-alkylboronic acids are of similar magnitude as is expected since the secondary binding is primarily due to a hydrophobic effect (the primary binding site is a constant throughout the series). Binding of the n-heptyl- and n-octylboronic acids, however, requires the alkyl chain to be bent to prevent unfavourable van der Waals interactions. This conformational energy change between solution and enzyme probably causes the levelling out of the experimental curve. Analysis Attention was focussed upon the ethyl to hexylboronic acids since the experimental binding energies are known for these compounds and the alkyl chain builds up one from another in its extended form (although the OBC& dihedral angle is 120.0”). Thus any conformational changes in the alkyl chain on moving from the solvent to the enzyme environment should be the same for these compounds. Consequently the inherent entropic and internal conformational energy changes are assumed constant. Table 3 shows the breakdown of the calculated binding energies into their electrostatic and polarisation energy components. The polarisation makes a TABLE 3 Breakdown of the binding energies (kcal mol-’ ) of the alkylboronic acids into their electrostatic and polarisation components Substrate
B( OH),CH,CH, B(OH),(CH,),CH, B(CH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH,
Electrostatic energy (kcal mol-’ ) -1.82 -1.82 -1.83 -2.01 -2.05
Polarisation energy (kcal mole1) -0.54 -0.59 -0.59 -0.58 -0.77
Total energy (kcal mol-‘) -2.36 -2.41 -2.42 -2.59 -2.82
68
relatively large significant contribution which increases at the hexylboronic acid whose alkyl chain extends the length of the pocket. The calculated energies represent the process Substrate (0 K)
AUcalculated -
Enzyme-Substrate (0 K)
Complex
whilst the experimental values are for AG
Substrate (solvated) 2 (298 K)
Enzyme-Inhibitor Tetrahedral Adduct (298 K)
From consideration of the thermodynamic cycle and assuming a direct correspondence between the complex and adduct [ 251 298 Aucalculated
= AGexp
+
+ AGsolution
S
bpt
C, Wq)
dT
+
;
C,(gas)
dT
bpt -AK,,
+
TbptfSgas
-
sliquid)
+
T298ASenz--sub
The most important term for this homologous series of molecules is the solvation term AGsoi. When the alkyl chain exceeds two carbon atoms in length the chain protrudes into the hydrophobic pocket leading to a hydrophobic effect which is of particular importance in aqueous solution and caused mainly by entropic changes in the surrounding water sheath. The difference in AG,,,for the n-alkylboronic acids may be estimated by assigning a value of 0.855 kcal mol-’ to each methylene group which is an average value estimated from studying the alkanes, isoalkanes, alcohols and carboxylic acids [26-281. (This assumes that the contribution of the hydrophilic and hydrophobic portions of the molecule to the solvent interaction energy are independent.) The enthalpy of hydration of butylboronic acid is 2.67 -1:0.06 kcal mol-’ [29]. Although this neglects the entropy of solvation, since no other experimentally determined thermodynamic quantity could be found it was used as the basis upon which the changes in the free enerm of solvation per CH2 group could be related. -A Gsoiution= -2.67
+ (4 - n)O.855
The binding energies in kcal mol-’ with the correction factor for the solvation energy term are shown in Table 4. Figure 3 shows a comparison of the experimental and calculated values. Further work - effects of substitution Calculations demonstrate that substitution of a methyl group into the a-position has little effect upon the binding whilst a methyl group in the S-position affects it adversely [ 211. The substrates used for this were based upon a main chain composed of three carbon atoms in the same conformation as that for n-propylboronic acid (see Fig. 4).
69
gn12 5.0
10.0
15.0
- AG Experimental
Fig. 3. Graph of calculated binding energies using the activated charge-relay system, against the experimentally determined binding energies.
Fig. 4. Diagram representing the dihedral angles for the a and P substituents.
The results are shown in Table 5. The p-methyl propylboronic acid with the additional methyl group at a dihedral angle of 300.0” is highly sensitive to the positioning of the charge-relay system. This is a consequence of the hydrogen of the P-methyl substituent pointing directly at the catalytic triad thus interfering with the rotation of the imidazole ring and preventing the attack of the OH of serine 195.
70 TABLE 4 The binding energies of the n-alkylboronic acids (kcal mol-I) to a-chymotrypsin with the thermodynamic solvation energy correction term incorporated; also shown are the experimental values Substrate
B( OH),CH,CH, B(OH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH,
Inactivated charge-relay system
Experimental
Activated charge-relay system
a
b
a
b
-3.20 -4.23 -5.09 -6.12 -7.20
-3.10 -4.03 -4.89 -5.97 -7.14
-2.48 -3.42 -4.32 -5.37 -6.30
-2.17 -3.13 -4.02 -5.17 -6.30
-5.79 -6.97 -9.28 -11.70 -14.87
aCalculated binding energies involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated binding energies with the active site charges derived from the conformationally averaged amino acid residues. TABLE 5 Calculated binding energies (kcal mol-I) for a- and p-methyl substituted propylboronic acid to cu-chymotrypsin using the conformationally averaged point-charge model (see Fig. 4) Substrate
B( OH),CH,CH, AA-B(OH),CHCH,CH,CH, AB-B( OH),CCH,HCH,CH, BA-B(OH),CH,CHCH,CH, BB-B(OH)&H,CCH,HCH,
Inactive charge-relay system -2.215 -2.369 -1.979 -1.078 -7.569
Activated charge-relay system -1.314 -1.444 -1.107 -0.838 -0.746
CONCLUSIONS
Many research groups are currently trying to model enzyme-substrate binding with the ultimate aim of designing inhibitors or false substrates of therapeutic value. In general the approach involves the use of a series of complex intermolecular potential functions to account for the electrostatic, polarisation, hydrogen bonding and other contributions. Generally, quantum-mechanical calculations are more attractive since there need be no assumptions about the specific interactions’ and, at the ab initio level, no empirical parameterisation. The only drawback is the immense amount of computer tie required. Hence, by using the device of replacing enzyme atoms and their electrons by effective point-charges an otherwise full ab initio calculation (in this case the Gaussian 70 program [30]) is possible with an increase in the computational time of only about 5% over that for the isolated molecule.
71
With the solvation effects being incorporated empirically the relative binding for a series of similar substrates may be determined. This result makes one optimistic about using the approach to aid in the design of molecules to fit a specific enzyme binding site. ACKNOWLEDGEMENT
S. A. R. thanks ICI Plant Protection Division for their support through a CASE award. This work is also supported by the National Foundation for Cancer Research. REFERENCES 1 D. M. Hayes and P. A. Kollman, J. Am. Chem. Sot., 98 (1976) 7811. 2 J. Aimlof and U. Wahlgren, Theor. Chim. Acta, 28 (1973) 161. 3 C. Ghio, E. Scrocco and J. Tomasi, in Environmental Effects on Molecular Structure and Properties, D. Reidel, Dordrecht, 1976, p. 239. 4 J. 0. Noel1 and K. Morokuma, Chem. Phys. Lett., 36 (1975) 465. 5 V. K. Antonov, T. V. Ivania, I. V. Berezin and K. Martinek, FEBS Lett., 7 (1970) 23. 6 D. M. Blow, M. J. Birktoft and B. S. Hartley, Nature (London), 221 (1969) 337. 7 J. J. Birktoft and D. M. Blow, J. Mol. Biol., 68 (1972) 187. 8 M. Hunkapiller, S. H. Smallcomb, D. R. Whitaker and J. H. Richards, J. Biol. Chem., 248 (1973) 8306. 9 R. M. Stroud, M. Kneger, R. E. Koeppe, A. A. Kossiakoff and J. L. Chambers, in Proteases and Biological Control, Cold Spring Harbor Press, Long Island, NY, 1975, p. 13. 10 R. Henderson, T. A. Steitz, C. S. Wright, G. P. Hess and D. M. Blow, Cold Spring Harbor Symp. Quant. Biol., 36 (1971) 63. 11 A. Tulinsky, L Mavridis and R. F. Mann, J. Biol. Chem., 253 (1978) 1074. 12 K. A. Koehler and G. E. Lienhard, Biochemistry, 10 (1971) 2477. 13 J. D. Rawn and G. E. Lienhard, Biochemistry, 13 (1974) 3124. 14 K. Hanai, J. Biochem., 81 (1977) 1273. 15 T. A. Steitz, R. Henderson and D. M. Blow, J. Mol. Biol., 46 (1969) 337. 16 R. L. Vandlen and A. Tulinsky, Acta Crystallogr. Sect. B., 27 (1971) 437; 29 (1973) 1309. 17 K. E. B. Platzer, F. A. Momany and H. A. Sheraga, Int. J. Pept. Protein Res., (1972) 201. 18 D. M. Hayes and P. A. Kollman, J. Am. Chem. Sot., 98 (1976) 3335. 19 P. A. Markley and I. Ibanez, Biochemistry, 15 (1976) 3339. 20 P. A. Kollman and D. M. Hayes, J. Am Chem. Sot., 103 (1981) 2955. 21 D. M. Blow, in The Enzymes, Vol. 3, Academic Press, New York, 1971, p. 185. 22 L. E. Sutton, in Tables of Interatomic Distances and Configurations in Molecules and Ions, Chemical Society (London) Spec. Publ. No. 11, 1956. Suppl. No. 28, 1959. 23 C. D. Barry, Molecular Modelling System-X Newsl., 20 (1980) 23. 24 P. Weiner and P. A. Kollman, J. Comput. Chem., 2 (1981) 287. 25 J. B. Jones, T. Kunitake, C. Niemann and G. E. Hein, J. Am. Chem. Sot., 87 (1965) 1977. 26 C. Tanford, in The Hydrophobic Effect, Wiley, New York, 1973, p. 207. 27 C. McAuliffe, J. Phys. Chem., 70 (1966) 1267. 28 R. Smith and C. Tanford, Proc. Nat. Acad. Sci. U.S.A., 70 (1973) 289. 29 L. Gmelin, Gmelin Handbuch der Anorganischen Chemie, Vol. 16, Springer Verlag, Berlin, 1979, p. 16. 30 W. J. Hehre, W. A. Latham, R. Ditchfield, R. D. Newton and J. A. Pople, GAUSSIAN 70, Q.C.P.E., No. 236, Indiana University, Bloomington, IN, U.S.A., 1973.
109 (1984) 61-71 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
THEORETICAL CALCULATIONS ON ENZYME-SUBSTRATE INTERACTIONS: THE BINDING OF n-ALKYLBORONIC ACIDS TO a-CHYMOTRYPSIN A
SANDRA A. LAMBROS and W. GRAHAM RICHARDS
Physical Chemistry Labomtory,
Oxford, Oxon (Ct. Britain)
ANTHONY F. MARCHINGTON
I.C.I. Plant Protection Division, Jealotts Hill Research Station, Bracknell, Berkshire (G t. Britain) (Received 1 December 1983)
ABSTRACT Modified ab initio SCF calculations are presented for the binding of n-alkylboronic acids to wchymotrypsin A. The enzyme active site is represented by 214 binding site atoms each carrying an effective point-charge incorporated into the one-electron Hamiltonian. The procedure requires only five per cent more CPU time than a typical calculation on the isolated molecule. INTRODUCTION
The rapid increase over the last few years in the knowledge of protein structures has prompted much theoretical interest in the binding of small substrates to biological binding sites. Enzyme-substrate complexes are too large to be studied using quantum-mechanical techniques directly and consequently much of the current work in this area is centred upon the use of molecular mechanics. The method presented here extends the work of Hayes and Kollman [l] in using modified ab initio SCF calculations to study the docking problem. Theoretical calculations on biological systems are usually concerned only with isolated molecules, whereas clearly it is the interactions of these molecules with three-dimensional macromolecules which is of importance. Solvation and entropy effects are normally ignored due to difficulties inherent in their calculation. A method of representing the environment, whether it be crystal [ 2, 31 solvent [4] or protein is by the use of partial point charges. These charges can then be incorporated into the one-electron Hamiltonian and in this way the electrostatic interaction and the polarisation of the substrate by its environment can be calculated. The reverse polarisation of the environment by the substrate, charge transfer and the exchange energy are neglected, although the latter can be explicitly con0166-1280/84/$03.00
o 1984 Elsevier Science Publishers B.V.
62
sidered by not allowing the substrate to penetrate within the van der Waals radii of surrounding atoms. EXPERIMENTAL
The enzyme--substrate system For a valid assessment of this technique for the calculation of binding energies, the chosen model system needs to conform to five main criteria. These are: (i) A knowledge of crystallographic structure, preferably for both the free enzyme and for enzyme-substrate complexes. (ii) The structural transitions which occur in the process of complexation should be small. (iii) The mechanism for binding should be well understood with measured thermodynamic quantities for the binding of similar substrates. (iv) There should be no allosteric effects. (v) In addition there are those limits imposed by the use of the ab initio method. The study, therefore, has been limited to those substrates which may be adequately described by 70 minimal basis functions and since the programme does not explicitly include d orbitals it was preferred that the enzyme system should contain no transition metal. The binding of the inhibitors, n-alkylboronic acids (B(OH),(CH,),H where n = O-8), to cu-chymotrypsin conforms to these criteria. The binding energies have been determined experimentally by Antonov et al. [5] using an aqueous solution of 0.1 M sodium chloride with 10% methanol present as solvent and p-nitrophenyltrimethylacetate, N-acetyl-ctyrosine ethyl ester and N-( 3 carboxypropionyl)-L-phenylalanine-p-nitroanilide as substrates. It was demonstrated that two competitive reactions occur: (i) Enzyme catalysis E+S
k, + E + P1 + P2 k-,
and (ii) Enzyme inhibition E + I k? EI i
The inhibition equilibrium constant ki is highly dependent upon the n-alkyl chain length as shown in Fig. 1. cu-Chymotrypsin is an endopeptidase with well studied kinetics from which a mechanism of action has been proposed [6-111. The general reaction scheme initially involves the formation of an enzyme-substrate complex. The charge-relay system of the enzyme is then activated enhancing the nucleophilicity of the serine-195 oxygen leading to the formation of a
63 -AG 15.c
I0.C
.
5.c 112345678 ”
Fig. 1. Graph of experimental binding energies of n-alkylboronic acids to cu-chymotrypsin as a function of chain length (ref. 5).
tetrahedral adduct. This tetrahedral intermediate then decomposes to the acyl enzyme which then undergoes deacylation. The boronic acids have been shown to be transition-state analogue inhibitors [12-141 and are consequently of importance in understanding the formation of the acyl intermediate. The energies calculated here are those for the formation of enzyme-substrate non-covalently bonded complex before and after activation of the chargerelay system. The formation of this complex can be seen to be a consequence of electrostatic, hydrophobic and steric interactions with also small conformational changes in the enzyme and substrate. Of those, the electrostatic component is implicitly considered in the calculation whilst the hydrophobic effect which is largely due to entropic changes in solvent is primarily considered through a thermodynamic correction term devised to correlate with the changes in free energy of solvation upon binding. Steric forces between enzyme and substrate are considered initially through the use of computer graphics by ensuring that there is no overlap of van der Waals radii. Modified ab initio calculations are then only performed on these configurations. In this case, changes in bond lengths and bond angles of the active site and substrate are ignored although conformational changes in the substrate are allowed. For this system such an approximation is justifiable since, from crystallographic studies [7, 15, 161 it is known that there are no large conformational changes upon complexation except for the charge-relay system. Also, previous molecular mechanical studies for the binding of ~-amino acids have found good agreement with experiment without geometry relaxation [ 171. Choice of poin t-charge model The crystallographic co-ordinates of cY-chymotrypsin A were obtained from the Brookhaven database from which the co-ordinates of the amino
64
acid active site residues were extracted. The catalytic pocket was taken to consist of histidine 57, aspartate 102, serine 189-serine 195, serine 214, cystine 220 and valine 227, i.e. 17 residues in total. The water molecules present in the crystallographic protein active site are not considered. As in previous work by Hayes and Kollman [ 181 charges can be assigned to each residue as determined from ab initio STO-3G calculations on the specimen structures NH?-CO-CHR-NH-CHO using the crystallographic coordinates of the amino acid main atoms with the hydrogens placed on the heavy atoms using standard bond lengths and angles. The Mulliken net atomic charges can be similarly adjusted to give neutrality for the unit -NH-CHR-CO-. Also, to assess the sensitivity of the results to the actual value used for the point charges, parallel calculations were performed using the set of charges as defined by Kolhnan which are invariant to conformational changes. The charge distribution is clearly different for the inactive and activated forms of the charge-relay system. Nucleophilic attack on the substrate results in the hydroxyl proton of serine 195 being transferred to histidine 57 which consequently becomes positively charged. The aspartate 102 residue is believed to maintain its negative charge [19, 201. This study examines the initial complex before the onset of covalent binding, therefore both serine 195 and histidine 57 are taken to be the neutral species whilst aspartate 102 (and also 194) is regarded as monoanionic. Determination of the position and conformation of the substrates in the binding site The docking of substrates [ 211 into the enzyme pocket (ca. 12 WX 6.5 A X 4.0 A) is best achieved using real-time computer graphics. In this case a PDPl1/60 with a DEC VT11 graphics terminal was used. Initially a least-squares fit is performed between the known position of a bound substrate, N-formyl-L-tryptophan and the alkylboronic acid. Standard geometries were used for the latter [22]. Where the boronic acid extends beyond the position occupied by the known substrate the method developed by Barry may be used to enable the sampling of the conformational and translational space without incurring unfavourable steric interactions with the protein [23]. The active site of the enzyme is displayed as a surface given by the sum of the van der Waals radii of the enzyme atoms plus that for a carbon atom. The stick model of the substrate can then be manipulated so that at no time does it protrude through this surface of effective van der Waals contact. Alternatively, force field calculations [24] could be used for further conformational adjustments and for optimising the internal energy. Since this was a test study the final conformational adjustments were made using the modified ab initio programme. As an example, Fig. 2 shows an ORTEP diagram of the lowest energy conformation of n-hexylboronic acid when bound to a-chymotrypsin A.
65
Fig. 2. An ORTEP diagram of n-hexylboronic the enzyme-substrate complex.
acid energy minimum conformation
in
Calculations The total energy of the substrate molecules both in free space and when perturbed by the point-charge model of the active site was calculated using a full SCF computation with an STO-3G basis set. The Hamiltonian to be solved is
electronic terms
nuclear terms where qv represents the partial point charges modelling the catalytic site, i and j are electron indicies and or and w nuclei. The binding energy so determined may be divided into its electrostatic and polarisation components. The electrostatic contribution is derived directly from the free space substrate wavefunction using the Hamiltonian for the enzyme complex. The polarisation component is then available by subtraction from the calculated total.
66
AE TOTAL
=AEELJNXROSTATIC
+AEPOLARISATION
Due to limits on computational time n-heplyl- and n-octylboronic acid substrates were studied using a fragmentation method, with n-hexylboronic acid also studied for comparison. The substrates were divided into the molecular fragments B(OH)z(CH2)4H and H(CH2),-4H. The binding energies of these two fragments, from the comparative study, were approximately additive (within 0.08 kcal moT’) for the point charge models used (see Tables 1 and 2). TABLE 1 Binding energies in kcal mol-’ for the formation of the enzyme-substrate cY-chymotrypsin in its natural form Substrate
Binding energy (kcal mol-’ ) a
WOW,
B(CH),CH, B(OH),CH,CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + HtCH,),H
complex with
-2.729 -2.083 -2.358 -2.410 -2.420 -2.590 -2.816 -2.867 -2.809 -2.848
b
-2.59 -1.852 -2.144 -2.215 -2.215 -2.449 -2.764 -2.691 -2.580 -2.661
%dculated involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated with the active site charges derived from the conformationally averaged amino acid residues. TABLE 2 Binding energies in kcal mol-’ for the formation of the enzyme-substrate the activated charge-relay system of cu-chymotrypsin Substrate
Binding energy (kcal mol-’ ) a
NOW,
B(CH),CH, B( OH),CH,CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,),CH, B(CH),(CH,)$H, B(CH),(CH,),H + H(CH,),H B(CH),(CH,),H + HtCH,),H B(CH),(CH,),H + H(CH,),H
complex using
-2.143 -1.447 -1.515 -1.605 -1.648 -1.841 -2.081 -2.103 -1.754 -1.77
b
-2.065 -1.147 -1.205 -1.314 -1.353 -1.642 -1.923 -1.843 -1.74 -1.821
Walculated involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated with the active site charges derived from the conformationally averaged amino acid residues.
67 RESULTS
The calculated binding energies in kilocalories for the substrate--enzyme complex with the charge-relay system in its inactive form and the partial point-charges derived from Mulliken population analysis of the amino acid residues using crystallographic co-ordinates and the conformationally averaged charges are shown in Table 1. Table 2 indicates the binding energies after the charge-relay system has been activated. The results show similar trends for the pointcharge models used although they differ in their absolute values, with the most favourable initial binding occurring before the chargerelay system has been activated. This would agree with the mechanism of action proposed for a-chymotrypsin, namely that the serine 195 OH rotates and activates the substrate only after the initial recognition of the enzymesubstrate complex has occurred The binding energies for all the n-alkylboronic acids are of similar magnitude as is expected since the secondary binding is primarily due to a hydrophobic effect (the primary binding site is a constant throughout the series). Binding of the n-heptyl- and n-octylboronic acids, however, requires the alkyl chain to be bent to prevent unfavourable van der Waals interactions. This conformational energy change between solution and enzyme probably causes the levelling out of the experimental curve. Analysis Attention was focussed upon the ethyl to hexylboronic acids since the experimental binding energies are known for these compounds and the alkyl chain builds up one from another in its extended form (although the OBC& dihedral angle is 120.0”). Thus any conformational changes in the alkyl chain on moving from the solvent to the enzyme environment should be the same for these compounds. Consequently the inherent entropic and internal conformational energy changes are assumed constant. Table 3 shows the breakdown of the calculated binding energies into their electrostatic and polarisation energy components. The polarisation makes a TABLE 3 Breakdown of the binding energies (kcal mol-’ ) of the alkylboronic acids into their electrostatic and polarisation components Substrate
B( OH),CH,CH, B(OH),(CH,),CH, B(CH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH,
Electrostatic energy (kcal mol-’ ) -1.82 -1.82 -1.83 -2.01 -2.05
Polarisation energy (kcal mole1) -0.54 -0.59 -0.59 -0.58 -0.77
Total energy (kcal mol-‘) -2.36 -2.41 -2.42 -2.59 -2.82
68
relatively large significant contribution which increases at the hexylboronic acid whose alkyl chain extends the length of the pocket. The calculated energies represent the process Substrate (0 K)
AUcalculated -
Enzyme-Substrate (0 K)
Complex
whilst the experimental values are for AG
Substrate (solvated) 2 (298 K)
Enzyme-Inhibitor Tetrahedral Adduct (298 K)
From consideration of the thermodynamic cycle and assuming a direct correspondence between the complex and adduct [ 251 298 Aucalculated
= AGexp
+
+ AGsolution
S
bpt
C, Wq)
dT
+
;
C,(gas)
dT
bpt -AK,,
+
TbptfSgas
-
sliquid)
+
T298ASenz--sub
The most important term for this homologous series of molecules is the solvation term AGsoi. When the alkyl chain exceeds two carbon atoms in length the chain protrudes into the hydrophobic pocket leading to a hydrophobic effect which is of particular importance in aqueous solution and caused mainly by entropic changes in the surrounding water sheath. The difference in AG,,,for the n-alkylboronic acids may be estimated by assigning a value of 0.855 kcal mol-’ to each methylene group which is an average value estimated from studying the alkanes, isoalkanes, alcohols and carboxylic acids [26-281. (This assumes that the contribution of the hydrophilic and hydrophobic portions of the molecule to the solvent interaction energy are independent.) The enthalpy of hydration of butylboronic acid is 2.67 -1:0.06 kcal mol-’ [29]. Although this neglects the entropy of solvation, since no other experimentally determined thermodynamic quantity could be found it was used as the basis upon which the changes in the free enerm of solvation per CH2 group could be related. -A Gsoiution= -2.67
+ (4 - n)O.855
The binding energies in kcal mol-’ with the correction factor for the solvation energy term are shown in Table 4. Figure 3 shows a comparison of the experimental and calculated values. Further work - effects of substitution Calculations demonstrate that substitution of a methyl group into the a-position has little effect upon the binding whilst a methyl group in the S-position affects it adversely [ 211. The substrates used for this were based upon a main chain composed of three carbon atoms in the same conformation as that for n-propylboronic acid (see Fig. 4).
69
gn12 5.0
10.0
15.0
- AG Experimental
Fig. 3. Graph of calculated binding energies using the activated charge-relay system, against the experimentally determined binding energies.
Fig. 4. Diagram representing the dihedral angles for the a and P substituents.
The results are shown in Table 5. The p-methyl propylboronic acid with the additional methyl group at a dihedral angle of 300.0” is highly sensitive to the positioning of the charge-relay system. This is a consequence of the hydrogen of the P-methyl substituent pointing directly at the catalytic triad thus interfering with the rotation of the imidazole ring and preventing the attack of the OH of serine 195.
70 TABLE 4 The binding energies of the n-alkylboronic acids (kcal mol-I) to a-chymotrypsin with the thermodynamic solvation energy correction term incorporated; also shown are the experimental values Substrate
B( OH),CH,CH, B(OH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH, B(OH),(CH,),CH,
Inactivated charge-relay system
Experimental
Activated charge-relay system
a
b
a
b
-3.20 -4.23 -5.09 -6.12 -7.20
-3.10 -4.03 -4.89 -5.97 -7.14
-2.48 -3.42 -4.32 -5.37 -6.30
-2.17 -3.13 -4.02 -5.17 -6.30
-5.79 -6.97 -9.28 -11.70 -14.87
aCalculated binding energies involving the use of active site charges derived from the amino acid residues with crystallographic co-ordinates. bCalculated binding energies with the active site charges derived from the conformationally averaged amino acid residues. TABLE 5 Calculated binding energies (kcal mol-I) for a- and p-methyl substituted propylboronic acid to cu-chymotrypsin using the conformationally averaged point-charge model (see Fig. 4) Substrate
B( OH),CH,CH, AA-B(OH),CHCH,CH,CH, AB-B( OH),CCH,HCH,CH, BA-B(OH),CH,CHCH,CH, BB-B(OH)&H,CCH,HCH,
Inactive charge-relay system -2.215 -2.369 -1.979 -1.078 -7.569
Activated charge-relay system -1.314 -1.444 -1.107 -0.838 -0.746
CONCLUSIONS
Many research groups are currently trying to model enzyme-substrate binding with the ultimate aim of designing inhibitors or false substrates of therapeutic value. In general the approach involves the use of a series of complex intermolecular potential functions to account for the electrostatic, polarisation, hydrogen bonding and other contributions. Generally, quantum-mechanical calculations are more attractive since there need be no assumptions about the specific interactions’ and, at the ab initio level, no empirical parameterisation. The only drawback is the immense amount of computer tie required. Hence, by using the device of replacing enzyme atoms and their electrons by effective point-charges an otherwise full ab initio calculation (in this case the Gaussian 70 program [30]) is possible with an increase in the computational time of only about 5% over that for the isolated molecule.
71
With the solvation effects being incorporated empirically the relative binding for a series of similar substrates may be determined. This result makes one optimistic about using the approach to aid in the design of molecules to fit a specific enzyme binding site. ACKNOWLEDGEMENT
S. A. R. thanks ICI Plant Protection Division for their support through a CASE award. This work is also supported by the National Foundation for Cancer Research. REFERENCES 1 D. M. Hayes and P. A. Kollman, J. Am. Chem. Sot., 98 (1976) 7811. 2 J. Aimlof and U. Wahlgren, Theor. Chim. Acta, 28 (1973) 161. 3 C. Ghio, E. Scrocco and J. Tomasi, in Environmental Effects on Molecular Structure and Properties, D. Reidel, Dordrecht, 1976, p. 239. 4 J. 0. Noel1 and K. Morokuma, Chem. Phys. Lett., 36 (1975) 465. 5 V. K. Antonov, T. V. Ivania, I. V. Berezin and K. Martinek, FEBS Lett., 7 (1970) 23. 6 D. M. Blow, M. J. Birktoft and B. S. Hartley, Nature (London), 221 (1969) 337. 7 J. J. Birktoft and D. M. Blow, J. Mol. Biol., 68 (1972) 187. 8 M. Hunkapiller, S. H. Smallcomb, D. R. Whitaker and J. H. Richards, J. Biol. Chem., 248 (1973) 8306. 9 R. M. Stroud, M. Kneger, R. E. Koeppe, A. A. Kossiakoff and J. L. Chambers, in Proteases and Biological Control, Cold Spring Harbor Press, Long Island, NY, 1975, p. 13. 10 R. Henderson, T. A. Steitz, C. S. Wright, G. P. Hess and D. M. Blow, Cold Spring Harbor Symp. Quant. Biol., 36 (1971) 63. 11 A. Tulinsky, L Mavridis and R. F. Mann, J. Biol. Chem., 253 (1978) 1074. 12 K. A. Koehler and G. E. Lienhard, Biochemistry, 10 (1971) 2477. 13 J. D. Rawn and G. E. Lienhard, Biochemistry, 13 (1974) 3124. 14 K. Hanai, J. Biochem., 81 (1977) 1273. 15 T. A. Steitz, R. Henderson and D. M. Blow, J. Mol. Biol., 46 (1969) 337. 16 R. L. Vandlen and A. Tulinsky, Acta Crystallogr. Sect. B., 27 (1971) 437; 29 (1973) 1309. 17 K. E. B. Platzer, F. A. Momany and H. A. Sheraga, Int. J. Pept. Protein Res., (1972) 201. 18 D. M. Hayes and P. A. Kollman, J. Am. Chem. Sot., 98 (1976) 3335. 19 P. A. Markley and I. Ibanez, Biochemistry, 15 (1976) 3339. 20 P. A. Kollman and D. M. Hayes, J. Am Chem. Sot., 103 (1981) 2955. 21 D. M. Blow, in The Enzymes, Vol. 3, Academic Press, New York, 1971, p. 185. 22 L. E. Sutton, in Tables of Interatomic Distances and Configurations in Molecules and Ions, Chemical Society (London) Spec. Publ. No. 11, 1956. Suppl. No. 28, 1959. 23 C. D. Barry, Molecular Modelling System-X Newsl., 20 (1980) 23. 24 P. Weiner and P. A. Kollman, J. Comput. Chem., 2 (1981) 287. 25 J. B. Jones, T. Kunitake, C. Niemann and G. E. Hein, J. Am. Chem. Sot., 87 (1965) 1977. 26 C. Tanford, in The Hydrophobic Effect, Wiley, New York, 1973, p. 207. 27 C. McAuliffe, J. Phys. Chem., 70 (1966) 1267. 28 R. Smith and C. Tanford, Proc. Nat. Acad. Sci. U.S.A., 70 (1973) 289. 29 L. Gmelin, Gmelin Handbuch der Anorganischen Chemie, Vol. 16, Springer Verlag, Berlin, 1979, p. 16. 30 W. J. Hehre, W. A. Latham, R. Ditchfield, R. D. Newton and J. A. Pople, GAUSSIAN 70, Q.C.P.E., No. 236, Indiana University, Bloomington, IN, U.S.A., 1973.