Proc. Natl. Acad. Sci. USA
Vol. 73, No. 12, pp. 4261-4265, December 1976 Chemistry
Prediction of three-dimensional structures of enzyme-substrate and enzyme-inhibitor complexes of lysozyme (enzyme-substrate interactions/conformational energy/protein x-ray structure/N-acetylglucosamine oligomers)
MATTHEW R. PINCUS, S. SCOTT ZIMMERMAN, AND HAROLD A. SCHERAGA Department of Chemistry, Cornell University, Ithaca, New York 14853
Contributed by Harold A. Scheraga, September 9, 1976
ABSTRACT Conformational energy calculations were used to predict the three-dimensional structures of enzymesubstrate and enzyme-inhibitor complexes of lysozyme. A global search method, involving the use of a disaccharide fragment molecule, was used initially to determine all favorable binding regions at the active site. It is shown that the binding of a series of (nonfragmented) oligomers of N-acetylglucosamine is highly specific. The results show further that (a) theenzyme recognizes only one backbone conformation of the oligomer, corresponding to a left-handed helix, and (b) for saccharides containing two or more N-acetylglucosamine residues, two residues bind preferentially to the C and D sites. The calculations also suggest that the chair form of N-acetylglucosamine can bind to the D region. The saccharide residues of tetra-N-acetylglucosamine bind to the A-B-C-D sites, with the residues at the A-B-C sites having essentially the same conformation and orientation as those in the x-ray structure of tetra-N-acetylglucosamine-6-lactone bound to lysozyme.
During the past several years, x-ray crystallographic studies have provided the three-dimensional structures of a number of different enzyme-inhibitor complexes. These studies provide much information about binding sites available to substrates and inhibitors, but only a limited understanding of the specificity of enzymatic reactions. However, additional information about the recognition process is obtainable with the aid of conformational energy calculations (1, 2). A number of conformational energy calculations have been performed on enzyme-substrate complexes (2-4). These studies have examined either structures close to the x-ray structure (2, 4) or ones that appeared to look reasonable as starting conformations for energy minimization (3). In this study of the enzyme-substrate and enzyme-inhibitor complexes of lysozyme, we present a method for thoroughly examining the active site of lysozyme for possible stable binding regions. We then use these regions as starting points for minimization of the conformational energy of enzyme-inhibitor and enzyme-substrate complexes of lysozyme, taking low energy minima (5) of the oligosaccharides as starting conformations for the substrate. From these minimizations, a clear trend can be perceived as to where and in what manner saccharide molecules bind to the active site of this enzyme. In this initial treatment, the enzyme structure (6) is held rigid, but the substrate is allowed to move within the region of the active site and change conformation during energy minimization. In a subsequent treatment (M. R. Pincus, S. S. Zimmerman, and H. A. Scheraga, manuscript in preparation), the conformation of the enzyme will be allowed to change as well. Here, we examine which regions of the active site are available to ligands and what conformations of these ligands can be accommodated therein. Our treatment is equivalent to the asAbbreviations: GlcNAc, /3-N-acetylglucosamine; (GIcNAc)2, di-Nacetylglucosamine, etc.; (GIcNAc)4-lactone, tetra-N-acetylglucos-
amine-b-lactone.
4261
sumption of a "lock-and-key" mechanism in which the enzyme has pre-existing structural features that allow for recognition of the substrate. METHODS Choice of Enzyme Residues toBe Included in the Calculation. To reduce computation time, only certain residues were included in the calculations. The decision as to which residues were to be included in the search for low-energy binding regions of the rigid enzyme was based on the crystallographic map of the active site (6). The following segments, involving 41 residues, were included: Ly 33 to Asn 37, Asn 39, Gln 41 to Asn 48, Ser 50 to Gln 57, Asn 59, Trp 62, Trp 63, Arg 73, Leu 75, lie 98 to Asp 103, Asn 106 to Ala 110, and Arg 112 to Arg 114. Geometry and Energy Parameters. The standard geometry of Arnott and Scott (7) for f sugars was used for the oligomers of N-acetylglucosamine (GlcNAc) in the studies on the binding regions of the active site. However, in energy minimizations involving tetra-N-acetylglucosamine-6-lactone [(GlcNAc)4lactone] in the active site, use was made of the x-ray structure (8) of this compound, which had been determined by basing the geometry of the GlcNAc residues on the structure of aGlcNAc (9). Diamond-refined coordinates of the x-ray structure (6) of lysozyme (obtained from the Brookhaven Data Bank) were used, with hydrogen atoms being generated onto the polar atoms by a method described earlier (3). Ionizable side chains of residues in the enzyme were treated as neutral. All CH, CH2, and CH3 groups of the saccharides and of the enzyme were treated as united atoms (5). The potentials and parameters will be described in detail elsewhere (L. G. Dunfield, A. W. Burgess, and H. A. Scheraga, manuscript to be submitted). Search for Low Energy Regions at the Active Site. The problem in searching for stable binding regions of an enzyme is that, in addition to the six external degrees of freedom (three translational and three rotational) allowed for the substrate, there are many allowed internal degrees of freedom for both the substrate and the enzyme, i.e., variable dihedral angles. To reduce the number of variables, we initially used a "stripped disaccharide" molecule from which all hydrogen atoms had been removed and CH20H groups had been replaced by united-atom methyl groups. All regions of the active site that are sterically disallowed for this "stripped" molecule must likewise be disallowed for the real (GicNAc)2 molecule. The stripped molecule contains only two internal degrees of freedom, the two inter-ring dihedral angles X and f (see ref. 5 for the conventions used). The two lowest energy values for these dihedral angles have been determined previously (5), one set corresponding to a left-handed helix (4 =-74°, /' = 1130), and the other to a right-handed helix ( =-136°, 4v = 680). A
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Proc. Natl. Acad. Scd. USA 73 (1976)
complete grid search of the active site was carried out for each of these two sets of values and for a third, intermediate set of values (O = -107°, ,6 = 92°), which represents a low energy region but not a minimum either for the stripped disaccharide or for the full molecule. A coordinate system for the enzyme-substrate complex was chosen such that a line connecting the Ca of Asn 46 and Ca of Ala 110 defines the X-axis. The X-axis and the line connecting the C" of Asn 46 and the Ca of Ile 48 define the X-Y plane, from which the Y and Z axes are defined. The reference position of the substrate a the active site was selected such that, for a chosen reference saccharide residue, the C2 atom (see Fig. 2 of ref. 5) is at the origin, the C2-C12 virtual bond lies along the X-axis, and the C2-N11 bond lies in the X-Y plane [with dihedral angle 1 = -600 (5)]. All rigid body operations were carried out first by rotating the substrate from its reference position by the angles a, /, and y about the X-, Y-, and Z-axes, respectively (clockwise rotations being defined as positive), and then by translating the reference C2 atom to the desired (X,YZ) position. Regardless of which residue was used to define the substrate reference system, the choice of the atom positions defining this reference system resulted in an initial orientation of the molecules with the nonreducing end (residue 1) higher along the Z-axis than the reducing end. In the search for low energy regions at the active site using the stripped disaccharide, only the nonbonded (and, where present, hydrogen bonding) energies between the enzyme and the disaccharide were calculated. We have recently developed a set of "united residue" potentials (M. R. Pincus and H. A. Scheraga, manuscript to be submitted) in which the attractive energies between two residues can be described by a single attractive coefficient, provided that the residues are separated by a sufficient distance. This treatment was used for the interactions of the residues of the substrate with those of the enzyme. For each choice of internal conformation of the stripped dimer, energy contour maps were obtained for Z against y. The Z-coordinates were chosen at 3 A intervals from 15 A down to -12 A, i.e., roughly from the position just above Asp 101 down to Gln 41, and the rotational angle y was incremented every 30° from 0 to 3600. Maps were determined for X = 4,7, and 10 A, Y = 5,7, 10, and 12 A, a = 0, 430, 4450, andB = 0, ±30, ±450. Minimization of the Conformational Energies of Inhibitors and Substrates at the Active Site. Using as starting points the values of the rigid body variables (X, Y, Z, a, /, -y) and the internal variables (k and x1) found to give low-energy complexes of the enzyme with the stripped disaccharide, the conformational energy of (GlcNAc)2 (complete molecule) was minimized with respect to both internal and rigid body degrees of freedom. Several combinations of the low energy positions for the side chains of (GlcNAc)2, determined previously (5), were selected for each starting disposition (defined in ref. 3) and for each set of values ofX andA. In treating the real (GlcNAc)2 molecule, the total conformational energy was calculated, i.e., nonbonded, electrostatic, hydrogen-bonding, and torsional energies (1). The total conformational energy of the enzyme-substrate complex, ECom, was calculated as
Eoor,= Esub
+
Ein
[1]
in which Esub is the conformational energy of the substrate or inhibitor, and Eint is the total energy of interaction between the active site of the enzyme and the substrate or inhibitor. As in the case of the stripped disaccharide, united atom potentials (L. G. Dunfield, A. W. Burgess, and H. A. Scheraga,
manuscript to be submitted) were used for all nonpolar carbon
atoms. In addition, united residue potentials (M. R. Pincus and H. A. Scheraga, manuscript to be submitted) were used for the interaction of each sugar residue with each residue of the enzyme provided that the two residues were separated at or beyond a critical distance. Minimization of the conformational energy of (GIcNAc)3 at the active site was started by adding a GIcNAc residue, in the left-handed helical conformation, to either end of a minimum-energy structure of (GlcNAc)2 (see Results and Discussion). The low energy conformations of the stripped disaccharide were also used for the (GIcNAc)2 molecule, in generating initial conformations of (GlcNAc)3. Minimization of the total conformational energy was performed as described for
(GIcNAc)2. The energy minima for (GIcNAc)4 at the active site were determined by adding a residue (in a left-handed helical conformation) to either end of (GlcNAc)3 in each of its lowest energy conformations. Extra starting conformations, as taken from the stripped disaccharide maps in the determination of stable conformations of (GlcNAc)3, were not used for (GlcNAc)4 because the conformational space available to oligomers over three units long at the active site is highly restricted. RESULTS AND DISCUSSION The energy maps for the stripped dimer molecule reveal the important feature that the regions accessible to the test molecule are quite limited; only 13 structures have interaction energies within 5 kcal (21 kJ) of the lowest energy position. Stripped disaccharide-lysozyme structures having energies within 7 kcal/mol (29 kJ/mol) of the lowest energy structure were selected as starting points for minimization of the total conformational energy of (GlcNAc)2. The lowest energy dispositions of the full dimer (upon minimization) were found to be in the active site in regions below the A site, the most stable of which corresponded roughly to the C and D sites, as defined in ref. 6. In addition, most of the lowest energy structures had inter-ring dihedral angles of 0 k-700, { 1100 (left-handed helix) regardless of the choice of conformations for the side chains. The minimized rigid body variables and inter-ring dihedral angles for the two lowest energy dimer conformations are listed in Table 1 (conformers 1 and 2). These calculated results agree qualitatively with the experimental results of Beddell et al. (10), who showed that the dimer N-acetylglucosaminyl-3-D-glucose binds to regions corresponding roughly to the C and D sites of the enzyme. The low energy conformations for (GIcNAc)2, as well as the low energy binding regions for the stripped dimer, were chosen as the starting points for energy minimization of (GlcNAc)3. The third or added residue was placed so that the dihedral angles between it and the adjoining residue were in the lefthanded helical region (,t -700, /t; 1100). This backbone conformation was chosen because it gave the lowest energy minima for (GlcNAc)2. The values of the rigid body variables and dihedral angles for the lowest energy structure of (GlcNAc)3 are listed in Table 1 (conformer 3). To examine the x-ray structure of the complex of lysozyme with (GIcNAc)3 (8) more closely, and to compare it with our calculated results, the x-ray coordinates of (GlcNAc)3 (8) were rotated into our reference frame and the rigid body variables (as well as the dihedral angles) were determined (conformer 4 in Table 1). These initial values were then used as another starting conformation for energy minimization (using standard geometry) of (GlcNAc)3 at the active site. The resulting structure, conformer 5 of Table 1 (also arrived at by minimization from a low energy region found for the stripped molecule) stays -
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Proc. Natl. Acad. Sci. USA 73 (1976)
4263
Table 1. Binding dispositions and conformations for oligosaccharides at the active site
Oligosaccharide 1. (GlcNAc)2 2. (GlcNAc)2 alternate minimum 3. (GlcNAc)3 lowest energy minimum 4. (GlcNAc)3 x-ray disposition 5. (GlcNAc)3 minimized from x-ray disposition 6. (GlcNAc)4 lowest minimum
Reference residuea X
Inter-ring dihedral
anglesb
Rigid body variables
Y
Z
a
13
ty,
Binding Esub Ecom Eint sitesc (kcal/mol)
1 1
7.90 7.43
6.55 6.51
6.07 6.15
44.3 22.9
-32.8 -50.6
-3.9 -3.9
-64.2 -71.4
111.9 114.3
C-D C-D
-18.7 -9.9
-45.5 -44.2
-64.2 -54.1
2
7.48
6.46
6.15
48.7
-24.0
-6.9
-74.4 -69.4
131.4 106.2
B-C C-D
-24.2
-63.2
-87.4
1 2
7.71 7.79
6.75 5.50
12.23 -7.2 10.79 -7.4
10.4 -0.2
116.6 137.7
5.90
11.55
-4.3
3.4
120.2
A-B -22.0 B-C A-B -28.7 B-C
314.0
7.71
111.8 126.1 108.2 129.7
336.0
2
-59.0 -84.5 -86.0 -78.7
-43.0
-71.8
2
7.71
6.75
12.23
-7.2
10.4
116.6
2
7.79
5.50
10.79
-7.4
-0.2
137.7
8. (GlcNAc)4-lactone minimized x-ray structure
2
7.48
6.11
12.04
-8.1
-1.1
122.7
109.3 131.4 106.2 111.8 126.1 118.8 120.8 134.6 99.7
A-B -36.9 -68.2 B-C C-D A-B -17.9 112.0 B-C C-D A-B -33.6 -61.0 B-C C-D
-105.1
7. (GlcNAc)4-lactone x-ray structure
-79.9 -74.4 -69.4 -59.0 -84.5 -106.5 -86.9 -82.1 -93.5
94.1 -94.6
Residue on which the substrate coordinate system is defined. The coordinates were selected such that the C2-C12 virtual bond formed the X-axis. The position of the C12 atom was that corresponding to dihedral angle 1 = -60° (ref. 5). C2 is the origin. b See ref. 5 for definition of dihedral angles. c Residue location at active site. Each set of O and 6 corresponds to the inter-ring dihedral angles between the residues at the binding sites listed to the right. a
close to the initial x-ray structure. The conformational energy of conformer 5 in Table 1 [(GlcNAc)3 in the A-B-C sites] is significantly higher than that of conformer 3 [(GIcNAc)3 in the B-C-D sites], our lowest energy structure. This energy difference results not from any bad contacts for conformer 5 but rather from the lack of any particularly favorable contacts between the first residue and the A site. The disposition of residue 1 of our lowest energy trimer structure, conformer 3 in Table 1, and that of residue 2 of the energy-minimized x-ray structure, conformer 5 in Table 1, are quite similar [compare rigid body variables for conformers 3 (with residue 1 as the reference) and 5 in Table 1]. The interring dihedral angles and 4, between residues 1 and 2 (occupying sites B and C, respectively, as shown for conformer 3 of Table 1) of our structure and between residues 2 and 3 (occupying sites B and C, respectively, in conformer 5 of Table 1) of the energy-minimized x-ray structure are quite similar also. Thus, residues binding to sites B and C in our structure bind in a manner quite similar to that found experimentally. The difference between our calculated structure and the x-ray structure (6, 11, 12) lies in the binding of our residue 3 to the D site, whereas site A is occupied in the x-ray structure. It is possible that some of the side chains in the A and B regions of the enzyme, where positions are not well defined (as in the case of the -COOH group of Asp 101), have not been optimally placed, causing the calculated binding energy to be less favorable. It is clear, nonetheless, that the D region is quite capable of binding to the chair form of the substrate, in agreement with recent experimental results (13) and earlier energy calculations (2, 4). Using the lowest energy forms of (GlcNAc)3 at the active site one can build up structures of (GlcNAc)4 in a manner similar
to that described for (GlcNAc)3. If another residue is added to the nonreducing end and the energy of the complex is minimized, a structure (conform-er 6 of Table 1) is obtained whose disposition is almost identical to that of the energy-minimized x-ray structure, conformer 5 of Table 1. Energy minimization of the tetramer hardly changes the positions of the residues in sites B, C, and D while the position of the first residue in site A was minimized to a position almost identical to that of the first residue in the A site of the energy-minimized x-ray structure of the trimer. The calculated conformation of the tetramer at the active site is shown in Fig. IA. It is observed that the fourth residue (in particular its Ci atom) is in close proximity to the side chain of Asp 52. In the postulated mechanism of action of the enzyme, a carbonium ion at Ci is thought to be stabilized by a carboxylate anion contributed by Asp 52 (2). As in the case of the lowest energy conformation of (GlcNAc)s, the lowest energy form of (GlcNAc)4 shown in Fig. IA, also binds well around the D region. it is possible that, if the saccharide residue at the D site of the tetramer could exist in the sofa form, it could bind with even greater affinity to the D site of the enzyme. Since there is no standard half-chair geometry for sugar rings, we minimized the conformational energy of the proposed x-ray structure for the (GlcNAc)4-lactone-lysozyme complex (8). The fourth residue of (GlcNAc)4-lactone is a lactone that exists in a "sofa" conformation, somewhat similar to a half-chair form (8). Conformer 7 of Table 1 is the x-ray structure of (GlcNAc)4-lactone (in our reference frame) and is shown in Fig. 1C. Conformer 8 of Table 1 is the energy-minimized x-ray structure and is shown in Fig. lB. Some relatively large changes occur between starting and energy-minimized structures, in particular a translation of about 1.2 A in the positive Z-direction.
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Proc. Natl. Acad. Sci. USA 73 (1976)
~ i&~o~0 ~~~~~~~~~~~~~LY
A~~~~~ 0O2
A
ASSP 03
10
a
Sc
ASP
ILE 95
ILEL9S
ASN
0 LA 0
ASN AL46p
0~~~~~~~~~~~~~~~~~~~~~~~~~~~~ T5T2 SPOL5
:52
GLSS
AARG
4 ASSN
ASN
*.
44
OLT02
a
ASP
i~ ~ ~~ASP
aP
03
0 AL
103
LESgS9
VALA 52~TRLP
0~~~~~~P0
C
L~ ~
~
~
~
OT0
0~~~~~~~~~~~~~~~~~L
55 OLE
ASP 52 ~
~
~
~
~
TP
58.>~~~~~~~~~~~~~~~5 52 0~~~~~~~~~~~~~~~~~~~~GN5 ASP
45 ASS
ALALLO
0~~~~~~~~~~~~~~~AS
C~~~~~~~OSTAP5 ASS44 0
0~~~~~~LY10 ASS44
caron atom of1th of etrasacharidesandsom of theamino aid resiues arond the ctive ste of lsozyme.All 1.Stereovews Fic. nzye ndof hepyanoylrigs f he ubtrte rereresntd y drkcicle. he acboe ntrge atmsoftheenym o te bacboe ste () negy b crcesfile wthobiqe ins.(A Clclaedloestenrg mniumfo (lc~c4 oud o heaciv areinicte of(GlcNc)4-lctoneboundto te actve sie. (C X-ra strctureof (GcN~c)-lactne bund t the ctivesite xray sructue minimzed
Chemistry:
Pincus et al.
The final binding energy (Eint) of the minimized structure of (GlcNAc)4-lactone is somewhat higher than that of minimized (GlcNAc)4. Part of this difference in energy may be due to the difference in the geometry of the two tetrasaccharides, as can be seen from the following. The geometry of the first three residues of (GlcNAc)4-lactone was based on that of a-GlcNAc (8, 9) even though all GlcNAc residues for substrates and inhibitors are in the d-form, a significantly different geometry from the a-form (7). It should be noted that, when the standard d-geometries were used here for energy minimization of (GlcNAc)3 in the x-ray disposition and conformation, there was a smaller change in the values of the variables after minimization (compare conformers 4 and 5, Table 1) than when ageometries were used for (GlcNAc)4-lactone (compare conformers 7 and 8, Table 1). A number of unfavorable contacts occur in the x-ray structure of (GlcNAc)4-lactone. In particular, close contacts occur (see Fig. 1C) between the aromatic ring of Trp 63 and the CH2 of residue 2 of (GlcNAc)4-lactone, between the aromatic ring of Trp 108 and the methyl group of residue 3 of (GlcNAc)4-lactone, and between the carboxyl group of Asp 52 and the ring oxygen and Ci of residue 4 of (GIcNAc)4-lactone (the residue in the lactone form). A number of less unfavorable contacts also occur between the generated hydrogen atoms of the enzyme and ligand. It is apparently necessary to effect relatively large changes in disposition to relieve them. It is possible that, if we were to use the fl-sugar geometries for the first three residues combined with the 6-lactone geometry for the last residue, at least some of these unfavorable contacts would not exist. It is also possible that the side chains of the active site move to accommodate the sofa form of the D ring. Further, the state of protonation of certain residues, especially Glu 35, is quite important in determining the affinity of (GlcNAc)4-lactone for the enzyme (8). The binding of (GlcNAc)4-lactone to the enzyme at pH 2.6, the pH at which the complex was crystallized, is over 10 times lower than at pH 4.7, and its affinity at this low pH is similar to that of (GlcNAc)4 (8). We are currently inves-
Proc. Natl. Acad. Sci. USA 73 (1976)
4265
tigating all of these possibilities. Using the current x-ray structure of the enzyme (held rigid, here), however, it appears that the D site has no special affinity for the sofa form. As will be demonstrated in a later paper, (M. R. Pincus, S. S. Zimmerman, and H. A. Scheraga, manuscript in preparation), there are other low energy positions, corresponding to the E and F sites, which have a lower affinity for GlcNAc residues than do sites B-D. This work was supported by grants from the National Institutes of Health and from the National Science Foundation. M.R. P. and S.S.Z. were supported by NIH Postdoctoral Research Fellowships.
1. Momany, F. A., McGuire, R. F., Burgess, A. W. & Scheraga, H. A. (1975) J. Phys. Chem. 79,2361-2381. 2. Warshel, A. & Levitt, M. (1976) J. Mol. Biol. 103,227-249. 3. Platzer, K. E. B., Momany, F. A. & Scheraga, H. A. (1972) Int. J. Pept. Protein Res. 4, 201-219. 4. Levitt, M. (1974) in Peptides, Polypeptides and Proteins, eds. Blout, E. R., Bovey, F. A., Goodman, M. & Lotan, N. (John Wiley, New York), pp. 99-113. 5. Pincus, M. R., Burgess, A. W. & Scheraga, H. A. (1976) Biopolymers, in press. 6. Blake, C. C. F., Johnson, L. N., Mair, G. A., North, A. C. T., Phillips, D. C. & Sarma, V. R. (1967) Proc. R. Soc. London Ser. B 167,378-388. 7. Arnott, S. & Scott, W. E. (1972) J. Chem. Soc. Perkin Trans. II 3,324-335. 8. Ford, L. O., Johnson, L. N., Machin, P. A., Phillips, D. C. & Tjian, R. (1974) J. Mol. Biol. 88, 349-371. 9. Johnson, L. N. (1966) Acta Crystallogr. 21, 885-891. 10. Beddell, C. R., Moult, J. & Phillips, D. C. (1970) in Molecular Properties of Drug Receptors, eds. Porter, R. & O'Connor, M. (Churchill, London), pp. 85-112. 11. Imoto, T., Johnson, L. N., North, A. C. T., Phillips, D. C. & Rupley, J. A. (1972) in The Enzymes, ed. Boyer, P. D. (Academic Press, New York and London), Vol. VII, pp. 665-868. 12. Rupley, J. A. (1967) Proc. R. Soc. London Ser. B 167, 416428. 13. Holler, E., Rupley, J. A. & Hess, G. P. (1975) Biochemistry 14, 1088-1094.
Vol. 73, No. 12, pp. 4261-4265, December 1976 Chemistry
Prediction of three-dimensional structures of enzyme-substrate and enzyme-inhibitor complexes of lysozyme (enzyme-substrate interactions/conformational energy/protein x-ray structure/N-acetylglucosamine oligomers)
MATTHEW R. PINCUS, S. SCOTT ZIMMERMAN, AND HAROLD A. SCHERAGA Department of Chemistry, Cornell University, Ithaca, New York 14853
Contributed by Harold A. Scheraga, September 9, 1976
ABSTRACT Conformational energy calculations were used to predict the three-dimensional structures of enzymesubstrate and enzyme-inhibitor complexes of lysozyme. A global search method, involving the use of a disaccharide fragment molecule, was used initially to determine all favorable binding regions at the active site. It is shown that the binding of a series of (nonfragmented) oligomers of N-acetylglucosamine is highly specific. The results show further that (a) theenzyme recognizes only one backbone conformation of the oligomer, corresponding to a left-handed helix, and (b) for saccharides containing two or more N-acetylglucosamine residues, two residues bind preferentially to the C and D sites. The calculations also suggest that the chair form of N-acetylglucosamine can bind to the D region. The saccharide residues of tetra-N-acetylglucosamine bind to the A-B-C-D sites, with the residues at the A-B-C sites having essentially the same conformation and orientation as those in the x-ray structure of tetra-N-acetylglucosamine-6-lactone bound to lysozyme.
During the past several years, x-ray crystallographic studies have provided the three-dimensional structures of a number of different enzyme-inhibitor complexes. These studies provide much information about binding sites available to substrates and inhibitors, but only a limited understanding of the specificity of enzymatic reactions. However, additional information about the recognition process is obtainable with the aid of conformational energy calculations (1, 2). A number of conformational energy calculations have been performed on enzyme-substrate complexes (2-4). These studies have examined either structures close to the x-ray structure (2, 4) or ones that appeared to look reasonable as starting conformations for energy minimization (3). In this study of the enzyme-substrate and enzyme-inhibitor complexes of lysozyme, we present a method for thoroughly examining the active site of lysozyme for possible stable binding regions. We then use these regions as starting points for minimization of the conformational energy of enzyme-inhibitor and enzyme-substrate complexes of lysozyme, taking low energy minima (5) of the oligosaccharides as starting conformations for the substrate. From these minimizations, a clear trend can be perceived as to where and in what manner saccharide molecules bind to the active site of this enzyme. In this initial treatment, the enzyme structure (6) is held rigid, but the substrate is allowed to move within the region of the active site and change conformation during energy minimization. In a subsequent treatment (M. R. Pincus, S. S. Zimmerman, and H. A. Scheraga, manuscript in preparation), the conformation of the enzyme will be allowed to change as well. Here, we examine which regions of the active site are available to ligands and what conformations of these ligands can be accommodated therein. Our treatment is equivalent to the asAbbreviations: GlcNAc, /3-N-acetylglucosamine; (GIcNAc)2, di-Nacetylglucosamine, etc.; (GIcNAc)4-lactone, tetra-N-acetylglucos-
amine-b-lactone.
4261
sumption of a "lock-and-key" mechanism in which the enzyme has pre-existing structural features that allow for recognition of the substrate. METHODS Choice of Enzyme Residues toBe Included in the Calculation. To reduce computation time, only certain residues were included in the calculations. The decision as to which residues were to be included in the search for low-energy binding regions of the rigid enzyme was based on the crystallographic map of the active site (6). The following segments, involving 41 residues, were included: Ly 33 to Asn 37, Asn 39, Gln 41 to Asn 48, Ser 50 to Gln 57, Asn 59, Trp 62, Trp 63, Arg 73, Leu 75, lie 98 to Asp 103, Asn 106 to Ala 110, and Arg 112 to Arg 114. Geometry and Energy Parameters. The standard geometry of Arnott and Scott (7) for f sugars was used for the oligomers of N-acetylglucosamine (GlcNAc) in the studies on the binding regions of the active site. However, in energy minimizations involving tetra-N-acetylglucosamine-6-lactone [(GlcNAc)4lactone] in the active site, use was made of the x-ray structure (8) of this compound, which had been determined by basing the geometry of the GlcNAc residues on the structure of aGlcNAc (9). Diamond-refined coordinates of the x-ray structure (6) of lysozyme (obtained from the Brookhaven Data Bank) were used, with hydrogen atoms being generated onto the polar atoms by a method described earlier (3). Ionizable side chains of residues in the enzyme were treated as neutral. All CH, CH2, and CH3 groups of the saccharides and of the enzyme were treated as united atoms (5). The potentials and parameters will be described in detail elsewhere (L. G. Dunfield, A. W. Burgess, and H. A. Scheraga, manuscript to be submitted). Search for Low Energy Regions at the Active Site. The problem in searching for stable binding regions of an enzyme is that, in addition to the six external degrees of freedom (three translational and three rotational) allowed for the substrate, there are many allowed internal degrees of freedom for both the substrate and the enzyme, i.e., variable dihedral angles. To reduce the number of variables, we initially used a "stripped disaccharide" molecule from which all hydrogen atoms had been removed and CH20H groups had been replaced by united-atom methyl groups. All regions of the active site that are sterically disallowed for this "stripped" molecule must likewise be disallowed for the real (GicNAc)2 molecule. The stripped molecule contains only two internal degrees of freedom, the two inter-ring dihedral angles X and f (see ref. 5 for the conventions used). The two lowest energy values for these dihedral angles have been determined previously (5), one set corresponding to a left-handed helix (4 =-74°, /' = 1130), and the other to a right-handed helix ( =-136°, 4v = 680). A
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Proc. Natl. Acad. Scd. USA 73 (1976)
complete grid search of the active site was carried out for each of these two sets of values and for a third, intermediate set of values (O = -107°, ,6 = 92°), which represents a low energy region but not a minimum either for the stripped disaccharide or for the full molecule. A coordinate system for the enzyme-substrate complex was chosen such that a line connecting the Ca of Asn 46 and Ca of Ala 110 defines the X-axis. The X-axis and the line connecting the C" of Asn 46 and the Ca of Ile 48 define the X-Y plane, from which the Y and Z axes are defined. The reference position of the substrate a the active site was selected such that, for a chosen reference saccharide residue, the C2 atom (see Fig. 2 of ref. 5) is at the origin, the C2-C12 virtual bond lies along the X-axis, and the C2-N11 bond lies in the X-Y plane [with dihedral angle 1 = -600 (5)]. All rigid body operations were carried out first by rotating the substrate from its reference position by the angles a, /, and y about the X-, Y-, and Z-axes, respectively (clockwise rotations being defined as positive), and then by translating the reference C2 atom to the desired (X,YZ) position. Regardless of which residue was used to define the substrate reference system, the choice of the atom positions defining this reference system resulted in an initial orientation of the molecules with the nonreducing end (residue 1) higher along the Z-axis than the reducing end. In the search for low energy regions at the active site using the stripped disaccharide, only the nonbonded (and, where present, hydrogen bonding) energies between the enzyme and the disaccharide were calculated. We have recently developed a set of "united residue" potentials (M. R. Pincus and H. A. Scheraga, manuscript to be submitted) in which the attractive energies between two residues can be described by a single attractive coefficient, provided that the residues are separated by a sufficient distance. This treatment was used for the interactions of the residues of the substrate with those of the enzyme. For each choice of internal conformation of the stripped dimer, energy contour maps were obtained for Z against y. The Z-coordinates were chosen at 3 A intervals from 15 A down to -12 A, i.e., roughly from the position just above Asp 101 down to Gln 41, and the rotational angle y was incremented every 30° from 0 to 3600. Maps were determined for X = 4,7, and 10 A, Y = 5,7, 10, and 12 A, a = 0, 430, 4450, andB = 0, ±30, ±450. Minimization of the Conformational Energies of Inhibitors and Substrates at the Active Site. Using as starting points the values of the rigid body variables (X, Y, Z, a, /, -y) and the internal variables (k and x1) found to give low-energy complexes of the enzyme with the stripped disaccharide, the conformational energy of (GlcNAc)2 (complete molecule) was minimized with respect to both internal and rigid body degrees of freedom. Several combinations of the low energy positions for the side chains of (GlcNAc)2, determined previously (5), were selected for each starting disposition (defined in ref. 3) and for each set of values ofX andA. In treating the real (GlcNAc)2 molecule, the total conformational energy was calculated, i.e., nonbonded, electrostatic, hydrogen-bonding, and torsional energies (1). The total conformational energy of the enzyme-substrate complex, ECom, was calculated as
Eoor,= Esub
+
Ein
[1]
in which Esub is the conformational energy of the substrate or inhibitor, and Eint is the total energy of interaction between the active site of the enzyme and the substrate or inhibitor. As in the case of the stripped disaccharide, united atom potentials (L. G. Dunfield, A. W. Burgess, and H. A. Scheraga,
manuscript to be submitted) were used for all nonpolar carbon
atoms. In addition, united residue potentials (M. R. Pincus and H. A. Scheraga, manuscript to be submitted) were used for the interaction of each sugar residue with each residue of the enzyme provided that the two residues were separated at or beyond a critical distance. Minimization of the conformational energy of (GIcNAc)3 at the active site was started by adding a GIcNAc residue, in the left-handed helical conformation, to either end of a minimum-energy structure of (GlcNAc)2 (see Results and Discussion). The low energy conformations of the stripped disaccharide were also used for the (GIcNAc)2 molecule, in generating initial conformations of (GlcNAc)3. Minimization of the total conformational energy was performed as described for
(GIcNAc)2. The energy minima for (GIcNAc)4 at the active site were determined by adding a residue (in a left-handed helical conformation) to either end of (GlcNAc)3 in each of its lowest energy conformations. Extra starting conformations, as taken from the stripped disaccharide maps in the determination of stable conformations of (GlcNAc)3, were not used for (GlcNAc)4 because the conformational space available to oligomers over three units long at the active site is highly restricted. RESULTS AND DISCUSSION The energy maps for the stripped dimer molecule reveal the important feature that the regions accessible to the test molecule are quite limited; only 13 structures have interaction energies within 5 kcal (21 kJ) of the lowest energy position. Stripped disaccharide-lysozyme structures having energies within 7 kcal/mol (29 kJ/mol) of the lowest energy structure were selected as starting points for minimization of the total conformational energy of (GlcNAc)2. The lowest energy dispositions of the full dimer (upon minimization) were found to be in the active site in regions below the A site, the most stable of which corresponded roughly to the C and D sites, as defined in ref. 6. In addition, most of the lowest energy structures had inter-ring dihedral angles of 0 k-700, { 1100 (left-handed helix) regardless of the choice of conformations for the side chains. The minimized rigid body variables and inter-ring dihedral angles for the two lowest energy dimer conformations are listed in Table 1 (conformers 1 and 2). These calculated results agree qualitatively with the experimental results of Beddell et al. (10), who showed that the dimer N-acetylglucosaminyl-3-D-glucose binds to regions corresponding roughly to the C and D sites of the enzyme. The low energy conformations for (GIcNAc)2, as well as the low energy binding regions for the stripped dimer, were chosen as the starting points for energy minimization of (GlcNAc)3. The third or added residue was placed so that the dihedral angles between it and the adjoining residue were in the lefthanded helical region (,t -700, /t; 1100). This backbone conformation was chosen because it gave the lowest energy minima for (GlcNAc)2. The values of the rigid body variables and dihedral angles for the lowest energy structure of (GlcNAc)3 are listed in Table 1 (conformer 3). To examine the x-ray structure of the complex of lysozyme with (GIcNAc)3 (8) more closely, and to compare it with our calculated results, the x-ray coordinates of (GlcNAc)3 (8) were rotated into our reference frame and the rigid body variables (as well as the dihedral angles) were determined (conformer 4 in Table 1). These initial values were then used as another starting conformation for energy minimization (using standard geometry) of (GlcNAc)3 at the active site. The resulting structure, conformer 5 of Table 1 (also arrived at by minimization from a low energy region found for the stripped molecule) stays -
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Proc. Natl. Acad. Sci. USA 73 (1976)
4263
Table 1. Binding dispositions and conformations for oligosaccharides at the active site
Oligosaccharide 1. (GlcNAc)2 2. (GlcNAc)2 alternate minimum 3. (GlcNAc)3 lowest energy minimum 4. (GlcNAc)3 x-ray disposition 5. (GlcNAc)3 minimized from x-ray disposition 6. (GlcNAc)4 lowest minimum
Reference residuea X
Inter-ring dihedral
anglesb
Rigid body variables
Y
Z
a
13
ty,
Binding Esub Ecom Eint sitesc (kcal/mol)
1 1
7.90 7.43
6.55 6.51
6.07 6.15
44.3 22.9
-32.8 -50.6
-3.9 -3.9
-64.2 -71.4
111.9 114.3
C-D C-D
-18.7 -9.9
-45.5 -44.2
-64.2 -54.1
2
7.48
6.46
6.15
48.7
-24.0
-6.9
-74.4 -69.4
131.4 106.2
B-C C-D
-24.2
-63.2
-87.4
1 2
7.71 7.79
6.75 5.50
12.23 -7.2 10.79 -7.4
10.4 -0.2
116.6 137.7
5.90
11.55
-4.3
3.4
120.2
A-B -22.0 B-C A-B -28.7 B-C
314.0
7.71
111.8 126.1 108.2 129.7
336.0
2
-59.0 -84.5 -86.0 -78.7
-43.0
-71.8
2
7.71
6.75
12.23
-7.2
10.4
116.6
2
7.79
5.50
10.79
-7.4
-0.2
137.7
8. (GlcNAc)4-lactone minimized x-ray structure
2
7.48
6.11
12.04
-8.1
-1.1
122.7
109.3 131.4 106.2 111.8 126.1 118.8 120.8 134.6 99.7
A-B -36.9 -68.2 B-C C-D A-B -17.9 112.0 B-C C-D A-B -33.6 -61.0 B-C C-D
-105.1
7. (GlcNAc)4-lactone x-ray structure
-79.9 -74.4 -69.4 -59.0 -84.5 -106.5 -86.9 -82.1 -93.5
94.1 -94.6
Residue on which the substrate coordinate system is defined. The coordinates were selected such that the C2-C12 virtual bond formed the X-axis. The position of the C12 atom was that corresponding to dihedral angle 1 = -60° (ref. 5). C2 is the origin. b See ref. 5 for definition of dihedral angles. c Residue location at active site. Each set of O and 6 corresponds to the inter-ring dihedral angles between the residues at the binding sites listed to the right. a
close to the initial x-ray structure. The conformational energy of conformer 5 in Table 1 [(GlcNAc)3 in the A-B-C sites] is significantly higher than that of conformer 3 [(GIcNAc)3 in the B-C-D sites], our lowest energy structure. This energy difference results not from any bad contacts for conformer 5 but rather from the lack of any particularly favorable contacts between the first residue and the A site. The disposition of residue 1 of our lowest energy trimer structure, conformer 3 in Table 1, and that of residue 2 of the energy-minimized x-ray structure, conformer 5 in Table 1, are quite similar [compare rigid body variables for conformers 3 (with residue 1 as the reference) and 5 in Table 1]. The interring dihedral angles and 4, between residues 1 and 2 (occupying sites B and C, respectively, as shown for conformer 3 of Table 1) of our structure and between residues 2 and 3 (occupying sites B and C, respectively, in conformer 5 of Table 1) of the energy-minimized x-ray structure are quite similar also. Thus, residues binding to sites B and C in our structure bind in a manner quite similar to that found experimentally. The difference between our calculated structure and the x-ray structure (6, 11, 12) lies in the binding of our residue 3 to the D site, whereas site A is occupied in the x-ray structure. It is possible that some of the side chains in the A and B regions of the enzyme, where positions are not well defined (as in the case of the -COOH group of Asp 101), have not been optimally placed, causing the calculated binding energy to be less favorable. It is clear, nonetheless, that the D region is quite capable of binding to the chair form of the substrate, in agreement with recent experimental results (13) and earlier energy calculations (2, 4). Using the lowest energy forms of (GlcNAc)3 at the active site one can build up structures of (GlcNAc)4 in a manner similar
to that described for (GlcNAc)3. If another residue is added to the nonreducing end and the energy of the complex is minimized, a structure (conform-er 6 of Table 1) is obtained whose disposition is almost identical to that of the energy-minimized x-ray structure, conformer 5 of Table 1. Energy minimization of the tetramer hardly changes the positions of the residues in sites B, C, and D while the position of the first residue in site A was minimized to a position almost identical to that of the first residue in the A site of the energy-minimized x-ray structure of the trimer. The calculated conformation of the tetramer at the active site is shown in Fig. IA. It is observed that the fourth residue (in particular its Ci atom) is in close proximity to the side chain of Asp 52. In the postulated mechanism of action of the enzyme, a carbonium ion at Ci is thought to be stabilized by a carboxylate anion contributed by Asp 52 (2). As in the case of the lowest energy conformation of (GlcNAc)s, the lowest energy form of (GlcNAc)4 shown in Fig. IA, also binds well around the D region. it is possible that, if the saccharide residue at the D site of the tetramer could exist in the sofa form, it could bind with even greater affinity to the D site of the enzyme. Since there is no standard half-chair geometry for sugar rings, we minimized the conformational energy of the proposed x-ray structure for the (GlcNAc)4-lactone-lysozyme complex (8). The fourth residue of (GlcNAc)4-lactone is a lactone that exists in a "sofa" conformation, somewhat similar to a half-chair form (8). Conformer 7 of Table 1 is the x-ray structure of (GlcNAc)4-lactone (in our reference frame) and is shown in Fig. 1C. Conformer 8 of Table 1 is the energy-minimized x-ray structure and is shown in Fig. lB. Some relatively large changes occur between starting and energy-minimized structures, in particular a translation of about 1.2 A in the positive Z-direction.
4264
Chemistry: Pincus et al.
Proc. Natl. Acad. Sci. USA 73 (1976)
~ i&~o~0 ~~~~~~~~~~~~~LY
A~~~~~ 0O2
A
ASSP 03
10
a
Sc
ASP
ILE 95
ILEL9S
ASN
0 LA 0
ASN AL46p
0~~~~~~~~~~~~~~~~~~~~~~~~~~~~ T5T2 SPOL5
:52
GLSS
AARG
4 ASSN
ASN
*.
44
OLT02
a
ASP
i~ ~ ~~ASP
aP
03
0 AL
103
LESgS9
VALA 52~TRLP
0~~~~~~P0
C
L~ ~
~
~
~
OT0
0~~~~~~~~~~~~~~~~~L
55 OLE
ASP 52 ~
~
~
~
~
TP
58.>~~~~~~~~~~~~~~~5 52 0~~~~~~~~~~~~~~~~~~~~GN5 ASP
45 ASS
ALALLO
0~~~~~~~~~~~~~~~AS
C~~~~~~~OSTAP5 ASS44 0
0~~~~~~LY10 ASS44
caron atom of1th of etrasacharidesandsom of theamino aid resiues arond the ctive ste of lsozyme.All 1.Stereovews Fic. nzye ndof hepyanoylrigs f he ubtrte rereresntd y drkcicle. he acboe ntrge atmsoftheenym o te bacboe ste () negy b crcesfile wthobiqe ins.(A Clclaedloestenrg mniumfo (lc~c4 oud o heaciv areinicte of(GlcNc)4-lctoneboundto te actve sie. (C X-ra strctureof (GcN~c)-lactne bund t the ctivesite xray sructue minimzed
Chemistry:
Pincus et al.
The final binding energy (Eint) of the minimized structure of (GlcNAc)4-lactone is somewhat higher than that of minimized (GlcNAc)4. Part of this difference in energy may be due to the difference in the geometry of the two tetrasaccharides, as can be seen from the following. The geometry of the first three residues of (GlcNAc)4-lactone was based on that of a-GlcNAc (8, 9) even though all GlcNAc residues for substrates and inhibitors are in the d-form, a significantly different geometry from the a-form (7). It should be noted that, when the standard d-geometries were used here for energy minimization of (GlcNAc)3 in the x-ray disposition and conformation, there was a smaller change in the values of the variables after minimization (compare conformers 4 and 5, Table 1) than when ageometries were used for (GlcNAc)4-lactone (compare conformers 7 and 8, Table 1). A number of unfavorable contacts occur in the x-ray structure of (GlcNAc)4-lactone. In particular, close contacts occur (see Fig. 1C) between the aromatic ring of Trp 63 and the CH2 of residue 2 of (GlcNAc)4-lactone, between the aromatic ring of Trp 108 and the methyl group of residue 3 of (GlcNAc)4-lactone, and between the carboxyl group of Asp 52 and the ring oxygen and Ci of residue 4 of (GIcNAc)4-lactone (the residue in the lactone form). A number of less unfavorable contacts also occur between the generated hydrogen atoms of the enzyme and ligand. It is apparently necessary to effect relatively large changes in disposition to relieve them. It is possible that, if we were to use the fl-sugar geometries for the first three residues combined with the 6-lactone geometry for the last residue, at least some of these unfavorable contacts would not exist. It is also possible that the side chains of the active site move to accommodate the sofa form of the D ring. Further, the state of protonation of certain residues, especially Glu 35, is quite important in determining the affinity of (GlcNAc)4-lactone for the enzyme (8). The binding of (GlcNAc)4-lactone to the enzyme at pH 2.6, the pH at which the complex was crystallized, is over 10 times lower than at pH 4.7, and its affinity at this low pH is similar to that of (GlcNAc)4 (8). We are currently inves-
Proc. Natl. Acad. Sci. USA 73 (1976)
4265
tigating all of these possibilities. Using the current x-ray structure of the enzyme (held rigid, here), however, it appears that the D site has no special affinity for the sofa form. As will be demonstrated in a later paper, (M. R. Pincus, S. S. Zimmerman, and H. A. Scheraga, manuscript in preparation), there are other low energy positions, corresponding to the E and F sites, which have a lower affinity for GlcNAc residues than do sites B-D. This work was supported by grants from the National Institutes of Health and from the National Science Foundation. M.R. P. and S.S.Z. were supported by NIH Postdoctoral Research Fellowships.
1. Momany, F. A., McGuire, R. F., Burgess, A. W. & Scheraga, H. A. (1975) J. Phys. Chem. 79,2361-2381. 2. Warshel, A. & Levitt, M. (1976) J. Mol. Biol. 103,227-249. 3. Platzer, K. E. B., Momany, F. A. & Scheraga, H. A. (1972) Int. J. Pept. Protein Res. 4, 201-219. 4. Levitt, M. (1974) in Peptides, Polypeptides and Proteins, eds. Blout, E. R., Bovey, F. A., Goodman, M. & Lotan, N. (John Wiley, New York), pp. 99-113. 5. Pincus, M. R., Burgess, A. W. & Scheraga, H. A. (1976) Biopolymers, in press. 6. Blake, C. C. F., Johnson, L. N., Mair, G. A., North, A. C. T., Phillips, D. C. & Sarma, V. R. (1967) Proc. R. Soc. London Ser. B 167,378-388. 7. Arnott, S. & Scott, W. E. (1972) J. Chem. Soc. Perkin Trans. II 3,324-335. 8. Ford, L. O., Johnson, L. N., Machin, P. A., Phillips, D. C. & Tjian, R. (1974) J. Mol. Biol. 88, 349-371. 9. Johnson, L. N. (1966) Acta Crystallogr. 21, 885-891. 10. Beddell, C. R., Moult, J. & Phillips, D. C. (1970) in Molecular Properties of Drug Receptors, eds. Porter, R. & O'Connor, M. (Churchill, London), pp. 85-112. 11. Imoto, T., Johnson, L. N., North, A. C. T., Phillips, D. C. & Rupley, J. A. (1972) in The Enzymes, ed. Boyer, P. D. (Academic Press, New York and London), Vol. VII, pp. 665-868. 12. Rupley, J. A. (1967) Proc. R. Soc. London Ser. B 167, 416428. 13. Holler, E., Rupley, J. A. & Hess, G. P. (1975) Biochemistry 14, 1088-1094.
