Computer modelling approach to study the modes of binding of and fl-anomers of D-galactose, D-fucose and D-glucose to L-arabinose-binding protein Chaitali Mukhopadhyay and V. S. R. Rao* Molecular Biophysics Unit, Indian Institute of Science, Bangalore-560012, India
(Received 10 February 1989; revised 14 March 1989) The modes of binding of ~- and fl-anomers of D-galactose, o-fucose and D-olucose to L-arabinose-binding protein (ABP) have been studied by energy minimization using the low resolution (2.4 ,~) X-ray data of the protein. These studies suggest that these sugars preferentially bind in the ~t-form to ABP, unlike L-arabinose where both ~tand fl-anomers bind almost equally. The best modes of binding of ~- and fl-anomers of D-galactose and D-fucose differ slightly in the nature of the possible hydrogen bonds with the protein. The residues At9 151 and Ash 232 of ABP j~om bidentate hydrogen bonds with both L-arabinose and o-galactose, but not with D-fucose or o-glucose. However in the case of L-arabinose, Arg 151 forms hydrogen bonds with the hydroxyl group at the C-4 atom and the ring oxygen, whereas in case of D-galactose it forms bonds with the hydroxyl groups at the C-4 and C-6 atoms of the pyranose ring. The calculated conformational energies also predict that D-galactose is a better inhibitor than D-fucose and D-glucose, in agreement with kinetic studies. The weak inhibitor D-glucose binds preferentially to one domain of ABP leading to the formation of a weaker complex. Thus these studies provide information about the most probable binding modes of these sugars and also provide a theoretical explanation for the observed differences in their binding affinities. Keywords: L-arabinose-bindingprotein; protein-carbohydrateinteraction;molecularfit; energyminimization
Introduction L-Arabinose-binding protein (ABP) acts as the periplasmic feceptor of the L-arabinose (L-Ara) transport system in Escherichia coli ~. Though the protein exhibits remarkable affinity and specificity towards its substrate, it is somewhat tolerant to modifications at the C5 position in the pyranose ring. Solution studies have revealed that D-galactose (o-Gal) inhibits the high affinity uptake of Larabinose 1. Its higher affinity is attributed to the possibility of formation of an extra hydrogen bond between the C6 hydroxyl group and the protein 2. DFucose (D-Fuc) can also act as an inhibitor, though with lower affinity2'a. Since in the case of ABP-L-Ara complex, the hydrophobic interaction between Trp 16 and the hydrogens at C5 atom of L-Ara seem to be important 4, one might expect that D-fucose with a - C H a group at the C5 position should be more active. Inhibition data further show that D-glucose (D-Glu) is a rather weak inhibitor 5, indicating the importance of the axially oriented - O H group at the C4 position for binding. In order to understand the driving forces and requirements necessary for the recognition of these inhibitors by the protein, a detailed knowledge of the three-dimensional structure of the protein-ligand complexes is required. However, no precise information is available on the modes of binding of these inhibitors to the L-Ara-binding protein either in the solid state or in solution. Hence an attempt has been made to generate the * To whom correspondenceshould be addressed.. 0141-8130/89/040194-07503.00 © 1989 Butterworth & Co. (Publishers) Ltd 194 Int. J. Biol. Macromol., 1989, Vol. 11, August
three-dimensional structures of these complexes using the 2.4,~ resolution X-ray coordinates of the protein available in the Protein Data Bank. Such studies throw light not only on the possible modes of binding of these sugars to the protein but also provide an explanation for the observed differences in their binding affinities.
Method of calculation In order to cut down the computational time the modelling study of the protein-sugar complexes was done in two steps using CCEM method6'V: (1) identification of stereochemically allowed orientations of the ligand in the binding site, followed by, (21 minimization of the conformational energy of the protein-ligand complex to identify the most probable mode of binding of the ligand to the protein. The binding site of the protein was constructed by considering residues from both the P and Q domains of the protein, which are lining the cleft (Table 1). The coordinates of protein atoms were taken from the available X-ray data at 2.4 A resolution, deposited by Quiocho et al. 8. The ligand was generated in the protein binding site using standard geometry 9. The rigid body rotation method 1o was used to place the ligand in the binding site in all the possible orientations using rotational and translational parameters. In the first step contact criteria 11 were used to identify the allowed orientations of the ligand in the binding site ot the protein. In all these allowed orientations a search was
Binding of ~- and fl-anomers of sugars to protein: C. Mukhopadhyay and V. S. R. Rag Table 1 Amino acid residues of ABP considered for the computer modelling of the binding site Val 9 Glu 14 Glu 20 Gin 91 Thr 147 Asn 177 Asn 232
Lys 10 Pro 15 Cys 64 Met 107 Ala 148 Met 204 Gly 233
Gin 11 Trp 16 Val 88 Met 108 Arg 150 Asn 205 Asp 235
Pro 12 Phe 17 Asp 89 Leu 145 Arg 151 Asp 206 Pro 256
Glu 13 Gin 18 Asp 90 Asp 146 Thr 152 Ile 231 His 259
Residues Val 9 to Gln 91 are from P domain, Leu 145 to Asp 235 are from Q domain and the rest are from the connecting strands
made for the possible hydrogen bonds between the protein and the ligand. These allowed orientations were then plotted on three-dimensional maps to show the stereochemically allowed binding regions of the ligand. Although this fitting method identifies all the possible binding modes of the ligand, it is difficult from these studies alone, to identify the most probable mode of binding. To arrive at that, in the next step, the conformational energy of the protein-ligand complex was minimized. Prior identification of the allowed regions avoided an unproductive search of the whole conformational space reducing the computational time drastically. The conformational energy of the complex is calculated by considering the non-bonded, electrostatic, torsional and hydrogen bond contributions. An exoanomeric energy term was included for the sugars. Energy terms for bond length stretching and bond angle bending were not included since a fixed geometry was assumed for the protein and the ligand. The non-polar atoms attached to one or more hydrogens were considered as 'united' atoms, whereas the polar hydrogens were generated using standard geometries. During minimization a distance of 2.6 A between hydrogen and accepter atom was used as the upper limit to identify a hydrogen bond. The minimization procedure treats the translational, rotational and torsional degrees of freedom of the ligand as variables. In addition, the torsional angles of the side chains of the protein residues in the binding site were also treated as variables. The minimization was carried out using Rosenbrock's modified Search method x2. The potential energy function used was:
An...x and Bn... x are specific coefficients for different combination of hydrogen bonded atoms. K® is the height of the n-fold torsional barrier. The values of the various constants used were taken from Nemethy et al. 16, those involving united atoms were taken from Dunfield et al.X7. For calculating the exo-anomeric energy the following expressionX s was used: Vano =0.9(1 - c o s ~)
[for axial OH(l)]
Vano=0.9[1--COS(O--60)]
[for equatorial O H ( l ) ]
• is the O5-C1-O1-H1 torsional angle. The ligand energy included in the total conformational energy of the complex was normalized with respect to the global minimum of the ligand.
Results and discussion The stereochemically allowed orientations determined for ~-D-Gal, ~-r)-Fuc, 7-r)-Glu have been displayed in Figures 1, 2 and 3. Steric diagrams for the fl-anomers have not been shown, since they are quite similar to those obtained for the corresponding ~-anomers. These maps indicate that although the number of allowed orientations are less for t~-Glu, all the three sugars can interact with the binding site in similar regions. The close resemblance of Figures 1 and 2 suggests that D-Gal and r~-Fuc may reach the binding site in very similar orientations. Comparison of Figures 1 and 3 suggests that the change in the orientation of the OH (4) group from axial to equatorial as in D-GIu slightly shifts the allowed regions. However, these studies are not enough to provide any explanation for the observed high and low binding affinities of D-Gal and D-Glu respectively. Conformational energy calculations were carried out using starting points from all the allowed regions (Table 2). It was found that the most favoured orientation of the sugar, in all the cases, occurs in region 1. It is interesting to note that in all the three cases ~-anomer is slightly more favoured and ABPo ~-D-Gal complex has the least energy and ABP-~-D-Glu complex has the highest in their respective most probable
270 U=
{F Aij
2 \ non-bonded pairs
ri..~
Bij ) qiqj 6 + E 332.0 rij , partial Orij charges -180
+
IV
hydrogen 12 bonds rH...X
10 rH...X /
-~ -90
+
~
K2* (1 - c o s n¢)
torsion angles II
Aij and Bij are repulsive and attractive terms. F is a factor having a value of 0.5 for 1-4 interactions and 1.0 for all other type of interactions. For the partial charges of protein atoms (qi, q~) the a and ~r charges were computed using Del Re's and Huckel's method 13,1'~ respectively. The partial charges on the sugar atoms were taken from Yathindra and Rag ~5. A value of 4.0 was used for the dielectric constant (D). For hydrogen bonded atoms ( H . . . X < 2.6 A) the 10--12 potential function was used to compute the energy instead of the 6-12 potential function.
iiiiiiiiiiiiiiiiiiiiii! -"; /~
..'z:'-~;;-S;;;;;-S;-S;;;;:'L-'.-':'f.";;~L-':" .~ . . . . . ~ : : : ~ : ~ : : : : ~ : ~ U
.
.
.
.
.
.
.
.
.
.
.
~::::::e°'''-~
~$$~$~$$$~$$$$~$$$~$~$$ff$$$ff$$$$~
;
~b
~o ~ (d~)
~o
b
~
~e l Steric map representing the allowed regions of e-~Gal. The length of the line joining the mark ~+' and the grid point gives the value of the angle ~. The grid point gives the values of the angles ~ and ~
Int. J. Biol. Macromol., 1989, Vol. 11, August
195
Bindin9 of ~- and fl-anomers of sugars to protein: C. Mukhopadhyay and V. S. R. Rao
270
III
1II
240
-180 ÷
IV
l
?
- 120
-~
I
0 .~5555"--¢....
~ " ~ ~ 5 5 ~ 5 5 5 ~ 5 5 ~ 5 ~ "
==============================
[I
::::::::::::::::::::::::::::::::: ~.~;;~E;~;~6~;;U"
~,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
," . . . . . . . . . . .
0
~ ...........
: ........
120
~'~-r
240
0
0
¢ (deg)
(~ (deg) ~
Figure 2 ~-D-Fuc
Table 2
fl-D-Gal
~-D-Fuc
196
Figure
Steric map representing the allowed regions of
3
270
0
=
Steric map representing the allowed regions of
~-D-Glu
Starting and final orientations of the ligands in the binding site
Ligand
~-D-Gal
180
90
Orientation of ligand
Conformational energy (kcal/mol)
•
®
°d
X
Y
Z
196 (190 195 (195 193 (220 194 (200 191 (210 183 (180 18 (20 17 (10 354 (360 359 (360
86 80 86 90 87 110 87 100 87 110 80 110 88 80 84 80 83 60 77 70
90 90 90 95 101 120 101 100 101 110 244 280 40 30 40 60 225 220 225 210
13.8 14.3 13.8 14.2 13.8 14.2 13.8 14.2 14.3 14.3 13.7 14.3 14.5 14.2 14.5 14.3 14.5 14.3 14.2 14.3
56.3 57.1 56.3 56.6 56.3 56.6 56.3 56.6 56.7 57.1 56.4 57.1 56.5 56.6 56.6 57.1 56.8 57.1 56.6 57.1
53.99 55.4) 53.99 53.6) 54.0 53.6 53.9 53.6 54.4 55.4 54.4 55.4 54.3 53.6 54.2 55.4 54.8 55.4 54.6 55.4
195 (195 190 (190 195 (200 188 (210
82 85 80 90 80 100 86 110
83 90 76 90 81 80 75 100
13.5 13.8 13.6 14.3 13.4 14.3 13.8 14.3
56.2 56.3 56.3 57.1 56.1 57.1 56.4 57.1
53.8 53.9) 53.7 55.4) 53.8 55.4) 53.9 55.4)
-55.8
192 (195 193 (200 208 (220 7 (10 11 (20
87 90 89 100 90 120 118 70 114 80
99 95 97 90 61 110 13 40 18 30
13.8 14.2 13.8 14.3 14.7 14.3 13.7 14.3 13.9 14.3
56.3 56.6 56.3 57.1 56.5 57.1 56.4 57.1 56.5 57.1
53.9 53.5) 53.9 55.4) 54.1 55.4) 53.9 55.4) 54.1 55.4)
-57.7
Int. J. Biol. M a c r o m o l . , 1989, Vol. 11, August
- 59.6 - 59.5 - 59.0
-58.8 - 47.9
- 42.9 - 4 1 .8 - 4 1 .5 - 40.6 - 40.0
- 5 5 .3 -54.2 - 49.5
-57.5 - 54.5 -
43.8
- 42.7
Binding of ~- and fl-anomers of sugars to protein: C. Mukhopadhyay and V. S. R. Rao Table 2--continued
Ligand
fl-D-Fuc
~t-D-Glu
Orientation of ligand •
O
•
X
Y
Z
185 (190 183 (180 7 (10
93 110 80 100 69 60
110 110 245 280 204 200
14.3 14.3 13.7 14.3 14.7 14.3
56.7 57.1 56.3 57.1 56.9 57.1
54.6 55.4) 54.4 55.4) 54.4 55.4)
-- 42.6
194 (210 193 (190 193 (200
77 110 76 90 75 110
86 100 86 100 87 90
13.7 14.3 13.7 13.8 13.6 14.3
56.2 57.1 56.2 56.3 56.2 57.1
54.1 55.4) 54.1 53.9) 54.0 55.4)
- 44.0
202 (200 178 (190 160 (180 360 (350 15 (10 30
70 90 121 110 124 120 242 220 49 50 24 30 322 320 289 300
14.7 14.3 13.6 14.3 14.2 14.7 13.9 14.3 14.4 14.2 14.2 14.3 14.0 14.3 14.5 14.3
56.6 57.1 56.6 57.1 56.8 56.6 56.5 57.1 56.5 56.6 56.6 57.1 56.8 57.1 57.9 57.1
54.7 55.4) 54.5 55.4) 55.5 54.7) 53.6 55.4) 54.3 54.5) 54.5 55.4) 53.6 55.4) 55.1 55.4)
-- 52.0
180 (190 128 (170
92 100 84 90 92 90 100 80 86 80 66 70 112 120 130 110
204 (200 203 (190 204 (180
91 100 91 90 91 90
67 70 68 80 70 110
14.7 14.7 14.6 14.3 14.7 14.3
56.6 56.6 56.6 57.1 56.6 57.1
54.8 54.7) 54.8 55.4) 54.7 55.4)
-- 51.0
(20
fl-D-GIu
Conformational energy (kcal/mol)
- 34.7 - 29.1
-- 43.4 -- 43.1
-- 50.2 -- 47.4 -- 40.3 -- 39.8 -- 38.8 -- 32.45 -4.1
-- 50.0 -49.3
Note: Values in brackets indicate the starting orientations
binding orientations, suggesting that ABP may form a strong complex with ~t-D-galactose and a weak complex with or-o-glucose. This is in agreement with the solution studies 5. The stereoprojections of the most probable binding orientations of ~-D-Gal, ~t-D-Fuc and ~-D-Glu are shown in Figures 4, 5 and 6. The possible hydrogen bonds are listed in Table 3. It is seen from Table 3 that ~t-D-Gal can form more hydrogen bonds with the protein than ct-o-Fuc and ~-OGlu. The best orientation and position of each of these sugars in the binding site (Table 3) differ slightly from each other. Such changes, however, lead to significant differences in the formation of possible hydrogen bonds between the sugar and the protein. The O H ( l ) forms hydrogen bonds with Lys 10 and Asp 89 in the case of ct-o-Gal and ~t-o-Glu whereas in the case of ~-o-Fuc it can form only with Asp 89. In all these cases OH(2) can form a hydrogen bond with Lys 10. In the cawe of ~t-t~Gal, OH(3) can form two hydrogen bonds with Asn 205 and Asn 232, in the case of ~-D-Fuc it forms only with Asn 205 and in ~-D-GIu it may not form any hydrogen bond with the protein. OH(4) in both ~t-D-Gal and ~-DFuc can form two hydrogen bonds with Arg 151 and Asn 232. In the case of ~t-D-Glu, which has an equatorial
OH(4) group, the possible hydrogen bond is with Asp 89. 0 5 may not form a hydrogen bond with the protein in any of the three complexes whereas OH(6) in ~-D-Gal forms a hydrogen bond with Arg 151. It is also interesting to compare the binding modes of ~D-Gal and ~-D-Fuc with that of fl-L-Ara 7, which differs in the nature of the substituent only at the C5 atom. The calculated conformational energies of the complexes of ABP with ~-t~-Gal and fl-L-Ara are quite similar (--59 kcal/mol). The possible hydrogen bonding schemes are also similar although a few differences exist. In both the complexes the planar side chains of Asn 232 and Arg 151 participate in unusual bidentate hydrogen bonds with the sugars. Asn 232 can form hydrogen bonds with OH(3) and OH(4). Arg 151 in fl-L-Ara-ABP complex can form hydrogen bonds with OH(4) and 0 5 , whereas in the case of ~-D-Gal it can form with OH(4) and OH(6). Further, in the complex with ~t-D-Gal, Lys 10 forms an extra hydrogen bond with OH(l). The other possible hydrogen bonds between the sugar and the protein are the same in both complexes (Table 3). This perhaps explains the observed similarity in binding affinities of both D-Gal and L-Ara. In the case of ~t-D-Fuc, however, the - C H a group at C5 position causes more
Int. J. Biol. Macromol., 1989, Vol. 11, August
197
Binding of ~- and fl-anoraers of sugars to protein: C. Mukhopadhyay and I/. S. R. Rao
"1 4.-~
"1
'~,.7
'~
F~g~re 4 Stereoproj~tion of the most probable mode of binding of e-~-Gal to ABP. Broken lines indicate the hydrogen bonds between the sugar and the protein. Details of the hydrogen bonds are given in Table 3
~1
~1
1~1
4-7
! ! t !~2
7
~o ~c~4
~
0
Figure 5 Stereoprojection of the most probable mode of binding of ~-D-Fuc to ABP drastic changes in the possible hydrogen bonding scheme. The multiple hydrogen bonding scheme proposed between Arg 151, Asn 232 and either fl-L-Ara of a-DGal may not be possible in the case of ~-t~-Fuc. In the latter, Arg 151 and Asn 232 can form hydrogen bonds with OH(4) only. Thus the comparison of the best possible binding modes of ~-D-Gal and ~-D-Fuc with that of /3-L-Ara (Table 3) clearly shows that the substituent at C5 atom of the ring may not be accommodated in the energetically most favoured orientation of fl-L-Ara. Both ~t-D-Gal and ~-t)-Fuc assume slightly different orientations from that of fl-L-Ara in the
198
Int. J. Biol. Macromol., 1989, Vol. 11, August
binding site. Such a change weakens the possibility of formation of hydrogen bond between 0 5 and Arg 151. However, c~-D-Gal, with a ~CH2OH group at C5 position has the potential to interact favourably with the guanidium group of Arg 151 and there is the possibility of formation of a hydrogen bond between OH(6) and Arg 151. For ~-D-Fuc, on the other hand, this possibility does not exist because of the presence of the non-polar CH 3 group at C5 position, ct-t~-Fuc prefers an orientation in which the hydrogen bond between Asn 232 and OH(3) is also not possible, whereas that such a hydrogen bond is possible in both ABP-~-r~-Gal
Binding of ~- and fl-anomers of sugars to protein: C. Mukhopadhyay and V. S. R. Rao
~1 ~1
~/~1..~ 1
\ Figure
Table
6
3
Stereoprojection of the most probable mode of binding of ~t-D-Glu to ABP Comparison of the most probable modes of binding of various sugars to ABP
Ligand
Orientation of ligand •
0
q~
X
Y
Z
Conformational energy (kcal/mol)
~-D-Gal
196
86
90
13.8
56.3
53.9
- 59.6
OH(I) - L y s I0, Asp 89 OH(2) - Lys 10 OH(3) - A s n 205, Asn 232 OH(4) - Arg 151, Asn 232 OH(6) - Arg 151
~-D-Fuc
192
88
99
13.8
56.3
53.9
-57.7
OH(l) - Asp 89 OH(2) Lys 10 OH(3) - Asn 205 OH(4) - Arg 151, Asn 232
~-D-Glu
202
92
70
14.7
56.6
54.7
-52.0
OH(l) - L y s 10, Asp 89 OH(2) - Lys 10 OH(4) - Asp 89
fl-D-Gal
195
82
84
13.5
56.2
53.8
-55.8
OH(I) - Lys OH(3) - A s n OH(4) - Arg OH(6) Arg
fl-D-Fuc
194
77
86
13.7
56.2
54.1
-44.0
OH(l) Lys 10 OH(2) - Lys 10 OH(3) - Ash 205, Asn 232
fl-D-Glu
204
91
67
14.7
56.6
54.8
- 51.0
OH(I) - Lys 10 OH(2) - Lys 10 OH(4) - Asp 89
fl-L-Araa
196
88
96
14.2
56.6
53.5
- 59.2
O H ( l ) - Asp OH(2) - Lys OH(3) - A s n OH(4) - Arg 05 - Arg
Hydrogen bonding scheme
10 205, Asn 232 151, Asn 232 151
89 10 205, Asn 232 151, Asn 232 151
"Ref. 7 a n d ABP-fl-L-Ara complexes. This p e r h a p s explains the e x p e r i m e n t a l l y o b s e r v e d low p o t e n c y of ~-D-Fuc as an i n h i b i t o r c o m p a r e d to ~t-o-Gal. Table 3 also shows t h a t a c h a n g e in o r i e n t a t i o n of the
O H ( 4 ) g r o u p from the axial to e q u a t o r i a l position, as in the case of a-D-glucose brings significant changes in the h y d r o g e n b o n d i n g scheme c o m p a r e d to b o t h fl-L-Ara a n d a-D-Gal. It is interesting to n o t e that, in the best possible
Int. J. Biol. M a c r o m o l . , 1989, Vol. 11, A u g u s t
199
Binding o f ~t- and fl-anomers o f sugars to protein: C. M u k h o p a d h y a y and I/. S. R. R a o
binding mode, ~Z-D-Glu forms hydrogen bonds with the residues of P domain only, i.e. Lys 10 and Asp 89, whereas the residues from the Q domain, i.e. Arg 151, Asn 205 and Asn 232 which form hydrogen bonds with the other sugars do not form any hydrogen bond in this complex. However, the preferential binding of ~-r~glucose to only the P domain clearly suggests that this sugar cannot hold the two domains tightly together which is very important for the functioning of the protein. This should lead to the formation of an unstable complex. In the next probable binding orientation of ~-D-GIu the total conformational energy increases by about 2 kcal/mol. Here O H ( l ) forms hydrogen bonds with Lys 10 and Asp 89, OH(2) forms with Lys 10, OH(3) and OH(4) can form hydrogen bonds with Asn 205 and Asn 232 respectively, Even in this mode of binding, the sugar does not form any hydrogen bond with Arg 151. These observations may perhaps explain the weaker affinity of Ct-D-Glu to ABP compared to fl-L-Ara, Ct-D-Gal or a-DFuc. Table 3 also shows that the conformational energies of the complexes with the fl-anomers are comparatively higher than the corresponding ~-anomers. These differences are least in the case of D-Glu and maximum in the case of o-Fuc. In the case of o-Fuc, the difference is as high as 13 kcal/mol, suggesting that the protein may preferentially bind to the ~-anomer only. In the case of oGal, the energy difference is 3.8 kcal/mol. It is known that in aqueous solution D-Gal exist in ~,~--fl equilibrium 19, the fl-anomer predominating by a factor of 2. Hence a part of the conformational energy of the complex with aanomer may be offset by the predominant occurrence of the fl-anomer in solution. This suggests that ABP may bind to both the ~- and fl-anomers of D-galactose. In conclusion the present studies using 2.4 ~ resolution data of ABP, provide information about the most probable mode of binding of D-Gal, D-Fuc and D-Glu to the protein
200
Int. J. Biol. Macromol., 1989, Vol. 11, August
and also a theoretical explanation for the observed differences in the binding affinities of these sugars.
Acknowledgement The work described herein was partially supported by the Department of Science and Technology, New Delhi, India.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Brown,C. and Hogg, R. W. J. Bacteriol. 1972, 111,606 Miller,D. M. III, Olson, J. S., Pflugrath, J. W. and Quiocho, F. A. J. Biol. Chem. 1983, 258, 13665 Parsons,R. G. and Hogg, R. W. J. Biol. Chem. 1974, 249, 3602 Quiocho,F. A. and Vyas, N. K. Nature 1984, 310, 381 Newcomer,M. E., Miller, D. M. III and Quiocho, F. A. J. Biol. Chem. 1979, 254, 7529 Rao, V. S. R., Biswas, M., Mukhopadhyay, C. and Balaji, P. V. J. Mol. Struct. 1989 (in press) Mukhopadhyay,C. and Rao, V. S. R. Int. J. Biol. Macromol. 1988, 10, 217 Newcomer,M. E., Gilliland, G. L. and Quiocho, F. A. J. Biol. Chem. 1981, 256, 13213 Arnott,S. and Scott, W. E. J. Chem. Sot., Perkins Trans. 1972,2, 324 Goldstein, H. in 'Classical Mechanics', Addison-Wesley, Massachussetts, 1950, p. 107 Ramachandran,G. N. R. and Sasisekharan, V. Adv. Prot. Chem. 1968, 23, 283 Rosenbrock,H. H. Computer J. 1960, 3, 175 Del Re, G., Pullman, B. and Yonezawa, T. Biochim. Biophys. Acta 1963, 75, 153 Polland,D. and Scheraga, H. A. Biochemistry 1967, 6, 3791 Yathindra,N. and Rao, V. S. R. Carbohydr. Res. 1972, 25, 256 Nemethy,G., Pottle, M. S. and Scheraga, H. A. J. Phys. Chem. 1983, 87, 1883 Dunfield,L. G,, Burgess, A. W. and Scheraga, H. A. J. Phys. Chem. 1978, 82, 2609 Prakash,S. PhD Thesis, Indian Institute of Science, Bangalore, India, 1980 Rao, V. S. R., Vijayalakshmi, K. S. and Sundararajan, P. R. Carbohydr. Res. 1971, 17, 341