Theoretical Studies on Peptidoglycans. 11. Conformations of the Disaccharide-Peptide Subunit and the Three-Dimensional Structure of Peptidoglycan*

Transcription

1 Theoretical Studies on Peptidoglycans. 11. Conformations of the Disaccharide-Peptide Subunit and the Three-Dimensional Structure of Peptidoglycan* R. VIRUDACHALAM and V. S. R. RAO, Molecular Biophysics Unit, Indian Institute of Science, Bangalore , India Synopsis Possible conformations of the disaccharide-peptide subunit of peptidoglycan (of Staphylococcus aureus or Micrococcus luteus) have been studied by an energy-minimization procedure. The favored conformation of the disaccharide 1-4)-Nacetylmuramic acid (NAG-NAM) is different from that of cellulose or chitin; this disagrees with the assumption of earlier workers. The disaccharide-peptide subunit favors three types of conformations, among which two are compact and the third is extended. All these conformations are stabilized by intramolecular hydrogen bonds. Based on these conformations of the subunit, two different models are proposed for the three-dimensional arrangement of peptidoglycan in the bacterial cell wall. INTRODUCTION Peptidoglycan is a netlike macromolecule that surrounds the plasma membrane of bacterial cells. It imparts rigidity to the cell wall and protects the organism from internal osmotic pressure. Interference with its synthesis or its removal results in the loss of this rigidity and leads to the formation of a fragile protoplast or spheroplast, which under normal hypotonic conditions swells and bursts. This macromolecule essentially contains glycan chains interconnected with short peptides. The disaccharide N-acetylglucosaminyl-P(1-4)-Nacetylmuramic acid (NAG-NAM) is the repeating unit of the glycan strand (Fig. l), and the peptide that is linked to NAM is a tetrapeptide. Prior to the last step of the biosynthesis of peptidoglycan, the peptide is actually a pentapeptide, with the general sequence L-Ala*-y-D-Glu2-L-R3-D-Ala4- ~-Ala~. The residue at position 3 differs from bacteria to bacteria (lysine in Staphylococcus aureus or Micrococcus luteus and diaminopimelic acid in Escherichia coli), and minor variations at position 1 are also observed. Figure 1 summarizes the observed variations in the pentapeptide moiety of peptidoglycan from various bacteria. * Part of this paper was presented at the International Symposium on Biomolecular Structure, Conformation, Function and Evolution held at Madras, India, January 4-7, 19. Biopolymers, Vol. 18, (1979) John Wiley & Sons, Inc /79/ $01.00

2 572 VIRUDACHALAM AND RAO Rj = L-Ornithyl, L-2-L-diomino NH butryl, L-Lysyl, moss0 I or LL diominopimolyl n-$-r3 L (3) to ----_-- - -I -- D - Alonino u3c-c-n o (41 - I CO YH Alonino YH H3C-C-H D (51 Coon _- - --_-- -_ Fig. 1. Disaccharide-peptide subunit of peptidoglycan and the observed variations in the pentapeptide moiety. In recent years the conformation of peptidoglycan has drawn the attention of several investigators, and various models have been In the model of Tipper' the glycan strand was assumed to be in a chitinlike conformation and the pentapeptide in a folded conformation. The loss of the intramolecular hydrogen bond (as compared with chitin or cellulose) between NAG and NAM can be compensated by a hydrogen bond between the carbonyl group of the lactyl residue of NAM and the CH2OH group of NAG. In the model of Keleman and Rogers2 the glycan strand of peptidoglycan was also assumed to be in a chitinlike conformation. A pseudo-p-conformation was proposed for the tetrapeptide, since it cannot assume a purely a-helical due to the occurrence of L and D residues and the unusual y-linkage (Fig. 1) between the D-G~u and the L-LYS residues of the peptide. To obtain a three-dimensional structure, the glycan strands were stacked in two separate parallel planes such that the strands in the two planes are antiparallel to each other and are in alignment. The peptides from the two sets of glycan strands facing each other are crosslinked to form a netlike structure. Extensive hydrogen bonding was assumed between the stacked rings in the glycan portion of the model, and also between the extended peptide chains crosslinking the two stacks. This model

3 THEORY OF PEPTIDOGLYCANS. I1 573 presents peptidoglycan as a fundamentally layered and ordered structure. Recently, Oldmixon et al.3 have considered two models for the disaccharide-pentapeptide. Their models differ from the earlier models mainly in the conformation of the peptide portion. Depending on the conformation of the pentapeptide, one model is termed as extended and the other as compact. In the extended model the pentapeptide is fully extended and projects away from the surface of the glycan chain. The shape of the pentapeptide in the extended conformation resembles a T in which the D-Lac-L-Ala-y-D-Glu portion forms the stem and the crossbridging portion (lysine side chain and D-Ala-D-Ala) forms the crossbar. It does not possess any stabilizing attachments with the glycan strand. In the compact model the pentapeptide is pressed to the surface of the glycan strand, which is stabilized by hydrogen bonds. According to these authors,3 the three-dimensional appearance of the peptidoglycan layer is such that the glycan strands form one plane, over which the crossbridging peptides form another parallel plane, the axis of the glycan strand being perpendicular to the axis of the crossbridge. Thus, if layers of such a model are placed one over the other, there will be alternating layers of peptides and saccharides resisting tension in different directions. Formanek et al4 have also proposed two models, A and B, for the subunit of peptidoglycan. In both these models the pentapeptide is arranged such that all the NH and CO groups are involved in hydrogen-bond formation. Model A differs from B only in the conformation of the lactyl residue. The nature of the stacking of the glycan strands is assumed to be like that of chitin. In all four different models described above, the glycan strand is assumed to be in a chitinlike conformation, and they differ only in the conformation of the peptide moiety. It is well known that the chitin or cellulose structure is stabilized by an intramolecular hydrogen bond between the ring oxygen atom of the ith residue and the hydroxyl group at the C3 atom of the (i + 1)th residue. Since the above type of hydrogen bond cannot form between NAG and NAM, it is unlikely that the glycan strand of peptidoglycan assumes a chitin- or cellulose-like conformation. Moreover, none of these models are substantiated by experiment or theory. Hence, in the present paper an attempt has been made to study the possible conformations of the subunit of peptidoglycan (of M. luteus or S. aureus) by theoretical method^,^ and their arrangement in three dimensions is discussed. Nomenclature, Geometry, and Fractional Charges The numbering of the atoms and the dihedral angles of the disaccharide-pentapeptide are shown in Fig. 2. The atoms used to define the dihedral angles of NAG-NAM are listed in Table I. The definitions of the backbone and side-chain rotational angles of the peptide segment are ac-

4 574 VIRUDACHALAM AND RAO Fig. 2. Numbering of atoms and dihedral angles in the disaccharide-peptide subunit of' peptidoglycan. cording to the IUPAC-IUB nomenclature.6 Clockwise rotation is considered as positive. The coordinates of the atoms of the disaccharide-pentapeptide were generated using standard structural parameters.7-9 The sugar rings were kept in the 4C1 conformation and the peptide units in the transplanar conformation. The fractional charges on the atoms of the disaccharide NAG-NAM were calculated by the molecular orbital The charges for the peptide segment were taken from reported value^.'^,'^ Figure 3 shows the charge distribution in the disaccharide-pentapeptide.

5 THEORY OF PEPTIDOGLYCANS. I1 575 TABLE I Atoms Used to Define the Dihedral Angles for NAG-NAM Dihedral Angle Atoms Defining Angle THEORETICAL Steric Maps It can be seen from models that the CB substituent of muramic acid will hinder the orientation of the preceding NAG but not the succeeding one. Hence the preferred conformation of NAM-NAG will be the same as that of the sugar residues in chitin or cellulose. The detailed analysis was therefore restricted to NAG-NAM. The effect of the lactyl residue on the orientation of NAG, and vice versa, was investigated by constructing various (x,, cpo) steric maps for fixed values of (@, p); (a, I,P) were fixed at all the allowed values of cellobiose. The allowed sets of (@, p) are shown in Fig. 4. While constructing these maps, only atoms up to Co in Fig. 2 were considered. In the second step the disaccharide with one peptide unit (up to C;' in Fig. 2) was considered and (a,#o) maps were constructed for various combinations I,P and xj. (Though the range -" to -" is allowed for xk, -100" and -145' are energetically favored.) The maps corre- sponding to two sets of (@, p, xi) are shown in Fig. 5. In all these calculations the dihedral angles were varied at 10" intervals, and the maps were constructed according to the contact criteria." Potential Energy Calculations The potential energy of the molecule was computed considering nonbonded, electrostatic, and torsional contributions. The form of the functions and the constants used are the ones reported by Momany et al9 The disaccharide-pentapeptide can assume a large number of conformations, since many rotational angles are involved in specifying its conformation. Therefore, a systematic analysis by varying these angles at discrete intervals is not practical with available computer facilities. To simplify the calculations, the molecule was divided into three fragments;

6 576 VIRUDACHALAM AND RAO H OL1 H n Fig. 3. Charge distribution in the disaccharide-peptide subunit of peptidoglycan (in fractions of an electronic charge). the disaccharide NAG-NAM with one peptide unit (up to Cy in Fig. 2) is considered as the first fragment (I), the segment from C$ to C$ as the second fragment (TI), and the remaining portion of the pentapeptide as the third fragment (111). The probable conformations of each of them was studied by the Fletcher-Powell-Davidon minimization procedure.16j7 The selection of the starting conformations of fragment I for minimization was made by combining various allowed values of (@, GS), xi, and (PO, $0). The remaining dihedral angles of NAG-NAM were fixed in the minimum energy conformation as found in the monosaccharides (unpublished results). About 70 conformations were minimized, and most of them lead to three different low-energy conformations (Table 11).

7 THEORY OF PEPTIDOGLYCANS. I1 577 TABLE I1 Some Minimum Energy Conformations for Fragment I S1. No. 8 v x3 m Relative Energy $0 (kcal mol-') For fragment I1 a combination of five sets of (cpl, $1) (corresponding to the five low-energy conformations of N-acetyl "-methyl L-alanyl amidel9 and seven sets of ((a, xi, xl, x:) (corresponding to the first seven low-energy conformations of N-acetyl "-methyl L-glutaminyl amidel9 were considered as the starting conformations for energy minimization. The angle $2 was fixed at -90" and -". Similarly, in fragment 111, five sets corresponding to the low-energy conformations of N-acetyl "-methyl L- alanine amide (sign changed for D residue) were considered for ((~4, $4) and (p5, +5), and combinations of them were minimized. Subsequently, a few low-energy conformations of fragments I1 and I11 1 / f- -" t -60" 1 1 I ' -60" - " O0 ' SO' Fig. 4. Steric map of the disaccharides cellobiose and NAG-NAM. Regions A and B are allowed for cellobiose and A alone is allowed for NAG-NAM; 0, observed conformation of cellulose or chitin.

8 5 VIRUDACHALAM AND RAO 00 Fig. 5. Steric map of the lactyl residue in NAG-NAM for fixed values of J.", xi). Con- tours enclosed by the solid line correspond to J.", xi) = (50, O", -looo) and the dashed line to (60, lo", -145'). The 27a and 27b conformations of the lactyl residue are indicated by the solid and open circles. were selected, and combinations of them were considered as the starting conformations for the pentapeptide. Since the torsional angles of lysine residue (a, $3) are not included in either of the fragments, three different starting values-namely, (-60, -60 ), (-, ), and (-SO0, SO0) -were considered. The energy of the pentapeptide was minimized with respect to backbone angles, fixing the side groups in their favored positions In all, about 100 conformations have been minimized, and only those conformers whose energy is within 3 kcal mol-' are given in Table 111. To study the probable conformations of the disaccharide-pentapeptide, many different low-energy conformations of the pentapeptide were combined with the low-energy conformations of the disaccharide and the energy was minimized. In all, about 50 conformations were minimized, and only the first 20 in the increasing order of energy are given in Table IV. Minimization of each conformation required about an hour of IBM computer time.

9 THEORY OF PEPTIDOGLYCANS. I1 579 RESULTS AND DISCUSSION Conformation of NAG-NAM Figure 4 indicates that the allowed conformations of NAG-NAM are highly restricted compared to cellobiose. Further, the favored conformation of cellulose or chitin (@ N ", $s N -") is disallowed for NAG-NAM, suggesting that the glycan strand of peptidoglycan cannot assume a conformation similar to that of chitin or cellulose. This contradicts the as~umptionl-~ that such a conformation is possible. Energy calculations (Table 11) show that (@, p) favors a value around (50, 0"). It is interesting to note that this conformation is close to the solid-state conformation of acetyl cellobiose.21 The xi angle favors values around -100" or -145" (Table 11), and the preferred values of (a, $0) seem to depend on xi (Fig. 5 and Table 11). When xi N -loo", (a, $0) favors values around (, 40") or (, -"). In the former conformation an intramolecular hydrogen bond between the NH of L-Alal and the CH20H of NAG is possible, and in the latter conformation the CO group of the lactyl residue can form a hydrogen bond with the CH20H of NAG, similar to the one suggested by Tipper.l When xi N -145", (a, $0) favors avalue around (BOO, -160 ), and no intramolecular hydrogen bond is possible. For the two favored values of x$, the 27a and 27b type of conformations assumed by Formanek et al.4 for the lactyl residue are disallowed (Fig. 5). However, the 27b form is very close to the allowed region. Conformation of the Pentapeptide Table I11 shows that the energy of the pentapeptide is minimum when the lysine side chain is fixed at x,: = -60". For xi = 60", the energy increases by at least 3 kcal mol-'. The backbone angles of L-Alal and L-LYS" mostly favor values around (-SO0, ") or (-, ), and D-Ala4 favors (SO", -") or (, -"). The terminal D-Ala residue assumes a conformation around ((~5, $5) N (, "). The *angle of D-Glu residue mostly favors a value around 90". However, when $2 = -, cp2 also changes to ". The remaining dihedral angles are not significantly affected by the change in $2, but the energy of the molecule increases slightly. The angles (xi, x;, xl) favor values around (1" or 60", 1, -"). Conformation of the Disaccharide-Pentapeptide Subunit Table IV shows that the disaccharide-lactyl residue portion of the subunit can assume four different conformations. Three of them are similar to the three low-energy conformations of fragment I (Table 11), whereas the fourth one (conformers 1 and 6 of Table IV) differs in (a, $0); it prefers a value around (,-40"). In this conformation, (M, $1) favors a value around (-170", 60 ), and an intramolecular hydrogen bond between the NH of D-G~u and the CH2OH of NAG is possible. The general features

10 TABLE 111 Starting and Minimized Conformations* of the Pentapeptide for $2 = -90" c Vexb S1. NO. 'pi $1 P2 X:: X% Xl m $3 v4 $4 P5 $5 (kcal mol-') xi = -60' c i;l d U > z $ U $? 0

11 ~ ~~ x:t = a In each set the second row is the starting conformation and the first row is the minimized conformation. Vex is the excess energy over the global minimum

12 SI. $ xh a $ : TABLE IV Starting and Minimized Conformations of the Disaccharide-Pentapeptide 5 Vexh n $1 X: xf xi ca:1 $3 $4 $4 e.5 $S xi (kcalmol- ) c tl : : :1u R il 1.35 F r 1.45 i 1.89 $ u 2.04 s k 0

13 I I a In each set the second row is the starting conformation and the first row is the minimized conformation. 'I V,, is the excess energy over the global minimum I a Y 7.12 'd 7.19 M 'd 2 tl F.c 0 3 z 'J) U

14 584 VIRUDACHALAM AND RAO of the pentapeptide conformation are nearly the same as those described in the earlier section. A cursory look at Table IV shows that among the first 10 conformations, where the energy is less than 4 kcal mol-l, the first four (sets 1-4) are typical conformers, and the remaining six (sets 5-10) are similar to the first four. For example, conformer 5 is nearly the same as 4, conformers 6-9 (or 10) differ significantly from 14, respectively, only in the (ps angle. The change in (p5 affects the orientation of the terminal D-Ala5, but the overall shape of the subunit remains nearly the same. The projections of the first four low-energy conformers are shown in Figs In all these projections the molecule is projected onto the plane formed by the atoms Ci, Oi, and Ci. For clarity, only the backbone atoms are shown. Depending on the orientation of the pentapeptide with respect to the glycan strand, the above conformers can be divided into three broad types: (1) compact conformation 1, (2) compact conformation 2, and (3) extended conformation. Compact Conformation 1 In the compact conformation 1 (Fig. 6), the segment C,U --- CF rises above the plane of the disaccharide (the molecule is viewed from NAG to NAM, keeping the pentapeptide on the right-hand side), and the segment C$ --. CT moves towards NAG. At the C;l atom of lysine, the D-Ala-D-Ala segment and the side chain of lysine move in opposite directions, such that they are placed across the glycan strand from above. The following hydrogen bonds are possible in this conformation: (1) The NH of D-G~u donates its hydrogen to the CH2OH oxygen of NAG. (2) The NH of L-Ala donates its hydrogen to the carbonyl oxygen of the N-acetyl group of NAM. (3) The N,H, at the ~-Glu donates its hydrogen to the carbonyl oxygen of L-Ala (27 type). c? Fig. 6. Projection of conformer 1 of Table IV (compact conformation 1): 0, carbon; 0, oxygen; 8, nitrogen.

15 THEORY OF PEPTIDOGLYCANS. I1 585 Fig. 7. Projection of conformer 2 of Table IV (compact conformation 2). Symbols as in Fig. 6. (4) The NH of D-Ala4 donates its hydrogen to the carbonyl oxygen on the y-carbon of D-G~u (27 type). (5) The NH of D-Ala5 donates its hydrogen to the carbonyl oxygen of L-LYS (27 type). Another hydrogen bond between the carbonyl group of D-Ala4 and the CHzOH group of NAM is also possible when x; = 60". Compact Conformation 2 In the compact conformation 2 (Figs. 7 and 8), the peptide segment C; Cy moves down the mean plane of the disaccharide, and the segment CI -C,* is oriented nearly parallel to the axis of the glycan strand. The crossbridging portion of the peptide (side chain of lysine and D-Ala-D-Ala) is placed below the glycan strand. The axis of the crossbridging portion is approximately perpendicular to that of the glycan strand. Compared to the compact conformation 1, the above conformation has about 1.4 kcal mol-l higher energy. Fig. 8. Projection of conformer 3 of Table IV (compact conformation 2). Symbols as in Fig. 6.

16 586 VIRUDACHALAM AND RAO The conformer shown in Fig. 8 differs from the one shown in Fig. 7 only in the orientation of the crossbridging portion of the peptide; in the former, the direction of the crossbridge is opposite to that of the latter. Both these conformers are stabilized by the following hydrogen bonds: (1) The NH of D-G~u donates its hydrogen to the carbonyl oxygen of the lactyl residue (27 type). (2) The N,H, at the D-G~u donates its hydrogen to the carbonyl oxygen of L-Ala (z7 type). (3) The NH of D-Ala4 donates its hydrogen to the carbonyl oxygen on the y-carbon of D-Glu (27 type). In the conformer shown in Fig. 7, a 27-type hydrogen bond between the NH of D-Ala5 and the carbonyl oxygen of L-LYS is also possible. Extended Conformation Conformer 4 of Table IV has about 2 kcal mol-' higher energy and is an example of the extended conformation (Fig. 9). In this conformation, atoms up to Cg of the peptide assume an extended conformation and move away from the disaccharide. At the C$ atom, the D-Ala-D-Ala segment and the lysine side chain (crossbridging portion of the peptide) move in opposite directions, such that the axis of the crossbridging portion is nearly perpendicular to the axis of the glycan strand. This conformation is stabilized by the following hydrogen bonds: (1) The NH of L-Ala donates its hydrogen to the CHzOH oxygen of NAG. (2) The N,H, at D-G~u donates its hydrogen to the carbonyl oxygen of L-Ala (27 type). (3) The NH of D-Ala4 donates its hydrogen to the carbonyl oxygen on the y-carbon of D-G~u (27 type). CLa Fig. 9. Projection of conformer 4 of Table IV (extended conformation). Symbols as in Fig. 6.

17 THEORY OF PEPTIDOGLYCANS. I1 587 (4) The NH of D-Ala5 donates its hydrogen to the carbonyl oxygen of L-LYS (27 type). In conformer 20 of Table IV the type of hydrogen bond proposed by Tipper1 is possible, but the peptide assumes an extended conformation instead of a folded conformation. However, it is energetically unfavorable. The energy of a few conformations with L-D-bend in the L-Ala-D-Glu segment and the pentapeptide in a conformation similar to that proposed by Formanek et al.4 have also been calculated. But all of them lead to high energy. Hence the first four conformations of Table IV or slight modifications of them seem to be most probable for the disaccharide-pentapeptide. Though the overall shapes of the above conformations appear to be similar to the compact and extended models of Oldmixon et al.,3 they differ significantly in detail and in the hydrogen-bonding scheme. Three-Dimensional Structure of Peptidoglycan Based on the three types of conformations described in the earlier section, two different models are proposed for the arrangement of peptidoglycan in cell walls. Covalently Linked Monolayer Structure In Fig. 10, the repeating unit is assumed to be in the compact conformation 1, and the glycan strands are arranged parallel to one another in the same plane. The crossbridging portion of the peptide (lysine side chain Fig. 10. Covalently linked monolayer structure of peptidoglycan.

18 588 VIRUDACHALAM AND RAO and the D-Ala-D-Ala segment) crosses the glycan strand from above and can be crosslinked to the neighboring strands as indicated. This leads to an infinite sheet in which the glycan strands form one layer and the crosslinked peptides form another layer. Compact conformation 2 or the extended conformation also leads to similar arrangements. When the subunit assumes the compact conformation, the mean plane of the pyranose ring in the above arrangement of peptidoglycan is approximately in the plane of the glycan strands; whereas in the extended conformation, it will be approximately perpendicular. To form a thick peptidoglycan layer in the cell wall it may be imagined that many monolayers are stacked one over the other, as was pointed out by Oldmixon et al.3 The multilayer arrangement may be stabilized by secondary interactions between the layers. Covalently Linked Multilayer Structure Figure 11 shows another arrangement that leads to a covalently linked multilayer structure for peptidoglycan. In this arrangement the glycan strands run through the edges and the axis of a hexagon, and the repeating unit (disaccharide-peptide) assumes the compact conformations 1 and 2 alternatively. The seven strands shown in Fig. 11 form three layers-a, b, and c. The strands (1 - l, 2-2 and 4-4,5-5 ) running on the edges of the longitudinal faces of the hexagon form layers a and c, respectively. The strands running on the diagonally opposite edges (3-3, 6-6 ) and Layer la1 Layer Ibl Layer Icl Fig. 11. Covalently linked multilayer structure of peptidoglycan. The glycan strands in layers a, b, and care distinguished by giving different shadings to NAG.

19 THEORY OF PEPTIDOGLYCANS. I1 589 along the axis (7-7 ) of the hexagon form layer b. The strands in the successive layers are mutually displaced by a distance d/2 (where d is the side of the hexagon) along the diagonal of the hexagonal face. Since the crossbridging peptides come alternately above and below the glycan strand, each of the glycan strands can be covalently crosslinked with four other strands (2 above and 2 below). This is illustrated for the strand 7-7 in Fig. 11. This pattern can repeat to form a covalently linked multilayer of any thickness. Since all the strands in different layers are covalently linked with one another, this arrangement will be very strong and stable and able to withstand the high internal osmotic pressure of the cell. In the above model, the subunits are assumed to be in the compact conformations 1 and 2 alternatively. However, in reality there may be some amount of randomness in their arrangement. This work was partially supported by a grant from the Department of Science and Technology, India. References 1. Tipper, D. J. (1970) Int. J. Systematic Bacteriol. 20, Keleman, M. V. & Rogers, H. J. (1971) Proc. Natl. Acad. Sci. USA 68, Oldmixon, E. H., Glauser, S. & Higgins, M. L. (1974) Biopolymers 13, Formanek, H., Formanek, S. & Wawra, H. (1974) Eur. J. Biochem. 46, Ramachandran, G. N. & Sasisekharan, V. (1968) Adu. Protein Chem. 23, IUPAC-IUB Commission on Biochemical Nomenclature (1970) Biochemistry 9, Arnott, S. & Scott, W. E. (1972) J. Chem. SOC. Perkin Trans. 2, Corey, R. B. & Pauling, L. (1953) Proc. R. Soc. London, Ser. B 141,lO Momany, F. A., McCuire, R. F., Burgess, A. W. & Scheraga, H. A. (1975) J. Phys. Chem. 79, Del Re, G. (1958) J. Chem. Soc., Del Re, G., Pullman, B. & Yonezawa, T. (1963) Biochim. Biophys. Acta 75, Berthod, H. & Pullman, A. (1965) J. Chem. Phys. 62, Pullman, B. & Pullman, A. (1963) Quantum Biochemistry, Interscience, New York, pp Poland, D. & Scheraga, H. A. (1967) Biochemistry 6, Srinivasan, A. R. & Rao, V. S. R. (1975) Pramana 4, Fletcher, R. & Powell, M. J. D. (1963) Computer J. 6, Davidon, W. C. (1959) AEC Research and Development Report, ANL Lewis, P. N., Momany, F. A. & Scheraga, H. A. (1973) Isr. J. Chem. 11, Bhat, T. N. (1976) Ph.D. thesis, Indian Institute of Science, Bangalore, India. 20. Bhat, T. N. & Vijayan, M. (1976) Acta Crystallogr., Sect. B. 32, Marchessault, R. H. & Sundararajan, P. R. (1975) Pure Appl. Chem. 42, Received March 29,19 Accepted June 12,19