.I. Mol.

Hid.

(1978)

119. 329-351

An Analysis of the Structure of Triose Phosphate Isomerase and its Comparison with Lactate Dehydrogenase 1). (1. PHILLIPS.

I)p~.xrtmend

M.

J. M. THORNTON

r all

Il. C. PHILLIPS

342

ET

AL.

strands have a similar twist (e.g. the average a,, for the prealbumin strands is 194”). The rotation angles0 do not suggestany specific correlation. In the TIM&e-LDHase comparisons(Fig 5 ; Table 6), unit ABC in TIMase is most similar to ABC of LDHase (r.m.s. deviation = 3.21 A) and EFG of TIMase is most similar to DEF of LDHase (r.m.s. deviation = 3.00 A). However, there are other @a)&? units in TIMase which have similar r.m.s. deviations, e.g. GEIA in TIMase with DEF in LDHase. Thus the structural similarity of the first two pairs cannot be considered remarkable and could simply be the result of convergence to a similar favourable conformation. However, the alternative explanation of a single, ancestral gene coding for a pair of (fia).&i units cannot be discounted. The divergence of two such units could have produced ABC-DEF in LDHase and ABC-EFG in the TIMase cylinder. Such a schemerequires a large insertion in TIMase (of approx. 40 amino acids) to give the C helix and the D pa unit. A similar insertion has been postulated in the evolution of the NAD binding domain of GPDHase (Rossmann et al., 1974; Ohlssonet al., 1974). There is currently no clear evidence to distinguish between these two possibilities. The result of the LDHase-ADHase comparison for unit ABC (r.m.s. deviation = 2.46 A), is lower than any of the 44 TIMase-LDHase and TIMase-TIMase comparisons. Thus the similarity of this unit in LDHase-ADHase is potentially significant. However, for the LDHase-ADHase comparisons for unit DEF the r.m.s. deviation (5.50 8) is greater than 31 of the 44 comparisonswith TIMase. Therefore this structural similarity cannot be considered significant and is to be expected between substructures having a similar, favourable fold.

5. Sequence Studies (a) Method (i) Internal comparisons A complete, quantitative search for related sections within the sequenceof TIMase was performed using the method of McLachlan (1972a). A section of sequence of chosenlength is aligned with another section and a score of relatednessis calculated by summing the values of the relatednessbetween each equivalent pair of amino acids. Four different measures(listed below) of the relatednessbetween pairs of amino acids were used as we considered no single measuretotally superior to the others. The first three were taken from the literature, the fourth is original. (1) The minimum mutation distance (Fitch, 1966) which representsthe smallest number of nucleotides which must have altered to change the coding from one amino acid to another. (2) A scorerepresenting the chemical similarity between amino acids (McLachlan, 1972a). (3) A measure based on the observed frequency of amino acid substitution at corresponding points in families of ancestrally related proteins (McLachlan, 1971). (4) A score basedon a simple measureof hydrophobicity (seeTable 7).

STRUCTURE

OF

TRIOSE

PHOSPHATE

TABLE Hydrophobicity

ISOMERASE

343

7 scale

HL

0

1

4

6

HS

1

0

2

4

GS

4

2

0

I

CL

6

4

1

0

Lim (1974a,b) has shown that there are patterns of hydrophobic and hydrophilic a-helices and ,%strands. These patterns may have persi&ed during evolution and measure of relatedness between residues was used. Lim’s classification of side-chains and the above scores between the different classes of residues chosen arbitrarily. H,, large hydrophobic side-chains: Cys, Ile, Leu, Met, Phr, Trp, Tyr, Val. Hs, small hydrophobic side-chains: Ala, Pro. GL, long hydrophilic side-chains: Arg, Gln, Glu, His, Lyn. Gs, short hydrophilic side-chains: Am, .4sp, Ser, Thr. Gly is assigned to Gs.

side-chains in so the above was adopted

In each measure a low score indicates closely related amino acid residues. Every section of sequence is compared with every other section in the protein, provided the same residue number is not in both sections. The results of the comparison were output from the computer as a square matrix of the TIMase sequence against itself. The ijth element of the matrix represents the score for comparing two sections whose central residue numbers were i and j. Comparisons whose sequence comparison scores were lower than a given threshold, and therefore are closely related, were marked on this matrix. Thus marks on the matrix at (i.j), (i + 1, j 7 1) , . . (; + k, j + k), which would appear as a line parallel to the main diagonal of the matrix, indicate that residues i to i -t k are closely related to j to j + k. Four thresholds were used in each comparison, and they were chosen so that the cumulative probability of obtaining a score as low as that by chance, was 1 x 10e3, 3 x 10V3, 1 x 10e2 and 3 x 10m2. In order to detect both short and extended regions of similar sequence, comparisons were made for sections of length 31, 11 and 5 residues. There is some evidence from the bacterial ferredoxins that genetic sequence repeats are more easily detected in prokaryotes than in eukaryotes (McLachlan, 1972a). Thus the procedure was applied both to the sequence of chicken (Banner et al., 1975) and that of the thermophile Bacillus stearothemophilus TIMase (Artavanis, 1974; Dr J. I. Harris, personal communication). A problem associated with this search procedure is that every possible overlap is performed and it is difficult to fmd weak repeats amongst the repeats which are due to chance. However, the structural studies determined equivalent residues forming the /3u units, and, if there were a common genetic origin for these units, one may find significant sequence similarities between these pairs of aligned amino acids. Thus, the comparison scores were calculated between the sequences of the structurally equivalenced pairs of residues. The importance of this approach is emphasised by the fact that the sequence similarities between different dehydrogenases were found only when the structurally equivalenced residues were aligned (Ohlsson et al.: 1974).

I).

344

(ii) External

C.

PHILLIPS

ET

AL.

comparisons

The same method that was applied to the search for internal repeats in TIMase (i.e. McLachlan, 1972a) was used to compare the sequence of chicken TIMase with dogfish LDHase (Eventoff et al., 1977). I n addition, the comparison scores were calculated between the sequences of the residues which were superposed in the @c~)s-fi overlaps of TIMase with LDHase. Sequence comparisons were made between each pair of p-strands that were overlapped, between each pair of a-helices, and between each pair of (/3a)z-p units. (b) Results and discussion (i) Internal

within

comparisons

TIMase

The presence of significant repeats would be indicated by a higher occurrence of closely related sections (i.e. low scores) than expected by chance. This can be expressed by S(P), S(P) where

observed

=

P is the cumulative

cumulat)ive

frequency

Measure

sequence

of relatedness

Minimum mutation Observed substitution Chemical similarity Hydrophobicity Values of S(P) B. atearothermophilus

of a low score

of obtaining TABLE

Results of internal

frequency P

that

score by chance.

Repeats

8

comparisons

in

triose

Chicken TIMase, length of sections 31 11 5

phosphate

H. steam. TIMase, length of sections 31 11 5

0.6

1.0 1.3 0.9

1.7 1.1 2.1

3.4

3.4

“4

1.0

0.4

0.4

0.5

0.1 7.6

for P 21 1 x 10e3 are given for sequence (stearo.) TIMase sequence.

isomeruse

comparisons

1.2 1.6 1.1 1.1 within

2.0 1.4 1.1 1.1 the chicken

and

which might be significant would be indicated by S(P) > 1.0, for low values of P. Table 8 gives the values of S(P) for the internal comparisons in the chicken and B. stearothermophdus TIMase sequences for P around 1 x 10e3. Similar results were obtained for the other thresholds. Table 8 shows that the majority of runs gave values of S(P) around or below 1.0 indicating that the number of closely related sections were of the order expected by chance. Only the results with the chicken sequence with the hydrophobic score gave a significantly higher value of S( P) (between 3.4 and 7.6). This aligned residues 77 to 114 with 105 to 149 (N.B. 105 to 114 is common); this overlaps CUD, with D,eE,. This overlap is not significant as searches for internal repeats in random sequences also revealed regions of around 44 residues that were as closely related. -4s the other runs did not show these sections to be closely related, and because of the occurrence of residues common to both of the overlapped sections, this is probably the result of a

STRUC!TURE

OF

TRTOSE

PHOSI’H.~TE

ISONERASE

345

TABLE I) Results of sequence comparisons

Measure

of relatedness

Minimum mutation Observetl substitution Chemical nimilarit~ Hydrophobicit) Valws

of S(P)

*w

given

for

P -

between TlMase

and LDHase

TIMase-LDHase, length of sect,ions 31 11 5 1 .:I 1 .ll I.1 0.4

I.0

1.2

1.L’ I.1 1.4

I,:! 1.7 1 .:t

1 S 1OF”.

similar pattern of hydrophobic and hydrophilic groups forming these substructures (Lim. 1974a,b) rather than an indication of a common genetic origin. The sequence comparisons between residues of the /3a units that were superposed in t,hc structural comparisons did not reveal any closely related sequences. There is no strong correlation between units that were found to be structurally closely related and those with the greatest similarity in their sequence. Thus the sequence comparisons within TTMase have not provided evidence for gene replication. (ii)

External

comparisons

with LDHase

The values of S(P) obtained from the comparisons of chicken TIMase with dogfish LDHase are given in Table 9. None of the values are above 1.8 and so this result, by itself, does not suggest any significant overlap. In addition, the comparison scores hetwcen the amino acids of the @a)~-/3 units which were superposed in the structural comparisons did not find a significant similarity. However, the sequence comparisons of t,he structurally equivalent residues in individual strands and helices revealed potentially significant similarities. The lowest score with both the minimum mutation distance and the observed substitution measure of similarity were for strand g in TlMase with strand f in LDHase (e.g. mutation distance = 050 bases per codon). In addition, excluding the above sequence similarity, only four other pairs of strands had closer sequence similarities than that found between strand c in TIMase and strand c in LDHase in which the mutation distance was 0.80 bases per codon. Each of these two pairs of strands (g/f and c/c) formed part of the (,3a)2-/l units that were found to have the closest structural similarity. As only six out of the 48 comparisons l&wren individual strands correspond to the overlap of strands in the (/3a)2-p units ~\hich were structurally closest. this suggests a sequence similarity between these (/3a)2-/3 units. In particular, the similarity of strand g in TIMase and strand f in LDHase is due t)o a common tripeptide, Arg-He-Ile. In a sequence comparison hetwccn TIMase and LDHase only one in 5000 pairs of tripeptides would be identical 1)~ chance. Thus it is potentially significant that bhese three residues in TIMase and LDHasc both had the same amino acids and were equivalent structurally, even though a charged residue is frequently found at the beginning of an internal @strand and Ile is commonly found in sheets (e.g. Chou & Fasman, 1974a,b; Lim, 1974a,b). .A further search was made for common tripeptides between the TIMase and the

346

D.

C. PHILLIPS TABLE

Common

tripeptides

ET

AL.

10

in TIMase and

TIMase First residue in tripeptide or tetrapeptide

LDHase Order from N terminus

32 51 57 83 90 103 108 109 117 121 152 154 163 168t 205 218 236 t Common

LDHme

First residue in tripeptide or tetrapeptide

1 2 3 4 5 6 7 x 9 10 11 12 13 14 15 16 17

Order from N terminus

151 100 76 281 190 106 7 19% 257 180 283 275 236 248t 169 210B 307

5 3 2 15 8 4 1 9 13 7 16 14 11 12 6 10 17

tetrapeptide.

TABLE

Sequence alignments Comparison no.

set

between TIMaee Average minimum change/residue

and LDHase base

Structurally equivalenced atoms

1 2 3

1.10 1.00 1.00 1.04

No Yes Yes

4 5 6 7

NO

4$5+6+7

1.10 1.06 1.29 1.00 1.13

8 9 10 11 8+9+10+11

1.18 0.75 1.00 1.18 1.06

NO NO

1.10 1.06

NO NO

1+2+3

1+2+3+4+5+6+7 1+2+3+8+9+10+11 The comparison are equivalenced

11

set refers to the alignment in the sequence alignment

NO

Yes NO

Yes NO

NO No No

in Fig. 6. The Table shows whether were also found to be structurally

the residues equivalent.

that

STRUCTURE

OF TRIOSE

PHOSPHATE

ISOMERASE

347

LDHase sequences by use of the method of McLachlan (1972a). Sixteen common tripeptides and one common tetrapeptide were found, but as about 80,000 pairs of tripeptides were compared this number would be expected by chance alone. However, the locations of the common tripeptides and tetrapeptide along the two polypeptide chains are not random (see Table 10) but some of the peptides appear to lie in the same order along the two chains. The correlation between the orders along the chains is given by Spearman’s rank correlation coefficient p. p-l-

6x(X,

-

n(n2 -

Yi)” -> 1)

where n is the number of common pairs of peptides, Xi the order along the polypept.ide chain of a peptide in TIMase and Y i is the order of the corresponding peptide in LDHase (Seigel, 1956). The correlation coefficient is 0*55 and the probability of observing this correlation by chance is less than 5:/o, which is significant. Finally, the results from all the sequence comparisons were used to suggest possible consecutive alignments between parts of TIMase and LDHase. Table 11 and Figure 6 show 11 sets of related sections of residues. Only some of these sections (sets 2, 3, 5 and 7) align residues that were structurally equivalent. The other sets were chosen so that there was a close sequence relationship between either parts of (/3ct)&3 units (sets 1, 4 and 6) or parts of the active sites of TIMase and LDHase (sets 8, 9, 10 and 11). Sets 1, 2 and 3 overlap strands a, b and c in TIMase with strands a, b and c in LDHase. Sets 4, 5, 6 and 7 overlap strands e, f and g and part of helix F, in TIMase with strands d, e and f and helix F, in LDHase. There are two ways of combining these sets: either 1, 2, 3 with 4, 5, 6, 7 (average minimum base-change = 1.10) 01 1, 2, 3 with 8, 9, 10, 11 (average minimum base-change = 1.06). These values for the minimum base-change are comparable with those reported for the sequence comparisons between the coenzyme binding domains of the dehydrogenases (Rossmann et al.. 1974). Thus there is some weak evidence from sequence comparisons that ABC-EFG in TIMase is related to ABC-DEF in LDHase. ,4 major problem is to assess the significance of these values for the average minimum base-change, considering that structurally similar regions are compared. Dickerson (1971) has estimated that an average minimum base-change of 1.24 can be expected in a comparison between two sequences where corresponding residues in each sequence are either both buried or both exposed to solvent. Both the values for the TIMase/LDHase. alignments (Table 11) and the values for the dehydrogenase comparison are below 1.24 bases per codon and, by this criterion, indicate related sequences. This figure of 1.24 bases per codon does not consider either the preferences for certain residues to be found in a-helices or b-strands (e.g. Chou & Fasman. 1974a,b: Lim, 1974a,b) or the effect of the introduction of gaps (Haber & Koshland. 1970). Consideration of all these factors would be expected to reduce the average minimum base-change between unrelated sequences forming similar structures below l-24, and so reduce the significance of thr resuks for t’he TIMase-LDHase sequence comparison.

6. Conclusion The sequence and structural studies provide no definitive evidence of gene replication within TIMase although there is an overall repeating fold of the eight /?a and the eight pa/? units. Tn all units the helix lies close to the p-strand and runs approximately

348

(1)

(4)

(5)

1-l. C. PHILLIPS 2

4

TIMase

I’

R

K

F

LDHase

Y

N

0 K

I

LDHase

H

T

A

TIMase

G

L

LDHase

K

1

TIMase

0 I

V

G

G

K

I

V

S

G

G

V

I

A

L

v

$00

A

I)

N

V

K

I

0 V

0 KHSPNC

N

K

ILXV@@@ 132a

121

TIMase

A

T

P

Q

Q

A

Q

LDHase

N

P

V

D

V

L

TYVAWKLS

14” Bs

E

V 0

IW

H

E

K 0

L 0

R

G 0 G

W L

L P 1.56

209

TIMase

Q

S

R

1

I

Y

LDHase

11

H

0 R

0 I

0 I

G

85

(8)

140

r5e

aF*

203 (7)

132b

UF,

176

(6)

.4 L.

12

@I

F

I’

E’T

S

Pi’

TIMase

D

I

LDHase

V Y 81

1oc

GAA~~VILG~00RR00FGESl) 0.0 AGSKLVV@@@G

A@@& P-d

EG103 106

109

STRUCTURE 121 (9) TIM&se L G 0 0 LDHase L G 180

OF TRIOSE V 0 V

I

Be A@1

H

S

C

I’HOSPHATE @@aL 0 S G V

ISORIERASE 131 I>

L

W IQ

V 191

aF,

168

(11)

TIM&se

W

:149

A@GTGKT

0.0 LDHrtve W A@GL 248

A

T

P

Q

Q

A

181

Q

E

V

M

K

N 264

l S

VADLAETI aG,

FIG. 6. Sequence alignmant~s between TIMase and LDHae. In each alignment the 2 sequences are continuous. The one-letter code for amino acids is used (H&hem. J. (1969) 113, l-4). Residues that form a-helices or @&ands have, respectively, a wavy or a straight line above them. A circle around a residue indicates that it forms part of the active site. Dots between the 2 sequences indicate identical residues. The information for TIMase is from Banner et al. (1975). The sequence for LDHase is from Eventoff et crl. (1977) and the “old” numbering system is used so that residues are numbered as in Adams et nl. (1973). The details of the LDHasc secondary structure are from Holbrook et nl. (1975).

antiparallel to the strand direction. In addition. each ,%$? unit has the usual right hand (Sternberg & Thornton, 1976; Richardson, 1976): if one views a given strand from the N terminus and the connecting helix lies above. the next strand lies to the right of the previous one. However, from the schematic diagrams of protein structure in Sternberg & Thornton (1977), it can be seen that there are 36 substructures in which one or more helices (but no strands) connect two parallel, adjacent ,&strands. In all but one of these substructures, we find that there is a helix which runs approximately antiparallel to the strand direction. It is very unlikely that all these pu/? units have evolved from a common ancestor with a /3c$? fold. The similarity in the overall conformation is most probably the result of a fold which is energetically and/or tiynamically favourable and which forms a building block of protein structure (i.e. a super-secondary structure). In the absence of internal repeats with a greater similarity than those between the same type of super-secondary structures. one cannot establish that TlMase has evolved by gene replication from a structure with four or less /3x nnits. ?‘hc structural comparisons between (/3a)2-/3 unit.3 of TIMase and LDHase show a closer similarity than any observed within TIMase. Again the structural similarity is bet,ween right-handed pap units (see above). Units ABC and EFG in TIMase are particularly similar to units ABC and DEF in LDHase. However, the r.m.s. deviations are not markedly lower than those obtained from other TIMase-LDHase comparisons. several resemblances in parts of the sequences of LDHase and TIMase have been found. In one possible alignment, the sequences of t,he strands in units ABC and EFG

350

D.

C.

PHILLIPS

ET

AL.

in TIMase were found to be similar to the strands in ABC and DEF in LDHase. In the other alignment, the sequence similarities were between the strands of ABC in TIMase and those of ABC in LDHase, and between the C-terminal section of TIMase and the catalytic domain of LDHase. Only for some of the pairs of strands is there a correspondence between the structural and the sequence alignments. Some sequences similarities are to be expected between proteins that have converged to a similar fold (see before). However, there are more sequence similarities between TIMase and LDHase than within TIMase which suggests that the TIMaseLDHase similarities may be the result of divergent evolution. One would only expect fairly weak similarities in sequence between proteins that have evolved from a common ancestor a long time ago (on the evolutionary scale). In the comparisons of the u-chain of carp haemoglobin and sperm whale myoglobin. only 2194, of the residues are the same and it is accepted that they have evolved from a common ancestor (Dayhoff, 1972). We accept that one cannot distinguish with any certainty between a divergent and a convergent explanation for the similarities observed between TIMase and LDHase. More significant results are likely to be obtained in the comparisons between pyruvate kinase and TIMase which are being carried out at present (Dr H. Muirhead, personal communication). Pyruvate kinase has recently been shown to have as part of its structure an eight-stranded p-barrel with surrounding helices strikingly similar to the TIMase structure (Stammers t Muirhead, 1977 ; Stammers et aZ., 1977). However, until more quantitative comparisons of protein structures like these are completed, the criteria for deciding between convergent or divergent evolution as the origin of such resemblances will remain uncertain.

We thank Drs C. Chothia, script. The Medical Research is an ICI. Research Fellow.

M. Levitt, Council

and D. Richardson provided financial

for a preprint support. One

of their manuof us (I. A. W.)

REFERENCES Adams, M. J., Ford, G. C., Liljas, A. & Rossmann, M. G. (1973). Biochem. Biophys. Res. Commun. 53, 4651. Artavanis, S. (1974). Ph.D. thesis, University of Cambridge. Banner, D. W., Bloomer, A. C., Petsko, G. A., Phillips, D. C., Pogson, C. I., Wilson, I. A., Corran, P. H., Furth, A. J., Milman, J. D., Offord, R. E., Priddle, J. D. & Waley, S. G. (1975). Nature (London), 255, 609-614. Banner, D. W., Bloomer, A. C., Petsko, G. A., Phillips, D. C. & Wilson, I. A. (1976). Biochem. Biophys. Res. Commun. 72, 146-155. Birktoft, J. J. & Blow, D. M. (1972). J. Mol. Biol. 68, 187-240. Burnett, R. M., Darling, G. D., Kendall, D. S., LeQuesne, M. E., Mayhewr, S. G., Smith, W. W. & Ludwig, M. L. (1974). J. Biol. Chem. 249, 438334392. Chothia, C. (1973). J. Mol. Biol. 75, 295-302. Chou, P. Y. & Fasman, G. D. (1974a). Biochemistry, 13, 211-222. Chou, P. Y. & Fasman, G. D. (19745). Biochemistry, 13, 222-245. Dayhoff, M. 0. (1972). In Atlas of Protein Sequence and Structure, vol. 5, National Biomedical Research Foundation, Maryland, U.S.A. Dickerson, R. E. (1971). J. Mol. Biol. 57, 1-15. Eventoff, W., Rossmann, M. G., Taylor, S. S., Torff, H.-J., Meyer, H. & Kiltz, H.-H. (1977). Proc. Nat. Aead. Sci., U.S.A. 74, 2677-2681. Fitch, W. M. (1966). J. Mol. Biol. 16, 9-16. Haber, J. E. & Koshland, D. E., Jr (1970). J. Mol. Biol. 50, 617-639.

STRUCTURE

OF

TRIOSE

PHOSPHATE

ISOMERASE

351

Holbrook, J. J., Liljas, A., Steindel, S. J. & Rossmann, M. G. (1975). In Th,e Enzymes (Boyer, P. D., ed.), vol. 11, 3rd edit., pp. 191-292, Academic Press, New York. Lim, V. I. (1974a). J. Mol. Biol. 88, 857-872. Lim, V. I. (19745). J. Mol. Biol. 88, 873-894. McLachlan, A. D. (1971). J. Mol. BioE. 61, 409-424. McLachlan, A. D. (1972a). J. Mol. BioZ. 64, 417-437. McLachlan, A. D. (19725). Nature (London), 240, 83-85. Nishikawa, K., Ooi, T., Isogai, Y. & Saito, N. (1972). J. Phys. Sot. Japan, 32, 1331-1337. Ohlsson, I., Nordstrom, B. & Branden, C.-I. (1974). J. Mol. BioZ 89, 339-354. Perntz, M. F., Kendrew, J. C. & Watson, H. C. (1965). J. Mol. BioZ. 13, 669-678. Phillips, D. C. (1970). In British Biochemistry Past and Present (Goodwin, T. W., ed.), pp. 11-28, Academic Press, London. Rao, S. T. & Rossmann, M. G. (1973). J. Mol. BioZ. 76, 241-256. Richards, F. M. (1974). J. Mol. BioZ. 82, 1-14. Richardson, J. S. (1976). Proc. Nut. Acad. Sci., lJ.S.,4. 73, 2619-2623. Richardson, J. S., Richardson, D. C., Thomas, K. A., Silverton, E. W. & Davies, D. R. (1976). J. Mol. BioZ. 102, 221-235. Rossmann, M. G. & Argos, P. (1977). J. Mol. BioZ. 109, 99-129. Rossmann, M. G., Moras, D. & Olsen, K. W. (1974). Nature (London), 250, 1944199. Seigel, S. (1956). In Non-parametric Statistics for the Behavioural Sciences, pp. 202-213, McGraw-Hill, New York. Srinivasan. R., Balasubramanian, R. & Rajan, S. S. (1975). J. Mol. BioZ. 98, 739-747. Stammers, D. K. & Muirhead, H. (1977). J. Mol. Biol. 112, 309-316. Stammers, D. K., Levine, M., Stuart, D. I. $ Muirhrad, H. (1977). Biochem. Sot. Trans. 5, 654-657. Stellwagen, E., Cass, R., Thompson, S. T. & Woody, M. (1975). Nature (London), 257, 716m-718. Sternberg, M. J. E. & Thornton, J. M. (1976). J. Mol. Biol. 105, 367-382. Sternberg, M. J. E. & Thornton, J. M. (1977). J. Mol. BioZ. 110, 269-283.