Int. J. Peptidehorein Rex 9, 1977, 157-160 Published by Munksgaard, Copenhagen, Denmark N o part may be reproduced by any process without written permission from the author(s)
A NOTE ON THE TWO-DIMENSIONAL REPRESENTATION O F HYDROGEN BONDING SCHEME IN TRIOSE PHOSPHATE ISOMERASE* R. BALASUBRAMANIAN
Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras, India
Received 12 May 1976
When the backbone hydrogen bonding scheme of the protein triose phosphate isomerase is represented in the two-dimensional map where the donor residue number (i) is taken along the x-axis and the acceptor residue number ( j ) is taken along the y-axis, the (i, j)-map shows a characteristic pattern of (fla)8-supersecondary structure.
Though the atomic coordinates of protein molecules, reported by X-ray crystallographers, give the complete architecture of the molecule, they are sometimes found unwieldy for getting a quick picture of the conformational aspects of the polypeptide chain. In order t o overcome this difficulty, many workers in the field of conformational analysis have proposed several simplified methods for representing the folding of the polypeptide chains in protein molecules. Jtamachandran et al. (1963) suggested the so-called ($, $)-map, $ representing the dihedral angle of rotation around the bond, N-Ca and $, around C"-C in a polypeptide chain. Phillips (1970) propounded the (i, j)distance map which gives most of the important features of the three-dimensional architecture bf a protein molecule in a two-dimensional representation. The method has been improved upon and used for the conformational analysis ef various proteins (Ooi & Nishikawa, 1973; Rossman & Liljas, 1974; Dunn & Klosz, 1975).
Very recently, some new types of representations have been proposed from this laboratory (Srinivasan et ul., 1975; Balasubramanian & Srinivasan, 1976). In particular, the (i, j)-distance map at once gives a compact picture of the features of folding with regard to the secondary structure (see Rosman & Liljas, 1974). However, since the hydrogen bonding scheme in a protein molecule is the basic feature of any secondary structure, a unique method of representing them would at once give a precise picture of the regular folding in a protein molecule. Recently, the author has suggested such a method (Balasubramanian, 1976). The purpose of this communication is to highlight some important features of such a representation by applying it to triose phosphate isomerase (TIM), and the representation reveals interesting features of this rather regularly folded protein (Banner et al., 1975).
Method of representing hydrogen bonding *Contribution No. 441 from the Department of scheme in protein molecules Crystallography and Biophysics, University of Madras, Guindy Campus, Madras-600025, India.
Different groups of protein-crystallographers depict the hydrogen bonding scheme in protein 157
R. BALASUBRAMANIAN
molecules by different methods of representation (e.g. Banner er d., 1975; Watson, 1969; Wyckoff e t al., 1973; Birktoft & Blow, 1972). One of the simplest ways of representing the hydrogen bonding scheme is to take the donor residue number (i) along the x-axis and acceptor residue number (j)along the y-axis and plot a hydrogen bond in this (i, j)-plane. This two-dimensional representation at once gives a compact picture of the hydrogen bonding arrangement in a protein chain. Moreover, this method can be uniformly applied to all protein molecules, irrespective of the different individual arrangement of the secondary structures in proteins, particularly the segments of the S-stretches*.
et ~ l . 1975) , from residues 36 to 43. The alternative residues, 38, 40, 42 serve as donors to the residues 5, 7, 9, respectively, of 0-stretch ‘a’, while the residues 39, 4 1 , 43 of ‘b’ serve as donors to the residues 58, 60, 62, respectively of 0-stretch ‘c’. Thus the single 0-stretch ‘b’ of the real structure (Banner et al., 1975) comer out as two supplementary strings of points denoted as ‘bl’ and ‘b2’ in this representation, and are connected by the s y m b o l 1 . Thus this symbol connects points that have contiguous donor residue numbers (i’s). What is true of the 0-stretch ‘b’ is also true of other 0-stretches. Hence the &stretches ‘a’, ‘b’, ‘c’, etc., of the real protein-structure are represented by pairs of strings of dots (a1 Xaz), (bl b2), (cl 1c2), etc., in this representation. The usefulness of the vertical line ( ) will be shown presently. So far, we have been considering the role of a &stretch as a donor to other 0-stretches. H o w ever, a 0-stretch, say ‘by, not only serves as donor to the 0-stretches ‘a’ and ‘c’ but also serves as acceptor. Hence the strings of points b l and a, are symmetrically situated about the diagonal in the Figure; this is indicated by a symbol * , and this arrow is perpendicular to the diagonal. The usefulness of these symbols in the representation will become obvious if we trace along these line symbols as follows:
Some important features o f the representation The backbone hydrogen bonds in TIM are given in Fig. 1 which shows some important features of this type of representation of the hydrogen bonding scheme. The a-helices come out as strings of contiguous points, parallel to, and just below the diagonal. The strings of points corresponding to ahelices named A, B, C, etc., by Banner er d. (1975) have been similarly labelled in this Figure. The parallel 0-stretches come out as strings of points, parallel to, but away from the diagonal. Moreover, there are alternately missing points in the string (in contrast to the strings of contiguous points corresponding to al 0 b l H b2 * c1 t-(c2 * d l H d2 * e l t ( e a-helices) and this is usually supplemented by * f l H f2 *gl H g2 * h l H h2 * a 2 w a l . another string of points situated vertically above or below the former. In Fig. 1 these two This kind of tracing between the alternate supplementary strings are marked with a vert- symbols becomes a closed circuit, starting from ‘al’ and ending at ‘al’ itself. This indicates the ical line symbol . In this representation, this situation arises closed cylindrical nature of the @-sheetoccurbecause in a real structure a particular 0-stretch ring in the structure of TIM (Banner er d., can serve as donor to two other 0-structures, 1975); if it were not a closed cylinder of physically situated on two sides of it; but the &sheet the above type of tracing in the repreneighbouring 0-stretches may be widely sep- sentation would not lead to a closed circuit. arated in terms of the primary sequence. For Thus the above described arrow-headed example, consider the 0-stretch ‘b’ (Banner symbols enable one to recognize how the 0stretches are arranged in juxtaposition, and to show whether the 0-sheet is an open, or a closed * In showing the secondary structure of a p-sheet in cylinder. However, such details are not at once the form of a Figure, the particular segments have to available from an (i, j)-distance map (Dunn & be properly juxtaposed (as in Fig. 2 of Banner et al. Klotz, 1975). Though at first sight the arrow-headed (1975) which represents the hydrogen bonding symbols seem to complicate a simple (i, j) arrangement of TIM).
1
158
2D REPRESENTATION OF HYDROGEN BONDS IN TIM TRIOS PnoJPnATE K Q E W ( T I M )
DONOR
RESIDJE
NUMBER ( i l
-
0
’FIGURE 1 The two-dimensional representation of backbone hydrogen bonds in triose phosphate isomerase.
representation of the hydrogen bonding scheme in a protein molecule, they are not only necessary for a comprehensive description of the hydrogen bonding scheme, but also easy to mark on the (i, j)-map. Once the dots corresponding to the hydrogen bonding schemes are plotted, for parallel &structures, one has to join parallel strings of points that are vertically situated in the diagram by the symbol 1.Next, strings of points that are symmetrically situated with respect to the diagonal are joined by the symbol *. Then the nature of the &sheet will at once be recognized. In TIM, the adjacent 8-stretches are (primary-structurewise) separated by a-helices. This is readily seen in this kind of representation. For example, the &strings al and bl are interby the representing an string a-helix.Of points (denoted by A)’ super-secondary structure Of Thus the @ah is elegantly depicted in this particular type of two-dimensional representation of the
hydrogen bonding scheme of chain molecules. Discussion on some interesting conformational featuresin TIM
The a-helices starting from ‘C’ seem to steadily increase in length (though with breaks) up to the ‘F’ helix, and then decrease in length. A corresponding fluctuation in length of the 0stretches ‘d’ to ‘g’ is also Seen from this representation. Moreover, long a-helices are invariably seen to have breaks (see a-helices D, E and F). REFERENCES Balasubramanian, R. (1976) Indian J. Biochem. B b p h ~ s . , 1 3 9 289-292 Balasubramanian, R. & Srinivasan, R. (1976) Curr. Sci. (India) 45,397-398 Banner, D.W., Bloomer, A.C., Petsko, G.A., Phillips, D.C., Pogson, C.I., Wilson, LA., Corran, P.H., Furth, A.J., Milman, J.D., Offord, R.E., Priddle, J.D. & Waley, S.G. (1975) Nuture (Lond.) 255, 609-614
159
R. BALASUBRAMANIAN
Birktoft, J.J. & Blow, D.M. (1972) J. Mol. Biol. 68, 187-240 Dunn, J.B.R. & Klotz, I.M. (1975) Arch. Biochem. Biophys. 167,615-626 Ooi, T. & Nishikawa, K. (1973) in The Jerusalem Symposia on Quantum Chemistry and Biochemistry (Bergamann, B.D. & Pullman, B., eds.), No. 5 , pp. 173 - 187, Academic Press, London Phillips, D.C. (1970) in British Biochemistry, “Past and Present” (Goodwin, T.W., ed.), pp. 11-28, Academic Press, London Ramachandran, G.N., Ramakrishnan, C. & Sasisekharan, V. (1963) J. Mol. Biol. 7,95-99 Rossmann, M.G. & Liljas, A. (1974) J. Mol. Biol. 85, 177-181 Srinivasan, R., Balasubramanian, R. & Rajan, S.S.
160
(1975) J. Mol. Biol. 98,739-747 Watson, H.C. (1969) Progress in Stereochemistry 4, 229-333 Wyckoff, H.W.,Tsernoglou, D., Hanson, A.W., Knox, J.R., Lee, B. & Richards, F.M. (1973) J. Biol. Chem. 245,305-328
Address: R. Balasubramanian Department of Crystallography & Biophysics University of Madras Guindy Campus Madras - 600025 India
A NOTE ON THE TWO-DIMENSIONAL REPRESENTATION O F HYDROGEN BONDING SCHEME IN TRIOSE PHOSPHATE ISOMERASE* R. BALASUBRAMANIAN
Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras, India
Received 12 May 1976
When the backbone hydrogen bonding scheme of the protein triose phosphate isomerase is represented in the two-dimensional map where the donor residue number (i) is taken along the x-axis and the acceptor residue number ( j ) is taken along the y-axis, the (i, j)-map shows a characteristic pattern of (fla)8-supersecondary structure.
Though the atomic coordinates of protein molecules, reported by X-ray crystallographers, give the complete architecture of the molecule, they are sometimes found unwieldy for getting a quick picture of the conformational aspects of the polypeptide chain. In order t o overcome this difficulty, many workers in the field of conformational analysis have proposed several simplified methods for representing the folding of the polypeptide chains in protein molecules. Jtamachandran et al. (1963) suggested the so-called ($, $)-map, $ representing the dihedral angle of rotation around the bond, N-Ca and $, around C"-C in a polypeptide chain. Phillips (1970) propounded the (i, j)distance map which gives most of the important features of the three-dimensional architecture bf a protein molecule in a two-dimensional representation. The method has been improved upon and used for the conformational analysis ef various proteins (Ooi & Nishikawa, 1973; Rossman & Liljas, 1974; Dunn & Klosz, 1975).
Very recently, some new types of representations have been proposed from this laboratory (Srinivasan et ul., 1975; Balasubramanian & Srinivasan, 1976). In particular, the (i, j)-distance map at once gives a compact picture of the features of folding with regard to the secondary structure (see Rosman & Liljas, 1974). However, since the hydrogen bonding scheme in a protein molecule is the basic feature of any secondary structure, a unique method of representing them would at once give a precise picture of the regular folding in a protein molecule. Recently, the author has suggested such a method (Balasubramanian, 1976). The purpose of this communication is to highlight some important features of such a representation by applying it to triose phosphate isomerase (TIM), and the representation reveals interesting features of this rather regularly folded protein (Banner et al., 1975).
Method of representing hydrogen bonding *Contribution No. 441 from the Department of scheme in protein molecules Crystallography and Biophysics, University of Madras, Guindy Campus, Madras-600025, India.
Different groups of protein-crystallographers depict the hydrogen bonding scheme in protein 157
R. BALASUBRAMANIAN
molecules by different methods of representation (e.g. Banner er d., 1975; Watson, 1969; Wyckoff e t al., 1973; Birktoft & Blow, 1972). One of the simplest ways of representing the hydrogen bonding scheme is to take the donor residue number (i) along the x-axis and acceptor residue number (j)along the y-axis and plot a hydrogen bond in this (i, j)-plane. This two-dimensional representation at once gives a compact picture of the hydrogen bonding arrangement in a protein chain. Moreover, this method can be uniformly applied to all protein molecules, irrespective of the different individual arrangement of the secondary structures in proteins, particularly the segments of the S-stretches*.
et ~ l . 1975) , from residues 36 to 43. The alternative residues, 38, 40, 42 serve as donors to the residues 5, 7, 9, respectively, of 0-stretch ‘a’, while the residues 39, 4 1 , 43 of ‘b’ serve as donors to the residues 58, 60, 62, respectively of 0-stretch ‘c’. Thus the single 0-stretch ‘b’ of the real structure (Banner et al., 1975) comer out as two supplementary strings of points denoted as ‘bl’ and ‘b2’ in this representation, and are connected by the s y m b o l 1 . Thus this symbol connects points that have contiguous donor residue numbers (i’s). What is true of the 0-stretch ‘b’ is also true of other 0-stretches. Hence the &stretches ‘a’, ‘b’, ‘c’, etc., of the real protein-structure are represented by pairs of strings of dots (a1 Xaz), (bl b2), (cl 1c2), etc., in this representation. The usefulness of the vertical line ( ) will be shown presently. So far, we have been considering the role of a &stretch as a donor to other 0-stretches. H o w ever, a 0-stretch, say ‘by, not only serves as donor to the 0-stretches ‘a’ and ‘c’ but also serves as acceptor. Hence the strings of points b l and a, are symmetrically situated about the diagonal in the Figure; this is indicated by a symbol * , and this arrow is perpendicular to the diagonal. The usefulness of these symbols in the representation will become obvious if we trace along these line symbols as follows:
Some important features o f the representation The backbone hydrogen bonds in TIM are given in Fig. 1 which shows some important features of this type of representation of the hydrogen bonding scheme. The a-helices come out as strings of contiguous points, parallel to, and just below the diagonal. The strings of points corresponding to ahelices named A, B, C, etc., by Banner er d. (1975) have been similarly labelled in this Figure. The parallel 0-stretches come out as strings of points, parallel to, but away from the diagonal. Moreover, there are alternately missing points in the string (in contrast to the strings of contiguous points corresponding to al 0 b l H b2 * c1 t-(c2 * d l H d2 * e l t ( e a-helices) and this is usually supplemented by * f l H f2 *gl H g2 * h l H h2 * a 2 w a l . another string of points situated vertically above or below the former. In Fig. 1 these two This kind of tracing between the alternate supplementary strings are marked with a vert- symbols becomes a closed circuit, starting from ‘al’ and ending at ‘al’ itself. This indicates the ical line symbol . In this representation, this situation arises closed cylindrical nature of the @-sheetoccurbecause in a real structure a particular 0-stretch ring in the structure of TIM (Banner er d., can serve as donor to two other 0-structures, 1975); if it were not a closed cylinder of physically situated on two sides of it; but the &sheet the above type of tracing in the repreneighbouring 0-stretches may be widely sep- sentation would not lead to a closed circuit. arated in terms of the primary sequence. For Thus the above described arrow-headed example, consider the 0-stretch ‘b’ (Banner symbols enable one to recognize how the 0stretches are arranged in juxtaposition, and to show whether the 0-sheet is an open, or a closed * In showing the secondary structure of a p-sheet in cylinder. However, such details are not at once the form of a Figure, the particular segments have to available from an (i, j)-distance map (Dunn & be properly juxtaposed (as in Fig. 2 of Banner et al. Klotz, 1975). Though at first sight the arrow-headed (1975) which represents the hydrogen bonding symbols seem to complicate a simple (i, j) arrangement of TIM).
1
158
2D REPRESENTATION OF HYDROGEN BONDS IN TIM TRIOS PnoJPnATE K Q E W ( T I M )
DONOR
RESIDJE
NUMBER ( i l
-
0
’FIGURE 1 The two-dimensional representation of backbone hydrogen bonds in triose phosphate isomerase.
representation of the hydrogen bonding scheme in a protein molecule, they are not only necessary for a comprehensive description of the hydrogen bonding scheme, but also easy to mark on the (i, j)-map. Once the dots corresponding to the hydrogen bonding schemes are plotted, for parallel &structures, one has to join parallel strings of points that are vertically situated in the diagram by the symbol 1.Next, strings of points that are symmetrically situated with respect to the diagonal are joined by the symbol *. Then the nature of the &sheet will at once be recognized. In TIM, the adjacent 8-stretches are (primary-structurewise) separated by a-helices. This is readily seen in this kind of representation. For example, the &strings al and bl are interby the representing an string a-helix.Of points (denoted by A)’ super-secondary structure Of Thus the @ah is elegantly depicted in this particular type of two-dimensional representation of the
hydrogen bonding scheme of chain molecules. Discussion on some interesting conformational featuresin TIM
The a-helices starting from ‘C’ seem to steadily increase in length (though with breaks) up to the ‘F’ helix, and then decrease in length. A corresponding fluctuation in length of the 0stretches ‘d’ to ‘g’ is also Seen from this representation. Moreover, long a-helices are invariably seen to have breaks (see a-helices D, E and F). REFERENCES Balasubramanian, R. (1976) Indian J. Biochem. B b p h ~ s . , 1 3 9 289-292 Balasubramanian, R. & Srinivasan, R. (1976) Curr. Sci. (India) 45,397-398 Banner, D.W., Bloomer, A.C., Petsko, G.A., Phillips, D.C., Pogson, C.I., Wilson, LA., Corran, P.H., Furth, A.J., Milman, J.D., Offord, R.E., Priddle, J.D. & Waley, S.G. (1975) Nuture (Lond.) 255, 609-614
159
R. BALASUBRAMANIAN
Birktoft, J.J. & Blow, D.M. (1972) J. Mol. Biol. 68, 187-240 Dunn, J.B.R. & Klotz, I.M. (1975) Arch. Biochem. Biophys. 167,615-626 Ooi, T. & Nishikawa, K. (1973) in The Jerusalem Symposia on Quantum Chemistry and Biochemistry (Bergamann, B.D. & Pullman, B., eds.), No. 5 , pp. 173 - 187, Academic Press, London Phillips, D.C. (1970) in British Biochemistry, “Past and Present” (Goodwin, T.W., ed.), pp. 11-28, Academic Press, London Ramachandran, G.N., Ramakrishnan, C. & Sasisekharan, V. (1963) J. Mol. Biol. 7,95-99 Rossmann, M.G. & Liljas, A. (1974) J. Mol. Biol. 85, 177-181 Srinivasan, R., Balasubramanian, R. & Rajan, S.S.
160
(1975) J. Mol. Biol. 98,739-747 Watson, H.C. (1969) Progress in Stereochemistry 4, 229-333 Wyckoff, H.W.,Tsernoglou, D., Hanson, A.W., Knox, J.R., Lee, B. & Richards, F.M. (1973) J. Biol. Chem. 245,305-328
Address: R. Balasubramanian Department of Crystallography & Biophysics University of Madras Guindy Campus Madras - 600025 India
