{"title": "A Novel Approach to Prediction of the 3-Dimensional Structures of Protein Backbones by Neural Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 523, "page_last": 529, "abstract": null, "full_text": "A Novel Approach to Prediction of the \n\n3-Dimensional Structures of Protein Backbones \n\nby Neural Networks \n\nHenrik Fredholrn l ,5 \n\nHenrik Bol1l' 2 , Jakob Bohr3 , S0ren Brunak4 , \n\nRodney M.J. Cotterill\\ Benny Lautrup5 and Steffen B. Petersenl \n\nand \n\n1 MR-Senteret, SINTEF, N-7034 Trondheim, Norway. \n2University of Illinois, Urbana, IL 61801, USA. \n3Ris!3 National Laboratory, DK-4000 Roskilde, Denmark. \n4Technical Univ. of Denmark, B. 307, DK-2800 Lyngby, Denmark. \n5Niels Bohr Institute, Blegdamsvej 17, DK-2100 Cph. 0, Denmark. \n\nAbstract \n\nThree-dimensional (3D) structures of protein backbones have been pre(cid:173)\ndicted using neural networks. A feed forward neural network was trained \non a class of functionally, but not structurally, homologous proteins, us(cid:173)\ning backpropagation learning. The network generated tertiary structure \ninformation in the form of binary distance constraints for the Co atoms \nin the protein backbone. The binary distance between two Co atoms was \no if the distance between them was less than a certain threshold distance, \nand 1 otherwise. The distance constraints predicted by the trained neu(cid:173)\nral network were utilized to generate a folded conformation of the protein \nbackbone, using a steepest descent minimization approach. \n\n1 \n\nINTRODUCTION \n\nOne current aim of molecular biology is determination of the (3D) tertiary struc(cid:173)\ntures of proteins in their folded native state from their sequences of amino acid \n\n523 \n\n\f524 \n\nFredholm, Bohr, Bohr, Brunak, Cotterill, Lautrup, and Thtersen \n\nresidues. Since Kendrew & Perutz solved the first protein structures, myoglobin \nand hemoglobin, and explained from the discovered structures how these proteins \nperform their function, it has been widely recognized that protein function is inti(cid:173)\nmately linked with protein structure[l]. \n\nWithin the last two decades X-ray crystallographers have solved the 3-dimensional \n(3D) structures of a steadily increasing number of proteins in the crystalline state, \nand recently 2D-NMR spectroscopy has emerged as an alternative method for small \nproteins in solution. Today approximately three hundred 3D structures have been \nsolved by these methods, although only about half of them can be considered as \ntruly different, and only around a hundred of them are solved at high resolution \n(that is, less than 2A). The number of protein sequences known today is well over \n20,000, and this number seems to be growing at least one order of magnitude faster \nthan the number of known 3D protein structures. \n\nObviously, it is of great importance to develop tools that can predict structural \naspects of proteins on the basis of knowledge acquired from known 3D structures. \n\n1.1 THE PROTEIN FOLDING PROBLEM \n\nIt is generally accepted that most aspects of protein structure derive from the prop(cid:173)\nerties of the particular sequence of amino acids that make up the protein 1 \u2022 The \nclassical experiment is that of Anfinsen et al. [2] who demonstrated that ribonucle(cid:173)\nase could be denatured and refolded without loss of enzymatic activity. \n\nThis has led to the formulation of the so-called protein folding problem: given the \nsequence of amino acids of a protein, what will be its native folded conformation? \n\n1.2 SECONDARY STRUCTURE PREDICTION \n\nSeveral methods have been developed for protein structure prediction. Most abun(cid:173)\ndant are the methods for protein secondary structure prediction [3, 4, 5, 6]. These \nmethods predict for each amino acid in the protein sequence what type of secondary \nstructure the amino acid is part of. Several strategies have been suggested, most \nof which are based on statistical analysis of the occurrence of single amino acids \nor very short stretches of amino acids in secondary structural elements in known \nproteins. In general, these prediction schemes have a prediction accuracy of 50-60% \nfor a three-category prediction of helix-, sheet- and coil conformations. \n\nRecently neural networks have been applied to secondary structure prediction with \nencouraging results [7, 8, 9, 10]; on three-category prediction the accuracy is 65%; \non two-catagory prediction of helix- and coil conformations the accuracy is 73%; \nand on a two-category prediction of turn- and coil conformations the accuracy is \n71 %. In all the three cases this is an improvement of the traditional methods. \n\n1 Although recent results indicate that certain proteins catalyze, but do not alter, the \n\ncourse of protein folding. \n\n\fA Novel Approach to Prediction of the 3-Dimensional Structures \n\n525 \n\n1.3 TERTIARY STRUCTURE PREDICTION \n\nThe methods that exist for 3D structure prediction fall in three broad categories: (1) \nuse of sequence homology with other protein with know 3D structure; (2) prediction \nof secondary structure units followed by the assembly of these units into a compact \nstructure; and (3) use of empirical energy functions ab initio to derive the 3D \nstructure. \n\nNo general method for 3D structure prediction exists today, and novel methods \nare most often documented through case stories that illustrate best or single case \nperformance. The most successful methods so far has been those based on sequence \nhomology; if significant sequence and functional homology exists between a protein \nof interest and proteins for which the 3D structures are known, it is possible (but \ncumbersome) to build a reasonable 3D model of the protein structure. \n\n2 METHOD \n\n\\fo,le here describe a new method for predicting the 3D structure of a protein backbone \nfrom its amino acid sequence [11]. The main idea behind this approach is to use a \nnoise tolerant representation of the protein backbone that is invariant to rotation \nand translation of the backbone2 , and then train a neural network to map protein \nsequences to this representation. \n\n2.1 REPRESENTATION OF 3D BACKBONE STRUCTURES \n\nThe folded backbone structure of a protein brings residues that are distantly posi(cid:173)\ntioned in sequence close to each other in space. One may identify such close contacts \nand use them as constraints on the backbone conformation. \n\nWe define the binary distance D( i, j) between two residues i and j as 0 if the \ndistance between the Ca atom in residue i and the Ca atom in residue j is less than \na given threshold and as 1 if it is above or equal to the threshold, a typical choice \nof threshold being sA. Organizing these distances as a binary distance matrix gives \nrise to a two dimensional representation of the protein backbone (figure 2a depict \nsuch matrix). \n\nMost secondary motifs can be distinguished in this representation; helices appear \nas thickenings of the diagonal and anti-parallel and parallel sheets appear as stripes \northogonal and parallel to the diagonal. \n\nIt is possible to reconstruct the 3D backbone from the binary distance matrix rep(cid:173)\nresentation by minimizing the \"energy function\" , \n\nE = L g(dij(1 ta(i) - taU) I - 0\u00bb \n\nitj \n\nwhere dij = 1 - 2D(i,j), g(x) = 1/(1 + exp(-x\u00bb and 0 is the distance threshold. \nThe initial positions of the ta atoms are chosen at random. The motif for this \n\n2The (\u00a2,,p) torsion-angle representation is also rotation- and translation invariant, but \n\nit is not noise tolerant. \n\n\f526 \n\nFredholm, Bohr, Bohr, Brunak, Cotterill, Lautrup, and ~tersen \n\n, './I \n\n_ 1 c \n\nSequellC8 of 4IJ1ino ilC:lds \n\u00b71 \n\n1 \n\n0 \n\nS \n\nL \n\n'0 \nE \n\n1 _ \n\nOutput \n\n\u2022 \n\n-\n\no \n-\n10 I \n\nex:\u00bb \n\n\u2022 \n\nII I o \n\n-I \n\u2022 .lIl \n0iscaDce caasnina \n\nSecooclary sauc:ture \n\nFigure 1: The input to the network consists of 61 contiguous amino acids, where each \namino acid is represented by a group of 20 neurons (only seven neurons/group are illus(cid:173)\ntrated). At the output layer, a set of binary distances, between the centrally positioned \nresidue and those lying to the left of it in the input window, is produced. Secondary \nstructure assignment for the centrally positioned residue, in the three categories of helix, \nsheet and coil, is also produced. Regarding the binary distance matrix, the network is \ntrained to report which of the 30 preceding Ca atoms are positioned within a distance of \nsA to the centrally placed amino acid. The input layer had 1220 (61 x 20) neurons, the \nhidden layer had 300 neurons and the output layer had '33 neurons. \n\nenergy function is that constraints that do not hold should contribute with large \nvalues, while constraints that do hold should contribute with small values. \n\nFor small proteins of the order of 60 residues the reconstruction is very accurate. \nFor Bovine Pancreatic Trypsin Inhibitor (6PTI), a 56 residue long protein, we were \nable to generate a correctly folded backbone structure. The binary distance matrix \nwas generated from the crystallographic data of 6PTI using a distance threshold \nof B.A. After convergence of the minimization procedure the errors between the \nreconstructed structure and the correct structure lay within 1.2A root mean square \n(rms). \n\nPreliminary results (unpublished) indicate that backbone structures for larger prcr \nteins can be reconstructed with a deviation from the correct structure down to 2A \nrms, when a distance threshold of 16A is used. \\Vhen 5% random noise is added to \nthe distance matrix the deviation from the correct structure grows to 4-5A rms. \n\n2.2 DISTANCE MATRIX PREDICTION \n\nA backpropagation network [12] was used to map protein sequences to distance \nmatrices. To simplify the task the neural network had to learn, it was not taught \nto predict all constraints in the distance matrix. Only a band along the diagonal \nwas to be predicted. More specifically, the network was taught to predict for each \nresidue in the protein sequence the binary distances to the 30 previous residues. \nFurthermore it had to classify the central residue in question as either helix, sheet \nor coil, see figure 1. Hence, the trained neural network produced, when given a \nprotein sequence, a secondary structure prediction and a distance matrix containing \n\n\fA Novel Approach to Prediction of the 3-Dimensional Structures \n\n527 \n\nRESIDUE NliMBER \n\nRESIDUE NUMBER \n\n(a) \n\n(b) \n\nFigure 2: Binary distance matrices for 1TRM. The matrices (:!23 x 223) show which \nCo. atoms are within an sA distance to each other Ca atom in the folded protein. a) The \nmatrix corresponding to the structure determined from the X-ray data. b) Neural network \nprediction of an sA distance matrix. A 61-residue band centered along the diagonal is \ngenerated. The network predicts this band with an accuracy of 96.6%. \n\nbinary distance constraints for a lower diagonal-band matrix of width 30. Due to \nsymmetry in the distance matrix and the diagonal being always zero, the resulting \nbinary distance matrix contained a diagonal-band of predicted distance constraints \nof width 61. \n\n3 CASE STORY \n\nA neural network with this architecture was trained on 13 different proteases [13] \nfrom the Brookhaven Protein Data Bank, all having their data collected to a nom(cid:173)\ninal resolution better than 2A. The 13 proteases were of several structural classes \nincluding trypsins and subtilisins. This training set generated 3171 different exam(cid:173)\nples (input windows) which were presented to the network. After 200 presentations \nof each example, the network had learned the training set to perfection3 . A 14th \nprotease, 1TRM (Rat Trypsin), with a length of 223 residues, was used to test the \nnetwork. This protease was 74% homologous to one of the 13 proteases that the \nnetwork was trained on. The distance matrix derived from X-ray diffraction for \nthis protein is shown in figure 2a. The ability of the network to correctly assign \nstructural information is amply illustrated in figure 2b, where the network is pre(cid:173)\ndicting the distance constraints around the diagonal for 1TRM. Although a high \ndegree of sequence homology exists between 1 TRM and the trypsins included in the \ntraining set, not a single input window presented to the network was identical to \nany window in the training set. The prediction thus illustrates the ability of the \nnetwork to generalize from the training set. In the prediction (figure 2b), a clear \ndistinction can be made between helices and anti-parallel sheets as well as other \ntertiary motifs. \n\nIf the whole binary distances matrix had been predicted, it would have been possible \n\n3The training lasted 2 weeks on an Apollo 10000 running at 10 Mflops. \n\n\f528 \n\nFredholm, Bohr, Bohr, Brunak, Cotterill, Lautrup, and ~tersen \n\n(a) \n\n(b) \n\nFigure 3: Backbone conformation for the 223 residue long trypsin 1 TRM. a) The crystal \nstructure for 1TRM, as determined by X-ray data. b) The predicted structure of 1TRM \nsuperimposed on the crystal structure. The nns deviation calculated over all the CQ atoms \nwas 3A. The largest deviations were present in surface loops, some of which are fixed by \nseveral disulphide bridges. \n\nto construct the backbone conformation directly from the prediction. However, since \nonly a truncated version was predicted, a good guess of the backbone conformation \nis needed for the minimization4 . By using as initial guess the backbone conformation \nfor a homologous protein, the backbone conformation of 1 TRM was predicted with a \n3A rms deviation from the coordinates determined by X-ray diffraction, see figure 3. \nIn this particular case, the length of the sequence used for the starting configuration \nwas identical to that of the protein to be reconstructed. vVhen the sequences are of \nunequal length, on the other hand, it is clear that additional considerations would \nhave to be taken into account during the minimization process. \n\n4 DISCUSSION \n\nThe single main achievement of this study has been the generation of a 3D structure \nof a protein from its amino acid sequence. The approach involved first the prediction \nof a distance matrix using a neural network and subsequently a minimization fitting \nprocedure. \n\nBinary distance matrices were introduced as a noise tolerant translation- and ro(cid:173)\ntation invariant representation of 3D protein backbones, and a neural network was \ntrained to map protein sequences to this representation. \n\nThe results reported here are predictions of folded conformations, illustrated with \nthe trypsin ITRM. Our neural network is clearly capable of generalizing the folding \n\n4For large proteins, where the band of distance constraints does not cover all spatial \n\ncontacts, local folding domains may acquire different chiralities, leading to improper pack(cid:173)\ning of the domains in the protein. However, new experiments indicate that the backbone \nstructure of proteins that are 200-300 residues long can be reconstructed with good results \nfrom a random configuration, if the width of the band in the distance matrix is 121 and \nthe distance threshold is 16A. \n\n\fA Novel Approach to Prediction of the 3-Dimensional Structures \n\n529 \n\ninformation stemming from known proteins with homologous function. Current \ninvestigations have shown that the network is robust towards mutation of amino \nacids in the protein sequence, whereas it is very sensitive to insertions and deletions \nin the sequence. Thus, new network architectures will have to be developed, if this \nmethod is to be useful for proteins with low homology; a bigger training set alone \nwill not do it. \n\nDistance constraints can also be derived from experimental procedures such as \nNMR, in which they take the form of nuclear Overhauser enhancement (nOe) fac(cid:173)\ntors. Structural information can be successfully derived from such data using re(cid:173)\nstraint dynamics which in its essential form bears some resemblance to the approach \nemployed here, the most salient difference being that the potential energy function \nin our work is much simpler. \n\nAcknowledgements \n\nHF thanks the Danish Research Academy, Novo-Nordisk and UNI-C for grants. \n\nReferences \n\n[1] Jaenicke, R. (1987) Prog. Biophys. Molec. BioI. 49,117-237. \n[2] Anfinsen, C.B et al. (1961) Proc. Natl. Acad. Sci. USA, 47,1309-1314. \n[3] Chou, P.Y, and Fasman, G.D. (1974) Biochemistry 13, 211-245. \n[4] Garnier, J., Osguthorpe, D.J., and Robson, B. J. (1978) Mol. BioI., 120, 97-\n\n120. \n\n[5] Lim, V.I. (1974) J. Mol. BioI., 88, 857-894. \n[6] Robson, D., and Suzuki, E. (1976) J. Mol. BioI., 107, 327-356. \n[7] Qian N., and Sejnowski, T.J. (1988) J. Mol. BioI., 202, 865-884. \n[8] Bohr, H., Bohr, J., Brunak, S., Cotterill, R.M.J., Lautrup, B., N~rskov, L., \n\nOlsen, O.H, and Petersen, S.B (1988) FEBS Letters, 241, 223-228. \n\n[9] McGregor, M.J., Flores, T.P., and Sternberg, M.J .E. (1989) Protein Engineer(cid:173)\n\ning, 2, 521-526. \n\n[10] Kneller, D.G., Cohen, F.E., and Langridge, L. (1990) J. Mol. BioI., 214,171-\n\n182. \n\n[11] Bohr, H., Bohr. J, Brunak, S., Cotterill, R.M.J., Fredholm, H., Lautrup, B., \n\nand Petersen, S.B. (1990) FEBS Letters, 261,43-46. \n\n[12] Rummelhart, D.E., Hinton, G.E., and Williams, R.J. (1986) Parallel Dis(cid:173)\n\ntributed Processing, 1, 318-362. Bradford Books, Cambridge, MA. \n\n[13] Brookhaven Protein Data Bank entry codes: ISGT (Streptomyces Trypsin), \n2EST (Porcine Pancreatic Elastase), 4PTP (Bovine Pancreatic beta Trypsin), \n2KAI (Porcine Pancreatic Kallikrein A), lCHG (Bovine Chymotrypsin A), \n2PRK (Fungal Proteinase K), ISEC (Subtilisin Carlsberg), ISGC (Strepto(cid:173)\nmyces Proteinase A), 2ALP (Lysobacter Alfalytic Protease), 3APR (Rhizopus \nAcid Proteinase), 3RP2 (rat Mast Cell Proteinase), 2SBT (Subtilisin NOVO) \nand ISAV (Subtilisin Savinase). \n\n\f", "award": [], "sourceid": 380, "authors": [{"given_name": "Henrik", "family_name": "Fredholm", "institution": null}, {"given_name": "Henrik", "family_name": "Bohr", "institution": null}, {"given_name": "Jakob", "family_name": "Bohr", "institution": null}, {"given_name": "S\u00f8ren", "family_name": "Brunak", "institution": null}, {"given_name": "Rodney", "family_name": "Cotterill", "institution": null}, {"given_name": "Benny", "family_name": "Lautrup", "institution": null}, {"given_name": "Steffen", "family_name": "Petersen", "institution": null}]}