Amyloids are proteins capable of forming fibrils whose intramolecular contact sites assume densely packed zipper pattern. Their oligomers can underlie serious diseases, e.g. Alzheimer’s and Parkinson’s diseases. Recent studies show that short segments of aminoacids can be responsible for amyloidogenic properties of a protein. A few hundreds of such peptides have been experimentally found but experimental testing of all candidates is currently not feasible. Here we propose an original machine learning method for classification of aminoacid sequences, based on discovering a segment with a discriminative pattern of site-specific co-occurrences between sequence elements. The pattern is based on the positions of residues with correlated occurrence over a sliding window of a specified length. The algorithm first recognizes the most relevant training segment in each positive training instance. Then the classification is based on maximal distances between co-occurrence matrix of the relevant segments in positive training sequences and the matrix from negative training segments. The method was applied for studying sequences of aminoacids with regard to their amyloidogenic properties.
Our method was first trained on available datasets of hexapeptides with the amyloidogenic classification, using 5 or 6-residue sliding windows. Depending on the choice of training and testing datasets, the area under ROC curve obtained the value up to 0.80 for experimental, and 0.95 for computationally generated (with 3D profile method) datasets. Importantly, the results on 5-residue segments were not significantly worse, although the classification required that algorithm first recognized the most relevant training segments. The dataset of long sequences, such as sup35 prion and a few other amyloid proteins, were applied to test the method and gave encouraging results. Our web tool FISH Amyloid was trained on all available experimental data 4-10 residues long, offers prediction of amyloidogenic segments in protein sequences.
We proposed a new original classification method which recognizes co-occurrence patterns in sequences. The method reveals characteristic classification pattern of the data and finds the segments where its scoring is the strongest, also in long training sequences. Applied to the problem of amyloidogenic segments recognition, it showed a good potential for classification problems in bioinformatics.
Amyloids are proteins which aggregate into oligomers and then fibrils that accumulate in cells. Their intramolecular contact sites form a characteristic zipper pattern. Although a few functional amyloids are known, the majority of proteins lose their physiological function when they aggregate and they become cytotoxic for cells [1–5]. The exact reason for this cytotoxicity is still unclear but many studies show that intermediate oligomeric structures are the main culprits. The number of amyloidogenic diseases following misfolding of a protein into the amyloid is constantly increasing and include Alzheimer’s disease (amyloid-β, tau), Parkinson’s disease (α-synuclein), type 2 diabetes (amylin), Creutzfeldt-Jakob’s disease (prion protein), Huntington’s disease (huntington), amyotrophic lateral sclerosis (SOD1), and many others (for a review see e.g. ). They affect constantly increasing number of people, especially in well developed countries. Recognition of factors responsible for protein misfolding can contribute to better understanding of its mechanisms and potential drug design. Recent studies indicate that there may be certain protein sequence determinants responsible for their affinity to form amyloids. These may be short segments of aminoacids, which are called hot spots [7, 8]. Those fragments are harmless only when they are buried inside a protein. The amyloidogenic fragments responsible for amyloidogenicity of the whole protein are believed to be 4-10 residues long and it is often assumed that 6-residue fragments of amyloidogenic properties are typical “hot spots” . Recognition of amyloidogenic fragments can be obtained by computational approach, for example physico-chemical methods, e.g. Tango , ZipperDB [10, 11], FoldAmyloid [12, 13], Pasta [14, 15], AggreScan , PreAmyl , Zyggregator , CamFold , NetCSSP , AmyloidMutant [21, 22], BetaScan , and consensus AmylPred . Statistical methods have also been employed in the classification. In our previous work we used classical machine learning methods  implemented in WEKA . Other methods include Waltz  using Position Specific Scoring Matrices (PSSM), or Bayessian classifier and weighted decision tree applied to long sequences of bacterial antibodies . A few hundreds of amyloid peptides have been experimentally found, although the dataset is very limited. Also computational methods generate databases of potential amyloids, such as 3D profile [9, 29], which is a physicochemical method that generated the most numerous computational dataset – ZipperDB .
In this manuscript we propose a new machine learning method for the identification of amyloidogenic segments in amino acid sequences, based on the presence of a segment with the highest scoring for co-occurrence of residue pairs. By application of a sliding window, the algorithm all by itself recognizes the most relevant training segments in positive training instances.
Machine learning method
Our classification method is based on the assumption that aminoacid sequences (such as amyloidogenic fragments) exhibit certain, well defined, pattern of residue distribution, which is position specific and, most importantly, involves co-occurrence of two aminoacids at different positions. For example, the pattern would not only include a high chance of valine occurrence at position 2, but also the valine would entail isoleucine at position 4. The pattern should be contained in one segment and limited in length. A pattern in the negative dataset is not important, as long as it is different from that of the positive set. However, it may happen that the discriminative pattern is more pronounced in the negative set - we also test our method with this regard. To investigate the co-occurrence pattern, a relevant window length needs to be specified. This window is equivalent to the minimal fragment of a protein sequence displaying the classification property.
First, the negative training dataset (NO) is divided into segments of the selected length n (here 5 or 6) by shifting the window of one position each time. We assume that there is no special segment in peptides from the negative dataset. Therefore, all generated negative segments equally contribute to their representative pattern and calculation of the classification threshold (described later in this section) used for discrimination between negative and positive test sequences. If the negative instances exhibit a pattern, it will be naturally averaged, hence removed, due to the shifting window. Pairs of aminoacids from all the segments are counted in the matrix MatrixNO (the explanation of co-occurrence matrices is presented in Figure 1), which represents occurrence of specific aminoacid couples with regard to their positions in the segments.
Next, the dataset of positive training instances (YES) undergoes similar procedure, generating MatrixYES. However, in contrast to the negative training instances, each positive training sequence can include segments responsible for amyloidogenicity of the sequence, whose location is not known, as well as segments lacking the pattern. Our method finds and takes into account only those segments which display the classification co-occurrence pattern in the most pronounced way, neglecting others. Hence, only one window (e.g. with the highest chance of amyloidogenicity) is selected in each positive training sequence, and each positive training sequence contributes only one segment to MatrixYES. Graphical representation of the final matrix which is used in the classification is presented in Figure 2. The most frequent couples of aminoacids (represented by numbers 1-20), from the selected 5-residue windows, assume the darkest color of the dot.
The most relevant segments in positive training sequences, carrying the classification pattern, are found in the iterative procedure that selects those which are most distant from the averaged pattern of negative segments, as well as closest to the segments selected from other positive sequences. The distance, w, between positive and negative segments is represented by a sum of elements of array MatrixYES divided by MatrixNo. The procedure, resulting with the choice of optimal segments in the set of positive training fragments, gives the maximum distance value, wd, which is used in the classification procedure as a threshold value.
In the classification of test sequences, a distance wl is defined, which is an a’priori assumed ratio of wd (between 0 and 1), providing a threshold value used in the classification test of sequences. Detailed training algorithm of the method is presented in Figure 2. In the classification of the test set (or a set of unclassified sequences), the greatest actual distance ratio, ws, between MatrixYES of the tested sequence and MatrixNO is calculated. If ws assumes a value greater than a selected value of wl then the window is classified as positive (Figure 2).
The overall quality of the classifier was evaluated with Area under Receiver Operating Characteristic (ROC) curve (AUC ROC). The value of the AUC ROC can range from zero to one, with the score of 0.5 corresponding to random guess and the score of 1 indicating perfect separation. Two methods of testing our machine learning method were applied: either the same set was used for training and validation or the method was trained on one dataset and tested on another one. In the first case, 4-fold cross-validation method was used and the mean result of AUC ROC was reported. Additionally, for evaluation of the method, we used Sensitivity (Sn), which is the ratio of correctly classified positive fragments and Specificity (Sp), the ratio of correctly classified negative fragments. They are defined in the following:
where TP, FP, FN and TN represent the numbers of true positives, false positives, false negatives and true negatives, respectively.
Our classification method was first trained and validated on 3 experimental datasets of short peptide fragments, specifying their amyloid or β-aggregation propensities: AmylHex  with 6-residue sequences including 67 positive and 91 negative, Waltz  with 6-residue sequences including 49 positive and 71 negative, Tango (TG, tested for aggregation)  with a variable (4-43) residue fragments including 71 positive and 172 negative instances, downloaded from FoldAmyloid database . The choice of experimental datasets is very limited since very few data are available, and our choice included all of them. Unfortunately, all these datasets are biased, which can influence the results of machine learning.
To compare the performance of our classification method with classical machine learning methods, we used another dataset of 4481 hexapeptides, which was computationally obtained with the 3D profile method . The 3D profile method was originally proposed in  and applied in ZipperDB to generate the database of amyloidogenic hexapeptides. This computational dataset was generated with a faster version of the 3D profile algorithm . It is not as biased as the experimental datasets and it was previously used in tests with a number of classical machine learning methods .
Then, our classification method, trained with 5-residue sliding window on the set of short peptides from Waltz dataset , was tested on 4 full length amyloidogenic proteins: amyloid-β and tau (Alzheimer’s disease), α-synuclein (Parkinson’s disease), amylin (type 2 diabetes), and prion protein sup-35 (Creutzfeldt-Jakob’s disease). The Waltz dataset was selected for the training since it did not contain fragments of the tested proteins. In these proteins, the method indicated amyloidogenic regions, classified with various values of the classification threshold wl, which were compared with experimentally validated data.
Finally, we merged all the experimental datasets. The full dataset included all experimentally tested peptides from different groups, whose length did not exceed 10 aminoacids, and involved also fragments from prion sup35. The full dataset consisted of 436 (146 positive and 290 negative) fragments (see Additional file 1). This dataset was first used in 4-fold cross-validation of our method, and then to train our web service FISH Amyloid, which is now freely available for classification.
Results and discussion
Our method was trained on hexapeptides from different datasets, using two sliding window lengths: 5 and 6 (note that training on the 6-residue fragments with a window of length 6 eliminates the stage of finding the most relevant pattern-carrying, windows in the training and testing sequences). The results, obtained with different classification threshold wl were represented as ROC curves.
Testing the quality of our new classification method and comparing it with different methods could only be possible while working with the same datasets as those state-of the-art methods. Therefore, to compare the performance of our method to classical machine learning methods, first we ran tests on the non-biased computational dataset generated with the physicochemical 3D profile method . The result can be used for comparison with other machine learning methods since the same dataset was previously classified with several classical machine learning methods implemented in WEKA . In this case, AUC ROC obtained with our method was 0.95 for a 6-residue window and 0.87 for a 5-residue sliding window. Top results of the state of the art methods from WEKA, working on hexapeptides, were very similar. For example, neural network (multilayer perceptron – MLP) and alternating decision tree, which showed the highest performance for this dataset from over 100 machine learning methods available in WEKA, obtained AUC ROC = 0.96 . This is very similar to our results with the method presented here, obtained for the 6-residue window. Other classical methods implemented in WEKA obtained lower quality. Moreover, the result of new method was not significantly worse when it worked on a sliding window of length 5, although it first required that the algorithm finds the most relevant windows in the training and testing sequences. Hence, the classification quality of the new method presented here was very close to the top results obtained with classical machine learning methods on the same dataset. Moreover, none of the classical methods was capable of finding the most relevant training window, which is an asset of our new method.
Then, the performance of our method was tested on experimental datasets, which are scarce and possibly incompatible with each other. Hence, we first used those datasets separately. Depending on the applied experimental dataset, the AUC ROC varied from 0.69 to 0.81 for a sliding window of length 5 and between 0.69 and 0.79 for a window of length 6 (Table 1, main diagonals, bold font). Additionally, to test if negative datasets could have discriminative patterns, we ran the classifications in which the negative sets were treated as “positive”. The results are presented in Table 1 as a second number in each field, showing that many of those negative datasets are biased. Only the values close to 0.5 mean the lack of any characteristic pattern. By combining different datasets and testing one versus another, we could observe how compatible they are with each other (Table 1, non-diagonal). The AUC ROC values were lower in this case, showing that the available datasets are often incompatible.
Training set (horizontal)
Tested set (vertical)
sliding window of length 5
0.75 | 0.62
0.82 | 0.21
0.77 | 0.42
0.62 | 0.60
0.69 | 0.60
0.59 | 0.51
0.69 | 0.60
0.84 | 0.31
0.81 | 0.47
sliding window of length 6
0.76 | 0.57
0.77 | 0.30
0.78 | 0.44
0.54 | 0.45
0.69 | 0.61
0.61 | 0.43
0.48 | 0.57
0.82 | 0.25
0.79 | 0.47
AUC ROC of the classification results with two window lengths. To test if a classification pattern is observable in the negative datasets, the training and testing procedures were also applied on negative datasets (POSITIVE | NEGATIVE); the positive datasets are in bold. Training dataset is defined horizontally; testing dataset – vertically. Random classification (or no pattern in a dataset) would obtain 0.5 and an ideal classifier 1.
The performance of our method was then compared to two state of the art tools for classification of amyloidogenic hot spots: Waltz, which was based on the most numerous individual dataset tested above, and FoldAmyloid using a combination of several experimental datasets. The authors of Waltz show [27, Addenum Figure 1] that their method trained on Waltz hexapeptides and tested on AmylHex dataset generated ROC curve with diagonal coordinates Sn = 83% and Sp = 83% (Waltz) and Sp = 89% and Sn = 89% (cross-validated Waltz), AUC ROC was not reported. Our method, trained on 5-residue sliding windows from Waltz dataset and tested on AmylHex obtained Sn = 79%, Sp = 78%, and AUC ROC = 0.81. Cross-validation of Waltz was reported at the level of Sn = 84%, Sp = 92% . (Our method, in the more demanding mode i.e. with a sliding window of length 5, trained on the Waltz dataset, obtained AUC ROC of 0.69 and diagonal point of the ROC curve was Sn = 63% and Sp = 63%). However, an independent test on fragments from prion sup35 showed the adventage of our method. Waltz authors reported Sn = 58%, Sp = 90%, while our method (also trained on the Waltz dataset but with a 5-residue long sliding window) obtained Sn = 70% and Sp = 91% (Table 2). For comparison, the authors of Waltz also reported the sensitivity of computational 3D profile method on sup35 positive set, which was Sn = 67% .
Tests on prion sup35 fragments
Classification efficiency tested on fragments of prion sup35. The method was trained on Waltz dataset with a sliding window 5-residue long, classification coefficient was set to wl = 0.13. Emphasized are windows recognized by the classification method as potentially the most positive (amyloidogenic) of the whole tested fragment; the fragments obtained the actual distance value ws (window of a greatest distance).
With the optimal parameters, FoldAmyloid was reported to obtain: for the scale of the expected packing density Sn = 75%, Sp = 74%, for the donor scale Sn = 69%, Sp = 78%, for the acceptor scale Sn = 0.77 and Sp = 74% . Our method, trained on the same dataset as FoldAmyloid, with a 5-residue sliding window, obtained AUC ROC = 0.82, the diagonal point of the ROC curve was Sn = 75% and Sp = 75%.
We also tested our method on full length amyloid proteins. For all full protein independent tests we were using our method trained on hexapeptides from Waltz dataset, which does not include their fragments . To apply a full version of our algorithm, with recognition of the most relevant windows in the positive training instances, we applied a window of length 5. Four full-length amyloid proteins were tested: amyloid-β, τ, amylin, and alpha-synuclein. The results are presented in Figure 3, where black blocks indicate location of amyloidogenic segments obtained with wl = 0.14, which was equivalent to the specificity of 60% obtained on Waltz dataset with a cross-validation method. The brown blocks at the top of lines indicate where the amyloidigenic segments would begin if a different wl value would be assumed. We compared the classification results to the experimental data. The circles show amyloidogenic segments obtained experimentally by different groups, working on protein fragments of various lengths. Amyloid-β: 13-24 HHQKLVFFAED, 11-26 EVHHQKLVFFAEDVG 48-53 , amylin: 48-53 FLVHSS, 55-60 NFGAIL ; Alpha-syn: 35-40 EGVLYV , 61-73 EQVTNVGGAVVTG, 66-74 VGGAVVTGV ; Tau: 274-279 KVQIIN , 306-311 VQIVYK [9, 10, 27].
The method was capable of finding most of the segments that have already been experimentally confirmed. It can be observed that other fragments have also been shown as potential hot-spots, however most of them have not been experimentally tested.
Finally, we merged all the experimental datasets to study the application of our method for practical recognition of the amyloidogenic sequences. The extended dataset contained all experimentally studied peptides of 4-10 aminoacids. Figure 4 presents the average-value ROC curve obtained with our method on this dataset from 40 independent trials by 4-fold cross-validation. The total AUC ROC was 0.80 and the optimal (diagonal) classification point had sensitivity Sn = 74% and specificity Sp = 74%. The quantiles of 0.95, 0.85 and median are presented as a boxplot at the diagonal classification point of the ROC curve.
Based on this extended experimental dataset, we trained our method for finding amyloidogenic windows in aminoacid sequences, and made it available as a web tool called FISH Amyloid (Hot Spot Is Found in Amyloid - reversed), which is currently available at http://www.comprec.pwr.wroc.pl/COMPREC_home_page.html. The service uses 5-residue sliding windows, both for training and classification, displaying the score value at the beginning of each window. Those residues that belong to at least one positive window are classified as positive and denoted by “1”. The list of fragments that constituted the extended dataset is also available at the service site.
The classification on the extended dataset was also compared with the performance of Waltz and FoldAmyloid (packing density) methods. Using 75% of data in each of 4 test, FoldAmyloid showed Sn = 58%, Sp = 75%, Waltz obtained Sn = 71%, Sp = 83%, and FISH Amyloid in the same 4 tests achieved Sn = 76% and Sp = 76% (see Additional file 1).
The most interesting feature of the method presented here is its ability to reveal a co-occurrence pattern found in the positive training dataset. The pattern includes pairs of aminoacids with their positions, which most frequently occur together. The patterns found in the full experimental dataset is presented in Figure 5. Table 3 shows the final pairs after executing the cut-off at the threshold of 0.4.
Co-localized pairs of aminoacids
All + sup35
S-I, Y-Y, L-Y, I-I
V-I, T-I, V-Y, F-I
R-R, T-I, V-I
V-I, L-I, N-Y
I-I, I-F, Y-R, Y-I
The co-occurrence pattern obtained with the sliding window of length 5 after training on extended experimental dataset. The first letter of each pair corresponds to the window location indicated by vertical numbers, the second letter to a number indicated horizontally. The table was obtained from data presented in Figure 5 after executing the cut off for the threshold of 0.4.
We proposed an original classification method which recognizes classification pattern in sequences, taking into account position dependent frequency of aminoacids and site specific co-occurrence between their pairs. The method reveals the characteristic co-occurrence pattern of the data. Moreover, it is able to find the segments with the co-occurrence pattern of the highest scoring, also in long training sequences, and use them for the training. Our method was applied to the problem of recognition of amyloidogenic segments and it showed a good potential for their classification. We obtained good results for a sliding window of lengths 6 and 5. The web tool FISH Amyloid, using this method trained on full experimental dataset of amyloid fragments 4-10 aminoacids long, with 5-residue sliding window, is currently available at our server: http://www.comprec.pwr.wroc.pl/COMPREC_home_page.html (it will be moved to http://www.comprec.edu.pwr.wroc.pl/COMPREC_home_page.html). FISH Amyloid offers prediction of amyloidogenic segments in protein sequences.
This work was in part supported by the grant N N519 643540 from National Science Center of Poland. The access to computers and clusters through Wroclaw Centre for Networking and Supercomputing at Wroclaw University of Technology is greatly acknowledged.
Institute of Biomedical Engineering and Instrumentation, Wroclaw University of Technology
Jaroniec CP, MacPhee CE, Bajaj VS, McMahon MT, Dobson CM, Griffin RG: High-resolution molecular structure of a peptide inan amyloid fibril determined by magic angle spinning NMR spectroscopy.Proc Natl Acad Sci U S A 2004, 101:711–716.PubMed CentralPubMedView Article
Makin OS, Atkins E, Sikorski P, Johansson J, Serpell LC: Molecular basis for amyloid fibril formation and stability.Proc Natl Acad Sci U S A 2005, 102:315–320.PubMed CentralPubMedView Article
Nelson R, Sawaya MR, Balbirnie M, Madsen AO, Riekel C, Grothe R, Eisenberg D: Structure of the cross- beta spine of amyloid-like fibrils.Nature 2005, 435:773–778.PubMed CentralPubMedView Article
Sawaya MR, Sambashivan S, Nelson R, Ivanova MI, Sievers SA, Apostol MI, Thompson MJ, Balbirnie M, Wiltzius JJW, McFarlane HT, Madsen AØ, Riekel C, Eisenberg D: Atomic structures of amyloid cross β-spines reveal varied steric zippers.Nature 2007, 447:453–457.PubMedView Article
Fernandez-Escamilla AM, Rousseau F, Schymkowitz J, Serrano L: Prediction of sequence-dependent and mutational effects on the aggregation of peptides and proteins.Nat Biotechnol 2004, 22:1302–1306.PubMedView Article
Thompson MJ, Sievers SA, Karanicolas J, Ivanova MI, Baker D, Eisenberg D: The 3D profile method for identifying fibril-forming segments of proteins.Proc Natl Acad Sci U S A 2006, 103:4074–4078.PubMed CentralPubMedView Article
Goldschmidt L, Tenga PK, Riek R, Eisenberg D: Identifying the amylome, proteins capable of forming amyloid-like fibrils.PNAS 2010, 107:3487–3492.PubMed CentralPubMedView Article
Galzitskaya OV, Garbuzynskiy SO, Lobanov MY: Prediction of amyloidogenic and disordered regions in protein chains.PLoS Comput Biol 2006, 2:e177.PubMed CentralPubMedView Article
Garbuzynskiy SO, Lobanov MY, Galzitskaya OV: FoldAmyloid: a method of prediction of amyloidogenic regions from protein sequence.Bioinformatics 2010, 26:326–332.PubMedView Article
Trovato A, Chiti F, Maritan A, Seno F: Insight into the structure of amyloid fibrils from the analysis of globular proteins.PLoS Comput Biol 2006, 2:e170.PubMed CentralPubMedView Article
Trovato A, Seno F, Tosatto SC: The PASTA server for protein aggregation prediction.Protein Eng Des Sel 2007, 20:521–523.PubMedView Article
Conchillo-Solé O, de Groot NS, Avilés FX, Vendrell J, Daura X, Ventura S: AGGRESCAN: a server for the prediction and evaluation of "hot spots" of aggregation in polypeptides.BMC Bioinformatics 2007, 8:65.PubMed CentralPubMedView Article
Zhang Z, Chen H, Lai L: Identification of amyloid fibril-forming segments based on structure and residue-based statistical potential.Bioinformatics 2007, 23:2218–2225.PubMedView Article
Tartaglia GG, Vendruscolo M: The Zyggregator method for predicting protein aggregation propensities.Chem Soc Rev 2008, 37:1395–1401.PubMedView Article
Tartaglia GG, Vendruscolo M: Proteome-level interplay between folding and aggregation propensities of proteins.J Mol Biol 2010, 402:919–928.PubMedView Article
Kim C, Choi J, Lee SJ, Welsh WJ, Yoon S: NetCSSP: web application for predicting chameleon sequences and amyloid fibril formation.Nucleic Acids Res 2009, 37:W469-W473.PubMed CentralPubMedView Article
O'Donnell CW, Waldispühl J, Lis M, Halfmann R, Devadas S, Lindquist S, Berger B: A method for probing the mutational landscape of amyloid structure.Bioinformatics 2011, 27:i34-i42.PubMed CentralPubMedView Article
Bryan AW Jr, O'Donnell CW, Menke M, Cowen LJ, Lindquist S, Berger B: STITCHER: dynamic assembly of likely amyloid and prion β-structures from secondary structure predictions.Proteins 2011, 80:410–420.PubMed CentralView Article
Bryan AW Jr, Menke M, Cowen LJ, Lindquist SL, Berger B: BETASCAN: probable beta-amyloids identified by pairwise probabilistic analysis.PLoS Comput Biol 2009, 5:e1000333.PubMed CentralPubMedView Article
Frousios KK, Iconomidou VA, Karletidi CM, Hamodrakas SJ: Amyloidogenic determinants are usually not buried.BMC Struct Biol 2009, 9:44.PubMed CentralPubMedView Article
Stanislawski J, Kotulska M, Unold O: Machine learning methods can replace 3D profile method in classification of amyloidogenic hexapeptides.BMC Bioinformatics 2013, 14:21.PubMed CentralPubMedView Article
Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH: The WEKA data mining software: an update.ACM SIGKDD Explorations Newsletter 2009, 11:10–18.View Article
Maurer-Stroh S, Debulpaep M, Kuemmerer N, de la Paz Lopez M, Martins IC, Reumers J, Morris KL, Copland A, Serpell L, Serrano L, Schymkowitz JW, Rousseau F: Exploring the sequence determinants of amyloid structure using position-specific scoring matrices.Nat Methods 2010, 7:237–242.PubMedView Article
David MP, Concepcion GP, Padlan EA: Using simple artificial intelligence methods for predicting amyloidogenesis in antibodies.BMC Bioinformatics 2010, 11:79.PubMed CentralPubMedView Article
Kuhlman B, Baker D: Native protein sequences are close to optimal for their structures.Proc Natl Acad Sci U S A 2000, 97:10383–10388.PubMed CentralPubMedView Article
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