Continuous Distributed Representation of Biological Sequences for Deep Proteomics and Genomics

Continuous Distributed Representation of Biological Sequences for Deep Proteomics and Genomics Ehsaneddin Asgari Mohammad R. K. Mofrad

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Continuous Distributed Representation of Biological Sequences for Deep Proteomics and Genomics 2015 PLOS ONE 10.1371/journal.pone.0141287 asgari2015-protvec asgari2015-protvec.txt, the project's staged copy 86c263d6db8785ddf6ea74c6e6ab9b67fd10ecaa cc-by biology

the paper's own words

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137 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them Protein and gene sequences treated as text, and whether a word-embedding trained on them captures biophysical and biochemical structure. method distributed vector representation of protein sequences system-or-tool-buildingsystem-or-tool-building mechanismsembedding overlapping k-mers (n-grams) of a sequence as a single dense vector via a neural Skip-gram model A protein is split into three shifted non-overlapping 3-gram sequences rather than one overlapping stream, which triples the corpus and was chosen by cross-validation Because Skip-gram places sequences with similar contexts near each other, 3-grams sharing biophysical properties end up adjacent without ever being told those properties The embedding is trained once on the whole database and then reused as a feature extractor, so downstream tasks need no retraining Continuity of a property over the space is measured by the smallest Lipschitz constant, and read against the same measure on a space with the labels shuffled Families with fewer than ten instances have validation sets the authors describe as statistically insufficient, so a weighted rather than plain average accuracy had to be used.what this limits: the per-family accuracy figures for small families: FOR THE FAMILIES WITH NUMBER OF INSTANCES LESS THAN 10, THE VALIDATION [set is statistically insufficient], which is why a weighted average is reported The DisProt visualisations are not on a comparable scale to the FG-Nups ones because the DisProt set is much smaller.what this limits: any visual comparison between the DisProt and FG-Nups panels: THE SCALES OF COLUMNS (A),(B) WERE NOT COMPARABLE WITH COLUMN (C) Almost all FG-Nup sequences used are computational predictions rather than curated entries.what this limits: the disorder demonstration as an empirical result: ONLY 10 SEQUENCES OUT OF 1,138 DISORDERED SEQUENCES EXIST IN SWISS-PROT - the set is mostly computational prediction, not curated observation The headline accuracy is the mean over 7,027 SEPARATE binary classifications, each with equal numbers of positive and negative sequences, so the chance baseline for each is 50% - not an assignment among 7,027 familieswhat this limits: the headline accuracy: it is the mean over 7,027 separate binary family classifications, each built with equal numbers of positives and negatives That figure is nonetheless compared against studies doing different and harder tasks - 54 families in one case, SCOP family detection in anotherwhat this limits: the comparison against prior work: THE REPORTED ACCURACIES OF A PREVIOUS STUDY ... HAVE BEEN IN THE RANGE OF 69.1-99.6% FOR 54 PROTEIN FAMILIES - a wide band, and a different family count Accuracy falls monotonically as rarer families are included, from 94% over the top thousand to 91% over the top four thousand, and the overall figure is weighted to reduce the influence of the rarestwhat this limits: the headline accuracy figure: it is a WEIGHTED AVERAGE ACCURACY, and accuracy falls as rarer families are included The disordered-protein results are at or near 100%, which for a sequence task on two databases invites the question of what distinguishes the two sets besides disorderwhat this limits: the disordered-protein result, and this is an IDENTIFIED concern rather than an author concession: near-total separation (99.8%) of two databases invites the question whether something other than the biology distinguishes them The FG-Nups set is largely computational rather than experimental - only ten of its 1,138 sequences are in Swiss-Protduplicate of: limitations[2] · what this limits: the same scope as limitations[2], with the count: the FG-Nup set is largely computational, only ten of its 1,138 sequences being curated entries Window size and embedding size were chosen on the same cross-validation used to justify the representationwhat this limits: the choice of window and embedding size: they were selected on the SAME 2-FOLD CROSS-VALIDATION used to justify the representation, so the reported consistency is partly a property of the selection distributed word representations / the Skip-gram model, applied to protein sequences The Skip-gram model and the whole distributional idea that meaning is fixed by context, carried over by treating a 3-residue k-mer as a word and a protein as a sentence The word-analogy demonstration (king - man + woman = queen) imported as the evidence that embedding spaces carry structure worth looking for in sequences Content-addressable memory as the original motivation for distributed representation, credited explicitly rather than assumed the PDB comparison set chosen so its AVERAGE LENGTH MATCHES the FG-Nup set, which is longer on averageeliminates: sequence LENGTH as the feature separating the two classes - a classifier handed systematically shorter negatives learns to count residues, and would score well while knowing nothing about the biology · outcome (stated by the tagger, no quotation): held protein familyprotein family DisProtDisProt language of lifelanguage of life conceptual analogyconceptual analogy content-addressablecontent-addressable partial descriptionspartial descriptions contextcontext positive training samplespositive training samples general-purpose representationgeneral-purpose representation sub sequencessub sequences shifted non-overlapping wordsshifted non-overlapping words three sequencesthree sequences corpus consisting of 546,790 × 3 = 1,640,370 sequences of 3-gramscorpus consisting of 546,790 × 3 = 1,640,370 sequences of 3-grams negative samplingnegative sampling positive samplespositive samples negative samplesnegative samples incorrect (w, c) pairsincorrect (w, c) pairs vector of size 100vector of size 100 summation of the vector representation of overlapping 3-gramssummation of the vector representation of overlapping 3-grams negative examplesnegative examples 10 × fold cross-validations10 × fold cross-validations specificityspecificity sensitivitysensitivity primary sequence information aloneprimary sequence information alone extensive information for feature extractionextensive information for feature extraction continuity of these propertiescontinuity of these properties best Lipschitz constantbest Lipschitz constant protein-spaceprotein-space random spacerandom space randomly shuffling the labels of 3-gramsrandomly shuffling the labels of 3-grams short mapshort map contractioncontraction physical and chemical propertiesphysical and chemical properties informative and dense representationinformative and dense representation continuity of these properties → best Lipschitz constantThe best Lipschitz constant is calculated to measure property continuity; measured-by is absent from the edge registry. summation of the vector representation of overlapping 3-grams → vector of size 100Summing the overlapping 3-gram vectors produces a sequence vector of size 100; represented-as is absent from the edge registry. language of life → human languagesThe paper draws an analogy between biological and human languages; analogous-to is absent from the edge registry. context → meaning of a wordContext characterizes word meaning; characterizes is absent from the edge registry. negative sampling → positive samplesNegative sampling uses observed positive pairs; composed-from is absent from the edge registry. negative sampling → negative samplesNegative sampling uses generated negative pairs; composed-from is absent from the edge registry. embedding → encode biological sequences in a given problemTraining once enables later reuse for sequence encoding; enables-reuse is absent from the edge registry. k = 1 → short mapA function with k equal to one is called a short map; threshold-name is absent from the edge registry. 0 ≤ k < 1 → contractionA function with k below one is called a contraction; threshold-name is absent from the edge registry. word - in natural language: a semantic or syntactic unit whose meaning is fixed by the words around it word - biological: three consecutive amino acids, defined outright as the unit that plays the role a word plays in text family - the broad sense: a set of evolutionarily related proteins, which is what the classification task means by it family - the Pfam sense: one of four sibling categories, so that a Pfam 'family' is a species of the very thing the word names accuracy - per-family binary: one classifier per family with equal positives and negatives, which is what every number in Table 2 is smoothness - measured against a shuffled control rather than in absolute terms, so the reported figure is a ratio and not a value Language of life - conceptual analogy mapping biological sequences to human language Content-addressable representation - nearby storage of items and properties enabling partial-cue recall Embedding context - neighboring words that characterize a word’s meaning Shifted 3-gram construction - three non-overlapping offset tokenizations per protein ProtVec training corpus - 1,640,370 shifted 3-gram sequences derived from Swiss-Prot Negative sampling - observed pairs pulled together and incorrect pairs used to prevent vector collapse Protein sequence vector - sum of all overlapping 3-gram representations Balanced one-family classifier - equal positive and randomly sampled negative instances Specificity / sensitivity - true-negative and true-positive family-classification rates Sequence-only feature learning - contrast with methods requiring extensive engineered properties Best Lipschitz constant - smallest bound quantifying continuity of embedding-space properties Scrambled space - control created by randomly shuffling 3-gram property labels phenomenon: distributed vector representation of protein sequencesa second reading reaching the same value. Recorded: distributed vector representation of protein sequences — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. builds-on → NLP / word2vec methods builds-on → the Skip-gram / Word2Vec word embedding model replicates → the prior study of biophysical differences between FG-Nups and typical DisProt disordered proteins (ref. 29) extends → the Skip-gram word-embedding model of Mikolov et al. critiques → existing family classification methods that require hand-engineered biophysical features supports → the earlier finding of biophysical differences between FG-Nups and typical DisProt sequences ProtVec —is-a→ BioVecstrength of the relation: 1ProtVecBioVec GeneVec —is-a→ BioVecstrength of the relation: 1GeneVecBioVec EVIDENCE CORRECTED (RE-GROUNDED) · distributed representation —operationalised-as→ ProtVecEVIDENCE CORRECTED: RE-GROUNDED. The old span named only 'distributed representation'. This sentence names both and identifies the one as the other: the distributed representation 'called ProtVec'. — strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the representation is CALLED ProtVec; same-as fits, operationalised-as is the wrong type.distributed representationProtVec EVIDENCE CORRECTED (RE-GROUNDED) · protein family —operationalised-as→ PfamEVIDENCE CORRECTED: RE-GROUNDED. The old span named only ProtVec's use. This sentence names both and states what Pfam is FOR protein families - a source of them. — strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the study used Pfam information to classify protein families; operationalised-as is loose.protein familyPfam FG-Nups —is-a→ disordered proteinsstrength of the relation: 1FG-Nupsdisordered proteins DisProt —operationalised-as→ disordered proteinsstrength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its span and kept, but DisProt is a database OF disordered proteins; operationalised-as is the wrong type.DisProtdisordered proteins FG-Nups —distinct-from→ DisProtstrength of the relation: 1FG-NupsDisProt ProtVec —operationalised-as→ pre-trainingstrength of the relation: 0.9 · note: DOUBTFUL, found by an audit that read the edge against its span: type: 'can be considered as' is closer to is-a. The edge is kept live; a reader should weigh it with this in mind. Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says ProtVec 'can be considered' pre-training; operationalised-as overstates a hedge.ProtVecpre-training EVIDENCE CORRECTED (RE-GROUNDED) · feature extraction —contrasted-with→ distributed representationEVIDENCE CORRECTED: RE-GROUNDED. The old span named neither endpoint. This sentence names both and states the contrast in the paper's own voice: n-grams used for TRAINING A REPRESENTATION rather than AS FEATURES. — strength of the relation: 0.9feature extractiondistributed representation primary sequence information alone —contrasted-with→ extensive information for feature extractionthe relation itself is separately evidenced · strength of the relation: 1 · note: The paper explicitly contrasts its sequence-only method with feature-rich existing methods.primary sequence information aloneextensive information for feature extraction protein-space —distinct-from→ random spacethe relation itself is separately evidenced · strength of the relation: 1 · note: The protein space is reported as twice as smooth as the random control space.protein-spacerandom space 93% ± 0.06% — average protein-family classification accuracy of ProtVecabout this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. 100-dimensional — dimensionality of the 3-gram embedding space 546,790 sequences — the Swiss-Prot training corpus 1,640,370 — training sequences after the three-way shifted split 324,018 protein sequences in 7,027 families — the classification benchmark 100-dimensional — the embedding size before projection 0.50 versus 1.01, ratio 0.51 — average Lipschitz constant in the protein space against the scrambled control 694 proteins, 1539 disordered and 95 ordered regions — the DisProt release used A protein sequence is represented as one dense n-dimensional vector learned with neural-network methods. On protein family classification, ProtVec reaches 93% ± 0.06% average accuracy, outperforming existing methods.about this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. 3-grams sharing biophysical and biochemical properties cluster together in the embedding. the protein space is on average about twice as smooth in physical and chemical properties as a random space weighted average accuracy of 93% across 7,027 protein families, more reliable than existing methods accuracy declines steadily as rarer families are added, 94% to 91% between the top 1,000 and top 4,000 disordered sequences were separated from structured ones at 99.8% and 100.0% the embedding needs training only once and can then serve any downstream sequence task EVIDENCE CORRECTED (RE-GROUNDED) · 3-gramEVIDENCE CORRECTED: RE-GROUNDED. The published string was not verbatim in EITHER copy of the paper. A quote field promises the author's words; this held 'each protein sequence IS represented'. The paper says WILL BE - it is describing a procedure it is about to apply, not a property that holds.3-gram family classification accuracyabout this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted.family classification accuracy primary sequenceprimary sequence protein familyprotein family window sizewindow size embedding vector sizeembedding vector size ProtVecProtVec EVIDENCE CORRECTED (RE-GROUNDED) · n-gramEVIDENCE CORRECTED: RE-GROUNDED. The published string was not verbatim in EITHER copy of the paper. A quote field promises the author's words; this held 'Every biological sequence involves fixed-length overlapping n-grams'. THE PAPER'S SENTENCE IS ABOUT A TECHNIQUE, NOT ABOUT SEQUENCES: 'the simplest and most common technique in bioinformatics to study sequences involves fixed-length overlapping n-grams'. The rewrite turned a statement about method into a statement about nature.n-gram distributed representationdistributed representation protein familyprotein family biological wordbiological word disordered proteinsdisordered proteins feature extractionfeature extraction scrambled spacescrambled space statistical-significancestatistical-significance specificityspecificity sensitivitysensitivity cross-validationcross-validation weighted averageweighted average

Abstract

We introduce a new representation and feature extraction method for biological sequences. Named bio-vectors (BioVec) to refer to biological sequences in general with protein-vectors (ProtVec) for proteins (amino-acid sequences) and gene-vectors (GeneVec) for gene sequences, this representation can be widely used in applications of deep learning in proteomics and genomics. In the present paper, we focus on protein-vectors that can be utilized in a wide array of bioinformatics investigations such as family classification, protein visualization, structure prediction, disordered protein identification, and protein-protein interaction prediction. In this method, we adopt artificial neural network approaches and represent a protein sequence with a single dense n-dimensional vector. To evaluate this method, we apply it in classification of 324,018 protein sequences obtained from Swiss-Prot belonging to 7,027 protein families, where an average family classification accuracy of 93%±0.06% is obtained, outperforming existing family classification methods. In addition, we use ProtVec representation to predict disordered proteins from structured proteins. Two databases of disordered sequences are used: the DisProt database as well as a database featuring the disordered regions of nucleoporins rich with phenylalanine-glycine repeats (FG-Nups). Using support vector machine classifiers, FG-Nup sequences are distinguished from structured protein sequences found in Protein Data Bank (PDB) with a 99.8% accuracy, and unstructured DisProt sequences are differentiated from structured DisProt sequences with 100.0% accuracy. These results indicate that by only providing sequence data for various proteins into this model, accurate information about protein structure can be determined. Importantly, this model needs to be trained only once and can then be applied to extract a comprehensive set of information regarding proteins of interest. Moreover, this representation can be considered as pre-training for various applications of deep learning in bioinformatics. The related data is available at Life Language Processing Website: http://llp.berkeley.edu and Harvard Dataverse: http://dx.doi.org/10.7910/DVN/JMFHTN .

Introduction

Nature uses certain languages to describe biological sequences such as DNA, RNA, and proteins. Much like humans adopt languages to communicate, biological organisms use sophisticated languages to convey information within and between cells. Inspired by this conceptual analogy, we adopt existing methods in natural language processing (NLP) to gain a deeper understanding of the “language of life” with the ultimate goal to discover functions encoded within biological sequences [ 1 – 4 ].

Feature extraction is an important step in data analysis, machine learning and NLP. It refers to finding an interpretable representation of data for machines that can increase performance of learning algorithms. Even the most sophisticated algorithms would perform poorly if inappropriate features are used, while simple methods can potentially perform well when they are fed with the appropriate features. Feature extraction can be done manually or in an unsupervised fashion. In this paper, we propose an unsupervised data-driven distributed representation for biological sequences. This method, called bio-vectors (BioVec) in general and more specifically protein-vectors (ProtVec) for proteins, can be applied to a wide range of problems in bioinformatics, such as protein visualization, protein family classification, structure prediction, domain extraction, and interaction prediction. In this approach, each biological sequence is embedded in an n-dimensional vector that characterizes biophysical and biochemical properties of sequences using neural networks. In the following, we first explain how this method works and how it is trained from 546,790 sequences of Swiss-Prot database. Subsequently, we will analyze the biophysical and the biochemical properties of this representation qualitatively and quantitatively. To further evaluate this feature extraction method, we apply it in classification of 7,027 protein families of 324,018 protein sequences in Swiss-Prot. In the next step, we use this approach for visualization and characterization of two categories of disordered sequences: the DisProt database as well as a database of disordered regions of phenylalanine-glycine nucleoporins (FG-Nups). Finally, we classify these protein families using support vector machine (SVM) classifiers [ 5 ]. As a key advantage of the proposed method, the embedding needs to be trained only once and then may be used to encode biological sequences in a given problem. The related data and future updated will be available at: http://llp.berkeley.edu and Harvard Dataverse: http://dx.doi.org/10.7910/DVN/JMFHTN .

Distributed Representation

Distributed representation has proved one of the most successful approaches in machine learning [ 6 – 10 ]. The main idea in this approach is encoding and storing information about an item within a system through establishing its interactions with other members. Distributed representation was originally inspired by the structure of human memory, where the items are stored in a “content-addressable” fashion. Content-based storing allows for efficiently recalling items from partial descriptions. Since the content-addressable items and their properties are stored within a close proximity, such a system provides a viable infrastructure to generalize features attributed to an item.

Continuous vector representation, as a distributed representation for words, has been recently established in natural language processing (NLP) as an efficient way to represent semantic/syntactic units with many applications. In this model, each word is embedded in a vector in an n-dimensional space. Similar words have close vectors, where similarity is defined in terms of both syntax and semantic. The basic idea behind training such vectors is that the meaning of a word is characterized by its context, i.e. neighboring words. Thus, words and their contexts are considered to be positive training samples. Such vectors can be trained using large amounts of textual data in a variety of ways, e.g. neural network architectures like the Skip-gram model [ 10 ].

Interesting patterns have been observed by training word vectors using Skip-gram in natural language. Words with similar vector representations show multiple degrees of similarity. For instance, K i n g → - M a n → + W o m a n → resembles the closest vector to the word Q u e e n → [ 11 ].

In this work, we seek unique patterns in biological sequences to facilitate biophysical and biochemical interpretations. We show how Skip-gram can be used to train a distributed representation for biological sequences over a large set of sequences, and establish physical and chemical interpretations for such representations. We propose this as a general-purpose representation for protein sequences that can be used in a wide range of bioinformatics problems, including protein family classification, protein interaction prediction, structure prediction, motif extraction, protein visualization, and domain identification. To illustrate, we specifically tackle visualization and protein family classification problems.

Protein Family Classification

A protein family is a set of proteins that are evolutionarily related, typically involving similar structures or functions. The large gap between the number of known sequences versus the amount of known functional information about sequences has motivated family (function) identification methods based on primary sequences [ 12 – 14 ]. Protein Family Database (Pfam) is a widely used source for protein families [ 15 ]. In Pfam, a family can be classified as a “family”, “domain”, “repeat”, or “motif”. In this study, we utilize ProtVec to classify protein families in Swiss-Prot using the information provided by Pfam database and we obtain a high classification accuracy.

Protein family classification based on the primary structures (sequences) has been performed using classifiers such as support vector machine classifier (SVM) [ 16 – 18 ]. Besides the primary sequence, the existing methods typically require extensive information for feature extraction, e.g. hydrophobicity, normalized Van der Waals volume, polarity, polarizability, charge, surface tension, secondary structure and solvent accessibility. The reported accuracies of a previous study on family classification have been in the range of 69.1–99.6% for 54 protein families [ 16 ]. In another study, researchers used motifs from protein interactions for detecting Structural Classification of Proteins (SCOP) [ 19 ] families for 368 proteins, and obtained a classification accuracy of 75% at sensitivity of 10% [ 20 ]. In contrast, our proposed approach is trained based solely on primary sequence information, yet achieving high accuracy when applied in classifications of protein families.

Disordered Proteins

Proteins can be fully or partially unstructured, i.e. lacking a secondary or ordered tertiary three-dimensional structure. Due to their abundance and the critical roles they play in cell biology, disordered proteins are considered to be an important class of proteins [ 21 ]. Several studies have focused on disordered peptides and their functional analysis in recent years [ 22 – 24 ].

In the present work, we introduce ProtVec for the visualization and characterization of two categories of disordered proteins: DisProt database as well as a database of disordered regions of phenylalanine-glycine nucleoporins (FG-Nups) [ 25 ].

DisProt is a database of experimentally identified disordered proteins that categorizes disordered and ordered regions of a collection of proteins [ 26 ]. DisProt Release 6.02 consists of 694 proteins presenting 1539 disordered, and 95 ordered regions. FG-Nups dataset is a collection of FG-Nups disordered sequences [ 27 ]. Nucleoporins form the nuclear pore complex (NPC), the sole gateway for bidirectional transport of cargo between the cytoplasm and the nucleus in eukaryotic cells [ 28 ]. Since FG-Nups are mostly computationally identified, only 10 sequences out of 1,138 disordered sequences exist in Swiss-Prot. A recent study on features of FG-Nups versus DisProt showed biophysical differences between FG-Nups and average DisProt sequences [ 29 ].

We further propose using protein-vectors for the visualization of biological sequences. Simplicity and biophysical interpretations encoded within ProtVec distinguishes this method from the previous work [ 30 , 31 ]. As an example, we use ProtVec for the visualization of FG-Nups, DisProt, and structured PDB proteins. This visualization confirms the results obtained [ 29 ] on the biophysical features of FG-Nups and typical disordered proteins. Furthermore, we employ ProtVec to classify FG-Nups versus random PDB sequences as well as DisProt disordered regions versus disport ordered regions.

Methods

Protein-Space Construction

Our goal is to construct a distributed representation of biological sequences. In the training process of word embedding in NLP, a large corpus of sentences should be fed into the training algorithm to ensure sufficient contexts are observed. Similarly, a large corpus is needed to train distributed representation of biological sequences. We use Swiss-Prot as a rich protein database, which consists of 546,790 manually annotated and reviewed sequences.

The next step in training distributed representations is to break the sequences into sub sequences (i.e. biological words). The simplest and most common technique in bioinformatics to study sequences involves fixed-length overlapping n-grams [ 32 – 34 ]. However, instead of using n-grams directly in feature extraction, we utilize n-gram modeling for training a general purpose distributed representation of sequences. This so-called embedding model needs to be trained only once and may then be adopted in feature extraction part of specific problems.

In n-gram modeling of protein informatics, usually an overlapping window of 3 to 6 residues is used. Instead of taking overlapping windows, we generate 3 lists of shifted non-overlapping words, as shown in Fig 1 . Evaluating K-nearest neighbors in a 2xfold cross-validation for different window sizes, embedding vector sizes and overlapping versus non-overlapping n-grams showed a more consistent embedding training for a window size of 3 and the mentioned splitting.

Fig 1. Protein sequence splitting.

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In order to prepare the training data, each protein sequence will be represented as three sequences (1, 2, 3) of 3-grams.

The same procedure is applied on all 546,790 sequences in Swiss-Prot, thus at the end we obtain a corpus consisting of 546,790 × 3 = 1,640,370 sequences of 3-grams (3-gram is a “biological” word consisting of 3 amino acids). The next step is training the embedding based on such data through a Skip-gram neural network. In training word vector representations, Skip-gram attempts to maximize the probability of observed word sequences (contexts). In other words, for a given training sequence of words we would like to find their corresponding n-dimensional vectors maximizing the following average log probability function. Such a constraint allows similar words to assume a similar representation in this space.

argmax v , v 1 N ∑ i = 1 N ∑ - c ≤ j ≤ c , j ≠ 0 log p ( w i + j | w i ) p ( w i + j | w i ) = exp ( v ′ w i + j T v w i ) ∑ k = 1 W exp ( v ′ w k T v w i ) , (1)

where N is the length of the training sequence, 2 c is the window size we consider as the context, w i is the center of the window, W is the number of words in the dictionary and v w and v w ′ are input and output n-dimensional representations of word w , respectively. The probability p ( w i + j | w i ) is defined using a softmax function. Hierarchical softmax or negative sampling are efficient approximations of such a softmax function. In the implementation we use (Word2Vec) [ 10 ] negative sampling has been utilized, which is considered as the state-of-the-art for training word vector representation. Negative sampling uses the following objective function in the calculation of the word vectors:

arg max θ ∏ ( w , c ) ∈ D p ( D = 1 | c , w ; θ ) ∏ ( w , c ) ∈ D ′ p ( D = 0 | c , w ; θ ) , (2)

where D is the set of all word and context pairs (w, c) existing in the training data (positive samples) and D ′ is a randomly generated set of incorrect (w, c) pairs (negative samples).

p ( D = 1| w , c ; θ ) is the probability that (w, c) pair came from the training data and p ( D = 0| w , c ; θ ) is the probability that ( w , c ) did not come from the training data. The term p ( D = 1| c , w ; θ ) can be defined using a sigmoid function on the word vectors:

p ( D = 1 | w , c ; θ ) = 1 1 + e - v c · v w ,

where the parameters θ are the word vectors we train within the optimization framework: v c and v w ∈ R d are vector representations for the context c and the word w respectively [ 35 ]. In Eq (2) , the positive samples maximize the probabilities of the observed (w, c) pairs in the training data, while the negative samples prevent all vectors from having the same value by disallowing some incorrect (w, c) pairs. To train the embedding vectors, we consider a vector size of 100 and a context size of 25. Thus each 3-gram is presented as a vector of size 100.

Protein-Space Analysis

To qualitatively analyze the distribution of various biophysical and biochemical properties within the training space, we project all 3-gram embeddings from 100-dimensional space to a 2D space using Stochastic Neighbor Embedding [ 36 ]. Mass, volume, polarity, hydrophobicity, charge, and van der Waals volume properties were analyzed. The data is adopted from [ 37 ]. In addition, to quantitatively measure the continuity of these properties in the protein-space, the best Lipschitz constant, i.e. the smallest k satisfying is calculated:

d f ( f p r o p ( w 1 ) , f p r o p ( w 2 ) ) ≤ k × d w ( w 1 , w 2 ) , (3)

where f is the scale of one of the properties of a given 3-grams (e.g., average mass, hydrophobicity, etc.), d is the distance metric, d f is the absolute value of score differences, and d w is Euclidian distance between two 3-grams w 1 and w 2 . The Lipschitz constant is calculated for the aforementioned properties.

Protein Family Classification

To evaluate the strength of the proposed representation, we set up a classification task on protein families. Family information of 324,018 protein sequences in Swiss-Prot is extracted from the Protein Family (Pfam) database, resulting in a total of 7,027 distinct families for Swiss-Prot sequences. Each sequence is represented as the summation of the vector representation of overlapping 3-grams. Thus, each sequence is presented as a vector of size 100. For each family type, the same number of instances from Swiss-Prot are selected randomly to form the negative examples. Support vector machine classifiers are used to evaluate the strength of ProtVec in the classification of protein families through 10 × fold cross-validations. We perform the classification over 7,027 protein families consisting of 324,018 sequences. For the evaluation we report specificity (true negative rate), sensitivity (true positive rate), and the accuracy of family classifications.

S e n s i t i v i t y = T P r a t e = T P T P + F N

S p e c i f i c i t y = 1 - F P r a t e = T N F P + T N

A c c u r a c y = T P + T N P + N

Visualization and Classification of Disordered Proteins

Two databases of disordered proteins are used for disordered protein prediction: DisProt database (694 sequences) and FG-Nups dataset (1,138 sequences).

FG-Nups Characterization

To distinguish the characteristics of FG-Nups, a collection of 1,138 FG-Nups and two random sets of 1,138 structured proteins from Protein Data Bank (PDB) [ 38 ] are compared. Since PDB sequences on average have a shorter length than disordered proteins, the two sets are selected from PDB in such a way that they have an average length of 900 residues, the same as the average length of the disordered protein dataset. For visualization purposes, the ProtVec is reduced from 100 dimensions to a 2D space using Stochastic Neighbor Embedding [ 36 ].

We quantitatively evaluate how ProtVec can be used to distinguish between FG-Nups versus typical PDB sequences using a support vector machine binary classifier. The positive examples were the aforementioned 1,138 disordered FG-Nups proteins and the negative examples (again 1,138 sequences) are selected randomly from PDB with the same average length of disordered sequences (≈ 900 residues). We present each protein sequence as a summation of its ProtVecs of all 3-grams. Since the average length of structured proteins is shorter than FG-Nups, and to avoid trivial cases, the PDB sequences are selected in a way to maintain the same average length.

DisProt Characterization

To distinguish the characteristics of DisProt sequences, we use DisProt Release 6.02, consisting of 694 proteins presenting 1539 disordered and 95 ordered regions, and perform the same experiment as for FG-Nups with DisProt sequences.

Results

Protein-Space Analysis

Although the protein-space is trained based on only the primary sequences of proteins, it offers several interesting biochemical and biophysical implications. In order to study these features, we visualized the distribution of different criteria, including mass, volume, polarity, hydrophobicity, charge, and van der Waals volume in this space. To do so, for each 3-gram we conducted qualitative and quantitative analyses as described below.

Qualitative Analysis

In order to visualize the distribution of the aforementioned properties, we projected all 3-gram embeddings from 100-dimensional space to a 2D space using Stochastic Neighbor Embedding (t-SNE) [ 36 ]. In the diagrams presented in Fig 2 , each point represents a 3-gram and is colored according to its scale in each property. Interestingly, as can be seen in the figure, 3-grams with the same biophysical and biochemical properties were grouped together. This observation suggests that the proposed embedding not only encodes protein sequences in an efficient way that proved useful for classification purposes, but also reveals some important physical and chemical patterns in protein sequences.

Fig 2. Normalized distributions of biochemical and biophysical properties in protein-space.

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In these plots, each point represents a 3-gram (a word of three residues) and the colors indicate the scale for each property. Data points in these plots are projected from a 100-dimensional space a 2D space using t-SNE. As it is shown words with similar properties are automatically clustered together meaning that the properties are smoothly distributed in this space.

Quantitative Analysis

Although Fig 2 illustrates the smoothness of protein-space with respect to different physical and chemical meanings, we required a quantitative approach to measure the continuity of these properties in the protein-space. To do so, we calculated the best Lipschitz constant. For all 6 properties presented in Fig 2 , we calculated the minimum k . To evaluate this result we made an artificial space called “scrambled space” by randomly shuffling the labels of 3-grams in the 100 dimensional space. Table 1 contains the values of Libschitz constants for protein-space versus the “scrambled space” with respect to different properties and also their ratio.

Table 1. Using Lipschitz number to evaluate the continuity of ProtVec with respect to biophysical and biochemical properties.

Lipschitz Number

Property protein-Space The scrambled space Ratio

Mass 0.3137 0.6605 0.4750

Volume 0.3742 0.6699 0.5586

Van Der Waal Volume 0.3629 0.6431 0.5643

Polarity 0.4757 1.2551 0.3790

Hydrophobicity 0.608 1.448 0.4203

Charge 0.8733 1.3620 0.6412

Average 0.50 1.01 0.51

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Normally if k = 1 the function is called a short map, and if 0 ≤ k < 1 the function is called a contraction. The results suggest that the protein-space is on average 2-times smoother in terms of physical and chemical properties than a random space. This quantitative result supports our qualitative observation of the space structure in Fig 2 , and suggests that our training space encodes, 3-grams in an informative manner.

Protein Family Classification

In order to evaluate the strength of ProtVec, we performed classifications of 7,027 protein families and obtained a weighted average accuracy of 93 ± 0.06%, which exhibits a more reliable result than the existing methods. In contrast to the existing methods, our proposed approach is trained based on primary sequence information alone.

Table 2 shows the sensitivity, specificity, and the accuracy for the most frequent families in Swiss-Prot. These results suggest that structural features of proteins can be accurately predicted from the primary sequence information solely. The results for all 7,027 families can be found in Supplementary Information, see S1 File . The average accuracy for the first 1,000 (261,149 sequences), 2,000 (293,957 sequences), 3,000 (308,292 sequences), and 4,000 (316,135 sequences) frequent families were respectively 94% ± 0.05%,93% ± 0.05%, 92% ± 0.06%, and 91% ± 0.08%. To compute the overall accuracy for all 7,026 families, we calculated the weighted average accuracy, because for the families with number of instances less than 10, the validation set are not statistically sufficient and they should have less contribution in the overall accuracy. The weighted accuracy of all 7,027 families (weighted based on the number of instances) was 93% ± 0.06%.

Table 2. Performance of protein family classification using SVM and ProtVec over some of the most frequent families in Swiss-Prot.

Families are sorted with respect to their frequency in Swiss-Prot.

Training instances Classification Result

Family name # of positive sequences # of negative sequences Specificity Sensitivity Accuracy

50S ribosome-binding GTPase 3,084 3,084 0.95 0.93 0.94

Helicase conserved C-terminal domain 2,518 2,518 0.83 0.80 0.82

ATP synthase alpha-beta family, nucleotide-binding domain 2,387 2,387 0.98 0.97 0.97

7 transmembrane receptor (rhodopsin family) 1,820 1,820 0.95 0.96 0.95

Amino acid kinase family 1,750 1,750 0.91 0.92 0.91

ATPase family associated with various cellular activities (AAA) 1711 1711 0.92 0.90 0.91

tRNA synthetases class I (I, L, M and V) 1,634 1,634 0.97 0.97 0.97

tRNA synthetases class II (D, K and N) 1,419 1,419 0.88 0.83 0.85

Major Facilitator Superfamily 1,303 1,303 0.95 0.97 0.96

Hsp70 protein 1,272 1,272 0.97 0.97 0.97

NADH-Ubiquinone-plastoquinone (complex I), various chains 1,251 1,251 0.97 0.97 0.97

Histidine biosynthesis protein 1,248 1,248 0.96 0.97 0.97

TCP-1-cpn60 chaperonin family 1,246 1,246 0.95 0.96 0.95

EPSP synthase (3-phosphoshikimate 1-carboxyvinyltransferase) 1,207 1,207 0.96 0.96 0.96

Aldehyde dehydrogenase family 1,200 1,200 0.93 0.94 0.94

Shikimate–quinate 5-dehydrogenase 1,128 1,128 0.87 0.89 0.88

GHMP kinases N terminal domain 1,120 1,120 0.88 0.92 0.90

Ribosomal protein S2 1,083 1,083 0.95 0.96 0.95

Ribosomal protein S4–S9 N-terminal domain 1,072 1,072 0.95 0.97 0.96

Ribosomal protein L16p-L10e 1,053 1,053 0.95 0.96 0.96

KOW motif 1,047 1,047 0.93 0.95 0.94

Uncharacterized protein family UPF0004 1,044 1,044 0.95 0.97 0.96

Ribosomal protein S12-S23 1,016 1,016 0.94 0.98 0.96

GHMP kinases C terminal 1,011 1,011 0.88 0.92 0.90

Ribosomal protein S14p-S29e 997 997 0.93 0.98 0.95

Ribosomal protein S11 980 980 0.96 0.98 0.97

UvrB-uvrC motif 968 968 0.94 0.96 0.95

Ribosomal protein L33 958 958 0.96 0.98 0.97

BRCA1 C Terminus (BRCT) domain 956 956 0.94 0.95 0.95

RF-1 domain 950 950 0.93 0.97 0.95

Ankyrin repeats (3 copies) 944 944 0.89 0.88 0.88

Ribosomal protein L20 932 932 0.96 0.99 0.97

RNA polymerase beta subunit 912 912 0.94 0.97 0.95

Ribosomal protein S18 908 908 0.93 0.97 0.95

ATP synthase B-B CF(0) 900 900 0.92 0.94 0.93

Peptidase family M20-M25-M40 889 889 0.92 0.93 0.93

Ribosomal protein L18e-L15 887 887 0.93 0.96 0.95

Glucose inhibited division protein A 886 886 0.95 0.96 0.95

NADH-ubiquinone-plastoquinone oxidoreductase chain 4L 885 885 0.94 0.97 0.96

lactate-malate dehydrogenase, NAD binding domain 880 880 0.92 0.94 0.93

HD domain 879 879 0.93 0.93 0.93

Ribosomal protein S10p-S20e 873 873 0.95 0.97 0.96

Pyridoxal-phosphate dependent enzyme 870 870 0.91 0.91 0.91

Ribosomal L18p-L5e family 860 860 0.93 0.96 0.94

Ribosomal protein L3 855 855 0.94 0.97 0.96

tRNA synthetases class I (M) 843 843 0.94 0.96 0.95

UbiA prenyltransferase family 841 841 0.94 0.95 0.95

Ribosomal protein L4–L1 family 841 841 0.94 0.95 0.95

Ribosomal protein S16 840 840 0.93 0.97 0.95

Ribosomal protein S13-S18 840 840 0.94 0.97 0.95

MraW methylase family 837 837 0.95 0.98 0.96

Ribosomal L32p protein family 825 825 0.94 0.97 0.95

Elongation factor TS 819 819 0.94 0.97 0.96

Tetrahydrofolate dehydrogenase-cyclohydrolase, catalytic domain 817 817 0.94 0.96 0.95

ATP synthase delta (OSCP) subunit 813 813 0.93 0.96 0.94

tRNA synthetases class I (C) catalytic domain 812 812 0.95 0.97 0.96

SecA Wing and Scaffold domain 805 805 0.95 0.97 0.96

Ribonuclease HII 795 795 0.93 0.94 0.93

Ribosomal protein L31 795 795 0.97 0.99 0.98

Ribosomal L27 protein 794 794 0.98 0.99 0.99

IPP transferase 794 794 0.93 0.95 0.94

GTP-binding protein LepA C-terminus 793 793 0.96 0.98 0.97

Ribosomal protein L17 791 791 0.92 0.96 0.94

Ribosomal protein L23 790 790 0.91 0.96 0.94

Ribosomal protein L10 781 781 0.90 0.92 0.91

Ribosomal protein L19 780 780 0.94 0.97 0.95

Ribosomal protein S20 774 774 0.95 0.97 0.96

Ribosomal protein L35 769 769 0.93 0.97 0.95

Phosphoglucomutase-phosphomannomutase, C-terminal domain 768 768 0.92 0.96 0.94

AMP-binding enzyme 767 767 0.87 0.89 0.88

Ribosomal prokaryotic L21 protein 766 766 0.93 0.96 0.95

tRNA methyl transferase 759 759 0.94 0.96 0.95

Ribosomal L29 protein 757 757 0.95 0.97 0.96

Glycosyl transferase family, a-b domain 754 754 0.90 0.91 0.91

Translation initiation factor IF-2, N-terminal region 750 750 0.96 0.98 0.97

Ribosomal L28 family 749 749 0.93 0.98 0.95

Glycosyl transferase family 4 739 739 0.96 0.98 0.97

tRNA synthetases class I (R) 736 736 0.93 0.96 0.95

Bacterial trigger factor protein (TF) C-terminus 733 733 0.95 0.96 0.95

For the first 1,000 families 261,149 261,149 0.92 0.95 0.94

For the first 2,000 families 293,957 293,957 0.90 0.96 0.93

For the first 3,000 families 308,292 308,292 0.89 0.96 0.92

For the first 4,000 families 316,135 316,135 0.87 0.96 0.91

Weighted average for all 7,027 families 324,018 324,018 0.91 0.95 0.93

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Disordered Proteins Visualization and Classification

Due to the functional importance of disordered proteins, prediction of unstructured regions of disordered proteins and determining the sequence patterns featured in disordered regions is a critical problem in protein bioinformatics. We evaluated the ability of ProtVec to characterize and discern disordered protein sequences from structured sequences.

FG-Nups Characterization

In this case study, we used the FG-Nups collection of 1,138 disordered proteins containing disorder regions with a fraction of at least one third of the sequence length. For comparison purposes, we also collected two sets of structured proteins from Protein Data Bank (PDB).

In order to visualize each dataset, we reduced the dimensionality of the protein-space using Stochastic Neighbor Embedding [ 36 , 39 ] and then generated the 2D histogram of all overlapping 3-grams occurring in each dataset. As shown in Fig 3 (see column (b)), the two random sets from structured proteins had nearly identical patterns. However, the FG-Nups dataset exhibits a substantially different pattern. To amplify the characteristic of disordered sequences we have also examined the histogram of disordered regions of FG-Nups (see Fig 3 , column (a)).

Fig 3. Visualization of protein sequences using ProtVec can characterize FGNUPs versus Disport disordered sequences and structured sequences.

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Column (a) compares FG Nup sequences 2D histogram (at the bottom) with 2D histogram of FG Nup disordered regions (on top). Column (b) compares 2D histogram two random sets of structured sequences with the same average length as the FG-Nups. Column (c) compares between 2D histogram of DisProt sequences (at the bottom) and 2D histogram of DisProt disordered regions (on top).

In the next step, we quantitatively evaluated how ProtVec can be used to distinguish between FG-Nups versus typical PDB sequences using a support vector machine binary classification. The positive examples were the above mentioned 1,138 disordered FG-Nups proteins and negative examples (again 1,138 sequences) were selected randomly from PDB with the same average length of disordered sequences (≈ 900 residues). We represented each protein sequence as a summation of its ProtVecs of all 3-grams. Since on average the length of structured proteins were shorter than FG-Nups, in order to avoid trivial cases, the PDB sequences were selected in such a way as to maintain the same average length. But still, an accuracy of 99.81% was obtained with high sensitivity and specificity ( Table 3 ). The distribution of the classified proteins in a 2D space is shown in Fig 4 .

Table 3. The performance of FG-Nups disordered protein classification in a 10xFold cross-validation using SVM.

Sensitivity Specificity Accuracy

0.9987 0.9974 0.9981

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Fig 4. Classification of FG-Nups versus PDB structured sequences.

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In this figure, each point presents a protein projected into a 2D space.

DisProt characterization

In this part, we used DisProt consisting of 694 proteins presenting 1539 disordered, and 95 ordered regions. We performed the same analysis as we did for FG-Nups with DisProt sequences (see Fig 3 column (c)). Since the size of DisProt was relatively small compared to that of the FG-Nups, the scales of columns (a),(b) were not comparable with column (c) (see Fig 3 ). The visualization of disordered regions of DisProt sequences ( Fig 3 column (c), on top) revealed a different characteristic than FG-Nups disordered regions ( Fig 3 column (a), on top). A visual comparison between Figs 3 and 2 suggest that the FG-Nups have a significantly higher amount of hydrophobic residues and less polar residues in their disordered regions than the experimentally identified disordered proteins in DisProt [ 27 , 29 ]. Additionally, the DisProt disordered regions versus DisProt ordered regions can be classified with 100% accuracy respectively using SVM and ProtVec.

Conclusions

An unsupervised data-driven distributed representation, called ProtVec, was proposed for application of machine learning approaches in biological sequences. By training this representation solely on protein sequences, our feature extraction approach was able to capture a diverse range of meaningful physical and chemical properties. We demonstrated that ProtVec can be used as an informative and dense representation for biological sequences in protein family classification, and obtained an average family classification accuracy of 93%.

We further proposed ProtVec as a powerful approach for protein data visualization and showed the utility of this approach by providing an example in characterization of disordered protein sequences vs. structured protein sequences. Our results suggest that ProtVec can characterize protein sequences in terms of biochemical and biophysical interpretations of the underlying patterns. In addition, this dense representation of sequences can help to discriminate between various categories of sequences, e.g. disordered proteins. Furthermore, we demonstrated that ProtVec was able to identify disordered sequences with an accuracy of nearly 100%. The related data is available at: http://llp.berkeley.edu and Harvard Dataverse: http://dx.doi.org/10.7910/DVN/JMFHTN .

Another advantage of this method is that embeddings could be trained once and then used to encode biological sequences in any given problem. In general, machine learning approaches in bioinformatics can widely benefit from bio-vectors (ProtVec and GeneVec) representation. This representation can be considered as pre-training for various applications of deep learning in bioinformatics. In particular, ProtVec can be used in protein interaction predictions, structure prediction, and protein data visualization.

Supporting Information

S1 File. The results of family classification task for all 7,027 families. (XLSX)

Click here for additional data file. (316.7KB, xlsx)

Acknowledgments

Fruitful discussions with Kiavash Garakani, Mohammad Soheilypour, Zeinab Jahed, Mohaddeseh Peyro, Hengameh Shams and other members of the Molecular Cell Biomechanics Lab at the University of California Berkeley are gratefully acknowledged.

Data Availability

All relevant data are within the paper and its Supporting Information files. Our web-based tools and trained data are available at Life Language Processing website: http://llp.berkeley.edu and through the Dataverse database: http://dx.doi.org/10.7910/DVN/JMFHTN , and will be regularly updated for calculation/classification of ProtVecs as well as visualization of biological sequences.

Funding Statement

Financial support from National Science Foundation through a CAREER Award (CBET-0955291) is gratefully acknowledged. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.