Deep Learning Meets Biology: How Does a Protein Helix Know Where to Start and Stop?

Machine Learning for Classification of Protein
Helix Capping Motifs
Sean Mullane, Ruoyan Chen, Sri Vaishnavi Vemulapalli,
Eli J. Draizen, Ke Wang, Cameron Mura, Philip E. Bourne
University of Virginia, spm9r, rc3my, sv2fr, ed4bu, kw5na, cmura, peb6a@virginia.edu
Abstract - The biological function of a protein stems from
its 3-dimensional structure, which is thermodynamically
determined by the energetics of interatomic forces
between its amino acid building blocks (the order of amino
acids, known as the sequence, defines a protein). Given the
costs (time, money, human resources) of determining
protein structures via experimental means like X-ray
crystallography, can we better describe and compare
protein 3D structures in a robust and efficient manner, so
as to gain meaningful biological insights? We begin by
considering a relatively simple problem, limiting
ourselves to just protein secondary structural elements.
Historically, many computational methods have been
devised to classify amino acid residues in a protein chain
into one of several discrete “secondary structures”, of
which the most well-characterized are the geometrically
regular ɑ-helix and β-sheet; irregular structural patterns,
such as ‘turns’ and ‘loops’, are less understood. Here, we
present a study of Deep Learning techniques to classify the
loop-like end cap structures which delimit ɑ-helices.
Previous work used highly empirical and heuristic
methods to manually classify helix capping motifs.
Instead, we use structural data directly—including (i)
backbone torsion angles computed from 3D structures, (ii)
macromolecular feature sets (e.g., physicochemical
properties), and (iii) helix cap classification data (from
CAPS-DB)—as the ground truth to train a bidirectional
long short–term memory (BiLSTM) model to classify
helix cap residues. We tried different network
architectures and scanned hyperparameters in order to
train and assess several models; we also trained a Support
Vector Classifier (SVC) to use as a baseline. Ultimately,
we achieved 85% class-balanced accuracy with a deep
BiLSTM model.
Index Terms – Bidirectional LSTM, Deep learning, Helix
capping, Protein structure
INTRODUCTION
Proteins, which are one of the basic types of biological
macromolecules (along with the nucleic acids DNA and
RNA), consist of long, polymeric chains of amino acid
residues [1]. The vast array of known protein functions
includes structuring and organizing the cell, binding and
transporting molecules, transducing signals, and catalyzing
biochemical reactions (enzymes). The detailed function of a
protein is tied to its 3-dimensional structure and dynamics,
and is ultimately governed by the statistical mechanics of the
forces (atomic interactions) between its constituent amino
acid residues; in general, the 3D structure is uniquely
determined by the amino acid sequence.
Misfolding or alterations in protein structure and
dynamics often compromise normal cellular functions, and
such disruptions are often linked to disease states (hereditary
and otherwise). For example, proteopathic diseases such as
prion (e.g. Creutzfeldt-Jakob disease) and various
amyloidoses are considered diseases of protein folding and
aggregation. By understanding how sequences fold into
unique structures, we can broaden our understanding of
protein function and potentially develop novel medical
treatments. At present, the 3D structures of only ~30% of
human proteins have been empirically determined [2]. Thus,
the problem of computationally predicting the 3D structure of
a protein, given the amino acid sequence, remains as a grand
challenge in biology.
Partitioning the backbone of a peptide chain (or really
any biopolymer) into discrete, well-defined geometric
segments is a first step of many common algorithms and
workflows in structural bioinformatics, e.g. for the
comparison and analysis of 3D protein structure. Many such
approaches, while effective, often include at least one crucial
step that is highly subjective in nature; for instance, the cutoff
values for the ϕ/ψ values of a Ramachandran map may lead to
the exact border of loop regions varying across algorithms, or
even different implementations of the same structural
assignment algorithm. A statistically well-principled,
objective, and minimally heuristic segmentation approach
would be a boon towards the development of improved
automated methods for structural analysis, and would also
provide a layer of abstraction (coarsening) from the peptide
chain that could facilitate robust (quantitative) comparisons
of structures across large databases (on genomic levels), with
less computational expense. In addition, such an approach
would bear upon quantitative definition of the ‘fold’ of a
protein (and other biopolymers, such as RNA, where the
problem of structural classification and comparison is even
more difficult). As an initial sub-problem in this broader field,
we consider the task of predicting helix capping motifs. In
particular, we demonstrate that machine learning models can
be trained to predict helix cap positions, offering a first step
towards more robust and statistically-based classification
systems for protein structural elements.

PRIOR WORK
Prior work on helix capping has used heuristic, highly manual
approaches to study the residues in the cap regions that define
the N- and C-termini of α-helices (these residues are termed
‘Nt’ and ‘Ct’, respectively). Historically, these cap regions
have been grouped with “loop”-type secondary structures;
however, in light of findings that their hydrophobic
interactions are critical to the stability of helices and to super-
secondary structural groups (e.g. α-α) [3], further
subclassification may be warranted. Therefore, Aurora &
Rose [3] described seven distinct capping motifs. More
recent work used a density-based clustering approach—based
on geometric quantities called the ‘D’ and ‘delta’ values of a
cap, and the distribution of ϕ/ψ backbone torsion (i.e.,
Ramachandran) values—to identify 905 distinct clusters [4].
In another recent effort, 3D conformational clustering was
used to map helix cap side-chain motifs to the loop structures
that they support; this ability could be useful in de novo
protein synthesis [5].
A common approach to protein secondary structure
prediction is to use non-sequential models, typically feed-
forward neural networks or SVMs [6]. However, these
models (i) are not ideal for classifying data which cannot be
naturally represented as a vector of fixed dimensionality, and
(ii) cannot capture long-range dependencies in the data.
Several authors have demonstrated the use of bidirectional
LSTM networks for prediction of protein secondary structures
and protein homology detection respectively ([7], [8]). Also
recently, a feed-forward neural network has been trained to
use NMR chemical shift information in order to predict
structural motifs such as helix caps at the N-terminus, C-
terminus and five types of β-turns [9].
DATA PRE-PROCESSING
Three data sources were chiefly used in this project. The first
data source consists of all known protein structures from the
full Protein Data Bank (PDB), in “macromolecular
transmission format” (MMTF) format. The PDB has nearly
150,000 3D biomolecular structures, determined via
experimental methods such as X-ray crystallography, nuclear
magnetic resonance (NMR) spectroscopy, and cryo-electron
microscopy. For all protein entries, we extracted secondary
structural information (protein identifier, chain, residue type,
and torsion angles.). The PDB does not contain information
about helix caps, so we used CAPS-DB [4]—a relational
database containing 67,530 helix caps (across 7390
proteins)—as the source of ground truth for the data we
extracted from the PDB. In order to label the data for
supervised learning, we merged the two datasets so that only
proteins with known helix capping information were
preserved. Based on capping information shown in Figure 1,
residues in between the “startcap” and “endcap” positions
were labeled as [0,1], to indicate helix caps. All other residues
were given labels of [1,0]. We used this “one-hot encoding”
of the binary variable so that we could use a Softmax output
layer activation. The data pre-processing was done using the
MMTF PySpark environment, which is a Python package that
contains APIs for distributed analysis and scalable mining of
3D biomacromolecular structures, such as available from the
PDB archive [10].
FIGURE I
PARTIAL CAPS-DB SAMPLE
A major challenge in working with multiple types of data,
generally from multiple sources (and with multiple degrees of
standards compliance, if indeed there are standards at all), is
ensuring that the data sets are merged correctly; indeed, “data
wrangling” is such a major activity, from the perspective of
software engineering in computational biology (and beyond),
that entire books are dedicated to the topic [11]. Although the
protein and protein chain IDs both used the standard PDB
identification labels, the CAPS-DB data source utilizes a
different resource, known as UniProtKB [12][13] for residue
numbering. Therefore, we developed an intermediate
“mapping layer” to bring the residue numbering schemes into
proper correspondence. We used files downloaded from
SIFTS [12][13] to determine the PDB ↔ UniProtKB
mapping. Although this provided the correct residue
numbering in the majority of cases, some mapping
information was found to be missing in 1,962 chains out of
6,714, accounting for ≈1.7% of all residues and including 490
entire chains. In cases where residues were missing from a
mapping file, we defaulted to labeling those residues as “not
cap”, the rationale being that this is (by far) the majority class
and so, given no information, is more likely to be the correct
label.
FEATURE ENGINEERING
From the PDB MMTF files we extracted the residue identity
and atomic positions in 3D space, from which we calculated
the ϕ and ψ backbone torsion angles. In CAPS-DB, cappings
were extracted from high-quality protein structures and
structurally clustered based on geometry and backbone
conformation (i.e., ϕ/ψ values). Because the conformation of
a given cap is encoded by a string of characters, each of which
describes a precise region of the (ϕ/ψ)-space, torsion angles
are among the most important features to consider in
predicting helix cap positions [4]. Because neural networks
typically train better when input features are distributed in
roughly the range of a standard normal distribution, we
normalized the torsion angles. This was done losslessly by
using both the sine and cosine values of each torsion angle; in

this way an angular value lying within [-180°, 180°] can be
precisely represented, in a normalized form, by a pair of
values, each lying between [-1, 1]. The four angular features
and twenty one-hot encoded residue features comprised our
basic, 24-feature data set.
We created a second dataset with additional features
using a third data source, FEATURE [14]. This software
computes various atomic features, as physicochemical
descriptors, for each atom within each residue in an input
protein structure. FEATURE calculates a quantized measure
of these properties for the six concentric shells around each
atomic site. The combination of six shells for each of the nine
properties results in 54 additional features. In order to coarsen
this data representation (from the atomic to the residue level),
we took the maximum value of each feature, considered
across all atoms in a given residue. Our basic feature set (i.e.,
the 24 descriptors mentioned above), combined with these
additional properties, yields a total of 78 features.
TABLE I
RESIDUE CLASS FEATURES (PER SHELL)
Class Number Residue Class
1 IS_HYDROPHOBIC
1 IS_CHARGED
1 IS_POLAR
1 IS_UNKNOWN
2 IS_NONPOLAR
2 IS_POLAR
2 IS_BASIC
2 IS_ACIDIC
2 IS_UNKNOWN
In terms of data preparation for the SVC model, a new
dataset was generated by adding neighboring rows as features
to each residue so as to account for the sequential nature of
the data. A ‘window size’ parameter was used to determine
the number of rows that would be added as features. For
residues at the protein termini, rows before the residue were
considered. In case of shorter sequences, for residues in the
center, rows before and after it were considered. Sequences
with length less than the window size were removed from the
original data before these operations; this is done to avoid
padding the data for sequences that are shorter than the
window size. As a representative example, a window size of
10 resulted in this filtering operation removing 18 protein
chains. Because of the added features (790 per residue), we
used principal component analysis (PCA) to reduce the
dimensionality of the feature space to 40 (accounting for
67.7% of variance in the data). Because the computational
complexity of an SVC model with a nonlinear kernel (e.g., the
radial basis function) is supra-quadratic (O(nfeatures*nsamples
2
)),
we sampled 10% of the data rows (98,078 samples spanning
3,968 protein chains) and divided into train and validation sets
in a ratio of 70:30.
For the deep neural network models, we kept the protein
chains intact as sequential data for the LSTMs. We used a
random 80/20 training/validation split, separated at the
protein chain level. We stored these as separate Pickle [15]
files for predictors, labels and (for the encoder/decoder
model) lagged labels.
MACHINE LEARNING MODELS
As a baseline approach for predicting helix caps, we trained a
supper-vector clustering (SVC) model using a Radial Basis
Function (RBF) kernel, with low γ and C values to get a
simpler decision function [16].
For streams of data which are inherently sequential in
nature (e.g., time-series), Recurrent Neural Networks (RNN)
are frequently employed. These networks feed the hidden
state of one timestep as an input to the next timestep.
Recurrent networks are some of the most widespread deep
learning techniques and are particularly effective for data
which has sequential information with cyclic connections.
This family of models includes the Long Short-Term Memory
(LSTM) and Gated Recurrent Units (GRU), among others.
LSTMs [17] are particularly useful when there are long-range
dependencies within the sequential data; they can
automatically detect both the long-term and short-term
dependency relationships, and determine how to process a
current subsequence according to the information extracted
from the prior subsequences [8]. Because proteins are
generally quite compact, globular entities—with chains that
can tightly fold back upon themselves—they do indeed
exhibit a network of long-range dependencies: the string of
amino acids defines the residue sequence, and residues far
apart in the linear sequence are often proximal in 3D space.
Compared to other methods, LSTMs can better identify
patterns of protein homology in purely sequence-based data
[8]. In our study, the primary model was a bidirectional‒
LSTM model. The bidirectional layer, added to a normal
LSTM, allows the model to deal with both forward and
backward dependencies and enhances predictive performance
[18].
MODEL OPTIMIZATION AND EVALUATION
To evaluate our models, we used three measures of
performance: accuracy, balanced accuracy (Qα) (1) , and F1
score (2).
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%
∗ (𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑟𝑒𝑐𝑎𝑙𝑙) (1)
𝐹1 = 2 ∗
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(2)
Precision and recall are defined as:
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 =
BC
BCADE
(3)
𝑟𝑒𝑐𝑎𝑙𝑙 =
BE
BEADC
(4)
In a binary classification framework, assuming equal
weight per residue and independence among residues, the
performance of a classifier can be fully described by the four
values True Negative, False Negative, True Positive and False
Positive [19]. No single measure can perfectly distill this
information, but in light of the class imbalance in our problem
(namely, that ~85% of all residues in our dataset are not caps),

we primarily consider the Qα and F1 metrics; these two
quantities account for the class imbalance, whereas the raw
accuracy (a single-class measure) can be misleadingly high,
even in the case of completely uninformative (i.e., random)
predictions, simply by virtue of the class imbalance.
Although evaluating protein structure prediction methods
can be confounded somewhat when homologous sequences
occur in the data set, for the sake of simplicity we did not try
to account for effects of protein homology in this work. To
mitigate overfitting on particular protein chains or chain
families in the training data set, our neural network
architecture employed regularization [20]. Also, note that we
took each residue in a helical cap as being equally informative
in weighting for our training loss function and evaluation
metrics. In future work, it may be helpful to consider some
parts of a cap, e.g. the central Ct and Nt residues, as being
more informative than, e.g., the last residue of the cap;
potentially, this could be achieved by encoding as a feature
various quantities such as the information content of each
position (number of bits, e.g. in a profile hidden Markov
model).
We examined several different BiLSTM model
architectures in order to try to find the optimum classifier
performance with our datasets. The variations included (i)
single-layer as well as deep LSTMs, (ii) the number of nodes
in the BiLSTM hidden layers, (iii) the weighting of the loss
function, (iv) the addition of dropout layers with varying drop
ratios, and (v) single as well as multiple dense layers after the
BiLSTM layers, with and without activation functions. We
implemented these models using Keras 2.2.4 with a
TensorFlow 1.12.0 backend.
Each model was trained using cross-entropy loss
functions and using the Adam optimizer, which is a form of
stochastic gradient descent [21]. Training periods varied from
30 to 75 epochs. We trained the models with a batch size of
unity. The rationale for this was that, because of the varying
sequence lengths in the data, batched training would require
padding to equalize these lengths. However, technical
limitations in the CuDNNLSTM layer in Keras [22], which
provides a GPU-enabled library for deep neural networks,
would cause the padded values to be considered in training
and evaluation (this layer does not support masking), and that
would be problematic for both training and evaluation.
In addition to varying the basic model architecture itself,
we also trained models with both the smaller set of 24 features
and the expanded set of 78 features, so as to determine the
relative utility of the additional features. The results of our
calculations are summarized in the remainder of this work.
TABLE II
MODEL ARCHITECTURE
Run Feats. LSTM
Layers
LSTM
Nodes
Dense
Layers
Dense
Activ.
Weight
Ratio
Drop-
out %
1 78 1 100 1 NA 1:1 0
2 78 1 100 1 NA 8:1 0
3 78 1 100 1 NA 8:1 25
4 78 1 100 1 NA 8:1 50
5 24 1 100 1 NA 8:1 0
6 24 1 20 1 NA 8:1 0
7 24 1 40 1 NA 8:1 0
8 24 1 40 1 NA 8:1 50
9 24 1 40 1 NA 7:1 50
10 24 1 40 1 NA 6:1 50
11 24 1 40 1 NA 5:1 50
12 24 1 40 2 ReLU 8:1 50
13 24 2 40,20 2 ReLU 8:1 50
14 24 3 40,30,
20
2 ReLU 8:1 50
15 78 2 100,50 1 NA 8:1 50
16 78 2 100,50 2 None 8:1 50
17 78 2 40,10 1 NA 8:1 50
RESULTS
The SVC model did not perform well, as might be
expected. The class-balanced accuracy was only 50.25%, and
the recall values indicate that the predictions were nearly
single-class and thus nearly devoid of information. The
model’s deficiency may stem from its inability to capture
long-ranged patterns/dependencies in the data—e.g., between
amino acid residues that are quite distant in sequence, but
potentially correlated (near one another) in 3D space.
TABLE III
SVC MODEL PERFORMANCE
Class Precision Recall F1
Not Cap 0.87 0.99 0.93
Cap 0.72 0.01 0.01
Of the BiLSTM models, the best-performing overall was
a deep model built with three BiLSTM layers (with 40, 30,
and 20 hidden nodes), followed by two dense layers with 50%
dropout between each layer. The first of these dense layers
used nodes with rectified linear unit (ReLU) activation
functions, and it had 10 hidden nodes.
TABLE IV
BILSTM MODEL PERFORMANCE, BY BEST VALIDATION SET F1 SCORE
Run Accuracy F1 Qa Best Epoch
1 0.8764 0.4791 0.6896 11
2 0.8155 0.5228 0.7907 12
3 0.8132 0.5212 0.8000 6
4 0.8034 0.5182 0.8078 8
5 0.8155 0.5228 0.7907 12
6 0.8188 0.5392 0.8264 36
7 0.8262 0.5489 0.8297 11
8 0.8213 0.5454 0.8318 15
9 0.8219 0.5429 0.8273 26
10 0.8369 0.5535 0.8202 13
11 0.8504 0.5612 0.8096 15
12 0.8030 0.5321 0.8376 12
13 0.8145 0.5480 0.8457 48
14 0.8234 0.5551 0.8430 31
15 0.8087 0.5332 0.8223 11
16 0.8096 0.5254 0.8103 31
17 0.8070 0.5236 0.8109 41
In general, we found improved performance across our
metrics with each additional layer; we did not test models
deeper than those described above. The best performance was
achieved with those models that used an initial hidden layer
with a node count moderately larger than the feature count;

significantly more hidden nodes than features resulted in
overfitting, while fewer resulted in lower overall accuracy
statistics.
FIGURE II
EFFECT OF NEURAL NETWORK LAYER DEPTH
The loss function weighting scheme had a large effect, as
might be anticipated. The models trained with the unweighted
binary cross-entropy loss were found to heavily optimize for
overall accuracy, at the expense of recall; this result is
reflected in the lower Qα and F1 scores. When using a cross-
entropy loss with a class weighting inversely proportional to
the prevalence of each of the two classes (cap, not cap), the
Qα and F1 scores were found to be maximal. However, we
observed a trade-off in terms of the Qα and F1 scores, as we
varied the class weight ratio from the 8:1 to 5:1; the latter had
a higher F1 score while the former had higher Qα as it more
severely over-predicted the cap class compared to the training
set prevalence.
FIGURE III
EFFECT OF NEURAL NETWORK LOSS FUNCTION WEIGHTING
Inclusion of additional features, as derived from
FEATURE, were not found to improve the predictive
performance of our models. This is a surprising result, since
hydrophobicity and polarity are believed to be important
physicochemical factors in helix capping interactions. Our
aggregation method (taking the maximal atom-based value
per residue) was potentially not ideal; future work can
consider other schemes for combination/aggregation of these
numerical values.
CONCLUSION
Our results reveal that the residue positions of helix caps—or
at least some sort of non-random (detectable) structural
‘signature’, which we take as being helix caps—can be
learned purely from amino acid sequences along with
corresponding conformational data (backbone φ/ψ angles).
This finding demonstrates that machine learning can be used
to identify patterns of helix capping, and suggests the
possibility of discovering a statistically robust, objective cap
classification scheme (i.e., minimal heuristics). We also find
that bidirectional LSTMs are particularly well-suited to
classifying protein sequences, likely because of the
importance of both long-term and short-term atomic
interactions in dictating protein folding and structural
stability. In future work, we could focus on developing an
encoder/decoder sequence-to-sequence BiLSTM model, as
such approaches offer superior performance (versus standard
BiLSTM models) in some scientific domains.
In terms of broader biomedical relevance, we note that
helices are viewed by many protein biophysicists as being less
prone to aggregation, versus β-rich elements; see, for
instance, various reviews in the extensive amyloid/protein
aggregation literature (e.g., [23]). Indeed, it has been argued
that sequestering sequences with β-propensities into helices
may offer a way to avoid aggregation [24]. As a potentially
interesting future direction, we can consider questions such as
whether engineering helix-capping signals into particular
disease-associated (β-forming) peptide regions (e.g., via the
CRISPR technology) may be a way to reduce their
amyloidogenicity? In this sense, note that studies of protein
helix capping are potentially of both fundamental significance
as well as more applied relevance.
ACKNOWLEDGMENT
We thank P. Alonzi (UVA) for AWS support. UVA’s Open
Data Lab and Data Science Institute provided computational
resources that contributed to our results. Portions of this work
were also supported by UVA and NSF CAREER award
MCB-1350957.
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AUTHOR INFORMATION
Sean Mullane, Data Scientist, UVA Health System, M.S.
Student, Data Science Institute, University of Virginia
Ruoyan Chen, M.S. Student, Data Science Institute,
University of Virginia
Sri Vaishnavi Vemulapalli, M.S. Student, Data Science
Institute, University of Virginia
Eli J. Draizen, PhD Student, Bourne and Mura
Computational Biosciences Lab, Department of Biomedical
Engineering, University of Virginia
Ke Wang, Research Scientist, Department of Computer
Science
Cameron Mura, Senior Scientist, Bourne and Mura
Computational Biosciences Lab, Department of Biomedical
Engineering, University of Virginia
Philip E. Bourne, Stephenson Chair of Data Science and
Director of the Data Science Institute and Professor of
Biomedical Engineering Director, University of Virginia

Deep Learning Meets Biology: How Does a Protein Helix Know Where to Start and Stop?

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