R E S E A R C H A R T I C L E
A protein sequence fitness function for identifying natural and
nonnatural proteins
Rahul Kaushik | Kam Y. J. Zhang
Laboratory for Structural Bioinformatics,
Center for Biosystems Dynamics Research,
Yokohama, Kanagawa, Japan
Correspondence
Kam Y. J. Zhang, Laboratory for Structural
Bioinformatics, Center for Biosystems
Dynamics Research, RIKEN, 1-7-22 Suehiro,
Yokohama, Kanagawa 230-0045, Japan.
Email: kamzhang@riken.jp
Funding information
Japan Society for the Promotion of Science,
Grant/Award Number: 18H02395
Abstract
The infinitesimally small sequence space naturally scouted in the millions of years
of evolution suggests that the natural proteins are constrained by some functional
prerequisites and should differ from randomly generated sequences. We have developed
a protein sequence fitness scoring function that implements sequence and
corresponding secondary structural information at tripeptide levels to differentiate
natural and nonnatural proteins. The proposed fitness function is extensively validated
on a dataset of about 210 000 natural and nonnatural protein sequences and
benchmarked with existing methods for differentiating natural and nonnatural proteins.
The high sensitivity, specificity, and percentage accuracy (0.81%, 0.95%, and
91% respectively) of the fitness function demonstrates its potential application for
sampling the protein sequences with higher probability of mimicking natural proteins.
Moreover, the four major classes of proteins (α proteins, β proteins, α/β proteins, and
α + β proteins) are separately analyzed and β proteins are found to score slightly
lower as compared to other classes. Further, an analysis of about 250 designed proteins
(adopted from previously reported cases) helped to define the boundaries for
sampling the ideal protein sequences. The protein sequence characterization aided
by the proposed fitness function could facilitate the exploration of new perspectives
in the design of novel functional proteins.
K E Y W O R D S
amino acid propensity, protein foldability, computational protein design, natural proteins,
protein sequence space, scoring of protein designs
1 | INTRODUCTION
Delineating the connection between protein sequence and its structure
is one of the most persuasive, debatable, and unresolved affairs
in the field of computational structure biology.1-3
In the last two
decades, the concepts of delicate contribution of natural selection
and the modest alteration by evolution in random copolymers in
emergence of known proteins is extensively discussed and argued for
its significance in origin of Life.4-8
The specificity of existent natural
proteins to encrypt unique protein structures is restricted within a limited
number of folds (1457 protein folds) which poses another scientific
challenge of quantifying the protein designability of sampled
sequences into the existing folds. Creating a protein to perform a
predefined or novel biological function(s) is often considered as protein
design. In general, protein design is formulated as composing an
amino acid sequence which should ideally fold into a stable structure,
meant to perform some biological function(s).9-13
The goals of protein
design include either desired optimization of certain characteristics
such as stability, solubility, and binding affinity or designing entirely
novel sequences resulting into novel structures or attaining remedial
or industrial utilities.14-17
A primary and a very crucial step of novel
protein design involves the computational identification or generation
of potential protein sequences having a considerably high probability
of mimicking the naturally occurring proteins and eventually folding
Received: 15 January 2020 Revised: 26 March 2020 Accepted: 7 May 2020
DOI: 10.1002/prot.25900
Proteins. 2020;88:1271–1284. wileyonlinelibrary.com/journal/prot © 2020 Wiley Periodicals, Inc. 1271
into a compact structure.18,19
Some of the earlier studies measured
the degree of randomness in the known protein sequences to explore
the logical explanations with conflicting inferences for constrained
available sequence space.5,7,8,19-22
Some of the previous computational
studies of random sequence proteins argued over the extent of
variability among natural protein sequences and random protein
sequences.23-25
In protein design regimes, folding into a distinct conformation
is foremost requirement. It is believed that the randomly
generated and de-novo evolved protein sequences tend to form a molten
globule state with marginal secondary structural elements.18,26,27
However, most of the recent approaches fortified with deep learning
and artificial intelligence have contributed significantly in classifying
the dataset6,7,19,28,29
but without exploring the underlying science.
For the 100 residue long protein sequences, the theoretical
sequences space of astronomically staggering 10130
proteins (20100
combinations) in contrast to the infinitesimal fraction of naturally
existing proteins. For instance, when a nonredundant dataset of all
available protein sequences in the UniProt database (22 million
sequences, excluding predicted, and uncertain proteins) is analyzed,
only 109
unique stretches of 100 residues could be extracted. This
huge decline in the number of available compact structures and
unique 100 residues polypeptides substantiate the possibility of some
underlying protein signatures at sequence level that lend the protein
with potential of imitating the natural proteins and fold into stable
structure. Some of the previous studies have utilized the concept of
neighboring effect of amino acid residues in dictating protein secondary
and tertiary structures.30-33
Here, we describe a sequence and secondary structure-based fitness
scoring function to identify potentially foldable/designable protein
sequences by differentiating them from nonnatural protein sequences.
The presented fitness function implements the competency scores
derived from sequences and corresponding secondary structures of
well-characterized known protein domains (natural proteins, NP) and
computationally generated nonnatural protein sequences with natural
amino acid compositions (NNP-NC) and with uniform amino acid compositions
(NNP-UC). The scoring function classifies a query protein
sequence into foldable (natural protein) or non-foldable (nonnatural
and/or random protein) depending on its competency scores compared
with natural and nonnatural protein sequences.
2 | MATERIALS AND METHODS
For the development of the scoring function, the datasets of natural
protein (NP) sequences (adopted from known protein domains) and
computationally generated nonnatural protein (NNP-NC and NNPUC)
sequences are compiled.
2.1 | Dataset compilation
The protein sequences and corresponding secondary structures of all
known protein domains in the latest stable release of the SCOPe
database,34
SCOPe 2.07 are extracted which comprises 274 230 protein
domains. These domains are subjected to clustering at 100%
sequence identity level using CD-HIT35
to filter out the redundant
proteins in the dataset. Post-clustering, resulting 77 280 domains are
further screened for the presence of non-standard amino acid residues,
missing residues (except for N and C terminals), domains having
less than 50 residues, domains having more than 700 residues, or
membrane protein domains. These filters resulted in a dataset of
58 758 globular protein domains as depicted in the Figure S1. The
100% sequence identity level filter is used to ensure the inclusion of a
maximum number of possible triplets of amino acid residues and
corresponding secondary structural elements. However, sequence
identity filters at 80%, 60%, and 40% sequence identity levels are also
used to explore the possibilities. A significant decline in the available
number of combinations of triplets of amino acid residues and
corresponding secondary structure is observed. The statistics related
to availability of combinations of triplets is shown in Figure S2 and
Supplementary Note I. The dataset corresponding to these protein
sequences is referred as natural proteins (NP) dataset hereafter, as it
is derived from naturally existing known proteins.
Similarly, a dataset of 65 000 proteins having sequence length varying
from 50 to 700 residues is generated computationally restraining
the amino acid compositions adopted from UniProtKB.36
Since the
dataset of computationally generated protein sequences is constrained
to the same amino acid composition as naturally existing proteins,
it is referred to as nonnatural protein dataset with natural distribution
of amino acid compositions (NNP-NC). The “makeprotseq” module
of EMBOSS37
is used for computationally generating these protein
sequences. As a cautionary measure, the NNP-NC dataset is also subjected
to clustering at 100% sequence identity level to avoid the
sequence redundancy. However, it is observed that these computationally
generated sequences did not have any redundancy at 100%
sequence identity.
2.2 | Extraction of secondary structural
information
For the selected natural protein (NP) dataset, the secondary structural
information at an individual residue level for each protein is extracted
using the standalone version of STRIDE secondary structure assignment
program.38
The 8-class secondary structure assignment of
STRIDE is converted into 3-class secondary structure assignment for
further processing. In this conversion, the 310 helices (G), π-helices (I),
and 4-turn helices (H) are grouped as helices, the extended strands in
β-sheet conformations (E) and isolated β-bridges (B) are pooled
together as strands (E), and the hydrogen bonded turns (T), coils
(C) and bends (S) are bundled as loops (C). For secondary structural
information corresponding to nonnatural proteins with natural AA
compositions (NNP-NC) dataset, secondary structure prediction using
standalone version PSIPRED (PSIPRED 4.02) is performed.39
Considering
the current state of the art for protein secondary structure prediction,
PSIPRED is reported to deliver a reasonably high accuracy
1272 KAUSHIK AND ZHANG
and thus used in present study. It is worth noting that the PSIPRED
failed to predict any secondary structure for 3862 proteins. These
proteins are discarded from any further processing. A sub-dataset of
58 758 proteins is selected from the nonnatural proteins (NNP-NC)
dataset (out of 61 138 proteins with predicted secondary structure).
This led into a total of 117 516 proteins sequences, comprising
58 758 proteins each in natural proteins (NP) and nonnatural proteins
with natural AA compositions (NNP-NC) datasets. To examine the differences
in amino acid neighbor preferences in different secondary
structures for computationally generated sequences NNP-NC, we
derived the conditional probabilities of triplets using natural protein
and nonnatural protein (NNP-NC) sequences and corresponding secondary
structures.
2.3 | Classifying into reference and test datasets
The natural proteins (NP) and nonnatural proteins (NNP-NC) datasets
are randomly separated into two parts each as reference dataset of
41 132 proteins and test dataset of 17 626 proteins (reference = 70%
and test = 30% of 58 758 proteins). This resulted into four subdatasets,
viz. natural proteins reference dataset (comprising 41 132
proteins), natural proteins test dataset (comprising 17 626 proteins),
nonnatural proteins (NNP-NC) reference dataset (comprising 41 132
proteins) and nonnatural proteins (NNP-NC) test dataset (comprising
17 626 proteins). The reference datasets are used for deriving a conditional
probability-based statistical model, leading to competency
scores of tripeptides and the test datasets are used for testing the
efficiency of competency scores in distinguishing the natural protein
(NP) and nonnatural protein (NNP-NC) sequences.
2.4 | Compiling sequence-based scoring libraries
For all the protein sequences in the natural proteins reference dataset,
tripeptides frequencies are calculated for all possible 8000 combinations.
Also, individual amino acid residues occurrence frequencies are
calculated from natural proteins reference dataset. It may be noted
that the natural protein reference dataset represents all the possible
combinations at tripeptides level sufficiently, encompassing more than
8 million tripeptides (depicted in Figure S3). The residue occurrence
frequencies and tripeptide frequencies are further used for calculating
tripeptide conditional probabilities using Equation (1). Notably, the
conditional probability calculated in Equation (1) considers forward
(C-terminal) and backward (N-terminal residue) neighborhoods of the
central residue. Also, this consideration takes care of directionality in
the tripeptides as P(YM|XNZC) is not same as P(YM|ZNXC). So, it may be
considered that the conditional probabilities of tripeptides calculated
in Equation (1) is inclusive of their residue-based adjacency and directionality
statistics.
P YMjXNZCð Þ =
P XYZð Þ
P Yð Þ
, ð1Þ
where X, Y, and Z belong to any of the standard amino acid residues;
P(YM|XNZC) is the conditional probability of residue “Y”, given a residue
“X” on its N-terminal and a residue “Z” on its C-terminal; P(XYZ) is the
probability of tripeptide “XYZ”; and P(Y) is the probability of residue
“Y”.
The conditional probabilities of all tripeptides as calculated using
Equation (1) are further used to compute a percentage sequence competency
score (CS-Score) at individual residue level by normalizing the
conditional probabilities with the maximum conditional probability in
all combinations of tripeptides. The CS-Score is calculated for the middle
residue in a tripeptide considering one adjacent residue on its
either side (one toward N-terminal and one toward C-terminal) using
Equation (2).
CS−score XNYMZCð Þ = 100
P YMjXNZCð Þ
Pmax AAMjAANAACð Þ
 
, ð2Þ
where CS-score (XNYM ZC) is the competency score of middle residue
“Y” given residues X and Z at its N-terminal and C-terminal, respectively;
P(YM|XNZC) is the conditional probability of residue “Y”, given a
residue “X” on its N-terminal and a residue “Z” on its C-terminal
(as computed in Equation (1)); and Pmax (AAM|AANAAC) is the maximum
conditional probability in all 8000 tripeptides.
The CS-Scores derived from Equation (2) resulted in 400 values
for an individual residue, accounting for the occurrence of any of the
20 amino acid residues on either side. The overall flow of computation
of CS-Scores is depicted in Figure 1A,B, with an example tripeptide,
Lys-Ala-Met. These scores are used to evaluate the overall competence
of protein sequences as discussed in results section.
2.5 | Compiling sequence and secondary structure
based scoring libraries
As mentioned above, the secondary structural information at 3-class
levels is compiled from natural proteins dataset. The tripeptide frequencies
along with corresponding secondary structure assignments
(Helix (H), Strand (E), and Coils (C)) are derived from the natural proteins
reference datasets for all possible combinations, that is, 216 000
combinations (203
× 33
). It may be noted that all the possible combinations
could not be observed in the natural protein reference dataset
as seven out of 27 secondary structure combinations are practically
not possible, viz. HEH, HEC, EHE, EHC, CHC, CHC, CEH. The secondary
structure directed tripeptide frequencies are used to derive the
probability of each available combination. Also, for all the individual
residues with their secondary structure assignment (20 × 3 combinations),
probabilities are calculated. The tripeptide and individual residue
probabilities are further used for calculating secondary structure
directed tripeptides conditional probabilities using Equation (3).
P Y
Sy
M jYSx
N YSz
C
 
=
P XSx
YSy
ZSz
 
P YSy
  , ð3Þ
KAUSHIK AND ZHANG 1273
where X, Y, and Z belong to any of the standard amino acid residues;
Sx, Sy, and Sz belong to any of the three secondary structure assignments
(H or E or C); P Y
Sy
M jYSx
N YSz
C
 
is the conditional probability of the
middle residue “Y” having secondary structure “Sy”, given a residue
“X” having secondary structure “Sx” toward N-terminal and a residue
“Z” having secondary structure “Sz” toward C-terminal; P XSx
YSy
ZSz
 
is the probability of a tripeptide “XYZ” having secondary structure
“SxSySz”; and P YSy
 
is the probability of middle residue “Y” having
secondary structure “Sy”. It may be noted that “S” can assume any of
the three secondary structure assignments (H, E, and C) but should be
exactly the same for corresponding middle, N-terminal, and C-terminal
residues to maintain the forward and backward neighborhood, and
directionality of secondary structural triplets.
The conditional probabilities calculated in Equation (3) are further
used for calculating sequence and secondary structure-based percentage
competency score (CSS-Score) at an individual residue level by
normalizing the conditional probabilities with the maximum conditional
probability in all available combinations of the tripeptides having
exactly same secondary structure assignment. The CSS-Score is
calculated for the middle residue in a tripeptide with its secondary
structure considering one adjacent residue of either side having specific
secondary structure assignments as shown in Equation (4).
CSS−score XSx
N Y
Sy
M Z
Sz
C
 
= 100
P Y
Sy
M jXSx
N ZSz
C
 
Pmax AA
Sy
M jAASx
N AASz
C
 
0
@
1
A, ð4Þ
where CSS−score XSx
N Y
Sy
M Z
Sz
C
 
is the sequence and secondary
structure-based competency score of the middle residue “Y” having a
secondary structure “Sy”, given a residue “X” having a secondary structure
“Sx” toward N-terminal and a residue “Z” having a secondary
structure “Sz” toward C-terminal; P Y
Sy
M jXSx
N ZSz
C
 
is the conditional
probability of the middle residue “Y” having a secondary structure
“Sy”, given a residue “X” having a secondary structure “Sx” toward
N-terminal and a residue “Z” having a secondary structure “Sz” toward
C-terminal; and Pmax AA
Sy
M jAASx
N AASz
C
 
is the maximum conditional
probability observed for any of the tripeptides with exactly the same
secondary structure for middle, N-terminal, and C-terminal residues.
The overall flow of computation of CSS-Scores is depicted in Figure 1C,
D with an example tripeptide, Lys-Ala-Met with helices as secondary
structure assignment for all the three residues. These scores are used
to evaluate the overall competence of natural and nonnatural protein
sequences. It is worth mentioning that the CS-Scores and CSS-Scores
are nonzero and positive values which may be maximum up to 100.
The presently used 100% sequence identity filter ensured inclusion
of the maximum number of possible triplets of amino acid residues and
corresponding secondary structural elements. The normalization used in
the Equations (2) and (4) calculates the score as a ratio of probabilities
and removes the statistical bias due to closely related sequences. To
investigate it further, all the natural protein sequences are clustered at
lower sequence identity filters viz. 80%, 60%, and 40% and CSS-Scores
libraries are compiled using Equations (3) and (4). A very high correlation
is observed among the CSS-Scores of the triplets derived from the
FIGURE 1 The overall flow of
compiling scoring libraries. (A) A
stepwise outline for calculating
sequence-based competency score
(CS-Score) of a residue by
considering its adjacent residues
toward N- and C-terminals. (B) A
stepwise depiction for calculation
of sequence-based competency
score of an example tripeptide
(Lys-Ala-Met is considered here).
(C) A stepwise outline for
calculating sequence and secondary
structure-based competency score
(CSS-Score) of a residue with a
specific secondary structure by
considering its adjacent residues
toward N- and C-terminals with
specific secondary structure
assignment. (D) A stepwise
depiction for calculation of
sequence and secondary structurebased
competency score of an
example tripeptide (Lys(H)-Ala(H)Met(H)
is considered here)
1274 KAUSHIK AND ZHANG
natural protein sequences at different sequence identity filters (40% and
100% = 0.95, 60% and 100% = 0.96%, 80% and 100% = 0.96) as shown
in Figure S2. Considering the high similarity in CSS-Score libraries and
the decline in triplet combinations at different sequence identity filters,
it may be posited that the filtering at 100% sequence identity should
not impart any bias to the statistics while ensuring the maximum utilization
of available information at triplet level.
2.6 | Calculation of competency score for a protein
sequence
For calculation of overall competency scores of a given protein
sequence, the CS- and CSS-Scores of individual residues are used. It
may be noted that the first residue (N-terminal residue) and the last
residue (C-terminal residue) do not have their individual CS- and CSSScores.
The overall CS- and CSS-Scores for a given protein may be
calculated as shown in Equations (5) and (6).
OverallCS−ScoreProtein =
Pi = N−1ð Þ
i = 2 CS−Score ið Þ
N−2ð Þ
, ð5Þ
where N is sequence length of the protein for which the overall CSScore
is to be calculated, CS-Score(i) is CS-Score of individual residues
as calculated in Equation (2).
OverallCSS−ScoreProtein =
Pi = N−1ð Þ
i = 2 CSS−Score ið Þ
N−2ð Þ
, ð6Þ
where N is sequence length of the protein for which the overall CSSScore
is to be calculated, CSS-Score(i) is CSS-Score of individual residues
as calculated in Equation (4).
2.7 | Competency scores for natural proteins
The sequence and sequence and secondary structure scoring libraries
(CS-scores and CSS-Scores) are used to calculate overall competency
scores for individual sequences in natural proteins reference dataset
of 41 132 proteins. The distribution curves for average competency
scores in terms of CS-Scores and CSS-Scores are shown in Figure 2
(colored in green). Additionally, the scatter plots of average competency
scores are shown in the Figure S4 for better insight. It is
observed that the sequence-based competency scores (CS-Scores)
averaged at 33.2 ± 3.14 and the sequence and secondary structurebased
competency scores (CSS-Scores) averaged at 18.0 ± 3.61 for
the reference dataset of natural protein sequences.
2.8 | Competency scores for nonnatural proteins
(NNP-NC)
For all the computationally generated protein sequences in nonnatural
protein (NNP-NC) reference dataset, the overall competency scores
for individual sequences are calculated by using tripeptide-based CSScores
and CSS-Scores. The distribution curves of CS-Scores and
CSS-Scores for nonnatural protein (NNP-NC) sequences are shown in
FIGURE 2 The distribution curves of
competency scores. (A) Distribution
curves for sequence-based competency
scores of natural (in green color) and
nonnatural (in red color) (CS-Scores).
(B) Distribution curve for sequence and
secondary structure-based competency
scores (CSS-Scores) for natural (in green
color) and nonnatural (in red color)
proteins in corresponding reference
datasets. The CSS-Scores are reflecting a
better differentiation of natural and
nonnatural proteins as compared to CS-
Scores
KAUSHIK AND ZHANG 1275
Figure 2 (colored in red). Also, the scatter plots of competency scores
of individual proteins in nonnatural proteins (NNP-NC) reference
dataset are depicted in the Figure S5. In case of reference dataset
of nonnatural protein (NNP-NC) sequences, the observed sequencebased
competency scores averaged at 31.7 ± 1.78 and the sequence
and secondary structure-based competency scores averaged at
14.6 ± 1.45.
In the present study, the secondary structure prediction is used
to estimate the likelihood of secondary structure for the nonnatural
proteins which is further utilized in performing overall scoring of nonnatural
proteins. Further, the method used here for the secondary
structure prediction is not exclusively dependent on amino acid substitution
matrix (viz. BLOSUM62), it also implements three different
neural network weights which are expected to improve the prediction
accuracy.
2.9 | Differences in competency scores of natural
proteins (NP) and nonnatural proteins (NNP-NC)
It is very difficult to conclude directly from the average competency
scores for natural proteins (NP) and nonnatural protein sequences
(NNP-NC) if these deviates meaningfully. For testing the significance
of differences in the average competency scores for natural (NP) and
nonnatural protein (NNP-NC) sequences in the reference datasets,
z-test of two samples for means is conducted on competency scores
of 41 132 natural protein sequences and 41 132 nonnatural protein
sequences (41 132 observations each). Based on the outcome of
z-test, in case of sequence-based competency scores (CS-Scores), the
natural protein sequences (μ = 33.2, σ = 3.14, n = 41 132) and nonnatural
protein (NNP-NC) sequences (μ = 31.7, σ = 1.78, n = 41 132)
are hypothesized to be different. The difference is very significant,
z = 96.73, P = .00 (two-tail). Also, in case of sequence and secondary
structure-based competency scores (CSS-Scores), the natural protein
sequences (μ = 18.0, σ = 3.61, n = 41 132) and nonnatural protein
(NNP-NC) sequences (μ = 14.6, σ = 1.45, n = 41 132) are hypothesized
to be different. The difference is very significant, z = 210.75,
P = .00 (two-tail). Further details of z-test statistics are provided in the
Table S1.
To investigate the differences in amino acid neighbor preferences
in different secondary structures for computationally generated nonnatural
protein sequences (NNP-NC), we derived the conditional probability
of triplets using these sequences and corresponding predicted
secondary structures. The conditional probabilities of triplets in natural
proteins and computationally generated nonnatural proteins showed a
correlation of 0.73, which supports the assumption that the computationally
generated protein sequences have differences in amino acid
neighbor preferences in different secondary structures. These differences
in the neighboring preferences may help in computational
sampling of protein sequences with higher potential of mimicking the
natural proteins. Further, to investigate the possibility of computational
bias, instead of their original secondary structures, the predicted
secondary structures for the natural proteins are used to recalculate
the CSS-Score libraries. It is observed that the CSS-Score libraries
computed using predicted secondary structures showed a significant
similarity (r = 0.94) with the CSS-Score libraries computed using
the experimental secondary structures. Additionally, a z-test is performed
to further analyze the differences in the CSS-Score libraries as
reported in the supplementary materials (Table S2). The CSS-Score
library derived from experimental secondary structures of natural protein
(μ = 5.68, σ = 8.00, n = 91 222) and the CSS-Score library derived
from predicted secondary structure of natural proteins (μ = 5.69,
σ = 8.29, n = 91 222) are hypothesized to be significantly similar
(z = −0.39, P = .69 (two-tail)). As the difference is not significant, it may
be assumed that in case of sampling and scoring novel proteins, the
performance of the proposed scoring function may not change significantly
upon using the predicted secondary structures.
2.10 | Efficacy of competency scores
The receiver operating characteristic curve (ROC Curve) is one of the
most prevalent and extensively instigated statistical tools for assessing
the discriminatory efficacy of a given classifier. Here, the average competency
scores of the individual proteins at sequence (CS-Score) and
sequence and secondary structural (CSS-Score) levels are assessed for
their potential to differentiate natural (NP) and nonnatural protein
(NNP-NC) sequences. Under the assumption that the higher CS-Score
and CSS-Score for a protein are indicative of its imitating behavior as
natural proteins and lower CS-Score and CSS-Score for a protein are
suggestive of imitating behavior as nonnatural proteins (NNP-NC). At
different threshold values of competency scores, different pairs of sensitivity
and specificity are derived from reference dataset of natural
and nonnatural proteins using Equation (7) as follows.
ROC tð Þ = FPR tð Þ,TPR tð Þð Þ,t Range of Competency Scoreð Þf g, ð7Þ
where FPR(t) is the false positive rate at a threshold value “t”; TPR(t) is
the true positive rate at a threshold value “t”.
The ROC curves are plotted with two underlying assumption,
(a) the potential of competency scores to identify the natural proteins
(NP) and (b) potential of competency scores to identify the nonnatural
proteins (NNP-NC). At different thresholds of CS-Scores, ROC(t)Natural,
and ROC(t)Nonnatural are calculated and plotted in Figure 3A. Similarly, at
different thresholds of CSS-Scores, ROC(t)Natural, and ROC(t)Nonnatural
are calculated and plotted in Figure 3B. The threshold values at point
of intersection ROC curves of natural and nonnatural proteins are
observed to be the optimum cutoff for differentiating natural and nonnatural
proteins.
The ROC curves of CS-Score for natural proteins (NP) and nonnatural
protein (NNP-NC) sequences are intersecting at a threshold
value of 32.15. At intersection point, the sensitivity and specificity in
identifying natural (NP) and nonnatural proteins (NNP-NC) is 0.62 and
0.63, respectively. However, the Mathews Correlation Coefficient
(MCC) at CS-Score cutoff value of 32.15 is 0.26 which indicates weak
prediction model for binary classification. The low value of MCC is
1276 KAUSHIK AND ZHANG
suggestive of inability of CS-Score in discriminating natural and nonnatural
proteins. The ROC curves of CSS-Score for natural (NP) and
nonnatural proteins (NNP-NC) showed a considerably improved sensitivity
and specificity at their intersection threshold value. The CSSScore
based ROC curves intersected at 15.5 where the sensitivity
is 0.76 and specificity is 0.77. Notably, the Mathews Correlation
Coefficient (MCC) at CSS-Score cutoff value of 15.5 is 0.54 which is
suggestive of strong prediction model for binary classification. The
calculation of sensitivity, specificity, and Mathews Correlation Coefficient
is explained in supplementary information (Supplementary Note
II). From ROC curves, sensitivity, specificity, and MCC values, it may
be interpreted that the only sequence-based competence score (CSScore)
is not very efficient in discriminating natural (NP) and nonnatural
proteins (NNP-NC). However, the sequence and secondary
structure-based competency score (CSS-Score) reflects a promising
potential of discriminating natural (NP) and nonnatural proteins (NNPNC).
The performances of CS- and CSS-Score are further evaluated
on different datasets and discussed in results section.
2.11 | Competency score analysis at residue level
in individual sequences
The efficacy of competency scores in discriminating natural proteins
(NP) and nonnatural protein (NNP-NC) sequences does not elucidate
the extent of its prediction reliability. To explore this further, a residue
level analysis of competency scores of individual proteins of natural
and nonnatural reference datasets is performed. In case of CS-Scores,
if a protein sequence is classified as natural protein (NP) on the basis of
its overall competency score (CS-Score ≥ 32.15) and more than 59% of
its residues are scoring above the threshold, then it is scoring better
than 80% of the natural proteins in reference dataset and may be considered
as natural protein with 80% confidence value. The required
number of percentage residues scoring above the threshold in a protein
increases to 69% for it to score better than 95% of the natural proteins
in reference dataset. Likewise, if a protein is classified as nonnatural
protein on the basis of competency score (CS-Score < 32.15), and more
than 61% of its residues are scoring below the threshold, then it is
scoring better than 80% of the nonnatural proteins and qualifies as
nonnatural protein with 80% confidence value. The required number of
percentage residues scoring below the threshold in a protein increases
to 67% for it to be classified as nonnatural protein with 95% possibility.
In case of CSS-Scores, for classifying a protein as natural protein,
having scored better than 80% of natural proteins in reference dataset,
it needs to have more than 62% of its residues scoring above the
threshold (CSS-Score ≥ 15.50). The required percentage number of
residues scoring above the threshold increases to 72% for classifying a
protein as natural with score better than 95% natural proteins. For
identifying a protein as nonnatural protein having outscored 80% of
nonnatural proteins, 64% of its residues must be scoring below the
threshold (CSS-Score < 15.50). The percentage number of residues
scoring below the threshold increases to 70% for identifying a protein
as nonnatural with outscoring 95% of nonnatural proteins. Figure 4A
shows the distribution of percentage number of proteins in natural and
nonnatural proteins reference datasets (on y-axis) against different cutoffs
of percentage residues scoring below the threshold values of CSScores.
Similarly, Figure 4B shows the distribution of percentage number
of proteins in natural and nonnatural proteins reference datasets
against different cutoffs of percentage residues scoring below the
threshold values of CSS-Scores. It is worth mentioning that in case of
natural proteins, the percentage of residues above threshold is considered
while in case of nonnatural proteins, the percentage of residues
scoring below the threshold is accounted. Thus, in case of natural protein
while referring to Figure 4, the percentage number of proteins at
different values of percentage number of residues scoring above the
threshold can be calculated by subtracting the corresponding value
from 100. Additionally, the different values of percentage residues
scoring above and below the threshold for natural and nonnatural proteins
in reference datasets are furnished in supplementary Table S3. It
may be noted that the extent of overlap in percentage number of residues
cutoffs is relatively less in case of CSS-Scores which is indicative
of its better discriminating potential of natural and nonnatural proteins.
The same is demonstrated on the different datasets and discussed in
results section.
FIGURE 3 The ROC curves for
identifying natural and nonnatural
proteins. (A) CS-Scores thresholdbased
ROC curves for natural and
nonnatural proteins. (B) CSS-Scores
threshold-based ROC curves for
natural and nonnatural proteins [Color
figure can be viewed at
wileyonlinelibrary.com]
KAUSHIK AND ZHANG 1277
2.12 | Competency score based prediction of
example protein
For a given target protein, the sequence-based competency scores
(CS-Score) for each residue (except for first and last residues) are calculated
using precompiled CS-Scores libraries (explained in Section 2.4).
The overall competency score is calculated from the scores of individual
residues as shown in Equation (5). Based on the average CS-Score,
the protein is predicted as natural (CS-Score ≥ 32.15) or nonnatural
protein (CS-Score < 32.15). Also, the percentage of residues scoring
below or above the threshold are calculated and employed for deriving
the possibility of the predictions accuracy by comparing it with the
values to the distribution of natural and nonnatural proteins. The overall
flow of carrying out CS-Score based prediction of a target protein is
demonstrated in Figure 5A. Further, the secondary structure prediction
of a target protein (if not known) is performed using the standalone
version of PSIPRED. The sequence and secondary structure information
is applied for calculating sequence and secondary structure-based
competency scores (CSS-Scores) for each residue (except for first and
last residues) by utilizing the precompiled CSS-Scores libraries. The
overall CSS-Score for the target protein is calculated and used for classifying
it as natural (CSS-Score ≥ 15.50) or nonnatural (CSS-Score
< 15.50). The percentage of residues scoring above or below the
threshold is used for deriving the possibility of prediction accuracy via
a comparison to the distribution of natural and nonnatural proteins in
reference datasets. The overall flow of performing CSS-Score based
prediction of a target protein is demonstrated in Figure 5B. In case of
CS-Score based prediction (Figure 5A), the example target protein is
identified as natural protein (CS-Score ≥ 32.15), having about 39% residues
scoring below threshold (61.2% residues scoring above threshold).
Referring to Table S3 (column 1 and 2, row 39), the example
target protein is scoring better than 85% natural proteins. Likewise, in
case of CSS-Score based prediction (Figure 5B), the example target
protein is identified as natural protein (CSS-Score ≥ 15.50), having
about 30% residues scoring below threshold (69.9% residues scoring
above threshold). Referring to Table S3 (column 1 and 4, row 30), the
example target protein is scoring better than 93% natural proteins.
Since the competency score libraries and threshold values are
precomputed from reference datasets of natural and nonnatural proteins,
the batch calculation of CS-Score and CSS-Score is very time
and computationally efficient.
3 | RESULTS AND DISCUSSION
The performance of CS- and CSS-Scores is evaluated on a test dataset
of natural proteins (NP) and nonnatural proteins (NNP-NC) (17 626
proteins each, as mentioned in Section 2.3). Additionally, a dataset of
FIGURE 4 Distribution of natural
(in green) and nonnatural (in red)
proteins at different values of their
percentage residues scoring below the
derived cutoffs from ROC curves. (A) CSScore
based distribution, highlighting
percentage residues scoring below
threshold for 80% of natural and
nonnatural proteins. (B) CSS-Score based
distribution, highlighting percentage
residues scoring below threshold for
80% of natural and nonnatural proteins
[Color figure can be viewed at
wileyonlinelibrary.com]
1278 KAUSHIK AND ZHANG
57 000 unique natural proteins (clustered at 40% sequence identity)
of sequence length varying from 50 to 700 residues from UniProtKB
is selected after excluding all the natural proteins of SCOPe database
(58 758 proteins). Further, two more datasets of 57 000 computationally
generated proteins, one with natural AA compositions and
another with uniform amino acid compositions constraint (NNP-NC
and NNP-UC) are considered for quantifying the ability of competency
scores in differentiating natural proteins from nonnatural
proteins.
3.1 | Evaluation on natural and nonnatural proteins
in test datasets
The test datasets of natural proteins (NP) and nonnatural proteins
(NNP-NC) are subjected to calculation of competency scores. For
CSS-Score calculation, the secondary structure of individual natural
protein is extracted from the corresponding structure, while the
secondary structure of individual nonnatural protein (NNP-NC) is
predicted using PSIPRED. The overall CS- and CSS-Scores of proteins
in test datasets are calculated and further used for categorizing them
into natural and nonnatural based on the threshold values (Natural
Proteins ≥ CS-Score 32.15 > Nonnatural Proteins; (Natural Proteins ≥
CSS-Score 15.50 > Nonnatural Proteins). The evaluation statistics of
CS- and CS-Scores are reported in Table 1. The distribution of CSand
CSS-Scores for all the proteins in the Test Dataset is shown in
Figure S6. Here, it may be noted that the CSS-Score based categorization
of natural and nonnatural proteins outperformed CS-Score based
categorization. It reflects the gain in prediction accuracy with the
addition of secondary structure information.
3.2 | Evaluation on external dataset of natural and
nonnatural sequences
For assessing the performance of the proposed competency scores,
an independent dataset of reviewed proteins from UniProtKB is
extracted by filtering out all the natural proteins considered in reference
and test datasets of natural proteins. The filtered reviewed proteins
are further clustered to 40% sequence identity to eliminate the
closely related proteins which resulted into 56 637 proteins. This
dataset of unique reviewed proteins from UniProtKB is referred to as
external dataset of natural proteins. For all the proteins in external
dataset of natural proteins, the CS- and CSS-Scores are calculated and
compared to threshold values identified in methods section, that is,
Natural Proteins (CS-Score ≥ 32.15; CSS-Score ≥ 15.50). Based on
CS-Score threshold, it is observed that only 33 729 (59%) proteins
could be identified as natural proteins. However, CSS-Score based
evaluation performed much better by identifying 45 876 (81%) proteins
as natural proteins.
In the nonnatural proteins dataset of 58 758 proteins, the amino
acid compositions were constrained to corresponding amino acid
compositions of natural proteins. Similarly, another dataset of nonnatural
proteins comprising 60 000 proteins is computationally generated
and clustered at 40% sequence identity to ensure the absence of
similar proteins. Further, the clustered proteins are screened against
the previously considered nonnatural proteins dataset to filter out the
similar proteins. The clustering and filtering resulted in a new dataset
of nonnatural proteins comprising 56 873 unique proteins, entirely
independent of the nonnatural proteins used in deriving thresholds
for CS- and CSS-Scores. This new dataset of 56 836 nonnatural proteins
is referred to as external dataset of nonnatural proteins (NNPNC).
The CS- and CSS-Scores for the external dataset of nonnatural
proteins are calculated and classified using the previously derived
thresholds for nonnatural proteins (CS-Score < 32.15; CSS-Score
< 15.50). The CS-Score based identification of nonnatural proteins
categorized 48 324 (85%) proteins as nonnatural while CSS-Score
could identify 51 153 (90%) proteins as nonnatural.
So far in this study, we have used natural proteins, adopted from
SCOPe and UniProtKB databases, and nonnatural proteins, computationally
generated with the same amino acid composition as the
FIGURE 5 Demonstration for prediction of a target protein as
natural or nonnatural protein. (A) Prediction for target protein derived
from average CS-Score and the percentage of residues scoring above
the threshold. (B) Prediction for a target protein derived from average
CSS-Score and the percentage of residues scoring above the
threshold [Color figure can be viewed at wileyonlinelibrary.com]
TABLE 1 Assessment of CS- and CSS-scores on test datasets of
35 252 proteins for identifying natural and nonnatural proteins
Statistics CS-score CSS-scores
Sensitivity 0.62 0.76
Specificity 0.62 0.75
Accuracy 0.62 0.74
Mathews correlation coefficient 0.25 0.53
KAUSHIK AND ZHANG 1279
natural proteins in UniProt database. Further, in this study, a dataset
of computationally generated 60 000 random proteins, with all amino
acid residues having equal probability of occurrence, is used for evaluating
the potential of the competency scores in discriminating natural
proteins from randomly generated proteins. This dataset of nonnatural
proteins with uniform composition of amino acid residues
(NNP-UC) is clustered at 40% sequence identity which resulted in
57 374 unique nonnatural proteins. All these proteins scored within
the threshold derived for nonnatural proteins (CS-Score < 32.15; CSSScore
< 15.50). A distribution of CS- and CSS-Scores of the proteins
in the external dataset of nonnatural proteins is shown in Figure 6. It
is worth mentioning that the CSS-Score based categorization of the
natural, nonnatural, and the random proteins performed consistently
on a considerably higher side. Clearly, the CSS-Score emerges as a
far better measure than CS-Score for identifying natural proteins
from nonnatural and random proteins. A summary of performance of
CS- and CSS-Score in identifying natural and nonnatural protein
sequences in external dataset of proteins is provided in Table 2.
For further statistical evaluation, the external datasets are combined
where the natural proteins are tagged as positives, and nonnatural
and random proteins are tagged as negatives. For CS-Score
identification, the sensitivity, specificity, and Mathews correlation
coefficient are observed to be 0.60, 0.92, and 0.57, respectively.
Likewise, for CSS-Score based identification, the sensitivity, specificity,
and Mathews correlation coefficient are 0.81, 0.95, and 0.79,
respectively.
3.3 | Benchmarking with existing methods
The CS- and CSS-Score based identification of natural and nonnatural
proteins is further benchmarked with existing methods. It is worth noting
that there are not many methods available for directly scoring the
protein sequences to classify them as natural and nonnatural proteins.
Here, we benchmarked the present scoring method with FoldIndex40
and FOLD.20,41
The FoldIndex method implements average residue
hydrophobicity and net charge to derive the foldability or unfoldability
of a given protein sequence where the positive score represents foldable
and the negative score represents unfoldable. Some of the proteins
scored very close to zero (−0.005 ≤ SCORE ≤ 0.005) which are
accounted as unreliable prediction. A very recently proposed method,
named FOLD, utilizes the precomputed triplet (FOLD3) and quadruplet
(FOLD4) frequencies in natural and random protein sequences to classify
a given protein sequence into any of the four classes, viz. sure
FIGURE 6 A comparison of CS- and CSS-Scores across external datasets of natural, computationally generated nonnatural (NNP-NC and
NNP-UC). A downward trend is observed from natural proteins to nonnatural proteins [Color figure can be viewed at wileyonlinelibrary.com]
TABLE 2 A summary of CS- and CSS-score identification on different external datasets
External dataset Total number of proteins CS-score natural CS-score nonnatural CSS-score natural CSS-score nonnatural
Natural 56 637 33 729 22 908 45 876 10 761
Nonnatural (NNP-NC) 56 873 8549 48 324 5720 51 153
Nonnatural (NNP-UC) 57 374 0 57 374 0 57 374
1280 KAUSHIK AND ZHANG
folded, sure random, guessed folded, and guessed random. While
benchmarking our method, we combined the sure folded and guessed
folded as the natural proteins, and the sure random and guessed random
as the nonnatural proteins. The summary of the predictions using
FoldIndex, FOLD, CS-Score, and CSS-Score for external datasets of
natural, nonnatural, and random proteins is shown in Table 3 and
Figure S8. For calculating sensitivity and specificity, the protein scored
as unreliable prediction are not considered.
Some other methods developed for characterization of protein
sequences into natural and random proteins,4-6,29,42
could not be
independently validated on the dataset of 170 884 proteins due
to unavailability of standalone versions. For such methods, the evaluation
statistics reported in respective research article is compiled and
provided in Table 4.
The benchmarking of CS- and CSS-Score with previously reported
methods in Table 3 demonstrates a reasonably better performance in
terms of sensitivity, specificity, and accuracy. Despite the fact that the
accuracy of the methods accounted in Table 4 is adopted from
respective research article, which is only restricted to a small dataset
of natural and random proteins in most cases, the accuracy of CSSScore
clearly outperformed most of these methods except Lucrezia
et al4
which is validated on a dataset of 1500 small proteins of 70
TABLE 3 The summary of benchmarking of CS-score and CSS-score with FoldIndex and FOLD on the dataset of 170 884 proteins,
comprising 56 637 natural and 114 247 nonnatural proteins
Method Predicted natural Predicted nonnatural Unreliable prediction Sensitivity Specificity Percentage accuracy (%)
FoldIndex 140 767 16 815 13 302 0.86 0.10 35
FOLD3* 63 941 105 924 1019 0.61 0.74 69
FOLD4* 49 443 107 508 13 933 0.63 0.84 77
FOLD5* 40 719 121 801 8364 0.41 0.82 69
CS-Score 42 278 128 606 0 0.60 0.92 82
CSS-Score 51 596 119 288 0 0.81 0.95 91
TABLE 4 Summary of articles reporting characterization of natural and random proteins by implementing various approaches
Method/reference Parameters/approach
Dataset
(N + R)
Accuracy
(%) Remark
Munteanu et al, 2008 Star network
topological indices
N = 1046
R = 1046
90 Bias for random
Santoni et al, 2016 ML on proximity measure between pair of amino
acids
N = 1047
R = 10 470
75 Small dataset for natural
Garbuzynskiy et al,
2004
Hydrophobicity and
contact number
N = 80
R = 90
83 Small dataset for natural
De Lucrezia et al, 2012 Evolutionary neural network on small protein
(70 aa)
N = 762
R = 762
94 Only small proteins accounted
Tsygvintsev, 2019 Neural network based on time series analysis N = 3502
R = 3502
85 24D vector used in complex
training
Present study
CS-score
Competency Scores derived from sequences N = 56 636
R = 114 247
82 Relatively lower accuracy
Present study
CSS-score
Scores derived from sequences and 2
structures N = 56 636
R = 114 247
91
FIGURE 7 A boxplot
representation of (A) CS- and (B) CSSScores
for four classes of proteins (α, β,
α/β, and α + β)
KAUSHIK AND ZHANG 1281
amino acid residues length. Also, the methods reported by Munteanu
et. al (26) was cross validated by Santoni et al6
to report an accuracy
of 79% with a very low true positive rate.
3.4 | Distribution for different protein classes
The competency scores are calculated for the unique protein
sequences of all alpha (α), all beta (β), alpha and beta (α/β), and alpha
plus beta (α + β) proteins representing 289, 178, 148, and 388 protein
folds. The average CS-Scores are observed to be 33.9 (±3.40), 32.7
(±3.00), 34.4 (±2.67), and 33.1 (±3.06) for all alpha (α), all beta (β),
alpha and beta (α/β), and alpha plus beta (α + β) proteins, respectively.
Likewise, the average CSS-Scores are found to be 19.5 (±3.20), 16.5
(±4.25), 18.4 (±2.27), and 16.9 (±2.50) for all alpha (α), all beta (β),
alpha and beta (α/β), and alpha plus beta (α + β) proteins, respectively.
A boxplot representation of CS- and CSS-Scores is shown in Figure 7
and the additional statistics are provided in Table S4.
TABLE 5 Summary of compiled designed proteins from previous research articles
Research article Designed proteins Expressed in E. coli Reported soluble Monomeric proteins Solved structures
Koga et al, 2012 54 49 45 19 16
Lin et al, 2015 49 49 45 31 10
Koepnick et al, 2019 144 119 99 65 55
Total 247 217 189 115 81
FIGURE 8 Competency score-based analysis of successful (green) designed and failed (red) proteins at (A) expression level, (B) solubility level,
(C) oligo-state level, and (D) structural level [Color figure can be viewed at wileyonlinelibrary.com]
1282 KAUSHIK AND ZHANG
It is worth noting that in case of all protein classes the average
CS- and CSS-Scores are beyond the minimum threshold for natural
proteins that is, CS-Score ≥ 32.15 and CSS-Score ≥ 15.50, respectively.
However, a further investigation is required to find out if the
scores are significantly deviating among different classes of proteins.
3.5 | Performance on reported designed proteins
A set of 247 designed protein sequences, reported in some previous
research articles43-45
is compiled for calculating the sequence and secondary
structure-based competency scores. The experimental results
of these designed proteins sequences are available for their expression,
solubility, monomeric state, and structure. According to their
respective articles, these sequences are selected for experimental validation
after screening through some comprehensive scoring functions
from more than 100 folds sampled sequences. Since only top ranked
protein sequences (less than 0.1% of sampled sequences) are considered
for experimental characterization, these are likely to score much
higher than the expected competency scores of natural proteins. The
details of the designed protein dataset are provided in Table S5 and a
summary is provided in Table 5.
In total, 81 designed proteins could be solved as well characterized
protein tertiary structures using X-ray crystallography and/or
NMR methods. The rationale of screening the designed protein
sequences using the CS- and CSS-Scores is to quantify the ability of
these scores at expression, solubility, oligo-state, and structural level.
In Figure 8, the CS- and CSS-Scores of designed proteins accounted
in Table 5 are plotted as success (green circles) and failure (red circles)
cases at expression, solubility, oligo-state, and structural levels.
It is observed that most of the proteins except one scored beyond
the minimum threshold of natural proteins for CSS-Score (above
15.50). However, the same is not true for CS-Score as several proteins
scored below the minimum threshold (below 32.15). It may also be
noted that as we move from expression to solubility to oligo-state to
structure, the upper-right quadrant (with CS-Score > 35 AND CSSScore
> 25) of the plots remains occupied by successful cases at all
four levels. This observation may help in designing novel protein
sequences with a higher potential of being successful at experimental
validation.
4 | CONCLUSION
The infinitesimally small sequence space naturally scouted in the millions
of years of evolution suggests that the natural proteins are
impeded by some specific prerequisites and should diverge from computationally
generated nonnatural protein sequences. Considering
this, here we studied natural and computationally generated nonnatural
proteins to develop a protein sequence fitness scoring function.
The scoring function implements sequence and corresponding
secondary structural information at tripeptide levels to differentiate
natural and nonnatural proteins. The proposed scoring function is
extensively validated on a dataset of about 210 000 natural and nonnatural
protein sequences and benchmarked with existing methods
for differentiating natural and nonnatural proteins. The high sensitivity,
specificity, and percentage accuracy (0.81%, 0.95%, and 91%
respectively) of the scoring function demonstrates its potential application
for sampling the protein sequences with higher probability
of mimicking natural proteins. Also, the four major classes of proteins
(α proteins, β proteins, α/β proteins, and α + β proteins) are separately
analyzed and β proteins are observed to scoring slightly on the lower
side as compared to other classes. Further, an analysis of about
250 designed proteins (adopted from previously reported cases) helped
in defining the boundaries for sampling the ideal protein
sequences which may prove advantageous in computational protein
design regimes.
ACKNOWLEDGMENTS
Authors are very grateful to Prof. Mihaly Mezei for help with running
FOLD3 and FOLD4. We gratefully acknowledge the suggestions from
Prof. Jaime Prilusky for automating the predictions using FoldIndex.
We acknowledge RIKEN ACCC for the computing resource used in
this study. This work is supported by Kakenhi 18H02395 from Japan
Society for the Promotion of Science.
CONFLICT OF INTERESTS
The authors declare no conflicts of interest.
DATA AVAILABILITY STATEMENT
All the datasets used in the present study are provided at http://
github.com/KYZ-LSB/ComProDes. Additionally, the programs for running
the proposed protein sequence fitness scoring function, user
tutorial, and readme files are provided for future use of the programs.
There is no additional dependency required for running the programs
in Linux environment.
ORCID
Kam Y. J. Zhang https://orcid.org/0000-0002-9282-8045
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SUPPORTING INFORMATION
Additional supporting information may be found online in the
Supporting Information section at the end of this article.
How to cite this article: Kaushik R, Zhang KYJ. A protein
sequence fitness function for identifying natural and
nonnatural proteins. Proteins. 2020;88:1271–1284. https://
doi.org/10.1002/prot.25900
1284 KAUSHIK AND ZHANG