A review of machine learning methods to predict the solubility of overexpressed recombinant proteins in Escherichia coli

Narjeskhatoon Habibi; Siti Z Mohd Hashim; Alireza Norouzi; Mohammed Razip Samian

doi:10.1186/1471-2105-15-134

Research article

Open Access

A review of machine learning methods to predict the solubility of overexpressed recombinant proteins in Escherichia coli

Narjeskhatoon Habibi¹Email author,
Siti Z Mohd Hashim¹,
Alireza Norouzi¹ and
Mohammed Razip Samian^{2, 3, 4}

BMC Bioinformatics201415:134

https://doi.org/10.1186/1471-2105-15-134

Received: 4 September 2013

Accepted: 25 March 2014

Published: 8 May 2014

Abstract

Background

Over the last 20 years in biotechnology, the production of recombinant proteins has been a crucial bioprocess in both biopharmaceutical and research arena in terms of human health, scientific impact and economic volume. Although logical strategies of genetic engineering have been established, protein overexpression is still an art. In particular, heterologous expression is often hindered by low level of production and frequent fail due to opaque reasons. The problem is accentuated because there is no generic solution available to enhance heterologous overexpression. For a given protein, the extent of its solubility can indicate the quality of its function. Over 30% of synthesized proteins are not soluble. In certain experimental circumstances, including temperature, expression host, etc., protein solubility is a feature eventually defined by its sequence. Until now, numerous methods based on machine learning are proposed to predict the solubility of protein merely from its amino acid sequence. In spite of the 20 years of research on the matter, no comprehensive review is available on the published methods.

Results

This paper presents an extensive review of the existing models to predict protein solubility in Escherichia coli recombinant protein overexpression system. The models are investigated and compared regarding the datasets used, features, feature selection methods, machine learning techniques and accuracy of prediction. A discussion on the models is provided at the end.

Conclusions

This study aims to investigate extensively the machine learning based methods to predict recombinant protein solubility, so as to offer a general as well as a detailed understanding for researches in the field. Some of the models present acceptable prediction performances and convenient user interfaces. These models can be considered as valuable tools to predict recombinant protein overexpression results before performing real laboratory experiments, thus saving labour, time and cost.

Keywords

Protein solubility Protein solubility prediction In silico prediction Recombinant protein expression Escherichia coli Machine learning Bioinformatics Computational biology

Introduction

In biotechnology, production of recombinant proteins is a crucial process in both biopharmaceutical industries and scientific research. So far, Escherichia coli (E. coli), a bacterium that requires simple conditions to grow is still the favoured host for cloning and overexpressing most proteins which are non-glycosylated and do not have many cysteine residues [1].

Even though logical strategies of genetic engineering are well established, such as strong promoters and codon optimization, protein overexpression is often, still an art. In particular, heterologous expression is often afflicted with low levels of production and insoluble recombinant proteins forming inclusion bodies (protein aggregations). Yet, there is no generic solution available to enhance heterologous overexpression. The use of fusion proteins can sometimes be more successful at the expense of decreased total yield as a result of the fusion partner production. Features that differentiate between proteins in the negative (non-expressed) and positive (expressed) classes might indicate sequence characteristics that could be modified in optimization, corresponding to what was attained with codon optimization, where sequences of gene are modified to become compatible with the translational apparatus [2]. As the host expresses the proteins, one cause of non-expression is the harmful interaction with the metabolism of the host [3].

For a given protein, the extent of its solubility can indicate the quality of its function. In general, over 30% of recombinant proteins are not soluble [4]. About 33 to 35 percent of all expressed non-membrane proteins are insoluble and about 25 to 57 percent of soluble proteins are prone to aggregate at higher concentrations [5]. For a determined experimental condition (i.e. temperature, expression host, etc.), the solubility of a protein is determined by its sequence [6].

The trial-and-error procedure of protein overexpression can be avoided by identifying the promising proteins to improve the experimental success rate [7]. There are two types of approach for predicting solubility of protein: sequence-based and structure-based. In the structure-based technique, the free energy difference between aggregation and solution phases is computed. This method demands experimentally obtained high resolutions 3D structures which are hard to acquire for aggregation-prone proteins. Hence, the sequence-based technique is a feasible and widely used method. Generally, the computational sequence-based prediction methods investigate the protein overexpression in E. coli at the normal growth temperature of 37°C [8].

The correlation of amino acid sequence and the tendency to form inclusion body was shown for the first time by Wilkinson and Harrison [9]. Later, numerous methods based on machine learning were proposed to predict the solubility of proteins merely from amino acid sequences [10].

Protein solubility prediction can be considered a binary classification task where a classifier should discriminate between soluble proteins (positive samples) and insoluble proteins (negative samples). There are several classification methods (learning algorithm) namely, decision tree (DT) (e.g. C4.5 [11]), k-nearest-neighbour (KNN) [12], neural network (NN) [13, 14], support vector machine (SVM) [15], etc.

The learning algorithm (i.e. the classification method) is selected based on numerous factors, such as the number of existing examples in the dataset, the data type to be classified (e.g. symbolic or numeric), and the number of examples probable to be inaccurate or noisy. The level of preferred interpretability of the outcomes is another issue to be considered [16].

The majority of current methods use SVM to build the model of solubility [4]. Appropriate SVM models can often achieve better performance in classification of biological sequence compared to other machine learning-based approaches [1]. Each study employs a different set of features. Considering the model performance, different results are obtained, but 70% is a common accuracy in many studies [4].

To date, all of the prediction approaches examined a single system of protein expression, such as the A. niger or the E. coli system. The works of Hirose et al. [3, 10] are exceptions that explored two different systems (E. coli and wheat germ).

Some of the suggested methods of prediction offer their work as widely accessible web servers [3, 10, 17–20].

In spite of more than two decades of research on the subject, there has been only one report, reviewing seven solubility prediction tools [21]. In their valuable review, the authors have compared seven existing prediction tools based-on the following factors: prediction accuracy, usability, utility, and prediction tool development and validation methodologies. Our aim is to evaluate and investigate all published methods to predict protein solubility, so as to offer a detailed as well as a general understanding for the researchers.

The organization of the paper is as follows. The major protein solubility prediction studies are reviewed in section 2, with emphasis on their datasets, features, feature selection methods, predictor models and performance results. Section 3 presents a discussion on the models details, the best models and the data challenge for solubility prediction task. Lastly, section 4 concludes the paper and proposes some future research directions.

Review

The methods to predict solubility of protein based on the machine learning are summarized in Table 1 in a chronological order, descending from the most recent. Due to space limitation, the reported performance of the works and the features used in each work are shown in Table 2 and Table 3 respectively. More detailed descriptions of the works are presented in “Additional file 1”.

Table 1

A summary of key components of studies to predict protein solubility (in chronological order)

#	Paper	Dataset(s)	Feature selection method(s)	Modeling technique(s)	Web server
1	[7]	Bacterial protein sequences with ‘soluble’ and ‘insoluble’ in NCBI are selected randomly.	Wrapper: SVM	Support vector machine	-
		Size: 5692
		Soluble: 2448
		Insoluble: 3244
2	[10]	HGPD	Filter: Student’s t-test	Two techniques:	ESPRESSO:
		E. coli		Support vector machine	http://mbs.cbrc.jp/ESPRESSO
		Size: 5100
		Soluble: 1774
		Insoluble: 3326
		Wheat germ		Sequence pattern-based method
		Size: 2939
		Soluble: 1941
		Insoluble: 998
3	[5]	eSol	Two methods:	Random forest	ProS:
		Size: 1918	1. Filter: Student’s t-test		http://shark.abl.ku.edu/ProS/
		Soluble: 886	2. Wrapper: Random forest
		Insoluble: 1032	2. Wrapper: Random forest
4	[8]	Four datasets:	-	Two methods:	SCM:
		Sd957		Support vector machine	http://iclab.life.nctu.edu.tw/SCM/
		Dataset Chan et al. [18] (Table 1, row 11)		Scoring card method (SCM)
		Solpro
		PROSO II
5	[4]	eSol	-	Four techniques:	-
		Size: 1600		1. Support vector machine
				2. Random forest
				3. Conditional inference trees
				4. Rule ensemble
6	[6]	PROSO II	Wrapper	A two-layer model:	PROSOII:
				1. Layer 1: Parzen window + logistic regression	http://mips.helmholtz-muenchen.de/prosoII
				2. Layer 2: Logistic regression	http://mips.helmholtz-muenchen.de/prosoII
7	[22]	eSol	-	Decision tree	-
		Size: 1625
		Soluble: 843
		Insoluble: 782
8	[23]	eSol	Wrapper: SVM	Support vector machine	-
		Size: 2159
		Soluble: 1081
		Insoluble: 1078
9	[3]	HGPD	Filer: Student’s t-test	Random forest	-
		E. coli
		Size: 7823
		Soluble: 2796
		Insoluble: 5027
		Wheat germ
		Size: 3955
		Soluble: 2739
		Insoluble: 1216
10	[24]	SOLP	Seven methods:	Support vector machine	-
			1. Filter: Information gain
			2. Filter: Gain ratio
			3. Filter: Chi squared
			4. Filter: Symmetrical uncertainty
			5. Wrapper: ReliefF
			6. Wrapper: SVM recursive feature elimination (SvmRfe)
			7. Embedded: One attribute rule
11	[16]	121genes from different species were expressed in 6 different vectors.	Feature selection package in LIBSVM: Filter (F-score) + Wrapper (SVM)	Support vector machine	-
		Size: 726
		Soluble: 231
		Insoluble: 236
		Non-expressed: 259
12	[20]	A database collected through literature search.	N/A	Logistic regression	http://www.biotech.ou.edu/
		Size: 212
		Soluble: 52
		Insoluble: 160
13	[17]	Solpro	Wrapper	A two- layer model:	SOLpro:
				1. Layer 1: 20 Support vector machines	http://scratch.proteomics.ics.uci.edu
				2. Layer 2: One support vector machine	http://scratch.proteomics.ics.uci.edu
14	[25]	eSol	Using histogram	Support vector machine	-
15	[19]	PROSO	Two methods:	A two-layer model:	PROSO:
			1. Wrapper	Layer 1: Support vector machine	http://mips.helmholtz-muenchen.de/proso/
			2. Filter: Symmetrical uncertainty	Layer 2: Naive Bayes	http://mips.helmholtz-muenchen.de/proso/
16	[26]	Idicula‒Thomas 2006	N/A	Support vector machine	-
17	[27]	Idicula‒Thomas 2006	Filter: Unbalanced correlation score	Support vector machine	-
18	[28]	Idicula‒Thomas 2005	Filter: Mann–Whitney test	Discriminant analysis (A heuristic approach of computing solubility index (SI))	-
19	[29]	Genes of C. elegans with one expression vector and one Escherichia coli strain.	Filter: Linear correlation coefficient (LCC)	-	-
		Size: 4854
		Soluble: 1536
		Insoluble: 3318
20	[30]	TargetDB	Wrapper: Random forest	Decision tree	-
20	[30]	Size: 27,000	Wrapper: Random forest	Decision tree	-
21	[14]	SPINE	Wrapper	Decision tree	-
21	[14]	Size: 562	Wrapper	Decision tree	-
22	[31]	SPINE	Embedded: Decision tree	Decision tree	-
		Size: 356
		Soluble: 213
		Insoluble: 143
23	[18]	Some genes of E. coli were expressed.	N/A	Regression	-
23	[18]	Size: 100	N/A	Regression	-
24	[9]	Some genes of E. coli were expressed.	N/A	Regression	-
24	[9]	Size: 81	N/A	Regression	-

Table 2

Reported prediction performances of the models (in chronological order)

#	Paper	Accuracy	Area under curve	F-score	Gain	Mathew correlation coefficient	Precision	Recall	Sensitivity	Specificity
1	[7]	0.88	-	-	-	0.76	-	-	-	-
2*	[10]	0.68	0.78	0.67	-	0.42	0.56	0.85	-	-
2*	[10]	0.75	0.75	0.82	-	0.42	0.79	0.86	-	-
3	[5]	0.84	0.91	-	-	0.67	-	-	0.82	0.85
4	[8]	0.84	-	-	-	-	-	-	-	-
5	[15]	0.90	-	-	-	-	-	-	0.80	0.80
6	[6]	0.75	-	-	1.69	0.39	0.65	0.76	0.73
7	[22]	0.75	0.81	-	-	-	-	-	-	-
8	[23]	-	-	-	-	-	-	-	-	-
9*	[3]	0.71	-	-	-	-	0.47	0.67	-	-
9*	[3]	0.71	-	-	-	-	0.85	0.74	-	-
10	[24]	-	-	-	-	-	-	-	-	-
11	[1]	0.83	0.89	0.75	-	-	0.73	0.78	-	-
12	[20]	0.94	-	-	-	-	-	-	-	-
13	[17]	0.74	0.74	-	1.49	0.49	0.74	0.74	-	-
14	[25]	0.80	-	-	-	-	-	-	-	-
15	[19]	0.72	0.78	-	1.43	0.43	-	0.72	-	-
16	[26]	0.79	0.76	-	-	-	-	-	0.68	0. 85
17	[27]	0.74	-	-	-	-	-	-	0.57	0.81
18	[28]	0.72	-	-	-	-	-	-	-	-
19	[29]	-	-	-	-	-	-	-	-	-
20	[30]	0.76	-	-	-	-	-	-	-	-
21	[16]	0.63	-	-	-	-	-	-	-	-
22	[31]	0.65	-	-	-	-	-	-	-	-
23	[18]	-	-	-	-	-	-	-	-	-
24	[9]	0.88	-	-	-	-	-	-	-	-

a. *Results for E. coli and wheat germ are shown respectively.

Table 3

Features used to predict protein solubility

#	Paper	Features
1	[7]	1. 2-level triangle CGR
		2. Entropy of “2-level triangle CGR”
		3. Dipeptide composition based on a different mode of pseudo amino acid composition (PseAAC)
		4. Entropy of “dipeptide composition”
2	[10]	Same as row 9 (Reference [3])
3	[5]	1. Counts of aromatic amino acids
		2. Counts of buried amino acids
		3. Counts of hydrogen bonds
		4. Counts of leucine amino acid
		5. Counts of arginine amino acid
		6. Negative charge
		7. Surface composition of amino acids in intracellular proteins of Mesophiles (percent)
		8. Beta-strand indices for beta-proteins
		9. Flexibility parameter for two rigid neighbours
		10. Net charge
		11. Counts of nitrogen atoms
		12. Long range non-bonded energy per atom
		13. Isometric point (pI)
		14. Free energies of transfer of AcWl-X-LL peptides from bilayer interface to water
		15. Ratio of negative charge amino acids
		16. Ratio of net charge of protein
		17. Dependence of partition coefficient on ionic strength
4	[8]	Dipeptide composition (400 features)
5	[4]	1. Reduced features (39 features produced by pepstats):
		a. Molecular weight, number of residues, average residue weight, charge and isoelectric point
		b. For each type of amino acid: number, molar percent and DayhoffStat
		c. For each physicochemical class of amino acid: number, molar percent, molar extinction coefficient (A280) and extinction coefficient at 1 mg/ml (A280)
		2. Dimers (2400 features):
		a. Dimers amino acid frequencies which are computed considering gaps of 1–5 amino acid
		3. Complete set
		a. Reduced features + Dimers
6	[6]	1. Amino acid frequencies (18 features): R, N, D, C, Q, E, G, H, I, K, M, F, P, S, T, W, Y, V
6	[6]	2. Dipeptide frequencies (13 features): AK, CV, EG, GN, GH, HE, IH, IW, MR, MQ, PR, TS, WD
7	[22]	1. Monomer, dimer and trimmers using 7 different alphabets (18 features)
		2. Sequence-computed features:
		a. Molecular weight
		b. Sequence length
		c. Isoelectric point
		d. GRAVY index
		3. Features used in Niwa et al. work [25]
		4. Combination of all the above features 1–3.
8	[23]	1. Coil
		2. Disorder
		3. Hydrophobicity
		4. Hydrophilicity
		5. β-turn
		6. α-helix
9	[3]	1. Nucleotide sequence information:
		a. 1-mer
		b. Frequencies of 64 codons (3-mer)
		c. GC-contents
		2. Amin acid sequence information:
		a. Polypeptide length
		b. Frequencies of 20 single amino acids (1-mer)
		c. Frequencies of 8 chemical property groups
		d. Frequencies of 5 physical property groups
		e. Repeat of amino acids
		f. Repeat of 8 chemical property groups
		g. Repeat of 5 physical property groups
		3. Amino acid structural information:
		a. Frequencies of single amino acids in surface area
		b. Frequencies of 8 chemical property groups in surface area
		c. Frequencies of 5 physical property groups in surface area
		d. Number of transmembrane regions
		e. Disordered regions:
		i. Number of occurrence
		ii. Length
		iii. Proportion
		f. Secondary structures:
		i. alpha-helix
		ii. Beta-sheet
		iii. Others
10	[24]	1497 features computed by Protein Feature Server (PROFEAT) [32]:
		1. Group 1:
		a. Amino acid composition
		b. Dipeptide composition
		2. Group 2: Autocorrelation 1
		a. Normalized Moreau-Broto autocorrelation
		3. Group 3: Autocorrelation 2
		a. Moran autocorrelation
		4. Group 4: Autocorrelation 3
		a. Geary autocorrelation
		5. Group 5:
		a. Composition
		b. Transition
		c. Distribution
		6. Group 6: Sequence order 1
		a. Sequence-order-coupling number
		b. Quasi-sequence-order descriptors
		7. Group 7: Sequence order 2
		a. Pseudo amino acid descriptors
11	[1]	1. Nucleotide information:
		a. 1-mer
		b. 2-mer
		c. 3-mer
		d. Sequence length
		e. GC content
		2. Amino Acid information:
		a. Features of Wilkinson and Harrison [9]
		b. Features of Idicula-Thomas et al. [27]
		c. Isoelectric point
		d. Peptide statistics
		3. Codon Adaptation Index
		4. PTMs
12	[20]	1. Molecular weight
		2. Cysteine fraction
		3. Hydrophobicity-related parameters:
		a. Fraction of total number of hydrophobic amino acids
		b. Fraction of largest number of contiguous hydrophobic/hydrophilic amino acids
		4. Aliphatic index
		5. Secondary structure-related properties:
		a. Proline fraction
		b. Alpha-helix propensity
		c. Beta-sheet Propensity
		d. Turn-forming residue fraction
		e. Alpha-helix propensity/b-sheet propensity
		6. Protein–solvent interaction related parameters:
		a. Hydrophilicity index
		b. pI
		c. Approximate charge average
		7. Fractions of: Alanine, Arginine, Asparagine, Aspartate, Glutamate, Glutamine, Glycine, Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Serine, Threonine, Tyrosine, Tryptophan and Valine
13	[17]	1. Frequencies of amino acid monomers, dimers and trimmers using 7 different alphabets:
		a. Monomer frequencies
		i. [Natural-20:M]
		ii. [ClustEM-17:M]
		iii. [ClustEM-14:M]
		iv. [PhysChem-7:M]
		v. [BlosumSM-8:M]
		vi. [ConfSimi-7:M]
		vii. [Hydropho-5:M]
		b. Dimer frequencies
		i. [PhysChem-7:D]
		ii. [ClustEM-14:D]
		iii. [ClustEM-17:D]
		iv. [BlosumSM-8:D]
		v. [Natural-20:D]
		vi. [ConfSimi-7:D]
		c. Trimmer frequencies
		i. [ClustEM-17:T]
		ii. [Hydropho-5:T]
		iii. [ConfSimi-7:T]
		iv. [ClustEM-14:T]
		v. [Natural-20:T]
		2. Features computed directly:
		a. Sequence length
		b. Turn-forming residues fraction
		c. Absolute charge per residue
		d. Molecular weight
		e. GRAVY index
		f. Aliphatic index
		3. Predicted features using the SCRATCH suite of predictors:
		a. Beta residues fraction (Predicted by SSpro)
		b. Alpha residues fraction (Predicted by SSpro)
		c. Number of domains (Predicted by DOMpro)
		d. Exposed residues fraction (Predicted by ACCpro, using a 25% relative solvent accessibility cut-off)
14	[25]	1. Molecular weight
		2. Isometric point (pI)
		3. Ratios of each amino acid content
15	[19]	4. For mono-domain proteins:
		a. Word size 1:
		S, IL, M, F, DE, A, C, G, R
		b. Word size 2:
		R + R, R + C, R + E, R + T, N + Q, N + H, N + L, C + S, Q + A, Q + G, Q + I, E + A, E + G, E + K, E + P, E + V, G + P, H + M, L + Y, K + G, K + K, M + G, S + S, T + I, Y + C, Y + I
		c. Word size 3:
		ST + ST + ST, ST + ST + N, ST + DQE + AH, ST + C + ST, G + M + R, G + K + G, G + P + G,
		G + P + N, M + AH + AH, M + C + Y, DQE + G + R, DQE + R + DQE, DQE + M + ST,
		DQE + Y + N, DQE + AH + IV, K + R + IV, K + K + ST, P + DQE + DQE, P + DQE + C,
		IV + G + IV, L + IV + DQE, N + FW + DQE, N + C + P, AH + ST + ST, AH + K + L, C + FW + Y, C + K + C
		5. For multi-domain proteins:
		a. Word size 1:
		R, D, C, E, G, L, K, M, S, W
		b. Word size 2:
		A + Y, A + V, R + N, R + E, R + S, R + Y, N + A, D + M, C + T, Q + A, Q + E, E + D, E + G, E + T, G + I,
		G + F, G + S, H + C, H + M, H + P, L + G, L + S, K + D, K + G, K + L, K + F, P + L, T + L, T + Y, V + R
		c. Word size 3:
		ST + ST + ST, ST + P + DQE, ST + IV + K, R + DQE + FW, R + DQE + IV, R + IV + FW,
		FW + DQE + FW, M + ST + DQE, M + G + AH, M + FW + DQE, DQE + ST + ST,
		DQE + ST + G, DQE + G + K, DQE + IV + R, DQE + IV + L, P + G + ST, IV + ST + P,
		L + K + FW, AH + ST + IV, AH + G + IV, AH + AH + M
16	[26]	1. Aliphatic index
		2. Frequency of occurrence of residues Cysteine (Cys), Glutanic acid (Glu), Asparagine (Asn) and Tyrosine (Tyr)
		3. Reduced class of conformational similarity [CMQLEKRA]
		4. Reduced classes of hydrophobicity [CFILMVW] and [NQSTY]
		5. Reduced classes of BLOSUM50 substitution matrix [CILMV]
		6. The 18 dipeptide composition: [VC], [AE], [VE], [WF], [YF], [AG], [FG], [WG], [HH], [MI], [HK], [KN], [KP], [ER], [YS], [RV], [KY], [TY]
17	[27]	1. Physicochemical properties (6 features):
		a. Length of protein
		b. Hydropathy index (GRAVY)
		c. Aliphatic index
		d. Instability index
		e. Instability index of N-terminus
		f. Net charge
		2. Mono-peptide frequencies (20 features)
		3. Dipeptide frequencies (400 features)
		4. Reduced alphabet set (20 features)
18	[28]	1. Aliphatic index (AI)
		2. Instability index of the N terminus
		3. Frequency of occurrence of Asn, Thr, and Tyr
		4. Tri-peptide score
19	[29]	1. Signal peptide
		2. GRAVY
		3. Transmembrane helices
		4. Number of Cysteines
		5. Anchor peptide
		6. Prokaryotic membrane lipoprotein lipid attachment site
		7. PDB identity
20	[30]	1. General sequence composition
		2. Clusters of orthologous groups (COG) assignment
		3. Length of hydrophobic stretches
		4. Number of low-complexity regions
		5. Number of interaction partners
21	[16]	1. Single residue composition: I, T, Y
		2. Combined amino acid compositions: KR, DE, DENQ
		3. Predicted secondary structure composition: α and coil
		4. Presence of signal sequence
		5. Amino acid sequence length
		6. Number of amino acids in both short and long low complexity regions (over sequence length)
		7. Normalized low complexity value for both short and long regions (over sequence length)
		8. Minimum GES hydrophobicity score calculated over all amino acids in a 20 residue sequence window
22	[31]	1. Hydrophobe
		2. Cplx: a measure of a short complexity region based on the SEG program.
		3. Gln composition
		4. Asp + Glu composition
		5. Ile-composition
		6. Phe + Tyr + Trp composition
		7. Gly + Ala + Val + Leu + Ile composition
		8. His + Lys + Arg composition
		9. Trp composition
		10. Alpha-helical secondary structure composition
23	[18]	Same as row 24 (Reference [9])
24	[9]	1. Charge average approximation (Asp, Glu, Lys and Arg)
		2. Turn-forming residue fraction (Asn, Gly, Pro and Ser)
		3. Cysteine fractions
		4. Proline fractions
		5. Hydrophilicity
		6. Molecular weight (Total number of residues)

In the following tables, for an entry which does not have the corresponding column value, symbol “-” is used. For an entry which we could not find its value, but may exist, symbol “N/A” is used (N/A: Not applicable, not available or no answer).”

In order to comprehend the details of the works which are presented in Table 1, Table 2 and Table 3, datasets used, feature selection methods and performance measures are described in greater details in Table 4, Table 5 and Table 6 respectively.

Table 4

Databases/datasets used to predict protein solubility (in chronological order)

#	Name	Reference	Size			Description	URL
#	Name	Reference	Total	Soluble	Insoluble	Description	URL
1	Sd957	[8]	957	285	672	It is made from 3 previous datasets: Idicula-Thomas et al. [28], Diaz et al. [20] and Chan et al. [1].	http://iclab.life.nctu.edu.tw/SCM/downloads.php
2	PROSO II	[6]	82,000	41,000	41,000	It is made from pepcDB and PDB and has been the largest dataset ever. It is balanced.	http://mips.helmholtz-muenchen.de/prosoII/img/Suppl_files.zip
3	HGPD	[33]	17,821 (As of June 9th, 2011)	N/A	N/A	Human full-length cDNA.	http://www.HGPD.jp
4	eSol	[25]	30,173	N/A	N/A	A database on the solubility of entire ensemble of E. coli proteins based on ASKA library.	http://www.tanpaku.org/tp-esol/index.php?lang=en
5	Solpro (SOLP)	[17]	17,408	8704	8704	It is collected from 4 different sources: PDB, SwissProt, TargetDB and dataset of “Idicula-Thomas, 2006”. The sequence redundancy is removed with 25% sequence similarity. It is balanced.	http://download.igb.uci.edu/SOLP.fa
6	PROSO	[19]	14,000	7000	7000	It is collected by merging 4 datasets: TargetDB, PDB and datasets of “Idicula-Thomas 2005” and “Idicula-Thomas 2006”.	-
7	pepcDB	[34]	N/A	N/A	N/A	It stored target and protocol information contributed by Protein Structure Initiative centres as well as targets imported from the TargetDB database. Now it has been replaced by TargetTrack.	http://pepcdb.rcsb.org
8	Idicula-Thomas 2006	[27]	192	62	139	It is collected from the literature.	-
9	Idicula-Thomas 2005	[28]	174	41	133	It is collected from the literature.	-
10	PDB	[35]	91,359 (As of 11 June 2013)	N/A	N/A	It is a repository of information about the 3D structures of large biological molecules, including proteins and nucleic acids.	http://www.rcsb.org/pdb/
11	SPINE	[16]	N/A	N/A	N/A	N/A	http://spine.nesg.org/user_login.cgi?url=http://spine.nesg.org/front_page.cgi?
12	TargetDB	[36]	295,041 (As of 29 March 2013)	N/A	N/A	It provided status information on target sequences and tracks their progress through the various stages of protein production and structure determination. Now it has been replaced by TargetTrack.	http://targetdb.rcsb.org
13	TargetTrack	-	316,424 (As of 14 June 2013)	N/A	N/A	It is a target registration database which provides information on the experimental progress and status of targets selected for structural determination by the Protein Structure Initiative and other worldwide high-throughput structural biology projects.	http://sbkb.org/tt

Table 5

Description of feature selection methods used in machine learning[37]

Method	Description	Examples
Filter	Filter methods evaluate the relatedness of features by looking at the inherent properties of the data. Usually a feature relevance score is computed, and the features with low scores are discarded.	Student’s t-test [N/A]
		Information gain [38]
		Gain ratio [38]
		Chi squared [N/A]
		Symmetrical uncertainty [39]
		Unbalanced correlation score [40]
		Mann–Whitney test [41]
		Linear correlation coefficient [N/A]
Wrapper	In wrapper methods various subsets of features are evaluated by training and testing a specific classification model, so a search algorithm is ‘wrapped’ around the classification model. This approach adapted to a specific classification algorithm.	Sequential forward selection [42]
		Sequential backward elimination [42]
		Beam search [43]
		ReliefF [44]
Embedded	Embedded methods, build the search for an optimal subset of features into the classifier construction, so they are specific to a given learning algorithm.	Random forest [45]
		SVM recursive feature elimination (SvmRfe) [46]
		One attribute rule [47]

Table 6

Performance measures used to evaluate protein solubility prediction (in alphabetical order)

#	Name	Abbr.	Formula	Description
1	Accuracy	ACC	(TP + TN)/(TP + TN + FP + FN)	The number of correctly classified instances divided by the total number of instances [6].
2	Area under ROC curve	AUC	-	It measures the discriminating ability of the model and it takes values between 0.5 for random drawing and 1.0 for perfect classifier [6].
3	Enrichment Factor	EF	[CS/(CS + WS)]/[S/(S + I)]	EF is especially suitable for the unbalanced datasets [27].
			CS: Number of correctly classified soluble proteins.
			WS: Number of soluble proteins wrongly classified as insoluble.
			S: total number of soluble proteins.
			I: total number of insoluble proteins.
4	False Negative	FN	-	The number of incorrectly predicted negatives [10].
5	False Positive	FP	-	The number of incorrectly predicted positives [10].
6	F-Score	FS	2 × Precision × Recall/(Precision + Recall)	The harmonic mean of recall and precision [10].
7	Gain	GAIN	Precision/proportion of the given class in the full data set.	It is an important performance measure that quantifies how much better the decision is in comparison with random drawing of instances [6].
8	Matthew’s Correlation Coefficient	MCC	(TP × TN - FP × FN)/((TP + FP)(TP + FN)(TN + FP)(TN + FN))	It indicates the correlation between the classifier assignments and the actual class in the two-class case. It is a good measure of classifier performance even when classes are unbalanced [6]. The MCC ranges between -1 and 1, and a large positive value indicates a better prediction [10].
9	Precision (Selectivity)	PRC	TP/(TP + FP) Or TN/(TN + FN)	The ratio of the number of correctly classified positive or negative instances to the number of all instances classified as positive or negative, for positive and negative class respectively [6].
10	ROC Curve	ROC	Plotting the “FP-rate” against the “TP- rate”, while the probability is increased from 0 to 1.0 with 0.01 increments.	The receiver-operator characteristic curve, showing the trade-off between the ratio of false positives and false negatives in testing a classifier [48]. A larger area value indicates a more robust prediction method [10].
11	Recall	REC	TP/(TP + FN)	The ratio of the number of correctly classified positive instances to the number of all instances from the positive class [6].
	(Sensitivity)
	(True positive rate)
	(TP- rate)
12	Specificity	SPC	TN/(TN + FP)	The ratio of the number of correctly classified negative instances to the sum of all negative instances [6].
	(True Negative Rate)
	(TN-rate)
13	True Positive	TP	-	The number of correctly predicted positives [10].
14	True Negative	TN	-	The number of correctly predicted negatives [10].

a. “TP” = True Positive; “TN” = True Negative; “FP” = False Positive; “FN” = False Negative; “+” = Add, “-” = Subtract; “×” = Multiply; “/” = Division.

It should be mentioned that in some works several modeling techniques are examined and then one or more are selected as the final model(s). In the “Modeling Technique(s)” column of Table 1, only the final models are shown. It is same true for the “Feature Selection Method(s)” column. In addition, in most of the works, first an initial feature set is considered, and then using feature selection methods, a smaller sub-set is obtained and employed in the modeling. Table 3 presents the final sets used in the modelings.

With respect to the data used in each study, some of the authors created a dataset harvested from the literature, some employed public datasets, while others performed experiments to generate their own dataset.

Discussion

This section investigates the works in more depth. In the following paragraph, the most used dataset, features, feature selection methods and learning techniques are presented. Afterwards, the best models based on the obtained accuracies are introduced. Then, the most convenient to use models are mentioned. Lastly, some data-related challenges are discussed.

In terms of data, eSol is the most widely used dataset in the field. Considering input features, the following features are the most common ones computed from the protein sequence: aliphatic index, amino acid sequence length, charge, amino acid compositions, instability, isoelectric point (pI), hydrophilicity, molecular weight, and predicted secondary structure. Filter methods (described in Table 5) are used more than the other feature selection techniques. Regarding the machine learning method, support vector machine is the most common technique to make prediction; random forest, decision tree and logistic regression are the next most common ones, respectively.

Based on the results, the method reported by Diaz et al. [20] obtained the best prediction accuracy (94%) on their generated dataset. Similar prediction accuracy was also reported by Samak et al. [4] with an accuracy of 90% on the eSol dataset, followed by the works of Xiaohui et al. [7], and Wilkinson and Harrison [9] with a prediction accuracies of 88% based on their generated datasets.

Comparing the different models in terms of convenience and ease of use, the ones with publicly accessible web servers can be considered the most convenient to use and evaluate. They are ProS [5], PROSOII [6], SCM [8], ESPRESSO [10], SOLpro [17], PROSO [19] and the model of Diaz et al. [20].

It seems that by using an appropriate dataset, as well as suitable machine learning techniques, reasonable prediction performance is attainable. In addition, feature selection methods can reveal, to some extent, influential factors on solubility and the sequence characteristics that could be modified in optimization.

Poor generalization ability is one of the limitations of sequence-based methods founded on a small dataset [35]. In general, extracting a reliable dataset, in terms of experimental conditions and expression system is challenging as the majority of databases that deliver the information on the solubility of proteins often do not provide comprehensive information about the experimental particulars of solubility assessment. Furthermore, researchers generally handle imbalanced (i.e. unequal number of soluble and insoluble samples) data when collecting protein solubility records. Consequently, numerous research teams used different methods to collect consistent datasets that divide proteins into insoluble and soluble categories [24, 27].

It is worth mentioning that the datasets employed to build SOLpro [17] and PROSOII [6] were gathered by integrating different search results of TargetDB, Protein Data Bank (PDB), and Swiss-Prot database. Then, the proteins were categorized into insoluble and soluble samples according to the proteins’ annotations. Although these methods were best working when an appropriate experimental dataset did not exist, they might not be reliable completely. A soluble protein without appropriate annotation, for example, may be incorrectly categorized as an insoluble protein and vice versa. Furthermore, annotations from diverse databases may not be consistent. Clearly, it is desirable to have a large protein set with solubility determined based on experiment by a single reliable protocol [5].

Conclusions

In this paper, the works to predict protein solubility prediction are reviewed in details. They are assessed and classified with regards to the datasets used, features used, feature selection methods, machine learning algorithms and performance results.

Since the early work of Wilkinson and Harrison [9], models later proposed became more complex in terms of dataset size, number and types of features employed, feature evaluation techniques and machine learning methods to make prediction. In general, the performances of the models have improved greatly as well.

Some of the models provide acceptable prediction performance (e.g. in terms of accuracy). Especially the ones with convenient user interfaces (e.g. web applications), can be considered valuable tools to anticipate recombinant protein overexpression results before performing real laboratory experiments. This capability will lead to significant reduction of labour, time and cost.

Generating larger and more accurate datasets, working on organisms other than E. coli and discovering other influential features, are some considerations for future directions in the protein solubility prediction field.

Authors’ information

NH received her M.Sc. in Artificial Intelligence from Isfahan University of Technology, Iran, in 2009 and B.Sc. in Software Engineering from the same university, in 2005. She is a faculty member of the Islamic Azad University (IAU) in Iran, since 2011. Presently she is pursuing Ph.D. in Computer Science at Universiti Teknologi Malaysia. Her research interests are bioinformatics, synthetic biology, artificial intelligence and machine learning.

SZMH is an Associate Professor at the Department of Software Engineering, Faculty of Computing, Universiti Teknologi Malaysia (UTM). She received her B.Sc. Degree in Computer Science from University of Harford, USA, M.Sc. in Computing from University of Bradford, UK and Ph.D. research in Soft Computing from University of Sheffield, UK. Her research interests are Soft Computing techniques and applications, System Development and Intelligent System. Currently she is the Deputy Dean of Academic, Faculty of Computing, UTM and a member of Soft Computing Research Group (SCRG), K-Economy, UTM.

AN received his M.Sc. in Computer Engineering from Islamic Azad University, Iran, in 2006 and B.Sc. in Computer Science from Yazd University, Iran, in 2003. He is a faculty member of the Islamic Azad University (IAU) in Iran, since 2007. Presently he is pursing Ph.D. in Computer Science at Universiti Teknologi Malaysia. His research interests focus on machine learning, pattern recognition and computer vision.

MRS received his Ph.D. from University of New South Wales, Australia, in Biotechnology. He is currently a faculty member (Professor) in the School of Biological Sciences, Universiti Sains Malaysia. The research in his laboratory focuses on molecular genetics and structural biology of proteins. He has published extensively in these areas.

Declarations

Acknowledgment

This work was supported by the Ministry of Higher Education of Malaysia [Grant No. KPT.B.600-18/3 (115) to NH]; Universiti Sains Malaysia [FRGS grant to MRS]; and Universiti Teknologi Malaysia. The authors appreciate the anonymous reviewers’ instructive suggestions.

Authors’ Affiliations

(1)

Faculty of Computing, Universiti Teknologi Malaysia

(2)

School of Biological Sciences, Universiti Sains Malaysia

(3)

Advanced Medical and Dental Institute, Universiti Sains Malaysia

(4)

Centre for Chemical Biology, Universiti Sains Malaysia

References

Chan WC, Liang PH, Shih YP, Yang UC, Lin WC, Hsu CN: Learning to predict expression efficacy of vectors in recombinant protein production. BMC Bioinform. 2010, 11 (Suppl 1): S21-10.1186/1471-2105-11-S1-S21.View ArticleGoogle Scholar
van den Berg BA, Reinders MJ, Hulsman M, Wu L, Pel HJ, Roubos JA, de Ridder D: Exploring sequence characteristics related to high-level production of secreted proteins in aspergillus Niger. PLoS One. 2012, 7 (10): e45869-10.1371/journal.pone.0045869.View ArticlePubMed CentralPubMedGoogle Scholar
Hirose S, Kawamura Y, Yokota K, Kuroita T, Natsume T, Komiya K, Tsutsumi T, Suwa Y, Isogai T, Goshima N, Noguchi T: Statistical analysis of features associated with protein expression/solubility in an in vivo Escherichia coli expression system and a wheat germ cell-free expression system. J Biochem. 2011, 150 (1): 73-81. 10.1093/jb/mvr042.View ArticlePubMedGoogle Scholar
Samak T, Gunter D, Wan Z: Prediction of Protein Solubility in E. coli. 2012, Chicago, IL: E-Science (e-Science), 2012 IEEE 8th International Conference on Date of Conference: 8-12 Oct. 2012, 1-8.Google Scholar
Fang Y, Fang J: Discrimination of soluble and aggregation-prone proteins based on sequence information. Mol BioSyst. 2013, 9 (4): 806-811. 10.1039/c3mb70033j.View ArticlePubMed CentralPubMedGoogle Scholar
Smialowski P, Doose G, Torkler P, Kaufmann S, Frishman D: PROSO II-a new method for protein solubility prediction. FEBS J. 2012, 279 (12): 2192-2200. 10.1111/j.1742-4658.2012.08603.x.View ArticlePubMedGoogle Scholar
Xiaohui N, Feng S, Xuehai H, Jingbo X, Nana L: Predicting the protein solubility by integrating chaos games representation and entropy in information theory. Expert Syst Appl. 2014, 41 (4): 1672-1679. 10.1016/j.eswa.2013.08.064.View ArticleGoogle Scholar
Huang H, Charoenkwan P, Kao T, Lee H, Chang F, Huang W, Ho S, Shu L, Chen W, Ho S: Prediction and analysis of protein solubility using a novel scoring card method with dipeptide composition. BMC Bioinfomratics. 2012, 13 (17): S3-Google Scholar
Wilkinson DL, Harrison RG: Predicting the solubility of recombinant proteins in Escherichia coli. Nat Biotechnol. 1991, 9 (5): 443-448. 10.1038/nbt0591-443.View ArticleGoogle Scholar
Hirose S, Noguchi T: ESPRESSO: a system for estimating protein expression and solubility in protein expression systems. Proteomics. 2013, 13 (9): 1444-1456. 10.1002/pmic.201200175.View ArticlePubMedGoogle Scholar
Quinlan JR: C4.5: Programs for Machine Learning. Vol: 1. 1993, USA: Morgan KaufmannGoogle Scholar
Cover T, Hart P: Nearest neighbor pattern classification. Inform Theory IEEE Transac. 1967, 13 (1): 21-27.View ArticleGoogle Scholar
Rosenblatt F: Principles of Neurodynamics. 1962, New York: SpartanGoogle Scholar
Rumelhart DE, Hinton GE, Williams RJ: Learning Internal Representations by Error Propagation. Parallel Distributed Processing: Explorations in the Microstructure of Cognition. 1985, California University San Diego La Jolla Institute for Cognitive Science, Technical rept. Mar-Sep 1985. (No. ICS-8506)Google Scholar
Cortes C, Vapnik V: Support-vector networks. Mach Learn. 1995, 20 (3): 273-297.Google Scholar
Bertone P, Kluger Y, Lan N, Zheng D, Christendat D, Yee A, Edwards AM, Arrowsmith CH, Montelione GT, Gerstein M: SPINE: An integrated tracking database and data mining approach for identifying feasible targets in high throughput structural proteomics. Nucleic Acids Res. 2001, 29 (13): 2884-2898. 10.1093/nar/29.13.2884.View ArticlePubMed CentralPubMedGoogle Scholar
Magnan CN, Randall A, Baldi P: SOLpro: accurate sequence-based prediction of protein solubility. Bioinformatics. 2009, 25 (17): 2200-2207. 10.1093/bioinformatics/btp386.View ArticlePubMedGoogle Scholar
Davis GD, Elisee C, Newham DM, Harrison RG: New fusion protein systems designed to give soluble expression in Escherichia coli. Biotechnol Bioeng. 1999, 65 (4): 382-388. 10.1002/(SICI)1097-0290(19991120)65:4<382::AID-BIT2>3.0.CO;2-I.View ArticlePubMedGoogle Scholar
Smialowski P, Martin-Galiano AJ, Mikolajka A, Girschick T, Holak TA, Frishman D: Protein solubility: sequence based prediction and experimental verification. Bioinformatics. 2007, 23 (19): 2536-2542. 10.1093/bioinformatics/btl623.View ArticlePubMedGoogle Scholar
Diaz AA, Tomba E, Lennarson R, Richard R, Bagajewicz MJ, Harrison RG: Prediction of protein solubility in Escherichia coli using logistic regression. Biotechnol Bioeng. 2010, 105 (2): 374-383. 10.1002/bit.22537.View ArticlePubMedGoogle Scholar
Chang CCH, Song J, Tey BT, Ramanan RN: Bioinformatics Approaches for Improved Recombinant Protein Production in Escherichia coli: Protein Solubility Prediction. 2013, Oxford: Briefings in bioinformatics, bbt057, First published online August 7, 2013. doi:10.1093/bib/bbt057Google Scholar
Stiglic G, Kocbek S, Pernek I, Kokol P: Comprehensive decision tree models in bioinformatics. PLoS One. 2012, 7 (3): e33812-10.1371/journal.pone.0033812.View ArticlePubMed CentralPubMedGoogle Scholar
Agostini F, Vendruscolo M, Tartaglia GG: Sequence-based prediction of protein solubility. J Mol Biol. 2012, 421 (2): 237-241.View ArticlePubMedGoogle Scholar
Kocbek S, Stiglic G, Pernek I, Kokol P: Stability of different feature selection methods for selecting protein sequence descriptors in protein solubility classification problem. Transition. 2010, 7 (21): 50-55.Google Scholar
Niwa T, Ying BW, Saito K, Jin W, Takada S, Ueda T, Taguchi H: Bimodal protein solubility distribution revealed by an aggregation analysis of the entire ensemble of Escherichia coli proteins. Proc Natl Acad Sci. 2009, 106 (11): 4201-4206. 10.1073/pnas.0811922106.View ArticlePubMed CentralPubMedGoogle Scholar
Kumar P, Jayaraman VK, Kulkarni BD: Granular Support Vector Machine Based Method for Prediction of Solubility of Proteins on Overexpression in Escherichia coli. Pattern Recognition and Machine Intelligence, Second International Conference, PReMI 2007, Kolkata, India. 2007, Berlin Heidelberg: Springer, 406-415. ProceedingsGoogle Scholar
Idicula-Thomas S, Kulkarni AJ, Kulkarni BD, Jayaraman VK, Balaji PV: A support vector machine-based method for predicting the propensity of a protein to be soluble or to form inclusion body on overexpression in Escherichia coli. Bioinformatics. 2006, 22 (3): 278-284. 10.1093/bioinformatics/bti810.View ArticlePubMedGoogle Scholar
Idicula‒Thomas S, Balaji PV: Understanding the relationship between the primary structure of proteins and its propensity to be soluble on overexpression in Escherichia coli. Protein Sci. 2005, 14 (3): 582-592. 10.1110/ps.041009005.View ArticleGoogle Scholar
Luan C, Qiu S, Finley JB, Carson M, Gray RJ, Huang W, Johnson D, Tsao J, Reboul J, Vaglio P, Hill DE, Vidal M, DeLucas LJ, Luo M: High-throughput expression of C. elegans proteins. Genome Res. 2004, 14 (10b): 2102-2110. 10.1101/gr.2520504.View ArticlePubMed CentralPubMedGoogle Scholar
Goh C, Lan N, Douglas SM, Wu B, Echols N, Smith A, Milburn D, Montelione GT, Zhao H, Gerstein M: Mining the structural Genomics Pipeline: identification of protein properties that affect high throughput experimental analysis. J Mol Biol. 2004, 336 (1): 115-130. 10.1016/j.jmb.2003.11.053.View ArticlePubMedGoogle Scholar
Christendat D, Yee A, Dharamsi A, Kluger Y, Savchenko A, Cort JR, Booth V, Mackereth CD, Saridakis V, Ekiel I, Kozlov G, Maxwell KL, Wu N, McIntosh LP, Gehring K, Kennedy MA, Davidson AR, Pai EF, Gerstein M, Edwards AM, Arrowsmith CH: Structural Proteomics of an archaeon. Nat Struct Mol Biol. 2000, 7 (10): 903-909. 10.1038/82823.View ArticleGoogle Scholar
Li ZR, Lin HH, Han LY, Jiang L, Chen X, Chen YZ: PROFEAT: a web server for computing structural and physicochemical features of proteins and peptides from amino acid sequence. Nucleic Acids Res. 2006, 34 (2): W32-W37.View ArticlePubMed CentralPubMedGoogle Scholar
Maruyama Y, Wakamatsu A, Kawamura Y, Kimura K, Yamamoto J, Nishikawa T, Kisu Y, Sugano S, Goshima N, Isogai T, Nomura N: Human Gene and Protein Database (HGPD): a novel database presenting a large quantity of experiment-based results in human proteomics. Nucleic Acid Research. 2009, 37 (1): D762-D766.View ArticleGoogle Scholar
Kouranov A, Xie L, de la Cruz J, Chen L, Westbrook J, Bourne PE, Berman HM: The RCSB PDB information portal for structural genomics. Nucleic Acids Res. 2006, 34 (1): D302-D305.View ArticlePubMed CentralPubMedGoogle Scholar
Berman HM, Battistuz T, Bhat TN, Bluhm WF, Bourne PE, Burkhardt K, Feng Z, Gilliland GL, Iype L, Jain S, Fagan P, Marvin J, Padilla D, Ravichandran V, Schneider B, Thanki N, Weissig H, Westbrook JD, Zardecki C: The Protein Data Bank. Acta Crystallographica Section D: Biological Crystallography. 2002, 58 (6): 899-907. 10.1107/S0907444902003451.View ArticleGoogle Scholar
Chen L, Oughtred R, Berman HM, Westbrook J: TargetDB: a target registration database for structural genomics projects. Bioinformatics. 2004, 20 (16): 2860-2862. 10.1093/bioinformatics/bth300.View ArticlePubMedGoogle Scholar
Saeys Y, Inza I, Larrañaga P: A review of feature selection techniques in bioinformatics. Bioinformatics. 2007, 23 (19): 2507-2517. 10.1093/bioinformatics/btm344.View ArticlePubMedGoogle Scholar
Ben-Bassat M: Pattern Recognition and Reduction of Dimensionality. Handbook of Statistics. Vol: 2. Edited by: Krishnaiah P, Kanal L. 1982, Amsterdam: North-Holland Publishing Co, 773-910.Google Scholar
Witten IH, Frank E: Data Mining: Practical Machine Learning Tools and Techniques. 2005, USA: Morgan Kaufmann, 2Google Scholar
Weston J, Pérez-Cruz F, Bousquet O, Chapelle O, Elisseeff A, Schölkopf B: Feature selection and transduction for prediction of molecularbioactivity for drug design. Bioinformatics. 2003, 19: 764-771. 10.1093/bioinformatics/btg054.View ArticlePubMedGoogle Scholar
Mann HB, Whitney DR: On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat. 1947, 18 (1): 50-60. 10.1214/aoms/1177730491.View ArticleGoogle Scholar
Kittler J: Feature Set Search Algorithms. Pattern Recognition and Signal Processing. Edited by: Chen C. 1978Google Scholar
Siedlecki W, Sklansky J: On automatic feature selection. Int J Pattern Recognit Artif Intell. 1998, 2 (02): 197-220.View ArticleGoogle Scholar
Kononenko I, Šimec E, Robnik-Šikonja M: Overcoming the Myopia of inductive learning algorithms with RELIEFF. Appl Intell. 1997, 7 (1): 39-55. 10.1023/A:1008280620621.View ArticleGoogle Scholar
Breiman L: Random forests. Mach Learn. 2001, 5 (1): 5-32.View ArticleGoogle Scholar
Guyon I, Weston J, Barnhill S, Vapnik V: Gene selection for cancer classification using support vector machines. Mach Learn. 2002, 46 (1-3): 389-422.View ArticleGoogle Scholar
Piatetsky-Shapiro G: Discovery, analysis and presentation of strong rules. Knowledge Discovery in Databases. Edited by: Piatetsky-Shapiro G, Frawley WJ. 1991, Cambridge: MAGoogle Scholar
de Ridder D, de Ridder J, Reinders MJ: Pattern recognition in bioinformatics. Brief Bioinform. 2013, 14 (5): 633-647. 10.1093/bib/bbt020.View ArticlePubMedGoogle Scholar

Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

A review of machine learning methods to predict the solubility of overexpressed recombinant proteins in Escherichia coli

Abstract

Background

Results

Conclusions

Keywords

Introduction

Review

Discussion

Conclusions

Authors’ information

Declarations

Acknowledgment

Authors’ Affiliations

References

Copyright

BMC Bioinformatics

Contact us