1. Introduction

Micellar electrokinetic chromatography (MEKC) is

a widely used technique in capillary electrophoresis

(CE) and is capable of separating neutral compounds

as well as charged solutes by including a pseudo-

stationary phase

[1-6]. This technique has great

utility in separating mixtures that contain both ionic

and neutral species, and has become a valuable tool

in separating very hydrophobic pharmaceuticals

from their very polar metabolites. The creation of

the pseudo-stationary phase is most easily achieved

using micelles of surfactants and depending on the

hydrophobicity, analytes partition between these

micelles and the mobile phase. The signiﬁcant features

of MEKC are the availability of a wide range of pseudo-

stationary phases that provide unique selectivities for

peptides and feasibility of manipulating the comparison

of the pseudo-phases since it is a completely solution-

based technique. Therefore, selectivity in MEKC can

be varied by altering the nature of the micelles

[6-8].

This could be achieved by altering the surfactant and

changing the size, charge or geometry of the micelles.

It is shown that not only the predominant hydrophobic

interaction but also other important solute-micelle

Determination and prediction of peptide mobilities by

micellar electro-kinetic chromatography using adaptive

neuro-fuzzy inference system as a feature selection method

Mostafa Hassanisadi

a,*

, Morteza G. Khaledi

and Mehdi Jalali-Heravi

Nanotechnology Research Center, Research Institute of Petroleum Industry, Tehran, Iran.

Department of Chemistry, Sharif University of Technology, P.O.Box9516-11365, Tehran, Iran

Department of Chemistry, North Carolina State University, NC8204-27695, USA

ABSTRACT

Mobility of 128 peptides composed of up to 14 amino acids is

determined for sodium dodecyl sulfate (SDS) micellar systems using

micellar electrokinetic chromatography (MEKC). The mobilities of

these peptides are predicted using back propagation of error artiﬁcial

neural networks (BP-ANNs). Adaptive neuro-fuzzy inference system

(ANFIS) which can deal with linear and nonlinear phenomena is

used to select the inputs of BP-ANN. A 3:4:1 BP-ANN model with

four variables of Kappa substituent constant, Kappa(H), number of

peptide bonds, (lnN), molar refractivity of C-terminal, MRC, and

steric effects at N-terminal, ES,N, which incorporate substituent,

steric and molar refractivity effects as its inputs was developed.

Comparison of Multiple Linear Regression (MLR) and ANN results

shows the nonlinear characteristic of the phenomena. The nonlinear

model was successful in predicting the mobilities of 120 peptides

except for the ones (8 peptides) with negatively charged amino acids.

It is shown that that most outlier peptides contain middle glutamic

acid (E) and aspartic acid (D) amino acids and their mobilities follow

a similar mechanism in MEKC.

Keywords:

Peptide mobilities,

Micellar ElectroKinetic Chromatography,

Artiﬁcial neural networks,

Adaptive neuro-fuzzy inference system

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

ARTICLE INFO:

Received 5 Mar 2020

Revised form 28 Apr 2020

Accepted 27 May 2020

Available online 28 Jun 2020

Corresponding Author: Mostafa Hassanisadi

Email: mhsaadi@ripi.ir

DOI: ttps://doi.org/10.24200/amecj

Research Article, Issue 2

Analytical Methods in Environmental Chemistry Journal

Journal home page: www.amecj.com/ir

AMECJ

------------------------

interactions such as electrostatic and hydrogen bonding

could manipulate the separation. In most MEKC

studies, sodium dodecyl sulphate (SDS) which is an

anionic micelle has been successfully used to separate

the hydrophobic and cationic analytes. An important

parameter for the separation of the peptides and

modeling of the electropherograms in CE and MEKC

is their mobilities. This parameter can be converted

to migration time and then electropherograms can

be simulated using gaussian function. A long-range

goal of our laboratory is developing experimental

and theoretical methods for peptide separations, and

mapping two-dimensional MEKC-CZE schemes.

Reaching this goal requires an in-depth understanding

of the effects of different factors on the CZE and

MEKC peptide mobilities. Quantitative models such as

quantitative structure-mobility relationships (QSMR)

can help us to gain this knowledge. We have started

with the prediction of electrophoretic mobilities of 125

peptides using CZE technique

[9]. A QSMR model has

been developed using Offord’s charge-over-mass term

(Q/M2/3) together with the corrected steric substituent

constant (ES,C)and molar refractivity (MR) as

descriptors. The latter two parameters, account for

the steric effects and bulkiness of amino acid side

chains, respectively

[9]. The robustness of this work

was shown by artiﬁcial neural network (ANN)

modeling of the mobilities of 102 larger peptides – up

to 42 amino acid residues – that also included highly

charged and hydrophobic peptides

[10]. Besides, to

explore the utility of the ANN model in simulation of

peptide maps, the proﬁle for the endoproteinase digest

of the melittin, glucagon and horse cytochrome C,

was also studied in the latter work

[10]. We intended

to examine the same route for the MEKC modeling

as we did for the CZE. Therefore, the main aim of the

present work was the determination of the mobilities

of a set of small peptides – up to 14 amino acid residues

– using MEKC and then modeling the mobilities by

applying different chemometric techniques. Artiﬁcial

neural networks (ANNs) are among the most

popular methods for modeling of the linear/nonlinear

phenomena

[11]. ANN-based approaches have the

ability of modeling the complex data without the

need for a detailed understanding of the underlying

phenomena. Back propagation (BP) learning rule is

the most popular learning algorithm adopted in neural

network technology. Hence in the present research,

a back-propagation of error artiﬁcial neural network

(BP-ANN) was used to predict the mobilities of 128

peptides obtained using MEKC with SDS micellar

system. However, the main problem in developing the

ANNs, is the selection of suitable descriptors for their

inputs. This is especially serious when the mechanism

of the phenomenon is complex or unknown. In

order to overcome this problem one needs to use a

powerful method for the feature selection. Therefore,

in the present work we have chosen adaptive neuro-

fuzzy inference system (ANFIS) for selecting the

most effective parameters on MEKC mobilities. This

method is capable in dealing with linear and nonlinear

phenomena. Success in modeling of the electrophoretic

mobilities of peptides using MEKC, together with our

previous achievements in modeling of CZE mobilities

might pave the way for developing and predicting the

two-dimensional MEKC-CZE maps of peptides.

2. Experimental

2.1. Chemicals and Materials

Sodium dodecyl sulfate (SDS), decanophenone, sodium

phosphate monobasic (NaH

O), hexanol, and

peptides were obtained from Sigma Chemical Co. (St.

Louis, MO). Different concentrations of 40, 60 and 80

mM SDS were prepared in 20 mM phosphate buffer

at pH 7 with 1.15 % (v/v) hexanol. The solutions

were ﬁltered through 0.2 μm acrodisc ﬁlter (STRL,

Eatontown, NJ) before use. All experiments were

carried out on a home-built CE system comprised

of a 0-30 kV high voltage power supply (Series EH,

Glassman High Voltage, Inc., White house Station,

NJ). Fused silica capillary (Polymicro Technologies,

Phoenix, AZ), with an inner diameter of 50 μm and

an outer diameter of 375 μm was used. The total

capillary length and the length from the inlet to the

detector were 71 and 47 cm, respectively. A circulating

mineral oil bath was used to maintain the temperature

of the two buffer reservoirs and the capillary at a

designed temperature in this experiment. A positive

voltage of 25 kV was applied during the experiments.

A variable-wavelength UV detector (Model 200,

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

Scientiﬁc System, Inc., State College, PA) was used,

and a wavelength of 214 nm was set in this work.

The chromatograms were collected using acquisition

software written in LabView (Austin, TX). Before

any injection was made, the untreated capillary was

conditioned by rinsing with deionized (DI) water for

20 minutes, sodium hydroxide dissolved in methanol

for 10-12 minutes, DI water for 20 minutes and ﬁnally

with the buffer for 15 minutes. The capillary was

vacuum rinsed with the buffer solution between each

injection.

2.2. Determination of mobility by measurement of

migration time of peptides

Electrophoretic mobility at a micelle concentration

can be determined from the migration times using

equation 10

[2,20]:















ttV



(10)

where Lt is the total length of the capillary, Ld is

the separation length (from the upstream end of the

capillary to the detection window). V is the applied

voltage. tr is the retention time of a solute at a given

micelle concentration, and to is the retention time

of an unretained solute. The determined mobility

values of peptides in 40, 60 and 80 mM SDS

solutions together with the peptides studied in this

work are shown in

Table 1.

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

Table 1. The values of electrophoretic mobilities of peptides using MEKC with different SDS concentrations

together with the calculated values of descriptors

Descriptors Mobility

Peptide E

S,C

ln(N) Kappa(H)

SDS 80

SDS

60mM

SDS

40mM

-0.70 5.65 0.69 0.67 -6.38 -6.10 -5.73

2 GY -0.50 1.03 0.69 0.46 -6.49 -5.55 -4.31

3 AY -0.70 5.65 0.69 0.67 -6.88 -6.23 -4.76

4 ASTTTNYT -3.88 5.65 2.08 -0.22 -8.71 -7.36 -5.15

5 VY -1.79 14.95 0.69 1.09 -8.74 -8.13 -6.60

6 YV -1.79 31.83 0.69 1.09 -10.04 -9.60 -8.58

7 YA -0.70 31.83 0.69 0.67 -10.17 -9.30 -8.12

8 GGF -0.30 1.03 1.10 1.06 -10.92 -9.61 -7.10

9 GF -0.50 1.03 0.69 1.06 -12.09 -10.49 -8.30

10 YY -1.40 31.83 0.69 0.92 -12.16 -11.49 -9.88

11 YG -0.50 31.83 0.69 0.46 -12.23 -10.71 -8.12

12 IY -2.31 19.59 0.69 1.41 -12.86 -11.42 -8.88

13 AF -0.70 5.65 0.69 1.27 -13.18 -11.25 -7.89

14 HY -1.36 23.79 0.69 0.90 -13.20 -11.63 -8.66

15 YI -2.31 31.83 0.69 1.41 -13.52 -11.70 -9.80

16 LY -1.94 19.59 0.69 1.40 -13.60 -11.97 -8.53

17 YGG -0.30 31.83 1.10 0.46 -16.03 -14.47 -11.45

18 FA -0.70 30.01 0.69 1.27 -16.43 -14.56 -11.52

19 FV -1.79 30.01 0.69 1.69 -16.43 -14.65 -11.79

20 YL -1.94 31.83 0.69 1.40 -16.72 -15.05 -11.45

21 GW -0.46 1.03 0.69 1.01 -16.79 -14.85 -10.49

22 AW -0.66 5.65 0.69 1.22 -17.89 -15.65 -11.99

23 VF -1.79 14.95 0.69 1.69 -19.52 -16.75 -12.04

24 YAG -0.50 31.83 1.10 0.67 -19.89 -17.00 -12.17

25 YYY -2.10 31.83 1.10 1.38 -20.00 -18.09 -13.31

26 WS -0.94 39.81 0.69 0.90 -20.57 -18.21 -13.89

27 FG -0.50 30.01 0.69 1.06 -21.47 -18.60 -15.43

28 PW -0.66 13.95 0.69 1.56 -21.78 -17.65 -13.05

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

29 VW -1.75 14.95 0.69 1.64 -22.08 -19.31 -13.51

30 FI -2.31 30.01 0.69 2.01 -22.10 -19.09 -15.68

31 WD -1.44 39.81 0.69 1.45 -22.22 -22.25 -19.11

32 DF -1.48 11.58 0.69 1.50 -22.54 -22.18 -21.82

33 WA -0.66 39.81 0.69 1.22 -22.60 -19.65 -14.85

34 D

-1.48 11.58 0.69 1.50 -23.16 -22.61 -21.64

35 FM -1.53 30.01 0.69 1.66 -23.23 -20.79 -15.57

36 GGFM -1.13 1.03 1.39 1.66 -23.74 -20.27 -14.12

37 WV -1.75 39.81 0.69 1.64 -23.83 -20.62 -16.14

38 FGG -0.30 30.01 1.10 1.06 -24.86 -22.50 -16.57

39 YGGF -1.00 31.83 1.39 1.52 -25.14 -23.13 -15.69

40 EW -1.28 16.23 0.69 1.43 -25.54 -22.75 -21.33

41 YW -1.36 31.83 0.69 1.47 -25.54 -21.90 -18.32

42 YYL -2.64 31.83 1.10 1.86 -25.68 -23.87 -16.44

43 DW -1.44 11.58 0.69 1.45 -25.77 -22.99 -21.18

44 MW -1.49 23.12 0.69 1.61 -25.77 -21.96 -18.07

Descriptors Mobility

Peptide E

S,C

ln(N) Kappa(H)

SDS 80

SDS 60

SDS 40

45 WE -1.28 39.81 0.69 1.43 -26.89 -21.82 -18.29

46 FL -1.94 30.01 0.69 2.00 -28.13 -25.32 -18.93

47 WG -0.46 39.81 0.69 1.01 -28.40 -25.57 -19.98

48 IW -2.27 19.59 0.69 1.96 -28.84 -25.41 -18.06

49 IF -2.31 19.59 0.69 2.01 -29.15 -25.04 -19.64

50 PPGFSP -0.78 13.95 1.79 2.60 -29.19 -25.75 -17.08

51 GGFL -1.54 1.03 1.39 2.00 -29.26 -26.34 -19.32

52 WM -1.49 39.81 0.69 1.61 -29.56 -26.25 -20.98

53 LF -1.94 19.59 0.69 2.00 -31.16 -28.17 -20.70

54 WP -0.66 39.81 0.69 1.56 -31.20 -27.36 -21.35

55 KF -1.32 25.05 0.69 2.20 -31.69 -29.11 -21.43

56 YPF -1.40 31.83 1.10 2.07 -31.97 -28.32 -20.78

57 WY -1.36 39.81 0.69 1.47 -32.60 -26.46 -20.86

58 L

-1.90 19.59 0.69 1.95 -32.61 -28.95 -22.63

59 FF -1.40 30.01 0.69 2.12 -32.72 -29.83 -22.99

60 F

-1.40 30.01 0.69 2.12 -32.84 -30.44 -23.48

61 K

-1.32 25.05 0.69 2.20 -32.87 -30.20 -21.63

62 LW -1.90 19.59 0.69 1.95 -33.11 -29.65 -21.60

63 GLF -1.74 1.03 1.10 2.00 -33.96 -31.49 -23.70

64 WGG -0.26 39.81 1.10 1.01 -34.06 -30.35 -24.09

65 GFL -1.74 1.03 1.10 2.00 -34.55 -31.48 -24.40

66 FW -1.36 30.01 0.69 2.07 -35.09 -32.21 -26.14

67 YGGFM -1.83 31.83 1.61 2.12 -35.13 -31.37 -22.40

68 WL -1.90 39.81 0.69 1.95 -35.27 -31.65 -25.71

69 MLF -2.77 23.12 1.10 2.60 -35.62 -32.99 -26.10

70 WGY -1.16 39.81 1.10 1.47 -36.11 -32.72 -26.61

71 YAGFL -2.44 31.83 1.61 2.67 -37.52 -34.85 -26.72

72 YGGFL -2.24 31.83 1.61 2.46 -37.59 -36.08 -26.09

73 WGGGY -0.76 39.81 1.61 1.47 -38.83 -35.78 -29.77

74 KW -1.28 25.05 0.69 2.15 -38.88 -36.79 -30.76

75 WGGY -0.96 39.81 1.39 1.47 -38.88 -35.47 -29.39

76 FGGF -1.00 30.01 1.39 2.12 -38.95 -35.19 -29.22

77 WF -1.36 39.81 0.69 2.07 -39.97 -37.28 -31.14

78 YSGFLT -3.25 31.83 1.79 2.20 -39.98 -35.47 -28.51

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

79 WW -1.32 39.81 0.69 2.02 -41.50 -39.25 -33.67

80 TRSAW -2.09 11.82 1.61 2.53 -41.52 -40.67 -33.07

81 YGGWL -2.20 31.83 1.61 2.41 -42.21 -40.85 -32.63

82 FGFG -1.00 30.01 1.39 2.12 -42.78 -39.83 -34.28

83 RW -1.28 30.05 0.69 2.58 -43.08 -41.39 -33.55

84 FFF -2.10 30.01 1.10 3.18 -44.33 -43.35 -38.04

85 RPPGK -1.04 30.05 1.61 3.81 -44.43 -42.77 -35.55

86 DRVYIHP -5.46 11.58 1.95 5.04 -44.53 -43.75 -37.60

87 KYK -1.94 25.05 1.10 2.74 -45.47 -45.20 -41.39

88 RPPGFSP -1.40 30.05 1.95 4.17 -45.63 -45.23 -41.06

89 WR -1.28 39.81 0.69 2.58 -46.11 -44.77 -38.45

90 DRVYIHPF -6.16 11.58 2.08 6.10 -46.54 -45.96 -41.39

91 ELYENKPRRPY -6.52 16.23 2.40 7.90 -46.61 -46.27 -43.06

92 DRVYVHPFHL -7.54 11.58 2.30 7.16 -47.11 -47.08 -45.15

93 NRVYVHPF -5.64 14.46 2.08 5.16 -47.12 -47.29 -44.15

Descriptors Mobility

Peptide E

S,C

ln(N)

Kappa(H)

SDS 80

SDS 60

SDS 40

94 YMEHFRW -4.79 31.83 1.95 5.56 -47.21 -46.98 -43.99

95 RYLGYL -4.30 30.05 1.79 4.37 -47.31 -46.99 -45.06

96 ELYENKPRRPYIL -9.37 16.23 2.56 9.79 -47.31 -46.57 -44.76

97 FFFF -2.80 30.01 1.39 4.24 -47.35 -47.43 -44.36

98 CGYGPKKKRKVGG -4.09 13.90 2.56 9.05 -47.48 -46.26 -41.74

99 RPKPQQFFGLM -5.75 30.05 2.40 7.59 -47.55 -47.82 -46.31

100 YRPPGFSPFR -3.42 31.83 2.30 7.26 -47.55 -47.82 -46.31

101 MEHFRWG -3.89 23.12 1.95 5.10 -47.56 -47.47 -43.97

102 DRVYIHPFHL -8.06 11.58 2.30 7.48 -47.66 -46.85 -43.59

103 ELYENKPRRPFIL -9.37 16.23 2.56 10.39 -47.71 -46.77 -44.90

104 AGCKNFFWKTFTSC -5.92 5.65 2.64 8.65 -47.71 -47.66 -45.63

105 RPKPQQF -3.18 30.05 1.95 4.99 -47.83 -47.28 -44.08

106 RPPGFSPFR -2.72 30.05 2.20 6.80 -47.85 -47.71 -46.02

107 RVYIHPI -6.29 30.05 1.95 5.55 -47.86 -47.41 -46.15

108 SYSMEHFRWG -5.15 7.20 2.30 5.34 -47.88 -47.54 -44.80

109 RVYVHPF -4.86 30.05 1.95 5.34 -47.92 -47.27 -45.34

110 FFFFF -3.50 30.01 1.61 5.30 -47.92 -48.27 -46.11

111 RPGFSPFR -2.72 30.05 2.08 6.25 -48.07 -46.91 -44.71

112 DRVYIHPFHLVIHN -12.20 11.58 2.64 9.32 -48.10 -47.43 -45.25

113 WQPPRARI -4.13 39.81 2.08 6.47 -48.11 -47.40 -45.77

114 RGPFPI -2.73 30.05 1.79 4.68 -48.12 -47.14 -42.36

115 IARRHPYFL -6.15 19.59 2.20 7.75 -48.21 -47.30 -44.58

116 WHWLQL -5.08 39.81 1.79 4.40 -48.28 -48.46 -45.62

117 PPGFSPFR -2.10 13.95 2.08 5.23 -48.42 -47.61 -45.54

118 YGGFMRF -3.15 31.83 1.95 4.75 -48.49 -47.09 -44.86

119 EGKRPWIL -5.17 16.23 2.08 6.58 -48.57 -47.47 -45.87

120 WWW -1.98 39.81 1.10 3.03 -48.66 -48.09 -45.97

121 HW -1.32 23.79 0.69 1.45 -40.97 -38.71 -31.77

122 RRPYIL -4.79 30.05 1.79 6.04 -32.39 -29.11 -22.96

123 YPFVEPI -4.72 31.83 1.95 4.62 -32.39 -29.11 -22.96

124 YLEPGPVTA -3.98 31.83 2.20 3.61 -18.05 -16.71 -14.09

125 RKDVY -3.81 30.05 1.61 4.24 -42.31 -40.11 -33.63

126 RFDS -2.38 30.05 1.39 2.96 -31.80 -28.57 -19.86

127 FLEEI -4.79 30.01 1.61 3.79 -27.60 -27.03 -25.53

128 VEPIPY -4.02 14.95 1.79 3.56 -14.58 -14.09 -12.70

2.3. Sequential forward search for input

selection using ANFIS

In this work, ANFIS-based sequential variable

selection program written in MATLAB is used

as a feature selection method

[21]. The algorithm

is based on selecting the best descriptor which

minimizes standard errors of calibration and

prediction and then repeatedly adds next best

descriptor to the previous one(s). In the ﬁrst step

after sorting the dataset based on the mobility

values

(Table 1), training and test sets in a ratio

of 4:1 were randomly chosen such that the test

set adequately represented the training set. Then

based on three iterations and two Gaussian bell

membership functions, 5 out of 41 descriptors were

selected using ANFIS. The selected parameters

were used as inputs for developing ANN models.

Analysis of the results obtained by the ANN

model showed some outliers. These outliers

were removed from the original dataset and the

sequential variable selection was repeated using

the remaining peptides of the dataset. In the ﬁnal

stage, a total of four descriptors were selected for

developing neural networks and further studies.

The values of these parameters are given in

Table 1

for all peptides studied in this work.

2.4. Descriptors

The following structural parameters for amino acids

were considered for calculating the descriptors of

peptides: The substituent constants (қ), steric effects

(ES,C) and molecular refractivity (MR)

[22,23].

The values of these descriptors for twenty amino

acids are listed in

Table 2. Molar refractivity and

residues mass are scaled by a factor of 0.1, such that

they will have the same scale according to Hansch

and Leo

[18]. Taft deﬁned the steric constant, ES, as

log (k/ko), where k and ko are the rate constants for

the acidic hydrolysis of a substituted ester and of a

reference ester (methyl group is usually used as the

reference, but H is sometimes used), respectively

[24]. Hankcock has stated that there is contribution of

hyper conjugation (α-hydrogen bonding) to the Taft

Es; therefore, it must be corrected as deﬁned by

[25]:

ES,C = ES + 0.306 (n-3) (11)

where ES,C is a corrected steric substituent constant

and Es is the “revised” Taft steric constant

[26]; n is

the number of α-hydrogens. As can be seen in

Table

, a small value of steric effect was observed for

“crowded” structures of α-branched side chain (V,

I, L). This means that they are large resistance to

the hydrolysis.

2.5. Artiﬁcial neural network

In the present work, the feed forward back

propagation of error artiﬁcial neural network (BP-

ANN) is written in C++. The input layer consisted of

the four parameters selected by ANFIS. The output

layer represents the electrophoretic mobilities of the

peptides. In this investigation, the bipolar sigmoid

function, i.e., f (x) = (1-exp (-x)) / (1+exp (-x)),

is used as the transfer function. The initial weights

were chosen randomly, and were optimized based

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

Table 2.

Physicochemical substituent parameters

for amino acids

AA Side Chains K E

S,C

alanine (A) 0.21 0.00 0.57

arginine (R) 1.57 -0.62 3.01

asparagine (N) -0.18 -0.78 1.45

aspartic acid (D) 0.44 -0.78 1.16

cysteine (C) 1.28 0.00 0.00

glutamine (Q) 0.06 -0.62 1.91

glutamic acid (E) 0.42 -0.62 1.62

glycine (G) 0.00 0.20 0.10

histidine (H) 0.44 -0.66 2.38

isoleucine (I) 0.95 -1.61 1.96

leucine (L) 0.94 -1.24 1.96

lysine (K) 1.14 -0.62 2.51

methionine (M) 0.60 -0.83 2.31

phenylalanine (F) 1.06 -0.70 3.00

proline (P) 0.55 0.00 1.40

serine (S) -0.11 -0.28 1.18

threonine (T) -0.15 -0.53 1.18

tryptophan (W) 1.01 -0.66 3.98

tyrosine (Y) 0.46 -0.70 3.18

valine (V) 0.63 -1.09 1.50

on the delta rule through back propagation of

errors. The program is written in such a way that

the range for initialization of the weights depends

on the number of input and hidden nodes. Before

training, the inputs were normalized between

-2 and 2 and the output between 0 and 1. The

network parameters such as the number of hidden

layer nodes, learning rate and momentum were

optimized. Optimizations of these parameters were

based on obtaining the minimum standard error of

calibration and prediction. Program automatically

avoids overﬁtting by stopping the training when the

increase in standard error of prediction commences.

After the analysis of ANN results and removing the

outliers, the new dataset consisted of 118 peptides

were sorted based on mobility values. This set was

divided into training, test and validation sets (in a

ratio of 4:1:1). However, in order to test the stability

of the model and making sure that the results are

not due to the chance, six different sets of training,

test and validation sets for each concentration of

SDS were created.

2.6. Methodology

The present work consists of three steps: (1)

experimental determination of the mobilities of

peptides using CE system in 40, 60 and 80 mM SDS

solutions for two purposes. First, to investigate the

effects of change of surfactant concentration on the

mobilities of peptides and secondly, exploration

of the ability and robustness of the generated

theoretical models in the prediction of the MEKC

mobilities at different SDS concentrations. (2)

Selecting the structural parameters which play the

major role in the migration behavior of peptides in

MEKC experiments. This is a challenging process,

since the mechanism of partitioning of the peptides

into the micelles and migration of the micelles due to

the electrophoretic and electroosmotic phenomena

are complex. In modeling, choosing suitable

features/descriptors is critical, because without

success in this step the development of a robust and

interpretable model is impossible. Therefore, we

were very anxious to search for a powerful method

as a feature selection technique. We have chosen

a neurofuzzy system for this purpose, which is a

combination of the neural network and fuzzy rules.

A neural network can model a process by means of

a linear/nonlinear regression algorithm, for which

the result is a network with adjusted weights and

approximates the property of interest. However,

the problem is that the knowledge is stored in

an opaque fashion; the learning result is a set of

parameter values, almost impossible to interpret

them in words. Conversely, a fuzzy rule-base

consists of readable if-then statements which are

very close to natural language, but cannot learn

the rules. These two are combined in neurofuzzy

systems in order to achieve readability and learning

ability at the same time. In this work a sequential

ANFIS is used as feature selection technique. We

have chosen ANFIS because of its much faster

convergence, much more repeatability and much

less preprocessing compared with ANN. (3) In

order to develop a model for predicting the MEKC

mobilities of peptides and also inspecting the

linear/nonlinear characteristics of the migration

behavior of peptides in MEKC, simple MLR as a

linear method and BP-ANN as a nonlinear method

are used. In both cases we use ANFIS for selecting

the features. These methods are very common and

frequently have been used in our laboratory and by

several other researchers

[12-16]. Therefore, for the

sake of brevity their description is not given here.

2.6.1.Adaptive Neuro-Fuzzy Inference System

(ANFIS)

By deﬁnition fuzzy logic is a type of logic that

recognizes more than simple true and false values

[17]. Fuzzy logic can represent propositions by

degrees of truthfulness and falsehood and has

proved to be particularly useful in expert systems

and other artiﬁcial intelligence applications. One

of the hallmarks of fuzzy logic is that it allows

nonlinear input/output relationships to be expressed

by a set of qualitative “if-then” rules. The theory of

fuzzy logic provides a mathematical morphology to

emulate certain perceptual and linguistic attributes

associated with human cognition. Most fuzzy

systems are hand-crafted by a human expert to

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

capture some desired input/output relationships that

the expert has in mind. However, often an expert

cannot express his or her knowledge explicitly;

and, for many applications, an expert may not

even exist. Hence, there is considerable interest in

being able to automatically extract fuzzy rules from

experimental input/output data. While fuzzy theory

provides an inference mechanism under cognitive

uncertainty, computational neural networks offer

exciting advantages such as learning, adaptation,

fault-tolerance, parallelism and generalization.

The computational neural networks are capable of

coping with computational complexity, nonlinearity

and uncertainty. In fact, the neural network approach

fuses well with fuzzy logic and by combining these

two techniques, beneﬁts of both would be acquired.

Fuzzy inference is the process of formulating the

mapping from a given input to an output using

fuzzy logic

(Fig. 1). The mapping then provides a

basis from which decisions can be made, or patterns

discerned. One type of fuzzy inference systems is

based on Takagi-Sugeno model

[18]. In the Takagi-

Sugeno model the idea is that each rule in a rule-

base deﬁnes a region for a model, which can be

linear. The left-hand side of each rule deﬁnes a fuzzy

validity region for the linear model on the right-

hand side. The inference mechanism interpolates

smoothly between each local model to provide

a global model. As an example consider a single

input, single output system with the following two

rules: 1) IF input is large THEN output is line 1. 2)

IF input is small THEN output is line 2. Where line

1 is deﬁned as 0.2 * input + 90 and line 2 is 0.6 *

input + 20. The rules interpolate between the two

lines in the region where the membership functions

overlap

(Fig. 2). Outside of that region the input is a

linear function of the error.

Fig. 2. Interpolation between two lines (top) in the

overlap of input sets (bottom).

2.6.2.ANFIS architecture

Without loss of generality we assume two inputs,

u1 and u2, and one output, y. Assume for now a

ﬁrst order Sugeno type rule-base composed of the

following two rules

[19]:

If u

is A

and u

is B

then

102121111

cucucy 

(1)

If u

is A

and u

is B

then

202221122

cucucy 

(2)

Incidentally, this fuzzy controller could interpolate

between two linear controllers depending on the

current state. If the ﬁring strengths of the rules are

α1 and α2 respectively, for two particular values of

the inputs u1 and u2, then the output is computed as

a weighted average

2211







(3)

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

Fig. 1. The basic structure of fuzzy inference system

Figure 3 shows corresponding ANFIS network. The

descriptions for the layers shown in the network are

as follows:

1. Each neuron i in layer one is adaptive with a

parametric activation function. Its output is the

grade of membership to which the given input

satisﬁes the membership function, i.e.,

),(),(),(

121

211

uuu

ABA



)(



An example of a membership function is the

generalized bell function:

)(









(4)

where {a, b, c} is the parameter set. As the values

of the parameters change, the shape of the bell-

shaped function varies. Parameters in that layer are

called premise parameters.

2. Every node in layer two is a ﬁxed node, whose

output is the product of all incoming signals.

In general, any other fuzzy AND operation can

be used. Each node output represents the ﬁring

strength αi of the ith rule.

3. Every node in layer three is a ﬁxed node which

calculates the ratio of the ith rule’s ﬁring strength

relative to the sum of all rule’s ﬁring strengths,





2,1i



(5)

The result is a normalized ﬁring strength.

4. Every node in layer four is an adaptive node

with a node output

)(

02211 iiiiii

cucucy 



2,1i

(6)

where i is the normalized ﬁring strength from layer

three and {ci1, ci2, ci0} is the parameter set of this

node. Parameters in this layer are called consequent

parameters.

5. Every node in layer ﬁve is a ﬁxed node which

sums all incoming signals. It is straightforward to

generalize the ANFIS architecture in

Figure 3 to a

rule-base with more than two rules.

2.6.3.The ANFIS learning algorithm

When the premise parameters are ﬁxed, the overall

output is a linear combination of the consequent

parameters. In symbols, the output y can be written

as:

yyy













(7)

)()(

202221212102121111

cucuccucucy 



(8)

2022222211210112211111

)()()()( ccucuccucuy





(9)

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

Fig. 3. Structure of the ANFIS network

Which is linear in the consequent parameters cij

(i=1, 2; j=0, 1, 2). A hybrid algorithm adjusts the

consequent parameters cij in a forward pass and the

premise parameters {ai, bi, ci} in a backward pass.

In the forward pass the network inputs propagate

forward up to layer 4, where the consequent

parameters are identiﬁed by the least-squares

method. In the backward pass, the error signals

propagate backwards and the premise parameters

are updated by gradient descent. Because the

update rules for the premise and consequent

parameters are decoupled in the hybrid learning

rule, a computational speedup may be possible

by using variants of the gradient method or other

optimization techniques on the premise parameters.

3. Results and discussion

The main goal of this work was to study the

mechanism of the migration of peptides in MEKC.

We hope that the results of this work together with

our previous works on CZE could pave the way for

further studies on the 2D MEKC-CZE simulations.

However, the best way of studying the mechanism

is gathering a set of the general parameters which

are responsible for the migration of the peptides

in MEKC. To achieve this, the mobility of a set

of different classes of peptides has to be modeled.

Mobilities of a set of 128 peptides composed of up

to 14 amino acids in 40, 60 and 80 mM solutions

of SDS was measured. The general strategy of

modeling the mobilities was as follows: Feature

selection using sequential ANFIS algorithm;

developing MLR and BP-ANN models using the

selected descriptors as the inputs; and analysis and

evaluation of the best model.

3.1. Application of ANFIS as feature selection

method

After obtaining the values of the mobilities of 128

peptides using MEKC method and calculating

41 descriptors for each one, the dataset was

divided into training (102 peptides) and test sets

(26 peptides). Then by applying ANFIS, ﬁve

descriptors of Kappa(H), ln(N), ARM, MRC and

ES,N which minimized the standard errors of

calibration and prediction were selected. These

descriptors were used as the inputs to develop a

network for modeling the mobility of peptides.

The results of the ANN showed that the network

is not able to predict accurately the mobility of ten

peptides and therefore they can be considered as

statistical outliers. These peptides were DF, DLFL,

DW, WD, EW, WE, FLEEI, VEPIPY, YPFVEPI

and YLEPGPVTA. This means that these peptides

have different characteristics compared with the

rest of the dataset, and the ANN model is unable

to learn and predict their behavior. Consequently,

due to the special characteristics of the above-

mentioned peptides there is the possibility of

misleading the ANFIS and this method may model

the noise. Hence, these peptides were removed

from the dataset and selection of the features was

repeated. Finally four descriptors (Kappa (H),

ln (N), MRn and ES,C) which could model the

mobility were chosen. The behavior of the outliers

will be discussed later in this section.

3.2. Modeling and prediction by Artiﬁcial Neural

Network

The investigations were started using SDS 80

mM dataset. Even though we had removed the ten

outliers in feature selection step, in order to study

the results of ANN calculations, we added them

to the dataset again. Then the dataset was divided

into training, test and validation sets. The network

was trained and the results were studied. Results

showed that some peptides cause instability and

premature training of the network. Therefore, the

outliers were removed one at a time and entered

into the validation set in order to study their

behavior when the network is completely trained

with the remaining peptides. It is obvious that

after removing the outliers the remaining peptides

were divided into new training, test and validation

sets. These sets are composed of random and

representative samples, but the validation set

encompasses the entered samples as well. In the

ﬁnal stage eight statistical outliers were obtained

which were HW, RRPYIL, RFDS, RKDVY

FLEEI, VEPIPY, YPFVEPI and YLEPGPVTA.

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

3.3. Analysis of residuals

Figure 4 depicts the residuals of ANN calculated

values versus the experimental mobilities. It can

be seen from this ﬁgure that the developed ANN

is not able to predict accurately the mobilities of

HW and RRPYIL. Also it can be seen that the

residuals of all of the outliers are located above

the zero axis. Statistically this means that there

should be a systematic error in the calculated

results of the ANN model. However, inspection of

the residuals reveals that the peptides containing

middle E and D amino acids together with the six

outliers lie on a line with a correlation of R2=

0.992. This implies that the mobility of these

peptides follows a similar mechanism which is

different from the mechanism for the remaining

peptides. Presumably a parameter appropriate

for accounting the inﬂuence of charge is missing.

Fundamentally a charge descriptor should be

able to introduce this characteristic to the model.

However, due to the small number of these type of

peptides in the dataset (18 peptides), the network

was not being able to receive enough information

to learn their behavior. On the other hand, positive

values of the residuals show that the ANN model

overestimates the mobilities of these peptides.

The repulsion between the negatively charged D

and E amino acids and the anionic SDS surfactant

could be responsible for this overestimation.

Because of this repulsion, these peptides spend

a shorter time in the micellar phase and move

slower. Consequently, one expects that in more

dilute solutions of SDS, this effect be more

pronounced.

3.4. Effect of SDS concentration on peptide

mobilities

In order to investigate the effect of concentration

on the migration of peptides, in addition to the

original model which was developed based on

the 80 mM SDS solution, two other models were

developed using the same descriptors and same

settings of the network for 40 and 60 mM SDS

solutions.

Figure 5 presents the predicted results

(validation set) versus the experimental values

for 80, 60 and 40 mM SDS solutions. Inspection

of the ﬁgures reveals that by decreasing the

SDS concentration the spread of points around

the correlation line has increased. Therefore, a

question arises regarding the effect of the SDS

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

= 0.992

-35

-25

-15

-5

-50 -30 -10

Experimental mobility

Residual

Fig. 4. Residuals of calculated ANN values of mobilities versus the experimental values. Δ , peptides containing

negatively charged middle amino acids (E and D); × , HW and RRPYIL; ▲, outliers

concentration on the mobility behavior of the

peptides. To explain the grounds, we refer to

Figures

which are obtained using purely experimental

values. These ﬁgures show the trend of mobility

changes due to changes in SDS concentration.

The vertical axis shows the change in mobility

for two solutions of SDS and the horizontal axis

is the mobility of the more concentrated one. By

inspection of these ﬁgures one may conclude that:

(1) Concentration increments have a profound

effect on the curvatures of the mobility trends.

Figure 6C with the highest concentration gradient

shows a high curvature. On the other hand,

although the concentration gradients are equal in

ﬁgures 6A and 6B (20mM),

Figure 6A shows a

very small curvature compared with

Figure 6B.

This shows that 40 and 60 mM solutions are below

the optimum level of SDS concentration. This may

be due to the fact that when the solution is more

dilute the effect of micelles is less profound, and

CZE mechanism prevails over MEKC. Since the

ANN model is trained based on the MEKC data,

the calculated values for the more dilute solutions

show a broader spread. (2) The compounds which

include E and D amino acids behave different in

comparison with the other peptides. This is more

pronounced for the dipeptides. Points marked

with hollow squares in

Figures 6 belong to FLEEI,

DW, WD, WE, EW, DF and DLFL. The ﬁgures

show that these peptides do not obey the general

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

= 0.937

-50

-40

-30

-20

-10

-50 -40 -30 -20 -10 0

(B) Experimental mobility SDS 60 mM

Predicted mobility

= 0.936

-50

-40

-30

-20

-10

-50 -40 -30 -20 -10 0

(A) Experimental mobility SDS 80mM

Predicted mobility

= 0.913

-50

-40

-30

-20

-10

-50 -40 -30 -20 -10 0

Predicted mobility

Fig. 5. Predicted values obtained by ANN model for the all 6 batches.

80 mM, (B) 60 mM and (C) 40 mM SDS solutions.

trend of mobility changes which exists for the

other peptides. FLEEI is the only peptide in the

dataset which contains two E amino acids, so it

would suffer more of the repulsion forces which

exists between E amino acids and the anionic

surfactant. The footprint of this interaction exits

in the outliers of the ANN (RFDS, RKDVY,

FLEEI, VEPIPY, YPFVEPI and YLEPGPVTA),

and ANFIS (DF, DLFL, DW, WD, EW, WE,

FLEEI, VEPIPY, YPFVEPI and YLEPGPVTA)

as well.

3.5. Comparison of MLR and ANN results

To investigate the linear/nonlinear characteristics

of the relation between mobility and the

descriptors, a similar MLR model was developed.

For a meaningful comparison, both the ANN and

MLR methods has to be trained using the same

training set and veriﬁed by the same validation set.

Despite the fact that we have used all of the peptides

(outliers of the ANN model were excluded) in the

regression step, the MLR calculated results for the

training set show a poor correlation of 0.71. This

demonstrates the inadequacy of MLR method

for the modeling of the peptide mobilities, and

irrational trend of residuals

(Fig. 7). This could be

due to nonlinear characteristics of the mobilities.

Such a trend is absent in ANN residuals

(Fig.

. In order to assess the role of each variable in

nonlinear characteristics of the peptide mobilities,

the MLR residuals for the variables are depicted in

Figure 8. These ﬁgures suggest that, kappa could

be the parameter responsible for the nonlinearity,

because the trend in its residuals is very similar to

the trend of the MLR residual plot.

3.6. Robustness of the ANN models

After the training of the ANN for the prediction

of peptide mobilities in different concentrations of

SDS, the outliers were expelled and the remaining

peptides were divided into six different batches

of training, test and validation sets. These batches

were chosen in a way that in each one every peptide

appeared in the test and validation sets once. Then

all six batches of training, test and validation sets

Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

-14

-12

-10

-8

-6

-4

-2

-50 -40 -30 -20 -10 0

(A) Experimental Mobility SDS 80mM

Experimental

Mobility 80mM - Mobility 60mM

-14

-12

-10

-8

-6

-4

-2

-50 -40 -30 -20 -10 0

(B) Experimental Mobility SDS 60mM

Experimental

Mobility 60mM - Mobility 40mM

-14

-12

-10

-8

-6

-4

-2

-50 -40 -30 -20 -10 0

Experimental

Mobility 80mM - Mobility 40mM

-20

-15

-10

-5

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Mobility

Fig. 6. Change in mobility due to SDS concentrations

changes.

the peptides with E and D amino acids

Fig. 7. MLR prediction residual plot.

were trained and applied for predicting the peptide

mobilities in solutions with different concentrations

of SDS. It can be seen from

Figures 5 and Tables

3 and 4

that the residuals are promising for all of

the six batches.

Table 3 is devoted to correlation

values for training, test and validation sets of

each batch. The values for the correlations were

in the range of 0.849 to 0.969 for all batches with

different concentrations of SDS, which show the

robustness of the model.

Table 4 shows the average

deviation (AD), average absolute deviation (AAD)

and standard deviation (SD) of the ANN predicted

values (validation sets) which have been calculated

through equations 12-14.









(12)







AAD

(13)























(14)

in these equations yi are calculated mobilities, ŷi

represents experimental mobilities and n is the

number of samples of the set. In these calculations

we have not considered the outlier peptides of the

validation sets which were outliers. The small values

of the deviations reveal the lack of systematic errors in

the model. It is noteworthy that the SD shows a range

of 3.410 to 4.040 which is close to the experimental

errors. These deviations also conﬁrm the predictive

ability and robustness of the model.

4. Conclusion

A long-range goal of our laboratory is the development

of experimental and theoretical methods for peptide

separations and mapping in two-dimensional MEKC-

CZE scheme. We have considered the speciﬁcations

of simplicity, accuracy and robustness of the models

in predicting the CZE and MEKC mobilities of the

peptides. In our previous works

[9-10], we showed

the ability of the artiﬁcial neural networks in modeling

of the CZE mobilities. This paper focuses on MEKC

with more complicated mechanism compared to

the CZE. Adaptive neuro-fuzzy inference system

(ANFIS) was successfully used to select the most

Anal. Method Environ. Chem. J. 3 (2) (2020) 5-20

Fig. 8.

MLR variables residual plots

-20

-10

-5.0 0.0 5.0 10.0 15.0

Kappa (H)

-20

-10

0.0 10.0 20.0 30.0 40.0 50.0

MRn

-20

-10

0.0 1.0 2.0 3.0

ln (N)

appropriate variables as ANN inputs. It is shown that

except for the peptides including negatively charged

amino acids the model holds promise for application

in predicting the peptide mobilities in MEKC

systems. However, researches are underway in our

laboratory to combine the CZE and MEKC models

to map the peptides in 2D CZE/MEKC scheme.

5. Acknowledgement

A research grant from the U.S. National Institutes of

Health (GM 38738) is gratefully acknowledged.

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Peptide mobilities by micellar electro-kinetic chromatography Mostafa Hassanisadi, et al

Table 4. Statistical deviations for the ANN predicted values of the peptide nobilities

Prediction

batch I batch II batch III batch IV batch V batch VI average

80 mM SDS

AD -1.143 -0.361 -1.712 -0.489 0.057 1.144 -0.417

AAD 3.467 2.527 2.536 2.283 1.935 2.879 2.605

SD 4.208 3.262 3.652 3.257 2.477 3.605 3.410

60 mM SDS

AD -1.754 0.029 -1.353 -0.769 -0.093 1.126 -0.469

AAD 3.871 2.542 2.383 2.174 2.196 2.693 2.643

SD 5.076 3.114 3.377 2.937 2.795 3.413 3.452

40 mM SDS

AD -0.222 -0.266 -1.724 -0.351 0.255 1.105 -0.201

AAD 4.299 2.610 3.016 2.696 2.312 2.989 2.987

SD 5.745 3.521 4.402 3.771 2.949 3.853 4.040

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Table 3. Statistical correlations using the ANN model for six different batches

batch I batch II batch III batch IV batch V

batch VI average

80 mM SDS

Training 0.956 0.952 0.951 0.964 0.951 0.949 0.954

test 0.955 0.969 0.941 0.924 0.947 0.947 0.947

prediction 0.921 0.943 0.947 0.943 0.963 0.939 0.943

60 mM SDS

Training 0.964 0.953 0.956 0.962 0.951 0.952 0.956

test 0.956 0.969 0.951 0.913 0.953 0.953 0.949

prediction 0.900 0.953 0.954 0.958 0.956 0.947 0.945

40 mM SDS

Training 0.937 0.941 0.948 0.953 0.948 0.945 0.945

test 0.953 0.961 0.932 0.900 0.942 0.924 0.935

prediction 0.849 0.944 0.924 0.928 0.954 0.931 0.922

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