partitioning of some amino acids and low molecular peptides in aqueous two-phase systems of...
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FLUIDPHASE EOuIUglHA
E L S E V I E R Fluid Phase Equilibria 137 (1997) 209-228
Partitioning of some amino acids and low molecular peptides in aqueous two-phase systems of poly(ethylene glycol) and dipotassium
hydrogen phosphate
C h r i s t o p h G r o B m a n n 1 R a l f T i n t i n g e r 2, J i a n d u n g Z h u 1, G e r d M a u r e r *
Lehrstuhl fiir Technische Thermodynamik, Fachbereich Maschinenbau und Verfahrenstechnik, Universitiit Kaiserslautern, D-67653 Kaiserslautern, Germany
Received 15 October 1996; accepted 18 April 1997
Abstract
Aqueous two-phase systems are discussed for the extraction of biomolecules like, for example, amino acids, peptides and enzymes from aqueous phases. The development of such extraction processes requires experimen- tal results for the partitioning of model substances, as well as methods for correlating and predicting such phase equilibria. The present contribution reports experimental results for the partitioning of small amounts (about 1 mg/g) of amino acids glycine, L-glutamic acid, L-phenylalanine and L-lysine and some of their low molecular peptides in aqueous two-phase systems of dipotassium hydrogen phosphate and poly(ethylene glycol) of molecular mass of about 6000 and 35 000 at about 293 K. The experimental results for the partitioning of the amino acids and some of their peptides are used to determine interaction parameters of a group contribution model for the excess Gibbs energy. The remaining experimental data are used to test the model for predicting partitioning of peptides in P E G / K z H P O 4 two-phase systems. © 1997 Elsevier Science B.V.
Keywords: Aqueous two-phase systems; Poly(ethylene glycol); PEG; K2HPO4; Phase equilibrium; Partitioning of amino acids, peptides, glycine, L-glutamic acid, L-phenylalanine, L-lysine; Modeling
1. Introduction
Aqueous two-phase systems are simultaneously dissolved in water. often provide ideal surroundings
found when two hydrophill ic but incompatible substances are The coexisting phases consist mainly of water, and, therefore, for the extractive separation of enzymes and proteins f rom
* Corresponding author. Tel,: + 49-631-205-2410; fax: + 49-631-205-3835. 1 Present address: BASF AG, 67056 Ludwigshafen, Germany. z Present address: DuPont de Nemours GmbH, 76677 0stringen, Germany.
0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0378-3812(97)00104-0
210 C. Groflmann et al. / Fluid Phase Equilibria 137 (1997) 209-228
fermentation broths. Partitioning of those substances in aqueous two-phase systems is governed by intermolecular forces, and should therefore be described by applying methods common in modeling liquid-liquid phase equilibria. However, as the phase forming substances are polymers a n d / o r salts, modeling such equilibria is not an easy task. During the last decade, quite a few models have been proposed for correlating phase equilibria in aqueous two-phase systems (e.g., [1-14]), but testing those models requires experimental data on well-defined model systems. Such data is scarcely available. The present work supplements a recent publication [15], where experimental results for the composition of coexisting phases in aqueous solutions of dipotassium hydrogen phosphate and poly(ethylene glycol), as well as partition coefficients for glycine (gly) and L-phenylalanine (phe), were reported with a model for the excess Gibbs energy appropriate to correlate and predict those liquid-liquid equilibria. Here, new experimental results are reported for the partitioning of small amounts (about 1 m g / g ) of glycine (gly), L-glutamic acid (glu), tAysine (lys) and L-phenylalanine (phe), 5 dipeptides (gly-gly, glu-glu, lys-lys, phe-phe), 3 tripeptides (3 * gly, 3 * glu, 3 * lys) and 3 higher peptides ( 4 . gly, 5 * gly and 5 * lys) in aqueous two-phase systems of dipotassium hydrogen phosphate (K2HPO 4) and two poly(ethylene glycol)s of number average molecular weight of about 6000 (PEG 6000) and 35 0000 (PEG 35 000) at 293 K. The experimental data are correlated applying a recently published group contribution model for aqueous polymer solutions [15]. Some experimental data for the partition coefficient had to be used to determine model parameters, whereas the remaining experimental data are used to test the predictive power of that model.
2. Experimental
2.1. Materials
Table 1 gives information on the chemicals used in the present investigation. Poly(ethylene glycol)s PEG 6000 and PEG 35 000 are polydisperse materials. Their number-averaged molecular mass Mn as determined by chemical end group analysis was provided by the supplier. It was checked by combining gel permeation chromatography (GPC) and multiangle laser light scattering (MALLS) using a refractive index detector (for details cf. Tintinger [16]): M~ (PEG 6000)= 6230; Mn (PEG 35 000) = 34 100 this work). The MALLS-data of the present work were also used to determine the weight averaged molecular mass M w. The ratio P = Mw:M,, is often used to characterize the polydispersity of a polymer. For both PEGs, that ratio is close to unity (1.04), thus indicating that both polymers are approximately monodisperse.
2.2. Liquid-liquid phase equilibrium measurements
Aqueous two-phase systems were prepared by mixing known amounts of aqueous stock solutions of the single components. Stock solutions were prepared using high-precision analytical balances. The amino acid/pept ide concentration in the final aqueous solution was approximately 0.001 g / g in most experiments. However, in some measurement, that concentration was increased to about 0.01 g / g . The aqueous two-phase systems were equilibrated for several hours in a thermostated, stirred separating funnel. Phase separation was achieved by keeping the unstirred samples at constant temperature for about 20 h before most of the upper phase was removed by a pipette. Finally, most of
C. Groflmann et al. / Fluid Phase Equilibria 137 (1997) 209-228 211
Table l Chemicals
m
Substance Supplier M, pK I pK u pKll I PKlv
PEG 6000 '~ Hoechst, Frankfurt, Germany 6230 PEG 35 0 0 0 b 34100 K2HPO 4 Merck, Darmstadt, Germany 174.18 11.98 c 7.21 d 2.11 c L-phenylalanine 165.19 1.83 9.13 Glycine Carl Roth, Karlsruhe, Germany 75.07 2.34 9.60 L-glutamic acid 147.13 2.19 9.67 4.25 L-lysine Serva, Heidelberg, Germany 146.19 2.20 8.90 10.28 gly-gly 132.12 2.34 9.60 glu-glu 27 6.25 2.19 9.67 4.25 phe-phe 312.37 1.83 9.13 lys-lys 274,36 2.20 8.90 10.28 gly-gly-gly 189,15 2.34 9.60 glu-glu-glu 405.36 2.19 9.67 4.25 lys-lys-lys 402.54 2.20 8.90 10.28 4 * gly 246.21 2.34 9.60 5 * gly 303.27 2.34 9.60 5 * lys 658.88 2.20 8.90 10.28 Water University of Kaiserslautern 18.06 14.17 f
4.40
10.5
4.40 10.5
10.5
Lot number: 664762. b Lot number: E 06373013. c PKv. d pKvp
PKvn" f p Kvlll '
the bot tom phase was removed through the drain of the separating funnel. Both phases were analyzed for all solutes. However , in some cases, the phases were only analyzed for amino ac ids /pept ides . In a large number of experiments it was shown that such small amounts of partitioning biomolecules do not change the composit ion of the phase-forming components beyond the limits of the experimental uncertainty of the analysis. PEG, K 2 H P O 4, amino acids and peptides were analyzed as described before [15,16]. The relative uncertainty of the experimental results for the concentration of PEG and K 2HPO 4 in the coexisting phases is about 3.5 and 2.0% respectively, whereas the relative uncertainty of the amino ac id /pep t ide concentration is about 3%. As amino acids and peptides are amphoteric substances, the pH of the solution is an important parameter for partitioning. In aqueous two-phase systems of PEG and K 2 H P O 4, the pH is about 9 to 10. The very small amounts of amino acids and peptides have no significant influence on that pH. Nevertheless, the pH was measured (uncertainty: _+ 0.1 pH) in both coexisting phases.
2.3. E x p e r i m e n t a l resu l t s
Experimental results for the partitioning of glycine (gly), L-glutamic acid (glu), L-phenylalanine (phe) and L-lysine (lys) are given in Table 2a (for PEG 6000) and Table 2b (for PEG 35 000). Experimental results for the partitioning of the peptides are similarly given in Table 3a,b. In most
Tab
le 2
(a
) Pa
rtiti
onin
g of
som
e am
ino
acid
s (A
A)
in a
queo
us t
wo-
phas
e sy
stem
s (P
EG
60
00
/K2
HP
O 4
) at
293
.15
K
¢3
Fee
d L
ower
pha
se
Upp
er p
hase
Wat
er
PE
G
K e
HPO
4 A
A
Wat
er
PE
G
K 2
HPO
4 A
A
pH
Wat
er
PE
G
K 2
HPO
4 A
A
(g/g
) (g
/g)
(g/g
) (r
ag/g
) (g
/g)
(g/g
) (g
/g)
(rag
/g)
(g/g
) (g
/g)
(g/g
) (r
ag/g
) pH
AA
= g
ly
0.79
84
0.10
55
0.08
55
10.5
6 0.
8541
0.
7694
0.
1296
0.
0903
1
0.6
5
0.84
22
0.71
79
0.16
69
0.10
47
10
.45
0.
8080
0.
6976
0.
1800
0.
1116
10
.83
0.79
31
AA
= g
lu
0.81
94
0.09
87
0.08
06
1.3
2
0.86
96
0.81
96
0.07
64
0.10
21
1.93
0.
8651
0.
8036
0.
0703
0.
1239
2
.21
0.
8460
0.
7718
0.
1053
0.
1212
1
.69
0.
8324
AA
~
@s
a
0.80
83
0.09
99
0.09
08
0.97
0.
8646
0.
7624
0.
1415
0
.09
51
0.
97
0.84
15
0.72
84
0.17
05
0.10
01
0.96
0.
8233
0.
7146
0
.17
41
0.
1104
0.
92
0.80
85
AA
=
ph
e
0.79
69
0.10
66
0.08
65
10
.04
0.
8520
0.
7689
0
.13
01
0.
0906
1
0.4
2
0.84
16
0.73
32
0.16
00
0.09
66
10
.17
0.
8257
0.
7155
0.
1732
0.
1014
9.
95
0.81
21
0.00
83
0.12
36
13.9
7 8.
48
0.00
20
0.14
16
14.3
7 8.
54
0.00
03
0.17
58
15.9
3 8.
61
0.00
02
0.19
06
16.1
0 8.
65
0.02
03
0.10
84
1.66
8.
40
0.00
52
0.12
74
2.27
8.
45
0.00
11
0.15
03
2.60
8.
50
0.00
02
0.16
53
2.14
8.
50
0.00
80
0.12
60
1.36
9.
09
0.00
10
0.15
60
1.52
8.
99
0.00
00
0.17
50
1.66
8.
93
0.00
00
0.19
00
1.54
9.
11
0.01
15
0.12
69
9.56
8.
46
0.00
26
0.14
61
9.65
8.
46
0.00
09
0.16
47
8.73
8.
50
0.00
05
0.17
92
8.15
8.
53
0.71
90
0.23
24
0.04
24
6.20
8.
55
0.67
27
0.28
64
0.03
54
5.85
8.
79
0.60
96
0.36
07
0.02
54
4.28
8.
75
0.55
22
0.38
44
0.02
25
4.09
8.
84
0,79
15
0.14
68
0.06
06
1.13
8.
50
0.77
25
0.22
63
0.04
47
1.18
8.
50
0.66
97
0.29
58
0.03
34
1.08
8.
60
0.65
43
0.31
53
0.02
96
0.82
8.
70
0.74
06
0.21
20
0.04
70
0.42
9.
05
0.68
47
0.28
20
0.03
30
0.26
8.
96
0.63
38
0.34
00
0.02
60
0.20
9.
09
0.61
28
0.36
40
0.02
30
0.17
9.
05
0.74
50
0.18
66
0.05
80
10.4
5 8.
60
0.68
73
0.25
68
0.04
39
11.9
5 8.
62
0.64
75
0.30
31
0.03
69
12.4
7 8.
76
0.62
39
0.33
02
0.03
26
13.2
5 8.
92
AA
=
g
~
0.81
68
0.10
17
0.08
02
0.77
81
0.13
53
0.08
50
0.73
45
0.16
55
0.09
81
0.71
33
0.18
03
0.10
50
AA
=
g
ly ~
0.83
31
0.08
36
0.08
23
0.81
42
0.09
87
0.08
61
0.74
77
0.15
21
0.09
92
0.69
54
O. 1
867
O. 1
170
AA
=
glu
0.82
82
0.10
0!
0.0
70
1
0.83
33
0.08
25
0.08
25
0.78
26
0.12
94
0.08
61
0.75
53
0.14
54
0.09
77
AA
= ~
s ~
0.83
25
0.08
62
0.08
02
0.81
41
0.09
97
0.08
52
0.74
63
0.15
28
0.09
99
0.71
64
0.17
55
0.10
71
AA
=
ph
e
0.85
04
0.07
17
0.07
63
0.79
91
0.13
02
0.06
91
0.78
52
0.12
57
0.08
76
0.75
62
0.13
13
0.11
10
1.34
1.
57
1.87
1.
37
1.01
1.
01
1.01
0.
99
1.57
1.
69
1.95
1.
62
1.00
1.
01
1.00
1.
00
1.62
1.
60
1.54
1.
51
0.88
29
0.86
14
0.82
83
0.81
80
0.88
74
0.87
75
0.83
54
0.79
62
0.89
25
0.88
64
0.86
13
0.83
57
0.88
87
0.87
65
0.83
23
0.81
33
0.89
16
0.88
07
0.86
09
0.82
96
0.00
10
0.00
03
0.00
08
0.00
00
0.00
10
0.00
10
< 0
.000
1 <
0.0
001
0.00
44
0.00
15
0.00
00
0.00
00
0.00
20
0.00
10
< 0
.000
1 <
0.0
001
0.00
58
0.00
13
0.00
04
0.00
01
0.11
44
0.13
60
0.16
85
0.18
00
0.11
00
0.12
00
0.16
30
0.20
20
0.10
11
0.11
00
0.13
60
0.16
20
0.10
80
0.12
10
0.16
60
0.18
50
0.10
11
0.11
67
0.13
75
0.16
92
1.74
2.
29
2.39
2.
01
1.58
1.
51
1.63
1.
75
2.03
2.
12
2.69
2.
33
1.35
1.
46
1.69
1.
68
1.46
1.
33
1.24
1.
09
8.90
8.
90
8.90
8.
90
9.12
9.
15
9.21
9.
28
8.25
8.
30
8.35
8.
40
9.49
9.
48
9.47
9.
50
8.70
8.
70
8.70
8.
70
0.73
57
0.69
16
0.63
14
0.61
14
0.75
24
0.72
85
0.65
55
0.58
86
0.80
73
0.76
88
0.71
18
0.66
71
0.76
05
0.72
46
0.65
07
0.61
88
0.80
41
0.75
16
0.69
82
0.63
89
0.22
44
0.27
52
0.34
29
0.36
30
0.20
40
0.23
10
0.31
50
0.38
50
0.13
69
0.18
50
0.25
10
0.30
00
0.19
50
0.23
70
0.32
10
0.35
40
0.13
75
0.20
50
0-26
42
0.32
92
0.03
90
0.03
23
0.02
49
0.02
50
0.04
30
0.04
00
0.02
90
0.02
60
0.05
45
0.04
50
0.03
60
0.03
20
0.04
40
0.03
80
0.02
80
0.02
70
0.05
66
0.04
16
0.03
57
0.02
96
0.89
0.
93
0.77
0.
61
0.59
0.
51
0.49
0.
39
1.29
1.
18
1.18
0.
88
0.49
0.
44
0.27
0.
23
1.77
1.
77
1.90
2.
28
8.90
8.
90
8.90
8.
90
9.18
9.
38
9.52
9.
80
8.30
8.
40
8.50
8.
60
9.67
9.
70
9.81
9.
85
8.79
8.
79
8.79
8.
79
,,q
t~
~PE
G a
nd K
2HP
O 4
not
anal
yzed
.
Tab
le 3
(a)
Pa~
itio
ning
of
som
e di
pept
ides
in
aqu
eous
tw
o-ph
ase
syst
ems
(PE
G 6
00
0/K
zHP
O4
) at
293
.15
Fee
d L
ower
pha
se
Wat
er
PE
G
K 2
HP
O4
Pe
ptid
e W
ater
P
EG
K
2 H
PO
4
Pept
ide
pH
(g/g
) (g
/g)
(g/g
) (m
g/g
) (g
/g)
(g/g
) (g
/g)
(mg
/g)
g~
- g@
0.82
43
0.08
35
0.09
12
1.03
0.
8678
0
.00
91
0.
1219
1.
21
8.77
0.
7977
0.
1002
0.
1011
1.
00
0.84
90
0.00
30
0.14
68
1.20
8.
83
0.77
29
0.12
02
0.10
59
1.00
0
.83
51
0.
0011
0.
1626
1.
18
8.85
0.
7396
0.
1384
0.
1204
1.
10
0.80
75
0.00
05
0.19
07
1.31
8.
90
g&
- g
~
0.79
64
0.10
79
0.08
57
10.0
2 0.
8551
0.
0115
0.
1200
13
.37
8.16
0.
7704
0.
1295
0.
0901
1
0.0
3
0.84
19
0.00
25
0.14
18
13.8
1 8.
19
0.73
35
0.15
63
0.10
04
9.75
0.
8195
0.
0007
0.
1650
14
.84
8.25
0.
7161
0
.17
21
0.
1015
1
0.3
0
0.80
93
0.00
04
0.17
45
15.8
0 8.
27
glu
- gl
u
0.82
11
0.0
90
1
0.08
84
0.49
4 0.
8679
0.
0115
0.
1200
0.
583
8.73
0.
8188
(I
.09
07
0.
0900
0.
498
0.87
12
0.01
20
0.11
62
0.56
0 8.
82
0.7
69
1
0.12
03
0.11
0!
0.49
7 0.
8416
0.
0010
0.
1568
0.
586
8.87
0.
7379
0.
1404
0.
1212
0.
508
0.81
67
0.00
03
0.18
23
0.65
5 8.
92
@S
--
@S
a
0.80
86
0.10
13
0.08
92
0.99
4 0.
8645
0.
0080
0.
1260
1.
47
9.23
0.
7648
0.
1399
0.
0944
1.
00
0.84
12
0.00
10
0.15
60
1.78
9.
19
0.72
95
0.16
94
0.10
01
1.00
0.
8232
<
0.0
001
0.17
50
1.84
9.
23
0.69
85
0.1
90
1
0.11
03
1.00
0.
7972
<
0.0
001
0.20
10
1.85
9.
27
ph
e-p
he
~
0.81
54
0.09
67
0.08
75
0.41
3 0.
8699
0.
0140
0.
1160
0.
117
8.97
0.
8089
0.
1003
0.
0904
0.
404
0.86
69
0.01
00
0.12
30
0.07
8 9.
00
0.78
75
0.11
03
0.10
18
0.39
5 0.
8555
0.
0030
0.
1415
0.
044
9.02
0.
7689
0.
1198
0.
1109
0.
387
0.84
50
0.00
10
0.15
40
0.02
3 9.
07
0.74
89
0.13
03
0.12
05
0.33
5 0.
8269
0.
0010
0.
1730
0.
018
-
3 *
g~
0.81
89
0.09
38
0.08
63
1.00
0.
8689
0.
0170
0.
1130
1.
15
8.90
0.
8030
0
.09
81
0.
0979
0.
983
0.86
22
0.00
65
0.13
00
1.27
8.
92
0.76
27
0.12
98
0.10
64
1.08
0.
8416
0.
0010
0.
1560
1.
41
8.98
0.
7212
0.
1387
0.
1391
0.
992
0.80
38
< 0
.000
1 0.
1950
1.
22
9.06
K
Upp
er p
hase
Wat
er
PE
G
K 2
HP
O4
Pe
ptid
e (g
/g)
(g/g
) (g
/g)
(rag
/g)
pH
b.a
4a.
0.75
98
0.19
00
0.04
95
0.74
2 8.
91
0.69
63
0.26
70
0.03
60
0.67
1 8.
92
0.64
68
0.32
50
0.02
75
0.71
8 9.
16
0.56
33
0.41
12
0.02
50
0.51
3 9.
11
0.74
22
0.21
00
0.04
70
0.75
6 9.
01
0.72
56
0.23
15
0.04
20
0.87
6 9.
06
0.67
28
0.29
30
0.03
30
1.16
9.
08
0.63
33
0.33
80
0.02
75
1.17
9.
00
0.61
70
0.35
60
0.02
60
1.04
-
0.73
86
0.21
47
0.04
59
0.81
4 8.
83
0.70
00
0.26
28
0.03
64
0.78
6 8.
90
0.66
39
0.30
47
0.03
07
0.71
0 8.
91
0.61
40
0.36
06
0.02
47
0.71
8 8.
99
0.72
82
0.22
00
0.04
50
6.76
8.
34
0.03
63
5.69
8.
36
0.68
34
0.27
46
0.64
60
0.32
00
0.02
90
5.01
8.
49
0.61
99
0.34
87
0.02
66
4.77
8.
57
v<
//.76
43
0.18
50
0.05
03
0.42
7 8.
76
"~
0.74
75
0.21
50
0.03
71
0.38
4 8.
85
~=:
0.67
19
0.29
69
0.03
09
(/.3
45
8.96
<m
0.
6015
0.
3739
0.
(/24
3 0.
315
9.03
0.74
(/6
0.21
20
0.04
70
0.36
5 9.
15
0.68
38
0.28
20
0.03
40
0.19
5 9.
42
0.63
39
0.34
00
0.02
60
0.13
1 9.
63
0.60
69
0.37
10
0.02
20
0.09
1 9.
73
v,D
3 *
glu
~
0.80
90
0.78
82
0.76
85
0.74
87
3 *
~S
a
0.79
19
0.72
70
0.69
75
4 *
g~
" 0.
8083
0.
7867
0.
7677
0.
7498
5 *
g~
0.
8077
0.
7882
0.
7692
0.
7512
5 ,
lys
~
0.76
08
0.72
81
0.69
91
0.09
99
0.11
19
0.12
07
0.13
02
0.14
46
0.17
53
0.18
97
0.10
02
O.1
100
0.12
03
0.12
93
O.lO
00
0.11
04
0.11
97
0.12
86
0.14
61
0.17
26
0.19
10
0.09
08
0.09
96
0.11
05
0.12
08
0.09
30
0.09
72
0.11
23
0.09
05
0.10
23
0.11
09
0.11
99
0.09
13
0.10
05
0.11
02
0.11
94
0.09
21
0.09
84
0.10
89
0.27
7 0.
277
0.27
6 0.
274
0.49
6 0.
488
0.49
9
1.00
1.
02
1.10
1.
02
0.99
0 0.
939
0.88
7 0.
838
0.98
1 0.
996
0.99
9
0.86
67
0.85
57
0.84
42
0.82
61
0.84
43
0.82
43
0.79
73
0.86
57
0.85
41
0.84
36
0.82
66
0.86
53
0.85
49
0.84
39
0.82
69
0.84
37
0.82
38
0.79
77
0.01
00
0.00
40
0.00
15
0.00
05
0.00
10
< 0
.000
1 <
0.0
001
0.01
00
0.00
30
0.00
10
0.00
01
0.01
00
0.00
40
0.00
10
0.00
01
0.00
10
< 0
.000
1 <
0.0
001
0.12
30
0.14
00
0.15
40
0.17
30
0.15
40
0.17
50
0.20
20
0.12
30
0.14
15
0.15
40
0.17
20
0.12
35
0.14
00
0.15
40
0.17
20
0.15
40
0.17
50
0.20
10
0.31
9 0.
327
0.32
6 0.
409
0.65
7 0.
690
0.72
1
1.26
1.
40
1.43
1.
32
1.22
1.
09
1.10
0.
992
1.35
1.
24
1.27
8.89
8.
94
9.02
9.
03
9.31
9.
34
9.38
8.99
9.
02
9.05
9.
09
9.02
9.
06
9.12
9.
15
9.23
9.
27
9.39
0.72
48
0.67
28
0.62
58
0.59
48
0.67
80
0.63
80
0.60
60
0.72
58
0.67
34
0.63
39
0.62
10
0.72
25
0.67
66
0.63
47
0.62
12
0.67
80
0.63
80
0.60
70
0.23
30
0.29
50
0.34
70
0.38
50
0.28
80
0.33
60
0.37
20
0.23
15
0.29
30
0.33
80
0.35
20
0.23
50
0.29
00
0.33
75
0.35
20
0.28
8O
0.33
60
0.37
10
0.04
20
0.03
20
0.02
70
0.02
00
0.03
40
0.02
60
0.02
20
0.04
20
0.03
30
0.02
75
0.02
65
0.04
20
0.03
30
0.02
75
0.02
65
0.03
40
0.02
60
0.02
20
0.23
5 0.
216
0.18
8 0.
191
0.03
1 0.
020
0.00
7
0.68
7 0.
637
0.56
8 0.
494
0.52
0 0.
367
0.31
3 0.
259
0.02
6 0.
018
0.01
2
8.85
8.
91
8.86
9.
07
9.38
9.
57
9.75
9.08
9.
20
9.27
9.
36
9.15
9.
22
9.35
9.
38
9.25
9.
55
9.68
"-4
"M
,f t~
Tab
le 3
(co
ntin
ued)
(b)
Part
ition
ing
of s
ome
dipe
ptid
es i
n aq
ueou
s tw
o-ph
ase
syst
ems
Fee
d L
ower
pha
se
Wat
er
PEG
K
2 H
PO4
Pept
ide
Wat
er
PE
G
(g/g
) (g
/g)
(g/g
) (m
g/g
) (g
/g)
(g/g
)
g~
- g
~
0.83
91
0.0
75
1
0.08
48
1.02
0.
8829
0.
0012
0
.79
91
0
.11
51
0.
0848
1.
02
0.86
58
0.00
04
0.77
95
0.12
94
0.09
01
1.02
0.
8516
0.
0003
0.
7641
0.
1506
0.
0843
1.
01
0.84
90
0.00
02
glu
- gl
u 0.
8488
0.
0754
0.
0753
0.
50
0.89
44
0.00
90
0.84
53
0.07
56
0.07
81
1.00
0.
8937
0.
0040
0.
8325
0.
0774
0.
0891
0.
98
0.88
17
0.00
20
0.79
92
0.11
43
0.08
60
0.50
0.
8728
0.
0005
0.
7800
0.
1294
0.
0901
0.
52
0.85
96
0.00
01
0.76
14
0.13
85
0.09
96
0.49
0.
8432
0.
0001
0.83
38
0.08
47
0.08
05
1.00
0.
8903
0.
0030
0
.81
41
0.
1004
0.
0845
1.
01
0.87
52
0.00
10
0.74
89
0.15
00
0.10
01
1.00
0.
8339
<
0.0
001
0.70
55
0.18
50
0.10
83
1.09
0.
8068
<
0.0
001
phe
phe
a 0.
8480
0.
0776
0.
0739
0.
49
0.82
50
0.09
28
0.08
19
0.28
0.
8093
0.
0999
0.
0905
0.
25
0.79
00
0.10
96
0.10
02
0.22
3 *
g@
0.8
39
1
0.07
49
0.08
50
1.05
0.
8474
0.
0762
0.
0753
1.
06
0.79
80
0.11
53
0.08
57
1.05
0.
7793
0
.13
01
0.
0896
1.
05
0.7
55
1
0.14
17
0.10
21
1.06
of P
EG
350
00 a
nd K
2HP
O 4
at 2
93.1
5 K
Upp
er p
hase
K 2
HP
O4
Pe
ptid
e pH
W
ater
P
EG
(g
/g)
(mg
/g)
(g/g
) (g
/g)
0.11
47
1.17
8
.81
0.
7395
0.
2187
0.
1326
1.
24
8.8
3
0.71
13
0.25
24
0.14
69
1.25
8.
85
0.68
67
0.28
02
0.14
95
1.32
8.
84
0.67
02
0.29
78
0.09
60
0.61
8.
82
0.78
46
0.16
00
0.10
10
1.29
8
.85
0.
7662
0.
1800
0.
1150
1.
25
8.87
0.
7492
0.
2100
0.
1261
0.
64
8.9
3
0.69
98
0.26
25
0.13
96
0.68
8
.85
0.
6840
0.
2813
0.
1560
0.
70
8.8
5
0.65
14
0.31
75
0.10
50
1.71
9.
10
0.77
14
0.18
20
0.12
20
1.83
9.
14
0.71
97
0.24
40
0.16
40
2.05
9.
23
0.65
48
0.31
60
0.19
10
2.19
9.
29
0.60
68
0.36
70
0.89
38
0.01
00
0.88
54
0.00
20
0.87
14
0.00
10
0.85
60
0.00
05
0.09
60
0.20
9.
28
0.80
42
0.14
00
0.11
25
0.11
9
.31
0.
7474
0.
2100
0.
1275
0.
062
9.34
0.
7204
0.
2400
0.
1430
0.
049
9.35
0.
6905
0.
2750
0.88
48
0.00
16
0.89
68
0.00
60
0.86
93
0.00
05
0.85
25
0.00
27
0.83
70
0.00
13
0.11
24
1.17
8.
96
0.76
63
0.19
00
0.09
60
1.23
8.
97
0.78
91
0.15
00
0.12
94
1.34
9
.01
0.
7028
0.
2589
0.
1435
1.
33
9.07
0.
6725
0.
2942
0.
1603
1.
38
9.10
0.
6427
0.
3276
K 2
HP
O4
P
epti
de
(g/g
) (r
ag/g
) pH
0.05
50
0.83
9.
41
0.04
20
0.60
9.
47
0.03
90
0.60
9.
55
0.03
40
0.54
8.
64
0.04
29
0.84
9.
04
0.06
00
0.92
9.
12
0.03
76
0.74
9.
20
0.03
26
0.67
9.
15
0.02
90
0.68
9.
10
0.04
10
0.81
8.
97
-~
0.03
55
0.76
9.
09
0.03
24
0.69
9.
04
0.03
13
0.70
9.
12
e~
0.05
50
0.41
8.
97
~"
0.05
30
(I.8
3 9.
10
0.04
00
0.79
9.
22
0.03
73
0.36
9.
15
~ 0.
0343
0.
36
9.22
0.
0307
0.
36
9.10
0.04
60
0.55
9.
12
"~
0.03
60
0.31
9.
26
0.02
90
0.16
9.
59
0.02
60
0.18
9.
63
I
3 *
glu
~
0.81
89
0.10
00
0.08
08
0.79
75
0.11
08
0.09
14
0.77
73
0.12
08
0.10
16
0.76
54
0.12
99
0.10
44
3*
ly
s
0.83
32
0.08
53
0.08
05
0.81
57
0.09
94
0.08
39
0.74
86
0.15
06
0.09
98
0.7
00
1
0.19
00
0.10
89
4 *
gly
~
0.81
28
0.10
67
0.07
95
0.79
05
O. 1
11
5
0.09
70
0.76
69
0.11
97
O. 1
125
0.74
47
0.13
06
0.12
40
5 *
gly
~
0.81
55
0.10
03
0.08
32
0.79
81
O. 1
10
1
0.09
08
0.77
78
O. 1
209
O. 1
004
0.75
74
0.13
17
0.11
00
5*
ty
s
0.83
44
0.08
46
0.08
00
0.81
33
0.10
03
0.08
54
0.74
47
0.15
24
0.10
19
0.69
75
0.19
25
0.10
90
0.28
0.
28
0.27
0.
27
0.99
0.
99
1.01
1.
00
1.01
0.
99
0.89
0.
71
0.99
0.
98
0.93
0.
87
1.00
1.
00
1.02
0.
98
0.88
41
0.86
56
0.85
01
0.84
51
0.89
06
0.87
65
0.83
41
0.80
10
0.88
18
0.85
93
0.83
58
0.81
95
0.88
08
0.86
59
0.85
09
0.83
23
0.89
04
0.87
64
0.83
31
0.80
49
0.00
20
0.00
10
0.00
05
0.00
05
0.00
30
0.00
10
< 0
.000
1 <
0.0
001
0.00
20
0.00
10
0.00
01
< 0
.000
1
0.00
20
0.00
10
0.00
05
0.00
01
0.00
30
0.00
10
< 0
.000
1 <
0.0
001
0.11
35
0.13
30
0.14
90
0.15
40
0.10
50
0.12
10
0.16
40
0.19
70
0.11
50
0.13
85
0.16
30
0.17
95
0.11
60
0.13
20
0.14
75
0.16
65
0.10
50
0.12
10
0.16
50
0.19
30
0.38
0.
42
0.43
0.
42
1.44
1.
52
1.92
1.
98
1.22
1.
15
1.10
1.
01
1.20
1.
12
1.14
1.
10
1.61
1.
58
1.91
2.
08
8.97
9.
05
9.09
9.
10
9.26
9.
28
9.37
9.
41
9.02
9.
11
9.15
9.
20
9.10
9.
13
9.19
9.
23
9.15
9.
18
9.27
9.
30
0.74
78
0.71
43
0.67
68
0.64
98
0.77
17
0.72
08
0.65
49
0.59
59
0.73
92
0.69
63
0.66
54
0.61
95
0.73
82
0.71
53
0.67
84
0.65
44
0.77
19
0.72
09
0.65
39
0.60
00
0.21
00
0.24
80
0.29
00
0.32
00
0.18
20
0.24
30
0.31
60
0.37
80
0.21
90
0.26
80
0.30
30
0.35
30
0.22
00
0.24
70
0.28
80
0.31
50
0.18
20
O.2
43O
0.
3170
0.
3740
0.04
20
0.03
75
0.03
30
0.03
00
0.04
60
0.03
60
0.02
90
0.02
60
0.04
10
0.03
50
0.03
10
0.02
70
0.04
10
0.03
70
0.03
30
0.03
00
0.04
60
0.03
60
0.02
90
0.02
60
0.25
0.
25
0.23
0.
19
0.28
0.
17
0.08
8 0.
053
0.79
0.
68
0.62
0.
52
0.78
0.
68
0.63
0.
59
0.14
0.
082
0.06
3 0.
032
9.12
9.
13
9.24
9.
35
9.41
9.
53
9.65
9.
78
9.16
9.
33
9.46
9.
51
9.27
9.
34
9.48
9.
62
9.25
9.
31
9.36
9.
44
~a
--.1
L
t,,a
PE
G a
nd K
2 H
PO4
not
anal
yzed
.
b~
218 C. GroJ3mann et al. / Fluid Phase Equilibria 137 (1997) 209-228
experiments, the amount of the partitioning substance in the feed solution was about 0.001 g / g ; however, in some experiments, it was reduced to about 0.0002 g / g or raised to about 0.01 g /g . However, that concentration was generally so small that within the experimental uncertainty, no effect of the concentration of the solute on its partition coefficient could be observed. Glycine, L-glutamic acid and L-lysine prefer the phosphate-rich lower phase over the PEG-rich upper phase, whereas L-phenylalanine prefers the PEG-rich over the salt-rich phase. The experimentally determined maximum difference of the amino acid concentrations corresponds to a partition coefficient of about 0.22 for glycine, 0.38 for L-glutamic acid, 0.11 for L-lysine and 2.1 for L-phenylalanine. Partition coefficient is defined here as the ratio of mass fractions in (PEG-rich) upper to (phosphate-rich) lower phase. Again, within the experimental uncertainty, nearly no influence of the molecular mass of the phase forming polymer PEG (either PEG 6000 or PEG 35 000) on that partitioning coefficient was observed. The peptides prefer the same phase as the corresponding amino acids. The extremes for the partitions coefficient of the investigated dipeptides are 0.3 (gly-gly), 0.48 (glu-glu), 0.05 (lys-lys) and 58 (phe-phe); whereas, for the higher peptides, those extremes amount to 0.49 (3*gly), 0.45 (3*glu), 0.027 (3*lys), 0.51 (4*gly), 0.54 (5*gly) and 0.015 (5*lys).
The difference in the experimental results for the pH of the coexisting phases is, in most cases, within the sum of the experimental uncertainties of pH measurements in both phases of about + 0.2. However, there seems to be a small, but systematic difference ApH=(pHuppe r phase--PH~ower pha*e) = 0.1 + 0.3 between both phases.
3. Correlation of partition coefficients
3.1. Properties of amino acids and peptides
The experimental data for the partitioning of amino acids and peptides are correlated with a recently published semi-empirical model for the excess Gibbs energy for aqueous solutions containing electrolytes and polymers [14,15]. The model is a combination of Pitzer's extension of the Debye- Hiickel limiting law for electrolyte solutions [17] with a modified osmotic virial equation. The modification mainly consists of introducing the group contribution concept and using relative surface fractions to describe the probability of interactions between those groups, i.e., a group contribution model based on surface fractions is used to calculate osmotic virial coefficients. As amino acids and peptides are amphoteric substances, the pH of the aqueous solution has an influence on the distribution of those biomolecules onto cationic, anionic and amphoteric (i.e., neutral) species. The dissociation reactions of an amino acid in pure water
NH~ NH~ R-C-COOH + H20 # R- C-COO-+ H30 + ( I )
H H
R-C-CO0-+ Hp R-C-COO-+ Hp ÷ H H
(II)
are described by the corresponding equilibrium constants pKl = - log l0 K~ and p K . = -log~0 K, .
C. Gr~mann et al. / Fluid Phase Equilibria 137 (1997) 209-228 219
K~ and K , are the chemical equilibrium constants defined with reference states as described in the following section. Numbers for pK~ and p K , at 293 K as taken from Yamamoto [18] are given in Table 1. In L-glutamic acid and in L-lysine, the hydrocarbonic residue R contains a dissociating group ( R - - ( C H ) 2 - C O O H in L-glutamic acid and R - - ( C H z ) 4 - N H 2 in L-lysine). The number for pK (293 K) for the dissociation of that carboxylic group, i.e., for the reaction
- ( C H 2 ) 4 - C O O H + H 2 0 ~ - ( C H 2 ) 4 - C O O - + H3 O+ (IIla)
and for the dissociation of the amino-group in the residue R of L-lysine, i.e., the reaction
- ( C H a ) 4 - N H ; + H 2 0 ~ - (CH2)4-NH 2 + H3 O+ (IIIb)
were also taken from that literature source: pKma = 4.25 and PKlu b = 10.28 (cf. pK,~ in Table 1). The peptides given in Table 1 are the result of a condensation reaction between molecules of the same amino acid.
900- [ 1 900- n NH~-C-R- ' ~Re -C-C- I -NH-C-C- I -NH-C-R e + (n-l) H2O
fi 6 [ H 6](~.2) A (IV)
Numbers for p K of the dissociation of the amino group NH3 ~ (according to Eq. (II)) and the dissociation of the carboxylic group - C O O H (according to Eq. (I)) of the peptide (right side of Eq. (IV)) were adopted without any change from the corresponding single amino acids (e.g., p K I = 2.19 and p K , = 9.67 in glu-glu). They are given as pK~ and pK H of the peptides in Table 1. If there is a dissociating group in residue R of a peptide, its p K was adopted without any change from the corresponding single amino acid when that dissociating group is in a terminal residue (i.e., R e of Eq. (IV)), it is given as pK m in Table 1, while it was modified when it is in a middle group (i.e., in R m of Eq. (IV)), it is given as pK w in Table 1 (e.g., p K m = 4.25 and pK w = 4.40 in glu-glu-glu; p K m = 10.28 and p K~v = 10.50 in lys- lys- lys) . Those modifications are based on recommendations by Horn and Heuck [19] and Laussac and Sarkar [20].
As in aqueous two-phase systems of PEG and K2HPO 4 the experimental results for pH range between about 8.2 and 9.5, it was assumed that all amino acids and peptides carry either no or a negative net charge. Thus, amino acids exist as neutral, i.e., amphoteric molecules and anions. In peptides, one has to distinguish between left-terminal, middle and right-terminal amino acid groups, as well as between charged and uncharged groups. The left-terminal group always carries the functional amino group of a peptide, whereas the right-terminal group carries its functional carboxylic group. For example, the tripeptide g ly -g ly -g ly consists of a left-terminal glycine-group (i.e., neutral (NH2) - (H2C) - (CO) - ) , a glycine middle group (i.e., - (NH) - (HzC) (CO) - ) and a right-terminal glycine group (i.e., in neutral form: - ( N H ) - ( H 2C)-(COOH) or as an anion: - ( N H ) - ( H 2C)-(COO-)) . Therefore, four different glycine groups are considered in the partitioning of g ly -g ly -g ly in an aqueous two-phase system of PEG and K2HPO 4. Glycine itself can be present in such two-phase systems either as ( N H ~ ) - ( H 2 C ) - ( C O O ) or (H 2C)(NH 2)(COO-). Table 4 gives those groups for all amino acids and peptides of interest in the present work with surface parameters calculated according to the method of Bondi [21]. All phase equilibrium calculations were performed using the model for the Gibbs excess energy described below and minimizing the Gibbs energy of the feed under the constraint that both phases are electroneutral (cf. Grogmann et al. [14,15] and Grogmann and Maurer [22]).
220 C. Groj3mann et al. / Fluid Phase Equilibria 137 (1997) 209-228
Table 4 Group assignment and group surface parameters Qk
Group Number k Qk
Water 1 H3 O+ 2 OH- 3 PEG-middle group: -CH 2 -O-CH 2 - 4 PEG-end group: -CH 2-OH 5 K + 6 PO4 3 - 7 HPO4 2- 8 HzPO 2 9 H3PO a 10 gly: (NH~)-(CH2)-(COO- ) 11 gly-anion: (NH2)-(CH2)-(COO) 12 Left terminal gly: (NH2)-(CH2)-(CO)- 13 Middle gly: -(NH)-(CH2)-(CO)- 14 Right terminal gly: -(NH)-(CH 2)-(COOH) 15 Right terminal gly-anion: -(NH)-(CH2)-(COO ) 16 glu: (NH~)-(HC-((CH2)2(COOH)))-(COO ) 17 glu-anion: (NH2)-(HC-((CH2)2(COOH)))-(COO-) 18 glu(d.c.-anion): (NH2)-(HC-((CH2)2(COO-)))-(COO- ) 19 Left terminal glu: (NH2)-(HC-((CHz)2(COOH)))-(CO)- 20 Left terminal glu-anion: (NH 2)-(HC-((CH 2)2(COO- )))-(CO)- 21 Middle glu: -(NH)-(HC-((CH 2)2(COOH)))-(CO)- 22 Middle glu-anion: -(NH)-(HC-((CH2)2(COO- )))-(CO)- 23 Right terminal glu: -(NH)-(HC-((CHz)2(COOH)))-(COOH) 24 Right terminal glu-anion: -(NH)-(HC-((CH 2)2(COOH)))-(COO- ) 25 Right terminal glu-(d.c.-anion): -(NH)-(HC-((CH2)2(COO )))-(COO ) 26 phe: (NH ~ )-(HC-((CH 2)(C 6 H 5 )))-(COO- ) 27 phe-anion: (NHz)-(HC-((CHz)(C6Hs)))-(COO) 28 Left terminal phe: (NH 2)-(HC -((CH 2)(C 6 H 5 )))-(CO)- 29 Middle phe: -(NH)-(HC-((CH2)(C6H5)))-(CO)- 30 Right terminal phe: -(NH)-(HC -((CH 2 XC 6 H 5)))-(COO H) 31 Right terminal phe-anion: -(NH)-(HC -((CH 2)(C 6 H 5)))- (COO-) 32 lys: (NH ~- )-(HC -((CH 2)4 (NH 2)))-(C00 - ) 33 lys-amph: (NH 2)-(HC-((CH 2)4 (NH ~ )))-(COO- ) 34 lys-anion: (NHz)-(HC-((CH2)4(NH2)))-(COO) 35 Left terminal lys: (NH2)-(HC-((CHz)a(NH2)))-(CO)- 36 Middle lys: -(NH)-(HC-((CH 2)4( NH 2)))-(CO)- 37 Right terminal lys: -(NH)-(HC-((CH2)4(NH2)))-(COOH) 38 Right terminal lys-anion: -(NH)-(HC-((CH2)4(NH 2)))-(COO- ) 39
1.40 1.40 1.40 1.32 1.74 1.40 1.40 1.40 1.40 1.40 2.460 2.460 1.788 1.488 2.160 2.160 4.452 4.452 4.452 3.780 3.780 3.480 3.480 4.152 4.152 4.152 4.808 4.808 4.136 3.836 4.508 4.508 5.004 5.004 5.004 4.332 4.032 4.704 4.704
3.2. M o d e l f o r the excess Gibbs energy G E
The model for the Gibbs energy G E applied in the present work has been described in detail recently [14,15]; therefore, only its most essential features are repeated here. The excess is defined using an asymmetr ic normalizat ion. For water, the reference state is the pure liquid, whereas for any
C. Groflmann et al. / Fluid Phase Equilibria 137 (1997) 209-228 221
solute, it is a hypothetical liquid one molal solution in water with interactions at infinite dilution in pure water. In both reference states, the temperature is the same as that of the system. The influence of pressure on G E is neglected. G E is assumed to be the sum of two contributions: a modified Debye-Hiickel term (Pitzer, [17]) is to account for nonspecific electrostatic interactions, whereas all other interactions (e.g., hydrophobicity, polarity, etc.) are summarized in an osmotic virial type of expression where concentrations are expressed through relative surface fractions.
G z M w 4I - 1000 A~-b - ln(1 + b y e ) + nwRT
I is ionic strength on molality scale:
1 U -- y 'm i z ~
I = 2i=1
1000 )2 [~i Oj
i~w j~w Ow Ow Aid (1)
(2)
A~p species i:
mi qi O i = ( 3 )
Y~ mjqj all comp. j
where m i and qi are molality and surface parameters of species i and A~,j is a binary parameter (i.e., second osmotic virial coefficient) characterizing interactions between surface sites of species i and j.
As a group-contribution approach is applied here, surface parameter of species i, qi, is calculated from the number of groups j in species i, @), and the surface parameter of group j, Qj:
qi = E /,j(i) Qj (4) all groups j
Similarly, the virial coefficient for interactions between species i and j, Aij, is calculated from the surface fraction of group 1 in species i, O~ (i), and those of group m in species j, O m G), and binary group interaction parameters al ,m:
(5)
is the Debye-Hi~ckel constant of water (A¢ (293 K ) = 0.3882). O i is the surface fraction of
O~ i) = u~i)Ql/qi (6)
Following the main idea of Pitzer's proposal for binary interaction parameters between ionic species in aqueous solutions of strong electrolytes, the binary group interaction parameter a], m is written as the sum of one term, that does not, and another term that does depend on ionic strength:
1 =.~(0) _[_.7(1) [1 - - (1 + 2v/-[) exp(--2V~)] (7) al,m ~l,ln ~l,m ~
Parameters _(o) and a (~) Ul,m 1.m are symmetric, i.e., ,,(o) = a(O) and ,,(]) = a (1) and are zero for m = 1 as ~l,m m,l ~l,rn m,l well as for m or 1 representing water.
Ai j = E E /'~ (i)/'~ (J)'a , Vl Vm ~l,m all groups 1 all groups m
Of i~ is the relative contribution of group 1 to the surface parameter of species i , qi.
222 C. GroJ3mann et al. / Fluid Phase Equilibria 137 (1997) 209-228
The resulting expressions for the activity of a solute species i 4= w and for the activity of water are:
[ v/)- 2 l n ( l + b f / ) ] l n a i . w = l n m i - a ~ z i 2 1 +b~/-/ + - b
1000 2 q__2_ i ~)J (0) A ( l ) f (
+ 2 ~ M-f-w qw j ~ w K [AiJ+''i'jJ2t')]
-- z ? f 3 ( I ) ~ E ("~),~ K j,k (8) jvew k
in a w - ,w[v w ,l.., ] (,ooo)
1 ~ - 0 m i - 2 A q~
X ~w E Oi OJ [A'°)+A(l!exp(-2ffl)] i j•w Ow Ow L i,j , , j
v ] Vm "l,ln all groups I all groups m
A(I) i,j E E (£1 (i)(k) (J) r'( I ) u I ~ ' J l l l u I , I n
all groups 1 all groups m
(9)
(10)
(11)
(12) 1
f2 ( I ) = ~ [ 1 - ( 1 + 2v/7) e x p ( - 2 v ~ ) ]
1 ~ ( I ) = ~--2 [ 1 - ( 1 + 2v~ + 21) e x p ( - Z f f ) ] (13)
For group assignment, a PEG molecule is split into two PEG end groups ( -CH2-OH) and (ripe G -- 1) PEG middle groups ( - C H 2 - O - C H 2 - ) , where ripe G is the degree of polymerization (PEG 6000: npm = 140; PEG 35 000: npm = 773). Water is treated as a single group. K2HPO 4 is assumed to dissociate completely to K + and HPO4-. Hydrogen phosphate is assumed to undergo further
(v) (vi)
(vii)
(VIII)
chemical reactions:
HPO 2- + H20 ~ PO2- + H30 +
H2PO 4 + HzO ~ HPO 2- + H30 +
H3PO 4 + H20 ~ H2PO 4 + H30 +
Furthermore the autoprotonation of water is taken into account:
2 H 2 0 ~ O H - + H30 +
Chemical equilibrium constants (as p K-numbers) for these reactions at 293 K are given in Table 1.
3.3. Parameter estimation and comparison between experimental and calculated data
Surface parameters for all groups present in aqueous two-phase systems of PEG and K2HPO 4 were taken from Grogmann et al. [15] (cf. Table 4). Interaction parameters necessary to describe liquid-liquid equilibrium in the systems of PEG and K2HPO 4 at 293 K were also taken from that
C. Groflmann et al . / Fluid Phase Equilibria 137 (1997) 209-228
Table 5 Binary interaction parameters ~,(0) and ,~1) ~k,m ~k,m
223
.,(0) k m ~k.m
4,5 4,5 0.00914 4,5 6 0.0450 4,5 8 0.0463
6 8 0.0662 6 7 0.425 6 7 6.568 a
4,5 11,12,15,16 0.0358 4,5 13 -0.0311 4,5 14 0.00845 4,5 17,18,19,24,25,26 0.0152 4,5 20,21 - 0.0384 4,5 22,23 - 0.00782 4,5 27,28,31,32 - 0.0150 4,5 29 - 0.0632 4,5 30 - 0.0278 4,5 33,34,35,38,39 0.0236 4~5 36 0.00149 4,5 37 - 0.0165
a ( 1 ) ~k,m"
literature source. They are given in Table 5 (i.e., first six binary parameters) together with all other interaction parameters. In principle, there are more parameters for interactions between solute species than can be determined from the experimental results of the present work. As has been observed before for the partitioning of glycine and L-phenylalanine in such systems (Grof~mann et al. [15]), a single parameter is sufficient for describing the partitioning of single amino acids in those systems. That parameter was assigned to interactions between PEG-groups (no difference is then made between PEG end or middle groups) and an amino acid (no difference is then made between neutral, amphoteric amino acid molecules and its anions). That parameter was fitted to experimental results for the partition coefficient of that amino acid in the aqueous two-phase system of PEG 6000 and K z H P O 4 at 293 K (i.e., the data given in Table 2a). The model correlates the experimental data presented in Table 2a within experimental uncertainty. This is also demonstrated in Figs. 1 and 2 where, as an example, the experimental results for the partition coefficients of L-glutamic acid and L-lysine are compared to calculated (i.e., correlated) data. In those figures, as well as all others, experimental data for the partition coefficient are assigned to experimental data for the difference in the concentration of PEG in both phases, A ~PE~, and calculated partition coefficients are assigned to calculated numbers for A S%EG" The model reliably predicts the influence of the molecular mass of PEG on the partition coefficient of the amino acids. That is shown in Fig. 3, where for some amino acids in aqueous two-phase systems of PEG 35000 and KzHPO 4 at 293 K, predicted partitions coefficients are compared to the experimental data presented in Table 2b.
For correlating the partitioning of peptides, the same procedure was adopted. Again, only experimental results for the partition coefficient in aqueous two-phase systems of PEG 6000 and KzHPO 4 (given in Table 3a) were used to determine interaction parameters, and only interaction
224 C. GroJ3mann et al. / Fluid Phase Equilibria 137 (1997) 209-228
j glu-glu-glu 0 ";'O .. "
-- T ~- exp. uncer ta in ty ~ "%,,~,[ g lu-g lu
i exp, corr. I ~ i 1%%D ' ~ ' ' i l u !g lu -g lu -g lu [] ...... ~ / , , [
g lu-g lu • ........... I ~ o ,--- glu o " 1 o
'o:o o'.1 o.2 o'.3 o!4 A~PEG 6000/(g ' g-~)
Fig. 1. Comparison between measured and correlated partition coefficients of L-glutamic acid and some of its peptides in aqueous two-phase systems of PEG 6000 and K2HPO 4 at 293.15 K (cf. Table 2a).
parameters between peptide groups and PEG-groups were determined. However, a distinction was introduced among three types of peptide groups (left-terminal, middle and right-terminal). The parameter for interactions between a right-terminal peptide group and a PEG-group was approximated by the corresponding parameter for interactions between the amino acid itself and PEG groups. Only parameters for interactions between PEG groups on one side and peptide middle or left-terminal groups on the other side were fitted to the experimentally determined partition coefficients of the di- and tripeptides. As that seems to be a rather crude approximation (e.g., no distinctions were made as
I
i 2 2 2 ~- i = p . Y " ' , , , • .....
~, - " " 7 . - •
I exp. corr. I "'"'!" ' • . ,~ lys- lys "I', : lys o , ".7.
lys- lys • ........... I ~1 lys- lys- lys ~ , lys-lys-lys I ""'"'" . . . . . . q
0.0 0.1 0.2 0.3 0.4 Z ~ P E G 6 0 0 0 / ( g . g l )
Fig. 2. Comparison between measured and correlated part i t ion coeff icients o f L-lysine and some of its peptJdes in aqueous two-phase systems of PEG 6000 and K z H P O 4 at 293.15 K (cf. Table 2a).
C. GroJ3mann et al. / Fluid Phase Equilibria 137 (1997) 209-228 225
. . . . . [ ]
[3
phe
i t--
~, phe glu gly lys
0.0
] exp. uncertainty
exp. pred. [2] . . . . . .
©
• - - . -
0H
glu gly
~ " ' 0 0 0
0.2 0.3 0.4 A~pE G 35000/(g " g l )
Fig. 3. Comparison between measured and predicted partition coefficients of some amino acids in aqueous two-phase systems of PEG 35000 and K2HPO 4 at 293.15 K (cf. Table 2b).
far as interaction parameters are concerned between charged and uncharged groups), the resulting parameters are regarded as preliminary. It is recommended to use those parameters only at pH ~ 9. The parameters are to be revised when new and more extensive experimental data on the partitioning of amino acids and peptides become available. The parameter values are given in Table 5. Typical comparisons between correlated and measured partition coefficients in aqueous two-phase systems of PEG 6000 and K z H P O 4 are shown in Fig. 1 (for di- and tripeptide of L-glutamic acid), Fig. 2 (for di- and tripeptide of L-lysine) and Fig. 4 (for some peptides of glycine). In most cases, correlated partition coefficients agree with experimental data within experimental uncertainty. The predicted
t -
Lf~
9
"T,
! exp. pred.
j 4*gly o
~ 1 5*gly • ............
#4 0.0 0~1 0.2 0.3
A~pE G 6000/(g . g-l)
%,
"̧̧ '̧%'̧ ̧ ~ 0 ',,%
• "1%, ©
0.4
Fig. 4. Comparison between measured and predicted partition coefficients of two glycine peptides in aqueous two-phase systems of PEG 6000 and K2HPO 4 at 293.15 K (cf. Table 3a).
226 C. Groflmann et a l . / Fluid Phase Equilibria 137 (1997) 209-228
values for the partition coefficients of these peptides in aqueous two-phase systems of PEG 35000 and K 2 HPO 4 reveal somewhat larger deviations from experimental results. However, the deviations rarely surmount the experimental uncertainty by a factor of more than three.
4. Conclusion
Experimental results for the partitioning of glycine, t,-glutamic acid, L-phenylalanine and L-lysine, as well as of small peptides of each of those single amino acids in aqueous two-phase systems of high molecular PEG and K2HPO 4 at 293 K are reported. The experimental results are correlated by means of a group contribution type of osmotic virial equation that uses surface fractions to account for the probability of interactions. Preliminary numbers for interaction parameters between amino acid/peptide groups and the phase-forming system are reported. Deviations between correlated and measured partitioning coefficients are predominantly within the experimental uncertainty.
Acknowledgements
Financial support for some parts of the investigation by the Deutsche Forschungs-gemeinschaft, Bonn-Bad Godesberg, Germany, is gratefully acknowledged.
Appendix A
List of symbols AA
Aq~
ai a(0) .1( I )
k,m, ~k,rn amph. b d.c. L , L G E
gly glu I Ki K x x lys
Amino acid Osmotic virial coefficient for interactions between species i and j Interaction parameters between species i and j Debye-Hiickel parameter Activity of species i Binary parameters for interactions between groups k and m Amphoteric 1.2 (parameter in modified Debye-Hiickel term) sDouble-charged Functions of ionic strength Excess Gibbs energy Glycine L-glutamic acid Ionic strength ~i.upper phase/~iA . . . . . phase = partition coefficient of component i Chemical equilibrium constant for reaction (XX) L-lysine
C. Gr(~mann et al. / Fluid Phase Equilibria 137 (1997) 209-228 227
m
Mn M w
Mw N ?1
H w
P PEG pH phe pK
Qi qi R T
Greek
6)
Subscripts
i , j , 1, m, k lower phase upper phase W
Molality Number-averaged molecular mass Weight-averaged molecular mass Molecular weight of water Number of species Stoichiometric number Number of moles of water Polydispersity Poly(ethylene glycol)
+ - log10 an L-phenylalanine - log10 K
Surface parameter of group i Surface parameter of species i Universal gas constant Absolute temperature Charge number
~i, upper phase -- ~i, lower phase Mass fraction of component i Surface fraction Relative contribution of group to surface parameter of species i Number of groups k in species i
Species Lower phase, i.e., salt-rich phase Upper phase, i.e., PEG-rich phase Water
R e f e r e n c e s
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