Mark James E. (ed.). Physical Properties of Polymers Handbook
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TABLE 8.1b. Continued.
T/K C
p
T/K C
p
T/K C
p
L-Glutamine (146.2 Da) [23]
10 0.728 90 72.55 220 144.06
15 2.460 100 78.99 230 149.45
20 5.791 110 84.94 240 154.72
25 10.48 120 90.67 250 159.91
30 15.91 130 196.23 260 165.02
35 21.80 140 101.76 270 170.04
40 27.72 150 107.28 280 175.10
45 33.46 160 112.63 290 180.12
50 38.93 170 117.95 300 185.10
55 44.06 180 123.18 310 189.83
60 48.87 190 128.37 273.15 171.63
70 57.66 200 133.60 298.15 184.18
80 65.48 210 138.74 310.15 189.91
Glycine (75.1 Da) [21]
10 0.255 90 39.53 220 77.49
15 0.967 100 43.26 230 80.08
20 2.393 110 46.69 240 82.84
25 4.464 120 50.00 250 85.60
30 7.037 130 53.09 260 88.45
35 9.933 140 56.07 270 91.25
40 13.00 150 58.91 280 94.06
45 16.12 160 61.67 290 96.90
50 19.25 170 64.39 300 99.75
55 22.26 180 67.03 310 102.63
60 25.15 190 69.66 273.15 92.13
70 30.49 200 72.30 298.15 99.20
80 35.26 210 74.89 310.15 102.68
Glycylglycine (132.1 Da) [25]
10 0.707 90 67.86 220 130.12
15 2.607 100 73.85 230 134.35
20 6.071 110 79.50 240 138.62
25 10.70 120 84.89 250 142.84
30 15.87 130 89.87 260 147.19
35 21.23 140 94.81 270 151.50
40 26.56 150 99.58 280 155.85
45 31.65 160 104.27 290 160.29
50 36.58 170 108.74 300 164.81
55 41.21 180 113.09 310 169.45
60 45.61 190 117.40 273.15 152.88
70 53.81 200 121.71 298.15 163.97
80 61.21 210 125.90 310.15 169.54
THERMODYNAMIC PROPERTIES OF PROTEINS / 107
TABLE 8.1b. Continued.
T/K C
p
T/K C
p
T/K C
p
L-HistidineHCl (191.6 Da) [22]
10 1.711 90 102.63 220 195.39
15 5.690 100 111.09 230 202.13
20 11.93 110 119.04 240 208.91
25 19.33 120 126.57 250 215.81
30 27.29 130 133.85 260 222.80
35 35.38 140 140.96 270 229.87
40 43.26 150 147.90 280 236.90
45 50.88 160 154.81 290 243.89
50 58.12 170 161.63 300 250.79
55 64.81 180 168.36 310 257.65
60 71.17 190 175.14 273.15 232.09
70 82.80 200 181.92 298.15 249.53
80 93.22 210 188.66 310.15 257.73
L-Isoleucine (131.2 Da) [26]
10 2.741 90 74.89 220 147.53
15 6.343 100 81.80 230 152.59
20 10.80 110 88.41 240 157.74
25 15.82 120 94.68 250 162.97
30 20.93 130 100.63 260 168.16
35 26.12 140 106.36 270 173.26
40 31.22 150 111.88 280 178.53
45 36.22 160 117.24 290 183.76
50 41.08 170 122.55 300 189.28
55 45.82 180 127.70 310 194.89
60 50.38 190 132.72 273.15 174.93
70 58.95 200 137.65 298.15 188.28
80 67.15 210 142.59 310.15 194.97
L-Leucine (131.2 Da) [26]
10 2.452 90 75.44 220 148.91
15 6.468 100 82.22 230 154.60
20 11.50 110 88.53 240 160.46
25 16.93 120 94.64 250 166.52
30 22.53 130 100.50 260 172.93
35 28.08 140 106.15 270 179.70
40 33.32 150 111.63 280 186.77
45 38.40 160 117.03 290 194.31
50 43.26 170 122.38 300 202.51
55 47.82 180 127.70 310 211.38
60 52.17 190 132.93 273.15 181.88
70 60.42 200 138.11 298.15 200.96
80 68.20 210 143.43 310.15 211.50
108 / CHAPTER 8
TABLE 8.1b. Continued.
T/K C
p
T/K C
p
T/K C
p
L-LysineHCl (182.7 Da) [22]
10 2.460 90 97.74 220 186.61
15 6.594 100 106.36 230 192.92
20 12.23 110 114.47 240 199.33
25 18.82 120 122.22 250 205.81
30 25.89 130 129.54 260 212.42
35 33.08 140 136.40 270 219.16
40 40.11 150 143.05 280 225.94
45 46.94 160 149.58 290 232.97
50 53.64 170 155.94 300 240.25
55 60.12 180 162.09 310 247.86
60 66.32 190 168.16 273.15 221.25
70 77.70 200 174.26 298.15 238.91
80 88.12 210 180.41 310.15 247.99
L-Methionine (149.2 Da) [24]
10 2.017 90 82.68 220 157.28
15 5.883 100 89.50 230 164.14
20 11.48 110 95.90 240 172.05
25 17.79 120 101.96 250 181.13
30 24.23 130 107.70 260 192.67
35 30.65 140 113.26 270 208.28
40 36.70 150 118.66 280 229.79
45 42.43 160 124.01 290 259.20
50 47.87 170 129.24 300 298.28
55 53.01 180 134.47 310 298.19
60 57.91 190 139.70 273.15 214.30
70 66.99 200 145.19 298.15 290.04
80 75.19 210 151.04 310.15 296.85
L-Phenylalanine (165.2 Da) [27]
10 2.594 90 74.73 220 152.05
15 6.682 100 80.96 230 158.49
20 11.87 110 86.94 240 165.02
25 17.36 120 92.72 250 171.54
30 23.16 130 98.49 260 178.07
35 28.93 140 104.31 270 184.60
40 34.36 150 110.17 280 191.13
45 39.44 160 116.11 290 197.69
50 44.23 170 122.01 300 204.22
55 48.74 180 127.95 310 210.71
60 53.01 190 133.93 273.15 186.65
70 60.79 200 139.87 298.15 203.01
80 67.99 210 145.85 310.15 210.79
THERMODYNAMIC PROPERTIES OF PROTEINS / 109
TABLE 8.1b. Continued.
T/K C
p
T/K C
p
T/K C
p
L-Proline (115.1 Da) [27]
10 1.301 90 59.08 220 116.06
15 4.105 100 63.60 230 120.50
20 8.314 110 67.91 240 124.93
25 13.01 120 72.17 250 129.33
30 17.85 130 76.36 260 133.85
35 22.65 140 80.63 270 138.16
40 27.17 150 84.98 280 142.67
45 31.42 160 89.45 290 147.28
50 35.38 170 93.93 300 152.09
55 39.02 180 98.41 310 156.98
60 42.43 190 102.84 273.15 141.00
70 48.62 200 107.24 298.15 151.17
80 54.10 210 111.63 310.15 157.07
L-Serine (105.1 Da) [28]
10 0.816 90 55.90 220 107.78
15 2.703 100 61.09 230 111.25
20 5.556 110 65.73 240 114.77
25 9.063 120 70.12 250 118.28
30 13.03 130 74.35 260 121.84
35 17.21 140 78.41 270 125.39
40 21.46 150 82.34 280 128.99
45 25.63 160 86.11 290 132.59
50 29.69 170 89.83 300 136.23
55 33.59 180 93.47 310 139.91
60 37.31 190 97.11 273.15 126.52
70 44.18 200 100.67 298.15 135.56
80 50.33 210 104.22 310.15 140.00
L-Tryptophane (204.2 Da) [27]
10 4.393 90 84.56 220 178.20
15 10.02 100 91.92 230 185.69
20 16.51 110 99.04 240 193.34
25 23.04 120 106.06 250 201.08
30 29.35 130 113.18 260 208.87
35 35.28 140 120.33 270 216.52
40 40.78 150 127.45 280 224.22
45 45.61 160 134.64 290 231.92
50 51.00 170 141.80 300 239.58
55 55.73 180 148.99 310 247.32
60 60.17 190 156.27 273.15 218.95
70 68.70 200 163.59 298.15 238.15
80 76.86 210 170.88 310.15 247.44
110 / CHAPTER 8
heat capacity of the denatured protein and the calculated one
for the unfolded polypeptide chain is a strong argument that
heat denatured proteins are indistinguishable thermodynam-
ically from fully unfolded (D U).
8.2 PARTIAL VOLUME
The partial specific volume of proteins can be measured
experimentally [11,12] or can be estimated from the amino
acid composition of the protein using equation
V
2
¼ (N 1) V
2
(-----CHCONH-----) þ
X
N
i¼1
V
2
( ----- R
i
), (8:2)
where N is number of amino acid residues in the protein
sequence, V
2
(-----CHCONH-----) is the contribution of a peptide
unit, and V
2
( ----- R
i
) is the contribution of the ith amino acid
side chain. These contributions are listed in Table 8.6. For
more details, compilation of the experimental data on the
partial volume of proteins is recommended [12].
8.3 THERMODYNAMIC FUNCTIONS
Because the absolute value of the heat capacity of the
native state is always larger than the heat capacity of the
unfolded state, and because they have different temperature
dependencies, the heat capacity change upon unfolding is
positive and temperature dependent itself:
D
U
N
C
p
(T) ¼ C
U
p
(T) C
N
p
(T), (8:3)
where D
U
N
C
p
(T) is a nonlinear function of temperature.
It has maximum at around 50 8C, decreases at high temper-
atures and appears to reach zero at 140 8C). The heat
capacities of proteins in the native and unfolded states and
the heat capacity change upon unfolding are presented in
Table 8.7.
TABLE 8.1b. Continued.
T/K C
p
T/K C
p
T/K C
p
L-Tyrosine (181.2 Da) [27]
10 1.389 90 75.06 220 162.72
15 3.908 100 82.05 230 169.45
20 7.724 110 88.83 240 176.23
25 12.57 120 95.56 250 183.05
30 18.07 130 102.26 260 189.91
35 23.91 140 108.87 270 196.86
40 29.62 150 115.52 280 203.84
45 35.24 160 122.26 290 210.79
50 40.59 170 128.99 300 217.74
55 45.56 180 135.77 310 224.60
60 50.29 190 142.38 273.15 199.08
70 59.20 200 149.12 298.15 216.44
80 67.49 210 155.81 310.15 224.72
L-Valine (117.2 Da) [24]
10 1.100 90 64.73 220 133.01
15 3.192 100 71.34 230 137.57
20 6.615 110 77.57 240 142.05
25 10.69 120 83.55 250 146.61
30 15.18 130 89.16 260 151.17
35 19.86 140 94.56 270 155.85
40 24.46 150 99.83 280 160.50
45 29.04 160 104.98 290 165.06
50 33.50 170 109.91 300 169.70
55 37.87 180 114.73 310 174.31
60 42.09 190 119.37 273.15 157.28
70 50.04 200 123.89 298.15 168.82
80 57.61 210 128.41 310.15 174.39
THERMODYNAMIC PROPERTIES OF PROTEINS / 111
The non-zero heat capacity change upon protein unfold-
ing means that all other thermodynamic functions are also
temperature dependent:
D
U
N
H(T) ¼ D
U
N
H(T
0
) þ
Z
T
T
0
D
U
N
C
p
(T)dT (8:4)
D
U
N
S(T) ¼ D
U
N
S(T
0
) þ
Z
T
T
0
D
U
N
C
p
(T)d ln T (8:5)
D
U
N
G ¼ D
U
N
H TD
U
N
S(8:6)
These functions are presented in Table 8.7 for a selected set
of 20 proteins, for which the thermodynamics of unfolding
have been measured with highest accuracy.
8.4 HYDRATION EFFECTS
The contribution of solvent (water) to the observed
changes of the thermodynamic parameters of proteins can
be assumed to be proportional to the changes in water
accessible surface area of the protein groups. The water
accessible surface area can be calculated from the X-ray or
NMR structure of the native protein by computing the sur-
face formed by the center of a spherical probe rolling on the
surface of the protein (see e.g., [13,14]). As was shown
earlier, the hydration effects of protein groups exposed to
water upon unfolding [15–18] can be expressed as follows:
DC
hyd
p
,k
(T) ¼
X
i
D
U
N
ASA
k,i
DC
^
hyd
p
,k,i
(T)(8:7)
DH
hyd
k
(T) ¼
X
i
D
U
N
ASA
k,i
DH
^
hyd
k
,i
(T)(8:8)
DS
hyd
k
(T) ¼
X
i
D
U
N
ASA
k,i
DS
^
hyd
k
,i
(T)(8:9)
DG
hyd
k
(T) ¼
X
i
D
U
N
ASA
k,i
DG
^
hyd
k
,i
(T), (8:10)
where D
U
N
ASA
k,i
is the change of water accessible surface
area of protein group i of type k upon unfolding and
DC
^
hyd
p
,k,i
(T), DS
^
hyd
k
,i
(T), DG
^
hyd
k
,i
(T), and D H
^
hyd
k
,i
(T) are the hy-
dration heat capacity change, enthalpy, entropy, and Gibbs
energy change of this type of group the normalized per
square angstrom. These normalized hydration effects were
determined by the transfer of model compounds from
the gaseous phase to water and their values are listed in
Table 8.8.
TABLE 8.2. Temperature dependence of the partial molar volumes (cm
3
mol
1
) of the peptide unit and of the side chains of amino
acid residues for the temperature range 5–125 8C [11].
Temperature (8C)
5 25 50 75 100 125
–CHCONH– 28.3 28.0 28.6 28.9 29.0 29.4
--- R
i
Ala 24.8 27.2 30.1 33.1 36.3 39.4
Arg 81.2 85.7 88.4 90.4 92.1 93.5
Asn 44.1 45.7 47.8 49.3 50.8 52.4
Asp 39.0 41.5 44.5 47.3 49.9 52.6
Cys 40.5 40.5 40.5 40.5 40.5 40.5
Gln 58.4 61.0 63.2 66.0 68.5 69.7
Glu 54.9 57.5 60.7 63.6 66.3 69.3
Gly 10.9 10.3 9.6 9.2 8.9 8.5
His 65.1 64.0 63.1 62.4 61.8 61.1
Ile 64.5 66.1 67.7 69.8 71.8 74.0
Leu 75.0 77.6 80.2 82.9 86.5 89.4
Lys 72.4 73.5 75.8 78.5 81.3 84.8
Met 73.3 72.1 70.2 69.0 67.9 66.7
Phe 82.0 86.3 92.0 97.9 102.6 107.9
Pro 36.0 35.8 34.1 33.7 33.5 33.2
Ser 27.1 27.8 28.8 29.7 30.7 32.0
Thr 44.2 44.7 45.9 47.6 50.9 54.6
Trp 110.9 110.9 110.9 110.9 110.9 110.9
Tyr 88.2 90.0 92.2 94.1 95.9 97.8
Val 60.7 63.0 65.7 68.5 71.7 74.5
112 / CHAPTER 8
TABLE 8.3. Heat capacities (J K
1
mol
1
) of solid poly (amino acids).
Poly-L-Alanine (m.w 15,000 Da) [29]
T /K C
p
T /K C
p
T /K C
p
0.1 0.00 190 42.65 590 120.06
0.2 0.00 200 44.96 600 121.57
0.3 0.00 210 47.19 610 123.07
0.4 0.00 220 49.46 620 124.55
0.5 0.00 230 51.71 630 126.02
0.6 0.00 240 53.93 640 127.47
0.7 0.00 250 56.18 650 128.91
0.8 0.00 260 58.39 660 130.34
0.9 0.00 270 60.61 670 131.76
1.0 0.00 273.15 61.30 680 133.16
1.2 0.00 280 62.79 690 134.56
1.4 0.00 290 64.97 700 135.95
1.6 0.00 298.15 66.76 710 137.32
1.8 0.00 300 67.17 720 138.69
2 0.01 310 69.30 730 140.05
3 0.02 320 71.40 740 141.40
4 0.05 330 73.54 750 142.75
5 0.10 340 75.60 760 144.08
6 0.17 350 77.64 770 145.41
7 0.27 360 79.65 780 146.74
8 0.40 370 81.64 790 148.06
9 0.56 380 83.72 800 149.38
10 0.75 390 85.66 810 150.70
15 1.95 400 87.58 820 152.01
20 3.31 410 89.47 830 153.32
25 4.66 420 91.35 840 154.63
30 5.95 430 93.31 850 155.94
40 8.40 440 95.13 860 157.25
50 10.75 450 96.93 870 158.55
60 13.06 460 98.72 880 159.86
70 15.35 470 100.48 890 161.16
80 17.63 480 102.22 900 162.47
90 19.89 490 103.94 910 163.78
100 22.15 500 105.64 920 165.10
110 24.43 510 107.32 930 166.41
120 26.70 520 108.98 940 167.74
130 28.99 530 110.62 950 169.06
140 31.25 540 112.24 960 170.39
150 33.52 550 113.84 970 171.73
160 35.78 560 115.42 980 173.09
170 38.05 570 116.98 990 174.44
180 40.37 580 118.53 1000 175.80
THERMODYNAMIC PROPERTIES OF PROTEINS / 113
TABLE 8.3. Continued.
Poly-L-ArginineHCl (m.w 132,000 Da) [30]
T /K C
p
T /K C
p
T /K C
p
0.1 0.00 190 168.39 590 410.48
0.2 0.00 200 174.72 600 415.75
0.3 0.00 210 180.99 610 420.90
0.4 0.00 220 187.37 620 426.02
0.5 0.00 230 193.59 630 431.08
0.6 0.00 240 199.90 640 436.12
0.7 0.00 250 206.23 650 441.09
0.8 0.00 260 212.56 660 446.07
0.9 0.00 270 218.86 670 451.00
1.0 0.01 273.15 220.85 680 455.91
1.2 0.01 280 225.21 690 460.79
1.4 0.01 290 231.62 700 465.91
1.6 0.02 298.15 236.88 710 470.48
1.8 0.03 300 237.99 720 475.28
2 0.04 310 244.49 730 480.05
3 0.14 320 250.83 740 484.81
4 0.34 330 257.21 750 489.54
5 0.66 340 263.60 760 494.23
6 1.13 350 269.96 770 498.98
7 1.77 360 276.31 780 503.65
8 2.57 370 282.71 790 508.31
9 3.51 380 289.10 800 512.93
10 4.58 390 295.25 810 517.55
15 10.76 400 301.53 820 522.18
20 17.16 410 307.69 830 526.80
25 23.29 420 313.80 840 531.38
30 29.14 430 319.89 850 535.98
40 40.34 440 325.97 860 540.57
50 51.21 450 332.02 870 545.16
60 61.91 460 338.03 880 549.75
70 72.42 470 343.99 890 554.32
80 82.61 480 349.82 900 558.90
90 92.43 490 355.58 910 563.48
100 101.85 500 361.27 920 568.07
110 110.73 510 366.89 930 572.67
120 119.11 520 372.45 940 577.26
130 127.01 530 377.96 950 581.87
140 134.57 540 383.44 960 586.49
150 141.75 550 388.86 970 591.12
160 148.67 560 394.31 980 595.77
170 155.41 570 399.73 990 600.42
180 161.97 580 405.15 1000 605.07
114 / CHAPTER 8
TABLE 8.3. Continued.
Poly-L-Aspartic acidNa (m.w 42,500 Da) [30]
T /K C
p
T /K C
p
T /K C
p
0.1 0.00 190 105.03 590 249.25
0.2 0.00 200 109.57 600 252.01
0.3 0.00 210 114.02 610 254.74
0.4 0.00 220 118.55 620 257.41
0.5 0.00 230 122.86 630 260.03
0.6 0.00 240 127.19 640 262.63
0.7 0.00 250 131.48 650 265.19
0.8 0.00 260 135.71 660 267.74
0.9 0.00 270 139.84 670 270.26
1.0 0.00 273.15 141.14 680 272.77
1.2 0.01 280 143.96 690 275.25
1.4 0.01 290 148.05 700 278.00
1.6 0.01 298.15 151.40 710 280.19
1.8 0.02 300 152.07 720 282.63
2 0.02 310 156.17 730 285.05
3 0.08 320 160.08 740 287.47
4 0.19 330 164.01 750 289.86
5 0.38 340 167.90 760 292.22
6 0.65 350 171.71 770 294.65
7 1.01 360 175.46 780 297.02
8 1.47 370 179.27 790 299.37
9 2.01 380 182.83 800 301.65
10 2.62 390 186.42 810 303.98
15 6.16 400 190.09 820 306.30
20 9.83 410 193.59 830 308.62
25 13.34 420 197.03 840 310.94
30 16.69 430 200.44 850 313.25
40 23.10 440 203.81 860 315.55
50 29.33 450 207.18 870 317.85
60 35.48 460 210.50 880 320.15
70 41.58 470 213.78 890 322.43
80 47.59 480 216.97 900 324.72
90 53.48 490 220.11 910 327.02
100 59.27 500 223.19 920 329.32
110 64.90 510 226.23 930 331.62
120 70.40 520 229.22 940 333.93
130 75.70 530 232.18 950 336.24
140 80.90 540 235.10 960 338.55
150 85.89 550 237.99 970 340.87
160 90.88 560 240.94 980 343.21
170 95.65 570 243.74 990 345.55
180 100.39 580 246.51 1000 347.89
THERMODYNAMIC PROPERTIES OF PROTEINS / 115
TABLE 8.3. Continued.
Poly-L-Asparagine (m.w 10,400 Da) [30]
T /K C
p
T /K C
p
T /K C
p
0.1 0.00 190 97 590 235.78
0.2 0.00 200 100.96 600 238.61
0.3 0.00 210 104.88 610 241.40
0.4 0.00 220 108.90 620 244.14
0.5 0.00 230 112.73 630 246.84
0.6 0.00 240 116.63 640 249.51
0.7 0.00 250 120.52 650 252.16
0.8 0.00 260 124.40 660 254.80
0.9 0.00 270 128.19 670 257.41
1.0 0.00 273.15 129.40 680 260.00
1.2 0.01 280 132.02 690 262.58
1.4 0.01 290 135.84 700 265.41
1.6 0.01 298.15 138.99 710 267.70
1.8 0.02 300 139.62 720 270.23
2 0.03 310 143.51 730 272.75
3 0.09 320 147.23 740 275.27
4 0.22 330 150.98 750 277.77
5 0.43 340 154.71 760 280.23
6 0.74 350 158.39 770 282.77
7 1.14 360 162.02 780 285.24
8 1.64 370 165.73 790 287.71
9 2.22 380 169.20 800 290.09
10 2.85 390 172.73 810 292.54
15 6.39 400 176.35 820 294.98
20 9.92 410 179.79 830 297.41
25 13.29 420 183.19 840 299.85
30 16.50 430 186.56 850 302.27
40 22.69 440 189.91 860 304.69
50 28.72 450 193.27 870 307.11
60 34.66 460 196.59 880 309.52
70 40.49 470 199.87 890 311.93
80 46.16 480 203.07 900 314.34
90 51.66 490 206.22 910 316.76
100 56.96 500 209.32 920 319.18
110 62.02 510 212.39 930 321.61
120 66.88 520 215.42 940 324.04
130 71.54 530 218.41 950 326.47
140 76.09 540 221.37 960 328.91
150 80.41 550 224.31 970 331.36
160 84.70 560 227.30 980 333.82
170 88.84 570 230.15 990 336.28
180 92.96 580 232.98 1000 338.75
116 / CHAPTER 8