# cluster centers of alpha and tau angles in paper: Empirical Potential Function for Simplified Protein Models: Combining Contact and Local Sequence-Structure Descriptors, by Jinfeng Zhang, Rong Chen, and Jie Liang.
# There are total 1318 non-homologous proteins used to calculate native alpha and tau angles for 20 amino acids. Calculated angles are clustered into k = 3-10 discrete states for each amino acids. 
# The data is formated as following: the first column is the amino acid type, the following columns are alpha_1, tau_1, alpha_2, tau_2, and so on.

# 3-state
A 105.038 -111.962 95.7051 53.8563 126.662 -179.726 
R 108.952 -113.846 97.0175 51.9836 123.108 176.39 
N 106.689 -112.311 99.2586 45.3921 119.754 172.695 
D 106.754 -113.667 97.907 48.8139 116.805 168.918 
C 113.883 -115.865 101.115 50.213 126.126 171.199 
Q 109.968 -118.637 96.2892 51.7383 122.744 170.498 
E 108.39 -114.849 95.7112 50.9767 121.603 169.619 
G 109.488 -102.563 105.78 39.7516 133.452 163.596 
H 109.862 -113.853 100.206 47.0569 124.966 171.933 
I 112.681 -123.33 97.3285 50.5975 121.121 -178.818 
L 111.876 -122.462 96.0057 52.042 119.796 179.595 
K 109.175 -117.485 97.0552 52.1898 120.676 171.92 
M 112.677 -118.819 96.171 51.7964 124.349 174.497 
F 114.003 -119.423 100.403 49.1667 125.345 177.893 
P 109.932 -110.42 94.2379 41.8763 104.086 -175.687 
S 114.766 -109.42 101.342 53.3819 123.905 173.308 
T 116.334 -115.95 101.617 51.0085 124.182 176.569 
W 113.364 -114.569 98.1913 51.703 123.924 177.125 
Y 114.756 -113.969 101.021 48.4435 125.878 179.456 
V 112.86 -120.425 98.9316 50.9233 122.599 -175.962 
# 4-state
A 112.772 -111.709 92.1052 49.952 129.085 -160.399 127.548 78.0247 
R 121.786 -108.605 93.3499 47.8293 121.836 -169.701 108.421 98.5722 
N 117.291 -95.8991 93.926 46.4804 112.584 -174.742 96.2399 111.259 
D 120.353 -99.6357 92.987 47.6624 110.665 -169.508 98.0185 112.722 
C 124.004 -112.461 95.4635 50.5563 119.448 -170.565 98.8581 125.275 
Q 121.426 -106.199 94.0018 47.329 119.968 -167.214 101.416 121.736 
E 120.298 -103.07 93.8934 46.8372 120.161 -162.827 99.9787 125.924 
G 137.142 -77.9649 99.7752 45.0838 122.026 -164.681 96.853 127.609 
H 127.739 -90.4368 95.2895 48.8195 121.222 -155.583 103.335 126.615 
I 123.757 -103.812 93.5288 47.5134 119.518 -159.273 108.436 132.433 
L 118.571 -108.081 93.1196 50.3686 118.272 -162.792 103.836 130.491 
K 121.405 -105.402 94.1483 47.0677 117.987 -164.56 98.1945 124.707 
M 117.261 -109.846 93.5766 49.3815 120.76 -165.424 106.994 127 
F 125.294 -111.575 94.2572 48.9047 123.989 -167.703 104.401 122.449 
P 119.009 -110.729 96.2572 47.7931 111.734 -166.519 101.066 131.207 
S 126.407 -107.97 94.2711 49.7933 124.982 -165.62 100.555 120.912 
T 124.584 -107.394 95.1823 46.6002 122.263 -164.443 99.5583 112.783 
W 114.314 -108.791 95.6459 47.9891 125.512 -165.958 104.207 112.397 
Y 121.614 -111.775 96.5267 47.0258 124.151 -166.418 103.448 112.924 
V 124.346 -114.455 94.5121 46.1956 121.927 -167.897 108.653 115.83 
#5-state
A 106.905 -134.19 93.4167 50.8078 113.955 -80.7034 126.248 179.698 113.719 113.567 
C 110.32 -112.348 93.9427 51.3898 121.634 3.92364 124.573 -170.083 121.096 116.286 
D 105.272 -108.056 94.1632 52.609 111.623 -7.71958 110.956 -160.428 115.342 119.842 
E 105.458 -107.166 92.6881 51.7906 121.125 1.44581 117.5 -163.271 116.514 116.201 
F 110.875 -110.736 93.7042 50.3038 123.085 17.9896 123.122 -167.722 120.42 115.508 
G 104.238 -106.024 95.5232 46.5603 115.871 -14.1251 124.547 -162.804 136.689 107.53 
H 107.655 -107.2 94.5565 51.4213 119.232 12.1758 120.1 -165.723 121.949 118.489 
I 111.16 -116.891 93.092 49.77 123.382 17.6558 119.539 -166.448 115.607 117.96 
K 106.802 -112.31 92.9418 51.8068 122.633 3.64587 117.288 -165.539 117.443 116.601 
L 110.096 -115.246 92.6909 50.5 120.191 11.7256 117.85 -165.695 115.412 113.577 
M 109.353 -111.776 92.5329 51.3285 124.036 6.34682 122.178 -167.04 118.59 116.723 
N 104.741 -110.916 95.7469 50.7088 106.404 -5.77949 115.169 -164.289 117.191 118.346 
P 110.151 -106.441 93.0026 45.0195 113.75 -69.6548 104.655 -139.679 101.622 179.428 
Q 107.095 -113 92.6113 51.7821 122.037 4.47204 119.303 -166.909 118.526 114.446 
R 107.847 -131.249 95.0523 49.4254 114.887 -73.1965 122.892 -176.74 115.479 113.28 
S 110.995 -108.847 93.1849 54.1824 130.253 1.64492 122.932 -167.068 119.536 117.657 
T 114.877 -115.281 93.7662 51.3299 124.798 15.4511 122.066 -170.48 121.362 117.068 
V 111.327 -116.781 93.0344 49.4056 124.975 20.3667 121.307 -167.305 117.526 114.984 
W 110.693 -110.659 93.2066 51.7667 121.04 9.14765 122.614 -169.217 115.807 114.762 
Y 111.397 -109.943 94.0525 50.2343 122.36 16.3981 124.685 -168.142 119.082 115.809 
#6-state
A 106.771 -140.126 91.8925 52.33 107.584 -95.7783 127.28 -179.436 114.143 116.094 128.98 0.150178 
C 112.576 -140.97 93.5426 51.3959 110.85 -95.1835 127.193 179.503 119.922 110.676 120.976 8.01738 
D 104.781 -134.839 93.8848 52.5611 106.555 -91.3916 115.664 -178.485 113.558 113.253 111.352 -3.00457 
E 107.491 -137.701 92.5102 51.7941 105.382 -94.0278 121.891 -177.138 115.555 111.946 120.936 6.65522 
F 114.253 -148.444 93.505 50.1523 110.093 -98.2552 128.356 178.273 117.584 107.808 122.436 19.4474 
G 102.244 -122.567 94.0145 49.7655 110.952 -77.8359 129.365 -176.575 135.286 99.8056 113.72 4.59637 
H 107.751 -133.85 94.1004 51.4245 109.43 -83.9566 123.926 -175.518 119.438 112.197 118.596 16.3667 
I 113.674 -141.162 92.7424 49.6004 109.101 -97.7957 120.688 -173.919 115.086 113.109 122.578 23.4571 
K 107.111 -138.25 92.7578 51.8034 107.957 -96.3037 121.128 -178.151 116.643 112.381 121.693 8.83364 
L 113.268 -144.372 92.5526 50.4859 108.606 -102.465 119.506 -177.123 114.874 110.223 119.495 15.8679 
M 112.181 -142.406 92.4301 51.2348 108.637 -98.2474 125.445 -177.122 117.561 112.579 123.626 7.99609 
N 105.82 -135.555 95.2486 50.8972 105.335 -91.1147 119.786 179.552 115.179 110.457 106.519 -0.176442 
P 105.902 -132.964 91.9893 44.706 111.423 -96.9858 101.876 -176.832 100.577 83.8905 112.881 -45.5258 
Q 109.456 -141.029 92.4256 51.7124 106.563 -96.7358 123.198 -179.354 117.732 110.427 121.908 8.57415 
R 109.296 -140.995 92.6953 51.5828 107.962 -97.8351 124.267 179.973 115.237 113.192 124.323 8.04823 
S 111.514 -139.304 92.8466 53.8992 111.312 -93.6759 128.151 177.155 117.315 111.355 130.393 5.57366 
T 115.526 -142.689 93.41 51.3045 114.395 -97.2027 124.454 178.111 119.931 110.799 123.238 18.9713 
V 116.478 -150.253 92.8182 49.1406 109.656 -105.742 123.474 -179.796 116.897 108.238 124.434 20.9767 
W 113.865 -144.838 92.8952 51.6425 109.907 -98.8825 125.999 178.492 113.643 109.094 120.794 12.8168 
Y 115.649 -148.553 93.819 50.2006 111.042 -96.345 129.379 178.712 117.221 110.617 121.496 18.8172 
#7-state
A 107.544 -145.175 91.8074 52.2521 106.591 -103.037 128.476 179.174 113.52 116.522 136.84 15.0584 109.379 -41.4128 
C 117.305 -152.368 92.9105 51.9075 108.775 -109.741 128.295 171.342 118.998 107.305 116.988 19.3386 119.594 -48.5326 
D 105.482 -141.57 92.9565 53.4896 105.598 -100.387 117.657 175.455 112.711 111.557 115.539 20.289 103.739 -26.7096 
E 111.794 -150.012 92.307 51.9327 103.306 -114.252 123.349 175.266 114.998 110.201 119.939 14.4453 108.819 -72.1909 
F 118.194 -161.212 93.3375 50.0104 110.097 -124.328 131.484 166.29 116.315 102.162 121.717 20.7513 111.207 -79.4609 
G 123.329 -141.176 93.2905 52.881 97.6 -110.847 130.213 164.859 136.277 90.9987 106.401 13.0455 117.291 -54.5033 
H 115.627 -157.097 93.7066 51.4429 106.039 -115.731 128.39 166.182 117.221 105.1 117.682 19.8226 111.417 -63.5838 
I 118.204 -159.025 92.5478 49.3915 109.877 -123.251 120.674 169.488 114.178 105.662 121.896 25.2561 111.318 -77.8113 
K 116.332 -158.098 92.5996 51.7436 104.318 -124.565 120.043 164.103 116.138 107.001 121.281 11.4703 109.301 -85.0558 
L 117.621 -158.57 92.409 50.4361 108.739 -125.285 117.711 167.208 114.292 104.623 118.287 18.5313 110.428 -86.0133 
M 118.74 -160.915 92.3241 51.0997 107.977 -125.885 128.347 165.977 115.995 106.44 123.375 10.7534 110.537 -86.0091 
N 107.598 -143.569 93.664 52.4898 104.466 -103.356 121.235 174.121 114.693 108.58 111.434 22.0395 99.4408 -23.4767 
P 104.012 -150.318 91.6706 46.3582 108.652 -117.177 99.4164 173.698 101.119 84.5834 109.251 -18.7922 112.385 -85.4605 
Q 112.954 -152.313 92.2133 51.8556 105.14 -115.042 125.164 172.644 116.66 108.993 121.767 18.8871 110.08 -64.0248 
R 110.456 -145.401 92.3659 51.6193 106.879 -105.893 124.968 178.316 114.228 114.024 128.347 26.2935 109.586 -35.4799 
S 115.754 -158.782 92.6758 53.8221 110.518 -121.15 131.678 164.809 115.755 108.178 130.534 8.93242 111.67 -79.7006 
T 117.72 -161.373 93.2043 51.2849 114.336 -123.67 127.391 164.971 118.568 105.318 122.332 21.1956 115.172 -77.5236 
V 120.014 -161.11 92.6295 49.1424 110.975 -128.791 123.102 168.575 116.28 104.208 123.376 23.7118 109.98 -87.2668 
W 118.669 -161.196 92.6323 51.4575 108.916 -121.601 128.221 163.052 112.005 103.033 119.908 15.7453 112.907 -80.4793 
Y 120.503 -160.909 93.6367 50.1077 110.499 -123.332 130.682 166.75 116.18 104.738 120.882 20.6042 112.397 -75.5913 
#8-state
A 94.6123 -142.592 91.8255 52.3547 121.966 -134.345 126.875 178.287 113.528 115.949 142.001 14.4754 103.983 -12.717 106.03 -93.3589 
C 98.9268 -138.745 93.3415 51.335 124.716 -150.001 126.582 172.58 118.118 110.089 141.607 25.5389 104.688 3.85059 111.748 -95.8014 
D 96.3154 -136.899 93.1097 52.8599 120.798 -133.248 115.621 178.488 113.116 112.698 125.968 18.8339 98.173 -13.8137 105.681 -91.0891 
E 95.6691 -137.628 92.3534 51.6901 123.23 -145.719 120.269 174.822 114.195 111.576 134.511 27.9801 103.415 -9.74292 106.282 -94.4051 
F 110.564 -124.05 93.2338 50.1603 115.88 -161.116 134.938 173.263 109.815 120.34 130.966 69.4875 116.797 13.6099 111.149 -80.8969 
G 94.3073 -123.737 93.8552 48.5422 128.621 -137.016 128.922 171.779 131.341 106.294 143.04 19.1464 99.81 -5.21642 107.357 -84.9479 
H 105.076 -121.485 93.6055 51.7506 115.9 -158.192 129.283 168.489 115.082 110.799 138.244 34.1728 102.92 14.721 110.472 -77.1978 
I 110.215 -125.258 92.3348 49.6552 117.893 -159.235 121.396 170.922 113.431 108.569 131.476 44.7112 108.167 17.915 110.953 -82.5558 
K 104.269 -124.383 92.4464 51.625 115.002 -156.756 121.791 168.429 112.981 113.354 132.572 61.5669 116.524 1.76568 109.349 -86.2063 
L 108.851 -125.677 92.2698 50.5198 117.227 -158.239 118.623 169.269 112.084 109.208 132.185 53.5213 108.509 12.7619 110.404 -86.9712 
M 107.368 -124.874 92.2016 51.0972 117.62 -158.489 128.939 171.898 111.675 116.283 131.441 72.191 118.933 2.4965 110.827 -87.3022 
N 96.2879 -136.346 93.8582 51.4682 122.033 -136.02 119.288 176.102 114.478 109.721 122.696 23.3028 95.7394 -8.84902 104.68 -90.5777 
P 109.406 -113.41 91.9029 43.5156 92.569 -143.407 121.136 -151.525 96.0474 174.158 94.2013 69.506 110.375 -22.7358 112.368 -83.952 
Q 96.6387 -140.78 92.2534 51.637 124.453 -148.263 121.503 172.678 115.858 110.754 137.922 32.8514 103.298 -2.7661 107.396 -96.4709 
R 95.318 -143.965 92.5162 51.4517 121.484 -138.133 124.397 178.384 113.925 114.469 135.493 28.9311 104.47 -15.0248 106.855 -97.0524 
S 113.871 -120.597 92.5101 53.5589 99.8139 -157.923 133.396 -172.568 117.48 139.466 117.169 97.2123 130.111 7.48609 110.052 -78.371 
T 115.496 -125.906 93.0839 51.1595 100.512 -167.541 131.315 -169.717 119.166 142.969 120.434 94.7169 120.994 18.8836 114.743 -80.3151 
V 113.457 -131.074 92.5702 48.9328 112.521 -162.322 130.641 -172.516 113.387 148.507 116.305 96.3342 123.265 21.9383 109.029 -90.4461 
W 110.285 -125.911 92.6465 51.0819 103.112 -168.161 132.408 -168.583 118.281 142.543 111.743 94.1032 119.45 13.4451 111.473 -84.9727 
Y 112.329 -126.58 93.4964 49.7925 108.907 -165.095 133.999 -171.24 116.433 139.504 119.034 89.3166 119.805 18.3299 111.892 -79.7406 
#9-state
A 93.1619 -132.574 91.7104 52.3495 117.363 -126.13 127.604 -176.749 113.348 119.35 138.783 29.4551 124.207 -10.8164 114.525 -84.9074 94.2147 -25.5797 
R 93.9707 -134.705 92.5832 51.4928 118.989 -129.979 123.727 -176.108 114.019 117.527 134.179 38.4432 127.416 -7.47377 109.307 -87.5456 95.9786 -21.0435 
N 95.0633 -133.901 94.0716 50.3813 119.343 -130.285 119.674 -177.631 114.157 116.246 127.993 41.7033 124.962 0.00541651 104.978 -88.2849 94.1062 -12.2832 
D 95.6692 -135.37 92.8649 52.5513 119.485 -129.947 115.802 -178.196 112.453 115.541 125.372 45.3811 128.164 -0.85851 105.442 -88.6983 95.2611 -11.9953 
C 95.9593 -135.637 92.7242 51.4092 122.627 -133.338 125.044 -178.111 117.988 116.769 127.024 51.6842 131.338 0.100564 108.732 -89.592 97.9053 -5.67014 
Q 95.2607 -137.772 92.1929 51.6652 122.156 -135.532 122.399 -177.783 115.842 116.104 130.736 57.7454 135.26 2.72319 106.992 -90.5359 98.7838 -3.50431 
E 94.538 -136.671 92.2638 51.7273 121.367 -134.904 121.229 -177.717 113.276 117.252 129.616 61.9658 136.166 3.0111 105.318 -91.0033 100.288 -3.01524 
G 93.4474 -128.352 93.3865 50.0298 127.92 -131.423 129.368 178.224 124.363 118.8 138.792 68.7142 140.477 -5.22419 104.504 -88.7637 97.297 0.591079 
H 96.6451 -134.549 94.0822 50.6335 122.73 -136.89 123.748 -178.163 115.841 118.823 132.531 62.8434 138.505 0.615662 106.779 -86.5395 101.773 6.38216 
I 99.2374 -136.188 92.6318 49.4466 119.978 -141.059 120.652 -174.637 113.096 119.376 125.891 68.3208 133.853 8.92038 109.655 -90.8716 106.251 12.1523 
L 97.4974 -136.671 92.2701 50.4247 120.896 -141.485 119.123 -175.179 112.124 119.467 123.292 75.5518 133.9 8.71799 109.737 -94.4159 103.333 14.2574 
K 95.0839 -136.004 92.1759 51.8243 122.171 -138.975 119.557 -178.173 113.13 121.864 122.737 79.6645 136.302 5.94823 108.586 -94.0524 101.951 13.4272 
M 95.2499 -137.929 92.0081 51.2629 123.224 -140.711 123.656 -177.002 114.317 124.438 121.617 83.3793 137.934 6.08508 108.94 -93.8432 101.276 12.7038 
F 97.1302 -140.693 93.1961 50.3253 122.883 -142.432 125.827 -177.16 114.909 128.38 122.827 80.8948 138.165 11.4397 109.315 -93.3174 103.684 18.1711 
P 93.5157 -140.784 90.7953 50.6455 120.297 -133.536 106.524 179.626 94.537 151.062 108.664 83.9138 122.735 -24.8661 111.023 -94.1943 97.3589 12.6753 
S 93.5534 -137.901 92.3602 52.987 125.559 -137.948 125.722 178.72 110.211 137.686 116.748 91.8028 134.116 -14.3695 110.079 -93.4913 107.512 17.7119 
T 95.8298 -142.961 92.808 51.7774 124.349 -138.672 125.92 -179.187 112.498 137.739 122.526 90.5073 134.668 -9.78312 112.413 -95.03 109.857 23.9229 
W 97.0945 -144.263 92.1909 51.9425 124.204 -140.057 126.867 -177.545 110.959 136.183 117.539 90.4381 131.25 -14.6594 109.318 -96.0723 108.212 24.0442 
Y 98.9289 -147.359 92.9489 51.0996 124.293 -141.819 128.871 -176.757 112.196 136.782 120.881 87.6233 131.176 -13.7622 109.256 -95.5288 109.814 26.8517 
V 101.624 -150.503 92.0505 49.686 121.902 -143.508 125.062 -174.737 112.777 138.578 118.812 89.5561 128.121 -13.324 108.076 -99.5064 112.661 29.839 
#10-state
A 93.1619 -132.574 91.7104 52.3495 117.363 -126.13 127.604 -176.749 113.348 119.35 138.783 29.4551 122.546 -3.58498 116.648 -90.536 91.818 -10.8664 108.723 -60.8917 
R 93.9672 -134.929 92.562 51.6061 118.938 -131.182 123.727 -176.108 114.019 117.527 135.794 40.4765 125.934 -0.0267262 110.84 -94.6138 93.9919 -6.46064 106.29 -61.5399 
N 94.9983 -134.761 94.0805 50.9808 119.629 -132.834 119.639 -177.895 114.04 116.407 131.046 48.2295 124.418 5.75162 105.825 -98.6124 93.9972 -3.39954 102.85 -59.9759 
D 95.65 -137.363 92.8867 52.6905 119.972 -133.909 115.902 -178.815 112.071 116.049 128.171 55.2337 127.521 5.05057 105.123 -99.7147 94.8073 -4.93573 106.136 -61.2364 
C 95.9294 -138.19 92.848 51.1371 123.782 -138.914 125.146 -179.448 117.038 117.925 130.354 64.9793 130.164 6.6667 108.592 -102.029 98.5739 2.61605 111.113 -63.065 
Q 95.5766 -141.735 92.1775 51.737 123.128 -140.741 122.627 -179.555 114.668 117.651 130.253 69.9659 135.316 11.0133 105.746 -103.991 98.8904 5.49544 109.714 -63.1902 
E 95.1279 -142.604 92.182 51.9015 122.526 -140.875 121.807 179.932 112.101 118.846 128.111 73.2797 136.048 12.5245 103.713 -104.304 100.816 8.0249 109.322 -64.2595 
G 93.3389 -136.489 93.1005 51.7806 128.47 -136.759 130.479 175.172 120.691 120.757 138.567 79.185 139.727 6.39039 101.078 -105.621 96.3351 11.0847 110.282 -58.2316 
H 97.66 -143.947 93.7442 51.6636 124.065 -142.484 125.158 179.016 113.593 120.699 132.048 73.2963 137.938 13.4043 104.834 -104.108 101.973 15.1509 109.011 -60.8477 
I 101.22 -148.008 92.4657 49.7831 121.12 -146.251 121.568 -177.457 112.205 121.594 123.616 77.0259 133.299 18.7733 107.664 -107.65 105.234 20.9123 111.412 -62.5328 
L 99.2768 -150.349 92.1136 50.6029 121.959 -146.155 120.692 -178.471 111.514 122.428 119.404 82.448 133.587 19.4637 107.62 -109.846 102.686 22.975 111.958 -63.6445 
K 95.5825 -149.432 91.9891 52.0005 123.332 -143.794 122.3 178.429 112.627 124.465 118.333 85.3515 136.581 17.2008 105.535 -110.711 101.816 21.8561 110.236 -64.6483 
M 97.1732 -152.978 91.8942 51.3893 124.242 -146.008 126.217 179.854 113.838 126.871 117.561 88.0062 137.788 16.4527 107.063 -110.395 101.117 21.6151 109.655 -66.2858 
F 100.005 -156.466 92.8653 50.8711 124.179 -147.438 129.342 179.483 114.02 131.265 118.883 86.0735 138.043 21.8581 107.486 -111.005 103.042 23.505 111.06 -66.66 
P 94.1316 -158.35 90.714 51.2048 121.012 -141.028 118.486 179.856 93.7572 154.621 107.908 86.1421 124.127 -10.1248 108.024 -109.689 97.0345 17.1801 113.148 -72.8239 
S 94.6431 -154.106 92.2582 53.3503 124.685 -140.978 132.012 175.271 106.06 142.407 115.47 94.2819 136.055 -0.174019 107.49 -110.717 102.16 19.8496 112.254 -73.2879 
T 97.8944 -159.86 92.7988 52.1055 124.873 -143.183 132.686 177.665 107.404 145.556 121.168 94.8735 137.65 15.8765 109.341 -111.678 104.083 22.9629 115.495 -72.0976 
W 100.371 -162.487 92.2682 52.1692 124.425 -146.036 133.655 179.633 107.981 144.422 115.43 96.7307 137.748 14.2222 106.468 -112.522 103.25 21.5053 113.295 -69.982 
Y 103.353 -163.413 93.1758 51.1665 124.353 -147.496 134.332 179.698 108.933 143.545 118.05 95.2547 138.255 23.7079 106.753 -113.178 103.271 23.0929 113.095 -67.5358 
V 106.642 -165.299 92.2602 49.758 122.256 -149.255 130.572 -178.357 111.09 145.187 117.068 96.314 134.222 28.0354 106.881 -115.257 104.482 25.6682 113.572 -69.2161