Development of a Polarizable Force Field For Proteins via Ab Initio Quantum Chemistry: First Generation Model and Gas Phase Tests
George A. Kaminski, Harry A. Stern, B. J. Berne, and Richard A. Friesner
Department of Chemistry, Columbia University, New York, New York 10027
Yixiang X. Cao, Robert B. Murphy, Ruhong Zhou, and Thomas A. Halgren,
Shrödinger, Inc., 120 West 45th Street, Tower 45, 8th Floor, New York, NY 10036
Supporting Materials
Listed below are parameters for all the dipeptides, also used in the alanine tetrapeptide and PDB proteins. Values for the parameters that are not listed (bond stretching, angle bending, some torsional parameters) are taken directly from the OPLS-AA (Jorgensen, W.L.; Maxwell D.S.; TiradoRives, J. J. Am. Chem. Soc., 1996, 113, 11225-11236).
All the di- and tetrapeptide backbone parameters are the same, taken from the alanine dipeptide set with no further adjustments.
Table S1. Lennard-Jones Parameters
Atom
/ s, Å / e, kcal/molCT, CT1, CP1 / 3.50 / 0.066
C, CG1, CO3 / 3.75 / 0.105
HC / 2.50 / 0.030
N / 3.30 / 0.280
O / 3.16 / 0.280
OH / 3.25 / 0.280
CA, CR, CV, CW, C*, CB9, CN, CX / 3.55 / 0.070
HA / 2.42 / 0.030
SH, S / 3.60 / 0.425
NA, NB / 3.25 / 0.170
OH6 / 3.20 / 0.190
O2 / 2.96 / 0.210
N3A / 3.00 / 0.080
NA, protonated histidine / 3.05 / 0.160
CA8 / 2.25 / 0.050
N2 / 3.20 / 0.100
Table S2. Torsional Parameters, kcal/mol
Angle
/ V1 / V2 / V3Alanine and all backbones
C-N-CT1-CT / -2.485 / 1.191 / -0.773
C-CT1-N-C / -0.330 / -1.113 / 1.276
N-C-CT1-N / -6.976 / 2.821 / -0.613
CT-CT1-C-N / -3.642 / 0.519 / 0.382
Serine
N-CT1-CT-OH / -2.165 / 1.510 / 0.580
CT1-CT-OH-HO / 1.502 / -1.728 / 1.581
C-CT1-CT-OH / -4.700 / -1.110 / 0.194
Phenylalanine
CA-CA-CT-CT1 / -0.530 / 0.519 / -1.744
C-CT1-CT-CA / 1.315 / 0.578 / -0.741
CA-CT-CT1-N / -2.221 / 2.173 / -0.301
Cysteine
N-CT1-CT-SH / -6.995 / 1.715 / -0.860
CT1-CT-SH-HS / -1.201 / -1.809 / 0.832
C-CT1-CT-SH / -6.647 / -0.703 / 0.962
Asparagine
C-CT-CT1-N / 5.632 / 3.182 / 4.353
CT1-CT-C-N / -3.060 / -0.115 / -0.418
C-CT-CT1-C / -2.114 / 0.935 / -2.618
Glutamine
CT-CT-CT1-N / 3.925 / 0.958 / -3.374
C-CT-CT-CT1 / -0.733 / -0.517 / 0.037
C-CT1-CT-CT / 0.539 / 1.424 / 4.422
CT-CT-C-N / -0.471 / -0.431 / -0.078
Histidine
CV-CT-CT1-N / -1.116 / 0.691 / -0.173
CT1-CT-CV-NB / 0.061 / 0.231 / -0.362
CT1-CT-CV-CW / 0.000 / 0.000 / 0.000
C-CT1-CT-CV / -1.944 / -0.466 / 0.012
Leucine
CT-CT-CT1-N / 5.246 / 0.874 / -2.843
C-CT1-CT-CT / 1.509 / 0.255 / 2.827
CT-CT-CT-CT1 / 0.335 / 0.302 / 0.141
Isoleucine
CT-CT-CT1-N / -5.102 / 2.334 / 1.578
C-CT1-CT-CT / -6.975 / 2.498 / -0.597
CT-CT-CT-CT1, CT-CT-CT-CT / 1.888 / -0.269 / 0.591
Valine
CT-CT-CT1-N / -6.039 / 1.446 / 0.286
C-CT1-CT-CT / -2.690 / 0.846 / 0.271
Methionine
CT-CT-CT1-N / -12.673 / 0.981 / -2.634
CT1-CT-CT-S / -0.430 / 0.135 / -0.173
C-CT1-CT-CT / -2.883 / 1.175 / 2.906
CT-CT-S-CT / -2.184 / -2.478 / 1.612
Tryptophan
C*-CT-CT1-N / -1.493 / 1.386 / -1.883
CT1-CT-C*-CW / -1.380 / 0.572 / 0.048
CB9-C*-CT-CT1 / 0.000 / 0.000 / 0.000
C-CT1-CT-C* / -1.079 / 0.419 / 1.849
Threonine
N-CT1-CT-OH / -9.964 / 0.906 / -2.414
CT1-CT-OH-HO / 1.502 / -1.728 / 1.581
C-CT1-CT-OH / -16.848 / 0.682 / 1.346
Tyrosine
CA-CT-CT1-N / 0.283 / 1.336 / -3.733
CA-CA-CT-CT1 / 0.000 / 0.000 / 0.000
C-CT1-CT-CA / -0.917 / 0.517 / 3.706
CA-CA-OH6-HO / 0.000 / 3.943 / 0.000
Aspartic Acid
CG1-CT-CT1-N / 3.712 / 1.813 / 0.301
CT1-CT-CG1-O2 / 0.000 / 0.695 / 0.000
C-CT1-CT-CG1 / -3.900 / 4.331 / -0.822
Glutamic Aced
CT-CT-CT1-N / -1.513 / 0.871 / 0.963
CO3-CT-CT-CT1 / -3.404 / 0.201 / 0.117
CT-CT-CO3-O2 / 0.000 / 0.820 / 0.000
C_CT1-CT-CT / -2.371 / 0.314 / 0.000
Lysine
CT-CT-CT1-N / -3.264 / -0.211 / 0.430
C-CT1-CT-CT / -1.027 / -0.426 / 0.133
CT-CT-CT-N3A / 2.144 / -1.352 / 2.069
Protonated Histidine
CX-CT-CT1-N / -5.864 / 1.304 / -0.513
CT1-CT-CX-NA / -0.139 / -0.558 / -1.320
CT1-CT-CX-CX / 0.000 / 0.000 / 0.000
C-CT1-CT-CX / -1.000 / 0.272 / 1.133
Agrinine
CT-CT-CT1-N / 2.359 / 0.813 / -0.568
CT-CT-CT-CT1 / -0.775 / 0.807 / -1.792
CT-CT-CT-N2 / 0.673 / 0.987 / -2.000
CA8-N2-CT-CT / -1.697 / 0.542 / 0.542
C-CT1-CT-CT / 2.416 / -0.689 / 1.860
Tables S3 and S4 list electrostatic parameters. Please note that we used a scaling factor of 1.0 for the electrostatic 1,4-interactions, unlike the 0.5 value for the van-der-Waals ones.
For the fixed bond charge increments – as an example – O236_X0 bci value of 0.326463 means an electron transfer from O to X (negative resulting charge on X)
Dipole c1 means internal electrostatic field, resulting in a point “permanent dipole” located on the first atom in the pair, dipole c2 means internal electrostatic field, resulting in a point “permanent dipole” located on the second atom in the pair. A positive c value means field producing a dipole directed toward the other atom in the pair, a negative value – away from the other atom.
Table S3. Fixed Bond Charge Increments, in e, and Dipole cs, in (kcal/mol)1/2·Å-3/2.
Atom Pair
/ Bond Charge Increment / Dipole c1 / c2Alanine
C135_C224 / 0.097985 / 0.607132 / 0.116592
C135_C235 / -0.0480366 / 0.153272 / 0.373441
C135_H140 / -0.110953 / -0.755875 / -
C224_C235 / -0.00735223 / -0.152324 / 0.279954
C224_H140 / -0.209973 / -2.04571 / -
C224_N238 / 0.208593 / 1.63831 / 0.396263
C235_N238 / -0.0327599 / 0.64934 / -0.0116159
C235_O236 / 0.227873 / -1.56473 / -
C242_H140 / -0.0998559 / -0.379682 / -
C242_N238 / 0.220074 / 0.273629 / 0.0340511
H241_N238 / 0.258316 / - / 0.56991
O236_X0 (lone pair) / 0.326463 / -
Serine
C157_C224 / 0.116725 / 2.18762 / -0.131951
C157_H140 / -0.136309 / 0.608399 / -
C157_O154 / -0.110053 / 0.643742 / -1.97661
H155_O154 / 0.122747 / -6.441 / -8.67218
O154_X0 / 0.600477 / -
Phenylalanine
C145_C149 / -0.0673306 / 0.000229846 / -0.000239204
C145_H146 / -0.102698 / 0.000403568 / -
C149_C224 / 0.0200496 / -0.00005505 / 0.00123112
C149_H140 / -0.0596082 / 0.000327497 / -
C145_C145 / - / -0.000633269
Cysteine
C206_C224 / -0.0534597 / 0.00563573 / -0.00236531
C206_H140 / -0.109281 / 0.0153869 / -
C206_S200 / 0.0903085 / -0.020398 / -0.00595555
H204_S200 / 0.130253 / - / 0.00719557
S200_X0 / 0.017169 / -
Asparagine
C136_C224 / 0.196372 / 0.977204 / -1.89449
C136_C235 / -0.13411 / -0.237043 / 1.45552
C136_H140 / -0.097974 / -0.418817 / -
C235_N237 / -0.102893 / 0.370868 / 3.17608
C235_O236 (side chain) / 0.273747 / -0.634036 / -
H240_N237 / 0.407637 / - / -0.298673
O236_X0 (side chain) / 0.240195 / -
Glutamine
C136_C224 / 0.0437679 / 0.0013247 / 0.00270597
C136_C235 / 0.164519 / -0.00533217 / 0.0133523
C136_H140 / 0.0337042 / 0.000494025 / -
C235_N237 / -0.196311 / 0.011942 / -0.00849117
C235_O236 (side chain) / 0.480364 / -0.0241726 / -
H240_N237 / 0.199717 / - / 0.00956328
O236_X0 (side chain) / 0.120912 / -
C136_C136 / - / 0.00306502
Histidine
C224_C505 / 0.0100364 / 0.00107392 / 0.00139211
C505_C507 / 0.0599774 / -0.00551098 / -0.00017132
C505_H140 / -0.0641425 / 0.00456435 / -
C506_H146 / -0.114389 / 0.0052744 / -
C506_N503 / -0.131173 / 0.00644356 / -0.00586025
C506_N511 / 0.191382 / -0.0120094 / 0.00528713
C507_C508 / -0.160069 / 0.000912032 / -0.0106541
C507_N511 / 0.0813819 / -0.000800828 / 0.00207551
C508_H146 / -0.102242 / 0.00826427 / -
C508_N503 / -0.0811045 / 0.00137659 / -0.00505754
H504_N503 / 0.161869 / - / 0.00916099
Leucine
C135_C137 / -0.146868 / 0.033175 / 0.000333922
C136_C137 / -0.124146 / 0.000621941 /0.0000245489
C136_C224 / 0.0166872 / -0.000208909 / -0.00630183
C136_H140 / -0.0678362 / -0.000535165 / -
C137_H140 / 0.116302 / -0.000450057 / -
Isoleucine
C135_C136 / 0.0 / 0.0 / 0.0
C135_C137 / -0.146868 / 0.033175 / 0.000333922
C136_C137 / -0.124146 / 0.000621941 / 0.0000245489
C136_C224 / 0.0166872 / -0.000208909 / -0.00630183
C136_H140 / -0.0678362 / -0.000535165 / -
C137_C224 / 0.0 / 0.0 / 0.0
C137_H140 / 0.116302 / -0.000450057 / -
Valine
C135_C137 / 0.0723389 / 1.23919 / 0.148709
C137_C224 / 0.104525 / -0.0868066 / -0.229779
C137_H140 / -0.00657239 / -0.0740794 / -
Methionine
C136_C210 / 0.0935418 / 1.38705 / 0.444529
C136_C224 / 0.0208381 / 0.801983 / 0.810454
C136_H140 / -0.162903 / -2.42772 / -
C209_H140 / -0.243665 / 0.291426 / -
C209_S202 / -0.155553 / 0.0724554 / 0.802467
C210_H140 / -0.125907 / -0.317935 / -
C210_S202 / 0.0600352 / -0.151669 / -1.37233
S202_X0 / 0.449691 / -
Proline
C136_C245 / 0.0729211 / 0.635282 / -0.233324
C136_C246 / 0.0957254 / 0.163052 / 0.216856
C136_H140 / -0.0532278 / -0.996827 / -
C235_C246 / -0.0176697 / 0.0542661 / -0.073014
C235_N239 / -0.0136698 / 1.0433 / 0.278585
C245_H140 / -0.0116227 / -0.321562 / -
C245_N239 / 0.26151 / 0.603253 / 0.288494
C246_H140 / -0.0779027 / -0.613241 / -
C246_N239 / 0.201598 / 0.52365 / -0.668299
C136_C136 / - / 0.234194
Tryptophan
C136_C224 / -0.00548767 / 0.000517722 / -0.000759049
C136_C500 / 0.0528376 / -0.00284223 / 0.000798661
C136_H140 / -0.0265289 / 0.00261878 / -
C145_C501 / -0.00191486 / 0.00572442 / -0.000158477
C145_C502 / 0.0173216 / -0.0015452 / -0.00160748
C145_H146 / -0.0768596 / 0.0000488274 / -
C500_C501 / 0.0772466 / -0.00130709 / 0.000248156
C500_C514 / -0.0572644 / 0.000327291 / -0.0000533602
C501_C502 / -0.0224854 / -0.0000905563 / -0.00552142
C502_N503 / -0.164221 / 0.00678851 / -0.0165872
C514_H146 / -0.063842 / 0.0000442391 / -
C514_N503 / -0.0521954 / 0.00000607413 / -0.0061889
H504_N503 / 0.241869 / - / 0.0196599
C145_C145 / - / -0.00465174
Threonine
C135_C158 / 0.112878 / 1.14045 / 0.737352
C158_C224 / 0.0992506 / 1.98056 / 0.588577
C158_H140 / -0.204639 / -2.43919 / -
C158_O154 / -0.10328 / -0.308812 / 3.56155
H155_O154 / 0.316595 / -1.58336 / -3.89152
O154_X0 / 0.239077 / -
Tyrosine
C145_C149 / -0.00579876 / -0.00000790066 / -0.00221347
C145_C166 / -0.0304862 / 0.00000958763 / -0.00378592
C145_H146 / -0.121312 / 0.0000371821 / -
C149_C224 / 0.0154813 / -0.00019629 / 0.00140221
C149_H140 / -0.0160531 / 0.00271868 / -
C166_O167 / 0.0325574 / 0.00219646 / -
H168_O167 / 0.254649 / -
O167_X0 / 0.159654 / -
C145_C145 / - / -0.0000376123
Aspartic Acid. Formal charge of –0.5 on O272
C224_C274 / -0.0977027 / 0.00507626 / -0.00648952
C271_C274 / 0.0304503 / 0.000875131 / 0.00783434
C271_O272 / 0.1368 / -0.000819109 / 0.00660001
C274_H140 / 0.0696202 / -0.00140657 / -
O272_X0 / 0.0748858 / -
Glutamic Acid. Formal charge of –0.5 on O272
C136_C224 / 0.0786512 / -0.00324192 / 0.00701377
C136_C274 / -0.0825442 / 0.0122969 / 0.0212826
C136_H140 / -0.0606561 / -0.0103197 / -
C271_C274 / 0.143842 / -0.135622 / -0.0297912
C271_O272 / 0.171253 / 0.124577 / -
C274_H140 / 0.0288231 / 0.0071406 / -
O272_X0 / 0.125131 / -
Lysine. Formal charge of +1.0 on N287
C136_C224 / 0.00763358 / -0.024419 / -0.0851402
C136_C292 / 0.0604499 / -0.0659708 / -0.053823
C136_H140 / -0.0343106 / -0.175439 / -
C292_H140 / -0.0282786 / 0.03601 / -
C292_N287 / 0.397861 / 0.0180809 / 0.114811
H290_N287 / 0.341731 / - / -0.113318
C136_C136 / - / 0.244323
Protonated Histidine. Formal charge of +0.5 on N512
C224_C505 / -0.0298412 / 0.32426 / 0.884187
C505_C510 / 0.185721 / 0.106838 / 0.0102203
C505_H140 / -0.15159 / -1.10232 / -
C509_H146 / -0.230999 / 0.0178131 / -
C509_N512 / 0.0689035 / -0.0214623 / -0.0158379
C510_H146 / -0.103774 / 0.0273401 / -
C510_N512 / 0.155405 / 0.0286613 / -0.0193385
H513_N512 / 0.297322 / - / 0.0208468
C510_C510 / - / -0.0858125
Arginine. Formal charge of +1.0 on C302
C136_C224 / -0.00283199 / 0.000661955 / -0.000863189
C136_C308 / -0.0342771 / 0.00201562 / -0.00164835
C136_H140 / 0.0592934 / -0.00287667 / -
C302_N300 / -0.10473 / 0.000889051 / -0.00918126
C302_N303 / 0.00782999 / -0.00082715 / -0.000867548
C307_C308 / -0.0918754 / 0.00793005 / -0.00502689
C307_H140 / 0.092882 / -0.0117669 / -
C307_N303 / -0.0280027 / 0.00315085 / -0.00211463
C308_H140 / -0.0876708 / 0.00743096 / -
H301_N300 / 0.217723 / - / 0.00991513
H304_N303 / 0.0997339 / - / 0.00312121
Table S4. Inverse Polarizabilities, Å-3
Atom / 1/aAlanine
C135 / 0.515642
C224 / 0.691837
C235 / 0.525854
C242 / 0.485997
N238 / 1.40464
Serine
C157 / 0.509135
H155 / 3.70039
O154 / 2.31814
Phenylalanine
C145 / 10.0
C149 / 10.0
Cysteine
C206 / 0.417752
S200 / 0.497968
Asparagine
C136 / 0.584073
N237 / 1.28334
Glutamine
C136 / 0.804315
N237 / 1.18945
Histidine
C505 / 0.391962
C506 / 0.758618
C507 / 5.70968
C508 / 0.719624
N503 / 1.01387
N511 / 1.01298
Leucine
C136 / 10.0
C137 / 10.0
Isoleucine
C136 / 10.0
C137 / 10.0
Valine
C137 / 1.71809
Methionine
C136 / 1.26937
C209 / 0.583708
C210 / 2.67492
S202 / 0.831939
Proline
C136 / 0.596225
C245 / 0.558897
C246 / 0.491165
N239 / 0.760093
Tryptophan
C136 / 0.312904
C145 / 0.69451
C500 / 2.19726
C501 / 12.5098
C502 / 0.798391
C514 / 100.0
N503 / 0.540221
Threonine
C158 / 1.1167
H155 / 3.08747
O154 / 1.63216
Tyrosine
C145 / 100.0
C149 / 0.30056
C166 / 0.312942
Aspartic Acid
C271 / 0.753218
C274 / 0.487163
O272 / 1.39829
Glutamic Acid
C136 / 1.51783
C271 / 0.301317
C274 / 0.631377
Lysine
C136 / 0.807484
C292 / 1.14114
N287 / 0.555973
Protonated Histidine
C505 / 0.57413
C509 / 0.870782
C510 / 0.882096
N512 / 1.41498
Arginine
C136 / 0.643049
C302 / 1.61209
C307 / 0.456629
C308 / 0.579122
N300 / 0.747804
N303 / 1.18755