SSIA - Simulation of Sterically Induced Alignment Tensor
(C) M. Zweckstetter, 1999


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DESCRIPTION for Version 2000.040.11.27

SSIA is a program for predicting the magnitude and orientation of a sterically induced alignment tensor from a solute's (protein or DNA/RNA) three-dimensional shape. There are three different modes:
  1. Prediction of dipolar coupling tensor for a PDB structure (no measured dipolar couplings are available). Usage and example: 
             

SSIA [pdbFileName]
SSIA 1IGD_H_s.pdb
  2. Prediction of dipolar coupling tensor for a PDB structure, with comparison of measured and predicted residual dipolar couplings. Usage and example: 
             

SSIA -D[dipolarFileName] [pdbFileName]
SSIA -Ddc_1igd.txt 1IGD_H_s.pdb
  3. Advanced mode (allowing adjustment of various simulation parameters). Usage and example: 
             

SSIA -A[paramFileName] -D[dipolarFileName] [pdbFilename]
SSIA -Apredict.inp -Ddc_1igd.txt 1IGD_H_s.pdb

REFERENCE

Markus Zweckstetter and Ad Bax (submitted) Journal of the American Chemical Society

PDB FORMAT REQUIREMENTS

In principal, both PDB files from XPLOR and MOLMOL can be used; however, the following requirements exist as far as the file format is concerned:

DIPOLAR COUPLING INPUT FORMAT

The dipolar coupling input format is a text file of three columns:
  1. Residue number
  2. Residual dipolar coupling [Hz]
  3. Dipolar coupling identification code:
    N(i) to HN(i) 0
    CA(i) to HA(i) 1
    CA(i) to CO(i) 2
    CO(i-1) to N(i) 3
    CO(i-1) to HN(i) 4

An excerpt of a dipolar coupling table is shown here: 

    2     8.17   0
    3    -8.27   0
    2     5.60   1
    3     8.98   1
    2     0.61   2
    3    -1.05   2
    2    -0.82   3
    3     2.11   3
    2     1.61   4
    3    -2.93   4
IMPORTANT: the sign of N(i) to HN(i) and CO(i-1) to N(i) dipolar couplings has to be supplied correctly, i.e. the negative sign of the gyromagnetic ratio of 15N has to be taken into account. Therefore:

N(i) to HN(i) isotropic - aligned
CO(i-1) to N(i) isotropic - aligned
CA(i) to HA(i) aligned - isotropic
CA(i) to CO(i) aligned - isotropic
CO(i-1) to HN(i) aligned - isotropic

NOTE: missing dipolar couplings can be accommodated by supplying a dummy value greater than 1000Hz in the dipolar coupling input file; in these cases, SSIA will still calculate a predicted coupling (e.g. '17 5000 1' would allow prediction of the missing CA(i) to HA(i) coupling for residue 17).

PARAMETER FILE FORMAT FOR ADVANCED MODE


The parameter file allows adjustment of various simulation parameters. The format of this parameter file (e.g. predict.inp) is as follows: 

ANISOTROPIC_MEDIUM:   1 
LIPID_CONCENTRATION:  0.05 
GRID_SPACING:         0.5
DIGIT_BETA:           9
DIGIT_GAMMA:          18
DIGIT_ALPHA:          18
ATOM_RADIUS:          3.0
SELECT_FLAG:          1
PROTON_FLAG:          0
NHerror:              1.5
PRINT_EIGEN:          2

The keywords in the parameter file are CASE SENSITIVE.
The meaning of the parameters follows:

ANISOTROPIC_MEDIUM Bicelle/Phage selection
1 bicelle
2 phage
LIPID_CONCENTRATION Total lipid/phage concentration [g/ml]
GRID_SPACING Spacing of translational grid [Angstr.]
(default: 0.2)
DIGIT_BETA Digitization of Euler angle beta (180 [deg.] / DIGIT_BETA)
(default: 9)
DIGIT_GAMMA Digitization of Euler angle gamma (360 [deg.] / DIGIT_GAMMA)
(default: 18)
DIGIT_ALPHA Digitization of Euler angle alpha (360 [deg.] / DIGIT_ALPHA)
(default: 18)
ATOM_RADIUS Radius of atoms selected with 'SELECT_FLAG: 2' when testing for allowed orientations
SELECT_FLAG Removal of part of atomic structure:
0Only 'PROTON_FLAG:' is active (default)
1 Removal of certain residues (the program asks for the residues)
2Selection of certain atom type (e.g. CA atom index: 114) (the program asks for the atom index) (see APPENDIX for list of atom indices)
PROTON_FLAG Inclusion of protons:
0Only heavy atoms (default)
1All atoms
NHerror Esimated error for N(i) to HN(i) dipolar couplings used in SVD module (error is scaled for other types of dipolar couplings)
(default: 1.5 Hz)
PRINT_EIGEN Flag for printing order matrix and eigensystem:
0Do not print order matrix and eigensystem (default)
1Print eigenvectors and eigenvalues
2Print order matrix and eigensystem

EXPLANATION OF OUTPUT

All results are written to standard output.

When supplied with a dipolar coupling file, SSIA will predict and report two complete sets of dipolar couplings. The first set will be calculated according to the predicted sterically induced alignment tensor. The second set will be calculated according to the best-fit method of Prestegard et al. (a minimum of 5 dipolar couplings are required). This best-fit method, using order matrix analysis of residual dipolar couplings via singular value decomposition, is described in: J.A. Losonczi, M. Andrec, M.W.F. Fischer and J.H. Prestegard (1999), JMR 138, 334-342.

A given alignment tensor is characterized as follows:

Statistics were computed according to methods given in:

W.H. Press, S.A. Teukolsky, B.P. Flannery and W.T. Vetterling: Numerical Recipies in C Cambridge, Cambridge University Press, 1988

IMPLEMENTATION

SSIA is written in the C programming language.

TIMING

On an SGI R10000 OCTANE workstation the simulation typically takes less than a second.

TEST FILES

1IGD_H_s.pdb PDB file of the protein G domain (shortened by 5 residues and protons added with MOLMOL)
dc_1igd.txt File with measured D(N-HN) dipolar couplings
predict.inp Configuration file

EXAMPLE SESSION 

% SSIA -Ddc_1igd.txt 1IGD_H_s.pdb

 *------------------------------------------------------------------*
 |             SSIA                      (C) M. Zweckstetter 1999   |
 *------------------------------------------------------------------*

bicelle (1) or phage (2): 1
total lipid/phage concentration [g/ml]: 0.05

Simulation
==========

Magnitude of alignment tensor
==============================
Da(NH) =  8.9 [Hz]     R = Dr/Da = 0.181

Orientation of alignment tensor
(Euler angles [deg.] for 4 equivalent orientations)
==================================================
alpha   :   321.97   141.97   218.03    38.03  
beta    :   128.59   128.59    51.41    51.41  
gamma   :    48.84    48.84   228.84   228.84  

Comparison of predicted residual dipolar couplings with measured ones [Hz]
==========================================================================
[statistics over all dipolar couplings normalized to 1D(NH)]
rmsd: 0.87 [Hz]   corr r = 1.00   Q = 0.12
linear regression:      offset: 0.79 +/- 0.14 [Hz]  slope: 0.98 +/- 0.01

resid  [DC type]    predicted    measured     pred. - meas.
-----  ---------    ---------    --------     -------------
 7        [0]        p:     0.11   m:   -1.46     diff:   1.58
 8        [0]        p:    -7.62   m:   -7.06     diff:  -0.57
 9        [0]        p:    -7.20   m:   -8.65     diff:   1.45
10        [0]        p:   -11.08   m:  -12.18     diff:   1.10
12        [0]        p:   -10.27   m:  -12.69     diff:   2.43
13        [0]        p:    -4.61   m:   -5.20     diff:   0.59
17        [0]        p:   -10.57   m:  -11.68     diff:   1.11
19        [0]        p:   -11.14   m:  -10.55     diff:  -0.58
20        [0]        p:   -10.03   m:  -11.15     diff:   1.12
21        [0]        p:   -10.39   m:  -11.01     diff:   0.62
22        [0]        p:    -8.00   m:   -8.87     diff:   0.87
23        [0]        p:    -5.51   m:   -5.52     diff:   0.01
24        [0]        p:    -5.92   m:   -5.65     diff:  -0.27
25        [0]        p:    -4.74   m:   -4.17     diff:  -0.57
26        [0]        p:    -4.27   m:   -4.80     diff:   0.53
27        [0]        p:     4.71   m:    4.29     diff:   0.42
28        [0]        p:     2.76   m:    2.33     diff:   0.43
29        [0]        p:    15.36   m:   13.43     diff:   1.93
30        [0]        p:    12.57   m:   10.60     diff:   1.97
31        [0]        p:     6.84   m:    5.41     diff:   1.43
33        [0]        p:    16.78   m:   16.16     diff:   0.62
35        [0]        p:     8.50   m:    8.66     diff:  -0.16
36        [0]        p:    14.98   m:   13.97     diff:   1.01
37        [0]        p:    16.67   m:   16.04     diff:   0.63
38        [0]        p:    12.79   m:   12.05     diff:   0.74
39        [0]        p:    10.49   m:    9.61     diff:   0.89
40        [0]        p:    16.46   m:   15.70     diff:   0.77
41        [0]        p:    14.87   m:   15.09     diff:  -0.22
42        [0]        p:     4.19   m:    3.69     diff:   0.50
43        [0]        p:     6.72   m:    8.06     diff:  -1.34
49        [0]        p:    -9.26   m:  -11.68     diff:   2.41
50        [0]        p:   -11.00   m:  -11.81     diff:   0.81
51        [0]        p:    -9.70   m:  -10.76     diff:   1.06
52        [0]        p:   -10.66   m:  -11.04     diff:   0.39
54        [0]        p:    -0.30   m:   -2.46     diff:   2.16
55        [0]        p:    -7.47   m:   -8.51     diff:   1.04
56        [0]        p:    -9.06   m:   -9.37     diff:   0.31
57        [0]        p:   -10.91   m:  -11.59     diff:   0.69
58        [0]        p:    -8.98   m:  -10.15     diff:   1.17
59        [0]        p:   -10.07   m:  -12.22     diff:   2.15
61        [0]        p:    -9.27   m:  -11.62     diff:   2.35
17        [1]        p:    21.02   m:     --      diff:    --

SVD
===
# of DC: 41
Predicted residual dipolar couplings not within the experimental range:

Magnitude of alignment tensor
==============================
Da(NH) =  9.0 [Hz]     R = Dr/Da = 0.252

Orientation of alignment tensor
(Euler angles [deg.] for 4 equivalent orientations)
==================================================
alpha   :   313.39   133.39   226.61    46.61  
beta    :   126.17   126.17    53.83    53.83  
gamma   :    53.55    53.55   233.55   233.55  

Comparison of predicted residual dipolar couplings with measured ones [Hz]
==========================================================================
[statistics over all dipolar couplings normalized to 1D(NH)]
rmsd: 0.65 [Hz]   corr r = 1.00   Q = 0.07
linear regression:      offset: 0.15 +/- 0.11 [Hz]  slope: 1.00 +/- 0.01

resid  [DC type]    predicted    measured     pred. - meas.
-----  ---------    ---------    --------     -------------
 7        [0]        p:    -0.85   m:   -1.46     diff:   0.61
 8        [0]        p:    -6.33   m:   -7.06     diff:   0.73
 9        [0]        p:    -7.67   m:   -8.65     diff:   0.98
10        [0]        p:   -12.10   m:  -12.18     diff:   0.08
12        [0]        p:   -11.93   m:  -12.69     diff:   0.77
13        [0]        p:    -5.62   m:   -5.20     diff:  -0.42
17        [0]        p:   -12.17   m:  -11.68     diff:  -0.50
19        [0]        p:   -11.96   m:  -10.55     diff:  -1.41
20        [0]        p:   -11.25   m:  -11.15     diff:  -0.10
21        [0]        p:   -11.38   m:  -11.01     diff:  -0.37
22        [0]        p:    -7.89   m:   -8.87     diff:   0.98
23        [0]        p:    -5.40   m:   -5.52     diff:   0.11
24        [0]        p:    -5.52   m:   -5.65     diff:   0.13
25        [0]        p:    -4.65   m:   -4.17     diff:  -0.47
26        [0]        p:    -4.39   m:   -4.80     diff:   0.41
27        [0]        p:     3.73   m:    4.29     diff:  -0.57
28        [0]        p:     1.71   m:    2.33     diff:  -0.61
29        [0]        p:    14.93   m:   13.43     diff:   1.49
30        [0]        p:    11.47   m:   10.60     diff:   0.87
31        [0]        p:     5.78   m:    5.41     diff:   0.37
33        [0]        p:    16.48   m:   16.16     diff:   0.32
35        [0]        p:     7.47   m:    8.66     diff:  -1.19
36        [0]        p:    14.78   m:   13.97     diff:   0.81
37        [0]        p:    16.14   m:   16.04     diff:   0.10
38        [0]        p:    11.77   m:   12.05     diff:  -0.27
39        [0]        p:     9.63   m:    9.61     diff:   0.02
40        [0]        p:    16.27   m:   15.70     diff:   0.57
41        [0]        p:    14.00   m:   15.09     diff:  -1.09
42        [0]        p:     3.14   m:    3.69     diff:  -0.54
43        [0]        p:     8.59   m:    8.06     diff:   0.52
49        [0]        p:   -10.63   m:  -11.68     diff:   1.05
50        [0]        p:   -11.50   m:  -11.81     diff:   0.31
51        [0]        p:   -10.51   m:  -10.76     diff:   0.25
52        [0]        p:   -11.38   m:  -11.04     diff:  -0.33
54        [0]        p:    -1.69   m:   -2.46     diff:   0.76
55        [0]        p:    -8.58   m:   -8.51     diff:  -0.06
56        [0]        p:    -9.19   m:   -9.37     diff:   0.18
57        [0]        p:   -11.02   m:  -11.59     diff:   0.58
58        [0]        p:   -10.50   m:  -10.15     diff:  -0.35
59        [0]        p:   -11.66   m:  -12.22     diff:   0.56
61        [0]        p:   -10.79   m:  -11.62     diff:   0.83
17        [1]        p:    23.72   m:     --      diff:    --

APPENDIX

SSIA uses a a database of atom types; any atom not listed in this database will be ignored during the simulation. Allowable atom types and index values follows: 

 C     1
 C1    2
 C1'   3
 C1'A  4
 C1'C  5
 C1'N  6
 C10   7
 C11   8
 C12   9
 C13  10
 C14  11
 C15  12
 C16  13
 C17  14
 C18  15
 C19  16
 C1A  17
 C1B  18
 C1C  19
 C1D  20
 C1M  21
 C2   22
 C2'  23
 C2'A 24
 C2'C 25
 C2'N 26
 C20  27
 C21  28
 C210 29
 C211 30
 C212 31
 C213 32
 C214 33
 C215 34
 C216 35
 C22  36
 C23  37
 C24  38
 C25  39
 C26  40
 C27  41
 C28  42
 C29  43
 C2A  44
 C2B  45
 C2C  46
 C2D  47
 C2N  48
 C3   49
 C3'  50

 C3'A 51
 C3'C 52
 C3'N 53
 C30  54
 C31  55
 C310 56
 C311 57
 C312 58
 C313 59
 C314 60
 C315 61
 C316 62
 C32  63
 C33  64
 C34  65
 C35  66
 C36  67
 C37  68
 C38  69
 C39  70
 C3A  71
 C3B  72
 C3C  73
 C3D  74
 C3N  75
 C4   76
 C4'  77
 C4'A 78
 C4'C 79
 C4'N 80
 C40  81
 C41  82
 C42  83
 C43  84
 C44  85
 C45  86
 C46  87
 C4A  88
 C4B  89
 C4C  90
 C4D  91
 C4N  92
 C5   93
 C5'  94
 C5'A 95
 C5'C 96
 C5'N 97
 C5A  98
 C5C  99
 C5M 100

 C5N 101
 C6  102
 C6A 103
 C6C 104
 C6N 105
 C7  106
 C7M 107
 C7N 108
 C8  109
 C8A 110
 C8M 111
 C9  112
 C9A 113
 CA  114
 CAA 115
 CAB 116
 CAC 117
 CAD 118
 CAL 119
 CAY 120
 CB  121
 CB1 122
 CB2 123
 CBA 124
 CBB 125
 CBC 126
 CBD 127
 CC  128
 CD  129
 CD1 130
 CD2 131
 CE  132
 CE1 133
 CE2 134
 CE3 135
 CED 136
 CF  137
 CF3 138
 CG  139
 CG1 140
 CG2 141
 CG3 142
 CGA 143
 CGD 144
 CH2 145
 CH3 146
 CHA 147
 CHB 148
 CHC 149
 CHD 150

 CL   151
 CL1  152
 CLP  153
 CM   154
 CM1  155
 CM10 156
 CM2  157
 CM3  158
 CM4  159
 CM5  160
 CM6  161
 CM7  162
 CM8  163
 CM9  164
 CMA  165
 CMB  166
 CMC  167
 CMD  168
 CP1  169
 CP10 170
 CP11 171
 CP12 172
 CP13 173
 CP14 174
 CP15 175
 CP16 176
 CP17 177
 CP18 178
 CP19 179
 CP2  180
 CP20 181
 CP3  182
 CP4  183
 CP5  184
 CP6  185
 CP7  186
 CP8  187
 CP9  188
 CR   189
 CRP  190
 CT   191
 CY   192
 CZ   193
 CZ2  194
 CZ3  195
 Cl   196
 FC1  197
 FC2  198
 FC3  199
 N1C  200

 N3C  201
 N4C  202
 NC   203
 O2'C 204
 O2C  205
 O3'C 206
 O4'C 207
 O5'C 208
 1NE2 209
 1ZN  210
 N    211
 N1   212
 N10  213
 N1A  214
 N1N  215
 N2   216
 N3   217
 N3A  218
 N4   219
 N5   220
 N6   221
 N6A  222
 N7   223
 N7A  224
 N7N  225
 N9   226
 N9A  227
 NA   228
 NB   229
 ND   230
 ND1  231
 ND2  232
 NE   233
 NE1  234
 NE2  235
 NH1  236
 NH2  237
 NL   238
 NR   239
 NT   240
 NZ   241
 NZ1  242
 Na   243
 O1PN 244
 O2'N 245
 O2PN 246
 O3'N 247
 O4'N 248
 O5'N 249
 O7N  250

 PN   251
 ZN   252
 O    253
 O1   254
 O10  255
 O11  256
 O12  257
 O13  258
 O14  259
 O1A  260
 O1B  261
 O1D  262
 O1P  263
 O1PA 264
 O2   265
 O2'  266
 O2'A 267
 O21  268
 O22  269
 O2A  270
 O2D  271
 O2P  272
 O2PA 273
 O3   274
 O3'  275
 O3'A 276
 O31  277
 O32  278
 O3P  279
 O4   280
 O4'  281
 O4'A 282
 O5   283
 O5'  284
 O5'A 285
 O6   286
 O7   287
 O8   288
 O9   289
 OBB  290
 OBD  291
 OD1  292
 OD2  293
 OE1  294
 OE2  295
 OF   296
 OF1  297
 OF2  298
 OF3  299
 OG   300

 OG1  301
 OG2  302
 OG3  303
 OH   304
 OH1  305
 OH2  306
 OH3  307
 OL   308
 OM   309
 OR   310
 OS1  311
 OS2  312
 OS3  313
 OS4  314
 OY   315
 SOD  316
 S    317
 S2   318
 S3   319
 SD   320
 SG   321
 FE   322
 MG   323
 P    324
 P1   325
 PA   326
 PF   327
 YB   328
 H    551
 H1   330
 H1'  331
 H10  332
 H101 333
 H102 334
 H10R 335
 H10S 336
 H10X 337
 H10Y 338
 H11  339
 H111 340
 H112 341
 H113 342
 H11A 343
 H11B 344
 H11R 345
 H11S 346
 H11X 347
 H11Y 348
 H12  349
 H121 350

 H122 351
 H123 352
 H12A 353
 H12B 354
 H12R 355
 H12S 356
 H12T 357
 H12X 358
 H12Y 359
 H12Z 360
 H13  361
 H13A 362
 H13B 363
 H13C 364
 H13R 365
 H13S 366
 H13X 367
 H13Y 368
 H14A 369
 H14B 370
 H14C 371
 H14R 372
 H14S 373
 H14T 374
 H14X 375
 H14Y 376
 H14Z 377
 H15A 378
 H15B 379
 H15C 380
 H15R 381
 H15S 382
 H15X 383
 H15Y 384
 H16R 385
 H16S 386
 H16T 387
 H16X 388
 H16Y 389
 H16Z 390
 H2   391
 H2'  392
 H2'' 393
 H2'A 394
 H2'C 395
 H2'N 396
 H21  397
 H211 398
 H212 399
 H213 400

 H22  401
 H23  402
 H2R  403
 H2S  404
 H2X  405
 H2Y  406
 H3   407
 H3'  408
 H3'A 409
 H3'N 410
 H31  411
 H32  412
 H33  413
 H3R  414
 H3S  415
 H3T  416
 H3X  417
 H3Y  418
 H4   419
 H4'  420
 H41  421
 H41C 422
 H42  423
 H42C 424
 H43  425
 H4R  426
 H4S  427
 H4X  428
 H4Y  429
 H5   430
 H5'  431
 H5'' 432
 H51  433
 H52  434
 H53  435
 H5R  436
 H5S  437
 H5T  438
 H5X  439
 H5Y  440
 H6   441
 H61  442
 H61A 443
 H62  444
 H62A 445
 H63  446
 H6R  447
 H6S  448
 H6X  449
 H6Y  450

 H7   451
 H71  452
 H71N 453
 H72  454
 H72N 455
 H73  456
 H7R  457
 H7S  458
 H7X  459
 H7Y  460
 H8   461
 H81  462
 H82  463
 H83  464
 H8R  465
 H8S  466
 H8X  467
 H8Y  468
 H9   469
 H91  470
 H92  471
 H9R  472
 H9S  473
 H9X  474
 H9Y  475
 HA   476
 HA1  477
 HA2  478
 HA3  479
 HAA1 480
 HAA2 481
 HAB  482
 HAC  483
 HAD1 484
 HAD2 485
 HB   486
 HB1  487
 HB2  488
 HB3  489
 HBA1 490
 HBA2 491
 HBB1 492
 HBB2 493
 HBC1 494
 HBC2 495
 HBD1 496
 HBD2 497
 HC   498
 HC1  499
 HC2  500

 HC3  501
 HD   502
 HD1  503
 HD11 504
 HD12 505
 HD13 506
 HD2  507
 HD21 508
 HD22 509
 HD23 510
 HD3  511
 HE   512
 HE1  513
 HE2  514
 HE21 515
 HE22 516
 HE3  517
 HG   518
 HG1  519
 HG11 520
 HG12 521
 HG13 522
 HG2  523
 HG21 524
 HG22 525
 HG23 526
 HG31 527
 HG32 528
 HH   529
 HH11 530
 HH12 531
 HH2  532
 HH21 533
 HH22 534
 HL   535
 HL1  536
 HL2  537
 HL3  538
 HMA1 539
 HMA2 540
 HMA3 541
 HMB1 542
 HMB2 543
 HMB3 544
 HMC1 545
 HMC2 546
 HMC3 547
 HMD1 548
 HMD2 549
 HMD3 550

 HN   551
 HN1  552
 HN2  553
 HN3  554
 HN5  555
 HO   556
 HO1  557
 HO2  558
 HO3  559
 HO4  560
 HO6  561
 HO7  562
 HO8  563
 HO9  564
 HR   565
 HR1  566
 HR2  567
 HR3  568
 HS   569
 HT   570
 HT1  571
 HT2  572
 HX   573
 HY   574
 HY1  575
 HY2  576
 HY3  577
 HZ   578
 HZ1  579
 HZ11 580
 HZ12 581
 HZ13 582
 HZ2  583
 HZ3  584
 1HG  585
 1HG1 586
 2HG  587
 2HG1 588
 OXT  -1
 OT1  -2
 OT2  -3
 OT3  -4
 1HA  1000
 2HA  1000
 1HB  1000
 2HB  1000
 3HB  1000
 1HG  1000
 2HG  1000
 1HG1 1000
 2HG1 1000
 3HG1 1000
 1HG2 1000
 2HG2 1000
 3HG2 1000
 1HE  1000
 2HE  1000

 3HE  1000
 1HE2 1000
 2HE2 1000
 1HD  1000
 2HD  1000
 1HD1 1000
 2HD1 1000
 3HD1 1000
 1HD2 1000
 2HD2 1000
 3HD2 1000
 1HZ  1000
 2HZ  1000
 3HZ  1000
 1HH1 1000
 2HH1 1000
 1HH2 1000
 2HH2 1000
 1HT  1000
 2HT  1000
 3HT  1000
 1H   330
 2H   391
 3H   407
 X    0
 QB   0