Shen S., Tuszynski J.A. Theory and Mathematical Methods for Bioformatics

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404 14 Semantic Analysis for Protein Primary Structure

Table 14.2. Joint probability distribution of dipeptides (100.0 × p(a, b))

One-letter

code

ARNDCQEGHI

A 0.76537 0.39096 0.28178 0.37277 0.11765 0.29835 0.48523 0.55710 0.15979 0.43803

R 0.38201 0.36240 0.21778 0.27674 0.08674 0.21473 0.34813 0.33846 0.12562 0.30029

N 0.29388 0.20178 0.23192 0.21355 0.07119 0.16826 0.25486 0.30345 0.09457 0.28579

D 0.38088 0.25462 0.21765 0.30138 0.08013 0.17400 0.37399 0.36371 0.10670 0.34148

C 0.10631 0.08940 0.06923 0.08561 0.04366 0.06543 0.08956 0.12952 0.04489 0.08495

Q 0.31392 0.22679 0.17286 0.18411 0.06314 0.24227 0.26160 0.24338 0.09281 0.22321

E 0.50501 0.35878 0.30708 0.36572 0.09053 0.26458 0.57415 0.38987 0.13739 0.40062

G 0.51538 0.36239 0.28144 0.35612 0.11160 0.25190 0.41022 0.56177 0.15732 0.41570

H 0.15288 0.12318 0.09023 0.09877 0.04571 0.09565 0.11834 0.15805 0.07984 0.13083

I 0.44105 0.28904 0.27924 0.33045 0.10024 0.21637 0.36631 0.37594 0.13426 0.36708

L 0.76506 0.52405 0.41123 0.49989 0.15044 0.39975 0.60975 0.62532 0.21746 0.51781

K 0.43623 0.31970 0.29318 0.32832 0.08609 0.22728 0.45619 0.35329 0.12500 0.37411

M 0.21003 0.12093 0.10774 0.12880 0.03391 0.08653 0.15529 0.15487 0.05190 0.13134

F 0.27427 0.19538 0.18369 0.23432 0.07325 0.15431 0.23798 0.29506 0.09590 0.24714

P 0.37621 0.23453 0.19209 0.25548 0.07115 0.19636 0.35396 0.37597 0.11270 0.24024

S 0.49778 0.35150 0.29734 0.35345 0.12012 0.27642 0.39911 0.52118 0.15754 0.39264

T 0.43252 0.25090 0.22992 0.27473 0.09673 0.20075 0.32007 0.40910 0.12336 0.32815

W 0.08342 0.06732 0.05894 0.06386 0.02053 0.05210 0.06772 0.08240 0.02972 0.07087

Y 0.20324 0.17052 0.14609 0.17386 0.05816 0.13009 0.18654 0.22707 0.07535 0.18135

V 0.52862 0.32743 0.28030 0.36796 0.11328 0.23625 0.42456 0.42717 0.14048 0.39462

14.1 Semantic Analysis for Protein Primary Structure 405

Table 14.2. (continued)

One-letter

code

LKMFPSTWYV

A 0.77063 0.42322 0.17673 0.29664 0.34644 0.51443 0.41759 0.08361 0.21116 0.54317

R 0.49873 0.31285 0.11488 0.21685 0.23865 0.33371 0.25895 0.06568 0.17469 0.33757

N 0.40347 0.26204 0.09420 0.18662 0.24167 0.30913 0.23280 0.05646 0.15246 0.27861

D 0.51897 0.29412 0.11104 0.23785 0.26769 0.34573 0.26183 0.07013 0.19042 0.36284

C 0.15066 0.08859 0.03041 0.06904 0.08920 0.12561 0.08722 0.02347 0.05353 0.10264

Q 0.38655 0.23968 0.08844 0.14327 0.19435 0.23981 0.20613 0.04958 0.11866 0.25011

E 0.60379 0.47997 0.14805 0.23310 0.23898 0.36464 0.33464 0.07261 0.18995 0.41787

G 0.61366 0.42341 0.15387 0.29662 0.29043 0.49632 0.38941 0.09033 0.23280 0.47256

H 0.22857 0.10892 0.04632 0.10621 0.13912 0.15904 0.12174 0.03050 0.08222 0.13916

I 0.54553 0.35519 0.11761 0.24300 0.29385 0.42543 0.34235 0.06332 0.18572 0.38177

L 0.97237 0.58216 0.19742 0.38382 0.48733 0.70084 0.53970 0.10246 0.27004 0.60292

K 0.53766 0.47457 0.12613 0.20728 0.26782 0.36416 0.33120 0.06473 0.19653 0.38002

M 0.21546 0.15529 0.06536 0.09118 0.10903 0.17159 0.13605 0.02380 0.06373 0.15826

F 0.40538 0.21864 0.08318 0.19305 0.18031 0.32761 0.23687 0.05348 0.14181 0.26289

P 0.43470 0.25264 0.09039 0.19595 0.32115 0.37428 0.27757 0.06108 0.15024 0.33794

S 0.68411 0.38268 0.14252 0.30264 0.36642 0.65234 0.40922 0.08769 0.21847 0.45245

T 0.54884 0.28878 0.11458 0.23100 0.31747 0.40661 0.35595 0.07044 0.16896 0.40420

W 0.12401 0.07429 0.03041 0.05196 0.04582 0.08136 0.06791 0.02176 0.04053 0.07504

Y 0.30093 0.17524 0.06603 0.14935 0.14852 0.22264 0.17620 0.04275 0.12169 0.19739

V 0.64004 0.38336 0.14311 0.27200 0.32753 0.46504 0.39540 0.07986 0.19772 0.48693

406 14 Semantic Analysis for Protein Primary Structure

Table 14.3. Probability distribution of 100.0 × q

(a, b) = 100.0 × p(a)p(b)

One-letter A R N D C Q E G H I

code

A 0.58635 0.39948 0.33278 0.40287 0.12503 0.30231 0.49680 0.52733 0.17310 0.44880

R 0.39895 0.27181 0.22642 0.27411 0.08507 0.20569 0.33802 0.35880 0.11778 0.30536

N 0.33237 0.22645 0.18864 0.22837 0.07087 0.17136 0.28161 0.29892 0.09812 0.25440

D 0.40276 0.27440 0.22859 0.27673 0.08588 0.20765 0.34125 0.36222 0.11890 0.30828

C 0.12484 0.08506 0.07085 0.08578 0.02662 0.06436 0.10577 0.11228 0.03686 0.09556

Q 0.30202 0.20576 0.17141 0.20751 0.06440 0.15571 0.25589 0.27162 0.08916 0.23117

E 0.49643 0.33822 0.28175 0.34109 0.10586 0.25594 0.42061 0.44646 0.14656 0.37998

G 0.52754 0.35941 0.29940 0.36246 0.11249 0.27198 0.44697 0.47444 0.15574 0.40379

H 0.17285 0.11776 0.09810 0.11876 0.03686 0.08911 0.14645 0.15545 0.05103 0.13230

I 0.44864 0.30566 0.25462 0.30825 0.09566 0.23130 0.38012 0.40348 0.13245 0.34339

L 0.73267 0.49917 0.41583 0.50341 0.15623 0.37774 0.62077 0.65893 0.21630 0.56080

K 0.45597 0.31066 0.25879 0.31329 0.09723 0.23509 0.38633 0.41008 0.13461 0.34901

M 0.18172 0.12381 0.10314 0.12486 0.03875 0.09369 0.15397 0.16343 0.05365 0.13909

F 0.31381 0.21380 0.17810 0.21561 0.06691 0.16179 0.26588 0.28222 0.09264 0.24019

P 0.37589 0.25610 0.21334 0.25827 0.08015 0.19380 0.31848 0.33806 0.11097 0.28772

S 0.54152 0.36894 0.30734 0.37207 0.11547 0.27919 0.45881 0.48701 0.15987 0.41449

T 0.42712 0.29100 0.24241 0.29347 0.09108 0.22021 0.36189 0.38413 0.12610 0.32693

W 0.09273 0.06318 0.05263 0.06372 0.01977 0.04781 0.07857 0.08340 0.02738 0.07098

Y 0.24165 0.16464 0.13715 0.16603 0.05153 0.12459 0.20474 0.21733 0.07134 0.18496

V 0.50825 0.34628 0.28846 0.34921 0.10838 0.26204 0.43063 0.45710 0.15005 0.38903

14.1 Semantic Analysis for Protein Primary Structure 407

Table 14.3. (continued)

One-letter L K M F P S T W Y V

code

A 0.73324 0.45717 0.16378 0.31425 0.37578 0.54169 0.42681 0.09286 0.24186 0.50833

R 0.49889 0.31106 0.11143 0.21381 0.25568 0.36856 0.29040 0.06318 0.16456 0.34587

N 0.41563 0.25915 0.09284 0.17813 0.21301 0.30705 0.24193 0.05264 0.13710 0.28815

D 0.50366 0.31403 0.11250 0.21585 0.25812 0.37208 0.29317 0.06378 0.16613 0.34917

C 0.15612 0.09734 0.03487 0.06691 0.08001 0.11533 0.09087 0.01977 0.05150 0.10823

Q 0.37768 0.23548 0.08436 0.16186 0.19356 0.27901 0.21984 0.04783 0.12458 0.26183

E 0.62079 0.38706 0.13866 0.26605 0.31815 0.45862 0.36135 0.07862 0.20477 0.43038

G 0.65969 0.41132 0.14735 0.28273 0.33809 0.48736 0.38400 0.08354 0.21760 0.45735

H 0.21615 0.13477 0.04828 0.09263 0.11077 0.15968 0.12582 0.02737 0.07130 0.14985

I 0.56103 0.34980 0.12531 0.24044 0.28752 0.41446 0.32657 0.07105 0.18506 0.38894

L 0.91622 0.57126 0.20465 0.39266 0.46956 0.67686 0.53332 0.11603 0.30222 0.63519

K 0.57020 0.35552 0.12736 0.24437 0.29223 0.42124 0.33191 0.07221 0.18808 0.39531

M 0.22725 0.14169 0.05076 0.09739 0.11646 0.16788 0.13228 0.02878 0.07496 0.15754

F 0.39242 0.24467 0.08765 0.16818 0.20111 0.28990 0.22842 0.04970 0.12944 0.27205

P 0.47006 0.29308 0.10499 0.20145 0.24090 0.34726 0.27362 0.05953 0.15505 0.32588

S 0.67717 0.42221 0.15125 0.29022 0.34705 0.50027 0.39417 0.08576 0.22337 0.46947

T 0.53413 0.33302 0.11930 0.22891 0.27374 0.39459 0.31091 0.06764 0.17618 0.37029

W 0.11596 0.07230 0.02590 0.04970 0.05943 0.08567 0.06750 0.01469 0.03825 0.08039

Y 0.30219 0.18841 0.06750 0.12951 0.15487 0.22324 0.17590 0.03827 0.09968 0.20950

V 0.63558 0.39628 0.14196 0.27239 0.32573 0.46954 0.36996 0.08049 0.20965 0.44063

408 14 Semantic Analysis for Protein Primary Structure

Table 14.4. The value of relative entropy density function k

(a, b)=log

p(a,b)

p(a)p(b)

One-letter A R N D C Q E G H I

code

A 0.38439 −0.03112 −0.24002 −0.11206 −0.08779 −0.01899 −0.03400 0.07922 −0.11549 −0.03505

R −0.06261 0.41499 −0.05614 0.01374 0.02799 0.06209 0.04254 −0.08417 0.09301 −0.02416

N −0.17757 −0.16636 0.29805 −0.09678 0.00654 −0.02635 −0.14396 0.02172 − 0.05321 0.16783

D −0.08060 −0.10796 −0.07074 0.12312 −0.10004 −0.25510 0.13219 0.00593 −0.15618 0.14757

C −0.23176 0.07182 −0.03349 −0.00285 0.71381 0.02375 −0.23999 0.20613 0.28448 −0.16978

Q 0.05580 0.14037 0.01220 −0.17265 −0.02857 0.63776 0.03187 −0.15838 0.05780 −0.05057

E 0.02473 0.08513 0.12421 0.10061 −0.22562 0.04785 0.44895 −0.19553 −0.09316 0.07633

G −0.03363 0.01189 −0.08924 −0.02547 −0.01149 −0.11068 −0.12376 0.24376 0.01455 0.04193

H −0.17707 0.06488 −0.12055 −0.26589 0.31066 0.10206 −0.30746 0.02396 0.64579

−0.01614

I −0.02460 −0.08066 0.13313 0.10034 0.06735 −0.09630 −0.05339 −0.10200 0.01965 0.09622

L 0.06240 0.07016 −0.01605 −0.01012 −0.05447 0.08169 −0.02584 −0.07553 0.00771 −0.11506

K −0.06387 0.04140 0.18002 0.06759 −0.17548 −0.04872 0.23978 −0.21505 −0.10692 0.10017

M 0.20889 −0.03390 0.06299 0.04480 −0.19228 −0.11467 0.01229 −0.07767 −0.04774 −0.08275

F −0.19429 −0.12999 0.04458 0.12002 0.13044 −0.06829 −0.15996 0.06416 0.04989 0.04113

P 0.00123 −0.12694 −0.15136 −0.01570 −0.17187 0.01892 0.15235 0.15333 0.02226 −0.26020

S −0.12148 −0.06987 −0.04771 −0.07407 0.05691 −0.01438 −0.20113 0.09784 −0.02114 −0.07811

T 0.01812 −0.21393 −0.07635 −0.09519 0.08691 −0.13348 −0.17717 0.09084 −0.03166 0.00538

−0.15276 0.09156 0.16336 0.00329 0.05386 0.12398 −0.21447 −0.01736 0.11836 −0.00231

Y −0.24973 0.05066 0.09117 0.06646 0.17474 0.06230 −0.13434 0.06329 0.07895 −0.02844

V 0.05669 −0.08072 −0.04138 0.07542 0.06381 −0.14946 −0.02049 −0.09770 −0.09505 0.02060

14.1 Semantic Analysis for Protein Primary Structure 409

Table 14.4. (continued)

One-letter L K M F P S T W Y V

code

A 0.07175 −0.11132 0.10986 −0.08316 −0.11728 −0.07449 −0.03150 −0.15141 −0.19587 0.09562

R −0.00047 0.00829 0.04391 0.02038 −0.09948 −0.14330 −0.16536 0.05587 0.08616 −0.03504

N −0.04286 0.01600 0.02109 0.06717 0.18213 0.00973 −0.05549 0.10119 0.15325 −0.04856

D 0.04320 −0.09449 −0.01882 0.14000 0.05252 −0.10599 −0.16309 0.13693 0.19685 0.05540

C −0.05132 −0.13592 −0.19742 0.04520 0.15688 0.12312 −0.05923 0.24724 0.05578 −0.07645

Q 0.03349 0.02550 0.06816 −0.17598 0.00593 −0.21842 −0.09293 0.05195 −0.07023 −0.06608

E −0.04006 0.31037 0.09453 −0.19076 −0.41284 −0.33082 −0.11078 −0.11461 −0.10839 − 0.04253

G −0.10436 0.04180 0.06252 0.06920 −0.21922 0.02630 0.02018 0.11260 0.09740 0.04721

H 0.08060 −0.30725 −0.05962 0.19733 0.32872 −0.00576 −0.04756 0.15590 0.20558 −0.10673

I −0.04042 0.02205 −

0.09146 0.01530 0.03142 0.03768 0.06809 −0.16609 0.00520 −0.02686

L 0.08581 0.02727 −0.05189 −0.03287 0.05360 0.05022 0.01716 −0.17947 −0.16239 −0.07522

K −0.08477 0.41671 −0.01404 −0.23747 −0.12581 −0.21008 −0.00309 −0.15785 0.06341 −0.05690

M −0.07681 0.13222 0.36472 −0.09511 −0.09517 0.03153 0.04060 −0.27387 −0.23408 0.00652

F 0.04687 −0.16231 −0.07545 0.19899 −0.15750 0.17641 0.05240 0.10577 0.13168 −0.04942

P −0.11282 −0.21423 −0.21600 −0.03995 0.41477 0.10808 0.02070 0.03718 −0.04549 0.05242

S 0.01471 −0.14183 −0.08578 0.06049 0.07837 0.38292 0.05403 0.03212 −0.03197 −0.05326

T 0.03921 −0.20565 −0.05828 0.01311 0.21385 0.04328 0.19521 0.05842 −0.06041 0.12641

W 0.09683 0.03918 0.23165 0.06407 −0.37534 − 0.07451 0.00878 0.56754 0.08348 −0.09934

Y −0.00601 −0.10458 −0.03176 0.20565 −0.06045 −0.00389 0.00250 0.15978 0.28785 −0.08587

V 0.01008

−0.04784 0.01159 −0.00206 0.00794 −0.01391 0.09595 −0.01138 −0.08453 0.14414

410 14 Semantic Analysis for Protein Primary Structure

Table 14.5. The value of relative entropy density function k

(a, b)=log

p(a,b)

p(b,a)

One-letter A R N D C Q E G H I

code

A 0.00000 0.03342 −0.06067 −0.03105 0.14615 −0.07340 −0.05766 0.11228 0.06371 −0.00991

R −0.03342 0.00000 0.11007 0.12018 −0.04358 −0.07882 −0.04345 −0.09855 0.02834 0.05510

N 0.06067 −0.11007 0.00000 −0.02742 0.04043 −0.03895 −0.26887 0.10863 0.06769 0.03346

D 0.03105 −0.12018 0.02742 0.00000 −0.09542 −0.08147 0.03226 0.03044 0.11145 0.04736

C −0.14615 0.04358 −0.04043 0.09542 0.00000 0.05153 −0.01547 0.21489 −0.02621 −0.23877

Q 0.07340 0.07882 0.03895 0.08147 −0.05153 0.00000 −0.01629 −0.04965 −0.04351 0.04488

E 0.05766 0.04345 0.26887 −0.03226 0.01547 0.01629 0.00000 −0.07340 0.21537 0.12918

G −0.11228 0.09855 −0.10863 −0.03044 −0.21489 0.04965 0.07340 0.00000 −0.00671 0.14502

H −0.06371 −0.02834 −0.06769 −0.11145 0.02621 0.04351 −0.21537 0.00671 0.00000 −0.03739

I 0.00991 −0.05510 −0.03346 −0.04736 0.23877 −0.04488 −0.12918 −0.14502 0.03739 0.00000

−0.01047 0.07144 0.02748 −0.05403 −0.00210 0.04846 0.01418 0.02715 −0.07187 −0.07522

K 0.04367 0.03126 0.16202 0.15870 −0.04117 −0.07662 −0.07330 −0.26120 0.19869 0.07487

M 0.24904 0.07413 0.19370 0.21404 0.15732 −0.03143 0.06885 0.00926 0.16403 0.15926

F −0.11315 −0.15046 −0.02283 −0.02160 0.08539 0.10706 0.02986 −0.00762 −0.14731 0.02435

P 0.11893 −0.02511 −0.33128 −0.06739 −0.32616 0.01479 0.56669 0.37242 −0.30390 −0.29066

S −0.04745 0.07490 −0.05612 0.03187 −0.06449 0.20496 0.13030 0.07052 −0.01370 −0.11572

T 0.05070 −0.04557 −0.01800 0.06938 0.14938 −0.03810 −0.06425 0.07116 0.01911 −0.06110

W −0.00330 0.03566 0.06200 −0.13519 −0.19316 0.07146 −0.10074 −0.13248 −0.03737 0.16236

Y −0.05512 −0.03483 −0.06155 −0.13124 0.11988 0.13267 −0.02613 −0.03593 −0.12574 −0.03435

−0.03916 −0.04399 0.00874 0.02020 0.14221 −0.08223 0.02288 −0.14570 0.01359 0.04776

14.1 Semantic Analysis for Protein Primary Structure 411

Table 14.5. (continued)

One-letter L K M F P S T W Y V

code

A 0.01047 −0.04367 −0.24904 0.11315 −0.11893 0.04745 −0.05070 0.00330 0.05512 0.03916

R −0.07144 −0.03126 −0.07413 0.15046 0.02511 −0.07490 0.04557 −0.03566 0.03483 0.04399

N −0.02748 −0.16202 −0.19370 0.02283 0.33128 0.05612 0.01800 −0.06200 0.06155 −0.00874

D 0.05403 −0.15870 −0.21404 0.02160 0.06739 −0.03187 −0.06938 0.13519 0.13124 −0.02020

C 0.00210 0.04117 −0.15732 −0.08539 0.32616 0.06449 −0.14938 0.19316 −0.11988 −0.14221

Q −0.04846 0.07662 0.03143 −0.10706 −0.01479 −0.20496 0.03810 −0.07146 −0.13267 0.08223

E −0.01418 0.07330 −0.06885 −0.02986 −0.56669 −0.13030 0.06425 0.10074 0.02613 −0.02288

G −0.02715 0.26120 −0.00926 0.00762 −0.37242 −0.07052 −0.07116 0.13248 0.03593 0.14570

H 0.07187 −0.19869 −0.16403 0.14731 0.30390 0.01370 −0.01911 0.03737 0.12574 −0.01359

I 0.07522 −

0.07487 −0.15926 −0.02435 0.29066 0.11572 0.06110 −0.16236 0.03435 −0.04776

L 0.00000 0.11471 −0.12622 −0.07884 0.16488 0.03485 −0.02423 −0.27546 −0.15625 −0.08618

K −0.11471 0.00000 −0.30005 −0.07692 0.08421 −0.07158 0.19771 −0.19886 0.16546 −0.01262

M 0.12622 0.30005 0.00000 0.13238 0.27042 0.26778 0.24783 −0.35355 −0.05106 0.14517

F 0.07884 0.07692 −0.13238 0.00000 −0.11999 0.11436 0.03619 0.04164 −0.07474 −0.04915

P −0.16488 −0.08421 −0.27042 0.11999 0.00000 0.03059 −0.19379 0.41490 0.01664 0.04514

S −0.03485 0.07158 −0.26778 −0.11436 −0.03059 0.00000 0.00923 0.10813 −0.02729 −0.03958

T 0.02423 −0.19771 −0.24783 −0.03619 0.19379 −0.00923 0.00000 0.05267 −0.06059 0.03175

W 0.27546 0.19886 0.35355 −0.04164 −0.41490 −0.10813 −0.05267 0.00000 −0.07700 −0.08969

Y 0.15625 −0.16546 0.05106 0.07474 −0.01664 0.02729 0.06059 0.07700 0.00000 −

0.00236

V 0.08618 0.01262 −0.14517 0.04915 −0.04514 0.03958 −0.03175 0.08969 0.00236 0.00000

412 14 Semantic Analysis for Protein Primary Structure

Table 14.6. The eigenvalues of relative entropy density function k

,andk

Mean (μ)Variance

(σ

)

Standard

deviation

(σ)

Maximum

(μ

)

Minimum

(μ

)

μ − 2σμ+2σ

−0.00633 0.01879 0.13708 0.71381 −0.41384 0.28049 −0.26783

0.00441 0.01274 0.11289 0.56669 −0.56669 0.23019 −0.22137

Determination of Fourth and Higher Ranked Local Words

The search for fourth ranked local words is similar to that of the second

and third ranked ones, while their relative entropy density functions are more

complex. For example, there are 11+18 = 29 relative entropy density functions

of fourth rank. We can also ﬁnd local words by choosing a proper value of τ.

Because of the amount of statistical data, local words with a rank higher than

fourth cannot be processed by the statistical methods used for the second and

third ranked ones. They must be processed by permutation and combination

methods or the method of combining lower ranked words. Permutation and

combination methods will be discussed in detail in the next section.

14.2 Permutation and Combination Methods

for Semantic Structures

In the previous section, informational and statistical analysis methods for the

semantic structure of protein primary structure have been given. In using this

method, we notice that the basis of the informational and statistical methods

is the computation of frequency numbers and probabilities for polypeptide

chains. However, if the lengths of the polypeptide chain vectors increase, the

number of combinations (20

of the polypeptide chain vector b

(k)

) will increase

rapidly. For example, 20

=6.4 ×10

. This exceeds the total number of amino

acids in the Swiss-Prot database (version 2000); hence the informational and

statistical methods no longer work. Therefore, other methods must be used

to analyze the semantic structures of higher ranked words.

In this section, we continue to analyze the semantic structure of protein

primary structures with combinatorial graph theory methods, and give the

deﬁnition of the key words and core words as well as their characteristic

parameters for protein primary structures in the Swiss-Prot database. The

concept of the key words and core words refers to a special type of polypep-

tide chains, which exist uniquely in a protein database (i.e., in nature). Hence

the key words and core words are actually special kinds of biological signa-

tures [91].

The concept of a biological signature occurs commonly in biological se-

mantic analysis. Besides the small-molecule library and conformation theory

mentioned above, many research institutions are building their own annotated

14.2 Permutation and Combination Methods 413

Table 14.7. Parameters of the second ranked local words determined by k

DipeptideAARRNNCCCH QQ EE EK HC HHHPKKMM

Type11111 1 1 1 1 1111

Relative 0.3843 0.4149 0.2980 0.7138 0.2844 0.6377 0.4489 0.3103 0.3106 0.6457 0.3287 0.4167 0.3647

entropy

Dipeptide PP SS WW YY EP ES HE HK MW NP CP EN GK

Type11112 2 2 2 2 3333

Relative 0.4147 0.3829 0.5675 0.2878 −0.4128 −0.3308 −0.3074 −0.3072 −0.2738 0.3312 0.3261 0.2688 0.2612

entropy

Dipeptide HP IC IP MA MK MP MS MT PE PG PW WL WM

Type33333 3 3 3 3 3333

Relative 0.3039 0.2387 0.2906 0.2490 0.3000 0.2704 0.2677 0.2478 0.5666 0.3724 0.4148 0.2754 0.3535

entropy