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Parikh vectors
5XWP_1 7SHG_1 8TWS_1 Letter Amino acid
60 49 10 F Phenylalanine
33 26 17 T Threonine
72 37 12 Y Tyrosine
45 29 25 R Arginine
14 23 10 H Histidine
100 63 15 I Isoleucine
114 54 29 L Leucine
39 30 15 G Glycine
170 49 11 K Lycine
2 3 5 W Tryptophan
43 36 15 V Valine
39 20 34 A Alanine
58 35 22 D Aspartic acid
28 27 13 Q Glutamine
21 14 5 M Methionine
58 49 33 S Serine
122 35 13 N Asparagine
3 5 4 C Cysteine
128 51 21 E Glutamic acid
11 13 14 P Proline 

5XWP_1|Chains A, F[auth B]|Uncharacterized protein|Leptotrichia buccalis (523794)
>7SHG_1|Chains A, B|Ribofuranosyl transferase|Thermobacillus composti (377615)
>8TWS_1|Chain A|Avirulence protein B|Pseudomonas syringae (317)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
5XWP , Knot 393 1160 0.79 40 273 891 
SMKVTKVGGISHKKYTSEGRLVKSESEENRTDERLSALLNMRLDMYIKNPSSTETKENQKRIGKLKKFFSNKMVYLKDNTLSLKNGKKENIDREYSETDILESDVRDKKNFAVLKKIYLNENVNSEELEVFRNDIKKKLNKINSLKYSFEKNKANYQKINENNIEKVEGKSKRNIIYDYYRESAKRDAYVSNVKEAFDKLYKEEDIAKLVLEIENLTKLEKYKIREFYHEIIGRKNDKENFAKIIYEEIQNVNNMKELIEKVPDMSELKKSQVFYKYYLDKEELNDKNIKYAFCHFVEIEMSQLLKNYVYKRLSNISNDKIKRIFEYQNLKKLIENKLLNKLDTYVRNCGKYNYYLQDGEIATSDFIARNRQNEAFLRNIIGVSSVAYFSLRNILETENENDITGRMRGKTVKNNKGEEKYVSGEVDKIYNENKKNEVKENLKMFYSYDFNMDNKNEIEDFFANIDEAISSIRHGIVHFNLELEGKDIFAFKNIAPSEISKKMFQNEINEKKLKLKIFRQLNSANVFRYLEKYKILNYLKRTRFEFVNKNIPFVPSFTKLYSRIDDLKNSLGIYWKTPKTNDDNKTKEIIDAQIYLLKNIYYGEFLNYFMSNNGNFFEISKEIIELNKNDKRNLKTGFYKLQKFEDIQEKIPKEYLANIQSLYMINAGNQDEEEKDTYIDFIQKIFLKGFMTYLANNGRLSLIYIGSDEETNTSLAEKKQEFDKFLKKYEQNNNIKIPYEINEFLREIKLGNILKYTERLNMFYLILKLLNHKELTNLKGSLEKYQSANKEEAFSDQLELINLLNLDNNRVTEDFELEADEIGKFLDFNGNKVKDNKELKKFDTNKIYFDGENIIKHRAFYNIKKYGMLNLLEKIADKAGYKISIEELKKYSNKKNEIEKNHKMQENLHRKYARPRKDEKFTDEDYESYKQAIENIEEYTHLKNKVEFNELNLLQGLLLRILHRLVGYTSIWERDLRFRLKGEFPENQYIEEIFNFENKKNVKYKGGQIVEKYIKFYKELHQNDEVKINKYSSANIKVLKQEKKDLYIANYIAAFNYIPHAEISLLEVLENLRKLLSYDRKLKNAVMKSVVDILKEYGFVATFKIGADKKIGIQTLESEKIVHLKNLKKKKLMTDRNSEELCKLVKIMFEYKMEEKKSEN
7SHG , Knot 254 648 0.84 40 270 591 
MGSSHHHHHHSSGLVPRGSHMASLHIKDRIDFDEYEYVFFDIFDTILLRNVYPEYTKMIWSKRMSVQFGDKLTAEEVYQLRSEIEARLCIENEQSGKDKEFHYMQLIEQLYRYFITKKIISDLSIQSFYDICINIETDVEIGVQYVDPHWLELVKHIKSDSRKIKVFCVSDFYLPKATLYSLFDYHGILRYVDEIYVSSEILLTKKSGRLFDFILELHKIAPSNVLMVGDNEISDYKVPIEKGMKAYLIDRTKQFNKYAEHERIHKINTIVGIESQLIKMANDFRKITPFHNIIFSLFYFIKKLHETLVNRGVKDVFFLSREGEYLKKLFDIYQGQEGFRNIQTINTHYLLVSRKATYLPSLKPIESETFNILFRQYRKISAYDFLSSINFTSDAMNLLSTELAFDLQRVEDDFPTSSTFQKLMKSDTFRNIYERERNEQNRLFKKYVDQFNVDLTNGMHIVDVGWKGTIQDNLFNIYNGEVSVFGYYLGIVAAGEMRPGNDKQGILFSSIPVMSSYFGVFNENRAIYEVLLGASHGSAERYNFNESGKIIVETSKNQREFEIYKNIVQHTQQAMEQSFIELCSVLCKKSIDISKYLEIFAKIHAEFILNPNKQELQFFDKLYHFENFGIFEYTEFQTKKNVGINERI
8TWS , Knot 140 323 0.83 40 196 307 
AHMGCVSSKSTTVLSPQTSFNEASRTSFRALPGPSQRQLEVYDQCLIGAARWPDDSSKSNTPENRAYCQSMYNSIRSAGDEISRGGITSFEELWGRATEWRLSKLQRGEPLYSAFASERTSDTDAVTPLVKPYKSVLARVVDHEDAHDEIMQDNLFGDLNVKVYRQTAYLHGNVIPLNTFRVATDTEYLRDRVAHLRTELGAKALKQHLQRYNPDRIDHTNASYLPIIKDHLNDLYRQAISSDLSQAELISLIARTHWWAASAMPDQRGSAAKAEFAARAIASAHGIELPPFRNGNVSDIEAMLSGEEEFVEKYRSLLDSDCF

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(5XWP_1)}(2) \setminus P_{f(7SHG_1)}(2)|=50\), \(|P_{f(7SHG_1)}(2) \setminus P_{f(5XWP_1)}(2)|=47\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:01010011110000000010110000000000001011101010101001000000000001101001100011010000101001000010000000011000100000111100101000100001011000100010010010001000010000100001001010000011000000010001010010011001000001101110100100100001001000111000000011011000100100100110011010010000110000100001000010011001101010011000100010010000100110000100110001100100010001000001001011000111000000111001111001101010011000000010101010010000100001010100100000000100010110000101000001001110100110010011101010101001111001110010001100010000101011001001011001000011001000010110001111101001000100100011101001000000000011010101100100101100110001011010001101000000010011001001001000110001101001011011000000000010110011101110011001010110110000000011000001001100000000101100100110010110110000010110111011000010010101000001000011000101101101000010001010100110110101001000001001000010101001100011001000111011001100110010100100000000010000010001000010100000100000000001100100000100010100101101111011001110001100010101010110000100110100000100011011000101000100000101000001010110000001011001111001101010110110010011000001001110011011000111101011100011100100001101001000011000000010011011100010000000
Pair \(Z_2\) Length of longest common subsequence
5XWP_1,7SHG_1 97 5
5XWP_1,8TWS_1 169 4
7SHG_1,8TWS_1 166 5

Newick tree

 
[
	8TWS_1:92.56,
	[
		5XWP_1:48.5,7SHG_1:48.5
	]:44.06
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{1808 }{\log_{20} 1808}-\frac{648}{\log_{20}648})=287.\)
Status Protein1 Protein2 d d1/2
Query variables 5XWP_1 7SHG_1 352 275
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]