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Parikh vectors
8XWO_1 9ETE_1 7FVT_1 Letter Amino acid
13 5 60 R Arginine
0 1 2 C Cysteine
20 11 54 E Glutamic acid
8 3 24 P Proline
37 7 52 A Alanine
34 6 52 D Aspartic acid
15 6 24 Q Glutamine
1 3 11 H Histidine
20 9 70 L Leucine
13 14 33 K Lycine
13 13 35 T Threonine
12 7 56 I Isoleucine
9 4 24 M Methionine
20 4 32 N Asparagine
46 9 49 G Glycine
16 6 20 F Phenylalanine
21 7 34 S Serine
10 1 1 W Tryptophan
25 2 20 Y Tyrosine
17 11 39 V Valine 

8XWO_1|Chains A, B, C, D, E, F|Chitoporin|Vibrio harveyi (669)
>9ETE_1|Chains A, B|Fatty acid-binding protein, liver|Gallus gallus (9031)
>7FVT_1|Chains A, B|DNA gyrase subunit B,DNA gyrase subunit A Chimera|Staphylococcus aureus subsp. aureus N315 (158879)
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 \(w=f(c)\)
8XWO , Knot 150 350 0.83 38 191 322 
DGANSDAAKEYLTKDSFSYEVYGIIAMQAAYRDYDSGDAKQDDNLGGMQLNNESRIGFRGKKQFANFEPTFIWQIEGGYVDPSFGGEGAGLGERDTFVGFESASWGQVRLGRVLTPMYELVDWPASNPGLGDVYDWGGAIGGAKYQDRQSNTIRWDSPMYADKFSIDAAVGAGDKAGLGAGDDYWGGIAAHYKLGPLQLDAAYEGNRNIEAEGQTWENNTYLVGVQGWFENGISFFAQYKYMEADASNGVNEKQDAMSAGLMYTTGDWQYKLGYAANFDLERDGKTLSNTSDDVVSAQIMYFVDPSAVLYARARMNDFNEGLDGLDDAARWTSGTNGDYNEYSVGVEYYF
9ETE , Knot 66 129 0.82 40 106 127 
GSHMAFSGTWQVYAQENYEEFLKALALPEDLIKMARDIKPIVEIQQKGDDFVVTSKTPRQTVTNSFTLGKEADITTMDGKKLKCTVHLANGKLVTKSEKFSHEQEVKGNEMVETITFGGVTLIRRSKRV
7FVT , Knot 271 692 0.85 40 266 644 
MDVASLPGKLADCSSKSPEECEIFLVEGDSAGGSTKSGRDSRTQAILPLRGKILNVEKARLDRILNNNEIRQMITAFGTGIGGDFDLAKARYHKIVIMTDADVDGAHIRTLLLTFFYRFMRPLIEAGYVYIAQPPTGYKGLGEMNADQLWETTMNPEHRALLQVKLEDAIEADQTFEMLMGDVVENRRQFIEDNAVYANLDFAELPQSRINERNITSEMRESFLDYAMSVIVARALPDVRDGLKPVHRRILYGLNEQGMTPDKSYKKSARIVGDVMGKYHPHGDSSIYEAMVRMAQDFSYRYPLVDGQGNFGSMDGDGAAAMRFTEARMTKITLELLRDINKDTIDFIDNYDGNEREPSVLPARFPNLLANGASGIAVGMATNIPPHNLTELINGVLSLSKNPDISIAELMEDIEGPDFPTAGLILGKSGIRRAYETGRGSIQMRSRAVIEERGGGRQRIVVTEIPFQVNKARMIEKIAELVRDKKIDGITDLRDETSLRTGVRVVIDVRKDANASVILNNLYKQTPLQTSFGVNMIALVNGRPKLINLKEALVHYLEHQKTVVRRRTQYNLRKAKDRAHILEGLRIALDHIDEIISTIRESDTDKVAMESLQQRFKLSEKQAQAILDMRLRRLTGLERDKIEAEYNELLNYISELETILADEEVLLQLVRDELTEIRDRFGDDRRTEIQLG

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 \(c\).

\(|P_{f(8XWO_1)}(2) \setminus P_{f(9ETE_1)}(2)|=136\), \(|P_{f(9ETE_1)}(2) \setminus P_{f(8XWO_1)}(2)|=51\). 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 1:01100011000100001000101111101100000010100000111101000001110100011010101110101101010111011111000011110010110101101101100110111001111010011111111000000000101001101001010111111001111110001111110001111010110010001010100100000111101110011011100001010100110000011011110001010001101101010001001000000110101101101011101010100100110110011010010010000001110001
Pair \(Z_2\) Length of longest common subsequence
8XWO_1,9ETE_1 187 3
8XWO_1,7FVT_1 147 4
9ETE_1,7FVT_1 196 4

Newick tree

 
[
	9ETE_1:10.12,
	[
		8XWO_1:73.5,7FVT_1:73.5
	]:28.62
]

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 \((0.85)(0.8)(\frac{479 }{\log_{20} 479}-\frac{129}{\log_{20}129})=104.\)
Status Protein1 Protein2 d d1/2
Query variables 8XWO_1 9ETE_1 130 89
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]