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Parikh vectors
7LTA_1 5IVS_1 7VAW_1 Letter Amino acid
5 0 23 S Serine
4 8 27 T Threonine
1 2 8 W Tryptophan
2 1 21 Y Tyrosine
10 6 56 V Valine
13 4 10 N Asparagine
12 12 47 L Leucine
10 2 19 F Phenylalanine
4 13 35 I Isoleucine
13 3 56 A Alanine
9 4 26 D Aspartic acid
2 1 6 H Histidine
5 4 38 R Arginine
8 6 24 K Lycine
7 6 35 P Proline
11 13 55 G Glycine
1 2 19 M Methionine
6 2 3 C Cysteine
3 6 17 Q Glutamine
7 4 53 E Glutamic acid 

7LTA_1|Chains A, B|Galectin-1|Homo sapiens (9606)
>5IVS_1|Chains A, B|Protease|Human immunodeficiency virus 1 (11676)
>7VAW_1|Chains A, B, C|V-type ATP synthase alpha chain|Thermus thermophilus HB8 (300852)
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 \(w=f(c)\)
7LTA , Knot 67 133 0.82 40 104 129 
CGLVASNLNLKPGECLRVRGEVAPDAKSFVLNLGKDSNNLCLHFNPRFNAHGDANTIVCNSKDGGAWGTEQREAVFPFQPGSVAEVCITFDQANLTVKLPDGYEFKFPNRLNLEAINYMAADGDFKIKCVAFD
5IVS , Knot 52 99 0.80 38 80 94 
PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMNLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNF
7VAW , Knot 224 578 0.82 40 243 526 
MIQGVIQKIAGPAVIAKGMLGARMYDICKVGEEGLVGEIIRLDGDTAFVQVYEDTSGLKVGEPVVSTGLPLAVELGPGMLNGIYDGIQRPLERIREKTGIYITRGVVVHALDREKKWAWTPMVKPGDEVRGGMVLGTVPEFGFTHKILVPPDVRGRVKEVKPAGEYTVEEPVVVLEDGTELKMYHTWPVRRARPVQRKLDPNTPFLTGMRILDVLFPVAMGGTAAIPGPFGAGKSVTQQSLAKWSNADVVVYVGCGERGNEMTDVLVEFPELTDPKTGGPLMHRTVLIANTSNMPVAAREASIYVGVTIAEYFRDQGFSVALMADSTSRWAEALREISSRLEEMPAEEGYPPYLAARLAAFYERAGKVITLGGEEGAVTIVGAVSPPGGDMSEPVTQSTLRIVGAFWRLDASLAFRRHFPAINWNGSYSLFTSALDPWYRENVAEDYPELRDAISELLQREAGLQEIVQLVGPDALQDAERLVIEVGRIIREDFLQQNAYHEVDAYCSMKKAYGIMKMILAFYKEAEAAIKRGVSIDEILQLPVLERIGRARYVSEEEFPAYFEEAMKEIQGAFKALA

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 \(c\).

\(|P_{f(7LTA_1)}(2) \setminus P_{f(5IVS_1)}(2)|=79\), \(|P_{f(5IVS_1)}(2) \setminus P_{f(7LTA_1)}(2)|=55\). 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 1:0111100101011001010101110100111011000001010101010101010011000001111100000111110110110101010010101011010010110010101100111010101001110
Pair \(Z_2\) Length of longest common subsequence
7LTA_1,5IVS_1 134 2
7LTA_1,7VAW_1 207 4
5IVS_1,7VAW_1 201 4

Newick tree

 
[
	7VAW_1:11.25,
	[
		7LTA_1:67,5IVS_1:67
	]:44.25
]

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 \((0.85)(0.8)(\frac{232 }{\log_{20} 232}-\frac{99}{\log_{20}99})=42.8\)
Status Protein1 Protein2 d d1/2
Query variables 7LTA_1 5IVS_1 56 48
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]