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Parikh vectors
3EBA_1 1FDV_1 5HUM_1 Letter Amino acid
2 13 9 F Phenylalanine
14 19 37 S Serine
9 16 22 T Threonine
4 1 12 W Tryptophan
11 37 22 A Alanine
2 6 18 C Cysteine
4 23 25 E Glutamic acid
4 9 21 K Lycine
9 6 11 Y Tyrosine
4 24 19 R Arginine
3 5 23 N Asparagine
6 6 11 H Histidine
3 20 22 P Proline
6 17 17 D Aspartic acid
15 32 36 G Glycine
2 6 8 M Methionine
9 32 17 V Valine
8 8 8 Q Glutamine
5 4 33 I Isoleucine
7 43 20 L Leucine 

3EBA_1|Chain A|CAbHul6|Camelus dromedarius (9838)
>1FDV_1|Chains A, B, C, D|17-BETA-HYDROXYSTEROID DEHYDROGENASE|Homo sapiens (9606)
>5HUM_1|Chains A, B, C, D|neuraminidase|Influenza A virus (A/chicken/Sichuan/NCJPL1/2014(H5N6)) (1529593)
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 \(w=f(c)\)
3EBA , Knot 60 127 0.76 40 101 121 
QVQLVESGGGSVQAGGSLRLSCSASGYTYISGWFRQAPGKGLEWVAAIRSSDGTTYYADSVKGRFTISQDNAKNTVYLQMNSLKPEDTAMYYCAATEVAGWPLDIGIYDYWGQGTQVTVSSHHHHHH
1FDV , Knot 138 327 0.81 40 177 306 
ARTVVLITGCSSGIGLHLAVRLASDPSQSFKVYATLRDLKTQGRLWEAARALACPPGSLETLQLDVRDSKSVAAARERVTEGRVDVLVCNAGLGLLGPLEALGEDAVASVLDVNVVGTVRMLQAFLPDMKRRGSGRVLVTGSVGGLMGLPFNDVYCASKFALEGLCESLAVLLLPFGVHLSLIECGPVHTAFMEKVLGSPEEVLDRTDIHTFHRFYQYLALSKQVFREAAQNPEEVAEVFLTALRAPKPTLRYFTTERFLPLLRMRLDDPSGSNYVTAMHREVFGDVPAKAEAGAEAGGGRGPGAEDEAGRSAVGDPELGDPPAAPQ
5HUM , Knot 165 391 0.84 40 221 374 
PGGHLLNLTKPLCEVNSWHILSKDNAIRIGEDAHIIVTREPYLSCDPQGCRMFALSQGTTLRGKHANGTIHDRSPFRALVSWEMGQAPSPYNTRVECIGWSSTSCHDGISRMSICISGPNNNASAVVWYGGRPVTEIPSWAGNILRTQESECVCHGGICPVVMTDGPANNRAETKIIYFKEGKIKKIEELKGDAQHIEECSCYGASEMIKCICRDNWKGANRPVITIDPEMMTHTSKYLCSKILTDTSRPNDPTNGKCEAPITGGSPDPGVKGFAFLDGENSWLGRTISKDSRSGYEMLKVPNAETDTQSGAISHQIIVNNQNWSGYSGAFIDYWANKECFNPCFYVELIRGRPKESSVLWTSNSIVALCGSKERLGSWSWHDGAEIIYFK

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 \(c\).

\(|P_{f(3EBA_1)}(2) \setminus P_{f(1FDV_1)}(2)|=41\), \(|P_{f(1FDV_1)}(2) \setminus P_{f(3EBA_1)}(2)|=117\). 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 1:0101100111010111010100010100010111001110110111110000100001001010101000010001010100101000110001100111111011100011010010100000000
Pair \(Z_2\) Length of longest common subsequence
3EBA_1,1FDV_1 158 3
3EBA_1,5HUM_1 198 3
1FDV_1,5HUM_1 166 4

Newick tree

 
[
	5HUM_1:95.11,
	[
		3EBA_1:79,1FDV_1:79
	]:16.11
]

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 \((0.85)(0.8)(\frac{454 }{\log_{20} 454}-\frac{127}{\log_{20}127})=97.7\)
Status Protein1 Protein2 d d1/2
Query variables 3EBA_1 1FDV_1 123 84
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]