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Parikh vectors
3IFX_1 3UEH_1 6BTM_1 Letter Amino acid
1 7 16 D Aspartic acid
14 2 35 V Valine
1 6 12 C Cysteine
4 20 22 E Glutamic acid
21 11 31 L Leucine
2 11 14 F Phenylalanine
5 5 29 S Serine
9 7 23 T Threonine
9 6 6 R Arginine
0 5 24 N Asparagine
4 0 18 Y Tyrosine
14 7 32 G Glycine
8 4 16 H Histidine
3 5 24 I Isoleucine
1 16 37 K Lycine
3 3 13 M Methionine
5 10 18 P Proline
18 14 53 A Alanine
2 4 15 Q Glutamine
5 3 6 W Tryptophan 

3IFX_1|Chains A, B, C, D|Voltage-gated potassium channel|Streptomyces lividans (1916)
>3UEH_1|Chains A, B|Baculoviral IAP repeat-containing protein 5|Homo sapiens (9606)
>6BTM_1|Chain A|Alternative Complex III subunit A|Flavobacterium johnsoniae UW101 (376686)
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 \(w=f(c)\)
3IFX , Knot 59 129 0.74 38 85 121 
MPPMLSGLLARLVKLLLGRHGSALHWRAAGAATVLLVIVLLAGSYLACLAERGAPGAQLITYPRALWWSVETATTVGYGDLYPVTLWGRLVAVVVMVAGITSFGLVTAALATWFVGREQERRGHHHHHH
3UEH , Knot 71 146 0.80 38 109 138 
GSHEMGAPTLPPAWQPFLKDHRISTFKNWPFLEGCACTPERMAEAGFIHCPTENEPDLAQCFFCFKELEGWEPDDDPIEEHKKASSGCAFLSVKKQFEELTLGEFLKLDRERAKNKIAKETNNKKKEFEETAKKVRRAIEQLAAMD
6BTM , Knot 181 444 0.82 40 234 406 
MKKVGNHNSISRKLLLSLSLTLIFSLTSFAQDPAAAPAATEAAAPAAASGGDPVKGKELFNANCAACHKLDAKSTGPALRGVASKHDMAWIYKWVHNSSDMIKSGDPVAVKLFEENNKAVMTSFPQLSTGDIDNIIAYTSEVKAEPAAAAGGAATPPGTNVEGGGISNNIILGALALVMAILVVMLFMVNKVLTKVASNNGIEVAPKEGRTPIWKAFAKNQFLVLVTSIFLLLASGYFVYGYLMQVGVDQNYEPIQPIHYSHKIHAGDNEINCKYCHSAARVSKTAGIPSLNVCMNCHKNISEVAETTATAEYSKAFYDAQIQKLYDAVGWDKTKQAYTGKTQPVKWVRIHNLPDFVYFNHSQHVSVAGVECQTCHGPVQEFEIMKQYSKLTMGWCVDCHRKTDVKMEGNAYYEKIHAELSKKYGVEKLTAAQMGGLECGKCHY

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 \(c\).

\(|P_{f(3IFX_1)}(2) \setminus P_{f(3UEH_1)}(2)|=59\), \(|P_{f(3UEH_1)}(2) \setminus P_{f(3IFX_1)}(2)|=83\). 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 1:111110111101101111001011010111110111111111100110110011111011001011110100100110101011011101111111111100111101111011110000001000000
Pair \(Z_2\) Length of longest common subsequence
3IFX_1,3UEH_1 142 3
3IFX_1,6BTM_1 213 4
3UEH_1,6BTM_1 201 3

Newick tree

 
[
	6BTM_1:11.31,
	[
		3IFX_1:71,3UEH_1:71
	]:41.31
]

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 \((0.85)(0.8)(\frac{275 }{\log_{20} 275}-\frac{129}{\log_{20}129})=45.6\)
Status Protein1 Protein2 d d1/2
Query variables 3IFX_1 3UEH_1 59 54.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]